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Determination of stability delay margins for multi-area load frequency control systems with incommensurate time delays through eigenvalue tracing method

Control systems and interorganizational identification in technology parks cooperation.

ABSTRACT The aim of this study was to analyze the influence of the design of management control systems (MCSs) on interorganizational cooperation and the moderating role of companies’ identification with their technology park. The conditions that promote the emergence of interorganizational cooperation are indicated in the literature as an important research gap, as well as the little evidence about how MCS design influences cooperation, especially in relationships based on innovation. MCSs in interorganizational partnerships have been shown to be relevant for the coordination and maintenance of the relationship, and this study reveals that MCSs promotes cooperative behaviors among the companies associated with the technology parks. The interorganizational identification of the companies with their park was moderately present, thus prompting the inclusion of social and relational aspects in interorganizational studies, which remain scarcely explored in the literature. The MCSs of the parks are focused on stimulating the companies’ cooperation, which is one purpose of this partnership. By not confirming the moderating effect of identification, it was verified that this construct drives cooperation in a way that is dissociated from the MCSs. A survey was conducted in organizations associated with Porto Digital and with the São José dos Campos Technology Park, and it had the participation of 187 managers. To analyze the data the partial least squares structural equation modeling technique was applied and the differences between the two parks were further analyzed. The MCSs design and interorganizational identification act as antecedents of the companies’ cooperation with their technology park. On the other hand, the direct and positive effect of the MCS design on cooperation is not moderated by how much these companies identify with the interorganizational relationship established. The paper contributes by identifying ways of fostering cooperation, one of the purposes of interorganizational agreements, as well as by providing evidence in a context that is scarcely addressed in the literature.

Baseline Control Systems in the Intelligent Building Agents Laboratory

Converse lyapunov theorems for control systems with unbounded controls, afmt: maintaining the safety-security of industrial control systems, the potential of building automation and control systems to lower the energy demand in residential buildings: a review of their performance and influencing parameters, reliability analysis and safety model checking of safety-critical and control systems: a case study of npp control system, 2021: the ieee control systems society…under review [president’s message], ieee control systems society, optimal control input for discrete‐time networked control systems with data dropout, export citation format, share document.

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The word technology is from the Greek technologia. The modern meaning is a scientific method to achieve a practical purpose. Control Systems Technology includes all aspects of control engineering needed to implement practical control systems, from analysis and design, through simulation and hardware. A primary purpose of the IEEE Transactions on Control Systems Technology is to have an archival publication, which will bridge the gap between theory and practice. Papers are published in the IEEE Transactions on Control System Technology which disclose significant new knowledge, exploratory developments, or practical applications in all aspects of technology needed to implement control systems, from analysis and design through simulation, and hardware. 

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Review on model predictive control: an engineering perspective

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• Published: 11 August 2021
• Volume 117 , pages 1327–1349, ( 2021 )

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• Max Schwenzer   ORCID: orcid.org/0000-0002-3422-8631 1 ,
• Muzaffer Ay 2 ,
• Thomas Bergs 1 , 3 &
• Dirk Abel 2  

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Model-based predictive control (MPC) describes a set of advanced control methods, which make use of a process model to predict the future behavior of the controlled system. By solving a—potentially constrained—optimization problem, MPC determines the control law implicitly. This shifts the effort for the design of a controller towards modeling of the to-be-controlled process. Since such models are available in many fields of engineering, the initial hurdle for applying control is deceased with MPC. Its implicit formulation maintains the physical understanding of the system parameters facilitating the tuning of the controller. Model-based predictive control (MPC) can even control systems, which cannot be controlled by conventional feedback controllers. With most of the theory laid out, it is time for a concise summary of it and an application-driven survey. This review article should serve as such. While in the beginnings of MPC, several widely noticed review paper have been published, a comprehensive overview on the latest developments, and on applications, is missing today. This article reviews the current state of the art including theory, historic evolution, and practical considerations to create intuitive understanding. We lay special attention on applications in order to demonstrate what is already possible today. Furthermore, we provide detailed discussion on implantation details in general and strategies to cope with the computational burden—still a major factor in the design of MPC. Besides key methods in the development of MPC, this review points to the future trends emphasizing why they are the next logical steps in MPC.

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1 Introduction

For the automation of technical systems, feedback controllers (also called closed-loop controllers) compare a reference r with a measured variable y determining a suitable value for the manipulated variable u on the basis of the resulting deviation e = r −y (Fig.  1 ). Based on the working principle, they can be divided into the categories: classical controllers, predictive controllers, and repetitive controllers. Classical controllers, such as PID controllers, bang-bang controllers, or state controllers, only consider past and current system behavior (i.e. they are “reactive” to a deviation). Predictive controllers use a system model to predict the future behavior anticipating deviations from the reference [ 101 ]. Repetitive controllers, on the other hand, consider the system behavior of the previous cycle and calculate an optimal trajectory for the next cycle [ 46 ].

Block diagram of a classical feedback control loop (e.g. PID control)

The PID controller is the best known controller with an outstanding importance and spread in industrial applications [ 4 ]. Although there exist several setup rules, it is often difficult to find a parametrization—especially for nonlinear or time-variant systems [ 131 ].

“ The effectiveness of any feedback design is fundamentally ” limited by system dynamics and model accuracy. Hence, even in theory, perfect tracking of time-varying reference trajectories is not possible with feedback control alone—regardless of design methodology [ 58 ].

Special cases, such as technical limitations of actuators, require individual solutions that are often heuristically based, hard to understand, and maintain. Higher control methods, such as sliding mode controllers or back-stepping controllers, are similarly abstract and complex in their interpretation [ 146 ].

In fact, the founders of MPC theory ([ 34 ] and [ 104 ]) stressed that classic control suits 90% of all control problems perfectly. Only for the remaining fraction advanced control needs to be applied. Instead, we want to argue that MPC is a decent approach in almost all problems—even in those, which have not been controlled so far due to a lack of control theoretic understanding or of missing trust in feasibility. MPC is based on a repeated real-time optimization of a mathematical system model [ 101 ]. Based on this system model, the MPC predicts the future system behavior considering it in the optimization that determines the optimal trajectory of the manipulated variable u , Fig.  2 . Thus, MPC comes with an intuitive parameterization through adjusting a process model at the cost of a higher computational effort than classical controllers.

Simplified block diagram of a MPC-based control loop

The anticipating behavior and the fact that it can consider hard constraints makes the method so valuable for controlling real systems. Aligned with the rise of computational power and as models of complex processes become more and more available for all kinds of different systems, MPC now enables for the control of systems that were previous unthinkable.

MPC relies on models, which are available in almost every discipline. This allows to make use of this long-grown knowledge and saves the tedious formulation of an explicit control law—a task that is usually reserved for control experts. Instead, MPC determines the control law automatically through a model-based optimization. This implicit formulation, the flexibility, and the explicit use of models are the main advantages of MPC and the reasons for us to campaign for MPC in the engineering community. This paper shall give a summary from the application point of view, but it shall not claim the MPC to be the optimal choice over all control algorithms in every particular problem.

When MPC was new, several widely noticed review paper have been published on both, theory [ 13 , 44 , 77 , 85 ] and applications [ 99 ]. In contrast, this review is driven by the idea that MPC does not remain forever a topic for control engineers. Today, the development of MPC theory is pulled forward by application, in which manufacturing technology just emerged to make an important contribution—often having challenging requirements on reliability, constraints, and time. The work should inspire non-control experts to jump on the bandwagon and to develop new use cases pushing the barriers of technological limitations further.

The article starts with the fundamental theory and a rough sketch of the historic evolution to learn from the visions and detours of the beginnings. The focus lies on practical considerations of feasibility, stability, and robustness together with representative applications. On our way, we discuss the different flavors of MPC, of which related keywords are DMC, model(-based) predictive control, receding horizon control, etc. [ 12 , 70 , 101 ].

MPC is a set of advanced control methods, which explicitly use a model to predict the future behavior of the system. Taking this prediction into account, the MPC determines an optimal output u by solving a constrained optimization problem. It is one of the few control methods that directly considers constraints. Often, the cost function is formulated in such a way that the system output y tracks a given reference r for a horizon N 2 , Fig.  3 . Only the first value of the optimized output trajectory is applied to the system. This prediction and optimization is repeated in each time instance. This is why MPC is also referred to as “receding horizon” control. In essence, the idea is that a short-term (predictive) optimization achieves optimality over a long time. This is assumed to be true since the error of a proximal forecast is considered to be small compared to a distant prediction. The combination of prediction and optimization is the main difference from conventional control approaches, which use precomputed control laws [ 77 ].

Function principle of a model-based predictive with horizons N 1 , N 2 , N u (in accordance to [ 105 ])

The prediction horizon N 2 must be long enough to represent the effect of a change in the manipulated variable u on the control variable y . Delays can be considered by the lower prediction horizon N 1 or by incorporating them into the system model. Often, the latter is more intuitive and the lower prediction horizon is set to N 1 = 1 to account for the computation time (hence the computation is conducted in one time step, the solution u is implemented not before the next time step).

Assuming an arbitrary system

MPC minimizes a user-defined cost function J , Eq.  3 , e.g. the tracking error between the reference vector r and the model output y , Eq.  4 :

This formulation uses an arbitrary norm \(\lVert \cdot \rVert \) .

We will refer to the predicted state k + i at time point k as x(k + i |k). Bold written variables A indicate higher dimensions, i.e. a vector (lowercase characters) or a matrix (uppercase characters). A sequence of states will be indicated by x(⋅):

In this way, the constraint formulation will be abbreviated by

indicating that the sequence x(⋅) being in the feasible set \(\mathbb {X}_{f}\) .

In the late 1970s, [ 105 ] and [ 24 ] independently laid the foundation of MPC theory. With the upcoming digital controllers, they were able to efficiently control complex problems demonstrating a massive economic potential. [ 105 ] introduced model predictive heuristic control (MPHC) in 1978, which already included all characteristics of a MPC:

an explicit process model, described by impulse response functions (IRFs),

a receding horizon,

input and output constraints, and

an iterative determination of the controls (value of the manipulated variable u ).

However, [ 105 ]) did not claim to obtain optimal controls. Instead, the future controls where determined iteratively until they met the constraints. The additional term “heuristic” stressed the missing explicit control law. The technique was developed for the process industry with their multiple input multiple output (MIMO) systems, distinctive delays, and long processing times [ 105 ]. They even considered to identify the process model on-line—although only for changes in the set points.

Roughly at the same time, [ 24 ] from Shell Oil Company developed dynamic matrix control (DMC). They used a piecewise linear model to predict the future behavior of a catalytic cracking unit. Thus, the controller gained awareness of the plant’s time delay and its dynamic system behavior. Cutler and Ramaker used a receding prediction horizon and updated the model coefficients based on the error between the previously predicted output and the currently measured output. They showed that DMC outperformed classic cascaded PID control claiming that DMC has been applied to control problems at Shell Oil since 1974. The main difference to MPHC was that DMC calculates optimal control variables. However, the matrix formulation of the control problem restricts DMC to linear process models.

Both works laid the basis for a wide and fast spread of MPC in the petrochemical process industry. Even with linear models, the sampling times were several hours [ 97 ]. At the beginning, the focus was on simplifying the controller design and establishing a comprehensive theory so that the method could be used in industry [ 24 , 34 , 105 ]. The potential of MPC was not solely based on prediction but also on the fact that it can use non-linear models—both not supported by classic control. In fact, the process model formulation was a hot topic in the beginning of MPC theory: impulse response formulation (IRF) [ 105 ], piecewise linear step response functions [ 24 ], ARMA models [ 22 , 23 ], or state space formulations [ 56 ]. This flexibility in the choice of model formulation was one of the key reasons for the fast success of MPC.

The first approaches simply neglected model uncertainties and process instabilities—because most chemical engineering processes were open-loop stable [ 35 ]. From the late 1980s on, the research focus shifted to robustness and stability of MPC, which was especially pursued by the research group around Manfred Morari [ 13 , 18 , 19 , 53 , 144 ]. A detailed discussion about stability and robustness of MPC provides Section  4 .

With a finite horizon, i.e. a fixed moving window, the (linear) estimation problem could be formulated as a quadratic programming problem [ 100 ], which was computationally favorable. With computation pressing [ 14 ]) introduced “explicit MPC” which shifts the computation to massive a priori optimization (Section  8.1 ).

With the millennium and computers becoming more and more powerful, research shifted towards application. The trend was coming from large problems and long calculation times towards problems with less control variables and much faster requirements to computational time.

4 Feasibility, stability, and robustness

One has to distinguish several aspects of MPC:

feasibility of the open-loop optimization problem,

stability of the closed-loop controller, and

robustness regarding uncertainties.

The first concerns the formulation of the optimization problem, the second the controller as a whole with regard to disturbances, and the last mainly the accuracy of the process model.

In a stable system, the controller manages to get the output to a constant value at the end of the horizon N 2 , in spite of disturbances to the control loop. Robustness, in contrast, aims at uncertainties. It is mostly related to model inaccuracies regarding the output prediction. The model is the key element of MPC, but it is never perfect [ 101 ]. However, for stability analysis, a perfect model is assumed. Only in a subsequent step robustness is examined. Furthermore, signal noise is an important topic for robustness [ 13 ]. Garcia and Morari [ 34 ] pointed out early that optimal control improves the control behavior but complicates robustness examination. Robustness does not follow from stability or vice versa [ 13 ] but a closed-loop stable system always reduces the effect of disturbances.

This work draws crisp lines in the following between those separated problems of MPC design.

4.1 Feasibility

Hard input constraints (on u ) represent physical limitations of, e.g. actuators, which in fact must not be violated. In contrast, hard output constraints (on y ) are often rather desired than required. They may render the optimization problem infeasible. Relaxing these output constraints by introducing slack variables ξ to the optimization problem creates an extra degree of freedom [ 84 ]. The extend of violation is penalized in the objective function:

Both terms posse an individual weighting matrix W . If the norm is quadratic, it can be resolved to a matrix multiplication: \(\lVert \boldsymbol {x}\rVert ^{2}_{\boldsymbol {W}} = \boldsymbol {x}^{\intercal } \boldsymbol {W} \boldsymbol {x}\) .

The weight W ξ is a trade-off between the amount and duration of a violation [ 101 ]. The slack variables ξ do not resemble a function but represent individual series for every time step k . Note that they are vectors of length N 2 − N 1 as they cover the prediction horizon.

All commercial (linear) MPC software packages soften hard output constraints through slack variables to guarantee feasibility [ 85 ].

Nevertheless, the input constraints are still hard and turn the optimization problem to be non-linear [ 101 ]. A non-feasible desired trajectory w provokes instabilities [ 112 ]. To tackle the problem of unfeasible desired trajectories, [ 39 ] suggested to filter the trajectory w generating a feasible reference trajectory r . Thereby, the problem of stabilizing a closed-loop system with input constraints was separated from the problem of fulfilling these constraints [ 13 , 39 ]. This approach was called “reference governor”. It avoided constraint violations on the input by adjusting the desired trajectory beforehand with regard to the response behavior of the plant. This adjustment could be a simple smoothing of abrupt changes [ 13 ] or a dynamic optimization of its own [ 112 ]. Even a second MPC could be used to build the new reference trajectory r [ 112 ]. The separation was charming as it was applicable to non-linear problems in discrete and continuous time.

4.2 Stability

In its most basic formulation, stability is the property of a system that a bounded input results in a bounded output: the BIBO stability. In case that the transient behavior converges against an equilibrium, the closed-loop system is called to be asymptotically stable. Furthermore, if the equilibrium is reached from every possible initial state, then the system is labeled “globally asymptotically stable”. This can be guaranteed for all linear time invariant (LTI) discrete time systems with hard input and soft output constraints if the optimization problem is solved over infinite horizons [ 144 ]. Infinite prediction and control horizon \(N_{2} = N_{u} = \infty \) results in a linear quadratic gaussian (LQG) optimal control problem, for which a comprehensive stability theory exists: global asymptotic stability is guaranteed if and only if all eigenvalues of the closed-loop system are located inside the unit disk.

However, finite prediction horizon obviously is an extreme restriction. Computational restrictions limit the MPC in general to a finite horizon. To still guarantee asymptotic stability, the optimal cost function of the MPC must be monotonically decreasing over time.

To illustrate this, let us assume a system behaving as illustrated in Fig.  4 . It could constitute a continuous active cooling of glass at the end of the production line. In this case, the measurement y would be the temperature difference between glass and environment. The same way, the optimal control applied at time t 0 would correspond to u 0 , whereas the according value of the objective function would be J 0 .

Example of an stable closed-loop system with its objective function

The depicted output y as well as the change in u 0 tend towards the system’s equilibrium (as desired for the stable closed-loop behavior).

The cost J is not explicitly a function of time, so the desired monotonically decreasing behavior over time needs to be artificially imposed on it. One way to do this is to formulate an optimization problem that the control function is bounded by a Lyapunov function.

A Lyapunov function is a continuously differentiable scalar function \(V\left (\boldsymbol {x} \right ):\mathbb {R}^{n} \rightarrow \mathbb {R}\) with \(V \left (\boldsymbol {0} \right ) =\boldsymbol {0}\) . It is always positive and does not increase over time:

The Lyapunov theorem essentially defines a prototypical function resulting in a bounded system state over time. Thus, the state of the art for stability schemes for (non-linear) MPC is to define the cost function in such a way that the optimal cost behaves as a Lyapunov function—or to prove this to be the case respectively. For this purpose, the optimization problem is extended by additional cost terms or constraints.

An adequate Lyapunov function to the optimal cost J 0 of Fig.  4 is illustrated in Fig.  5 , where the decreasing optimal cost is depicted over two system states.

Example of an Lyapunov function

One approach to make the optimal cost J 0 behave like a Lyapunov function is to introduce a terminal cost J (k + N 2 ). This nullifies the advantage of an infinite horizon, since the cost stays the same until infinity \(J(\textit {\textbf {k}}+N_{2}) \approx J(\infty )\) [ 75 , 77 ]. Whereby, more constraints to guarantee stability of the controller may again cause feasibility problems of the optimization—especially for short prediction horizons. Therefore, it is common practice to constraint a terminal region instead of, e.g. a zero terminal constraint \(\lVert \textit {\textbf {x}}(\textit {\textbf {k}}+N_{2})\rVert =0\) .

The most common stability approach, which avoids a Lyapunov analysis, is to introduce so-called “contraction constraints” ensuring that (usually the euclidean norm of) the state vector is decreasing over time [ 13 ]:

Some applications even use both, a Lyapunov -based cost function and contraction constraints, e.g. [ 116 ].

Mayne et al. [ 75 , 77 ] concluded that stability of MPC-controlled (linear) systems was at a “mature” stage in 2000, whereas for robustness, only conceptual approaches existed.

With the understanding of stability analysis for linear MPC, [ 44 ] pointed out that a stability analysis for non-linear MPC became more urgent.

While the approaches to design a stable system that was elaborated above ( Lyapunov -based cost function or contraction constraints) apply equally for linear and non-linear systems, still, many implementations of MPC meet non-linearity by successive linearization avoiding a non-linear stability analysis [ 101 ], Section  7 .

For a more complete discussion and mathematical foundation regarding stability, the authors refer to [ 3 , 72 , 77 , 98 ] and [ 31 , 81 , 87 ].

4.3 Robustness

In contrast to what have been claimed, [ 35 ] stressed that MPC is not inherently more or less robust than classic feedback control (e.g. PID controller).

Robustness follows stability of the closed-loop system only if no input constraints are present [ 106 ]. “ When we say that a control system is robust we mean that stability is maintained and that the performance specifications are met for a specified range of model variations (uncertainty range) ” [ 85 ].

Essentially, robustness deals with model uncertainty, which can be formulated in several ways [ 13 ]:

by uncertainty intervals,

by structured feedback, or

by using a set of models.

For the latter, one describes the plant by multiple models and optimize, e.g. the worst-case of them ( \(L_{\infty }\) -norm) [ 19 ].

A similar approach was pursued by [ 53 ] distinguishing different types of uncertainty: uncertainty in the gain, the time constant, and time delay. They considered them all simultaneously. The approach was taken up again later as matrix formulation [ 25 ]. This assumes structured noise in the feedback loop so that it can be considered in the model. Assuming a linear time invariant (LTI) system and (linear time invariant (LTI)) uncertainty to be present in the feedback loop, robustness can be guaranteed if the norm of the uncertainty matrix is lower than a defined threshold [ 13 ].

Uncertainty intervals can often be assigned to model coefficients of an empirical transfer function. In this idea, the model structure remains the same and only the coefficients change. However, [ 13 ] concluded that allowing model coefficients to vary within intervals is not sufficient to achieve robustness. A comprehensible example is that oscillating step responses would be allowed.

For all these approaches you need to quantify uncertainty in the model of the system. The robustness calculations come at the cost of performance (regarding optimality and computation) [ 13 ].

An entirely different approach is to define a cost function that favors robustness by design: e.g. minimizing the maximum error in the prediction horizon would result in less extreme control actions, which in turn lead to a smoother process guidance [ 18 ]. This suggests to use the \(L_{\infty }\) -norm to formulate the optimization problem instead of a—standard—least squares ( L 2 ) formulation.

In this case, the \(L_{\infty }\) norm is the maximum of all errors between the predicted model outcome and the desired reference. [ 18 ] motivated its use with the smoothing influence on the control outputs u . Using the \(L_{\infty }\) -norm hinders the controller to make full use of the plant potential due to very conservative control actions [ 13 ]. However, if the process model is linear, the optimization problem becomes quadratic if the cost function is expressed as a L 2 - or a \(L_{\infty }\) -norm [ 13 ]—supposed that there are no constraints present. Quadratic problems are favorable because they can be solved efficiently.

Both approaches, a more elaborate model or a special objective function, undermine the key advantage of MPC: optimality. One idea to overcome this is to enforce robustness by introducing a contraction constraint (similar to stability), i.e. requiring the worst-case prediction to contract [ 85 , 144 ]. This let MPC still implement the optimal trajectory as long as the additional constrained is fulfilled.

4.4 Summary on feasibility, stability, and robustness

García et al. [ 35 ] noted that for every unconstrained, linear MPC there exist an equivalent classic feedback controller with all benefits of its well-proven stability theory. However, not using constraints loses much of the charm of MPC. Therefore, it is more an academic twitch than a practical option. The same is true for infinite horizon MPC.

There exists an extensive stability theory for linear MPCs. For systems in state space form, the stability analysis is based on eigenvalues and on the unit disk as it is familiar from the stability analysis of conventional (linear) control [ 144 ]. However, optimization problems with hard input constraints are often non-linear [ 101 ].

Establishing stability—especially robust stability—is extremely difficult for non-linear problems. This is mainly due to the lack of an explicit functional description of the control algorithm, which is required for most stability analysis [ 84 ]. Today, stability of non-linear, constrained, finite-horizon MPC is achieved by formulating the cost function as a Lyapunov function and introducing a terminal set constraint [ 75 , 77 ]. Using a terminal set links the stability problem with the constraint satisfaction problem [ 17 ]—ironically, additional constraints stabilize a constrained , non-linear MPC.

Robustness is a trade-off to performance. Several approaches increase robustness at the cost of computation and optimality (e.g. HCode \(L_{\infty }\) -norm). Nevertheless, it can only be achieved if the amount of uncertainty can be quantified.

A practical compromise to maintain optimality—the key feature of MPC—is to add the requirement the the worst-case prediction must contract [ 85 , 144 ].

5 Recent developments in MPC theory

Once again, motivated by the chemical process industry, [ 58 ] integrated a MPC into an iterative learning control (ILC) building a controller dedicated for batch processing. A classic iterative learning control (ILC) works during the process as open-loop control but adjusts this profile of commands between cycles or “iterations”. In this way, it approaches the ideal profile incrementally from cycle-to-cycle and may react to trends over multiple cycles. The essence is that the “ information gathered during previous runs can be used to improve the performance of a present run” [ 57 ]. In contrast to this, MPC is a closed-loop controller but considers repetitive tasks as independent of each other.

Combining both methods builds a system that reacts to disturbances within a cycle or process (“ as they occur” ) and minimizes the tracking error over multiple cycles. However, integrating MPC to iterative learning control (ILC) limits the use to fixed-time operations, i.e. the number of time samples must stay the same over cycles [ 58 ]. Splitting both techniques, let the iterative learning control (ILC) work as an upper-level reference governor for the MPC as was conducted, e.g. by [ 86 ], and may overcome such limitations. In this combination, MPC introduces constraints to iterative learning control (ILC) [ 57 ].

Li et al. [ 59 ] presented a third flavor of such a combination effectively being an optimal iterative learning control (ILC): They took the optimization part of MPC, i.e. optimizing the manipulated variable over a horizon, transplanting it into an iterative learning control (ILC). The resulting system determined an optimal profile of the manipulated variable(s) for each cycle. In a subsequent work, [ 60 ] suggested to smooth the commands over cycles. This essentially states that the optimal solution is not entirely trusted. Such systems only touch MPC in general, because they lack of a receding horizon and effectively filter their optimal control recursively.

Among the works of [ 66 ] and [ 128 ] lies the combination of iterative learning MPC and the uprising field of data-based learning in control theory. The former extracts new trajectories of a linear-quadratic regulator (LQR) based on overall objectives and data of previous trajectories with the help of the k-nearest-neighborhood algorithm. The latter extends the idea of an iterative, data-driven adjustment of trajectories to the application of MPC.

Although also applied to a repetitive task, [ 78 ] focused on learning a model of the system dynamics rather than a trajectory. The authors took advantage of data and weighted linear Bayesian regression to model uncertainties of vehicle dynamics on a repeating path. The same way [ 50 ] applied Gaussian process modeling to elaborate confidence intervals on possible trajectories to guarantee safety.

Data-driven modeling, such as machine learning, can be used for the system model that the MPC uses in its optimization, or to approximate the solution space of an explicit MPC, as e.g. in [ 45 , 71 , 88 ], Section  8.1 .

The possibilities of learning are enhanced especially for multi-agent systems, where every single agent contributes to the data-acquisition and policy exploration. [ 68 ] utilized such a swarm intelligence to learn the trajectory for a distributed MPC. The learning problem for this purpose was defined as a quadratic optimization problem under the condition of collision avoidance as constraint.

6 Applications

The idea of optimal control in the presence of constraints and the intuitive design of the control law as an optimization problem has made MPC interesting for many different tasks. Applications have spread wide recently throughout all fields of engineering. The following highlights main movements.

6.1 Process industry

For a long time, the process industry used MPC almost exclusively. This is not surprising as the petrochemical industry promoted the development decisively [ 24 , 97 , 99 , 105 ]. Motivated by its complex, multi-variable processes with time delay, MPC spread quickly since optimal control lead to significant economic benefit due to the large throughput. Darby et al. [ 26 ] acknowledged that MPC is “ the standard approach for implementing constrained, multi-variable control in the process industries today”.

In the founding paper of MPC, [ 105 ] described three applications: a distillation column of a catalytic cracker in oil refinery, a steam generator, and a polyvinyl chloride (PVC) plant. The catalytic cracker had two manipulated variables (mass flow rates) and three control variables (temperatures), of which only one was constrained. The plant was modeled through twelve impulse response functions and the sample time was \(T_{s} = 3 \min \limits \) – manageable only because it used a heuristic control law.

With the control of the polyvinyl chloride (PVC) plant, they wanted to demonstrate the versatility of MPC by controlling five subprocesses. The results showed a severe reduction in variance of the controlled variables yielding to higher quality and energy savings. The impressive demonstration paved the way for the popularity of MPC. Richalet later also described how a distillation column and a vacuum unit was controlled in a refinery of Mobil Oil [ 104 ]. The objective function was already formulated as a quadratic Lyapunov function, which—as was shown—is favorable for stability. He did not address robustness but mentioned a back-up control system in case of failure. The results showed that the controller reduced the variance in the quality criteria resulting in a payout time of less than a year.

Oil companies were the promoters of model-based advanced controllers. Cutler and Ramaker [ 24 ] used a piecewise-linear model to control the furnace of a catalytic cracking unit at Shell Oil . With a prediction horizon of N 2 = 30 and a control horizon of N u = 10, they exploited the predictive potential.

Prett and Gillette 97 used even longer horizons ( N 2 = 35, N u = 15) with a sampling time of “ a few hours”. They successively linearized a non-linear process model determining the optimal operation point of the reactor and the regenerator of a catalytic cracker.

With distillation being one of the workhorses of the chemical process industry for the separation of molecules, it is still today a popular application examples for MPC, as in [ 21 , 80 ], which both were a simulation study on linear MPC. Only that [ 80 ] successively linearized a non-linear model of a methanol/water mixture to apply linear MPC.

Piche et al. [ 95 ] introduced a neural network (NN) in MPC to control the set point change in an polyethylene (PE) reactor. A neural network (NN) is a non-linear empirical model based on historic data. This type of machine learning model is experiencing extraordinary attention nowadays. Linear dynamic models were constructed from conventional (open-loop) plant tests to control the plant at its set points. Piche et al. achieved 30% faster transitions and an overall reduction in variation of the controlled variables. The idea is still under active research. Li et al. [ 63 ] also explored successive linearization of a neural network (NN) in MPC but to control the temperature of a stirred reactor—a common application in process industry, e.g. for bioreactors. Shin et al. [ 117 ] used a neural network (NN) (fully connected, 14-15-2) with MPC for a propane devaporizer (e.g. specialized distillation column). Although claiming that neural network (NN)–based non-linear MPC achieved better performance than linear MPC, they benchmarked the new controller on conventional PI control demonstrating a 60% quicker settling time (35 min with neural network (NN)-MPC to 92 min with PI control). They further stressed easier modeling of data-driven models as an additional benefit of using NNs in conjunction with MPC. Nunez et al. [ 89 ] used a more complicated neural network (NN) structure, a recurrent neural network (RNN) (in fact, an attention-based encoder decoder recurrent neural network (RNN) with 23,000 free parameters) to model an industrial past thickening process. The sampling time was T s = 5 m i n giving the controller enough time to conduct a global optimization with particle swarm optimization (PSO) – a rather unusual choice – for a prediction and control horizon of N 2 = 10 and N u = 5 respectively. Presenting one rare example of an actual industrial deployment, they demonstrated the effectiveness of the control on an industrial plant for a working day. The recurrent neural network (RNN)–based MPC was capable of maintaining the target concentration of the paste thickener in spite of a severe disturbance when a pump failed. A recurrent neural network (RNN) structure was also used to control chained stirred reactors [ 136 ]. There are applications with further network types with distinct features, such as echo state networks to model time delay of buffer tanks, e.g. for a refrigerator compressor test rig with (non-linear) MPC [ 9 ].

In general, besides oil and gas, and the chemical industry, pharmaceutical and biology industry use MPC to manage the non-linearity coupled with large time-delays of their processes, e.g. in a fermentation process [ 42 ]. Ławryńczuk [ 6 ] compared linear MPC to non-linear MPC again for a stirred reactor and for a distillation column. He concluded that, in particular for the distillation process, the non-linear controller was more economic. On this background, he suggested to combine both approaches reducing the computational burden of pure non-linear MPC: applying non-linear optimization only for the first time instant k = 1 and using a linearized model for the other steps 1 < k < N 2 . To the knowledge of the authors, such an approach has not been examined further.

Prasad et al. [ 96 ] took a different route, preferring to use multiple linear models rather than a single non-linear one. They controlled the filled-height of a conical shaped tank. Since the diameter varies continuously with the height, they suggested to identify three separate linear models at different heights, to design one controller for each and combine the outputs as an ensemble to obtain a general output for the manipulation variable (the inlet flow rate).

In 2003, [ 99 ] already counted over 4 600 industrial applications reviewing the available commercial software packages for MPC. They differed in the model structure, its identification, and in how constraints were implemented (as hard constraints or as an additional penalization term in the cost function). Nevertheless, all models were linear, time-invariant, and derived by empirical test data. Online adaption of the model was not supported by any software, although there had been (academic) works on this issue already from the beginning, e.g. [ 105 ].

Although stability theory is at a mature level, AspenTech as a major vendor of commercial MPC software assumed an infinite horizon control to ensure stability, which was implemented in practice by a prediction horizon much larger than the reaction time of the system [ 33 ]. With regard to academia, the software MATLAB/Simulink from The Mathworks is very popular, e.g. [ 80 , 96 , 108 ].

Today, process industry is still the major user of MPC [ 76 ] evolving towards faster, mechanical processes such as paper machines [ 145 ] or stone mills [ 108 , 124 ].

Again, a report of an industrial application was presented by the Anglo American Platium company, where a linear MPC (to be more precise: (DMC)) outperformed a back-than famous fuzzy controller [ 124 ]. The power consumption of a large stone mill was reduced by 66% using the commercial system from AspenTech . Nevertheless, no fully thrusting the novel control method, the established fuzzy controller was run as back-up option for abnormal states.

Olivier and Craig [ 92 ] and coworkers [ 55 ] detected faults of actuators within the process to update the available manipulated variables of the MPC maintaining the control performance. They used a particle filter in order to estimate whether a certain actuator could still be used or not (binary decision). Self-awareness was especially important for continuously-running large systems in rough environments. They simulated a mill of a mining facility to grind ore. The simulation demonstrated that the MPC can manage actuator failure if it knew about it.

Table  1 summarizes the key parameters of the discusses works in process industry. Only works are listed that provided their implementation details on MPC. The order has no significance besides order of publication.

MPC often served as a supervisory control of classic PID controllers forming a cascaded control loop. Large multiple input multiple output (MIMO) systems, empirical models—mostly derived through step or impulse tests [ 99 ]—and long calculation times T s > 1 h favored MPC in process industry. Today, the sampling times have largely decreased to the region of minutes and seconds [ 26 ], Table  1 . Complex couplings between process variables require empirical, nonlinear models, which are at the beginning often linearized.

6.2 Power electronics

Not until the mid 2000s, an opposite trend has taken shape in power electronics. These extremely fast single input single output (SISO) systems used pure analytical models to work at sampling frequencies below the ms-range [ 15 , 52 , 65 , 129 ]. The characteristics are diametrically different to process industry. Richalet [ 104 ] foresaw this counter movement early reporting from an application to control a servo drive with a sampling time of T s < 1 m s . To achieve such short sample times, relatively simple models, short horizons, and often an explicit solution of the optimization problem were used. Explicit MPC solves the optimization in advance for a variety of cases to obtain a polytope of explicit (linear) control laws [ 14 ]. This increases the overall computational effort but shifts it to offline optimization.

Linder and Kennel [ 65 ] applied MPC for “field oriented control” of electrical AC drives using such an explicit MPC. The results were sobering: there was hardly any improvement to a conventional PID controller for large signal steps. For small steps, the MPC reached the new target value faster and better, but in summary, Linder and Kennel attributed potential of MPC more due to features like intuitive tuning and constraint satisfaction.

Nevertheless, Bolognani et al. [ 15 ] saw MPC as being ideal for electric motor control since there existed analytical linear models describing the motor behavior accurately. They also used an explicit MPC formulation to achieve an sample time of T s = 83 m s . Since the prediction horizon N 2 = 5 was far from covering the complete drive dynamics, the assumption of an infinite prediction horizon did not hold, making stability a major (unconsidered) concern. The control was perfect if the load torque matched the design torque of the MPC design. Otherwise, there occurred an offset between the desired and the actual values (current, voltage, etc.). Nevertheless, the controller worked stable and enforced the current and voltage limits reliably.

Kouro et al. [ 52 ] examined MPC regarding control of power converters. Power converters have only a finite number of discrete states n . This handicaps an optimization requiring heuristic approaches (mixed-integer optimization). They took a brute force approach testing every possible control action resulting in an exponential increase of calculations: \(n^{N_{2}}\) . With n = 7 converter states the prediction horizon was limited to N 2 = 2 in order to achieve a sample time of T s = 100 m s . Compared to a classic PID control, they concluded that the advantage of MPC is its flexibility regarding control variables and constraints—similar to [ 65 ] before.

Geyer et al. [ 38 ] used MPC for direct torque control of electrical drives. The control problem consisted of keeping the motor toque, the magnitude of the stator flux, and the inverter’s neutral point potential within their (hysteresis) bounds minimizing the switch frequency of the inverter. To reduce the computational complexity and to solve the MPC within T s = 25 m s , the control and prediction horizon were limited to N u = N 2 = 2. As a compromise between computational effort and system behavior, the value of the prediction horizon was extrapolated linearly 100 steps to roughly recognize future system behavior. The simulation results showed that MPC respected the constraints only slightly better but reduced the switching frequency on average by 25% thus reducing the power dissipation.

As an experimental validation for this, Papafotiou et al. [ 93 ] implemented MPC for direct torque control on a 1.5 MW motor drive. Again, the major concern was on the computational speed, so that the control horizon was further reduced to a single step N u = 1. The two control tasks, motor flux and motor speed, were split into separate control tasks with different execution times (25 ms and 100 ms respectively). The results could not hold the euphoria of the simulation above. On average the control reduced the inverter’s switching frequency by 16.5% maintaining the same output quality as standard control. For motor drives of this size, the achieved faster torque response was even more valuable for certain applications. Especially high-voltage applications, such as motor control, must consider the time delay of the converter [ 10 ]. Converters often exhibit a programmed time delay after switching in order to avoid a shoot-through. Model-based predictive control (MPC) can manage this naively, e.g. in the system model [ 10 ].

The number of applications in power electronics increased so rapidly that Vazquez et al. [ 129 ] felt impelled to give an extensive review of the academic implementations. They concluded that the lack of proper models is still the major obstacle towards an industrial application. And MPC for power converters and rectifiers (electrical devices that convert alternating current (AC) to direct current (DC)) is still subject of active research due to their ubiquity. It is likely to increase even further due to the transformation of society in the context of combating climate change and the accompanying electrification of whole industries. Efficiency is prime and researchers found MPC to provide valuable contribution, e.g. for determining optimal switching sequences of converters and rectifies already for mid-level voltage ratings [ 40 , 83 ]. Although computation is still an issue, e.g. [ 2 ], both formulations are still competing in the this field of very fast control problems in power electronics: The standard implicit formulation of MPC with solving the control problem online and the explicit formulation where the optimization problem is solved a priori for all cases. A detailed general discussion on explicit MPC includes Section  8.1 .

Again, Table  2 provides a condensed overview of the works on the application of MPC in power electronics. It emphasizes the diversity of the used parameters of MPC in this field. Having started with the control of individual electrical components, in particular converters, the application in electrical engineering has widened towards the control of systems of multiple components as the next section will show.

6.3 Building climate and energy

Since 2010, MPC has attracted notice to the community of building climate control. Analytical and empirical models were combined in non-linear multiple input multiple output (MIMO) systems with long prediction horizons. Typical sample times were in the order of minutes to 1 h with prediction times usually smaller than 48 h [ 113 ]. The objective was always to reduce the energy consumption while maintaining a certain (thermal) comfort. The success of MPC in this field was due to that it allows to incorporate statistical uncertainties and even weather forecasts [ 5 ], e.g. as in [ 90 ].

MPC for heating, ventilation and air conditioning (HVAC) had been applied to a broad range of buildings, starting from a single room to large spaces as airport buildings or multi-room problems as office buildings [ 1 ]. The overwhelming majority of the works addressed non-residential buildings, where only 4% included residential buildings often as one energy sink among others in a micro-grid [ 74 ]. In their latest review, they noted that heating, ventilation and air conditioning (HVAC) plays an important role in the field of building energy management systems with more than 50% of all publications; and that MPC is the most used strategy. The authors ascribed this to its native consideration of weather and occupation forecasts, e.g. demand forecasting. Google reported that MPC increased the efficiency of the air handling in one of their data centers so that they cut cooling costs by 9% [ 54 ].

Most works in the field of climate and energy management were simulations due to the large implementation effort and the risk of discomfort. Gunay et al. [ 43 ] actually demonstrated their findings on an actual room of their university offices; and Ma et al. [ 69 ] implemented a MPC controller to the cooling system of their university building. The main component was a cold water storage tank, whose operation was controlled (when to fill, how fast to fill, how cold should the water input be—coming from the chillers, etc.). They reduced the energy costs by 19%, introducing the interesting idea of optimizing financial costs instead of pure energy consumption, [ 1 ] later picked-up again in this filed. With “MPC”, nowadays a dedicated term for such formulations exist.

Yu et al. [ 141 ] conducted a whole benchmark of different temperature control approaches on a small mock-up building in a thermal chamber. Model-based predictive control (MPC) outperformed the other approaches—including a commercial thermostat with a programmable schedule—and reduced the energy consumption by 43% compared to a constant temperature controller. However, the results suggested that for small buildings the main benefit came from an enhanced temperature measurement.

Industrial applications of MPC in building climate control are still rare, which is due to the enormous modeling effort (being up to 70% of the control effort) [ 5 , 94 ].

Often, individual rooms were modeled as capacity resistor elements [ 82 , 90 , 91 , 107 ]. Coupled resistance-capacitance models based on physical principles and pure empirical approaches are the two main types of modeling building energy systems for MPC [ 113 ].

One way to approach the modeling effort and the related requirement of domain knowledge was to use black box modeling approaches, namely from the field of machine learning. Already Qin and Badgwell [ 99 ] noted that NNs were popular to model unknown non-linear behavior for MPC. Afram et al. [ 1 ] used NNs to model the individual subsystem of an energy management system, such as ventilation, heat storage, or a heat pump. The increase in model accuracy came at the cost of a non-linear optimization in the MPC. The system was tested on historic weather data—assuming an ideal weather forecast at every point as it is common practice, e.g. also in [ 36 , 90 , 91 ]. Unfortunately, no details on the MPC parameters were given in [ 1 ]. The objective was to optimize the cost of the energy consumption and not the amount of consumption itself. For this, the proposed neural network (NN)–based MPC shifted the energy consumption to the off-peak hours of the electricity price using the mass of the building as a storage. This worked excellent for moderate weather conditions but failed at extreme conditions as in midsummer when such passive thermal storage are not sufficient.

The interlaced individual models in building climate control let to a complex optimization problem, where gradient-based algorithms may fail and heuristic-based global optimization were more desirable [ 82 ]. This increased the computational effort further and, thus, enlarged the sample time, which was seldom a problem due to the inertial nature of thermal behavior. If the number of rooms became large, the control problem was broken down into multiple decoupled MPCs achieving a near optimal solution at a lower computational cost [ 82 ]. Shaltout et al. [ 5 ] plead for a distributed network of MPC controllers cooperating with each other.

Gunay et al. [ 43 ] claimed that shorter sample time favors temperature control ( T s , s h o r t = 10 m i n compared to T s , l o n g = 1 h , both N 2 = 6) since the model accuracy usually deteriorates with the predicted time. Furthermore, long horizons may be torpedoed by stochastic disturbances such as the occupancy behavior. They claimed that a short prediction horizon of \(T_{N_{2}} = 6 h\) would have even eliminated the need for accurate weather forecasts and make the MPC more reactive. Yu et al. [ 141 ] supported the finding that shorter horizons enabled for a more accurate tracking of a given temperature reference. In contrast, [ 91 ] argued that \(T_{N_{2}}=24 h\) should be used as a prediction horizon for heating, ventilation and air conditioning (HVAC) systems.

Park and Nagy [ 94 ] identified MPC as recent trend in heating, ventilation and air conditioning (HVAC) control through mining the keywords of publications and predict that it will spread towards the control of smart grids. Another recent review on MPC for heating, ventilation and air conditioning (HVAC) systems [ 113 ] stressed that it is importance will increase in step with the transformation in power generation towards renewable sources and its higher variability. And in fact, the increasing pressure to integrate flexible sources and sinks into power grids (introduced by renewable energy plants and PEVs) called for advanced control methods, e.g. [ 126 ].

In particular, the ability to include stochastic models and, thus, modeling uncertainty explicitly was considered a unique feature especially in the field of energy management [ 11 ]. Oldewurtel et al. [ 91 ] formulated the MPC problem as a probability problem considering the uncertainty of weather forecast. Instead of using weather forecasts, Morrison et al. [ 86 ] learned the day-to-day changes in solar radiation due to seasonal trends. The algorithm learned the behavior of humans in terms of hot water demand over days and weeks, while the MPC implements this learned reference on a lower-level ( \(T_{N_{2}} = 12 h\) ). In a simulation study, they mimicked four weeks from midsummer to midwinter for the considered thermal-storage-tank system.

Also in the field of renewable energies, Dickler et al. [ 27 ] applied a time-variant MPC for load alleviation and power leveling of wind turbines, where the model for the mechanical demand on the turbine was linearized at every control step for the current prediction and control horizon. The wind speed as one major load on the mechanical structure was handled by incorporating wind speed predictions. Sun et al. [ 125 ] used MPC to smooth the effect of fluctuations in wind speed for wind turbines on resulting frequency of the power generation. The idea was to consider both, the dynamics of the turbine and of the wind itself, in a linearized MPC. Shaltout et al. [ 114 ] picked up the same idea coupling the wind turbine with an energy storage system. Targeting multiple objectives, some with non-technical motivation, they formulated a so-called economic MPC. Adding fluctuating energy consumers to such a system, [ 126 ] simulated a (connected) micro grid with an wind power supplier and 100 PEVs. The objective was to minimize the overall operation costs: maximizing the consumption of wind energy and minimizing the exchange to the main grid, i.e. balancing the energy consumption over consumption and production peaks. PEVs could be used as sources or sinks as long as they were fully charged at the end of a working day. The energy demand of the PEVs was modeled as a truncated Gaussian model; the supply of a wind turbine in an auto-regressive integrated moving average model (ARIMA). They proposed a two-layer MPC where the top layer balanced the overall power demand aggregating the PEVs to a single value, while the underlying MPC handled the energy distribution to the individual PEVs. The top layer optimized the cost of the energy and the risk, which was determined through a Monte Carlo simulation and stochastic models. A simulation showed that the costs was be reduced by more than 30% compared to an immediate maximum charge strategy, in which the batteries were charged to full capacity as soon as it was connected to the grid. This may exacerbate the energy imbalance of the micro grid at peak hours. Schmitt et al. [ 109 ] optimized energy management for hybrid electric vehicles by establishing also a two-layer MPC. On the higher level non-linear MPC, the driving strategy including a rule-based gear selection was optimized, and the control and actuation of the physical system were realized on the faster lower level linear MPC.

In the advent of the electrification of the mobility, MPC experiences a new blossom, e.g. in balancing the fuel consumption of a hybrid-electric vehicle taking also the individual driving behavior into account [ 61 ], or in health-aware battery charging [ 147 ].

Again, the mega trend of energy transition and energy efficiency will lead to an increasing demand of intelligent strategies for energy balancing in (micro) grids and for building energy management systems. This in turn will call for more applications of advanced control strategies, especially MPC [ 74 , 113 ]. The field has developed from the control of pure heating, ventilation and air conditioning (HVAC) systems to entire consumer-producer systems (or grids). The complexity of the models represent this evolution, Table  3 .

6.4 Manufacturing

Manufacturing is a comparably new field for MPC and can be considered representative for a new development: MPC does not substitute existing controllers anymore but exploits new control tasks.

We want to emphasize the field of manufacturing in general and cutting technology in particular, where several papers already showed the potential benefit of advanced control, e.g. on a conceptual basis [ 28 ].

Nevertheless first, fixed-gain controllers for the position control loop of machining centers were substituted to achieve higher precision [ 122 , 123 ]. Compensating the dynamics in high-precision milling with MPC is still an active field of research, e.g. [ 73 ]. Nonetheless, the application evolved towards introducing additional high-level control with MPC. The control turned into process control rather than implementing machine tool settings, creating before unseen benefit. Mehta and Mears [ 79 ] described a concept for controlling the deflection of slender bars in turning. And Zhang et al. [ 142 ] examined MPC to avoid chatter—an undesired resonance phenomenon—in milling. The MPC used a linearized oscillation model assuming that mass, damping, and stiffness were given. The controller manipulated an external force actuator at the tool holder. In simulation, the system enlarged the chatter-free region by 60%.

The first constrained MPC for force control in milling was implemented at the RWTH Aachen University, Germany [ 111 , 112 , 119 , 120 ]. They manipulated the feed velocity in order to achieve a constant force in this highly dynamic process. Later, a black box model (support vector regression (SVR)) was added to consider non-linearities of machining centers [ 7 , 8 ].

Staying in the area of metal processing, Liu and Zhang [ 67 ] introduced MPC-based control to welding. Predicting the N 2 = N u = 5 next steps ( T s = 0.5 s ), they controlled the penetration depth of the weld as a measure of quality. While the first approach relied on a dedicated vision system and a linearized model of the penetration depth, a newer approach dropped the vision system: [ 148 ]. The feedback loop was closed by identifying a model online, which described the relation to the penetration depth. This was a similar set-up as for the milling process above. The approaches demonstrated the control of system variables that were hard to impossible to control without MPC.

Wehr et al. [ 133 ] applied a linear MPC to control the gap during precision cold rolling of thin and narrow strips. The structure of the given process is anatomically overactuated by the existence of two redundant actuators for gap control. The overactuation and computational effort of the MPC are tackled at the same time by the introduction of a single time-varying optimization variable, which exploits the different availability of the actuators during the process.

A different field of production technology addressed Wu et al. [ 135 ], who optimized the air-jet to insert the weft in weaving. This is the key to reduce the energy consumption (in terms of compressed air) of weaving machines.

And for injection molding of plastics, Reiter et al. [ 103 ] (conceptual) and later Stemmler et al. [ 121 ] built a MPC controlling the pressure within the mold. The idea was to obtain constant weight of the product as a quality criterion. It was standard to control the process with separate controllers for the different phases (injection and packing phases), while MPC was able to handle both phases and optimizing the transition (which was originally a switch of the controller) [ 121 ]. The contribution to a higher usability of the MPC was the main driver in this work.

A bit more general, the field of “production” adds automation and handling systems to the scope. These are often graph or state-based modeled, e.g. by Petri Nets as Cataldo et al. [ 20 ] did with a palette transportation and processing system. Using an MPC, they enabled the system to adapt to faults on the transportation line such as a blocked section. Automation applications with discrete states present mixed-integer optimization problems. They require dedicated solver, which often are heuristic-based and come with a larger computational burden than gradient-based optimizers.

Table  4 provides a quick overview on the chosen parameters. The sampling times are quite low with rather large prediction horizons compared to the early works on power electronics.

6.5 Further applications

Apart from these main movements, the range of applications in engineering is immense. From balancing walking robots [ 134 ], hanging crane loads [ 110 ], and cruise control for heavy duty trucks [ 62 , 140 ], to optimizing buffering and quality in video streaming [ 138 ]. Even for path tracking of underwater robots, MPC was applied [ 116 ]. In almost all applications, MPC outperforms classic controllers.

In particular, robotics is an emerging field of applications of MPC, e.g. [ 47 , 88 , 134 ]. While humanoid robots are a special case [ 134 ], industrial robots are ubiquitous in the shop floors today. The success of light-weight, economic, and collaborating robots has contributed to a significant increase of MPC related works in this field. Nubert et al. [ 88 ] improved the tracking robustness in general with a robust MPC. While [ 47 ] made use of the force feedback of a lightweight robot to polish the free-form surface of a metal workpiece. The MPC maintained a given pressure on a varying area while moving over the surface.

With the upcoming of new concepts of how vehicles are powered was accompanied with new applications of control strategies and applications of MPC. Be it traction control of in-wheel electric motors [? ], cruise control [ 61 , 62 ], or path planning for autonomous driving [ 48 ]. The focus of advanced cruise control is yet on larger commercial vehicles, such as (hybrid) electric buses [ 61 , 137 ], due to its faster return on invest. It seems that the electrification of the power train spread electrical-engineering know-how to the development cycle of vehicles and with it, control engineering expertise.

While many researchers show an extraordinary meticulousness when describing the models they have used, some miss to provide basic information on MPC tuning. We want to emphasize that at least the sample time T s and all horizons (lower prediction horizon N 1 , upper prediction horizon N 2 , and the control horizon N u ) should be listed, as Table  1 to Table  4 demonstrate.

Ideally, also the cost function should be provided including the weights of the slack variables ξ . With the horizons given, applications can be compared and and the computational effort can be estimated. The exact cost function is required to reproduce the results ensuring good scientific practice.

7 Controller design and tuning

The initial hurdle to use MPC is relatively small—provided you have an adequate model describing the process in question. The effort is shifted from controller design towards modeling [ 35 , 104 , 105 ]. Nonetheless, the MPC offers an enormous flexibility regarding its design and tuning [ 37 ]. The most significant effect have:

the cost function,

the constraints (what is constrained and how it is: bound, inequality, or non-linear constraints), and

the choice of the solver itself.

The model is the essence of a MPC. As [ 101 ] put it: “ models are not perfect forecasters, and feedback can overcome some effects of poor models, but starting with a poor process model is akin to driving a car at night without headlights; the feedback may be a bit late to be truly effective”.

Both, theory and commercial application software favor linear models or a linear MPC. To apply linear control even to non-linear systems successive lineraization can be used, e.g. [ 6 , 8 , 63 , 80 , 97 , 147 ], or model switching, e.g. [ 95 ]. The idea is to take advantage of a linear optimization, i.e. linear MPC, with a comparably low computational burden and a non-linear prediction.

Few applications use non-linear MPC meeting the fact that often the available models are non-linear. However, not all check stability. Others focus explicitly on the stability aspect in their applications, e.g. [ 116 ]. In particular with the popularity of machine learning model, non-linear MPC applications increase. A sometimes ignored drawback of non-linear MPC is the larger computation of non-linear optimization. However, there was a new computation scheme introduced recently: RTI. Gros et al. [ 41 ] summarizes this approach presenting linear MPC as a special case of it. The main idea is as simple as it is charming, making use of the previous solution. At time step k , the controller calculates a solution for time steps k + 1 to k + N u . A good optimization given, the solution for time step k + 2 presents a rationally good starting point for the next optimization at time step k + 1. Thus, one can limit the number of iterations of each optimization assuming that the next optimizations continue improving the solution of the trajectory of the manipulation variable. “ The RTI approach consists in performing the Newton steps always using the latest information on the system evolution ” [ 41 ]. This idea of “warm starting” relies on a sufficiently high sampling frequency to ensure only small changes between iterations. Because the RTI scheme implements one single full Newton step per time step, it generally works better if the non-linearity between time steps is mild and if the prediction horizon is longer.

Controlling large multiple input multiple output (MIMO) systems with a single MPC may be difficult [ 32 ], that is why cascaded or hierarchical MPC structures are some times suggested, e.g. a two-layer MPC [ 112 , 126 ] running at different sample rates.

Slack variables soften constraints moving it to the cost function where the amount of its violation is penalized. This generates the additional tuning factor W ξ , which is a weight matrix ensuring feasibility by softening constraints on the model output (and with this, on the reaction of the system). It is usually an identity matrix, whose entries are several orders higher than the weight matrix of the control error W w .

A trade-off between accurate tracking of the reference and smooth control behavior can be performed by considering the change of the manipulated variable in the cost function:

The same constraints apply as before in Eq.  5 . The cost function minimizes the deviation from the reference r over the prediction horizon N 2 . It additionally considers the change in the manipulated variable Δ u k = u k −u k − 1 . The last term includes the slack variables ξ , which quantify the violation of output constraints. It must be tuned manually until the controller reflects the desired behavior. To the experience of the authors, a good starting point lies within W u = (0.01I,1I), with the lower values let the MPC use its potential unhindered at the exchange of more (usually small) violations of the boundaries.

Typical solvers are based on linear programming (LP) or quadratic programming (QP) [ 26 ]. If one uses the commercial tools, i.e. from the popular program MATLAB by The MathWorks , the choice of an optimization algorithm is not a question. But, for deeper dives into the design, a good option for a solver is quadratic programming online active set strategy (qpOASIS). It is an open-source optimization algorithm for linear problems, which has “ several theoretical features that make it particularly suited for model predictive control (MPC) applications” as the project stated [ 30 ]. The choice of the solver influences the demand of computational resources.

Besides those major design building blocks, the MPC exhibits a whole slew of tuning parameters: the horizons ( N 1 , N 2 , N u ), the weights in the cost function, Eq.  11 , and the time step or sampling time T s . It is unique for every case but this review can provide tips and best practices for the other tuning parameters.

The horizons are crucial of the system’s performance and must be determined for every case. The prediction horizon N 2 must be long enough to capture the effect of a change of the manipulated variable u . In this way the minimum length of the manipulation horizon N u can be estimated by

To reduce the complexity of algorithmic tuning, [ 118 ] suggested to neglect the difference of the prediction and the manipulation horizon: N 2 = N u . The effect on computation is small if the time delay of the system is small in terms of multiples of the sampling time.

The lower prediction horizon describes the time delay of the system. It is best practice to consider this in the model of the system and, therefore, setting N 1 = 1. This considers that the manipulated variable is not implemented instantly, which would make the exact moment indeterministic as it depends on the time the MPC requires for solving the optimization problem. Instead, the obtained optimal command u is implemented at the next time step. These considerations reduce the problem of finding suitable prediction horizons to the problem of determining the necessary prediction horizon N 2 . Its choice can be estimated using the system model by simulating all possible step changes in the manipulated variable(s). If the combination that has the longest effect on the control variable is known, it is sufficient to simulate this.

8 Computation

It does not help to talk about MPC, i.e. repeatedly solving an optimization problem online, without talking about its computational effort. In the control of power electronics, the prediction horizon was often limited to N 2 = 1 due to tight time requirements [ 38 ]. Nevertheless, there are more sophisticated strategies to reduce computation than wrecking prediction. Morari [ 84 ] argued that computational effort was irrelevant based on the computing power in 1994. This is remarkable from today’s perspective: although computing power increased exponentially, Fig.  6 , at the same time control intervals have shrunken and thus computation is still an issue.

Overview of the evolution of the computation power (data taken from [ 49 , 132 ])

Moore ’s law states that the number of transistors on a microprocessor doubles roughly every two years [ 132 ]. That usually implies that computational performance doubles too – and prices dropped in sync, Fig.  6 . This comfortable development may not continue forever; in fact, special-purpose chips are on the advance (think of low energy CPUs that power smartphones) letting the microprocessor landscape diverge. The tremendous success of machine learning techniques and the increasing parallelization in software were paved by the replacement of CPUs for GPU chips. At the same time, the clock speed had been limited because of the heat dissipation in the resistors. To still keep up with Moore ’s law, multiple cores were integrated on the same chip from the early 2000s on. With this in mind, strategies to reduce the computational load become very well important again. With increasing computational resources, more demanding systems were controlled that were not even imaginable before.

8.1 Explicit MPC

In the year 2000, [ 14 ] still claimed that MPC was only applicable to slow or small systems due to the computational effort that solving an optimization problem imposes. Parallel to the increasing computational power, many dedicated approaches have been introduced bringing MPC towards more efficiency. As an intermezzo hybrid MPC or explicit MPC approaches popped up [ 13 ]. They combine an offline solved optimization problem with online control. The optimization problem—and thereby the control law—is solved for a multitude of possible situations and stored in a look-up table. This shifts the task of computation to a non-time-critical offline calculation. Essentially, MPC in this was becomes an online gain-scheduling algorithm. The advantage is that closed-loop control can be performed at higher rates which, in some cases, made closed-loop control feasible in the first place and, in other cases, improved the control behavior due to quicker feedback.

The major drawback is the increasing computational effort solving the problem for all possible situations in conjunction with the increasing memory demand. It lacks of flexibility regarding unexpected disturbances and of the opportunity to adjust the process model.

Explicit MPC increases the overall computation because every possible state needs to be calculated a priori . This might be the reason why it emerged from the control of power converters with simple (mostly binary) problems, short horizons, and almost no time for calculation [ 130 ]. For complex systems, the advantage at execution is somewhat diminished if searching the a priori solved result takes long [ 122 ]. The solution space scales exponentially with the problem size making look-up-table-approaches inefficient – this is sometimes dubbed “curse of dimensionality” [ 102 ].

One way to reduce the general computational effort is to approximate the solution-space by a non-linear function. Recent studies suggested to use NNs for this [ 64 , 143 ]. This sped up the required online computation by a factor of 65–100 in [ 143 ]. Approximating the solution space by a function let the MPC work with near optimal solutions but shifts the computational burden may allow to decrease the online computation time. [ 143 ] built a second model to quantify the approximation error at every point in the solution space. The charm of an approximation through machine learning is that the training can be flexibly stopped if a defined accuracy is reached. Hertneck et al. [ 45 ] took this thought focusing on accurate learning of the solution space by the neural network (NN). They quantified the probability of a wrong approximation. In this way, they were able to adjust and extend the training until it reached the desired quality. The procedure was demonstrated on a simple numerical example reducing the computation time by a factor of 200—at the cost of a training effort of 20 days. Only recently the idea was tested on an industrial robot as real system [ 88 ]. The to-be-approximated MPC was designed for robust control with regard to the output of the MPC. In this way, measurement noise—or an inaccurate approximation of the solution space through the neural network (NN)—did not affect the stability of the to-be-controlled system.

Maddalena et al. [ 71 ] generalized the idea proposing a neural network (NN) with two linear layers and a parametric quadratic program layer in between to learn the control law of any linear MPC with A quadratic cost function. They showed that the resulting explicit MPC was still closed-loop stable in the sense of Lyapunov by using out-of-the-box the certification technique proposed by [ 51 ]. The technique was applicable because the neural network (NN) structure essentially presented a linear mapping with polynomial inequalities. In fact, [ 102 ] concluded that NNs—in particular with rectified linear units (ReLUs)—present a continuous piece-wise linear mapping ideal for approximating large solution spaces of explicit MPC policies.

8.2 Move blocking

Move blocking strategy for MPC (in sense of input blocking as its most common formulation) is a scheme, where the degree of freedom for the optimization is reduced by trimming the number of calculated control outputs. Thereby, the control output is held constant at defined steps over the control horizon. In this way, the computational burden decreases because the control output does not have to be calculated at every time step over the control horizon anymore.

Overall, the result of move blocking strongly depends on the choice of blocked time steps. One conceivable approach is to block the later time steps to obtain a higher degree of freedom at the beginning of the control horizon. Such an approach is appealing for uncertain systems, where the predicted system behavior is more trusted at early time steps. Nevertheless, one has to be aware of the aforementioned drawback. A more sophisticated, but also more computationally expensive, approach is to optimize the choice of blocked time steps as a mixed-integer problem [ 115 ].

One major drawback of the strategy is that the continuity of the optimization for a receding horizon can no longer be ensured. This is due to the shift of fixed (or blocked) time steps with the receding horizon between iterations. Therefore, the degree of freedom at a certain point in time in the future cannot be guaranteed at the following iteration of the optimization. In the worst case, neither the satisfaction of constraints for the optimization, nor the controller stability can be met. One way to overcome this is to adapt the fixed time steps, such that the degree of freedom is defined at the same time [ 16 ].

9 Conclusion

Popularity of MPC “ comes in great part from the fact that a suitable model being given, the controller can be easily implemented with a direct physical understanding of the parameters to be tuned and easy constraints handling” [ 104 ]. With the great advances in microprocessors and the omnipresent availability of models, this is more true than ever. One key characteristic of MPC is the implicit determination of the control law by solving the constrained optimization problem online. The incorporation of physical constraints in the optimization problem shifts the effort of designing a controller towards modeling the to-be-controlled system [ 35 , 104 , 105 ].

The hurdle to overcome for a lasting impact of MPC on industry is the complexity of modeling and algorithmic tuning. In most cases, the potential benefit is not worth the effort of building up expert knowledge in modeling, optimization, and control theory.

Modeling is often the most time consuming activity [ 44 ]. As the age of microprocessors removed computational resources as the largest obstacle and paved the way for an enduring success of MPC, the second era may be herald by the use of data-driven modeling lowering the barriers even more. Machine learning enables an easy description of complex systems lowering the hurdle of applying MPC to new processes.

For applications first the extreme have been covered: large and complex multiple input multiple output (MIMO) systems with long sample times (petrochemical industry). Then, almost as a counter movement, fast systems with short sample times and often an explicit formulations were developed (power converters). These days, the craziness has settled leaving the field to reasonable sample times. Although computational power has increased tremendously, even today, an efficient calculation should always be the dictum but requires expert knowledge in programming hindering a plug&play usage. Forbes et al. [ 32 ] concluded that a higher usability of existing techniques is required by industry rather than new MPC algorithm. Nowadays, it is almost as if the focus has shifted from theory to application letting both advance in conjunction. The theory becomes application-driven again—as it was in its beginnings.

We are convinced that the global mega trend of decarbonization will further boost MPC applications in electronics, due to the expansion of electrification as well as the constantly pressing demand for high efficiency of electric components. Model-based predictive control (MPC) can contribute to efficiency in many fields, e.g. in climate control systems (precisely heating, ventilation and air conditioning (HVAC)) They deal with sluggish systems and comparably precise forecasting models, e.g. for room occupations or for the weather, what makes MPC predestined for them.

The buds of the new trends and the thick trunks of the established disciplines suggest, to our eyes, that one step way from an exponential increase in the number of MPC applications.

Model-based predictive control (MPC) enables controlling high-level objectives rather than machine tool set points. This review shall encourage domain experts to apply this intelligent control method to their fields seeding the next level of manufacturing.

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All authors contributed to the study conception and design. In the conception phase, the authors were supported by Sebastian Stemmler, who was not considered as author. Visualization was performed by Max Schwenzer and Muzaffer Ay. The first draft of the manuscript was written by Max Schwenzer and supported by Muzaffer Ay, who contributed details on stability, the latest developments and computation. Thomas Bergs and Dirk Abel acquired the funding for the project leading to this publication. All authors read and approved the final manuscript.

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Schwenzer, M., Ay, M., Bergs, T. et al. Review on model predictive control: an engineering perspective. Int J Adv Manuf Technol 117 , 1327–1349 (2021). https://doi.org/10.1007/s00170-021-07682-3

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A Review on Control System Applications in Industrial Processes

P K Juneja 1 , S K Sunori 2 , A Sharma 3 , A Sharma 4 , H Pathak 5 , V Joshi 5 and P Bhasin 5

Published under licence by IOP Publishing Ltd IOP Conference Series: Materials Science and Engineering , Volume 1022 , 1st International Conference on Computational Research and Data Analytics (ICCRDA 2020) 24th October 2020, Rajpura, India Citation P K Juneja et al 2021 IOP Conf. Ser.: Mater. Sci. Eng. 1022 012010 DOI 10.1088/1757-899X/1022/1/012010

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1 Department of ECE, Graphic Era University, Dehradun, India

2 Department of ECE, Graphic Era Hill University, Bhimtal, Nainital, India

3 Department of PDP, Graphic Era University, Dehradun, 248001, India

4 Department of PDP, Graphic Era Hill University, Dehradun, India

5 Department of EE, Graphic Era University, Dehradun, India

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Present paper attempts to review the literature related to design of P-I-D control for time delayed complex industrial process for single as well as for multivariable process with interaction considerations, their decoupler design and time delay compensators. General instrumentation of the industrial feedback control systems along with control system analysis has been covered. Also it covers, control features of some paper mill sub-processes like headbox operation, basis weight and retention. The importance of eliminating the effects of interactions, among the process control loops inside a multi input multi output industrial control system, has been discussed with the help of literature study. The importance of the process dynamics knowledge for designing a control system has also been investigated. This paper also investigates the significance and effectiveness of PID controllers through various literature studies. The problems of the classical PID controllers such as constraints, presence of disturbances etc.) can be removed by designing in combination with soft computing techniques. Moreover, possibility of further enhancements in the PID controller with the utilization of various schemes available, has been presented. The present status of control systems in industrial processes in terms of various control parameters such as stability, dead time compensation etc. has been presented and the future improvements have been stated.

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Modular, scalable hardware architecture for a quantum computer

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Quantum computers hold the promise of being able to quickly solve extremely complex problems that might take the world’s most powerful supercomputer decades to crack.

But achieving that performance involves building a system with millions of interconnected building blocks called qubits. Making and controlling so many qubits in a hardware architecture is an enormous challenge that scientists around the world are striving to meet.

Toward this goal, researchers at MIT and MITRE have demonstrated a scalable, modular hardware platform that integrates thousands of interconnected qubits onto a customized integrated circuit. This “quantum-system-on-chip” (QSoC) architecture enables the researchers to precisely tune and control a dense array of qubits. Multiple chips could be connected using optical networking to create a large-scale quantum communication network.

By tuning qubits across 11 frequency channels, this QSoC architecture allows for a new proposed protocol of “entanglement multiplexing” for large-scale quantum computing.

The team spent years perfecting an intricate process for manufacturing two-dimensional arrays of atom-sized qubit microchiplets and transferring thousands of them onto a carefully prepared complementary metal-oxide semiconductor (CMOS) chip. This transfer can be performed in a single step.

“We will need a large number of qubits, and great control over them, to really leverage the power of a quantum system and make it useful. We are proposing a brand new architecture and a fabrication technology that can support the scalability requirements of a hardware system for a quantum computer,” says Linsen Li, an electrical engineering and computer science (EECS) graduate student and lead author of a paper on this architecture.

Li’s co-authors include Ruonan Han, an associate professor in EECS, leader of the Terahertz Integrated Electronics Group, and member of the Research Laboratory of Electronics (RLE); senior author Dirk Englund, professor of EECS, principal investigator of the Quantum Photonics and Artificial Intelligence Group and of RLE; as well as others at MIT, Cornell University, the Delft Institute of Technology, the U.S. Army Research Laboratory, and the MITRE Corporation. The paper appears today in Nature .

Diamond microchiplets

While there are many types of qubits, the researchers chose to use diamond color centers because of their scalability advantages. They previously used such qubits to produce integrated quantum chips with photonic circuitry.

Qubits made from diamond color centers are “artificial atoms” that carry quantum information. Because diamond color centers are solid-state systems, the qubit manufacturing is compatible with modern semiconductor fabrication processes. They are also compact and have relatively long coherence times, which refers to the amount of time a qubit’s state remains stable, due to the clean environment provided by the diamond material.

In addition, diamond color centers have photonic interfaces which allows them to be remotely entangled, or connected, with other qubits that aren’t adjacent to them.

“The conventional assumption in the field is that the inhomogeneity of the diamond color center is a drawback compared to identical quantum memory like ions and neutral atoms. However, we turn this challenge into an advantage by embracing the diversity of the artificial atoms: Each atom has its own spectral frequency. This allows us to communicate with individual atoms by voltage tuning them into resonance with a laser, much like tuning the dial on a tiny radio,” says Englund.

This is especially difficult because the researchers must achieve this at a large scale to compensate for the qubit inhomogeneity in a large system.

To communicate across qubits, they need to have multiple such “quantum radios” dialed into the same channel. Achieving this condition becomes near-certain when scaling to thousands of qubits. To this end, the researchers surmounted that challenge by integrating a large array of diamond color center qubits onto a CMOS chip which provides the control dials. The chip can be incorporated with built-in digital logic that rapidly and automatically reconfigures the voltages, enabling the qubits to reach full connectivity.

“This compensates for the in-homogenous nature of the system. With the CMOS platform, we can quickly and dynamically tune all the qubit frequencies,” Li explains.

Lock-and-release fabrication

To build this QSoC, the researchers developed a fabrication process to transfer diamond color center “microchiplets” onto a CMOS backplane at a large scale.

They started by fabricating an array of diamond color center microchiplets from a solid block of diamond. They also designed and fabricated nanoscale optical antennas that enable more efficient collection of the photons emitted by these color center qubits in free space.

Then, they designed and mapped out the chip from the semiconductor foundry. Working in the MIT.nano cleanroom, they post-processed a CMOS chip to add microscale sockets that match up with the diamond microchiplet array.

They built an in-house transfer setup in the lab and applied a lock-and-release process to integrate the two layers by locking the diamond microchiplets into the sockets on the CMOS chip. Since the diamond microchiplets are weakly bonded to the diamond surface, when they release the bulk diamond horizontally, the microchiplets stay in the sockets.

“Because we can control the fabrication of both the diamond and the CMOS chip, we can make a complementary pattern. In this way, we can transfer thousands of diamond chiplets into their corresponding sockets all at the same time,” Li says.

The researchers demonstrated a 500-micron by 500-micron area transfer for an array with 1,024 diamond nanoantennas, but they could use larger diamond arrays and a larger CMOS chip to further scale up the system. In fact, they found that with more qubits, tuning the frequencies actually requires less voltage for this architecture.

“In this case, if you have more qubits, our architecture will work even better,” Li says.

The team tested many nanostructures before they determined the ideal microchiplet array for the lock-and-release process. However, making quantum microchiplets is no easy task, and the process took years to perfect.

“We have iterated and developed the recipe to fabricate these diamond nanostructures in MIT cleanroom, but it is a very complicated process. It took 19 steps of nanofabrication to get the diamond quantum microchiplets, and the steps were not straightforward,” he adds.

Alongside their QSoC, the researchers developed an approach to characterize the system and measure its performance on a large scale. To do this, they built a custom cryo-optical metrology setup.

Using this technique, they demonstrated an entire chip with over 4,000 qubits that could be tuned to the same frequency while maintaining their spin and optical properties. They also built a digital twin simulation that connects the experiment with digitized modeling, which helps them understand the root causes of the observed phenomenon and determine how to efficiently implement the architecture.

In the future, the researchers could boost the performance of their system by refining the materials they used to make qubits or developing more precise control processes. They could also apply this architecture to other solid-state quantum systems.

This work was supported by the MITRE Corporation Quantum Moonshot Program, the U.S. National Science Foundation, the U.S. Army Research Office, the Center for Quantum Networks, and the European Union’s Horizon 2020 Research and Innovation Program.

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Automatic rainwater quality monitoring system using low-cost technology, 1. introduction, 2. case study, 3. methodology, 3.1. selection of monitored water quality parameters, 3.2. analysis of requirements.

• Power supply: The prototype will be connected to the SAIH stations and powered through the electrical network.
• Connectivity: SAIH stations and the developed prototype connect to the internet wirelessly via Wi-Fi.
• Visualization: SAIH stations display their information in real-time on a web page using ThingSpeak platform widgets. However, the free version only stores data for a month before deleting it. To overcome this limitation, a database was developed for this project on web hosting.
• Operating conditions: The water quality sensors consist of a circuit and a probe. The probes are waterproof, but the circuits are not. To protect the circuits from the elements, a housing was designed to store them, while the probes were left exposed to collect and renew rainwater. The maintenance of probes due to corrosion or sensor replacement, estimating that this could potentially increase the total cost by 5%.

3.3. Design and Development

3.3.1. calibration.

• Clean the sensor probe with distilled water and dry it with a disposable tissue.
• Correctly place the sensor inside the calibration standard solution.
• Carry out the measurement.
• Record the parameter value and the voltage read by the device.
• Remove the probe from the calibration standard solution.
• Repeat steps 1 to 5 10 times.
• Calculate the relative error percentage using Equation (1). If it is greater than that guaranteed by the manufacturer, the sensor is calibrated.
• Repeat steps 1 through 7 for each sensor.

3.3.2. Validation

3.3.3. data visualization.

• Analysis of requirements: The monitoring stations were displayed on a map with markers to visualize them and show the latest information upon interaction.
• Architecture and technology: A hosting provider was hired for platform development. A dynamic website was developed using web technologies such as HTML, PHP, JavaScript, and CSS. MySQL 8.0.17 was used as the database manager. A free Bootstrap web template (SB Admin 2) was used as a base [ 25 ] to develop the web application and mobile-first sites with a layout that adapts to the user’s screen [ 26 ].
• Design of the logical and physical structure of the site: The main page contains the map with the monitoring stations. The site contains several sections with different functions, such as selecting consulted parameters in real-time, downloading data for a given period, and consulting data recorded on a specific time and date. Additionally, complementary pages such as Team and Contact were added.
• Content creation: The platform’s content is primarily graphic, with more extensive text found in the Team and Contact tabs. The rest of the site contains short indications for the user or information on the indicators.
• Graphic design: The interface features various shades of white, blue, gray, black, and green. White is used for the navigation bar, page background, and pop-up windows. Blue is used for some text, radio buttons, weather indicators, and real-time graphs. Gray is used for some text, station markers, indicator icons, and back buttons. Black is used for most text, and green is used for water quality indicators and some text. The default typography was retained from the Bootstrap template, and the sizes were adapted according to the device accessing the site. The indicator icons were obtained from the Font Awesome platform [ 27 ], which offers free icons that can be added to the website.
• Creation of the static pages: The static pages include the Team and Contact pages, which will not change according to the database.
• Creation of the dynamic pages: The dynamic page is the home page, where the station markers are displayed on the map. These markers change color based on the intensity of precipitation, and the magnitude of the indicators is updated in real-time.
• Verification of the site’s operation: The page’s connection with the database was verified, ensuring that the most recent data was updated. The links within the site were also confirmed to redirect to the correct site. The site was tested on different browsers and devices, and the content was adjusted to fit the screen size. Finally, the site’s loading time was tested.
• Start-up: After verifying the site’s operation locally, it was published on the web domain, making it accessible to the public.

3.3.4. Materials

4. discussion and results, 4.1. selection of monitored water quality parameters, 4.2. design and development, 4.3. calibration, 4.4. validation, 4.5. implementation of the interface to visualize the data, 5. conclusions, author contributions, data availability statement, acknowledgments, conflicts of interest.

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Mejía-Ferreyra, L.D.; García-Romero, L.; Sánchez-Quispe, S.T.; Apolinar-Cortés, J.; Orantes-Avalos, J.C. Automatic Rainwater Quality Monitoring System Using Low-Cost Technology. Water 2024 , 16 , 1735. https://doi.org/10.3390/w16121735

Mejía-Ferreyra LD, García-Romero L, Sánchez-Quispe ST, Apolinar-Cortés J, Orantes-Avalos JC. Automatic Rainwater Quality Monitoring System Using Low-Cost Technology. Water . 2024; 16(12):1735. https://doi.org/10.3390/w16121735

Mejía-Ferreyra, Luis Daniel, Liliana García-Romero, Sonia Tatiana Sánchez-Quispe, José Apolinar-Cortés, and Julio César Orantes-Avalos. 2024. "Automatic Rainwater Quality Monitoring System Using Low-Cost Technology" Water 16, no. 12: 1735. https://doi.org/10.3390/w16121735

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Research into the operating modes of a stand-alone dual-channel hybrid power system

• Andrey Dar'enkov 1 , 
• Aleksey Kralin 2 , 
• Evgeny Kryukov 3 ,  ,  , 
• Yaroslav Petukhov 3
• 1. Department of Electrical Equipment, Electric Drive and Automation, Nizhny Novgorod State Technical University n. a. R.E. Alekseev, 603155 Nizhny Novgorod, Russia
• 2. Department of Theoretical and General Electrical Engineering, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 603155 Nizhny Novgorod, Russia
• 3. Department of Electric Power Engineering, Power Supply and Power Electronics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 603155 Nizhny Novgorod, Russia
• Received: 01 April 2024 Revised: 28 May 2024 Accepted: 11 June 2024 Published: 18 June 2024
• Full Text(HTML)
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The article describes the development and simulation of a stand-alone hybrid power system based on a variable-speed diesel generator and a hydrogen fuel cell generation system. The goal of the research was to investigate the electromagnetic processes of this power system, which supplies power to autonomous energy consumers with varying load demand. MATLAB Simulink was used to simulate the proposed hybrid power system and check its operating capacity. The results of the simulation include the dependencies of current and voltage changes in the critical components of the hybrid system at stepwise load rate changes. In the future, the developed models and simulation results will allow researchers to select semiconductor devices and create microprocessor-based control systems for electric power installations that meet specific requirements. The dual-channel power system can provide a required power output of 3 kW when powered by a diesel generator and 1 kW when powered by a hydrogen fuel cell. At the same time, the total harmonic distortion (THD) at a load between 100 W and 3 kW varies within acceptable limits between 3.6% and 4.4%. It is worth noting that these higher power complexes can be incorporated into stand-alone electrical grids as well as centralized distribution systems for power deficit compensation during peak loads.

• hybrid power system ,
• diesel generator ,
• hydrogen fuel cell ,
• electromagnetic processes ,
• DC-DC converter ,
• PWM inverter

Citation: Andrey Dar'enkov, Aleksey Kralin, Evgeny Kryukov, Yaroslav Petukhov. Research into the operating modes of a stand-alone dual-channel hybrid power system[J]. AIMS Energy, 2024, 12(3): 706-726. doi: 10.3934/energy.2024033

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• Figure 1. Stand-alone dual-channel hybrid power system structure
• Figure 2. SDHPS simulation model
• Figure 3. Structural diagram of a diesel engine simulation model
• Figure 4. Synchronous generator simulation model
• Figure 5. Hydrogen fuel cell model parameters
• Figure 6. SDHPS experimental prototype blocks: (a) HFC, (b) DG
• Figure 7. Time dependencies: (a) load current, (b) internal combustion engine (ICE) speed variation, (c) bridge-circuit thyristor delay angle, (d) bridge-circuit rectifier output voltage
• Figure 8. The time dependence of the line voltage effective value on the load
• Figure 9. Voltage spectral analysis: (a) after the filter, (b) after the transformer or on-load
• Figure 10. The change in THD depends on the load power
• Figure 11. DC-DC converter time diagrams: (a) output voltage, (b) output current, (c) IGBT current, (d) voltage on IGBT

This paper is in the following e-collection/theme issue:

Published on 20.6.2024 in Vol 26 (2024)

Effect of Digital Early Warning Scores on Hospital Vital Sign Observation Protocol Adherence: Stepped-Wedge Evaluation

Authors of this article:

Original Paper

• David Chi-Wai Wong 1 , MEng, DPhil   ; 
• Timothy Bonnici 2 , BSc, MBBS, PhD   ; 
• Stephen Gerry 3 , BSc, MSc   ; 
• Jacqueline Birks 3 , MA, MSc   ; 
• Peter J Watkinson 4, 5, 6 , MD  

1 Leeds Institute of Health Sciences, School of Medicine, University of Leeds, Leeds, United Kingdom

2 Critical Care Division, University College Hospital London NHS Foundation Trust, London, United Kingdom

3 Centre for Statistics in Medicine, University of Oxford, Oxford, United Kingdom

4 Oxford University Hospitals NHS Trust, Oxford, United Kingdom

5 NIHR Biomedical Research Centre, Oxford University Hospitals NHS Foundation Trust, Oxford, United Kingdom

6 Nuffield Department of Clinical Neurosciences, Kadoorie Centre for Critical Care Research and Education, University of Oxford, Oxford, United Kingdom

Corresponding Author:

David Chi-Wai Wong, MEng, DPhil

Leeds Institute of Health Sciences

School of Medicine

University of Leeds

Worsley Building

Leeds, LS2 9JT

United Kingdom

Phone: 44 113 343 0806

Email: [email protected]

Background: Early warning scores (EWS) are routinely used in hospitals to assess a patient’s risk of deterioration. EWS are traditionally recorded on paper observation charts but are increasingly recorded digitally. In either case, evidence for the clinical effectiveness of such scores is mixed, and previous studies have not considered whether EWS leads to changes in how deteriorating patients are managed.

Objective: This study aims to examine whether the introduction of a digital EWS system was associated with more frequent observation of patients with abnormal vital signs, a precursor to earlier clinical intervention.

Methods: We conducted a 2-armed stepped-wedge study from February 2015 to December 2016, over 4 hospitals in 1 UK hospital trust. In the control arm, vital signs were recorded using paper observation charts. In the intervention arm, a digital EWS system was used. The primary outcome measure was time to next observation (TTNO), defined as the time between a patient’s first elevated EWS (EWS ≥3) and subsequent observations set. Secondary outcomes were time to death in the hospital, length of stay, and time to unplanned intensive care unit admission. Differences between the 2 arms were analyzed using a mixed-effects Cox model. The usability of the system was assessed using the system usability score survey.

Results: We included 12,802 admissions, 1084 in the paper (control) arm and 11,718 in the digital EWS (intervention) arm. The system usability score was 77.6, indicating good usability. The median TTNO in the control and intervention arms were 128 (IQR 73-218) minutes and 131 (IQR 73-223) minutes, respectively. The corresponding hazard ratio for TTNO was 0.99 (95% CI 0.91-1.07; P =.73).

Conclusions: We demonstrated strong clinical engagement with the system. We found no difference in any of the predefined patient outcomes, suggesting that the introduction of a highly usable electronic system can be achieved without impacting clinical care. Our findings contrast with previous claims that digital EWS systems are associated with improvement in clinical outcomes. Future research should investigate how digital EWS systems can be integrated with new clinical pathways adjusting staff behaviors to improve patient outcomes.

Introduction

Avoidable mortality from unrecognized clinical deterioration is an internationally recognized problem [ 1 ]. Such deterioration often corresponds with deviations in patient vital signs early warning score (EWS) algorithms have been introduced to improve the recognition of abnormal vital signs [ 2 ]. They assign a score to each vital sign value according to the degree of abnormality. The total score is a measure of patient risk. Many EWS algorithms have been published and their use is mandated by the National Institute of Health and Care Excellence in the United Kingdom [ 3 , 4 ]. Since 2018, 1 standard EWS, the National Early Warning Score 2, has been mandated in acute hospital trusts [ 5 ].

EWS algorithms are accompanied by an escalation protocol, which dictates how frequently the patient should be monitored and what other actions staff should take for each value of the total score. If the EWS score exceeds the “trigger threshold” defined in the escalation protocol, the nursing staff must call a doctor to review the patient.

Despite the widespread adoption of EWS algorithms and associated escalation protocols, patient outcomes have not improved significantly [ 6 , 7 ]. It is possible that errors in the calculation of the EWS are partially to blame. Studies have shown that errors in the calculation of EWS are common and failure to calculate the correct EWS may result in failure to take the correct action [ 8 , 9 ]. Other barriers to escalation include delays in documentation, lack of familiarity with the escalation protocol, failure to follow the protocol, and poor communication [ 10 , 11 ].

Digital EWS systems have been proposed as a solution. These systems automatically calculate the EWS based on data input by staff and display relevant information from the escalation protocol. These data may be displayed to the staff at the bedside, on mobile devices, or at nursing station dashboards, enabling senior clinicians to rapidly survey patient acuity across an area.

At present there is no robust evidence of changes in clinical outcomes to support or refute the case for the introduction of electronic EWS systems. Most recent studies focus on improving the predictive ability of the scoring system itself [ 12 , 13 ], ignoring the complex interaction with health care staff and infrastructure required to affect clinical decision-making. The limited number of studies of digital EWS systems in clinical practice have shown inconsistent results [ 14 - 16 ]. Some have used uncontrolled “before and after” design methodologies, comparing data from periods several years apart, which are limited by their inability to control for temporal confounding such as changes in case mix [ 17 ]. Furthermore, very few existing studies have not provided insight into the mechanisms by which any reported improvements were achieved [ 18 ].

This study aimed to examine whether the introduction of a digital EWS charting system leads to improvements in patient care. Our causal hypothesis is that, compared with paper charting, the use of a digital EWS system leads to better recognition of patient deterioration and closer adherence to the hospital escalation protocol. These behavior changes would lead to the more frequent observation of patients with abnormal vital signs and therefore earlier escalation. Earlier escalation would lead to improvements in both process metrics and patient outcomes.

The staged replacement of paper EWS charting with a digital EWS charting system at the Oxford University Hospitals Foundation NHS Trust (OUHFT) provided us the opportunity to conduct a natural experiment using a nonrandomized stepped wedge trial design.

Ethical Considerations

The study protocol was reviewed by the OUHFT’s Research and Development department, and based upon Health Care Quality Improvement Partnership guidelines and was deemed to be a service evaluation (ID: 3196), not requiring review by the National Research Ethics Service. All methods were carried out in accordance with the Declaration of Helsinki. As patient data were collected without their consent, permission for informed consent waiver was obtained from the Trust’s Caldicott Guardian and Medical Director in accordance with the Health Research Authority Confidentiality Advisory Group guidelines. All study data were deidentified and patients were not compensated. The full study protocol has previously been published and is summarized below [ 19 ].

Study Setting

The OUHFT is comprised of 4 hospitals: 1 large teaching hospital, a small district general hospital, and 2 specialist hospitals that do not have emergency departments. Two of the hospitals have intensive care units (ICU) that also act as high-dependency units, and 2 have high-dependency units only.

The digital EWS implemented at OUHFT was the system for electronic notification and documentation (SEND) system [ 20 ], a system in which clinical users manually enter vital sign observation data onto a tablet PC. The system then automatically calculates an EWS and displays relevant advice from hospital escalation protocols.

The tablet is physically mounted to a roll-stand with a blood pressure monitor, as shown in Figure 1 . The system displays historical vital sign observations of a patient ( Figure 1 ), and ward-level and hospital-level overviews are available via desktop computers.

The EWS used at OUHFT was the centile early warning score (CEWS) [ 21 ]. CEWS uses 6 vital signs as input parameters, which are each scored from 0 to 3 ( Table 1 ). The trigger threshold is set at 3. For any CEWS greater than or equal to the trigger threshold, the escalation protocol mandates hourly observations and review by a senior doctor. CEWS also allows a nurse to indicate clinical concern. When a nurse is concerned, hourly observations and escalation to a doctor are mandated, irrespective of the CEWS score. A copy of the paper EWS chart and a full description of the escalation protocol are provided in Multimedia Appendix 1 .

a Not available.

b SpO 2 : peripheral arterial oxygen saturation.

c AVPU: Alert, Voice, Pain, Unresponsive.

d GCS: Glasgow coma scale.

Trial Design

The stepped-wedge study comprised 2 arms, a control arm in which vital signs were recorded using paper observation charts and an intervention arm where the digital EWS system, SEND, was used. The EWS and escalation protocol were identical in both arms.

The study consisted of 20 clusters (and 21 steps). We defined a cluster as a group of between 1 and 5 eligible wards that implemented SEND simultaneously. All wards that were due to switch to the SEND system were eligible for inclusion in a cluster; we defined these as “study wards.” Study wards included all adult wards across the Trust, except for the obstetric wards, emergency departments, day units, high dependency units, ICUs, and investigation suites, which were excluded as they did not use standard hospital observation recording and escalation policies. We also excluded the 3 wards where the SEND system was initially developed and piloted, as the control condition, paper charting, was no longer used at the commencement of the study.

Clusters of wards were determined by pragmatic considerations related to the safe conduct of the rollout. For example, each cluster only contained wards from an individual hospital. The sequence of study clusters was predetermined by the system rollout strategy and was therefore not randomized.

The rollout schedule is depicted in Figure 2 . The time period between the start of each step was typically 2 weeks. The period was occasionally lengthened to account for project management issues such as reduced staffing over the Christmas holidays (exact dates are provided in Multimedia Appendix 2 ). The final period, which occurred after SEND was fully deployed to all wards, lasted 3 months. The extended period was designed to capture any delayed effects caused by wards adapting to the new system.

Each study ward admitted multiple patients during each step. Data for this study was obtained at an individual patient level. A patient’s data belonged to only 1 step, that is, each cluster and period contained data pertaining to different people. We included all patient admissions to the study wards during the study period rather than censoring data from repeated admissions. Therefore, some patients could potentially contribute data to multiple steps on different admissions. We treated multiple episodes within the same patient as independent, reasoning that the primary outcome was unlikely to be causally related to patient characteristics. We excluded data from admissions where patients crossed study arms (ie, the ward moved from paper to digital EWS) during their admission.

Data Collection

Data from the control arm were collected by 7 research assistants transcribing data from paper charts located on each study ward into a bespoke electronic form. This was a resource-intensive process, making it unfeasible to collect data from all clusters simultaneously for the duration of the study. Therefore, we commenced data for the control arm at the start of the roll-out to each hospital site and limited it to the site where SEND was actively rolled out (illustrated in Figure 2 ). To make this tractable, we further split the largest hospital (Hospital D), into 2 sites (Main Wing, second Wing). Data from the intervention arm was continued even once the roll-out of the intervention at a given hospital was complete such that patients from the hospital contributed more data to the intervention arm than data in subsequent hospitals. In summary, data collection may be considered as separate stepped wedges associated with each of the 5 sites, with varying lengths of data from after the intervention.

For each patient admission within each study cluster, we collected patient characteristics (age, gender, Charlson score, admission type, and admitting specialty), the date and times of admission to the ward; first observation with CEWS ≥3 and the immediate subsequent observation; hospital discharge; hospital mortality; transfer to ICU; cardiac arrest call; and theatre admission.

Outcome Measures

The primary outcome measure was the time to next observation (TTNO), defined as the time between a patient’s first triggering observations set (CEWS score ≥3) and the subsequent observations set. To address potential confounding by length of ward stay, analysis of the primary outcome measure was restricted to triggering observation sets that occurred within 48 hours of transfer to the first study ward of an admission.

Secondary outcome measures were time to death in the hospital, time to unplanned ICU admission, time to cardiac arrest call, and hospital length of stay (LOS). In each case, the start time was the time of the initial triggering set of observations.

We reported these outcomes for the subgroup included in the analysis of the primary outcome measure (ie, those patients who had a CEWS score ≥3), in line with our causal hypothesis. We also reported the secondary outcomes for all eligible admissions. In these analyses, we used the time of admission to the study ward as the start time.

Finally, we reported system usability to provide further context. System usability was measured using the system usability scale, a validated 10-item questionnaire that is used to generate a score between 0 and 100 [ 22 ]. We delivered the questionnaire electronically to all users of the digital system. The questionnaire is included in Multimedia Appendix 3 .

Sample Size

The upper bound on the number of patient admissions included in the study was determined by the pragmatic roll-out schedule of the intervention. To determine whether this would be sufficient, we initially undertook a power calculation for steps 1-8, using unpublished pilot data from the Computer Alerting Monitoring System 2 study [ 23 ]. We assumed that the proportion of patients who have a further observation within 3 hours of recording an EWS ≥3 would be 0.5 in the paper arm and 0.6 in the electronic arm, that there would be an average of 11 patients with an initial CEWS ≥3 per cluster, and conservatively that the intracluster correlation will be 0.15. The power was then estimated to be 79.3% for a 5% α level. While the calculation depended on statistics estimated from limited pilot data, it indicated that the inclusion of all steps would be sufficiently powerful to detect a difference of 10% in the primary outcome between groups. Full details of this calculation are provided in Multimedia Appendix 4 .

Statistical Methods

The primary outcome, the difference in TTNO between arms, was analyzed using a mixed-effects Cox model with a random intercept for cluster and a fixed effect for time as described by Hussey and Hughes [ 24 ]. The model included in-hospital death, ICU admission, theatre admission, and cardiac arrest calls as competing events.

We conducted a sensitivity analysis using 5 variants of the basic Hussey and Hughes model, as originally proposed by Hemming et al [ 25 ]. The five variants were: (1) time by strata interaction (fixed effects), (2) time by cluster interaction (random effects), (3) treatment by strata interaction (fixed effects), (4) treatment by cluster interaction (random effects), and (5) treatment by time interaction (fixed effects). Secondary outcomes were analyzed using the same method.

To aid interpretation, we calculated the average TTNO in each arm as the mean of the median (IQR) TTNO within each unit of the stepped wedge cluster.

We reported baseline descriptive statistics on patient characteristics, including age and sex, by study arm. We also reported these data for each time period to help understand whether trends in baseline characteristics differed between the control and intervention arms.

We conducted the study between January 2015 and September 2016, after the conclusion of the rollout of SEND. During this time, there were 90,262 admissions to the study wards. For 2927 (3%) of admissions, vital signs were recorded on both paper and SEND systems and thus excluded. Of the remaining 87,335 admissions, 40,885 (47%) had vital signs recorded exclusively on paper (control arm) and 46,450 (53%) admissions involved patients who had vital signs recorded exclusively using SEND (intervention arm). Of the admissions in the control arm, 11,597 occurred during the implementation period and were available for data capture. In total, 12,802 admissions were entered into the analysis, consisting of 1084 admissions in the control arm and 11,718 admissions in the intervention arm that had a triggering observation within 48 hours of arrival on their first study ward ( Figure 3 ).

Admission characteristics for the control and intervention are presented in Table 2 . Admissions in the intervention arm tended to be slightly older (median age 65 vs 70 years), more likely to be male (49.3% vs 45.6%), and have a higher number of comorbidities (median Charlson score 3 vs 4).

a SEND: system for electronic notification and documentation.

The proportion of male to female sex in both study arms was similar across all steps apart from cluster 1, in which there were a small number of admissions on paper (n=10). There were no males in cluster 20, a cluster that contained only obstetrics and gynecology wards. Proportions of elective and emergency admissions, and medical and surgical admissions, were similar for each study arm across all clusters.

Primary Outcome

There was no significant difference in the TTNO between the 2 arms after adjustment for competing events ( Table 3 ). The median TTNO in the control arm was 128 (IQR 73-218) minutes. The median TTNO in the observation arm was 131 (IQR 73-223) minutes. The hazard ratio of the TTNO using paper charting and the TTNO using SEND was 0.99 (95% CI 0.91-1.07, P =.73). All model variants in the sensitivity analysis gave results consistent with the Hussey and Hughes model primary analysis. The numbers of each type of competing events in each arm are shown in Table 4 .

a FE: Fixed Effects.

b Not available.

c RE: Random Effects.

b ICU: intensive care unit.

Figure 4 shows the TTNO for each step during the study. Confidence intervals for the electronic arm were much narrower than the electronic arm because there was more electronic data (collected after the initial intervention rollout period). There was a marked variation in the TTNO according to cluster ( Figure 4 ); the introduction of the digital system did not reduce this variance. There was insufficient power to determine if the intervention had an impact at a cluster level. However, we note that there appeared to be a large reduction in TTNO for cluster 12, which were acute general medicine wards.

Secondary Outcomes

The introduction of SEND had no significant effect on time to death in hospital, LOS, or time to unplanned ICU admission for the cohort included in the primary analysis ( Table 5 ). There were only 48 cardiac arrest calls across the 2 arms of the study, therefore, there were insufficient events to model this outcome. The findings were consistent irrespective of modeling assumptions. Sensitivity analyses are reported in Multimedia Appendix 5 .

a ICU: intensive care unit.

We also calculated the same secondary measures for the entire patient population (11,597 control and 46,450 intervention), including all those who did not score a CEWS ≥3 within the first 48 hours of admission ( Multimedia Appendix 6 ). For this population, the start time was taken to be the time of admission to the study ward. In this group, there were no significant differences in time to death or LOS. However, there was a borderline reduction in time to ICU admission from the initial triggering set of observations in the intervention arm (hazard ratio 1.25, 95% CI 1.02-1.54).

System usability scores were only available from Hospital A. The feedback questionnaire was sent to 1891 users, of which 208 (11%) responded. The system usability score was 77.6.

Principal Findings

In this large, stepped wedge trial conducted across 4 hospital sites of the same National Health Service trust, the introduction of a digital charting system did not affect the frequency of vital signs recording, nor was it associated with changes in hospital mortality, cardiac arrest rates, or hospital LOS within the subgroup of patients who had a triggering EWS.

Our findings contrast with previous studies of digital vital signs charting. Jones et al [ 26 ] reported a reduction in the mean LOS from 9.7 to 6.9 days following the introduction of Patientrack (Alcidion Group Ltd). Schmidt et al [ 15 ] reported a reduction in hospital mortality following the introduction of VitalPAC (System C Healthcare Ltd).

The differences between our findings and those of previous researchers may be related to trial design and statistical analysis. A significant strength of our work is the use of a stepped-wedge trial design and a large data set, in line with international recommendations regarding digital health evaluation [ 27 ]. Furthermore, we did not institute any new clinical workflows when implementing SEND, which would have confounded the results.

Beyond issues related to design and analysis, 4 other hypotheses could explain our findings. First, it might be that the design or usability of SEND meant that nurses did not engage with the system. However, the system has previously been shown to be more efficient than the charting on paper and the score of 77.6 on the system usability scale is representative of good usability [ 28 , 29 ].

A second possibility is that, although the system was well-liked by staff, advice was not presented at the right time or in the right context and was therefore ineffective in reminding nurses to recheck vital signs [ 30 ]. Advice from the hospital protocol was presented at the time of observation recording but there was no mechanism for automatically notifying staff that the next set of observations was due and our implementation did not include the display of the time to the next observations on a dedicated screen at the nursing station. The understanding of how digital systems influence behavior is poorly understood.

A third possibility is that the system was effective in reminding nurses to recheck observations more frequently, but that the reminder alone was insufficient to trigger behavior change. Behavior change requires a combination of capability, opportunity, and motivation [ 31 ]. Even if a digital charting system positively alters motivation (through user prompts) and capability (through increased efficiency), these influences may be nullified by competing demands.

Finally, there is the possibility that, even with an effective reminder and supportive context, nurses were exercising clinical judgment and deliberately choosing to deviate from the hospital protocol. The gap between hospital protocols (“work as imagined”) and routine clinical practice (“work as done”) is well recognized and is often an essential adaptation to ensuring that hospitals continue to function [ 32 ]. While the hospital protocol recommended the same frequency of monitoring for all patients with an EWS greater than or equal to 3, our results showed that nurses increased the frequency of vital signs monitoring with the EWS score. It is possible that increasing the frequency of vital signs recording would not improve patient outcomes and rather than the nurses changing practice to match the hospital protocol, the protocol should be changed to match nursing practice more closely.

An unexpected finding was that when including all patients, irrespective of whether they had a triggering observation, the time to ICU admission in the intervention arm was less than in the control arm. Similar reductions in time to ICU transfer have recently been observed in a pre and postintervention study of a digital EWS system that used the electronic Cardiac Arrest Risk Triage EWS [ 33 ]. The difference was observed without any difference in the primary outcome measure, which might be explained in 2 ways. Either the result may not correspond to a true effect (which is consistent with the associated wide confidence intervals), or else SEND may be exerting effects via a mechanism other than increased frequency of patient observations.

Limitations

The primary limitation of the study design was that clusters were not randomized but were instead determined by the predetermined phased rollout plan for SEND. Lack of randomization may be a problem since the estimate of the treatment may be unbiased if secular trends exist. To mitigate against this, we included a large number of clusters and explored a variety of analysis methods to examine the possibility of a secular trend. The stepped approach retains advantages over a simple before-after design. The presence of a control group available throughout the study period means that system-level changes may be detected.

A further limitation was the relatively small number of secondary end points. This led to instances in which some clusters had zero secondary end point events. Therefore, conclusions from the secondary outcome analysis ought to be interpreted with caution.

Caution is also required in interpreting the usability survey results. In our original study protocol, we had intended to obtain system usability score data from all new users of the system at the end of roll-out to each hospital site. However, flaws in our survey administration procedures inhibited us from identifying new users versus clinical users who worked in multiple hospitals. Therefore, we only surveyed users of the first site. It is possible that they were not representative of all users. Furthermore, there may be responder bias associated with the low response rate. However, the results obtained in this study are consistent with the findings of questionnaires from staff on pilot wards during the SEND development process [ 28 ].

Although data in this study were collected in 2016, we emphasize that the findings remain highly relevant to both the United Kingdom and international health care providers. In the United Kingdom, digital EWS systems are not yet ubiquitous and have been implemented at multiple hospital Trusts in the last year [ 34 , 35 ]. Internationally, the use of both EWS and an accompanying digital system is an emerging practice [ 36 ]. More pertinently, the effectiveness of EWS and the mechanism by which any potential benefits are obtained is still an open question. Indeed, a recent pre- and postevaluation of a digital sepsis score system highlighted the ongoing need for understanding how the use of alert systems evolves over time and impacts clinical workflow [ 37 ].

Finally, the findings presented here likely underestimate the true overall benefit of the system. We only examined the effects of SEND using a single measure of observation recording practice, the time between observations, is primarily a reflection of the impact of the system on nursing processes. We did not examine the impact of SEND on other clinical processes or the benefits of secondary use of the data for clinical governance and research.

The introduction of a digital vital signs charting system had no effect on the frequency of vital signs observation or the time to ICU admission, hospital LOS, and hospital mortality in patients with a high EWS. Our findings stand in contrast to previous claims that the introduction of a digital vital signs charting system is associated with significant improvement in clinical outcomes. Future research should continue to investigate the mechanisms by which digital vital signs charting systems alter staff behaviors and improve patient outcomes.

Acknowledgments

The authors thank Soubera Yousefi, Samuel Wilson, Alan Dodge, David Vallance, Simon Kerr, Deolyn Makoni, and Giovanni Rizzo for transcribing information from paper observation charts during the study. This study was supported by the National Institute for Health and Care Research (NIHR) Biomedical Research Centre, Oxford. System for electronic notification and documentation (SEND) was developed and implemented with funding from the National Health Service England Safer Wards Safer Hospitals Fund. PJW is employed by the OUH Foundation National Health Service Trust. PJW, TB, and DC-W were supported by the National Institute for Health and Care Research Biomedical Research Centre, Oxford.

Data Availability

The data sets generated and analyzed during this study are not publicly available as they are recorded at the patient level, such that it might be possible to reidentify individuals. They are available from the corresponding author on reasonable request.

Authors' Contributions

TB, SG, DC-W, JB, and PJW have substantially contributed to the design of the study and the writing of this manuscript. Statistical analysis was undertaken by SG and JB. All authors read and approved the final manuscript. The funders have not been involved in the study design or reporting.

Conflicts of Interest

TB, DC-W, and PJW were part of the team that developed the system for electronic notification and documentation (SEND). Sensyne Health has since purchased the sole license for SEND. DC-W has previously undertaken consultancy for Sensyne Health. PJW was previously employed part-time and held shares in Sensyne Health. SG and JB declare that they have no competing interests.

EWS chart and escalation protocol.

Dates of steps.

System Usability Scale questionnaire adapted for SEND.

Power calculation.

Sensitivity analysis.

Secondary outcomes for the entire patient population (11,597 control and 46,450 intervention), including all those who did not score a CEWS≥3 within the first 48 h of admission.

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Abbreviations

Edited by A Mavragani; submitted 21.02.23; peer-reviewed by SB Ho, D Barra, C Subbe; comments to author 30.10.23; revised version received 17.11.23; accepted 08.04.24; published 20.06.24.

©David Chi-Wai Wong, Timothy Bonnici, Stephen Gerry, Jacqueline Birks, Peter J Watkinson. Originally published in the Journal of Medical Internet Research (https://www.jmir.org), 20.06.2024.

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