disadvantages of model predictive control

This in turn will call for more applications of advanced control strategies, especially MPC [74, 113]. The increase in model accuracy came at the cost of a non-linear optimization in the MPC. Int J Adv Manuf Technol 117, 13271349 (2021). The weight W is a trade-off between the amount and duration of a violation [101]. Piche et al. This sped up the required online computation by a factor of 65100 in [143]. [80, 96, 108]. This let MPC still implement the optimal trajectory as long as the additional constrained is fulfilled. Big Chemical Encyclopedia Advantages and Disadvantages of MPC Model predictive control offers a number of important advantages in comparison with conventional multiloop PID control . They showed that DMC outperformed classic cascaded PID control claiming that DMC has been applied to control problems at Shell Oil since 1974. They used a piecewise linear model to predict the future behavior of a catalytic cracking unit. [6, 8, 63, 80, 97, 147], or model switching, e.g. In simulation, the system enlarged the chatter-free region by 60%. Typical sample times were in the order of minutes to 1 h with prediction times usually smaller than 48 h [113]. Automatica 37(3):483, https://doi.org/10.1016/S0005-1098(00)00173-4, Mayne DQ (2014) Model predictive control: Recent developments and future promise. Automatica 14(5):413428, https://doi.org/10.1016/0005-1098(78)90001-8, Rouhani R, Mehra RK (1982) Model algorithmic control (mac); basic theoretical properties. A Lyapunov function is a continuously differentiable scalar function \(V\left (\boldsymbol {x} \right ):\mathbb {R}^{n} \rightarrow \mathbb {R}\) with \(V \left (\boldsymbol {0} \right ) =\boldsymbol {0}\). Its choice can be estimated using the system model by simulating all possible step changes in the manipulated variable(s). balancing the energy consumption over consumption and production peaks. The impressive demonstration paved the way for the popularity of MPC. The challenges and benefits of predictive modeling were the focus of one presentation during Business Insurance's 2012 Worker's Compensation Virtual Conference on Oct. 25. They manipulated the feed velocity in order to achieve a constant force in this highly dynamic process. [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. 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. The same way [50] applied Gaussian process modeling to elaborate confidence intervals on possible trajectories to guarantee safety. Aachen, Germany, Schwenzer M, Adams O, Klocke F, Stemmler S, Abel D (2017) Model-based predictive force control in milling: determination of reference trajectory. If one uses the commercial tools, i.e. J Manuf Sci Eng 140(061010), https://doi.org/10.1115/1.4038074, Dragicevic T (2018) Model predictive control of power converters for robust and fast pperation of AC microgrids. The last term includes the slack variables , which quantify the violation of output constraints. In this way, it approaches the ideal profile incrementally from cycle-to-cycle and may react to trends over multiple cycles. A novel ancillary controller for tube-based control of constrained nonlinear systems with additive disturbances that overcomes some disadvantages of a previous version and is relatively simple to implement is described and assessed; the addition of a terminal equality constraint to the nominal optimal control problem and its removal from the anc. 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 this way, measurement noiseor an inaccurate approximation of the solution space through the neural network (NN)did not affect the stability of the to-be-controlled system. However, the results suggested that for small buildings the main benefit came from an enhanced temperature measurement. We will discuss another non-geometric controller which is the Model Predictive Controller known as MPC. With regard to academia, the software MATLAB/Simulink from The Mathworks is very popular, e.g. MPC often served as a supervisory control of classic PID controllers forming a cascaded control loop. 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]. 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. The effectiveness of any feedback design is fundamentally limited by system dynamics and model accuracy. It is one of the few control methods that directly considers constraints. It must be tuned manually until the controller reflects the desired behavior. TL;DR: In this article, the advantages and limitations of tube-based model predictive control for dealing with uncertainty of various forms are discussed, firstly in the context of constrained linear systems, and an extension to deal with robustness against unstructured uncertainty is briefly described. Sun et al. Using a terminal set links the stability problem with the constraint satisfaction problem [17]ironically, additional constraints stabilize a constrained, non-linear MPC. A similar approach was pursued by [53] distinguishing different types of uncertainty: uncertainty in the gain, the time constant, and time delay. One major drawback of the strategy is that the continuity of the optimization for a receding horizon can no longer be ensured. The solution space scales exponentially with the problem size making look-up-table-approaches inefficient this is sometimes dubbed curse of dimensionality [102]. 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]. 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. 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. The different advantages and disadvantages of each method are summarized in Table 1. Since such models are available in many fields of engineering, the initial hurdle for applying control is deceased with MPC. Gunay et al. 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. [95]. the tracking error between the reference vector r and the model output y, Eq. We lay special attention on applications in order to demonstrate what is already possible today. It additionally considers the change in the manipulated variable uk = uk uk 1. One key characteristic of MPC is the implicit determination of the control law by solving the constrained optimization problem online. https://linkinghub.elsevier.com/retrieve/pii/S0306261918318518, Yin X, Jindal A, Sekar V, Sinopoli B (2015) A control-theoretic approach for dynamic adaptive video streaming over http. [18] motivated its use with the smoothing influence on the control outputs u. Also in Rosolia et al. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. How Does MPC Work? The charm of an approximation through machine learning is that the training can be flexibly stopped if a defined accuracy is reached. In this way the minimum length of the manipulation horizon Nu can be estimated by. The anticipating behavior and the fact that it can consider hard constraints makes the method so valuable for controlling real systems. [141] conducted a whole benchmark of different temperature control approaches on a small mock-up building in a thermal chamber. Already Qin and Badgwell [99] noted that NNs were popular to model unknown non-linear behavior for MPC. The top layer optimized the cost of the energy and the risk, which was determined through a Monte Carlo simulation and stochastic models. 1). The field has developed from the control of pure heating, ventilation and air conditioning (HVAC) systems to entire consumer-producer systems (or grids). 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). This review article should serve as such. 8.4 provides an overview of the predictive control model, Sect. The additional term heuristic stressed the missing explicit control law. The potential of MPC was not solely based on prediction but also on the fact that it can use non-linear modelsboth not supported by classic control. International Journal of Applied Mathematics and Computer Science 17(2):217232, https://doi.org/10.2478/v10006-007-0020-5. 4 is illustrated in Fig. However, the matrix formulation of the control problem restricts DMC to linear process models. a two-layer MPC [112, 126] running at different sample rates. [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. 2019 18th European Control Conference (ECC), Naples, Italy pp 33463352, https://doi.org/10.23919/ECC.2019.8795826, Djurdjanovic D, Mears L, Niaki FA, Haq AU, Li L (2018) State of the art review on process, system, and operations control in modern manufacturing. In a simulation study, they mimicked four weeks from midsummer to midwinter for the considered thermal-storage-tank system. https://linkinghub.elsevier.com/retrieve/pii/S2405896320325532, de Nicolao G, Magni L, Scattolini R (1996) On the robustness of receding-horizon control with terminal constraints. With the great advances in microprocessors and the omnipresent availability of models, this is more true than ever. Afram et al. Based on the working principle, they can be divided into the categories: classical controllers, predictive controllers, and repetitive controllers. IEEE Transactions on Systems, Man, and Cybernetics: Systems 46(6):740749, https://doi.org/10.1109/TSMC.2015.2465352, Linder A, Kennel R (2005) Model predictive control for electrical drives. With n =7 converter states the prediction horizon was limited to N2 =2 in order to achieve a sample time of Ts =100ms. IEEE Trans Control Sys Technol 20(3):796803, https://doi.org/10.1109/TCST.2011.2124461, Maciejowski JM (2002) Predictive control: with constraints. Moores law states that the number of transistors on a microprocessor doubles roughly every two years [132]. As an intermezzo hybrid MPC or explicit MPC approaches popped up [13]. Several approaches increase robustness at the cost of computation and optimality (e.g. 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. IEEE Trans Ind Electron 67(4):31163125, https://doi.org/10.1109/TIE.2019.2910034, Li L, You S, Yang C, Yan B, Song J, Chen Z (2016b) Driving-behavior-aware stochastic model predictive control for plug-in hybrid electric buses. The power consumption of a large stone mill was reduced by 66% using the commercial system from AspenTech. 2015 ACM Conf. Sci., Springer Berlin Heidelberg, https://books.google.de/books?id=KcxrCQAAQBAJ, Zou C, Hu X, Wei Z, Wik T, Egardt B (2018) Electrochemical estimation and control for lithium-ion battery health-aware fast charging. Automation applications with discrete states present mixed-integer optimization problems. These considerations reduce the problem of finding suitable prediction horizons to the problem of determining the necessary prediction horizon N2. Model-based predictive control (MPC) outperformed the other approachesincluding a commercial thermostat with a programmable scheduleand reduced the energy consumption by 43% compared to a constant temperature controller. In: 2020 First IEEE International Conference on Measurement, Instrumentation, Control and Automation (ICMICA), IEEE, Kurukshetra, India, pp 15, https://doi.org/10.1109/ICMICA48462.2020.9242772. For . The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. MPC uses a model of the system to make predictions about the system's future behavior. The cost function minimizes the deviation from the reference r over the prediction horizon N2. In: Proceedings of the Thirty-second Conference on neural information processing systems (NeurIPS-18), Montreal, QC, pp 38183827. PID controller). This, in turn, leads to increased working hours for irrigation pumps and higher electricity consumption. In 2003, [99] already counted over 4 600 industrial applications reviewing the available commercial software packages for MPC. http://www.mdpi.com/1996-1073/11/3/631, Shaltout ML, Alhneaish MM, Metwalli SM (2020) An Economic Model Predictive Control Approach for Wind Power Smoothing and Tower Load Mitigation. Automatica 29(5):12511274, https://doi.org/10.1016/0005-1098(93)90049-Y, Richalet J, Rault A, Testud JL, Papon J (1978) Model predictive heuristic control. 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. \end{array} $$, $$ \textbf{\textit{x}}_{lb} \leq \textbf{\textit{x}}(\cdot) \leq \textbf{\textit{x}}_{ub} \Rightarrow \textbf{\textit{x}} \in \mathbb{X}_{f}, $$, $$ \begin{array}{@{}rcl@{}} \min_{\textbf{\textit{u}},\boldsymbol{\xi}} & \lVert \textbf{\textit{r}}(\textbf{\textit{k}}+i\arrowvert \textbf{\textit{k}}) - \textbf{\textit{y}}(\textbf{\textit{k}}+i\arrowvert \textbf{\textit{k}}) \rVert_{\boldsymbol{W_{w}}} + \underbrace{\lVert \boldsymbol{\xi}(\textbf{\textit{k}}+i\arrowvert \textbf{\textit{k}})\rVert_{\boldsymbol{W_{\xi}}} }_{\text{softening}}, \end{array} $$, $$ \begin{array}{@{}rcl@{}} \text{s.t.} A sometimes ignored drawback of non-linear MPC is the larger computation of non-linear optimization. Model Predictive Control (MPC) is a control methodology which has been satisfactorily applied to solve complex control problems in the industry and also currently it is widely researched and adopted in the research community. Therefore, it is more an academic twitch than a practical option. \end{array} $$, $$ \begin{array}{@{}rcl@{}} \textbf{\textit{x}}(\textbf{\textit{k}}+i) &\forall i \in (0, \cdots, N_{2}) \Rightarrow \textbf{\textit{x}}(\cdot), \\ \textbf{\textit{u}}(\textbf{\textit{k}}+i) &\forall i \in (0, \cdots, N_{u}) \Rightarrow \textbf{\textit{u}}(\cdot), \\ \textbf{\textit{y}}(\textbf{\textit{k}}+i) &\forall i \in (N_{1}, \cdots, N_{2}) \Rightarrow \textbf{\textit{y}}(\cdot). This is mainly due to the lack of an explicit functional description of the control algorithm, which is required for most stability analysis [84]. 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 functionor to prove this to be the case respectively. MPC solves an online optimization algorithm to find the optimal . Such systems only touch MPC in general, because they lack of a receding horizon and effectively filter their optimal control recursively. This generally involves parameters of comparison between different possibilities of actions, such as minimization of error from the reference trajectory, minimization of jerk, obstacle avoidance, etc. FIR, SR and TF models are of historical interest and will be presented Int J of Robust and Nonlinear Control 9(15):11171141, https://doi.org/10.1002/(SICI)1099-1239(19991230)9:15<1117::AID-RNC447>3.0.CO;2-I, Gong Z, Wu X, Dai P, Zhu R (2019) Modulated model predictive control for mmc-based active front-end rectifiers under unbalanced grid conditions. Shaltout et al. In: 2019 IEEE Innovative Smart Grid Technologies - Asia (ISGT Asia), IEEE, Chengdu, China, pp 13871392, https://doi.org/10.1109/ISGT-Asia.2019.8881147, https://ieeexplore.ieee.org/document/8881147/, Tavakoli M, Shokridehaki F, Marzband M, Godina R, Pouresmaeil E (2018) A two stage hierarchical control approach for the optimal energy management in commercial building microgrids based on local wind power and pevs. Computational restrictions limit the MPC in general to a finite horizon. The contribution to a higher usability of the MPC was the main driver in this work. The proposed method employs several novel features including: a more general parameterization of the state and control tubes based on homothety and invariance; a more flexible form of the terminal constraint set; and a relaxation of the dynamics of the sets that define the state and control tubes. There are applications with further network types with distinct features, such as echo state networks to model time delay of buffer tanks, e.g. also in [36, 90, 91]. They controlled the filled-height of a conical shaped tank. Springer-Verlag GmbH. 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). In: 2019 Moratuwa Engineering Research Conference (MERCon), IEEE, Moratuwa, Sri Lanka, pp 366369, https://doi.org/10.1109/MERCon.2019.8818777, https://ieeexplore.ieee.org/document/8818777/, Michalska H, Mayne DQ (1993) Robust receding horizon control of constrained nonlinear systems. [116]. 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]. by Petri Nets as Cataldo et al. Analytical and empirical models were combined in non-linear multiple input multiple output (MIMO) systems with long prediction horizons. Predicting the N2 = Nu =5 next steps (Ts =0.5s), they controlled the penetration depth of the weld as a measure of quality. Agriculture accounts for approximately 70% of the world's freshwater consumption. The prediction horizon extends past the control horizon to predict the final CV outcomes but without MV movement. IFAC-PapersOnLine 53(2):1136211367, https://doi.org/10.1016/j.ifacol.2020.12.546. Today, the sampling times have largely decreased to the region of minutes and seconds [26], Table1. . They quantified the probability of a wrong approximation. [63] also explored successive linearization of a neural network (NN) in MPC but to control the temperature of a stirred reactora common application in process industry, e.g. Notes Control Inform. Visualization was performed by Max Schwenzer and Muzaffer Ay. We should first know the cost function. 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. on a conceptual basis [28]. https://linkinghub.elsevier.com/retrieve/pii/S2405896320308442, Magni L, Nicolao G, Magnani L, Scattolini R (2001) A stabilizing model-based predictive control algorithm for nonlinear systems. Therefore, it is common practice to constraint a terminal region instead of, e.g. Algorithms are compared. The idea was to consider both, the dynamics of the turbine and of the wind itself, in a linearized MPC. This essentially states that the optimal solution is not entirely trusted. 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 technique was developed for the process industry with their multiple input multiple output (MIMO) systems, distinctive delays, and long processing times [105]. In a subsequent work, [60] suggested to smooth the commands over cycles. PhD thesis RWTH Aachen University. 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]. There exists an extensive stability theory for linear MPCs. Since 2010, MPC has attracted notice to the community of building climate control. Targeting multiple objectives, some with non-technical motivation, they formulated a so-called economic MPC. Using the \(L_{\infty }\)-norm hinders the controller to make full use of the plant potential due to very conservative control actions [13]. Nevertheless, one has to be aware of the aforementioned drawback. In the late 1970s, [105] and [24] independently laid the foundation of MPC theory. 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]. They concluded that the lack of proper models is still the major obstacle towards an industrial application. The MPC maintained a given pressure on a varying area while moving over the surface. Cutler and Ramaker [24] used a piecewise-linear model to control the furnace of a catalytic cracking unit at Shell Oil. 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.

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