Model predictive control (MPC) design and implementation using 3, e.g. AIChE Journal 45(10):21752187, https://doi.org/10.1002/aic.690451016, Li D, Xi Y, Lu J, Gao F (2016a) Synthesis of real-time-feedback-based 2d iterative learning controlmodel predictive control for constrained batch processes with unknown input nonlinearity. The wind speed as one major load on the mechanical structure was handled by incorporating wind speed predictions. The increase in model accuracy came at the cost of a non-linear optimization in the MPC. Robust model predictive control: advantages and disadvantages of tube 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. Power converters have only a finite number of discrete states n. This handicaps an optimization requiring heuristic approaches (mixed-integer optimization). Not until the mid 2000s, an opposite trend has taken shape in power electronics. Minerals Eng 64:9296, https://doi.org/10.1016/j.mineng.2014.03.029, Schmitt L, Keller M, Albin T, Abel D (2020) Real-time nonlinear model predictive control for the energy management of hybrid electric vehicles in a hierarchical framework*. 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]. [73]. The lower prediction horizon describes the time delay of the system. The number of applications in power electronics increased so rapidly that Vazquez et al. The paper provides a reasonably accessible and self-contained tutorial exposition on model predictive control (MPC). However, not all check stability. The PID controller is the best known controller with an outstanding importance and spread in industrial applications [4]. Process control in industries is becoming more critical due to demands on reducing consumed energy, reducing cost, and improving system efficiency and performance. 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. Garca et al. This shifts the task of computation to a non-time-critical offline calculation. IEEE Trans Ind Inform 9(2):808816, https://doi.org/10.1109/TII.2012.2223222, Steyn CW, Sandrock C (2013) Benefits of optimisation and model predictive control on a fully autogenous mill with variable speed. This work draws crisp lines in the following between those separated problems of MPC design. The impressive demonstration paved the way for the popularity of MPC. A specific type of multivariable control, model predictive control, has had a major impact on industrial practice, as discussed in Chapter 20. [1] used NNs to model the individual subsystem of an energy management system, such as ventilation, heat storage, or a heat pump. 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. Furthermore, long horizons may be torpedoed by stochastic disturbances such as the occupancy behavior. Yu et al. 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: \(\lVert \boldsymbol {x}\rVert ^{2}_{\boldsymbol {W}} = \boldsymbol {x}^{\intercal } \boldsymbol {W} \boldsymbol {x}\). (PDF) Robust Model Predictive Control: Advantages and Disadvantages of IFAC-PapersOnLine 52(13):630635, https://doi.org/10.1016/j.ifacol.2019.11.094, Wu Z, Rincon D, Christofides PD (2020) Process structure-based recurrent neural network modeling for model predictive control of nonlinear processes. Sun et al. This sped up the required online computation by a factor of 65100 in [143]. It lacks of flexibility regarding unexpected disturbances and of the opportunity to adjust the process model. In fact, the founders of MPC theory ([34] and [104]) stressed that classic control suits 90% of all control problems perfectly. 6, at the same time control intervals have shrunken and thus computation is still an issue. 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. as in [90]. 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]. https://ieeexplore.ieee.org/document/8672506/, Morari M (1994) Model predictive control: multivariable control technique of choice in the 1990s? Uncertainty intervals can often be assigned to model coefficients of an empirical transfer function. 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. The International Journal of Advanced Manufacturing Technology 104 (9-12):48034812, https://doi.org/10.1007/s00170-019-04335-4. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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]. 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). Forbes et al. In most cases, the potential benefit is not worth the effort of building up expert knowledge in modeling, optimization, and control theory. 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. To a certain degree, this may be taken into account by only the predictable dynamics of a closed-loop. 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. IEEE Trans Ind Electron 56(6):19061915, https://doi.org/10.1109/TIE.2008.2007032, Park JY, Nagy Z (2018) Comprehensive analysis of the relationship between thermal comfort and building control research - a data-driven literature review. 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 most significant effect have: the constraints (what is constrained and how it is: bound, inequality, or non-linear constraints), and. Hence, even in theory, perfect tracking of time-varying reference trajectories is not possible with feedback control aloneregardless of design methodology [58]. The main objective of this study is to develop and evaluate periodic model predictive control . 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]. A comprehensible example is that oscillating step responses would be allowed. [45] took this thought focusing on accurate learning of the solution space by the neural network (NN). Provided by the Springer Nature SharedIt content-sharing initiative, Review on model predictive control: an engineering perspective, The International Journal of Advanced Manufacturing Technology, $$ \begin{array}{@{}rcl@{}} \textbf{\textit{x}}(\textbf{\textit{k}}+1) &=& \boldsymbol{f}(\textbf{\textit{x}}(\textbf{\textit{k}}),\textbf{\textit{u}}(\textbf{\textit{k}})), \end{array} $$, $$ \begin{array}{@{}rcl@{}} \textbf{\textit{y}}(\textbf{\textit{k}}) &=& \boldsymbol{h}(\textbf{\textit{x}}(\textbf{\textit{k}})). what can MPC do in case of active suspension over other control techniques? https://www.tandfonline.com/doi/full/10.1080/00207179.2016.1222553, Guicheng W, Jinjin M, Min Z, Zhansheng Z, Jinna L (2013) Model predictive control for fermentation process. in the system model [10]. \end{array} $$, \(\lVert \boldsymbol {x}\rVert ^{2}_{\boldsymbol {W}} = \boldsymbol {x}^{\intercal } \boldsymbol {W} \boldsymbol {x}\), \(V\left (\boldsymbol {x} \right ):\mathbb {R}^{n} \rightarrow \mathbb {R}\), \(V \left (\boldsymbol {0} \right ) =\boldsymbol {0}\), $$ \begin{array}{@{}rcl@{}} V \left( \boldsymbol{x} \right) &> 0, \forall ~\boldsymbol{x} \neq \boldsymbol{0}, \end{array} $$, $$ \begin{array}{@{}rcl@{}} \dot{V} \left( \boldsymbol{x} \right) &\leq 0, \forall~ \boldsymbol{x} \neq \boldsymbol{0}. 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]. 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. AIChE Journal 65(6), https://doi.org/10.1002/aic.16615, https://onlinelibrary.wiley.com/doi/10.1002/aic.16615, Reiter M, Stemmler S, Hopmann C, Ressmann A, Abel D (2014) Model predictive control of cavity pressure in an injection moulding process. [69] implemented a MPC controller to the cooling system of their university building. Already Qin and Badgwell [99] noted that NNs were popular to model unknown non-linear behavior for MPC. [15] saw MPC as being ideal for electric motor control since there existed analytical linear models describing the motor behavior accurately. They even considered to identify the process model on-linealthough only for changes in the set points. Int J Machine Tools Manuf 91:5461, https://doi.org/10.1016/j.ijmachtools.2015.01.002, Zhang X, Bujarbaruah M, Borrelli F (2019) Safe and near-optimal policy learning for model predictive control using primal-dual neural networks. 8.4 provides an overview of the predictive control model, Sect. 4 is illustrated in Fig. 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]. [43] claimed that shorter sample time favors temperature control (Ts,short =10min compared to Ts,long =1h, both N2 =6) since the model accuracy usually deteriorates with the predicted time. - Model Predictive Control Toolbox: http://bit.ly/2xgwWvN- What Is Model Predictive Control. Journal of Building Engineering 33:101692, https://doi.org/10.1016/j.jobe.2020.101692, https://linkinghub.elsevier.com/retrieve/pii/S2352710220310627, Mayne D, Rawlings J (2001) Correction to constrained model predictive control: stability and optimality. When MPC was new, several widely noticed review paper have been published on both, theory [13, 44, 77, 85] and applications [99]. 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. Apart from these main movements, the range of applications in engineering is immense. The tremendous success of machine learning techniques and the increasing parallelization in software were paved by the replacement of CPUs for GPU chips. Model-based predictive control (MPC) can manage this naively, e.g. Special Interest Group on Data Com. Furthermore, signal noise is an important topic for robustness [13]. IFAC-PapersOnLine 52(13):17791784, https://doi.org/10.1016/j.ifacol.2019.11.459, Ji J, Khajepour A, Melek WW, Huang Y (2017) Path planning and tracking for vehicle collision avoidance based on model predictive control with multiconstraints. The prediction horizon extends past the control horizon to predict the final CV outcomes but without MV movement. This is why MPC is also referred to as receding horizon control. https://ieeexplore.ieee.org/document/8792151/, Yu N, Salakij S, Chavez R, Paolucci S, Sen M, Antsaklis P (2017) Model-based predictive control for building energy management: Part ii experimental validations. 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. Also in Rosolia et al. The MPC used a linearized oscillation model assuming that mass, damping, and stiffness were given. 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. Garcia and Morari [34] pointed out early that optimal control improves the control behavior but complicates robustness examination. 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 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. In: 2018 International Joint Conference on Neural Networks (IJCNN), IEEE, Rio de Janeiro, pp 18, https://doi.org/10.1109/IJCNN.2018.8489446, https://ieeexplore.ieee.org/document/8489446/, Barisa T, Iles S, Sumina D, Matusko J (2018) Model predictive direct current control of a permanent magnet synchronous generator based on flexible Lyapunov function Ccnsidering converter dead time. Accuracy definition. If the combination that has the longest effect on the control variable is known, it is sufficient to simulate this. IEEE Trans Control Sys Technol 20(3):796803, https://doi.org/10.1109/TCST.2011.2124461, Maciejowski JM (2002) Predictive control: with constraints. Using a terminal set links the stability problem with the constraint satisfaction problem [17]ironically, additional constraints stabilize a constrained, non-linear MPC. Again, Table2 provides a condensed overview of the works on the application of MPC in power electronics. Robust Model Predictive Control: Advantages and Disadvantages of Tube The combination of prediction and optimization is the main difference from conventional control approaches, which use precomputed control laws [77]. The hurdle to overcome for a lasting impact of MPC on industry is the complexity of modeling and algorithmic tuning. Machine learning enables an easy description of complex systems lowering the hurdle of applying MPC to new processes. [141] conducted a whole benchmark of different temperature control approaches on a small mock-up building in a thermal chamber. They considered them all simultaneously. With the millennium and computers becoming more and more powerful, research shifted towards application. Later, a black box model (support vector regression (SVR)) was added to consider non-linearities of machining centers [7, 8]. http://link.springer.com/10.1007/s00170-020-05719-7, Mariano-Hernndez D, Hernndez-Callejo L, Zorita-Lamadrid A, Duque-Prez O, Santos Garca F (2021) A review of strategies for building energy management system: Model predictive control, demand side management, optimization, and fault detect & diagnosis. a vector (lowercase characters) or a matrix (uppercase characters). repeatedly solving an optimization problem online, without talking about its computational effort. 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. in climate control systems (precisely heating, ventilation and air conditioning (HVAC)) They deal with sluggish systems and comparably precise forecasting models, e.g. https://ieeexplore.ieee.org/document/8865797/, Li Z, Deng J, Lu R, Xu Y, Bai J, Su CY (2016c) Trajectory-tracking control of mobile robot systems incorporating neural-dynamic optimized model predictive approach. http://resolver.caltech.edu/CaltechCDSTR:1993.024, Morari M, Lee JH (1999) Model predictive control: past, present and future. In its most basic formulation, stability is the property of a system that a bounded input results in a bounded output: the BIBO stability. Advantages and applications of model predictive control With the upcoming digital controllers, they were able to efficiently control complex problems demonstrating a massive economic potential. Autonomous racing using Linear Parameter Varying-Model Predictive 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. Classical controllers, such as PID controllers, bang-bang controllers, or state controllers, only consider past and current system behavior (i.e. Prentice Hall, Harlow, Maddalena E, da S Moraes C, Waltrich G, Jones C (2020) A neural network architecture to learn explicit MPC controllers from data. Schmitt et al. Function principle of a model-based predictive with horizons N1, N2, Nu (in accordance to [105]). Mehta and Mears [79] described a concept for controlling the deflection of slender bars in turning. 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. Few applications use non-linear MPC meeting the fact that often the available models are non-linear. The sampling times are quite low with rather large prediction horizons compared to the early works on power electronics. 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. The approaches demonstrated the control of system variables that were hard to impossible to control without MPC. a zero terminal constraint \(\lVert \textit {\textbf {x}}(\textit {\textbf {k}}+N_{2})\rVert =0\). One or multiple of the authors contributed to, in total, 14 cited works in this review. More recently, MPC has been extended to nonlinear model predictive control (NMPC) in order to realize high-performance control of highly nonlinear processes. This is 9% of all discussed papers. IFAC-PapersOnLine 50(1):1587115876, https://doi.org/10.1016/j.ifacol.2017.08.2336, Stemmler S, Ay M, Vukovic M, Abel D, Heinisch J, Hopmann C (2019) Cross-phase model-based predictive cavity pressure control in injection molding. &\textbf{\textit{u}}_{lb}\leqslant \textbf{\textit{u}}(\textbf{\textit{k}}+j\arrowvert \textbf{\textit{k}}) \leqslant \textbf{\textit{u}}_{ub},\\ &\textbf{\textit{y}}_{lb}-\boldsymbol{\xi}(\textbf{\textit{k}}+~i\arrowvert \textbf{\textit{k}})\leqslant \textbf{\textit{y}}(\textbf{\textit{k}}+i\arrowvert \textbf{\textit{k}}) \leqslant \textbf{\textit{y}}_{ub}+\boldsymbol{\xi}(\textbf{\textit{k}}+i\arrowvert \textbf{\textit{k}}),\\ &\text{where} \quad\boldsymbol{\xi}\geqslant 0,\\ & \forall i \in \{N_{1}, \cdots, N_{2}\} \quad \text{and}\quad j \in \{0, \cdots, N_{u}\}. A sometimes ignored drawback of non-linear MPC is the larger computation of non-linear optimization. Nonetheless, the connection of distributed generation resources to distribution networks has created new challenges in the control, operation, and management of network reliability. In particular with the popularity of machine learning model, non-linear MPC applications increase. 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. Automatica 37(9):13511362, https://doi.org/10.1016/S0005-1098(01)00083-8, Margolis BWL, Farouki RT (2020) Inverse dynamics toolpath compensation for CNC machines based on model predictive control. Appl. The main idea is as simple as it is charming, making use of the previous solution. 2021. We introduce the concepts, provide a framework in which the critical issues can be expressed and analyzed, and point out how . IEEE Control Sys 20(3):5362, https://doi.org/10.1109/37.845038, Prasad GM, Kedia V, Rao AS (2020) Multi-model predictive control (MMPC) for non-linear systems with time delay: an experimental investigation. In particular, robotics is an emerging field of applications of MPC, e.g. IEEE Trans Control Sys Technol 19(3):556566, https://doi.org/10.1109/TCST.2010.2049203, Li S, Jiang P, Han K (2019) RBF neural network based model predictive control algorithm and its application to a CSTR process. 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]. Journal of Dynamic Systems, Measurement, and Control 142(6):061005, https://doi.org/10.1115/1.4046278. https://linkinghub.elsevier.com/retrieve/pii/S095915241930825X, Xie S, Hu X, Xin Z, Brighton J (2019) Pontryagins Minimum Principle based model predictive control of energy management for a plug-in hybrid electric bus. The weight W is a trade-off between the amount and duration of a violation [101]. 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. IFAC Proc Vol 44(1):1451314518, https://doi.org/10.3182/20110828-6-IT-1002.00579, Stephens MA, Manzie C, Good MC (2013) Model predictive control for reference tracking on an industrial machine tool servo drive. Open Access funding enabled and organized by Projekt DEAL. 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]. However, not using constraints loses much of the charm of MPC. PubMedGoogle Scholar. 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. Comp & Chem Eng 30(1012):14261435, https://doi.org/10.1016/j.compchemeng.2006.05.044, Garcia CE, Morari M (1982) Internal model control. The focus lies on practical considerations of feasibility, stability, and robustness together with representative applications. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. [20] did with a palette transportation and processing system.
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