Model predictive control for maxminplusscaling systems ef. This paper gives an overview of robustness in model predictive control. Multicentric, randomized, controlled trial to evaluate. A set invariance condition for discretetime lpv systems with input saturation is identified and the invariant set is determined by solving an lmi optimisation problem, which directly incorporates input saturation. In recent years, much e ort has been spent to incorporate the robustness problem into this framework. Minmax model predictive control for uncertain maxmin. Bemporad, a decomposition algorithm for feedback minmax model predictive control, in proc. We first design a robust model predictive controller that allows for an explicit characterization of the set of initial conditions starting from where feasibility of the optimization problem and closedloop stability is guaranteed. This type of controller has been shown to be a continuous piecewise affine function of the state vector by geometrical methods.
Model predictive control for maxminplusscaling systems. A model based predictive control mbpc algorithm is described by using a model to compute the predicted process outputs. The control schemes the authors discuss introduce, in the control optimization, the notion that feedback is present in the recedinghorizon implementation of the control. Nonlinear outputfeedback model predictive control with moving horizon estimation. A chanceconstrained stochastic model predictive control.
To achieve control objective 10, we use minmax model predictive control proposed in 16. Feedback minmax mpc obtains a sequence of feedback control laws that minimizes the worst case cost, while assuring robust constraint handling. An algorithm for solving feedback minmax model predictive control for discrete time uncertain linear systems with constraints is presented in the paper. A minmax feedback model predictive control approach using disturbance feedback policies is also presented, which leads to improved performance compared to the openloop approach. Figure 1 depicts the basic principle of model predictive control. Minmax robust mpc was first proposed by campo and morari 1987. Minmax model predictive control of nonlinear systems using.
Recent developments in modelpredictive control promise remarkable opportunities for designing multiinput, multioutput control systems and improving the control of singleinput, singleoutput systems. Course on model predictive control part iii stability and robustness gabriele pannocchia department of chemical engineering, university of pisa, italy email. Feedback minmax model predictive control based on a. These properties however can be satisfied only if the underlying model used for prediction of. Introduction uncertainty demands that the optimal control problem employed in model predictive control should have a feedback control policy rather than an openloop control sequence as a deci. Control as a service caas proceedings of the second. Pdf feedback minmax model predictive control based on a. This paper is the 1st stage for the development of the bmi based wheelchair in practical use. Feedback minmax model predictive control using a single linear. The approach is based on the representation of the evolution of the uncertainty by a scenario tree.
Most importantly, mpc provides the flexibility to act while optimizingwhich is essential to the solution of many engineering problems in complex plants, where exact modeling is impossible the superiority of mpc is in its numerical solution. This work considers the problem of stabilization of nonlinear systems subject to constraints, uncertainty and faults in the control actuator. A few things i learned about process control and more. Explicit approximate approach to feedback minmax model. Fossstate output feedback nonlinear model predictive control.
Different from the stateoftheart robust model predictive control rmpc algorithm, the proposed is less conservative. Part of the lecture notes in control and information sciences book series lncis, volume 384. The proposed robust predictive controller uses a semifeedback formulation and the. Themain contribution is an algorithm for solving the minmax quadratic. Robust model predictive control design for faulttolerant. The basic idea in mpc is to repeatedly solve optimization problems online to nd an optimal input to the controlled system. Three decades have passed since milestone publications by several industrialists spawned a flurry of research and industrial commercial activities on model predictive control mpc. In this paper, robust mpc model predictive control with adaptive da converter method for the wheelchair using eeg electroencephalogram based bmi brain machine interface is discussed. Outputfeedback stochastic model predictive control for. This volume provides a definitive survey of the latest model predictive control methods available to engineers and scientists today. It leads to nonconservative robust control of the plant because it.
This thesis presents multistage nonlinear model predictive control multistage nmpc as a promising nonconservative robust nmpc control scheme, which is applicable in realtime. Minmax model predictive control mpc is one of the few techniques suitable for. On robustness of suboptimal minmax model predictive control defeng he, haibo ji, tao zheng. Abstractan algorithm for solving feedback minmax model predictive control for discrete time uncertain linear systems with constraints is presented in the paper. Robustly stable feedback minmax model predictive control conference paper in proceedings of the american control conference 4. This strategy consists of a modified quasiminmax outputfeedback mpc method. Model predictive control for nonlinear systems nmpc has received considerable attention over the past years. The main motivation behind explicit nmpc is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real. Minmax mpc algorithm for lpv systems subject to input. Model predictive control free ebook download as pdf file. On robustness of suboptimal minmax model predictive control.
Discontinuous feedback strategies are allowed in the solution of the minmax. He has written three books and authored or coauthored more than 150 technical papers in international journals and conference proceedings. This paper proposes a robust output feedback model predictive control mpc scheme for linear parameter varying lpv systems based on a quasiminmax algorithm. May 22, 2017 in the research field of model predictive control mpc, an output feedback type mpc method is consistently required for controlling a wide range of constrained systems. In this paper, we develop two algorithms for stochastic model predictive control smpc problems with discrete linear systems. In recent years it has also been used in power system balancing models and in power electronics. Minmax tubebasedrobustmpc 5 output feedback mpc stabilityanalysis o. Robust model predictive control, nonlinear model predictive control, discretetime systems, tubes, uncertain systems. The method is developed to apply to the obstacle avoidance system of wheelchair. With this proposal, the selection of voltage vectors does not need weighting factors that are normally used within the. Feedback minmax model predictive control based on a quadratic cost function d. The minmax operator is explored for the first time as an alternative to the traditional loss function. Index termsfeedback, minmax optimization, model predictive con trol.
Patients were randomized to either blood glucose management target range 80110 mgdl 4. Then, minmax feedback model predictive control using disturbance feedback policies is presented, which leads to improved performance compared to the openloop approach. Model predictive control optimal control mathematical. The implementation of minmax model predictive control for constrained linear systems with bounded additive uncertainties and quadratic cost functions is dealt with. Relying on measurements obtained at time tlet us assume, at. Feedback min max mpc obtains a sequence of feedback control laws that minimizes the worst case cost, while assuring robust constraint handling. Quasiminmax outputfeedback model predictive control for. Model predictive control receding horizon control implicitly defines the feedback law uk hxk analogy to chess playing my move. Minmax predictive control of a fivephase induction machine. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closedloop stability and performance.
Robust nonlinear receding horizon control with constraint. The basic principle of model predictive control model predictive control is formulated as a repeated solution of a finite horizon openloop optimal control problem subject to system dynamics and input and state constraints. Also, a cost function related to the closed loop performance of the system is defined, and the control signal is obtained by. Recent developments in model predictive control promise remarkable opportunities for designing multiinput, multioutput control systems and improving the control of singleinput, singleoutput systems. Minmax mpc using a tractable qp problem sciencedirect. Camacho abstract feedback minmax model predictive control based on a quadraticcost functionisaddressedin thispaper.
Nonlinear model predictive control nmpc has become the accepted methodology to solve complex control problems related to process industries. Minmax model predictive control of nonlinear systems using discontinuous feedbacks. Hence, the minmax model predictive control problem for mmps systems can be solved ef. Multicentric, randomized, controlled trial to evaluate blood. Minmax model predictive control of nonlinear systems. In an earlier paper, huang and riggs 2002a, b reported their work in incorporating proportionalintegral pi and mpc for controlling the level of a distillation column c3.
Model predictive control provides high performance and safety in the form of constraint satisfaction. Explicit nonlinear model predictive control theory and. Minmax model predictive control for uncertain maxminplus. Robustly stable feedback minmax model predictive control. Most importantly, mpc provides the flexibility to act while optimizing which is essential to the solution of many engineering problems in complex plants, where exact modeling is impossible.
Fontes and lalo magni abstract this paper proposes a model predictive control mpc algorithm for the solution of a robust control problem for continuoustime systems. It requires the solution of a very high dimensional problem that. Minmax feedback model predictive control for constrained linear. Ieee transactions on automatic control, 43 8 1998, pp. Discontinuous feedback strategies are allowed in the solution of the min max. Epidemiological studies have revealed a significant relationship between impaired glycemic control and poor outcome in patients with acute cardiovascular events, postoperative wound infections 4, 5, and trauma. In the research field of model predictive control mpc, an outputfeedbacktype mpc method is consistently required for controlling a wide range of constrained systems. However, most robust mpc schemes can be classified into two categories 33.
Min max mpc schemes can be classi ed in open loop and feedback min max controllers see mayne et al. Mayneminmax feedback model predictive control for constrained linear systems ieee transactions on automatic control, 43 8 1998, pp. In this paper, a new model predictive control mpc algorithm is developed for polytopic linear parametervarying lpv systems subject to input saturation. Different from the stateoftheart robust model predictive. The algorithm solves the corresponding multistage minmax linear optimization problem. Morari, robust model predictive control, proceedings of 1987 american control conference, minneapolis, 1012 june 1987, pp. This volume provides a definitive survey of the latest modelpredictive control methods available to engineers and scientists today. Course on model predictive control part iii stability and robustness. A decomposition algorithm for feedback minmax model predictive control d. This book was set in lucida using latex, and printed and bound by. Nonlinear predictive control of spacecraft journal of. Course on model predictive control part iii stability. However, no algorithm for computing the explicit solution has been given.
Nonlinear outputfeedback model predictive control with. Minmax mpc algorithm for lpv systems subject to input saturation. The first decade is characterized by the fastgrowing industrial adoption of the. On the other hand, the use of a nonlinear model implies higher di culties in the calculation of the control law and in the stability analysis of the obtained closedloop system. Outputfeedback stochastic model predictive control for glideslope tracking during aircraft carrier landing. Model predictive control mpc is a control methodology that is. Participially, chance constraints on the state and control are considered. The min max operator is explored for the first time as an alternative to the traditional loss function. Feedback minmax model predictive control based on a quadratic cost function conference paper pdf available in proceedings of the american control conference 2006. Suboptimal model predictive control feasibility implies. Pdf min max model predictive control for polysolenoid. Minmax model predictive control of nonlinear systems using discontinuous feedbacks fernando a. In this paper, we propose a twostage control strategy for polytopic linear parameter varying lpv systems subject to input constraints. Modern predictive control 1st edition ding baocang.
The algorithm solves the corresponding multistage min. The parameters of the model are obtained through an identification algorithm. Min, max selectors if then logics sequence logics other elements regulation constraint handling local optimization ad hoc strategies, heuristics inconsistent performance complex control structure not robust to changes and failures focus on the performance of a local unit model is not explicitly used inside the. Model predictive control college of engineering uc santa barbara. This strategy consists of a modified quasi min max output feedback mpc method and a. A decomposition algorithm for feedback minmax model. Min, max selectors if then logics sequence logics other elements regulation. Application of a model based predictive control algorithm. It has been in use in the process industries in chemical plant s and oil refineries since the 1980s. In this paper, a fuzzylogic based operator is used instead of a traditional cost function for the predictive stator current control of a fivephase induction machine im. It has been in use in the process industries in chemical plants and oil refineries since the 1980s.
Pdf a decomposition algorithm for feedback minmax model. Pdf minmax approaches to robust model predictive control. Minmax feedback model predictive control for constrained linear systems. Modern predictive control explains how mpc differs from other control methods in its implementation of a control action. Course on model predictive control part iii stability and. Robust multistage nonlinear model predictive control. Application to the control of a bioprocess 24 october 2019 international journal of robust and nonlinear control, vol. Minmax mpc schemes can be classi ed in open loop and feedback minmax controllers see mayne et al. Camacho minmax mpc 7 why minmax model predictive control. This approach involves an offline design of a robust state observer for lpv systems using linear matrix inequality lmi and an online robust output feedback mpc algorithm using. Minmax feedback model predictive control for constrained. Mayneminmax feedback model predictive control for constrained linear systems. Model predictive control mpc is an advanced method of process control that is used to control a process while satisfying a set of constraints.
Camacho abstractfeedback minmax model predictive control based on a quadraticcost functionisaddressedin thispaper. Tubebased robust nonlinear model predictive control. Then, minmax feedback model predictive control using disturbance feedback policies is presented. In dem jungst erschienenen handbook of model predictive control 26. A decomposition algorithm for feedback minmax model predictive control article pdf available in ieee transactions on automatic control 5110. A minmax control framework, based on alternate minimisation. In in position controller, we consider a d ual mode co ntrol law. Minmax feedback formulations of model predictive control are discussed, both in the fixed and variable horizon contexts. Min max model predictive control of nonlinear systems using discontinuous feedbacks fernando a. Output feedback model predictive control for lpv systems. Introduction an important class of discrete event systems is the class. Introduction onlinear model predictive control nmpc involves the solution at each sampling instant of a finite horizon optimal control problem subject to nonlinear system dynamics and state and input constraints.
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