Model predictive control with linear models muske 1993. Based on a generated model of this system, we design a set of control input sequences iteratively at successive time steps over some horizon from a. In standard linear model predictive control, the plant is modeled as a discrete linear system 4. If n is large, the part of the problem for t n can be neglected. Rawlingsexistence and computation of infinite horizon model predictive control with active steadystate input constraints ieee transactions on automatic control, 48 6 2003, pp.
Stability 2 of mpc 1 consider the system where f is continuously differentiable with respect to itsis continuously differentiable with respect to its arguments and f0,00. Igcc power plant dispatch using infinitehorizon economic. The infinitehorizon cost is enforced using a terminal cost. Model predictive control mpc, also known as receding horizon control or moving horizon control, uses the range of control methods, making the use of an explicit dynamic plant model to predict the effect. Infinite horizon model predictive control for periodic tasks with contacts. The term model predictive control does not designate a specific control strategy but rather an ample range of control methods which make explicit use of a model of the process to obtain the control signal by minimizing an objective function. Nmpc is interpreted as an approximation of infinite horizon optimal control so that important properties like closedloop stability, inverse optimality and suboptimality can be derived in a uniform manner. This article discusses the existing linear model predictive control concepts in a unified theoretical framework based on a stabilizing, infinite horizon, linear quadratic regulator. Pdf an overview of model predictive control semantic scholar. Introduct ion vac controllers generally do not use information on electricity price changes 1. Receding horizon control introduces the essentials of a successful feedback strategy that has emerged in many industrial fields. The fundamental formulation of the linear model predictive controller is the following infinitedimensional convex quadratic program. Model predictive control receding horizon control implicitly defines the feedback law uk hxk analogy to chess playing my move the opponents move new state my move his move my move. Nonlinear model predictive control is a thorough and rigorous introduction to nmpc for discretetime and sampleddata systems.
Most papers on constrained infinite horizon mpc rely on the as. Works in practice, without formal analysis theory requires large infinite prediction horizon or. Model predictive control certaintyequivalent control constrained linearquadratic regulator in nite horizon model predictive control mpc with disturbance prediction. Model constraints stagewise cost terminal cost openloop optimal control problem openloop optimal solution is not robust must be coupled with online state model parameter update requires online solution for each updated problem analytical solution possible only in a few cases lq control.
The fundamental formulation of the linear model predictive controller is the following infinite dimensional convex quadratic program. There are various control design methods based on model predictive control concepts. The quasi infinite horizon approach to nonlinear model predictive control. Infinitehorizon model predictive control for periodic tasks with contacts. Igcc power plant dispatch using infinite horizon economic model predictive control benjamin p. Existence and computation of infinite horizon model predictive. As in linear mpc, nmpc requires the iterative solution of optimal control problems on a finite prediction horizon. Nmpc is interpreted as an approximation of infinitehorizon optimal control so. Three decades have passed since milestone publications by several industrialists spawned a flurry of research and industrial commercial activities on model predictive control mpc. An infinite horizon model predictive control for stable and integrating processes. This paper presents an infinitehorizon differentiable linear quadratic mpc that can be learned. In contrast to the standard, discretetime nitehorizon model.
Estimates on the prediction horizon length in model predictive control illustrate how this generalization can be employed in order to further tighten the estimates on the horizon length from 7. At each time step, a finite horizon forecast is made from a predictive model of the system and the optimal. Robust model predictive control nominal model of the plant. Extended infinite horizon mpc process model in the incremental form. Application of interiorpoint methods to model predictive control. Pdf the quasiinfinite horizon approach to nonlinear model. The infinitehorizon cost is enforced using a terminal. Mpc model predictive control also known as dmc dynamical matrix control gpc generalized predictive control rhc receding horizon control control algorithms based on numerically solving an optimization problem at each step constrained optimization typically qp or lp receding horizon control. Based on these results, a procedure for systematically determining a terminal region and a terminal penalty matrix off. Model predictive control control theory mathematical. Estimates on the prediction horizon length in model predictive control illustrate how this generalization can be employed in order to further tighten the estimates on the horizon length. A quasiinfinite horizon nonlinear model predictive control.
Model predictive control mpc, also known as receding horizon control or moving horizon control, uses the range of control methods, making the use of an explicit dynamic plant model to predict the effect of future reactions of the manipulated variables on the output and the control signal obtained by minimizing the cost function 7. Igcc power plant dispatch using infinitehorizon economic model predictive control benjamin p. Model predictive control mpc principles of modeling for cps fall 2018 madhur behl madhur. In section 2 mpc is introduced and the methodology proposed in 7, 9 is concisely summarized. Parametrized infinitehorizon model predictive control for. The infinite horizon cost is enforced using a terminal cost function obtained from the discretetime algebraic riccati equation dare, so that the learned controller can be. Implementation of a parametrized infinitehorizon model. This combination of an offline solution of the infinite horizon problem with an online mpc controller is known as infinite horizon model predictive control ihmpc, and has previously been applied only to simple stabilization objectives. Model predictive control is the family of controllers, makes the explicit use of model to obtain control signal. In practice, this is often intractable and therefore the prediction horizon is typically truncated leading to the standard finitehorizon mpc formulation, 1, where the. The reason for its popularity in industry and academia is its capability of operating without. Introduction model predictive control refers to a control strategy in which a model of.
Dual mode control infinite horizon terminal constraint set. Online optimization is possible because this class of problems is relatively easy to solve, but may. An introduction to modelbased predictive control mpc by stanislaw h. Pdf we present a method that combines offline trajectory optimization and online model predictive control mpc, generating robust. This control technique has been successfully applied to many different dynamic systems. Model predictive control mpc has received widespread interest in both industry and academia since the technique was first proposed in the late 1970s by several researchers including. Nonlinear model predictive control, or nmpc, is a variant of model predictive control mpc that is characterized by the use of nonlinear system models in the prediction. In model predictive control, the prediction horizon, p is also an important consideration.
Institute of robotics and cybernetics, faculty of electrical engineering and information technology. The understanding of mpc properties has reached to a new level and has now built a framework that is. The infinite horizon cost is enforced using a terminal cost function obtained from the discretetime algebraic riccati equation dare, so that the learned controller can be proven to be stabilizing in closedloop. Infinitehorizon differentiable model predictive control. Index termscontrol system synthesis, model predictive control, infinite horizon optimal control, thermal variables control, energy management, optimization, linear matrix inequalities.
As the name implies, the model predictive control strategy also known as the receding horizon control is control method which is based on the sound knowledge of a systems model characteristics. Model predictive control part i utsa college of engineering. Receding horizon control rhc has a number of advantages over other types of control. Receding horizon control model predictive control for. In particular, recursive feasibility and closedloop stability are shown. Pdf an overview of model predictive control semantic. The consequences of applying the parametric description to receding horizon control model predictive control are discussed. Institute of robotics and cybernetics, faculty of electrical engineering and information technology, slovak university of technology in bratislava, ilkovicova 3, 812 19 bratislava.
Predictive control, robust stability, infinite horizon. Infinitehorizon differentiable model predictive control deepai. Pdf an infinite horizon model predictive control for stable. This paper proposes a differentiable linear quadratic model predictive control mpc framework for safe imitation learning. Nonlinear model predictive control theory and algorithms. The quasiinfinite horizon approach to nonlinear model predictive control. Introduction to model predictive control springerlink. Chmielewski1 department of chemical and biological engineering, illinois institute of technology, chicago, il 60616 the integrated gasification combined cycle igcc possesses a number of. Works in practice, without formal analysis theory requires large infinite prediction horizon or terminal constraint additional tricks for a separate static optimization step integrating and unstable dynamics. Index termsmodel predictive control mpc, optimal control, steady state constraints. Infinitehorizon model predictive control for periodic tasks. Pdf the quasiinfinite horizon approach to nonlinear. The vector xj represents the current estimate of the state at discrete time j, whereas xk represents the state at k sampling steps along the future.
A quasiinfinite horizon nonlinear model predictive control scheme with. Model predictive control mpc is an advanced method of process control that is used to control a process while satisfying a set of constraints. The idea behind this approach can be explained using an example of driving a car. Nonlinear model predictive control technique for unmanned. Infinite horizon model predictive control robotics. Pdf infinitehorizon differentiable model predictive control. Chmielewski1 department of chemical and biological engineering, illinois institute of. Infinitehorizon model predictive control for periodic. An introduction to modelbased predictive control mpc. Jan 07, 2020 this paper proposes a differentiable linear quadratic model predictive control mpc framework for safe imitation learning.
A quasiinfinite horizon nonlinear model predictive. A quasiinfinite horizon nonlinear model predictive control scheme 1207 state feedback. Pdf an infinite horizon model predictive control for. The reason for its popularity in industry and academia is its capability of operating without expert intervention for long periods. If one chooses to hold the prediction horizon duration the product pt s constant, p must vary inversely with t s. Index terms control system synthesis, model predictive control, infinite horizon optimal control, thermal variables control, energy management, optimization, linear matrix inequalities. It has been in use in the process industries in chemical. Introduction model predictive control mpc is the most popular advanced control technique in the process industry. Energyplus building model usmall office building with 3 zones uchicago weather file during winter umodel predictive control. Model predictive control mpc originated in the late seventies and has developed considerably since then. Finally, we use this quadratic approximation as the terminal cost of an online mpc. Application of interiorpoint methods to model predictive. The consequences of applying the parametric description to receding horizon control model predictive control are.
Based on these results, a procedure for systematically determining a terminal region and a terminal penalty matrix offline is sum marized. Pdf infinitehorizon model predictive control for periodic tasks. This combination of an offline solution of the infinitehorizon problem with an online mpc controller is known as infinite. Parametrized infinitehorizon model predictive control for linear. Introduction model predictive control refers to a control strategy in which a model of the process is used to predict its future behaviour.
Allgower, a quasiinfinite horizon nonlinear model predictive control scheme with guaranteed stability, automatica, vol. The term model predictive control does not designate a specific control strategy but rather an. The infinite horizon cost is enforced using a terminal cost function. In section 4, asymptotic stability of the proposed nonlinear mpc scheme is discussed and. The infinitehorizon cost is enforced using a terminal cost function obtained from. Receding horizon control model predictive control for state. A quasiinfinite horizon nonlinear model predictive control scheme. Infinite horizon model predictive control with no terminal. Control engineering 1521 technical detail tuning of mpc feedback control performance is an issue.
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