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Efficient suboptimal parametric solutions to predictive control for PLC applications

CONTROL ENGINEERING PRACTICE 2011年第7期19卷 732-743页

作者： Valencia-Palomo, G. Rossiter, J. A. Inst Tecnol Hermosillo Mexico City 83170 DF Mexico Univ Sheffield Dept Automat Control & Syst Engn Sheffield S1 3JD S Yorkshire England

The prime aim of this paper is to embed a predictive control (MPC) algorithm with constraint handling capabilities into a programmable logic controller (PLC). In order to achieve it, this paper develops parametric approaches to MPC but differs from more conventional approaches in that it predefines the complexity of the solution rather than the allowable suboptimality. The paper proposes a novel parameterisation of the parametric regions which allows efficiency of definition, effective spanning of the feasible region and also highly efficient search algorithms. Despite the suboptimality, the algorithm retains guaranteed stability, in the nominal case. A laboratory test was carried out to demonstrate the code on real hardware and the effectiveness of the solution. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Predictive control multi-parametric quadratic programming PLC

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Improving Reliability of Partition Computation in Explicit MPC with MPT Toolbox

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IFAC Proceedings Volumes 2011年第1期44卷 9260-9265页

作者： Samo Gerkšič Dept. of Systems and Control Jozef Stefan Institute Jamova 39 Ljubljana Slovenia

Abstract The paper addresses the problem of numerical issues and degeneracies in the parametric quadratic programming (pQP) algorithm, used for computing partitions of explicit model predictive controllers (eMPC) with the multi-parametric Toolbox (MPT). We summarise the pQP problem setup and the basic algorithm, analyse its implementation in MPT, expose the numerical issues and suggest a series of improvements for more reliable operation, which are relevant also for other pQP solvers.

关键词： explicit predictive control multi-parametric quadratic programming numerical methods

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Explicit Model Predictive Control of Networked Control Systems with Time-Delay

Explicit Model Predictive Control of Networked Control Syste...

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23rd Chinese Control and Decision Conference

作者： Zhang Ju Zhang Haihua Zhejiang Univ Technol Coll Informat Engn Hangzhou 310032 Zhejiang Peoples R China

ISBN: (纸本)9781424487363

In order to deal with random communication time delay in Networked Control Systems(NCS), an explicit model predictive control (eMPC) method is presented in this paper. The algorithm is based on multi-parametric quadratic programming to get a state feedback control law which is explicit to the states. And based on this control law, the piecewise affine model of the closed-loop model predictive control system is established. We show that the control law is piecewise linear and continuous for the finite horizon problem. Thus, the on-line control computation reduces to the simple evaluation of a piecewise affine model. Since the algorithm does not require repeated online optimization, it improves the on-line calculation speed of the controller, making the system better in real-time. The algorithm deals with the random communication time delay well. Simulation results show the effectiveness of the proposed method.

关键词： networked control system explicit model predictive control multi-parametric quadratic programming piecewise affine model

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Stabilizing model predictive control scheme for piecewise affine systems with maximal positively invariant terminal set

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Journal of Systems Engineering and Electronics 2010年第6期21卷 1090-1094页

作者： Fu Chen Guangzhou Zhao Xiaoming Yu College of System Science and Engineering Zhejiang University Hangzhou 310027 P. R. China Key Laboratory of Tobacco Processing Technology Zhengzhou Tobacco Research Institute of CNTC Zhengzhou 450001 P. R. China

An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control （CFTOC） problem for discrete-time piecewise affine （PWA） systems with a quadratic performance index. The maximal positively invariant terminal set, which is feasible and invariant with respect to a feedback control law, is computed as terminal target set and an associated Lyapunov function is chosen as terminal cost. The combination of these two components guarantees constraint satisfaction and closed-loop stability for all time. The proposed algorithm combines a dynamic programming strategy with a multi-parametric quadratic programming solver and basic polyhedral manipulation. A numerical example shows that a larger stabilizable set of states can be obtained by the proposed algorithm than precious work.

关键词： constrained optimal predictive control multi-parametric quadratic programming dynamic programming receding horizon control positively invariant set.

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Using Laguerre functions to improve efficiency of multi-parametric predictive control

Using Laguerre functions to improve efficiency of multi-para...

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American Control Conference

作者： G. Valencia-Palomo J.A. Rossiter Department of Automatic Control and Systems Eng. University of Sheffield South Yorkshire UK. S1 3JD

ISBN: (纸本)9781424474264

multi-parametric quadratic programming (mp-QP) is an alternative means of implementing conventional predictive control algorithms whereby one transfers much of the computational load to offline calculations. However, coding and implementation of this solution may be more burdensome than simply solving the original QP. This paper shows how Laguerre functions can be used in conjunction with mp-QP to achieve a large decrease in both the online computations and data storage requirements while increasing the feasible region of the optimization problem. Extensive simulation results are given to back this claim.

关键词： Predictive control multi-parametric quadratic programming Laguerre functions Laguerre functions Predictive control Feasible region lift efficiency

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Guaranteed Cost Control For Constrained Takagi-Sugeno Fuzzy Systems

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IFAC Proceedings Volumes 2009年第19期42卷 325-330页

作者： Carlos Ariño Emilio Pérez Antonio Sala Department of Industrial Systems Engineering and Design Universitat Jaume I Avenida Vicent Sos Baynat s/n. 12071 Castelló de la Plana Spain Dept. of Systems Engineering & Control at the Technical University of Valencia E-46022 Valencia Spain

Abstract This paper presents a novel control design technique in order to obtain a Guaranteed Cost Fuzzy Controller subject to constraints on the input channel. This Guaranteed cost control law is obtained via multi-parametric quadratic programming. The result is a piecewise fuzzy control law where the state partition is defined by fuzzy inequalities. The parameters of the Lyapunov function can be obtained previously using linear matrix inequalities optimization.

关键词： Takagi-Sugeno fuzzy control LMI quadratic stability parallel distributed compensation piecewise control multi-parametric quadratic programming Constrained Control

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Explicit model predictive control of gas-liquid separation plant via orthogonal search tree partitioning

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COMPUTERS & CHEMICAL ENGINEERING 2004年第12期28卷 2481-2491页

作者： Grancharova, A Johansen, TA Kocijan, J Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway Jozef Stefan Inst Dept Syst & Control Ljubljana 1000 Slovenia Nova Garcia Polytech Nova Garcia 5000 Slovenia

Solutions to constrained linear model predictive control (MPC) problems can be pre-computed off-line in an explicit form as a piecewise linear (PWL) state feedback defined on a polyhedral partition of the state space. This admits implementation at high sampling frequencies in real-time systems with high reliability and low software complexity. Recently, algorithms that determine an approximate explicit PWL state feedback solution by imposing an orthogonal search tree structure on the partition, have been developed, and it has been shown that they may offer computational advantages. This paper considers the application of an approximate approach to the design of an explicit model predictive controller for a two-input two-output laboratory gas-liquid separation plant, including experimental evaluation. The approximate explicit MPC controller achieves performance close to that of the conventional MPC, but requires only a fraction of the real-time computational machinery, thus leading to fast and reliable computations. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： constrained linear model predictive control multi-parametric quadratic programming gas-liquid separator

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Explicit approaches to constrained model predictive control: A survey

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MODELING IDENTIFICATION AND CONTROL 2004年第3期25卷 131-157页

作者： Grancharova, A Johansen, TA Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway Bulgarian Acad Sci Inst Control & Syst Res BU-1113 Sofia Bulgaria

This paper presents a review of the explicit approaches to constrained model predictive control. The main motivation behind the explicit solution is that it avoids the need for real-time optimization, and thus allows implementation at high sampling frequencies in real-time systems with high reliability and low software complexity. The paper is organized as follows. Section I includes formulation of the constrained linear quadratic regulation (LQR) problem, summary of the implicit approaches, and the basics of the model predictive control (MPC). Sections 2 and 3 consider respectively the exact and the approximate approaches to explicit solution of constrained MPC problems, together with several examples.

关键词： model predictive control constraints multi-parametric quadratic programming piecewise linear controllers

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A reference governor in a piecewise state affine function: The implementation and validation

A reference governor in a piecewise state affine function: T...

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SICE 2003 Annual Conference

作者： Kogiso, K Hirata, K Osaka Univ Suita Osaka 5650871 Japan

ISBN: (纸本)0780383524

This paper proposes a reference management technique of an original reference for closed-loop systems with state and control constraints. The management rule is represented in the form of a piecewise state affine function obtained from an explicit solution to a multi-parametric quadratic programming problem which explicitly considers not only a constraint fulfillment but also a tracking performance. Furthermore, effectiveness of the proposed approach is shown by simulation. It is more important to also perform the experimental evaluation to demonstrate its effectiveness using a, real position servomechanism.

关键词： reference governor systems with state and control constraint multi-parametric quadratic programming tracking control

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On-line optimization via off-line parametric optimization tools

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COMPUTERS & CHEMICAL ENGINEERING 2002年第2期26卷 175-185页

作者： Pistikopoulos, EN Dua, V Bozinis, NA Bemporad, A Morari, M Univ London Imperial Coll Sci & Technol Ctr Process Syst Engn Dept Chem Engn London SW7 2BY England ETH Zentrum Automat Control Lab CH-8092 Zurich Switzerland

In this paper, model predictive control (MPC) based optimization problems with a quadratic performance criterion and linear constraints are formulated as multi-parametric quadratic programs (mp-QP), where the input and state variables, corresponding to a plant model, are treated as optimization variables and parameters, respectively. The solution of such problems is given by (i) a complete set of profiles of all the optimal inputs to the plant as a function of state variables, and (ii) the regions in the space of state variables where these functions remain optimal. It is shown that these profiles are linear and the corresponding regions are described by linear inequalities. An algorithm for obtaining these profiles and corresponding regions of optimality is also presented. The key feature of the proposed approach is that the on-line optimization problem is solved off-line via parametric programming techniques. Hence (i) no optimization solver is called on-line, and (ii) only simple function evaluations are required, to obtain the optimal inputs to the plant for the current state of the plant. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： real-time optimization model predictive control multi-parametric quadratic programming

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