Model Predictive Control Part 1 potx

Chapter 1Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Preface VII Robust Model Predictive Control Design 1 Vojtech Veselý and Dan

Model Predictive Control

edited by

Tao ZHENG

SCIYO

Model Predictive Control

Edited by Tao ZHENG

Published by Sciyo

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Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Preface VII

Robust Model Predictive Control Design 1

Vojtech Veselý and Danica Rosinová

Robust Adaptive Model Predictive Control of Nonlinear Systems 25

Darryl DeHaan and Martin Guay

A new kind of nonlinear model predictive control algorithm

enhanced by control lyapunov functions 59

Yuqing He and Jianda Han

Robust Model Predictive Control Algorithms for Nonlinear

Systems: an Input-to-State Stability Approach 87

D M Raimondo, D Limon, T Alamo and L Magni

Model predictive control of nonlinear processes 109

Author Name

Approximate Model Predictive Control for Nonlinear

Multivariable Systems 141

JonasWitt and HerbertWerner

Multi-objective Nonlinear Model Predictive Control:

Lexicographic Method 167

Tao ZHENG, Gang WU, Guang-Hong LIU and Qing LING

Model Predictive Trajectory Control for High-Speed Rack Feeders 183

Harald Aschemann and Dominik Schindele

Plasma stabilization system design on the base of model predictive control 199

Evgeny Veremey and Margarita Sotnikova

Predictive Control of Tethered Satellite Systems 223

Paul Williams

MPC in urban traffic management 251

Tamás Tettamanti, István Varga and Tamás Péni

Contents

Chapter 12

Chapter 13

Off-line model predictive control of dc-dc converter 269

Tadanao Zanma and Nobuhiro Asano

Nonlinear Predictive Control of Semi-Active Landing Gear 283

Dongsu Wu, Hongbin Gu, Hui Liu

Since Model Predictive Heuristic Control (MPHC), the earliest algorithm of Model Predictive Control (MPC), was proposed by French engineer Richalet and his colleagues in 1978, the explicit background of industrial application has made MPC develop rapidly to satisfy the increasing request from modern industry Different from many other control algorithms, the research history of MPC is originated from application and then expanded to theoretical field, while ordinary control algorithms often has applications after sufficient theoretical research Nowadays, MPC is not just the name of one or some specific computer control algorithms, but the name of a specific thought in controller design, from which many kinds of computer control algorithms can be derived for different systems, linear or nonlinear, continuous or discrete, integrated or distributed The basic characters of the thought of MPC can be summarized as the model used for prediction, the online optimization based on prediction and the feedback compensation for model mismatch, while there is no special demands on the form of model, the computational tool for online optimization and the form of feedback compensation After three decades’ developing, the MPC theory for linear systems is now comparatively mature, so its applications can be found in almost every domain in modern engineering While, MPC with robustness and MPC for nonlinear systems are still problems for scientists and engineers Many efforts have been made to solve them, though there are some constructive results, they will remain as the focuses of MPC research for a period in the future

In first part of this book, to present the recent theoretical improvements of MPC, Chapter 1 will introduce the Robust Model Predictive Control and Chapter 2 to Chapter 5 will introduce some typical methods to establish Nonlinear Model Predictive Control, with more complexity, MPC for multi-variable nonlinear systems will be proposed in Chapter 6 and Chapter 7

To give the readers an overview of MPC’s applications today, in second part of the book, Chapter 8 to Chapter 13 will introduce some successful examples, from plasma stabilization system to satellite system, from linear system to nonlinear system They can not only help the readers understand the characters of MPC, but also give them the guidance for how to use MPC to solve practical problems

Authors of this book truly want to it to be helpful for researchers and students, who are concerned about MPC, and further discussions on the contents of this book are warmly welcome

Preface

Finally, thanks to SCIYO and its officers for their efforts in the process of edition and publication, and thanks to all the people who have made contributes to this book

Editor

Tao ZHENG

University of Science and Technology of China

Robust Model Predictive Control Design 1

Robust Model Predictive Control Design

Vojtech Veselý and Danica Rosinová

0

Robust Model Predictive Control Design

Vojtech Veselý and Danica Rosinová

Institute for Control and Industrial Informatics, Faculty of Electrical Engineering and

Information Technology, Slovak University of Technology, Ilkoviˇcova 3, 81219 Bratislava

Slovak Republic

1 Introduction

Model predictive control (MPC) has attracted notable attention in control of dynamic systems

and has gained the important role in control practice The idea of MPC can be summarized as

follows, (Camacho & Bordons, 2004), (Maciejovski, 2002), (Rossiter, 2003) :

• Predict the future behavior of the process state/output over the finite time horizon

• Compute the future input signals on line at each step by minimizing a cost function

under inequality constraints on the manipulated (control) and/or controlled variables

• Apply on the controlled plant only the first of vector control variable and repeat the

previous step with new measured input/state/output variables

Therefore, the presence of the plant model is a necessary condition for the development of

the predictive control The success of MPC depends on the degree of precision of the plant

model In practice, modelling real plants inherently includes uncertainties that have to be

considered in control design, that is control design procedure has to guarantee robustness

properties such as stability and performance of closed-loop system in the whole uncertainty

domain Two typical description of uncertainty, state space polytope and bounded

unstruc-tured uncertainty are extensively considered in the field of robust model predictive control

Most of the existing techniques for robust MPC assume measurable state, and apply plant

state feedback or when the state estimator is utilized, output feedback is applied Thus, the

present state of robustness problem in MPC can be summarized as follows:

Analysis of robustness properties of MPC.

(Zafiriou & Marchal, 1991) have used the contraction properties of MPC to develop

necessary-sufficient conditions for robust stability of MPC with input and output constraints for SISO

systems and impulse response model (Polak & Yang, 1993) have analyzed robust stability of

MPC using a contraction constraint on the state

MPC with explicit uncertainty description.

( Zheng & Morari, 1993), have presented robust MPC schemes for SISO FIR plants, given

un-certainty bounds on the impulse response coefficients Some MPC consider additive type of

uncertainty, (delaPena et al., 2005) or parametric (structured) type uncertainty using CARIMA

model and linear matrix inequality, (Bouzouita et al., 2007) In (Lovas et al., 2007), for

open-loop stable systems having input constraints the unstructured uncertainty is used The robust

stability can be established by choosing a large value for the control input weighting matrix R

in the cost function The authors proposed a new less conservative stability test for

determin-ing a sufficiently large control penalty R usdetermin-ing bilinear matrix inequality (BMI) In (Casavola

1

Model Predictive Control 2

et al., 2004), robust constrained predictive control of uncertain norm-bounded linear systems

is studied The other technique- constrained tightening to design of robust MPC have been

proposed in (Kuwata et al., 2007) The above approaches are based on the idea of increasing

the robustness of the controller by tightening the constraints on the predicted states

The mixed H2/H∞control approach to design of MPC has been proposed by (Orukpe et al.,

2007)

Robust constrained MPC using linear matrix inequality (LMI) has been proposed by (Kothare et

al., 1996), where the polytopic model or structured feedback uncertainty model has been used

The main idea of (Kothare et al., 1996) is the use of infinite horizon control laws which

guar-antee robust stability for state feedback In (Ding et al., 2008) output feedback robust MPC

for systems with both polytopic and bounded uncertainty with input/state constraints is

pre-sented Off-line, it calculates a sequence of output feedback laws based on the state estimators,

by solving LMI optimization problem On-line, at each sampling time, it chooses an

appro-priate output feedback law from this sequence Robust MPC controller design with one step

ahead prediction is proposed in (Veselý & Rosinová , 2009) The survey of optimal and robust

MPC design can be consulted in (Mayne et al., 2000) Some interesting results for nonlinear

MPC are given in (Janík et al., 2008)

In MPC approach generally, control algorithm requires solving constrained optimization

prob-lem on-line (in each sampling period) Therefore on-line computation burden is significant

and limits practical applicability of such algorithms to processes with relatively slow

dynam-ics In this chapter, a new MPC scheme for an uncertain polytopic system with constrained

control is developed using model structure introduced in (Veselý et al., 2010) The main

con-tribution of the first part of this chapter is that all the time demanding computations of output

feedback gain matrices are realized off-line ( for constrained control and unconstrained control

cases) The actual value of control variable is obtained through simple on-line computation of

scalar parameter and respective convex combination of already computed matrix gains The

developed control design scheme employs quadratic Lyapunov stability to guarantee the

ro-bustness and performance (guaranteed cost) over the whole uncertainty domain

The first part of the chapter is organized as follows A problem formulation and preliminaries

on a predictive output/state model as a polytopic system are given in the next section In

Section 1.2, the approach of robust output feedback predictive controller design using linear

matrix inequality is presented In Section 1.3, the input constraints are applied to LMI

feasi-ble solution Two examples illustrate the effectiveness of the proposed method in the Section

1.4 The second part of this chapter addresses the problem of designing a robust parameter

dependent quadratically stabilizing output/state feedback model predictive control for linear

polytopic systems without constraints using original sequential approach For the closed-loop

uncertain system the design procedure ensures stability, robustness properties and

guaran-teed cost Finally, conclusions on the obtained results are given

Hereafter, the following notational conventions will be adopted: given a symmetric matrix

P = P T ∈ R n×n , the inequality P > 0(P ≥ 0)denotes matrix positive definiteness

(semi-definiteness) Given two symmetric matrices P, Q, the inequality P > Q indicates that

P − Q > 0 The notation x(t+k)will be used to define, at time t, k-steps ahead prediction

of a system variable x from time t onwards under specified initial state and input scenario I

denotes the identity matrix of corresponding dimensions

1.1 Problem formulation and preliminaries

Let us start with uncertain plant model described by the following linear discrete-time uncer-tain system with polytopic unceruncer-tainty domain

x(t+1) =A(α)x(t) +B(α)u(t) (1)

y(t) =Cx(t)

where x(t) ∈ R n , u(t) ∈ R m , y(t) ∈ R lare state, control and output variables of the system,

respectively; A(α), B(α)belong to the convex set

S={ A(α)∈ R n×n , B(α)∈ R n×m } (2)

{ A(α) =

N

∑

j=1

A j α j B(α) =

N

∑

j=1

B j α j , α j ≥0 , j=1, 2 N,∑N

j=1

α j=1

Matrices A i , B i and C are known matrices with constant entries of corresponding dimensions.

Simultaneously with (1) we consider the nominal model of system (1) in the form

x(t+1) =A o x(t) +B o u(t) y(t) =Cx(t) (3)

where Ao, Bo are any constant matrices from the convex bounded domain S (2) The nominal

model (3) will be used for prediction, while (1) is considered as real plant description

provid-ing plant output Therefore in the robust controller design we assume that for time t output

y(t)is obtained from uncertain model (1), predicted outputs for time t+1, t+N2will be obtained from model prediction, where the nominal model (3) is used The predicted states

and outputs of the system (1) for the instant t+k, k=1, 2, N2are given by

• k=1

x(t+2) =A o x(t+1) +B o u(t+1) =A o A(α)x(t) +A o B(α)u(t) +B o u(t+1)

• k=2

x(t+3) =A2A(α)x(t) +A2B(α)u(t) +A o B o u(t+1) +B o u(t+2)

• for k

x(t+k+1) = A k A(α)x(t) +A k B(α)u(t) +k−1∑

i=0 A k−i−1 o B o u(t+1+i) (4) and corresponding output is

y(t+k) =Cx(t+k) (5)

Consider a set of k=0, 1, 2, , N2state/output model predictions as follows

z(t+1) =A f(α)z(t) +B f(α)v(t), y f(t) =C f z(t) (6) where

z(t)T = [x(t)T x(t+N2)T], v(t)T= [u(t)T u(t+N u)T] (7)

y f(t)T = [y(t)T y(t+N2)T]

and

B f(α) =







B(α) 0 0

A o B(α) B o 0 0

A N2

o B(α) A N o2−1 B o A N2−N u

o B o



