Actuator Saturation Control

by Kapila; Vikram

ISBN13: 9780824707514

ISBN10: 0824707516

Format: Hardcover

Pub. Date: 2002-02-20

Publisher(s): CRC Press

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Summary

Compiling the most significant advances from nearly a decade of research, this reference compares and evaluates a wide variety of techniques for the design, analysis, and implementation of control methodologies for systems with actuator saturation. The book presents efficient computational algorithms and new control paradigms for application in the mechanical, electrical, and aerospace industries. Offering real-world solutions to manage system constraints, Actuator Saturation Control provides concise tutorials on recent breakthroughs in the field; novel procedures to achieve global stability, optimal performance, and dynamic anti-windup; practical strategies to model and predict actuator dynamics; effective methods to reduce system sensitivity to external disturbances; equations within the stochastic linearization framework for actuator saturation control; current approaches to ensure graceful performance degradation in the presence of saturation phenomena; linear parameter-varying (LPV) formulations of state and output feedback controllers, and a comprehensive survey of optimal windup and directionality compensation.

Preface

Contributors

xvii

Anti-windup for Exponentially Unstable Linear Systems with Rate and Magnitude Input Limits

(32)

C. Barbu

R. Reginatto

A.R. Teel

L. Zaccarian

Introduction

(3)

The Anti-windup Construction

(10)

Problem Statement

(2)

The Anti-windup Compensator

(2)

Main Result

(6)

Anti-windup Design for an Unstable Aircraft

(7)

Aircraft Model and Design Goals

(2)

Selection of the Operating Region

(2)

The Nominal Controller

(3)

Simulations

(1)

Conclusions

(2)

Proof of the Main Result

(9)

References

(5)

Selecting the Level of Actuator Saturation for Small Performance Degradation of Linear Designs

(14)

Y. Eun

C. Gokcek

P.T. Kabamba

S.M. Meerkov

Introduction

(2)

Problem Formulation

(2)

Main Result

(351)

Examples

388

(30)

Conclusions

418

Appendix

(6)

References

(3)

Null Controllability and Stabilization of Linear Systems Subject to Asymmetric Actuator Saturation

(30)

T. Hu

A. N. Pitsillides

Z. Lin

Introduction

(2)

Preliminaries and Notation

(2)

Null Controllable Regions

(7)

General Description of Null Controllable Regions

(3)

Systems with Only Real Eigenvalues

(2)

Systems with Complex Eigenvalues

(2)

Domain of Attraction under Saturated Linear State Feedback

(9)

Semiglobal Stabilization on the Null Controllable Region

(8)

Second Order Anti-stable Systems

(7)

Higher Order Systems with Two Exponentially Unstable Poles

(1)

Conclusions

(2)

References

(2)

Regional H2 Performance Synthesis

(32)

T. Iwasaki

M. Fu

Introduction

(1)

Analysis

(5)

A General Framework

(2)

Applications---Linear and Circle Analyses

(3)

Synthesis

(12)

Problem Formulation and a Critical Observation

(3)

Proof of Theorem 4.1

(1)

Fixed-gain Control

(5)

Switching Control

(3)

Design Examples

(7)

Switching Control with Linear Analysis

(1)

Swithcing Control with Circle Analysis

(4)

Fixed Gain Control with Accelerated Convergence

100

(2)

Further Discussion

102

(7)

References

105

(4)

Disturbance Attenuation with Bounded Actuators: An LPV Approach

109

(26)

F. Jabbari

Introduction

109

(2)

Preliminaries

111

(2)

Parameter-independent Lyapunov Functions

113

(4)

Parameter-dependent Compensators and Lyapunov Functions

117

(1)

Numerical Example

118

(1)

Rate Bounds

119

(3)

Scheduled Controllers: State Feedback Case

122

(9)

Obtaining the Controller

126

(2)

Special case: Constant Q

128

(1)

A Simple Example

129

(2)

Conclusion

131

(4)

References

131

(4)

LMI-Based Control of Discrete-Time Systems with Actuator Amplitude and Rate Nonlinearities

135

(28)

H. Pan

V. Kapila

Introduction

135

(2)

State Feedback Control of Discrete-Time Systems with Actuator Amplitude and Rate Nonlinearities

137

(4)

State Feedback Controller Synthesis for Discrete-Time Systems with Actuator Amplitude and Rate Nonlinearities

141

(5)

Dynamic Output Feedback Control of Discrete-Time Systems with Actuator Amplitude and Rate Nonlinearities

146

(2)

Dynamic Output Feedback Controller Synthesis for Discrete-Time Systems with Actuator Amplitude and Rate Nonlinearities

148

(6)

Illustrative Numerical Examples

154

(3)

Conclusion

157

(6)

References

159

(4)

Robust Control Design for Systems with Saturating Nonlinearities

163

(26)

T. Pare

H. Hindi

J. How

Introduction

163

(4)

Problems of Local Control Design

167

(3)

The Design Approach

170

(1)

System Model

171

(2)

Design Algorithms

173

(6)

Stability Region (SR)

174

(1)

Disturbance Rejection (DR)

175

(2)

Local L2-Gain (EG)

177

(1)

Controller Reconstruction

178

(1)

Optimization Algorithms

179

(1)

L2-Gain Control Example

179

(2)

Conclusions

181

(1)

Appendix

182

(7)

Preliminaries

182

(1)

Region of Convergence Design

183

(1)

Local Disturbance Rejection Design

184

(1)

Local L2-Gain Design

184

(1)

References

184

(5)

Output Regulation of Linear Plants Subject to State and Input Constraints

189

(38)

A. Saberi

A.A. Stoorvogel

G. Shi

P. Sannuti

Introduction

190

(1)

System Model and Primary Assumptions

191

(3)

A Model for Actuator Constraints

194

(3)

Statements of Problems

197

(3)

Taxonomy of Constraints

200

(2)

Low-gain and Low-high Gain Design for Linear Systems with Actuators Subject to Both Amplitude and Rate Constraints

202

(7)

Static Low-gain State Feedback

203

(2)

A New Version of Low-gain Design

205

(2)

A New Low-high Gain Design

207

(1)

Scheduled Low-gain Design

208

(1)

Main Results for Right-invertible Constraints

209

(10)

Results

210

(2)

Proofs of Theorems

212

(7)

Output Regulation with Non-right-invertible Constraints

219

(2)

Tracking Problem with Non-minimum Phase Constraints

221

(2)

Conclusions

223

(4)

References

224

(3)

Optimal Windup and Directionality Compensation in Input-Constrained Nonlinear Systems

227

(20)

M. Soroush

P. Daoutidis

Introduction

227

(1)

Directionality and Windup

228

(3)

Directionality

228

(2)

Windup

230

(1)

Organization of this Chapter

231

(1)

Optimal Directionality Compensation

231

(9)

Scope

231

(1)

Directionality

232

(1)

Optimal Directionality Compensation

232

(4)

Application to Two Plants

236

(4)

Windup Compensation

240

(1)

Scope

240

(1)

Nonlinear Controller Design

240

(7)

Application to a Nonlinear Chemical Reactor

242

(2)

References

244

(3)

Output Feedback Compensators for Linear Systems with Position and Rate Bounded Actuators

247

(26)

S. Tarbouriech

G. Garcia

Introduction

247

(2)

Problem Statement

249

(7)

Nomenclature

249

(1)

Problem Statement

249

(7)

Mathematical Preliminaries

256

(3)

Control Strategy via Riccati Equations

259

(5)

Control Strategy via Matrix Inequalities

264

(3)

Illustrative Examples

267

(2)

Concluding Remarks

269

(4)

References

270

(3)

Actuator Saturation Control via Linear Parameter-Varying Control Methods

273

(26)

F. Wu

K.M. Grigoriadis

Introduction

273

(3)

LPV System Analysis and Control Synthesis

276

(5)

Induced L2 Norm Analysis

277

(1)

LPV Controller Synthesis

277

(4)

LPV Anti-Windup Control Design

281

(4)

Application to a Flight Control Problem

285

(8)

Single Quadratic Lyapunov Function Case

288

(3)

Parameter-Dependent Lyapunov Function Case

291

(2)

Conclusions

293

(6)

References

295

(4)

Index

299

Actuator Saturation Control

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