Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation (Princeton Series in Applied Mathematics) - Hardcover

Zaccarian, Luca; Teel, Andrew R.

Hardcover

ISBN 10: 0691147329 ISBN 13: 9780691147321

Verlag: Princeton University Press, 2011

Inhaltsangabe

This book provides a wide variety of state-space--based numerical algorithms for the synthesis of feedback algorithms for linear systems with input saturation. Specifically, it addresses and solves the anti-windup problem, presenting the objectives and terminology of the problem, the mathematical tools behind anti-windup algorithms, and more than twenty algorithms for anti-windup synthesis, illustrated with examples. Luca Zaccarian and Andrew Teel's modern method--combining a state-space approach with algorithms generated by solving linear matrix inequalities--treats MIMO and SISO systems with equal ease. The book, aimed at control engineers as well as graduate students, ranges from very simple anti-windup construction to sophisticated anti-windup algorithms for nonlinear systems. Describes the fundamental objectives and principles behind anti-windup synthesis for control systems with actuator saturation Takes a modern, state-space approach to synthesis that applies to both SISO and MIMO systems Presents algorithms as linear matrix inequalities that can be readily solved with widely available software Explains mathematical concepts that motivate synthesis algorithms Uses nonlinear performance curves to quantify performance relative to disturbances of varying magnitudes Includes anti-windup algorithms for a class of Euler-Lagrange nonlinear systems Traces the history of anti-windup research through an extensive annotated bibliography

Über diesen Titel

Über die Autorin bzw. den Autor

Luca Zaccarian is associate professor of control engineering at the University of Rome, Tor Vergata. Andrew R. Teel is a professor in the Electrical and Computer Engineering Department at the University of California, Santa Barbara.

Von der hinteren Coverseite

"This book goes a long way toward providing comprehensive coverage of systematic procedures for anti-windup synthesis, emphasizing algorithmic issues and modern design techniques. A valuable resource for researchers and practitioners, it should interest a broad audience in control engineering, as well as in other disciplines, such as mechanical and chemical engineering."--Prodromos Daoutidis, University of Minnesota

Aus dem Klappentext

"This book goes a long way toward providing comprehensive coverage of systematic procedures for anti-windup synthesis, emphasizing algorithmic issues and modern design techniques. A valuable resource for researchers and practitioners, it should interest a broad audience in control engineering, as well as in other disciplines, such as mechanical and chemical engineering."--Prodromos Daoutidis, University of Minnesota

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Modern Anti-windup Synthesis

Control Augmentation for Actuator SaturationBy Luca Zaccarian Andrew R. Teel

PRINCETON UNIVERSITY PRESS

Copyright © 2005 Princeton University Press
All right reserved.
ISBN: 978-0-691-14732-1

Contents

Preface.........................................................................................ixAlgorithms Summary..............................................................................xiPART 1. PREPARATION.............................................................................11. The Windup Phenomenon and Anti-windup Illustrated............................................32. Anti-windup: Definitions, Objectives, and Architectures......................................233. Analysis and Synthesis of Feedback Systems: Quadratic Functions and LMIs.....................48PART 2. DIRECT LINEAR ANTI-WINDUP AUGMENTATION..................................................754. Static Linear Anti-windup Augmentation.......................................................775. Dynamic Linear Anti-windup Augmentation......................................................109PART 3. MODEL RECOVERY ANTI-WINDUP AUGMENTATION.................................................1556. The MRAW Framework...........................................................................1577. Linear MRAW Synthesis........................................................................1748. Nonlinear MRAW Synthesis.....................................................................2009. The MRAW Structure Applied to Other Problems.................................................22610. Anti-windup for Euler-Lagrange Plants.......................................................24511. Annotated Bibliography......................................................................269Index...........................................................................................285

Chapter One

The Windup Phenomenon and Anti-windup Illustrated

1.1 INTRODUCTION

Every control system actuator has limited capabilities. A piezoelectric stack actuator cannot traverse an unlimited distance. A motor cannot deliver an unlimited force or torque. A rudder cannot deflect through an unlimited angle. An amplifier cannot produce an unlimited voltage level. A hydraulic actuator cannot change its position arbitrarily quickly. These actuator limitations can have a dramatic effect on the behavior of a feedback control system.

In this book, the term "windup" refers to the degradation in performance that occurs when a saturation nonlinearity is inserted, at the plant input, in an otherwise linear feedback control loop. Usually the term is reserved for the situation where this degradation is severe. The term has its origins in the fact that, among the simple analog control architectures that were used in the early days of electronic control, feedback loops with controllers that contained an integrator were the most likely to experience a severe performance degradation due to input saturation. Windup, as the term is use here, was said to occur because the saturation nonlinearity would slow down the response of the feedback loop and thus cause the integrator state to "wind up" to excessively large values.

"Anti-windup" refers to augmentation of a controller in a feedback loop that is prone to windup so that:

1. the closed-loop performance is unaltered when saturation never occurs, in other words, the augmentation has no effect for small signals;

2. acceptable performance is achieved, to the extent that it is possible, even when actuator saturation occurs.

Anti-windup synthesis refers to the design of such augmentation. This book provides principles, guidelines, and algorithms for anti-windup synthesis.

In order to motivate anti-windup synthesis, the rest of this chapter contains examples where windup occurs. In each of these examples, alternatives to anti-windup synthesis include investing in actuators with more capabilities, or redesigning the controller from scratch to account for input saturation directly. These strategies should be considered when the control system's actuators are continuously trying to act beyond their limits. On the other hand, suppose that hitting the actuator limits is the exception rather than the rule. In addition, suppose the operating budget or some physical constraint does not permit more capable actuators. Moreover, suppose the small signal performance is highly desirable and very difficult to reproduce with control synthesis tools that account for saturation directly. In this case, anti-windup synthesis becomes a very appealing design tool: it is uniquely qualified to address saturation with potentially dramatic performance improvement using the existing actuators without sacrificing the small signal performance for the sake of guaranteeing acceptable large signal behavior. The examples will illustrate these capabilities of anti-windup synthesis, without going into the synthesis details yet. The examples will be revisited after the anti-windup synthesis algorithms have been described.

1.2 ILLUSTRATIVE EXAMPLES

1.2.1 A SISO academic example

Consider the closed-loop system resulting from using a PID (proportional + integral + derivative) controller with unity gains to control a single integrator plant, as shown in Figure 1.1a. When the force applied to the object is not limited, the closed-loop system is linear and the related response to a unitary step reference corresponds to the dashed curves in Figure 1.2. During the initial transient, the applied force exhibits a large peak. Its maximum value, which exceeds the lower plot's range, is one unit. If the maximum force that the actuator can deliver is ±0.1 units, then undesirable input and output oscillations occur, as shown by the dotted curves in Figure 1.2. Although the velocity eventually converges to the desired steady-state value, the response is very sluggish: it takes approximately 60 seconds to recover the linear performance. The output oscillations consist of rising and falling ramps that correspond to large time intervals where the force sits on either its positive or negative limit.

Although the limits on the allowable input force imposed by saturation must cause some deviation from the ideal linear response, the large oscillations indicated by the dotted curve in Figure 1.2 are unacceptable. Since this undesirable response is induced by the large step reference input, in principle it could be avoided by shaping the reference signal so that it does not feed large and sudden changes to the control system. This solution does not address the core of the problem, however, because similar behavior will also occur whenever large enough disturbances affect the control system. Indeed, the response after 75 seconds in Figure 1.2 is due to an impulsive disturbance acting at the integrator's input, as drawn in Figure 1.1a. This impulsive disturbance resembles the action of an external element hitting the object being controlled and remaining in contact with it for a very short time interval. Mathematically, this is modeled as a very large pulse acting for a very short time.

The effect of the impulsive disturbance on the closed loop is essentially the same as that of the step reference input. However, the reference can be shaped to avoid input saturation and its undesired consequences, while the disturbance input cannot be changed. It is therefore desirable to insert extra compensation into the control scheme, aimed at eliminating the undesirable oscillatory...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 0691147329
• ISBN 13: 9780691147321
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 304
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar