Active Control of Flexible Structures: From Modeling to Implementation

by Alberto Cavallo, Giuseppe de Maria, Ciro Natale, Salvatore Pirozzi

Overview

A complete solution for problems of vibration control in structures that may be subject to a broadband primary vibration field, this book addresses the following steps: experimental identification of the dynamic model of the structure; optimal placement of sensors and actuators; formulation of control constraints in terms of controller frequency response shape; controller design and simulation; and controller implementation and rapid prototyping. The identification procedure is a gray-box approach tailored to the estimation of modal parameters of large-scale flexible structures. The actuator/sensor placement algorithm maximizes a modal controllability index improving the effectiveness of the control. Considering limitations of sensors and actuators, the controller is chosen as a stable, band-pass MIMO system resulting from the closed-form solution of a robust control problem. Experimental results on an aeronautical stiffened skin panel are presented using rapid-prototyping hardware.

Product Details

ISBN-13:	9781849962803
Publisher:	Springer London
Publication date:	08/02/2010
Series:	Advances in Industrial Control
Edition description:	2010
Pages:	197
Product dimensions:	6.30(w) x 9.20(h) x 0.70(d)

About the Author

Alberto Cavallo was born in Napoli, Italy, on 16th March 1964. In 1989 he obtained the Laurea degree at the Università di Napoli Federico II with Laude, discussing the thesis "Robust Stability Analysis for Linear Time-Invariant Systems", and in 1993 he completed his PhD discussing the thesis "A solution to tracking problems via sliding manifolds". Alberto Cavallo is currently Associate Professor both of Advanced Automatic Control and System Identification at the Seconda Università di Napoli. His research interests have dealt with many aspects of the theory of automatic control, including robust control techniques with aeronautical and aerospace applications, with parametric uncertainties and H-2 and H-infinity indices, high-order sliding-manifold control, active control of sound and vibration, modelling and control of smart actuators, control of systems with hysteresis, system identification, fuzzy control, modeling and control of water-resource systems and decision-support systems for hydraulic applications. He has published more than 70 journal and conference papers, and is also local team-leader for several national and international research projects connected with aeronautic applications of automatic control.He is the author of the book Using MATLAB, SIMULINK and Control System Toolbox: A Practical Approach (Prentice Hall), and has written more than 50 papers for journals and conference proceedings. Giuseppe De Maria was born in Napoli, Italy, in December 1948. In 1973 he received the Laurea degree in electronic engineering from the Università di Napoli. He was Associate Professor of Automatic Control at the University of Napoli Federico II. Since 1992 he has been full Professor of Automatic Control at the Faculty of Engineering of the Seconda Università di Napoli. His research interests include robust control, control of mechanical systems, industrial and advanced robotics, control of aerospace and aeronautical systems, and active noise and vibrationcontrol of flexible structures. At present, his research interests are focused on the control of smart materials, in particular piezoceramics and magnetostriction, with the aim of realising artificial muscles. Concerning this field of research he is responsible of national and European research contracts. He is the workpackage leader of the project MESEMA (Magnetostrictive Equipment and Systems for even more electric Aircraft) in the 6thFramework Programme of European Community. Ciro Natale was born in Caserta, Italy, on 12th December 1969. He received the Laurea degree and the Research Doctorate degree in Electronic Engineering from the Università di Napoli in 1995 and 2000, respectively. From 2000 to 2004 he has been Research Associate at the Department of Information Engineering of the Seconda Università di Napoli, where he currently holds the position of Associate Professor of Automatic Control and Industrial Robotics. From November 1998 to April 1999 he was a Visiting Scholar at the Institute of Robotics and Mechatronics of the German Aerospace Center in Oberpfaffenhofen, Germany. His research interests include modeling and control of industrial manipulators, force and visual control, cooperative robots. More recently, his activities are focused on modelling and control of flexible structures, active noise and vibration control and modelling, and identification and control of smart materials. He has published more than 50 journal and conference papers and he is author of the book: Interaction Control of Robot Manipulators: Six-degrees-of-freedom Tasks (Springer 2003). Salvatore Pirozzi was born in Napoli, Italy, on 21st April 1977. He received the Laurea and the Ph.D. degrees in electronic engineering from the Seconda Università di Napoli, Aversa, Italy, in 2001 and 2004, respectively. He is currently a Research Associate at the Seconda Università di Napoli. His research interests include modelling and control of smart actuators and sensors for advancedfeedback control systems as well as identification and control of vibrating systems.

Table of Contents

1 Introduction 1

2 Modelling of Flexible Structures 7

2.1 Introduction 7

2.2 Preliminary Definitions 8

2.3 The Boundary Value Problem 9

2.3.1 Uniform String 13

2.3.2 Uniform Cantilever Beam 15

2.4 Approximate Finite-dimensional Models 17

2.4.1 Damped Elastic Structures 20

2.4.2 Finite-dimensional Systems 22

2.5 Conclusions 27

References 27

3 Identification of Flexible Structures 29

3.1 Introduction 29

3.2 Basics of Subspace-based Identification 31

3.2.1 Time Domain Approach 32

3.2.2 Frequency Domain Approach 34

3.3 Identification Problem for a Flexible Structure 38

3.4 Identification Procedure 40

3.4.1 First Stage 40

3.4.2 Second Stage 41

3.4.3 Identification Procedure with Non-colocated Measurements 45

3.5 Application to Experimental Modal Analysis 46

3.6 Illustrative Examples 48

3 6.1 Identification of a Model for Control 48

3.6.2 Identification for Experimental Modal Analysis 51

3.7 Conclusions 53

References 53

4 Modal Feedback Control of Flexible Structures 55

4.1 Introduction 55

4.2 Spillover Problem 58

4.3 Internal Model Control 61

4.3.1 Basic Approach 62

4.3.2 Adaptive Approach 63

4.4 Modal Control 67

4.4.1 Case Study: State Feedback 72

4.4.2 State Observer 74

4.5 Conclusions 76

References 77

5 Optimal Feedback Control of Flexible Structures 79

5.1 Introduction 79

5.2 Control Model 81

5.3 Choice of the Disturbance Matrix 84

5.4 Bandpass Controllers 84

5.5 H∞ Controller Design 86

5.6 H₂ Controller Design 91

5.7 Numerical Example 92

5.8 Further Considerations on the H₂ Controller 94

5.9 Optimal Scaling Matrix Selection 98

5.9.1 Formulation of the Optimsation Problem 98

5.9.2 Scaling Matrix Selection Example 101

5.10 Seleclion of Individual Modes 104

5.10.1 Mode Selection and Non-colocated Feedback Example 108

5.10.2 Computing the Gramians 113

5.11 Conclusions 120

References 121

6 Implementation Issues 123

6.1 Introduction 123

6.2 Conventional Actuators 124

6.3 Smart Material-based Devices 126

6.3.1 Piezoelectric Ceramics 127

6.3.2 Magnetostrictive Materials 128

6.4 Effects of Hysteresis 129

6.4.1 Hysteresis Modelling 130

6.4.2 Hysteresis Compensation: Methodology 132

6.4.3 Hysteresis Compensation: Experimental Results 133

6.5 A Smart Auxiliary Mass Damper 134

6.5.1 Actuator Description and Modelling 136

6.5.2 The Optical Sensor 139

6.5.3 The Control System 141

6.5.4 Experimental Results of Actuator Control 143

6.6 Self-sensing Control 144

6.7 The dSPACE Platform for Rapid Control Prototyping 146

6.7.1 Processor Boards 147

6.7.2 I/O Boards 148

6.7.3 Software Development Environment 148

6.8 Conclusions 149

References 150

7 Experimental Results 153

7.1 Introduction 153

7.2 Identification of the Dynamic Model of the Panel 155

7.3 Active Control of Vibrations with Piezo Actuators 163

7.3.1 Analytically Designed Controllers 166

7.3.2 Numerically Designed Controller Using LMI 168

7.4 Active Vibration Control with a Smart Auxiliary Mass Damper 176

7.5 Conclusions 180

References 181

8 Conclusions and Future Developments 183

8.1 Conclusions 183

8.2 Future Developments 185

Appendix Dynamic Model of the Aeronautical Panel 187

Index 195

Editorial Reviews

From the reviews:

“Intended for graduate students and practicing engineers, this book treats vibration control for structural systems. It addresses identification of the dynamic model of the structure, placement of sensors and actuators, formulation of control constraints, controller design and simulation, and controller implementation and rapid prototyping. The material is based on the authors’ work on two projects financed by the European Community in the 5th and 6th Framework programs.” (IEEE Control Systems Magazine, February, 2012)

From the Publisher