Spatial Filtering for the Control of Smart Structures

An Introduction

By: James E. Hubbard

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Hardcover | 15 December 2009

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228 Pages

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What follows is my personal perspective on early events that played a signi?cant role in the formation of the ?eld now known as Smart Structures. It is by no means meant to be all inclusive or de?nitive in any way, but merely an account of personal experiences that ultimately lead to the development of the material contained and presented herein. On March 23, 1983 then President Ronald Reagan announced his intentions to develop a new system to reduce the threat of nuclear attack and end the strategy of mutual deterrence in an address to the nation entitled, Address to the Nation on Defense and National Security. The system he proposed became known as "Star Wars," after the popular movie, because it was meant to provide a protective shield over the nation from space. His speech mobilized the entire nation on a research and development path toward this end. Investigations were conducted into new areas such as space based radar, large aperture antennae and large ?exible mirror concepts. These proposed systems r- resented an entirely new class of structures that proved to provide new challenges in materials, structures, control systems and modeling. For example antennae needed to monitor large areas of real estate in the continental United States required ap- tures on the order of 100 m.

Industry Reviews

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"This book puts forward the author's ... unique experience, views, and contributions to the development of spatial filtering concepts and designs for the control of distributed flexible structures. ... The book is written in a clear and concise fashion ... and is a 'must-have' book for anyone seeking to expand their knowledge on the origins, developments, and state-of-the-art on transducer design and spatial filtering concepts for the control of smart material systems and structures." (C©sar M. A. Vasques, International Journal of Acoustics and Vibration, Vol. 16 (3), 2011)

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Smart Structure Systems	p. 1
Introduction	p. 1
Smart Structure Architecture and Performance	p. 1
Smart Material Transducer Considerations	p. 5
Continuum Representation of Smart Structures	p. 9
Time Domain Representation of Smart Structure Models	p. 15
Organization of the Book	p. 18
Problems	p. 19
Spatial Shading of Distributed Transducers	p. 25
Introduction	p. 25
Spatial Shading of Distributed Transducers	p. 26
Design by Example: A Center of Pressure Sensor	p. 26
Approximating Shaded Apertures	p. 29
Analytical Modeling of Spatial Shading Functions for Distributed Transducers	p. 34
A Compact Analytical Representation of Distributed Transducers	p. 35
Two Dimensional Representation of Distributed Transducers with Nearly Arbitrary Spatial Shading	p. 45
Application to Two-Dimensional Shading Using Skew Angle	p. 51
Applications Including Finite Skew Angle of Material Axes	p. 55
Summary	p. 60
Problems	p. 61
Active Vibration Control with Spatially Shaded Distributed Transducers	p. 69
Introduction	p. 69
Control System Synthesis Based on the Lyapunov Direct Method	p. 70
Control System Synthesis for Beams	p. 71
Collocated Distributed Transducers and Lyapunov Control	p. 74
Performance Limitations of Control Designs with Shaded Distributions	p. 76
Performance Limitations of Uniformly Shaded Transducers	p. 76
Performance Limitations of Linearly Shaded Transducers	p. 80
Design Guidelines on Spatial Shading for Vibration Control	p. 81
Control System Synthesis for Plates	p. 84
Performance Limitations of Uniformly Shaded Actuators for Plates	p. 86
Performance Limitations of Non-uniformly Shaded Actuators for Plates	p. 92
The Unique Compatibility of Distributed Transducers for Arbitrary Spatial Shadings	p. 94
Summary	p. 95
Notes	p. 95
Problems	p. 96
Multi-Dimensional Transforms and MIMO Representations of Smart Structures	p. 101
Introduction	p. 101
Convolution and the Spatially Distributed Plant	p. 105
Green's Function Representations for Temporally Stationary Systems	p. 107
Multi-Input Multi-Output (MIMO) Representations of Smart Structures	p. 113
Problems	p. 119
Performance Measures for Smart Structures with MIMO Representations	p. 121
Introduction	p. 121
Performance Metrics	p. 121
Assessment of Performance Metrics Using Singular Values	p. 124
Command Following	p. 124
Disturbance Rejection	p. 127
Sensor Noise	p. 128
Metrics for Controllability and Observability	p. 128
Controllability	p. 129
Observability	p. 130
Example: Active Damping of a Simply Supported Beam	p. 130
Spatially Uniform Actuator Distributions	p. 131
Linear or "Ramp" Actuator Distributions	p. 133
Metrics for Achieving Stability and Robustness for Control of Smart Structures	p. 137
Additive Error Uncertainty	p. 139
Multiplicative Error Uncertainty	p. 141
Summary	p. 142
Notes	p. 142
Problem	p. 143
Shape Control: Distributed Transducer Design	p. 145
Introduction	p. 145
Shape Control and the Notion of Discrete Spatial Bandwidth	p. 146
Orthonormal Expansions and the Discrete Spatial Transform	p. 147
Minimization of the Integrated Mean Square Profile Error	p. 149
Plant Representations in Terms of an Expansion Basis Set	p. 151
The Generic Green's Function Representation	p. 151
The Symmetric Green's Function Representation	p. 153
Input/Output Coupling and Transducer Shading	p. 155
The Singular Value Decomposition and Performance Metrics for Shape Control	p. 156
Spatially Distributed Sensors and Shape Estimation	p. 162
Summary	p. 166
Shape Control, Modal Representations and Truncated Plants	p. 167
Introduction	p. 167
Shape Error and Feed Forward Correction	p. 167
A Complete Dynamic Shape Control Case Study	p. 173
Case Background	p. 173
Airfoil Shapes and the Discrete Spectrum Parameterization	p. 174
The Concept of Eigenfoils	p. 176
Morphing Airfoil Design Considerations	p. 178
Actuator Placement and Input/Output Coupling	p. 179
Morphing Airfoil Rib: Discrete Parameterization and the System Model	p. 182
State Space Canonical Form	p. 183
Morphing Airfoil Closed Loop Shape Controller Synthesis	p. 184
Morphing Airfoil Closed Loop Shape Control Simulation	p. 191
Summary	p. 195
Problems	p. 196
References	p. 199
Index	p. 203
Table of Contents provided by Ingram. All Rights Reserved.

Spatial Filtering for the Control of Smart Structures

An Introduction

At a Glance

Hardcover

Industry Reviews

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How to return your order

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