Advanced Structural Dynamics and Active Control of Structures describes comparatively new areas of structural dynamics and control, and presents new tools to solve problems of dynamics and control. It applies control system methods (such as state space representation, controllability and observability, grammians, system norms, and Markov parameters) to solve structural dynamics problems (e.g., sensor and actuator placement, identification, or damage detection), It uses structural methods (such as modal analysis, and modal independence) to solve control problems (e.g., the design of LQG and H¥ controllers), and provides new insight into well-known control laws. It is based on practical applications, originated from developing and applying techniques of structural dynamics, identification, and control to antennas and radiotelescopes. It uses approximate approach in order to simplify analysis of large structural models (for example, to obtain Hankel singular values for a structure with thousands degrees of freedom), and to represent properties of large structures in closed form - a form that is simple and easy to apprehend. This book is a revision and continuation of Gawronski's previous book, Dynamics and Control of Structures. Three new chapters discuss special models, modal actuators and sensors, and system identification. Other chapters have been significantly revised and supplemented with new topics, including discrete-time models of structures, limited-time and frequency grammians and reduction, almost-balanced modal models, simultaneous placement of sensors and actuators, and structural damage detection. The updated and expanded appendices include programs that apply methods presented in the book in Matlab® simulations, Matlab programs that solve examples from each chapter, and additional appendix with data of models presented in the book. Appropriate for graduate courses on vibration and structural dynamics, and in control system courses with application to structural control, Advanced Structural Dynamics and Active Control of Structures will also be useful for engineers who deal with structural dynamics and control. Some praise for Wodek Gawronski's Dynamics and Control of Structures: A Modal Approach: "This book succeeds well in its intent to build a bridge between the structural engineer and the control engineer to control flexible structures. The needed ingredients to this end from both fields are presented side-by-side in an integrated fashion and illustrated by good design examples of increasing challenge. Dynamics and Control of Structures is a very good reference book ..." -Applied Mechanics Reviews "... An excellent, clearly written, up-to-date exposition which should serve graduate students and researchers as a bridge between structural and control engineering." -Zentralblatt für Mathematik Wodek K. Gawronski, Ph.D. is Principal Engineer, Antenna Control Systems for the Jet Propulsion Laboratory at California Institute of Technology, and is an Associate Editor of the Journal of Guidance, Control, and Dynamics (American Institute of Aeronautics and Astronautics).
From the reviews: "The monograph presents advanced structural dynamics and active control of structures. ... The monograph is well written and readable ... . The text can be used in graduate courses on structural dynamics and control. The book is an up-to-date authoritative reference supplied with numerous illustrative examples which will be useful to graduate students, professionals, researchers and practitioners in the field." (Lubomír Bakule, Zentralblatt MATH, Vol. 1064, 2005)
Science is for those who learn; poetry for those who know. Joseph Roux This book is a continuation of my previous book, Dynamics and Control of Structures 44]. The expanded book includes three additional chapters and an additional appendix: Chapter 3, Special Models; Chapter 8, Modal Actuators and Sensors; and Chapter 9, System Identification. Other chapters have been significantly revised and supplemented with new topics, including discrete-time models of structures, limited-time and -frequency grammians and reduction, almo- balanced modal models, simultaneous placement of sensors and actuators, and structural damage detection. The appendices have also been updated and expanded. Appendix A consists of thirteen new Matlab programs. Appendix B is a new addition and includes eleven Matlab programs that solve examples from each chapter. In Appendix C model data are given. Several books on structural dynamics and control have been published. Meirovitch s textbook 108] covers methods of structural dynamics (virtual work, d Alambert s principle, Hamilton s principle, Lagrange s and Hamilton s equations, and modal analysis of structures) and control (pole placement methods, LQG design, and modal control). Ewins s book 33] presents methods of modal testing of structures. Natke s book 111] on structural identification also contains excellent material on structural dynamics. Fuller, Elliot, and Nelson 40] cover problems of structural active control and structural acoustic control."
This book presents and integrates the methods of structural dynamics, structural identification, and structural control into a common framework. It aims to create a common languages between structual and control system engineers.
Preface
List of Symbols
Chapter 1 Introduction to Structures (examples, definition, and properties)
1.1 Examples
1.1.1 A Simple Structure
1.1.2 A 2D Truss
1.1.3 A 3D Truss
1.1.4 A Beam
1.1.5 The Deep Space Network Antenna
1.1.6 The International Space Station Structure
1.2 Definition
1.3 Properties
Chapter 2 Standard Models (how to describe typical structures)
2.1 Models of a Linear System
2.1.1 State-Space Representation
2.1.2 Transfer Function
2.2 Second-Order Structural Models
2.2.1 Nodal Models
2.2.2 Modal Models
2.3 State-Space Structural Models
2.3.1 Nodal Models
2.3.2 Models in Modal Coordinates
2.3.3 Modal Models
Chapter 3 Special Models (how to describe less-common structures)
3.1 Models with Rigid Body Modes
3.2 Models with Accelerometers
3.2.1 State-Space Representation
3.2.2 Second-Order Representation
3.2.3 Transfer Function
3.3 Models with Actuators
3.3.1 Model with Proof-Mass Actuators
3.3.2 Model with Inertial Actuators
3.4 Models with Small Non-Proportional Damping
3.5 Generalized Model
3.5.1 State-Space Representation
3.5.2 Transfer Function
3.6 Discrete-Time Models
3.6.1 State-Space Representation
3.6.2 Transfer Function
Chapter 4 Controllability and Observability (how to excite and monitor a structure)
4.1 Definition and Properties
4.1.1 Continuous-Time Systems
4.1.2 Discrete-Time Systems
4.1.3. Relationship between Continuous- and Discrete-Time Grammians
4.2 Balanced Representation
4.3 Balanced Structures with Rigid Body Modes
4.4 Input and Output Gains
4.5 Controllability and Observability of a Structural Modal Model
4.5.1 Diagonally Dominant Grammians
4.5.2 Closed-Form Grammians
4.5.3 Approximately Balanced Structure in Modal Coordinates
4.6 Controllability and Observability of a Second-Order Modal Model
4.6.1 Grammians
4.6.2 Approximately Balanced Structure in Modal Coordinates
4.7 Three Ways to Compute Hankel Singular Values
4.8 Controllability and Observability of the Discrete-Time Structural Model
4.9 Time-Limited Grammians
4.10 Frequency-Limited Grammians
4.11 Time- and Frequency-Limited Grammians
4.12 Discrete-Time Grammians in Limited Time Range
4.13 Discrete-Time Grammians in Limited Frequency Range
Chapter 5 Norms (how to quantify structural dynamics)
5.1 Norms of the Continuous-Time Systems
5.1.1 The H2 Norm
5.1.2 The H( Norm
5.1.3 The Hankel Norm
5.2 Norms of the Discrete-Time Systems
5.2.1 The Hankel norm
5.2.2 The H( Norm
5.2.3 The H2 Norm
5.3 Norms of a Single Mode
5.3.1 The H2 Norm
5.3.2 The H( Norm
5.3.3 The Hankel Norm
5.3.4 Norm Comparison
5.4 Norms of a Structure
5.4.1 The H2 Norm
5.4.2 The H( Norm
5.4.3 The Hankel Norm
5.5 Norms of a Structure with a Filter
5.5.1 The H2 Norm
5.5.2 The H( Norm
5.5.3 The Hankel Norm
5.6 Norms of a Structure with Actuators and Sensors
5.6.1 The H2 Norm
5.6.2 The H( Norm
5.6.3 The Hankel Norm
5.7 Norms of a Generalized Structure
5.8 Norms of the Discrete-Time Structures
5.8.1 The Hankel Norm
5.8.2 The H( Norm
5.8.3 The H2 Norm
5.8.4 Norm Comparison
Chapter 6 Model Reduction (how to obtain small and accurate models)
6.1 Reduction Through Truncation
6.2 Reduction Errors
6.2.1 H2 Model Reduction
6.2.2 H( and Hankel Model Reduction
6.3 Reduction in Finite Time and Frequency Intervals
6.3.1 Reduction in Finite Time Interval
6.3.2 Reduction in Finite Frequency Interval
6.3.3 Reduction in Finite Time and Frequency Intervals
6.4 Structures with Rigid-Body Modes
6.5 Structures with Actuators and Sensors
6.5.1 Actuators and Sensors in a Cascade Connection
6.5.2 Structure with Accelerometers
6.5.3 Structure with Proof-Mass Actuators
6.5.4 Structure with Inertial Actuators
Chapter 7 Actuator and Sensor Placement (how to set up test procedure and control strategy)
7.1 Problem Statement
7.2 Additive Property of Modal Norms
7.2.1 The H2 Norm
7.2.2 The H( and Hankel Norms
7.3 Placement Indices and Matrices
7.3.1 H2 Placement Indices and Matrices
7.3.2 H( and Hankel Placement Indices and Matrices
7.3.3 Actuator/Sensor Indices and Modal Indices
7.4 Placement for Large Structures
7.4.1 Actuator Placement Strategy
7.4.2 Sensor Placement Strategy
7.5 Placement for a Generalized Structure
7.5.1 Structural Testing and Control
7.5.2 Sensor and Actuator Properties
7.5.3 Placement Indices and Matrices
7.5.4 Placement of Large Number of Sensors
7.6 Simultaneous Placement of Actuators and Sensors
Chapter 8 Modal Actuators and Sensors (how to excite and monitor selected modes)
8.1 Modal Actuators and Sensors through Modal Transformations
8.1.1 Modal Actuators
8.1.2 Modal Sensors
8.2 Modal Actuators and Sensors through Grammian Adjustment
Chapter 9 System Identification (how to derive model from field data)
9.1 Discrete-Time Systems
9.2 Markov Parameters
9.3 Identification Algorithm
9.4 Determining Markov Parameters
9.5 Examples
9.5.1 Simple Structure
9.5.2 2D Truss
9.5.3 Deep Space Network Antenna
Chapter 10 Collocated Controllers (how to make the first step in structural control)
10.1 Low Authority Controller
10.2 Dissipative Controller
10.3 Properties
10.4 Root Locus
10.5 Controller Design Examples
10.5.1 A Simple Structure
10.5.2 The 2D Truss
Chapter 11 LQG Controllers (how to design an advanced feedback loop)
11.1 Definition and Gains
11.2 The Closed-Loop System
11.3 Balanced LQG Controller
11.4 Low Authority LQG Controller
11.5 Approximate Solutions of CARE and FARE
11.6 Root Locus
11.7 Almost LQG-Balanced Modal Representation
11.8 Three Ways to Compute LQG Singular Values
11.9 The Tracking LQG Controller
11.10 Frequency Weighting
11.11 Reduced-Order LQG Controller
11.11.1 The Reduction Index
11.11.2 The Reduction Technique
11.11.3 Stability of the Reduced-Order Controller
11.11.4 Performance of the Reduced-Order Controller
11.11.5 Weights of Special Interest
11.12 Controller Design Procedure
11.13 Controller Design Examples
11.13.1 A Simple Structure
11.13.2 The 3D Truss
11.13.3 The 3D Truss with Input Filter
11.13.4 The Deep Space Network Antenna
Chapter 12 H( and H2 Controllers (how to control a generalized structure)
12.1 Definition and Gains
12.2 The Closed-Loop System
12.3 The Balanced H( Controller
12.4 The H2 Controller
12.4.1 Gains
12.4.2 The Balanced H2 Controller
12.5 The Low Authority H( Controller
12.6 Approximate Solutions of HCARE and HFARE
12.7 Almost H(-Balanced Modal Representation
12.8 Three Ways to Compute H( Singular Values
12.9 Tracking H( Controller
12.10 Frequency Weighting
12.11 The Reduced-Order H( Controller
12.11.1 The Reduction Index
12.11.2 Closed-Loop Poles
12.11.3 Controller Performance
12.12 Controller Design Procedure
12.13 Controller Design Examples
12.13.1 A Simple Structure
12.13.2 The 2D Truss
12.13.3 Filter Implementation Example
12.13.4 The Deep Space Network Antenna with Wind Disturbance Rejection Properties
Appendix (Matlab functions, Matlab examples, and structural parameters)
A Matlab Functions
A.1 Transformation from an Arbitrary State-Space Representation to the Modal 1 State-Space Representation
A.2 Transformation from an Arbitrary State-Space Representation to the Modal 2 State-Space Representation
A.3 Transformation from Modal Parameters to the Modal 1 State-Space Representation
A.4 Transformation from Modal Parameters to the Modal 2 State-Space Representation
A.5 Transformation from Nodal Parameters to the Modal 1 State-Space Representation
A.6 Transformation from Nodal Parameters to the Modal 2 State-Space Representation
A.7 Determination of the Modal 1 State-Space Representation and the Time-Frequency Limited Grammians
A.8 Open-Loop Balanced Representation
A.9 H2 Norm of a Mode
A.10 H( Norm of a Mode
A.11 Hankel Norm of a Mode
A.12 LQG Balanced Representation
A.13 H( Balanced Representation
Appendix B Matlab Examples
B.1 Example 2.5
B.2 Example 3.3
B.3 Example 4.11
B.4 Example 5.3
B.5 Example 6.7
B.6 Example 7.2
B.7 Example 8.1
B.8 Example 9.1
B.9 Example 10.4.2
B.10 Example 11.13.1
B.11 Example 12.13.2
Appendix C Structural Parameters
C.1 Mass and Stiffness Matrices of the 2D Truss
C.2 Mass and Stiffness Matrices of the Clamped Beam Divided into 15 Finite Elements
C.3 State-Space Representation of the Deep Space Network Antenna
References
Index