Vibration Control of Active Structures An Introduction

Vibration Control of Active Structures An Introduction / by A. Preumont.

This text is an introduction to the dynamics of active structures and to the feedback control of lightly damped flexible structures; the emphasis is placed on basic issues and simple control strategies that work. Now in its third edition, more chapters have been added, and comments and feedback from...

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Bibliographic Details
Main Author: Preumont, A. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2011.
Edition:3rd ed. 2011.
Series:Solid Mechanics and Its Applications, 179
Springer eBook Collection.
Subjects:
Vibration.
Dynamical systems.
Dynamics.
Mechanical engineering.
Automotive engineering.
Noise control.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Preface to the third edition.-   Preface to the second edition.-   Preface to the first edition.-   1 Introduction.-   1.1 Active versus passive.-   1.2 Vibration suppression.-   1.3 Smart materials and structures.-   1.4 Control strategies.-   1.4.1 Feedback.-   1.4.2 Feedforward.-   1.5 The various steps of the design.-   1.6 Plant description, error and control budget.-   1.7 Readership and Organization of the book.-   1.8 References.-   1.9 Problems.-   2 Some concepts in structural dynamics.-  2.1 Introduction.-   2.2 Equation of motion of a discrete system.-   2.3 Vibration modes.-   2.4 Modal decomposition.-   2.4.1 Structure without rigid body modes.-   2.4.2 Dynamic °exibility matrix.-   2.4.3 Structure with rigid body modes.-   2.4.4 Example.-  2.5 Collocated control system.-   2.5.1 Transmission zeros and constrained system.-  2.6 Continuous structures.-   2.7 Guyan reduction.-   2.8 Craig-Bampton reduction.-   2.9 References.-   2.10 Problems.-   3 Electromagnetic and piezoelectric transducers.-   3.1 Introduction.-   3.2 Voice coil transducer.-   3.2.1 Proof-mass actuator.-   3.2.2 Geophone.-   3.3 General electromechanical transducer.-   3.3.1 Constitutive equations.-   3.3.2 Self-sensing.-   3.4 Reaction wheels and gyrostabilizers.-   3.5 Smart materials.-   3.6 Piezoelectric transducer.-   3.6.1 Constitutive relations of a discrete transducer.-   3.6.2 Interpretation of k2.-   3.6.3 Admittance of the piezoelectric transducer.-   3.7 References.-   3.8 Problems.-   4 Piezoelectric beam, plate and truss.-   4.1 Piezoelectric material.-   4.1.1 Constitutive relations.-   4.1.2 Coenergy density function.-   4.2 Hamilton's principle.-   4.3 Piezoelectric beam actuator.-   4.3.1 Hamilton's principle.-   4.3.2 Piezoelectric loads.-   4.4 Laminar sensor.-   4.4.1 Current and charge amplifiers.-   4.4.2 Distributed sensor output.-   4.4.3 Charge amplifier dynamics.-   4.5 Spatial modalfilters.-   4.5.1 Modal actuator.-   4.5.2 Modal sensor.-   4.6 Active beam with collocated actuator-sensor.-   4.6.1 Frequency response function.-   4.6.2 Pole-zero pattern.-   4.6.3 Modal truncation.-   4.7 Admittance of a beam with a piezoelectric patch.-   4.8 Piezoelectric laminate.-   4.8.1 Two dimensional constitutive equations.-   4.8.2 Kirchhoff  theory.-   4.8.3 Stiffness matrix of a multi-layer elastic laminate.-   4.8.4 Multi-layer laminate with a piezoelectric layer.-   4.8.5 Equivalent piezoelectric loads.-   4.8.6 Sensor output.-   4.8.7 Beam model vs. plate model.-   4.8.8 Additional remarks.-   4.9 Active truss.-   4.9.1 Open-loop transfer function.-   4.9.2 Admittance function.-   4.10 Finite element formulation.-   4.11 References.-   4.12 Problems.-   5 Passive damping with piezoelectric transducers.-   5.1 Introduction.-   5.2 Resistive shunting.-   5.3 Inductive shunting.-   5.4 Switched shunt.-   5.4.1 Equivalent damping ratio.-   5.5 References.-   5.6 Problems.-   6 Collocated versus non-collocated control.-   6.1 Introduction.-  6.2 Pole-zero flipping.-   6.3 The two-mass problem.-   6.3.1 Collocated control.-   6.3.2 Non-collocated control.-   6.4 Notch filter.-   6.5 Effect of pole-zero flipping on the Bode plots.-   6.6 Nearly collocated control system.-   6.7 Non-collocated control systems.-   6.8 The role of damping.-   6.9 References
  •   6.10 Problems ..-   7 Active damping with collocated system.-   7.1 Introduction.-   7.2 Lead control.-   7.3 Direct velocity feedback (DVF).-   7.4 Positive Position Feedback (PPF).-   7.5 Integral Force Feedback(IFF).-   7.6 Duality between the Lead and the IFF controllers.-   7.6.1 Root-locus of a single mode.-   7.6.2 Open-loop poles and zeros.-   7.7 Actuator and sensor dynamics.-   7.8 Decentralized control with collocated pairs.-   7.8.1 Cross talk.-   7.8.2 Force actuator and displacement sensor.-   7.8.3 Displacement actuator and force sensor.-   7.9 References.-   7.10 Problems.-   8 Vibration isolation.-   8.1 Introduction.-   8.2 Relaxation isolator.-   8.2.1 Electromagnetic realization.-   8.3 Active isolation.-  8.3.1 Sky-hook damper.-   8.3.2 Integral Force Feedback.-   8.4 Flexible body.-   8.4.1 Free-free beam with isolator.-   8.5 Payload isolation in spacecraft.-   8.5.1 Interaction isolator/attitude control.-   8.5.2 Gough-Stewart platform.-   8.6 Six-axis isolator.-   8.6.1 Relaxation isolator.-   8.6.2 Integral Force Feedback.-   8.6.3 Spherical joints, modal spread.-   8.7 Active vs. passive.-   8.8 Car suspension.-   8.9 References.-   8.10 Problems.-   9 State space approach.-   9.1 Introduction.-   9.2 State space description.-   9.2.1 Single degree of freedom oscillator.-   9.2.2 Flexible structure.-   9.2.3 Inverted pendulum.-   9.3 System transfer function.-   9.3.1 Poles and zeros.-   9.4 Pole placement by state feedback.-   9.4.1 Example: oscillator.-   9.5 Linear Quadratic Regulator.-   9.5.1 Symmetric root locus.-   9.5.2 Inverted pendulum.-   9.6 Observer design.-   9.7 Kalman Filter.-   9.7.1 Inverted pendulum.-   9.8 Reduced order observer.-   9.8.1 Oscillator.-   9.8.2 Inverted pendulum.-   9.9 Separation principle.-   9.10 Transfer function of the compensator.-   9.10.1 The two-mass problem.-   9.11 References.-   9.12 Problems.-   10 Analysis and synthesis in the frequency domain.-   10.1 Gain and phase margins.-  10.2 Nyquist criterion.-   10.2.1 Cauchy's principle.-   10.2.2 Nyquist stability criterion.-  10.3 Nichols chart.-   10.4 Feedback specification for SISO systems.-   10.4.1 Sensitivity.-   10.4.2 Tracking error.-   10.4.3 Performance specification.-   10.4.4 Unstructured uncertainty.-   10.4.5 Robust performance and robust stability.-  10.5 Bode gain-phase relationships.-  10.6 The Bode Ideal Cutoff.-  10.7 Non-minimum phase systems.-   10.8 Usual compensators.-   10.8.1 System type.-   10.8.2 Lead compensator.-   10.8.3 PI compensator.-   10.8.4 Lag compensator.-   10.8.5 PID compensator.-   10.9 Multivariable systems.-   10.9.1 Performance specification.-   10.9.2 Small gain theorem.-   10.9.3 Stability robustness tests.-   10.9.4 Residual dynamics.-   10.10References.-   10.11Problems.-   11 Optimal control.-   11.1 Introduction.-   11.2 Quadratic integral.-   11.3 Deterministic LQR.-   11.4 Stochastic response to a white noise.-   11.4.1 Remark.-   11.5 Stochastic LQR.-   11.6 Asymptotic behavior of the closed-loop.-   11.7 Prescribed degree of stability
  •   11.8 Gain and phase margins of the LQR.-   11.9 Full state observer.-   11.9.1 Covariance of the reconstruction error.-   11.10Kalman-Bucy Filter (KBF).-   11.11Linear Quadratic Gaussian (LQG).-  11.12Duality.-   11.13Spillover.-   11.13.1Spillover reduction.-   11.14Loop Transfer Recovery (LTR).-   11.15Integral control with state feedback.-   11.16Frequency shaping.-   11.16.1Frequency-shaped cost functionals.-   11.16.2Noise model ..-   11.17References.-   11.18Problems.-   12 Controllability and Observability.-   12.1 Introduction.-  12.1.1 Definitions.-   12.2 Controllability and observability matrices.-   12.3 Examples.-   12.3.1 Cart with two inverted pendulums.-   12.3.2 Double inverted pendulum.-   12.3.3 Two d.o.f. oscillator.-   12.4 State transformation.-   12.4.1 Control canonical form.-   12.4.2 Left and right eigenvectors.-   12.4.3 Diagonal form.-   12.5 PBH test.-   12.6 Residues.-   12.7 Example.-   12.8 Sensitivity.-   12.9 Controllability and observability Gramians.-   12.10Internally balanced coordinates.-   12.11Model reduction.-   12.11.1Transfer equivalent realization.-   12.11.2Internally balanced realization.-   12.11.3Example.-  12.12References.-   12.13Problems.-   13 Stability.-   13.1 Introduction.-   13.1.1 Phase portrait.-   13.2 Linear systems.-   13.2.1 Routh-Hurwitz criterion.-   13.3 Lyapunov's direct method.-   13.3.1 Introductory example.-   13.3.2 Stability theorem.-   13.3.3 Asymptotic stability theorem.-   13.3.4 Lasalle's theorem.-   13.3.5 Geometric interpretation.-   13.3.6 Instability theorem.-   13.4 Lyapunov functions for linear systems.-   13.5 Lyapunov's indirect method ..-  13.6 An application to controller design.-  13.7 Energy absorbing controls.-   13.8 References.-   13.9 Problems.-   14 Applications.-   14.1 Digital implementation.-   14.1.1 Sampling, aliasing and prefiltering.-   14.1.2 Zero-order hold, computational delay.-   14.1.3 Quantization.-   14.1.4 Discretization of a continuous controller.-   14.2 Active damping of a truss structure.-   14.2.1 Actuator placement.-   14.2.2 Implementation, experimental results.-   14.3 Active damping generic interface.-   14.3.1 Active damping.-   14.3.2 Experiment.-   14.3.3 Pointing and position control.-   14.4 Active damping of a plate.-   14.4.1 Control design.-   14.5 Active damping of a stiff beam.-   14.5.1 System design.-  14.6 The HAC/LAC strategy.-   14.6.1 Wide-band position control.-   14.6.2 Compensator design.-   14.6.3 Results.-   14.7 Vibroacoustics: Volume displacement sensors.-   14.7.1 QWSIS sensor.-   14.7.2 Discrete array sensor.-   14.7.3 Spatial aliasing.-  14.7.4 Distributed sensor.-   14.8 References.-   14.9 Problems.-   5 Tendon Control of Cable Structures.-   15.1 Introduction.-   15.2 Tendon control of strings and cables.-   15.3 Active damping strategy.-   15.4 Basic Experiment.-   15.5 Linear theory of decentralized active damping.-  15.6 Guyed truss experiment.-   15.7 Micro Precision Interferometer testbed.-   15.8 Free floating truss experiment.- .

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