Front Cover

Advanced Control Design with Application to Electromechanical Systems

Copyright

Contents

About the Author

Preface

Acknowledgment

1 Introduction

1.1 Modeling concepts

1.1.1 Mechanics paradigm

1.1.2 Electrical engineering paradigm

1.1.3 The control paradigm

1.1.4 Discrete-time systems

1.2 Principles of electrical circuits

1.2.1 Electrical circuit elements

1.2.2 Electrical systems

1.2.3 Simulation example 1.1

1.3 Electromagnetic devices

1.3.1 Faraday's law

1.3.2 Ampere's law

1.3.3 Force

1.3.4 DC machine construction

1.3.5 DC motor operation

1.3.6 DC motor equivalent circuit

1.3.7 DC generator operation

1.3.8 DC generator equivalent circuit

1.4 Principles of mechanical components

1.4.1 Mechanical elements

1.4.2 Mechanical systems

1.4.3 Simulation example 1.2

1.5 Electromechanical systems

1.5.1 Simulation example 1.3

1.6 Inverted pendulums

1.6.1 Dynamic modeling

1.6.2 Pendulums on cart

1.6.2.1 Single pendulum on cart

1.6.2.2 Double pendulums on cart

1.6.2.3 State-space representation

1.6.3 Inverted pendulum on pivot

1.6.3.1 Double inverted pendulum on pivot

1.6.3.2 Triple inverted pendulum on pivot

1.7 Feedback systems

1.7.1 Basic definitions

1.7.2 Feedback control systems

1.7.3 Open-loop control systems

1.7.4 Closed-loop control systems

1.7.5 Control systems design

1.7.6 Standard representations

1.7.7 State feedback

1.8 Basic structural properties

1.8.1 Stability

1.8.2 Controllability

1.8.3 Simulation example 1.4

1.8.4 Observability

1.8.5 Simulation example 1.5

1.8.6 Simulation example 1.6

1.8.7 Simulation example 1.7

1.8.8 Simulation example 1.8

1.9 Important notes

References

2 Mathematical Background

2.1 Finite-dimensional spaces

2.1.1 Vector spaces

2.1.2 Norms of vectors

2.1.3 Induced norms of matrices

2.1.4 Some basic topology

2.1.5 Convex sets

2.1.6 Continuous functions

2.1.7 Function norms

2.1.8 Mean-value theorem

2.1.9 Implicit function theorem

2.2 Matrix theory

2.2.1 Fundamental subspaces

2.2.2 Change of basis and invariance

2.2.3 Calculus of vector-matrix functions of a scalar

2.2.4 Derivatives of vector-matrix products

2.2.5 Quadratic forms and definiteness

2.2.6 Matrix ellipsoid

2.2.7 Power of a square matrix

2.2.8 Exponential of a square matrix

2.2.9 Eigenvalues and eigenvectors of a square matrix

2.2.10 The Cayley-Hamiltonian theorem

2.2.11 Trace properties

2.3 Partitioned matrices

2.3.1 The matrix inversion lemma

2.3.2 Strengthened version of lemma of Lyapunov

2.3.3 Kronecker product

2.3.4 Vec-operator

2.3.5 Relationships of vec-operator and Kronecker product

2.3.6 Kronecker sum

2.3.7 Application to Sylvester and Lyapunov equations

2.3.8 Simulation example 2.1

2.3.9 Simulation example 2.2

2.3.10 Simulation example 2.3

2.3.11 The singular-value decomposition

2.4 Important notes

References

3 Control Design of Continuous-Time Systems

3.1 Introduction

3.2 Linear control design

3.2.1 Nominal model

3.2.2 LQR: proportional gain

3.2.3 LQRI: proportional-integral gain

3.2.4 LQR+: proportional gain with disturbance rejection

3.2.5 LQRI+: proportional-integral gain with disturbance rejection

3.2.6 Deterministic minimum-energy estimation

3.2.7 Model predictive control

3.2.8 Dynamic feedback control design

3.3 Multiobjective state feedback

3.3.1 H2-performance

3.3.2 H2-design I

3.3.3 H8-performance

3.3.4 H8-design I

3.3.5 Mixed H2/H8-performance

3.4 Stabilization of distributed synchronous generators

3.4.1 Dynamics of the synchronous generator

3.4.2 Dynamic model of distributed synchronous generators

3.4.3 Equivalent linearized dynamics

3.4.4 State-space description

3.4.5 Model linearization

3.4.6 Improved H8-control

3.4.7 Lyapunov stability analysis

3.4.8 Robust state estimation

3.4.9 Control of an independently functioning synchronous generator

3.4.10 Control of the distributed synchronous generators

3.5 Rotational double inverted pendulum

3.5.1 Assumptions

3.5.2 Dynamic model

3.5.3 Single inverted pendulum-double inverted pendulum open-loop response

3.5.4 Single inverted pendulum LQR response

3.5.5 DIP on cart

3.5.6 Triple inverted pendulum

3.5.7 Simulation example 3.1

3.6 Wind turbines under islanded operation

3.6.1 Modeling of wind turbine systems

3.6.2 Aerodynamics modeling

3.6.3 Drivetrain modeling

3.6.4 Generator modeling

3.6.5 Integrated system model

3.6.6 Simulation example 3.2

3.7 Differentially steered wheeled mobile robot

3.7.1 Nonlinear dynamic modeling

3.7.2 Linearized model

3.7.3 LQR controller: proportional gain

3.7.4 LQRI controller

3.7.5 Backstepping control

3.7.6 Simulation example 3.3

3.8 Active vehicle suspension system

3.8.1 Introduction

3.8.2 Model of active suspension

3.8.3 Whole-preview control design

3.8.4 Partial-preview control

3.8.5 Simulation example 3.4

3.9 Important notes

References

4 Control Design of Discrete-Time Systems

4.1 Linear optimal control: discrete-time

4.1.1 A linear matrix inequality formulation

4.1.2 Linear quadratic integral: proportional-integral gain

4.1.3 Deterministic minimum-energy estimation

4.2 Dynamic feedback control

4.2.1 H2-design

4.2.2 H8-design

4.2.3 Case of modeling errors

4.2.4 Model predictive control

4.3 Simulation example 4.1

4.4 Simulation example 4.2

4.5 Important notes

References

5 Advanced Control Design

5.1 Introduction

5.1.1 Concept of sliding modes

5.1.2 Second-order relay systems

5.1.3 Nonlinear single-input system

5.1.4 Simulation example 5.1

5.1.5 Sliding mode of mechanical systems

5.1.6 Estimation and control of induction motors

5.2 Sliding-mode control of wind turbines

5.2.1 Introduction

5.2.2 Model of the doubly fed induction generator

5.2.3 Model of the grid side converter

5.2.4 Second-order sliding-mode control

5.2.5 Designing the rotor side converter controller

5.2.6 Designing the grid side converter controllers

5.2.7 Simulation example 5.2

5.2.8 Steady-state performances

5.2.9 Performances under external disturbances

5.3 Back electromotive force estimator for advanced control machines

5.3.1 NOx control in diesel engines

5.3.2 Automobile climate control

5.3.3 Binary sensor estimation

5.3.4 Antilock brake system control

5.3.5 Simulation example 5.3

5.4 Control of hard disk drive systems

5.4.1 Head tracking failure

5.4.2 Block diagram of hard disk drive

5.4.3 Design issues and objectives

5.4.4 Simulation example 5.5

5.4.5 A comparison

5.4.6 Simulation example 5.6

5.5 Continuous-time multimodel predictive control

5.5.1 Modeling of the wind turbine system

5.5.2 Aerodynamics

5.5.3 Drivetrain

5.5.4 Pitch actuator

5.5.5 Generator

5.5.6 Orthonormal set and Laguerre functions

5.5.7 Algorithm development

5.5.8 Multimodel predictive control

5.5.9 Simulation example 5.7

5.6 Important notes

References

6 Control Design of Electromechanical Systems

6.1 Magnetic levitation system

6.1.1 Principle of Maglev

6.1.2 Magnetic levitation control system: digital implementation

6.1.3 Magnetic-ball suspension system

6.1.4 Dynamic modeling of electromagnetic-suspension system

6.2 Dynamics and control of bicycles

6.2.1 System description

6.2.2 Problem statement

6.2.3 H2-control design

6.2.4 H8-control design

6.2.5 Simulation example 6.1

6.3 Double and triple inverted pendulums

6.4 Amplidyne-motor system

6.5 Inverted pendulum-type assistant robot

6.5.1 Simulation example 6.2

6.5.2 Simulation example 6.3

6.6 Mechanical elastic energy storage system

6.7 Microelectromechanical systems

6.7.1 Concept of piezoelectric energy conversion

6.7.2 Analysis of piezoelectric generators

6.7.3 Piezoelectric laminated-type generators

6.8 Wind turbine systems

6.8.1 Modeling of wind turbine systems

6.8.2 Aerodynamics modeling

6.8.3 Drivetrain modeling

6.8.4 Generator modeling

6.8.5 Grid modeling

6.8.6 Integrated system models

6.9 Continuous-time adaptive model predictive control

6.9.1 Introduction

6.9.2 Orthonormal set and Laguerre functions

6.9.3 System description

6.9.4 Adaptive updating law for the estimated system

6.9.5 Model predictive control design of the estimated system

6.9.6 Simulation example 6.7

6.10 Important notes

References

7 Multiagent Systems

7.1 Introduction

7.2 Elements of graph theory

7.2.1 Basic results

7.2.2 Laplacian spectrum of graphs

7.2.3 Properties of adjacency matrix

7.3 Linear quadratic regulator control

7.3.1 Computation of the L2-norm

7.3.2 Linear quadratic regulator performance region

7.3.3 LQR design

7.3.4 Application in multiagent supporting systems

7.3.5 Simulation example 7.1

7.3.6 Simulation example 7.2

7.3.7 Simulation example 7.3

7.4 Discrete-time multiagent systems

7.4.1 Introduction

7.4.2 Communication graph

7.4.3 Preliminaries

7.4.4 Stabilization

7.4.5 Illustrative example 7.4

7.5 Important notes

References

Appendix

A.1 Preliminaries and notations

A.2 Some bounding inequalities

A.2.1 Bounding inequality A

A.2.2 Bounding inequality B

A.2.3 Bounding inequality C

A.2.4 Bounding inequality D

A.2.5 Young's inequality

A.3 Gronwall-Bellman inequality

A.4 Schur complements

A.5 Main lemmas

A.6 Stability theorems

A.6.1 Lyapunov-Razumikhin theorem

A.6.2 Lyapunov-Krasovskii theorem

A.6.3 Halanay theorem

A.6.4 Practical stabilizability

A.6.5 Types of continuous Lyapunov-Krasovskii functionals

A.6.6 Some discrete Lyapunov-Krasovskii functionals

A.7 Linear matrix inequalities

A.7.1 Basics

A.7.2 Some standard problems

A.7.3 The S-procedure

A.8 Some Lyapunov-Krasovskii functionals

A.9 Some formulas on matrix inverses

A.9.1 Inverse of block matrices

A.9.2 Matrix inversion lemma

A.10 Partial differentiation

References

Index

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