An Introduction to Control Systems

The following sections are included:

• Contents

• Preface

• Preface to the Second Edition

• About the author

The following sections are included:

• General introduction

• A concise history of control

• Open-loop control

• Closed-loop control
  • Effects of feedback

• Some examples of control systems

• Definitions of standard terminology

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• Transfer functions
  • Transfer functions – worked example
  • The impulse response
  • Linear approximations
  • Linear approximations – worked examples

• Block diagrams
  • Basic building blocks
  • Block diagram manipulation
  • Block diagrams – worked examples

• Physical system realizations
  • Electrical networks
  • Mechanical systems
  • Analogous circuits

• Electromechanical devices
  • DC motors
  • Generator

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• Steady-state response
  • Control test inputs
  • Sinusoidal and polynomial inputs
  • Step, ramp and parabolic inputs

• Transient response
  • Overdamped response
  • Critically damped response
  • Underdamped response

• Errors
  • System type
  • Steady-state errors
  • Transient errors
  • Disturbances
  • Sensitivity

• Servomechanisms
  • Gears
  • Servomechanism transient response

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• The Routh–Hurwitz criterion
  • Routh–Hurwitz stability test
  • Special cases
  • Relative stability

• Root loci construction
  • Root loci: some basic properties
  • Branches and asymptotes
  • Angles of departure and arrival
  • Breakaway points
  • Worked example

• Application of root loci
  • Roots of a polynomial
  • Time delay systems
  • Sensitivity to parameter variations

• Compensation based on a root locus
  • First-order compensation
  • Phase and magnitude compensation

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• The Bode diagram
  • Logarithmic plots
  • Asymptotic approximations
  • Complex roots

• Compensation using the Bode plot
  • Gain and phase margins
  • Gain compensation
  • Lag/lead compensation

• The Nyquist stability criterion
  • Frequency response plots
  • The Nyquist criterion
  • Relative stability

• Compensation using the Nyquist plot
  • Gain compensation
  • Lag/lead compensation

• The Nichols chart
  • Relative stability
  • Closed-loop frequency response

• Compensation using the Nichols chart
  • Gain compensation
  • Lag/lead compensation

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• State equations from transfer functions
  • Matrix representations
  • Transfer functions
  • Worked example

• Solution to the state equations
  • The state transition matrix
  • Properties of the state transition matrix
  • General solution of the state equation
  • Worked example

• The characteristic equation
  • Eigenvalues and eigenvectors
  • Cayley–Hamilton theorem

• Canonical forms
  • State variable transformation
  • Phase variable canonical form
  • Diagonalization
  • Jordan canonical form

• Decomposition
  • Partial fraction decomposition
  • Direct decomposition

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• Controllability and observability
  • Concepts of controllability and observability
  • Tests for controllability and observability
  • Invariant theorems

• Controllability and observability in transfer functions
  • Transfer function realization
  • Pole-zero cancellation

• State variable feedback
  • Pole placement
  • Optimal control

• State estimation
  • Asymptotic estimation
  • Observer and system stability

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• Sampled data systems
  • Delay operator representation
  • Z-transform analysis
  • Properties of the z-transform

• Stability analysis
  • The unit circle
  • Zero order hold (ZOH)
  • Worked example for ZOH system

• Digital compensation
  • Transfer function time response
  • Time response – worked example
  • Compensator design

• State variable forms
  • State variables for discrete time systems
  • Solution of state equations
  • Worked example

• Pole placement design
  • State feedback pole placement
  • Worked example using state feedback
  • Polynomial pole placement
  • Worked example showing polynomial pole placement

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• System simulation
  • Analog models
  • Software models

• Computer control
  • Data logging
  • Real-time control
  • Simulated application
  • Expert systems and artificial intelligence
  • Fuzzy logic controllers
  • Operational problems

• Computer-aided design
  • Modeling and identification
  • Controller design

• Summary

• Problems

• Further reading

The following sections are included:

• Introduction

• Proportional control
  • Continuous-time proportional controller
  • Discrete-time proportional controller

• Proportional + integral control
  • Continuous-time proportional + integral controller
  • Discrete-time proportional + integral controller

• PID control
  • Proportional + derivative control
  • Proportional + integral + derivative control
  • Discrete-time P + I + D controller
  • Worked example

• Summary

• Problems

• Further reading

The following sections are included:

• Appendices
  • Appendix 1 Matrix algebra
    • Basic notations
    • Matrix operations
    • Matrix manipulation
    • Simultaneous equations solution
    • Further reading
  • Appendix 2 Tables of common transforms
  • Appendix 3 Nonlinear systems
    • Analysis at the extremes
    • Analysis about a fixed operating point
    • Describing functions
  • Appendix 4 Unity feedback loops

• Index