3rd Edition

Classical Feedback Control with Nonlinear Multi-Loop Systems
With MATLAB® and Simulink®, Third Edition

ISBN 9781138541146
Published August 21, 2019 by CRC Press
574 Pages 592 B/W Illustrations

USD $139.95

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Book Description

Classical Feedback Control with Nonlinear Multi-Loop Systems describes the design of high-performance feedback control systems, emphasizing the frequency-domain approach widely used in practical engineering. It presents design methods for high-order nonlinear single- and multi-loop controllers with efficient analog and digital implementations. Bode integrals are employed to estimate the available system performance and to determine the ideal frequency responses that maximize the disturbance rejection and feedback bandwidth. Nonlinear dynamic compensators provide global stability and improve transient responses. This book serves as a unique text for an advanced course in control system engineering, and as a valuable reference for practicing engineers competing in today’s industrial environment.

Table of Contents


To Instructors

  1. Feedback and Sensitivity
  2. 1.1 Feedback Control System

    1.2 Feedback: Positive and Negative

    1.3 Large Feedback

    1.4 Loop Gain and Phase Frequency Responses

    1.5 Disturbance Rejection

    1.6 Example of System Analysis

    1.7 Effect of Feedback on the Actuator Nondynamic Nonlinearity

    1.8 Sensitivity

    1.9 Effect of Finite Plant Parameter Variations

    1.10 Automatic Signal Level Control

    1.11 Lead and PID Compensators

    1.12 Conclusion and a Look Ahead


    Answers to Selected Problems

  3. Feedforward, Multi-loop, and MIMO Systems
  4. 2.1 Command Feedforward

    2.2 Prefilter and the Feedback Path Equivalent

    2.3 Error Feedforward

    2.4 Black’s Feedforward

    2.5 Multi-loop Feedback Systems

    2.6 Local, Common, and Nested Loops

    2.7 Crossed Loops and Main/Vernier Loops

    2.8 Block Diagram Manipulations and Transfer Function Calculations

    2.9 MIMO Feedback Systems


  5. Frequency Response Methods
  6. 3.1 Conversion of Time Domain Requirements to Frequency Domain

    3.2 Closed-Loop Transient Response

    3.3 Root Locus

    3.4 Nyquist Stability Criterion

    3.5 Robustness and Stability Margins

    3.6 Nyquist Criterion for Unstable Plants

    3.7 Successive Loop Closure Stability Criterion (Bode-Nyquist)

    3.8 Nyquist Diagrams for Loop Transfer Functions with Poles at the Origin

    3.9 Bode Phase-Gain Relation

    3.10 Phase Calculations

    3.11 From the Nyquist Diagram to the Bode Diagram

    3.12 Non-minimum Phase Lag

    3.13 Ladder Networks and Parallel Connections of M.P. Links

    3.14 Other Bode Definite Integrals


    Answers to Selected Problems

  7. Shaping the Loop Frequency Response
  8. 4.1 Optimality of the Compensator Design

    4.2 Feedback Maximization

    4.3 Feedback Bandwidth Limitations

    4.4 Coupling in MIMO Systems

    4.5 Shaping Parallel Channel Responses


    Answers to Selected Problems

  9. Compensator Design
  10. 5.1 Loop Shaping Accuracy

    5.2 Asymptotic Bode Diagram

    5.3 Approximation of Constant Slope Gain Response

    5.4 Lead and Lag Links

    5.5 Complex Poles

    5.6 Cascaded Links

    5.7 Parallel Connection of Links

    5.8 Simulation of a PID Controller

    5.9 Analog and Digital Controllers

    5.10 Digital Compensator Design


    Answers to Selected Problems

  11. Analog Controller Implementation
  12. 6.1 Active RC Circuits

    6.2 Design and Iterations in the Element Value Domain

    6.3 Analog Compensator, Analog or Digitally Controlled

    6.4 Switched-Capacitor Filters

    6.5 Miscellaneous Hardware Issues

    6.6 PID Tunable Controller

    6.7 Tunable Compensator with One Variable Parameter

    6.8 Loop Response Measurements


    Answers to Selected Problems

  13. Linear Links and System Simulation
  14. 7.1 Mathematical Analogies

    7.2 Junctions of Unilateral Links

    7.3 Effect of the Plant and Actuator Impedances on the Plant Transfer Function Uncertainty

    7.4 Effect of Feedback on the Impedance (Mobility)

    7.5 Effect of Load Impedance on Feedback

    7.6 Flowchart for Chain Connection of Bidirectional Two-Ports

    7.7 Examples of System Modeling

    7.8 Flexible Structures

    7.9 Sensor Noise

    7.10 Mathematical Analogies to the Feedback System

    7.11 Linear Time-Variable Systems


    Answers to Selected Problems

  15. Introduction to Alternative Methods of Controller Design
  16. 8.1 QFT

    8.2 Root Locus and Pole Placement Methods

    8.3 State-Space Methods and Full-State Feedback

    8.4 LQR and LQG

    8.5 H, µ-Synthesis, and Linear Matrix Inequalities

  17. Adaptive Systems
  18. 9.1 Benefits of Adaptation to the Plant Parameter Variations

    9.2 Static and Dynamic Adaptation

    9.3 Plant Transfer Function Identification

    9.4 Flexible and N. P. Plants

    9.5 Disturbance and Noise Rejection

    9.6 Pilot Signals and Dithering Systems

    9.7 Adaptive Filters

  19. Provision of Global Stability
  20. 10.1 Nonlinearities of the Actuator, Feedback Path, and Plant

    10.2 Types of Self-Oscillation

    10.3 Stability Analysis of Nonlinear Systems

    10.4 Absolute Stability

    10.5 Popov Criterion

    10.6 Applications of Popov Criterion

    10.7 Absolutely Stable Systems with Nonlinear Dynamic Compensation


    Answers to Selected Problems

  21. Describing Functions
  22. 11.1 Harmonic Balance

    11.2 Describing Function

    11.3 Describing Functions for Symmetrical Piece-Linear Characteristics

    11.4 Hysteresis

    11.5 Nonlinear Links Yielding Phase Advance for Large-Amplitude Signals

    11.6 Two Nonlinear Links in the Feedback Loop

    11.7 NDC with a Single Nonlinear Nondynamic Link

    11.8 NDC with Parallel Channels

    11.9 NDC Made with Local Feedback

    11.10 Negative Hysteresis and Clegg Integrator

    11.11 Nonlinear Interaction between the Local and the Common Feedback Loops

    11.12 NDC in Multi-loop Systems

    11.13 Harmonics and Intermodulation

    11.14 Verification of Global Stability


    Answers to Selected Problems

  23. Process Instability
  24. 12.1 Process Instability

    12.2 Absolute Stability of the Output Process

    12.3 Jump Resonance

    12.4 Subharmonics

    12.5 Nonlinear Dynamic Compensation


  25. Multiwindow Controllers
  26. 13.1 Composite Nonlinear Controllers

    13.2 Multiwindow Control

    13.3 Switching from a Hot Controller to a Cold Controller

    13.4 Wind-Up and Anti-Wind-Up Controllers

    13.5 Selection Order

    13.6 Acquisition and Tracking

    13.7 Time-Optimal Control

    13.8 Examples


  27. Nonlinear Multi-Loop Systems with Uncertainty

14.1 Systems with High-Frequency Plant Uncertainty

14.2 Stability and Multi-frequency Oscillations in Band-Pass Systems

14.3 Bode Single-loop Systems

14.4 Multi-Input Multi-Output Systems

14.5 Nonlinear Multi-loop Feedback

14.6 Design of the Internal Loops

14.7 Input Signal Reconstruction

Appendix 1: Feedback Control, Elementary Treatment

Appendix 2: Frequency Responses

Appendix 3: Causal Systems, Passive Systems, Positive Real Functions, and Collocated Control

Appendix 4: Derivation of Bode Integrals

Appendix 5: Program for Phase Calculation

Appendix 6: Generic Single-Loop Feedback System

Appendix 7: Effect of Feedback on Mobility

Appendix 8: Regulation

Appendix 9: Balanced Bridge Feedback

Appendix 10: Phase-Gain Relation for Describing Functions

Appendix 11: Discussions

Appendix 12: Design Sequence

Appendix 13: Examples

Appendix 14: Bode Step Toolbox

Appendix 15: Nonlinear Multi-loop Feedback Control (Patent Application)




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Boris J. Lurie worked for many years in the telecommunication and aerospace industries, and taught at Russian, Israeli, and American universities. He was a senior staff member of the Jet Propulsion Laboratory, California Institute of Technology.

Paul J. Enright currently works in the field of quantitative finance in Chicago. As a member of the technical staff at the Jet Propulsion Laboratory, California Institute of Technology, he designed attitude control systems for interplanetary spacecraft and conducted research in nonlinear control.