3rd Edition

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

By Boris J. Lurie, Paul Enright Copyright 2020
    594 Pages 592 B/W Illustrations
    by CRC Press

    594 Pages 592 B/W Illustrations
    by CRC Press

    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.


    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 H8, 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)





    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.