Feedback Principles

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This chapter presents examples that illustrate fundamental properties of feed- back: disturbance attenuation, reference signal tracking, robustness to uncertainty, and shaping of behavior. The analysis is based on simple static and dynamical mod- els. After reading this chapter, readers should have some insight into the power of feedback, they should know about transfer functions and block diagrams, and they should be able to design simple feedback systems. The basic concepts described in this chapter are explained in more detail in the remainder of the text, and this chapter can be skipped for readers who prefer to move directly to the more detailed analysis and design techniques.

Chapter contents

PDF (24 Jul 2020)

  1. Nonlinear Static Models
    • Response to Reference Signals
    • Robustness to Parameter Uncertainty
    • Load Disturbance Attenuation
  2. Linear Dynamical Models
    • Linear Differential Equations and Transfer Functions
    • Stability: The Routh--Hurwitz Criterion
    • Block Diagrams and Transfer Functions
    • Computations Using Transfer Functions
  3. Using Feedback to Attenuate Disturbances
    • Proportional Control
    • Proportional-Integral (PI) Control
    • Unmodeled Dynamics
  4. Using Feedback to Track Reference Signals
    • Controllers with Two Degrees of Freedom
  5. Using Feedback to Provide Robustness
    • Reducing Effects of Parameter Variations and Nonlinearities
    • Nonlinear Analysis and Approximations
  6. Positive Feedback
    • Hewlett's Oscillator
    • Implementation of Integral Action by Positive Feedback
    • Positive Feedback Combined with Saturation
  7. Further Reading

Teaching Materials

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  • Additional Exercises

Supplemental Information

Additional Exercises

The following exercises cover some of the topics introduced in this chapter. Exercises marked with a * appear in the printed text.

Frequently Asked Questions


Python code

The following Python scripts are available for producing figures that appear in this chapter.

See the software page for more information on how to run these scripts.

Additional Information