Frequency Domain Analysis

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Prev: Transfer Functions Chapter 10 - Frequency Domain Analysis Next: PID Control

In this chapter we study how the stability and robustness of closed loop systems can be determined by investigating how sinusoidal signals of different frequencies propagate around the feedback loop. This technique allows us to reason about the closed loop behavior of a system through the frequency domain properties of the open loop transfer function. The Nyquist stability theorem is a key result that provides a way to analyze stability and introduce measures of degrees of stability.

Chapter contents

PDF (24 Jul 2020)

  1. The Loop Transfer Function
  2. The Nyquist Criterion
    • The Nyquist Plot
    • The General Nyquist Criterion
    • Conditional Stability
  3. Stability Margins
  4. Bode's Relations and Minimum Phase Systems
  5. Generalized Notions of Gain and Phase
    • System Gain and Passivity
    • Extensions of the Nyquist Criterion
    • Describing Functions
  6. Further Reading

Teaching Materials

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  • Additional Exercises

Supplemental Information