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The Basics of the Nyquist Stability Criterion

The Basics of the Nyquist Stability Criterion
9
Submitted by Brian Douglas on 12/25/2020
Explanation 4 resources
Last Edited: 10/27/2023

The Nyquist Stability Criterion can be a bit confusing and daunting when you're first learning it.  This journey is set up to provide the basics in a straightforward and understandable way.  Once you understand these basics, you'll have a good foundation to build on.  This journey is broken up into several sections:

  1. Prerequisites - the information you might need before starting this journey
  2. Introduce the basic concepts - an overview of the criterion with minimal mathematics
  3. Fundamentals - A more mathematically rigorous approach to the criterion

Prerequisite - If you don't have a lot of experience with the Nyquist plot, then it might be useful to review the three major LTI plotting techniques first: Nichols chart, Bode plot, and Nyquist plot. If you understand the basics of the Nyquist plot then you can skip this resource.

Introduce the basic concepts - This video provides a gentle introduction to the Cauchy Argument Principle and shows an animation that I think will help the Nyquist Stability Criterion make more sense (part 1).

Introduce the basic concepts - This is a continuation of the above video.

Fundamentals - If you'd like to see a more rigourous explanation of the criterion the Wikipedia article is actually pretty great.  Hopefully, after the above resources the mathematics will make more sense.