June 2019 – Fundamentals of Linear Control: A Concise Approach

Step-by-step Nyquist plot example. Part III

One more on Nyquist plots this time for a non-minimum-phase transfer-function with a pole at the origin.

Step-by-step Nyquist plot example. Part II

Second part of our posts on the Nyquist plot. This time with a non-minimum-phase transfer-function.

Step-by-step Nyquist plot example. Part I

We went over how to sketch straight-line approximations in Bode plots in a series of posts. In this post we continue those examples by going from the Bode plot to a Nyquist plot.

The “correct” phase of the frequency response

When plotting the phase of a model’s frequency response there will always be ambiguity on representing angles, after all angles are equivalent modulus $2 \pi$. However, when plotting the frequency response in a Bode plot, it is customary to unwrap the phase and display the plot as a curve whose image often spans more than $2 \pi$. In that sense, one should also care about any potential integer multiples of $2 \pi$ shifts of the curve. Yet, I have never seen a discussion on what the “correct” shift should be.

Step-by-step Bode plot example. Part IV

We continue our saga of hand sketches of the straight-line approximations for the magnitude and phase of Bode plot diagrams (Section 7.1). This time we consider a non-minimum phase system with a pole at the origin. See Part I, Part II and Part III, for simpler examples.

Step-by-step Bode plot example. Part III

We have gone step-by-step over how to sketch straight-line approximations for the magnitude and phase diagrams of the Bode plot for a simple rational transfer-function. This transfer-function had only left-hand side poles and zeros, that is it was minimum-phase (see Section 7.2). In this post we consider a non-minimum phase transfer-function with a right-hand side zero. See Section 7.1 for details on the approximations.