Control Engineering Basics
Which of the following correctly describes the Nyquist stability criterion?
- AIt builds a table from the coefficients of the closed-loop characteristic equation and counts the poles in the right half of the s-plane from the number of sign changes in the first column of that table
- BIt determines the stability of the closed-loop system from how the polar plot of the frequency response L(jω) of the loop transfer function goes around the point −1
- CIt measures the closed-loop step response and judges the system stable if the overshoot is smaller than a fixed value
Show answer and explanation
Answer: B. It determines the stability of the closed-loop system from how the polar plot of the frequency response L(jω) of the loop transfer function goes around the point −1
The Nyquist stability criterion draws the frequency response of the loop transfer function L(s) as a polar plot (Nyquist plot) and examines the stability of the closed loop from its position relative to the point −1. When the loop transfer function has no poles in the right half of the s-plane, the closed loop is stable if the plot does not encircle the point −1. Its strengths are that the characteristic equation need not be solved and that it can be used with a measured frequency response and with systems containing a time delay. The gain margin and phase margin are measures of how far the plot stays from the point −1.
- A. This describes the Routh stability criterion.
- B. Correct. The open-loop frequency response tells the stability of the closed loop.
- C. The size of the overshoot gives an idea of the degree of stability, but it is not a stability criterion.