Nyquist Diagrams And Stability

Question 1

What points should you determine when sketching a Nyquist diagram?

Answer 1

Asymptotic behaviour (w —> 0, infinity), and a few points between

Question 2

Why does high gain at high freq lead to instability?

Answer 2

At higher freq, the inevitable delay in the feedback system means lag will eventually reach 180 degrees, at which point negative feedback becomes positive feedback in oscillating systems. If the gain at this point is not less than 1, this will lead to instability.

Question 3

What denotes instability on a Nyquist diagram?

Answer 3

If the loop passes through -1, the system is marginally stable. If it encloses -1, the system is unstable.

Question 4

What is the gain margin of a system?

Answer 4

The gain margin measures how much the gain of the return ratio can be increased before the closed loop system becomes unstable.

Question 5

What is the phase margin of a system?

Answer 5

A measure of how much phase lag can be added to the return ratio before the closed loop system becomes unstable

Question 6

How do you find gain margin from a Nyquist diagram?

Answer 6

The gain margin is 1/a, where a is the value at which the Nyquist curve crosses the real axis

Question 7

How do you find the phase margin from a Nyquist diagram?

Answer 7

The phase margin is the angle between the real axis and the point on the a Nyquist curve with a magnitude of 1

Question 8

How do you find gain margin from a bode plot?

Answer 8

Find the point at which the phase is -180, and measure the gain at that point, relative to 0db (1)

Question 9

How do you measure phase margin from a bode plot?

Answer 9

Find the point where gain is 0db, and measure the phase at that point relative to -180