Closed loop stability nyquist

Question 1

Define the nyquist criterion

Answer 1

A closed loop system is stable under unity feedback if:
-Frequency reponse magnitude is less than 1
-frequency response phase is 180

Question 1

In a closed loop system how does positive feedback occur?

Answer 1

When the phase of the system is 180

Question 2

For positive feedback, what makes a system unstable and why?

Answer 2

If the the magnitude is greater than 1, the sum becomes an infinte series, making it unstable.

Question 3

On a nyquist plot, how do we determine stability?

Answer 3

-Find the point where the plot crosses the negative real axis
-If the point is to the left of -1, the system is unstable
-If the plot doesnt cross, the CL system is stable

Question 4

How do we determine closed-loop stability from a bode plot?

Answer 4

-Find frequency at which phase is -180
-if the magnitude is above 0dB, the CL is unstable
-CL is also stable is phase is always above -180