Digital Controller Design

Question 1

Relation between S and Z plane

Answer 1

z = exp(s*T)
z: location in z plane
s: location in the s plane
T: sampling time

Question 2

Stability in z plane

Answer 2

Determined by unit circle

Question 3

Equations for Transient Response

1. Damping and natural frequency
2. Natural Frequency
3. Damping Ration

Answer 3

1. D*wn >= 4.6/Ts
2. wn >= 1.8/Tr
3. D = -ln(Mp)/(sqrt(pi^2 + ln^2(Mp))