Example Consider the system shown in Figure:
If 𝑲=𝟏, the input is a unit step input, the sampling period 𝑻=𝟎.𝟓 𝐬𝐞𝐜 and the plant transfer function is:
a. Determine open loop pulse transfer function 𝑪(𝒛)/𝑬(𝒛).
b. Determine steady state (Final) value of the open loop system output.
c. Determine open loop response.
d. Determine closed loop pulse transfer function.
e. Determine steady state (Final) value of the closed loop system output.
f. Determine closed loop response.
g. For 𝑲=𝟒, 𝑻=𝟎.𝟓 sec. Determine the error constants 𝑲_𝒑 & 𝑲_𝒗 & 𝑲_𝒂 and the related steady state error.
h. Find the range of gain 𝑲 to make the system stable by using the Jury’s stability test and Modified Routh (Bilinear Transforma...