Detemiine the range of values of k for the system to be

Question

Consider the system represented in the figure

where

G_p (s) = 1/s(10s + 1) and D(Z)= K(1 + z/z-1) and T = 0.1 s.

1. Obtain the closed loop r-to-y and e-to-y transfer functions in the z-domain

2. Obtain the characteritic equation

3. Obtain the static (dc) gain of the closed loop system

4. Detemiine the range of values of K for the system to be stable

5. Let K_max be the upper limit of K for stability. Obtain the response of the system to a unit step and check die steady-state error for K= K_max/2. Comment on the results.

6. For the same conditions of the previous question. obtain the response of the system to a ramp unput and check the steady-state error. Comment on the results