Consider the system represented in the figure
![2482_Obtain the response of the system.png](https://secure.tutorsglobe.com/CMSImages/2482_Obtain%20the%20response%20of%20the%20system.png)
where
Gp (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 Kmax 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= Kmax/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