1. HOMEWORK-04
Problem 04-01
In a closed loop control system shown in the figure, the process transfer function is Gp(s)=(2s+3)/(s3+6s2-28s) and Gc=K. a) Is the system stable for K=100? b) Find the steady-state error for a parabolic input when K=80.
Problem 04-02
Kuo-91 (Sh.302)
The closed loop control diagram of a motor control system with tachometer feedback is shown in the figure. Find Kt values for which the system is stable.
Answer:

2. Problem 04-03
Thompson (Sh. 131)
Find the PID coefficients of a closed-loop control system whose process transfer function is G(s) using Ziegler-Nichols design method. Write the MATLAB code to find the step response.
Answer:
Problem 04-04
A closed-loop control system becomes unstable when the controller gain is greater than For this gain, the roots of the denominator are -2.4, ±1.8i, -1±3.6i. Find the controller coefficients for a PI controller using Ziegler-Nichols design criteria.
Problem 04-05
Compare the step responses of the control system of Example 4.2 for P, PI and PID controllers.

3. 2K-28>0  K>14 SOLUTIONS Problem 04-01:
Transfer function of the closed-loop system is
According to Hurwitz
2K-28>0  K>14
For stability K>18.66
The control system is STABLE for K=100

4. SOLUTIONS
For K=80
The system can not follow the parabolic reference.

5. SOLUTIONS
Problem 04-02:
Transfer function of the closed-loop system is
According to Hurwitz

6. SOLUTIONS
Problem 04-03:
Transfer function of the closed-loop system is
According to Hurwitz K>0

7. SOLUTIONS
>>a=[ ];
>>roots(a)
ωcr=1 rad/s

8. SOLUTIONS
Problem 04-04:
A closed-loop control system becomes unstable when the controller gain is greater than For this gain, the roots of the denominator are -2.4, ±1.8i, -1±3.6i. Find the controller coefficients for a PI controller using Ziegler-Nichols design criteria.