Question

please explain your anwser and show your work.

4.37 Consider the process control system with, the plant transfer function G(s) 0.9 S+0.4)(s+1.2) (a) Design a PI controller such the rise time is less than 2 sec. (b) Design a PID controller so the system has no overshoot.

Answer 1

Matlab Code:

s = tf('s');
P = 0.9/(s^2 + 1.6*s + 0.48);
figure
step(P)
stepinfo(P)

%PI Controller Design to set rise time lessthan 2 sec%
Kp = 35;
Ki = 0.196;
C1 = pid(Kp,Ki)
T1 = feedback(C1*P,1)
figure
step(T1)
stepinfo(T1)

%PID Controller design to set overshoot = 0 %
Kp = 35;
Ki = 0.196;
Kd = 40;
C2 = pid(Kp,Ki,Kd)
T2 = feedback(C2*P,1);
figure
step(T2)
stepinfo(T2)

StepResponse:

oo x Figure 1 File Edit View 80 Insert Tools Desktop Window Help A 3 IE Step Response ------------------------------------------------- Amplitude 2 4 6 12 14 16 18. 8 10 Time (seconds)

PI Controller response:

oo x Figure 2 File Edit View DO Insert Tools Desktop Window DV. 3 Help O E - Step Response 000 1.4. Amplitude 23 567 Time (seconds)

PID Controller Response:

Figure 3 File Edit La View Insert Tools Desktop Window Help k s IE - Step Response Amplitude 0 0.2 0.4 0.6 0. 8 1.4 1.6 1.8 2. 1 1.2 Time (seconds)