Problem: Consider the system given
Design the value of K to yield 1.52% overshoot. Also estimate the settling time, peak
time and steady-state error.
pOS=1.52,
zeta=-log(pOS/100)/sqrt(pi^2+(log(pOS/100))^2)
>> s=tf('s')
Transfer function:
s
>> G=(s+1.5)/s/(s+1)/(s+10)
Transfer function:
s + 1.5
------------------s^3 + 11 s^2 + 10 s
>> rlocus(G)
The root locus plot from the book:
Step responses for three cases (case1, 2 and 3 are indicated in the table).
G=(s+1.5)/s/(s+1)/(s+10)
K=7.36,
T=feedback(K*G,1)
step(T)
hold on, pause
K=12.79,
T=feedback(K*G,1)
step(T), pause
K=39.64,
T=feedback(K*G,1)
step(T)
hold off
Example: 9.3 For the given system below, design a PD controller to yield 16% overshoot
with a threefold reduction in settling time.
Root locus of the system showing the gain for 16% os:
After PD control:
And now step responses for the uncompansated and PD controlled system: