Question

3. Nise(9.6) For a unity feedback system (s + 6) (s + 2)(s +3) (s +5) KG(s) G(s) Ts) a) Given a K-4.60, ζ;.707, on the 135° line, find the operating point on the root locus! NOTE: use the fact that 1 + KG(6) - 0 at all points on the root locus,so K r and Goi an KG(s)1 1(2k +1)180. Or use geometry using the point knowing that cose- b) Find the steady state error, and the steady state error constant c) What is the settling time & peak time for the current system? d) Design a proportional derivative compensator to reduce the settling time by 2. What is Ge (s), and what is the new Gn (s)- Ge(s).G(s), Where should the new zero be added at? What is the new gain at this new zero value. e) plot the step response for the old & new system to show the improvement

Answer 1

(St6) -2, 3149 2-3164」 726 2.3)49 fn) 356 3 Scanned withel CamScanner w2316u

The new setlin 0.8632 l4-63 a 63 + 4.63 GK(S+62-63) S4 63 463 Cs Scanned with CamScanner
step response:

clc;

clear all;

close all;

s=tf('s');

k=4.6;

g=(s+6)/((s+2)*(s+3)*(s+5));

gc=4.947*(s+6.7263);

step(feedback(k*g,1),feedback(g*gc,1))

legend('uncompensated system','compensated system')

File Edit View Insert Tools Desktop Window Help Step Response Sysiom: compensaed sysienm Seting ime (3econd):0.82 08 0.7 06 System: uncomcensaned systerm Setting time (seconds): 1.83 03 0.1 25 0.5 Time (seconds)
please rate