Question

2. Nise (9.3) For a unity feedback system with 10% OS: KG(s) Ts)- 1+ KGS) G(s) (s +2)(s +3) (s +7) NOTE: the 10% overshoot line is 126.16" with a 7-59. a. Find the K value of the system at 10% OS if this corresponds to a point on the root locus of s-1.87+j2.56 NOTE: use the fact that 1 + KG(6) -0 at all points on the root locus,so K -() convert your G(s) to a exponential magnitude to find K (only have to compute the magnitude in this casel) b. What is the system type of this transfer function and value of the appropriate steady state error constant (Kss)? NOTE: review the steady state error defintions & table from lecture & handouts b. Assuming that the steady state error constant for part b shows the current system has a is Ks .98, Design a lag compensator that improves the Kss to 4. NOTE: Remember the new Ks will be different from the old one by the following ratio: Pe c. Plot the tf step response of the old system and the new and show that the steady state error has improved

Answer 1

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matlab code:

clc;

clear all;

close all;

s=tf('s');

k=41.1243;

g=k/((s+2)*(s+3)*(s+7));%plant

gc=(s+0.01)/(s+0.0024);%controller

step(feedback(g,1));% step response

legend('uncompensated system')

figure

step(feedback(g*gc,1));% step response

legend('compensated system')

File Edit View Insert Tools Desktop Window Help Step Response Fina value: 0.485 04 0.1 25 0.5 Time (seconds)

File Edit View Insert Tools Desktop Window Help Step Response Final value: 0803 08 06 04 03 100 200 300 400 600 700 900 Time (seconds)