Question

13. Consider the unity feedback system of Figure P11.1 with G(s) s(s+5s 20) The uncompensated system has about 55% overshoot and a peak time of 0.5 second when K 10. Do the following: [Section: 11.4] . Use frequency response methods to design a lead compensator to reduce the percent overshoot to 10%, while keeping the peak time and steady-state error about the same or less. Make any required second-order approximations. b. Use MATLAB or any other computer MATLAB ML program to test your second order approximation by simulating the system for your designed value of K.

Answer 1

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loo o 白 GD Cind b ISIS (st 26- osis)

matlab:

clc;

clear all;

s=tf('s');

g=1000/(s*(s+5)*(s+20));% plant

gc=6.6138*(s+3.939)/(s+26.0525); % controller

margin(g*gc);grid

figure

step(feedback(g*gc,1));grid

Bode Diagram Gm = 12 dB (at 23.8 rad s), Pma 46.8 deg (at 10.1 rads) 20 20 80 120 90 135 8 180 225 10° 102 10P 10 Frequency (rads)

Step Response 1.4 System untitied Peak amplnude: 1.21 Attime (seconcs):0.279 12 System: niriedi Sening time (seconds):0 648 02 0.4 Time (seconds)