Question

Design three lead compensators for the system to reduce the settling factor by a factor of 2 while maintaining %30 overshoot for the system C(s) s(s 4) (s 6) Solution: Root-Locus and the desired pole location (-0.358 Desired compensated dominant pole -2.014 +j5.252 j5 j4 j3 j2 jl Uncompensated dominant pole s-plane -1.007 +j2.627 K = 63.21 110.98。 7 -6-5-4-321 0 X- Closed-loop pole x-open-loop pole

Can someone please show me how to perform this problem using MATLAB. My professor wants us to simulate this problem using MATLAB and create the graph. Any help would

be very much appreciated.

Answer 1

matlab simulation:

inornt 03 一2-014 2-2-01 0 525レ +2-2426 S 8286 (sナ2.7416) ,

clc;

clear all;

close all;

s=tf('s');

g=1/(s*(s+4)*(s+6)); % plant transfer function

gc=(s+2.7426)/(s+11.5286);% controller transfer function

rlocus(g,g*gc);grid % root locus of compensated and uncompensated system

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

File Edit View Insert Tools Desktop Window Help Root Locus 0.7 56. 042 0.82 0.91 10 Pole: -2.03+5.23 Damping: 0.362 Overshoot 25 Frequency (rads:5.61 Sysem: g Gat 58.2 Pole:-104-2.53 Damping: 0381 Overshoot (%): 27.4 Frequency (radis):2.74 30 .975 91 20 0 82 o.7 0.42 028 0.14 15 Real Axis (seconds ) 10 10

plz comment if ant thing else is required