Control system

Arif Hussain, COMSATS Abbottabad Pakistan Page 1

Task1. For following systems, Find pole zeros location? Also find rise time Tr and settling time Ts.

Coding in MATLAB

clc

clear all

close all

G1=tf([1],[1 1]);

[p,z]=pzmap(G1)

S1=stepinfo(G1)

G2=tf([5],[1 2]);

[p,z]=pzmap(G2)

S2=stepinfo(G2)

G3=tf([1],[3 1]);

[p,z]=pzmap(G3)

S3=stepinfo(G3)

G4=tf([1],[7 1]);

[p,z]=pzmap(G4)

S4=stepinfo(G4)

G5=tf([1],[1 -5]);

[p,z]=pzmap(G5)

S5=stepinfo(G5)

Results

systems poles zeros Rise time (Tr) Settling time

(Ts)

G1(s) -1 Empty matrix 2.1970 3.9121

G2(s) -2 Empty matrix 1.0985 1.9560

G3(s) -0.333 Empty matrix 6.5910 11.7362

G4(s) -0.1429 Empty matrix 15.3790 27.3845

G5(s) 5 Empty matrix NaN NaN

The values of poles, zeros, Tr and Ts, as were shown in command

window.

Task2. For following circuit find equation for output voltage, pole zero location, Tr, Ts. Vin(t) is step voltage. R=50 ohm, C=50 mF?

Control system

Arif Hussain, COMSATS Abbottabad Pakistan Page 2

First of all we derive the circuit equation for above circuit by applying’ KVL’ loop equation. Then form the system function and implement it on MATLAB to get the required results.

MATLAB Coding

clc

clear all

close all

R=50;

C=0.005;

R*C

G1=tf([1],[R*C 1])

pzmap(G1)

grid on

figure

grid on

stepinfo(G1)

step(G1)

grid on

Results system pole zero Rise time (Tr) Settling time (Ts)

G(s) -4 Empty matrix 0.5493 0.9780

The above values of poles, zeros, Tr and Ts, as were seen in MATLAB command window.