Poles and Zeros of a transfer function.

1. 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?

2. 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.