experiment

1. % Experiment-2 Identifiation of Pole and Zero of the given control system
%Ayush choudhary, Section A, Roll no. 18ESKEE024
%System-1
a=[1 2 13 45];
b=[10 12 14 15];
G=tf(a,b)% Creating transfer function of give coefficients
disp('Poles of the system are:')
pole(G) % Obtaining poles of the system
disp('Zeros of the system are:')
zero(G) % Obtaining Zeros of the system
disp('Zero Pole and Gain form of the given system is:')
zpk(G) % Creating transfer function (Pole and Zero)
disp('Step Response of the system is')
step(G) % Step response of the given system
Solution:
Transfer function:
s^3 + 2 s^2 + 13 s + 45
---------------------------
10 s^3 + 12 s^2 + 14 s + 15
Poles of the system are:
ans =
-1.1329
-0.0335 + 1.1502i
-0.0335 - 1.1502i
Zeros of the system are:
ans =
0.4449 + 3.9209i
0.4449 - 3.9209i
-2.8899
Zero Pole and Gain form of the given system is:
Zero/pole/gain:
0.1 (s+2.89) (s^2 - 0.8899s + 15.57)
------------------------------------
(s+1.133) (s^2 + 0.06708s + 1.324)
Step Response of the system is
Figure 1. Step Response of the System-1
0 50 100 150
0
1
2
3
4
5
Step Response
Time (sec)
Amplitude

2. % Experiment-2 Identifiation of Pole and Zero of the given control system
%Dr. Akash Saxena Section C-2, Roll no. SKITEE2021
%System-2
a=[17 22 13];
b=[100 12 65 14 15 97];
G=tf(a,b)% Creating transfer function of give coefficients
disp('Poles of the system are:')
pole(G) % Obtaining poles of the system
disp('Zeros of the system are:')
zero(G) % Obtaining Zeros of the system
disp('Zero Pole and Gain form of the given system is:')
zpk(G) % Creating transfer function (Pole and Zero)
disp('Step Response of the system is')
step(G) % Step response of the given system
Response
Transfer function:
17 s^2 + 22 s + 13
----------------------------------------------
100 s^5 + 12 s^4 + 65 s^3 + 14 s^2 + 15 s + 97
Poles of the system are:
ans =
0.6705 + 0.6889i
0.6705 - 0.6889i
-0.2848 + 1.0470i
-0.2848 - 1.0470i
-0.8914
Zeros of the system are:
ans =
-0.6471 + 0.5882i
-0.6471 - 0.5882i
Zero Pole and Gain form of the given system is:
Zero/pole/gain:
0.17 (s^2 + 1.294s + 0.7647)
----------------------------------------------------------
(s+0.8914) (s^2 - 1.341s + 0.9242) (s^2 + 0.5696s + 1.177)
Step Response of the system is
Figure 2. Step Response of System-2
0 5 10 15 20 25
-2
-1.5
-1
-0.5
0
0.5
1
x 10
6
Step Response
Time (sec)
Amplitude

3. % Experiment-2 Identifiation of Pole and Zero of the given control system
%Dr. Akash Saxena Section C-2, Roll no. SKITEE2021
%System-3
a=[17 22 ];
b=[12 65 97];
G=tf(a,b)% Creating transfer function of give coefficients
disp('Poles of the system are:')
pole(G) % Obtaining poles of the system
disp('Zeros of the system are:')
zero(G) % Obtaining Zeros of the system
disp('Zero Pole and Gain form of the given system is:')
zpk(G) % Creating transfer function (Pole and Zero)
disp('Step Response of the system is')
step(G) % Step response of the given system
Response
Transfer function:
17 s + 22
------------------
12 s^2 + 65 s + 97
Poles of the system are:
ans =
-2.7083 + 0.8650i
-2.7083 - 0.8650i
Zeros of the system are:
ans =
-1.2941
Zero Pole and Gain form of the given system is:
Zero/pole/gain:
1.4167 (s+1.294)
----------------------
(s^2 + 5.417s + 8.083)
Step Response of the system is
Figure 3. Step Response of System-3
0 0.5 1 1.5 2 2.5 3
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Step Response
Time (sec)
Amplitude

4. % Experiment-2 Identifiation of Pole and Zero of the given control system
%Dr. Akash Saxena Section C-2, Roll no. SKITEE2021
%System-4
a=[17 15 ];
b=[14 65 97];
G=tf(a,b)% Creating transfer function of give coefficients
disp('Poles of the system are:')
pole(G) % Obtaining poles of the system
disp('Zeros of the system are:')
zero(G) % Obtaining Zeros of the system
disp('Zero Pole and Gain form of the given system is:')
zpk(G) % Creating transfer function (Pole and Zero)
disp('Step Response of the system is')
step(G) % Step response of the given system
Response
Transfer function:
17 s + 15
------------------
14 s^2 + 65 s + 97
Poles of the system are:
ans =
-2.3214 + 1.2408i
-2.3214 - 1.2408i
Zeros of the system are:
ans =
-0.8824
Zero Pole and Gain form of the given system is:
Zero/pole/gain:
1.2143 (s+0.8824)
----------------------
(s^2 + 4.643s + 6.929)
Step Response of the system is
Figure 4. Step Response of System-4
0 0.5 1 1.5 2 2.5 3
0
0.05
0.1
0.15
0.2
0.25
Step Response
Time (sec)
Amplitude