-
Notifications
You must be signed in to change notification settings - Fork 0
/
Pole-zero plot for given DT system.m
102 lines (78 loc) · 3.21 KB
/
Pole-zero plot for given DT system.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
% Program V4_2
%%%Demo: % Pole-zero plot
%%% Developed by Dr. M. Venu Gopala Rao,
%%% Email: mvgr03@kluniversity.in, mvgr03@gmail.com,
clear all; close all;clc
%------------------------------------------------------------------------
%%% Demo1:
% Find the poles and zeros of the following transfer function and plot
% them onto the z plane. Is this system stable? Why?
% H[z]= 1/(1-0.9z^-1)
b = [1,0]; a = [1, -0.9];
[H1,H2,H3] = zplane(b,a);
set(H1,'markersize',10,'color',[0,1,0]);
set(H2,'markersize',10,'color',[1,0,0]);
title('Pole-Zero Plot');
text(0.85,-0.1,'0.9');text(0.01,-0.1,'0');
% Q. Is this system stable? Why?
%
% Ans. Yes the system is stable, since all of its poles lie inside of unit
% circle on the z-plane as shown in above figure.
%------------------------------------------------------------------------
%%% Demo2:
% Find the poles and zeros of the following transfer function and plot
% them onto the z plane. Is this system stable? Why?
% z^-1/1-1.4z^-1
num =[1,0] ;
den = [1 -1.4] ;
poles =roots(den);
zeroes = roots(num);
%%% Plotting Pole-zero diagram.
zplane(num,den);
title('Pole zero diagram');grid on
% Q. Is this system stable? Why?
%
% Ans. No the system is unstable, since all of its poles lie outside side of unit
% circle on the z-plane as shown in above figure.
%------------------------------------------------------------------------
%%% Demo3:
% Find the poles and zeros of the following transfer function and plot
% them onto the z plane. Is this system stable? Why?
% H(z) = (2-z^-1) / (1-0.1z^-1 - 0.02z^-2)
% Matlab algorithm is as follows
%
% Solution
num =[2 -1]
den = [1 -0.1 -.02]
poles = roots(den)
zeroes = roots(num)
figure(); zplane(num,den); grid on;
title('Pole-zero plot');
% Ans:
% poles = 0.2000, -0.1000
% zeroes = 0.5000
%
% Q. Is this system stable? Why?
%
% Ans. Yes the system is stable, since all of its poles lie inside of unit
% circle on the z-plane as shown in above figure.
%------------------------------------------------------------------------
%%% Demo4:
% Find the poles and zeros of the following transfer function and plot
% them onto the z plane.
% H(z) = (2.25-2.1z-1-3.95z-2 -1.6z-3 -0,2z-4) / (4-2.96z-1 +0,8z-2 -0,118z-3 -0,0064z-4)
%
% Solution
num =[2.25 -2.1 -3.95 -1.6 -0.2]
den = [4 -2.96 -0.8 -0.118 -0.0064]
poles =roots(den)
zeroes = roots(num)
figure(); zplane(num,den); grid
title('Pole-zero plot');
% poles = 0.9773, -0.0750 + 0.1147i, -0.0750 - 0.1147i, -0.0872
% zeroes = 2.0000, -0.4000, -0.3333, -0.3333
%
% Q. Is this system stable? Why?
%
% Ans. Yes the system is stable, since all of its poles lie inside of unit
% circle on the z-plane as shown in above figure.