Homework Answers
(a).
MatLab Code:
Gs=tf(1,[1 1 0]); % Open-Loop Transfer Function
%Closed-Loop System with
negative unity feedback system.
sysC=feedback(Gs,1)
Output:
sysC =
1
-----------
s^2 + s + 1
(b).
MatLab Code:
% Open-Loop System:
Gs=tf(1,[1 1 0]);%Original Continious time system
% Implementing ZOH by discretizing
Ts1=0.1;%Sampling Period
Gz1=c2d(Gs,Ts1); % Implement ZOH
sysD1=feedback(Gz1,1)%Closed-Loop system
Ts2=0.2;%Sampling
Period
Gz2=c2d(Gs,Ts2);% Implement ZOH
sysD2=feedback(Gz2,1) %Closed-Loop system
Ts3=2;%Sampling Period
Gz3=c2d(Gs,Ts3);% Implement ZOH
sysD3=feedback(Gz3,1) %Closed-Loop system
Output:
sysD1 =
0.004837 z + 0.004679
---------------------
z^2 - 1.9 z + 0.9095
Sample time: 0.1 seconds
Discrete-time transfer function.
sysD2 =
0.01873 z + 0.01752
--------------------
z^2 - 1.8 z + 0.8363
Sample time: 0.2 seconds
Discrete-time transfer function.
sysD3 =
1.135 z + 0.594
--------------------------
z^2 - 4.441e-16 z + 0.7293
Sample time: 2 seconds
Discrete-time transfer function.
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