MATLAB Simulink Assignment: Control Systems

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ASSIGNMENT I
QUESTION 1
Ships have fins which are the stabilizers in the reduction of the roll motion. The stabilizers can
be positioned by a closed-loop roll stabilizing system as designed in the MATLAB Simulink
figure below,
The transducer is the proportional controller for the open-loop transfer function,
G ( s ) H ( s ) = 22.5
( s+ 4 ) ( s2 +0.9 s+ 9 ) x 1 ( unity feedback )
G ( s ) H ( s ) = 22.5
( s3+ 4.9 s2 +12.6 s +36 ) x 1
Open-loop response c(t) to a unit impulse input,
Open-loop system response
1

QUESTION 2
The sampling theorem, according to Shannon-Nyquist, states that for one to recover the signal
function as sent, it is necessary to set a sample frequency of the time function at a rate greater
than twice its highest frequency component. By definition, it is given as,
f s ≥2 f c
Matlab Solution
%% Assignment 1: Question 2
GsHs=tf([22.5],[1 4.9 12.6 36])
bode(GsHs,{1,100})
grid on
2

-100
-50
0
50
Magnitude (dB)
100 101 102
-270
-180
-90
0
Phase (deg)
Bode Diagram
Frequency (rad/s)
At 3dB, the frequency in rad/sec is between 1-10 rad/sec as shown in the figure above.
T S= 1
f s
= 1
2 =0.5 seconds(sampling time)
f S=2rad /sec
QUESTION 3
To obtain a discrete-time system of the transfer function from the continuous open-loop system
transfer function,
%% discretizing the output
Ht=c2d(GsHs,0.5,'zoh');
figure(2)
bode(GsHs,Ht)
grid on
The function c2d is used to discretize the continuous system to discrete time system for the
dynamic system model using the zero-order hold on the inputs and a sample time of Ts seconds.
3