Page 190 - MATLAB an introduction with applications

Control Systems ——— 175

20log K = 7 dB
or K = 2.23
Example E3.23: Obtain the state-space representation of the following system using MATLAB.
Cs = 35s + 7 .
( )
()
Rs s + 5s + 36s + 7
3
2
Solution:
A MATLAB program to obtain a state-space representation of this system is given below.
% MATLAB Program
>> num=[0 0 35 7];
>> den=[1 5 36 7];
>> g=tf(num,den)

Transfer function:
+
35s 7
∧ ∧
+
+
+
s3 5s 2 36s 7
>> [A,B,C,D]=tf2ss(num,den)
A =
–5 –36 –7
1 0 0
0 1 0
B =
1
0
0
C =
0 35 7
D =
0

From the MATLAB output, we obtain the following state space equations:
7 
x   −  5 − 36 −  x  1  
 x 1  =  1 0 0   x 1   
+
0 u
 2     2   
0  
3 
 x  3     0 1 0     x   
x 
1

y = [0 7] x 2 + [0]u

x 

3

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