Page 212 - MATLAB an introduction with applications

Control Systems ——— 197

The matrices A, B, C, and D are:

 0 1 0  0
A =  0 0 1  B =  1 
   
− 150 − 50 − 15  − 15 


C = [10 0 ]
D = [] 0

P3.29: Obtain the Bode diagram of the following system using MATLAB.

x   0 1  x 1  0 
1
+
 =      u
x
30
  − 30 7 x 2  
 
2
x 
1
y = [10 ] 
x

2
The input of the system is u and the output is y.
P3.30: A control system is defined by
x  1   − 1 − 2  x 1  1 1 u  1
+
  =      
x
 x 2  7.5 0    1 0 u 2
 
2
y  1   10  x 1  0 0 u  1
+
  =      
x
 y 2  01    0 0 u 2
 
2
Write a MATLAB program to obtain the following plots:
(a) two Nyquist plots for the input u in one diagram
1
(b) two Nyquist plots for the input u in one diagram.
2
P3.31: Obtain the unit-ramp response of the system defined by

x   0 2  x 1 0  
1
+
 =      u
x
2
 
  − 3 − 1 x 2  
2
x 
1
y = [10 ] 
x

2
where u is the unit-ramp input. Use lsim command to obtain the response.
P3.32: Obtain the response curves y(t) using MATLAB for the following system.

x
x  −  11   0
1
1
+
 =      u
x
2
 
  − 10 x 2  
2
x 
1
y = [1 0] 
x

2
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