Page 213 - MATLAB an introduction with applications

198 ——— MATLAB: An Introduction with Applications

The input u is given by:
(a) u = unit-step input
(b) u = e –t
The initial state x(0) = 0.
P3.33: Plot the step response using MATLAB for the following system represented in state space, where
u(t) is the unit step.
−  3 2 0  0  

x =  0 − 7 1 x +   ( )

t
1 u

 

1  
 0 0 − 4   

y = [0 1 ] 1 ;x
0 

x(0) = 0

0 

P3.34: Diagonalize the following system using MATLAB.
−  10 − 5 7  1  

x =   15 4 − 12 x +  
2 r


 
 − 8 − 3 6    
3  

y = [1 – 2 ] 3 x
P3.35: Determine to unit-ramp response of the system defined by
x   0 2  x 1   0

+
1
 =       u
x
2
  − 3 − 3 x 2  
 
2
x 
y = [10 ] 
1
x

2
using MATLAB where u is the unit-ramp input. Use lsim command in MATLAB.
P3.36: Obtain the unit-impulse response of the following system using MATLAB
x   0 1  x 1   0

1
+
 =       u
x
1
  − 1 − 2 x 2  
 
2
x 
1
y = [11 ]  + [ ] 0 u .
x

2
P3.37: A control system is defined by
x  −  1 − 3 −  x 1   3

3 
1
 =  0 − 2 1     
+
x
0 u
x
      
2
2
x 

1

 
3 
   2 0 − 1 x     
3
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