7/21/2019 Tut Sheet 10

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Department of Electrical and Instrumentation Engineering

UEI501 (Control System)

Tutorial-10

Q-1.  Decompose the transfer function given below by using parallel decomposition

3 2

3 2

( ) 7 12 8

( ) 6 11 6

Y s s s s

U s s s s

 

Q-2.  Compute the state transition matrix by infinite series method0 1

1 2 A

 

 

Q-3.  Obtain the transfer function of the system described by

1 1

2 2

0 1 0

;2 3 1

 x x

u x x

 

1

(0) ,1 x

 

 

  1

21 0

 x

 y  x

   

Q-4.  Determine the stability of the system whose A matrix is:

(a) 0 2

1 3 A

 

(b) 0 0

1 1 A

 

 

Q-5.  Given the system

( ) Ax(t) Bu(t),x t  

( ) ( )y t Cx t    

where0 2

1 3

A ,1

2

B  , 1 1C   

Determine the state and output controllability.

Q-6.  Test the observability of the system described by

2 0

0 1

A ,3

1

B  , 1 0C   

Q-7.  Test the controllability and observability of the system described by

1 1

2 2

1 1 0 ;3 2 1

 x x u x x

    1

2

1 0  x y x