This question refers to the hypothetical system drawn below in Fig. 1. A table of transforms is...

Question

This question refers to the hypothetical system drawn below in Fig. 1. A table of transforms is given at the end of this exam paper (Table 1). Figure 1. a) Show that the impulse transfer function of the open-loop system is ?? 1 - ?? -??/?? ?? - ?? -??/?? [9 marks] b) Write the impulse transfer function of the closed-loop system. [4 marks] c) Assume that ?? = 1 ???????????? and ?? = 2 ??????????????. Draw the root-locus of the system’s pole(s) on the z-plane by plotting the following gain values: K = -2, 0, 0.5, 1.54, 3, 5.
	
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Department of Mechanical Engineering 
University College London

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EXAMINATION PAPER

CODE:   MECHGM04 / MECH4008 / MECHM008 
 
TITLE:   Vibrations, Acoustics, Control   
 
VERSION:  DRAFT

SESSION:   2014/15 QUALIFICATIONS:  MSc/MEng 
 
EXAM DATE:  TBC  TIME ALLOWED:   2 hours

Answer THREE questions. 
Rubric 
All questions carry equal weight. 
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THIS PAGE FOR DEPARTMENTAL USE ONLYMECHGM04 / MECHM008 / MECH XXXXXXXXXX/15 2 
 
Answer THREE questions. 
 
All questions carry equal weight.

1. This question refers to the hypothetical system drawn below in Fig. 1.  
A table of transforms is given at the end of this exam paper (Table 1). 
 
-????
+ 
??
1 - ??

+ 
1 + ????
??
-

Figure 1. 
 
a) Show that the impulse transfer function of the open-loop system is   
 
-?? /??
1 - ??
?? 
-?? /??
?? - ??
[9 marks]

b) Write the impulse transfer function of the closed-loop system.   
[4 marks]

c) Assume that ?? = 1 ???????????? and ?? = 2 ?????????????? . Draw the root-locus of the 
system’s pole(s) on the z-plane by plotting the following gain values: 
K = -2, 0, 0.5, 1.54, 3, 5.   
[4 marks]

d) Based on the root-locus diagram, consider the response of the system to a 
unit-step input, assuming zero initial conditions.  For each of the...

Robert · Accepted Answer

Solution
Solution: 
      ( )   ( )  
      
 

    

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 ( ) ( )   
      
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  [
 
 

  
 
 
] 
 ( ) ( )    [
 
   

    
 
 
]  
  (       )
(   )  (    
 
 )
 
Now we need to divide the whole term by z/z-1 
 ( ) ( )    [
 
   

    
 
 
]  
 (       )
(    
 
 )

Transforming s domain to z domain, we
     
 ( )
   ( ) ( )
 
 
      
 (    )
   
      
 (    )
 
 (      )
 (    )   (      )

Solution: 
   
 (       )
(    
 
 )
 
 (       )
(    
 
 )
 
 (       )
(       )

K=-2;
K=0
K=0.5
K=1.54
K=3
K=5
Solution: As K increase peak overshoot also increases. We can see that settling time is almost equal.
Solution: 
In signal processing and related disciplines, aliasing is an effect that causes different signals to 
become indistinguishable (or aliases of one another) when sampled.

This question refers to the hypothetical system drawn below in Fig. 1. A table of transforms is given at the end of this exam paper (Table 1). Figure 1. a) Show that the impulse transfer function of...

Solution

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