Topic #16 Pneumatic Controllers Reference textbook : Control - - PowerPoint PPT Presentation

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ME 779 Control Systems

Pneumatic Controllers

Topic #16

Reference textbook:

Control Systems, Dhanesh N. Manik, Cengage Publishing, 2012

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Learning Objectives

• Proportional and derivative controller
• Examples
• Proportional and integral controller
• Proportional, integral and derivative controller

Control Systems: Pneumatic Controllers

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Proportional plus derivative controllers

Control Systems: Pneumatic Controllers

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Control Systems: Pneumatic Controllers

Proportional plus derivative controllers

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( ) G s K 

( ) ( )( 1)

s

aA H s k a b RCs   

( ) ( ) ( ) 1 ( ) ( 1)

c s

bK P s a b KaA X s a b k Rcs     

1 ( ) ( 1)

s

KaA a b k Rcs   

Control Systems: Pneumatic Controllers

Proportional plus derivative controllers

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( ) ( 1) ( )

c s

P s bk Rcs X s aA  

 

( ) 1 ( )

c p d

P s K T s X s  

,

s p d

bk K T RC aA  

Control Systems: Pneumatic Controllers

Proportional plus derivative controllers

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EXAMPLE

Control Systems: Pneumatic Controllers

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( )

i

dp p p Rdt C  

i

dp RCp RCp dt  

( 1) ( ) ( )

i

s P s P s   

 

( ) ( ) ( )

i

X s K P s P s  

( ) ( ) 1

i

X s K s P s s    

Control Systems: Pneumatic Controllers

EXAMPLE

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ωt

Control Systems: Pneumatic Controllers

EXAMPLE

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Control Systems: Pneumatic Controllers

EXAMPLE

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• kx

p A 

• dp

q dt C 

i

• p

p q R  

• i
• dp

p p C dt R  

i

k p x Ck dx A A dt R  

( ) ( ) 1

i

A X s k P s RCs  

Control Systems: Pneumatic Controllers

EXAMPLE

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Proportional plus integral controllers

Control Systems: Pneumatic Controllers

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Control Systems: Pneumatic Controllers

Proportional plus integral controllers

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( ) G s K 

1 ( ) 1 ( ) 1

s

aA H s a b k RCs          

( ) 1 ( ) 1 1 ( ) 1

c s

b K P s a b aAK X s a b k RCs                  

Control Systems: Pneumatic Controllers

Proportional plus integral controllers

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( ) 1 1 ( )

c s

P s k b X s aA RCs        

,

s p i

bk K RC aA   

Control Systems: Pneumatic Controllers

Proportional plus integral controllers

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Proportional-integral-derivative controllers

Control Systems: Pneumatic Controllers

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Control Systems: Pneumatic Controllers

Proportional-integral-derivative controllers

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( ) G s K 

  

1 2 2 1 1 2

1 1 ( ) ( ) 1 1 ( ) 1 1

c c

P s P s R Cs R Cs R Cs R Cs P s R Cs R Cs                      

  

2 1 1 2

( ) ( ) 1 1

s

R Cs R Cs aA H s k a b R Cs R Cs             

Control Systems: Pneumatic Controllers

Proportional-integral-derivative controllers

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  

2 1 1 2

( ) ( ) ( ) 1 ( ) 1 1

c s

bK P s a b X s R Cs R Cs aAK k a b R Cs R Cs               

  

2 1 1 2

1 ( ) 1 1

s

R Cs R Cs aAK k a b R Cs R Cs             

Control Systems: Pneumatic Controllers

Proportional-integral-derivative controllers

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   

1 2 2 1

( ) 1 1 ( )

c s

P s bk R Cs R Cs X s aA R Cs R Cs    

1 2

( ) 1 1 ( )

c s

P s bk R Cs X s aA R Cs         

( ) 1 1 ( )

c p d i

P s K s X s s           

2 1

, ,

s p i d

bk K R C R C aA     

Control Systems: Pneumatic Controllers

Proportional-integral-derivative controllers

Control Systems: Pneumatic Controllers

Conclusion