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

ME 779 Control Systems Topic #16 Pneumatic Controllers Reference textbook : Control Systems, Dhanesh N. Manik, Cengage Publishing, 2012 1

Control Systems: Pneumatic Controllers Learning Objectives • Proportional and derivative controller • Examples • Proportional and integral controller • Proportional, integral and derivative controller 2

Control Systems: Pneumatic Controllers Proportional plus derivative controllers 3

Control Systems: Pneumatic Controllers Proportional plus derivative controllers 4

Control Systems: Pneumatic Controllers Proportional plus derivative controllers  aA G s K  ( ) H s ( )   k a ( b RCs )( 1) s bK  P s ( ) ( a b ) KaA  c  1 KaA X s ( )    1 a b k Rcs ( ) ( 1)   s ( a b k Rcs ) ( 1) s 5

Control Systems: Pneumatic Controllers Proportional plus derivative controllers  P s ( ) bk Rcs ( 1)  c s X s ( ) aA bk   s K , T RC p d P s ( )   aA X s   c K 1 T s p d ( ) 6

Control Systems: Pneumatic Controllers EXAMPLE 7

Control Systems: Pneumatic Controllers EXAMPLE dp   ( p p Rdt ) i C dp dt   RCp RCp i  X s ( ) K s    P s s ( ) 1 i    ( s 1) ( ) P s P s ( ) i     X s ( ) K P s ( ) P s ( ) i 8

Control Systems: Pneumatic Controllers EXAMPLE ω t 9

Control Systems: Pneumatic Controllers EXAMPLE 10

Control Systems: Pneumatic Controllers EXAMPLE kx  dp q  p p  p  o i o q o dt C A R  dp p p k   o i o p x C dt Ck dx i A  R A dt R A X s ( ) k   P s ( ) RCs 1 i 11

Control Systems: Pneumatic Controllers Proportional plus integral controllers 12

Control Systems: Pneumatic Controllers Proportional plus integral controllers 13

Control Systems: Pneumatic Controllers Proportional plus integral controllers  G s K ( )   aA 1     H s ( ) 1     ( a b k ) RCs 1 s   b   K    P s ( ) a b  c   aAK 1 X s ( )     1 1     ( a b k ) RCs 1 s 14

Control Systems: Pneumatic Controllers Proportional plus integral controllers   P s ( ) k b 1   c s   1   X s ( ) aA RCs bk  aA   s K , RC p i 15

Control Systems: Pneumatic Controllers Proportional-integral-derivative controllers 16

Control Systems: Pneumatic Controllers Proportional-integral-derivative controllers 17

Control Systems: Pneumatic Controllers Proportional-integral-derivative controllers    G s ( ) K  aA R Cs R Cs    2 1 H s ( )         k a ( b )  R Cs 1 R Cs 1  s 1 2   1 1     P s ( ) P s ( )   c   R Cs 1 R Cs 1 1 2    R Cs R Cs    2 1 P s ( )        c R Cs 1 R Cs 1   1 2 18

Control Systems: Pneumatic Controllers Proportional-integral-derivative controllers bK  P s ( ) ( a b )  c    X s ( ) aAK R Cs R Cs    2 1 1         k a ( b ) R Cs 1 R Cs 1   s 1 2    aAK R Cs R Cs    2 1 1         k a ( b ) R Cs 1 R Cs 1   s 1 2 19

Control Systems: Pneumatic Controllers Proportional-integral-derivative controllers P s ( ) bk       c s R Cs 1 R Cs 1   1 2 X s aA R Cs R Cs ( ) 2 1 bk        P s ( ) bk 1 s K , R C , R C    c s   p i 2 d 1 1 R Cs aA 1   X s ( ) aA R Cs 2   P s ( ) 1     c   K s 1  p d   X s ( ) s i 20

Control Systems: Pneumatic Controllers Conclusion