Topic #15 · 2017. 3. 16. · D.N. Manik 25 2 2 11 12 1 b s s W W WW ªº§· «»¨¸ ¬¼©¹ 2 1...

1

ME 779 Control Systems

Hydraulic Controllers

Topic #15

Reference textbook:

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

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Control Systems: Hydraulic Controllers

Learning Objectives

• Dashpot- derivative action- integral action

• Proportional and integral controllers• Proportional and derivative controllers• Dashpots connected in series• Proportional, integral and derivative controllers

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DASHPOT

1 2P Pq

R

q: flow rate

P1, P2 pressures

R: resistance


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DASHPOT: derivative action

1 2( )F A P P

1 2( )A P P kz

dy dz q

dt dt A

( )qdt A dy dz


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DASHPOT: derivative action

2

dy dz kz

dt dt RA

2

( )

( )

Z s s

kY ss

RA

2RA

k

( )

( ) 1

Z s

sY s s

The output has to be integrated to be compared with the input and hence the derivative action of the dashpot (you can only compare apples with apples at the summing point)


s

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DASHPOT- integral action

1 2( ) ( )k y z A P P

qdt A dz

1 2P Pq

R


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DASHPOT- integral action

( ) 1

( ) 1

Z s

Y s s

2RA

k

The output has to be differentiated to be comparedwith the input and hence the integral action of the dashpot (you can only compare apples with applesat the summing point)


s

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Hydraulic proportional plus

integral controller


Derivative action in the feedback loop

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Hydraulic proportional plusintegral controller


1

s

s

10

( ) ( ) ( )

( )1 1

( ) ( 1) ( )( 1)

b K b K

Y s a b s a b s

Ka s KaX s

a b s s a b s



11

( ) ( 1) 11

( )

Y s b s b

X s a s a s



12

Hydraulic proportional plus derivative controller


Integral action in the feedback loop

13



1

1s

14

( ) ( )

( )1

( ) ( 1)

b K

Y s a b s

KaX s

a b s s

( )

1( )

Y s bs

X s a



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Hydraulic proportional-integral-derivative controller


Derivative Integral

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Dashpots connected in series



Derivative Integral

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1 1 2( )k z A P P

1 21

1

P Pq

R

1 1 1k z AR q2 1 2 3 4( ) ( ) ( )k y u A P P A P P

1 ( )q dt A du dz

1

du dzq A

dt dt




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3 42

2

P Pq

R

1qdu dz

dt A dt

1

2

1

k zdu dz

dt R A dt

1

du z dz

dt dt

2q dt A du

2

duq A

dt

2

11

1

R A

k


Hydraulic proportional-integral-derivative controllerDashpots connected in series

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3 4 3 42

2

2 2

( )P P A P Pqdu

dt A R A R A

3 4

2 2

( )A P Pdu

dt k

2 1 2 2( )du

k y u k z kdt

2

22

2

R A

k




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2 2 1 2 2

duk y k u k z k

dt

2 2 2 2 1( ) ( ) ( )k Y s U s k k s k Z s

1

( ) 1( )

Z sU s s

s

1

1

1( ) ( )

sU s Z s

s




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12 2 2 1

1

1( ) 1 ( )

sk Y s k s k Z s

s

1

2 11 2 1 2 1

2

( )

( )( ) 1

sZ s

Y s ks s s

k




22

1 2

2 1

k

k

1

2

1 2 1 2

( )

( ) ( 2 ) 1

sZ s

Y s s s




23



24

1

2

1 2 1 2

( ) ( )

( )1

( ) ( 2 ) 1

b K

Y s a b s

sKaX s

a b s s s

1

2

1 2 1 2

1( ) ( 2 ) 1

sKa

a b s s s



D.N. Manik 25

22

1 1

2( ) 11

( )

Y s bs

X s a s

2

1

1

2

21

1

p

I

D

bK

a

bK

a

bK

a

( )

( )

Ip D

KY sK K s

X s s




Conclusion

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Topic #15 · 2017. 3. 16. · D.N. Manik 25 2 2 11 12 1 b s s W W WW ªº§· «»¨¸ ¬¼©¹ 2 1...

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