Automatic control by meiling chen1 Lesson 10 System design.

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Automatic control by meil ing chen 1 Lesson 10 System design

Transcript of Automatic control by meiling chen1 Lesson 10 System design.

Automatic control by meiling chen 1

Lesson 10

System design

Automatic control by meiling chen 2

Example : An Armature control DC motor

aR aL

ai

tea

fR

fL

teb

m

mJ LTArmature circuit Field circuit

te f

fi constant

)1()(

)(

ss

K

sE

s

m

m

a

m

Automatic control by meiling chen 3

)1( ss

K

m

m

m

aE

+-

)(sH

)(sGc)(sR

)1(1)(

2.0

2

s

m

m

sH

K

let Design controller

Sensor

Automatic control by meiling chen 4

Case I : Proportional control KsGc )(

Ksss

K

sssK

ssK

sR

sm

10)5)(1(

10

)1(1

)12.0(2

1

)12.0(2

)(

)(

01056 23 KsssCharacteristic function :

ks

Ks

ks

s

106

1030106

51

0

1

2

3

30 k

Automatic control by meiling chen 5

5 1 02

0k0k0kk

k

k

3k

3k

)5)(1(

10)(

ssssGH

Open loop transfer function : 707.0cos

Automatic control by meiling chen 6

5.0k

5.0k

978.0

395.0

n

Automatic control by meiling chen 7

)5)(1(

10)(

ssssGH Type I system

sss

as

Ksss

vs

sss

ps

eGHsKsR

esGHKsR

eGHKsR

v

2

0

1

1

0

10

1

lim)(

lim)(

0lim)(

3

2

Automatic control by meiling chen 8

)5)(1(

10)(

ssssGH )(dBGH

GH

1.0 1 10

0900180

090

0180

5

decdB20

decdB60

decdB40

0270

G.M.

P.M.

1g

Automatic control by meiling chen 9

g1=zpk([],[0 –1 –5],[10])margin(g1)

1g

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Case II : Proportional Integral control s

KKsG I

Pc )(

)1( ss

K

m

m

maE

+-

)(sH

)(sR

Sensor

PK

sK I

1

1

)5(

10)(

ssss

KsKsGH IpOpen loop transfer function :

a zero

a pole

Automatic control by meiling chen 11

1

1

)5(

10)(

ssss

KsKsGH Ip

Type II system

aksss

as

sss

vs

sss

ps

eGHsKsR

esGHKsR

eGHKsR

12

0

10

10

1

lim)(

0lim)(

0lim)(

3

2

The system order

sse

Automatic control by meiling chen 12

1

1

)5(

10)(

ssss

KsKsGH Ip

)(10)5)(1(

10

)5)(1(

)(101

)5)(1(10

1

2

2

Ip

Ip

KsKsss

s

sss

KsKsss

GH

G

I

P

IPp

Ip

p

I

KK

KKK

s

s

KK

s

Ks

Ks

101030

360100300

106

1030106

1051

2

0

1

2

3

4

Automatic control by meiling chen 13

5 1 02

0pk0pk0kk

k

k

3k

3k

1

1

)5(

10)2()(

2

1

1

)5(

10)(

1

ssss

sKsGH

K

Klet

ssss

KsKsGH

p

P

I

Ip

pk

pk

pk

2g

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1pk

1pk

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1g

2g

g2 (PI controller) is unstable g1 (P controller) is stable

2g

1g

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Case III : Proportional derivative control

)1( ss

K

m

m

maE

+-

)(sH

)(sR

Sensor

PK

sKD

sKKsG DPc )(

Sensor

1

1

)5(

10)()(

ssssKKsGH DpOpen loop transfer function :

a zero

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1

1

)5(

10)()(

ssssKKsGH Dp Type I system

sss

as

Ksss

vs

sss

ps

eGHsKsR

esGHKsR

eGHKsR

v

2

0

1

1

0

10

1

lim)(

lim)(

0lim)(

3

2

Automatic control by meiling chen 18

1

1

)5(

10)15.0()(

5.0

1

1

)5(

10)()(

1

ssssKsGH

K

Klet

ssssKKsGH

p

P

D

Dp

5 1 02

0pk0pk0kk

k

k

3k

3k

pk

pk

pk

3g

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1g

1g

3g

3g

..

..

3

3

MPPDg

MGPDg

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PDgred

PIggreen

Pgblue

3

2

1

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Case IV : Proportional Integral derivative control

)1( ss

K

m

m

maE

+-

)(sH

)(sR

PK

sKD

sKs

KKsG D

IPc )(

1

1

)5(

10)()(

ssssK

s

KKsGH D

IpOpen loop transfer function :

sK I

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)1)(5(

10)5.0()(

1,5.0

)1)(5(

10)(

1

1

)5(

10)()(

2

2

ssss

ssKsGH

K

K

K

Klet

ssss

sKK

KK

sK

ssssK

s

KKsGH

p

P

D

P

I

p

D

p

Ip

DI

p

Open loop transfer function :

Type II system

sse

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234

2

56

51010)(

sss

ssKsGH p

4g

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PIDg

Pg

4

1

1g

1g

4g

4g

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Case V : phase lead control

0,)(

)()(

abbs

assGc

b a

0)(tan)(tan,)(

)()( 11

babj

ajjGc

Case VI : phase lag control

0,)(

)()(

babs

assGc

ba

0)(tan)(tan,)(

)()( 11

babj

ajjGc

Automatic control by meiling chen 26

)1( ss

K

m

m

m

aE

+-

)(sH

)(sGc)(sR

)6(

)3()(

s

ssGc

Phase lead:

1

1

)5(

10

)6(

)3()(

ssss

ssGH 5g

)3(

)6()(

s

ssGc

Phase lag:

1

1

)5(

10

)3(

)6()(

ssss

ssGH 5g

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5g

1g

Green phase leadG.M. P.M.

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13k

13k

Phase lead

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Green phase lagG.M. P.M.

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1k

1k

Phase lag