model-driven pid control system, its properties and ...apc2004apc2004 toshiba toshiba it & control...

APC2004APC2004

TOSHIBA IT & CONTROL SYSTEMS CORPORATIONTOSHIBA

Model-Driven PID Control System, its properties and multivariable application

ModelModel--Driven PID Control System, its Driven PID Control System, its properties and multivariable applicationproperties and multivariable application

Takashi Takashi ShigemasaShigemasa, Masanori , Masanori YukitomoYukitomo, , Power and Industrial Systems Research and Development Center , Power and Industrial Systems Research and Development Center ,

Toshiba CorporationToshiba CorporationToshiba IT & Control Systems CorporationToshiba IT & Control Systems Corporation

APC2004APC2004


OutlineOutline

◇ Introduction

◇ Model Driven PID Control Systemstructure and properties

◇ Multivariable Model Driven PID Control System structure and simulations

◇ Conclusions

APC2004APC2004


IntroductionIntroduction

PID control system: widely used as a basic control technology,

however, is not always easy tuning and has control limitation for long

dead-time processes.

What is a simple, widely applicable process controller with easy to tune?

Based on the motief, we developed Model Driven PID Control System　ｂｙextending the Model Driven control concept proposed by Kimura.

Firstly, Model Driven PID Control System, its structure, properties.

Secondary, the Model Driven PID Control System for multivariable processes on regulatory control level and simulation results.

APC2004APC2004


Model Driven PID Control SystemModel Driven PID Control System

Model Driven Control Concept

Model Driven PID control system

Structure and Properties

APC2004APC2004


Model-Driven Control ConceptModel-Driven Control Concept

Definition:A control system architecture which uses a model of the plant as a

principal component of Controller is called a model-driven control.

Kimura(CDC2000Sydney)

Features of MDC

● Simple Structure

● Easy Tuning

● Proven Stability

and robustness

iff P(s) is stable

-

-

Controller Plant

IMC Architecture Morari, Zafirou,1989

Q(s) P(s)

(s)P̂

IMC

r y

ŷ

e u

Model-

APC2004APC2004


Structure of Model Driven PID Control SystemStructure of Model Driven PID Control SystemStructure of Model Driven PID Control System

・PD Feedback

・Main control ;

Gain , second order Q-filter and normalized first order delay

model with dead-time for inner loop

・Set-point filter

cK

sL

c

cesT

−

+11

Model

Q Filter Gain

r v + -

+

+

Main Controller

2)1()1)(1(

sTsTsT

c

cc

λα

+++

sTsT

c

c

αλ

++

11

Set Point Filter

sT

sTK

f

ff

κ+

+

1

)1(

)(sPProcess

PD Feedback

u y - +

d

+ +

)(sG

APC2004APC2004


Step 1 PD Feedback F(s)

Compensate inner loop dynamics G(s) to a first order system with dead time by using PD feedback F(s).

Design methods：partial model matching method,frequency region method,pole placement,simulation.

Wide applicability, for not only first order delay process with dead time but also integral process, oscillatory process and unstable process

sT 1

s)T(1KF(s)

f

ff

κ+

+=

y+

−P(s)v

F(s)

Design stepsDesign stepsDesign steps

TsLsK

sPsFsPsG

+−

≅

−= −

1)exp(

)()]()(1[)( 1

APC2004APC2004


0 20 50 60 900

1

2

4

5

6

sexp(

)s(P10

=-10s)

sexp(exp(

)s(G40+

4=

-10s)-10s)

s.exp(

)s(Ĝ428+1

4=

-11.8s)

4

sexp(

)s(P10

=-10s)

sexp(exp(

)s(G40+

4=

-10s)-10s)

s.exp(

)s(Ĝ428+1

4=

-11.8s)

250.KF(s) f ==

Example: A integral process can be converted to a first order delay system with dead time

APC2004APC2004


Step 2:Main controller and set-point filter

1) Kc=1/K

2) Tc=T

3) Lc=L

Step 3:TDOF property by adjusting λand α. 　　

　 λ: response speed α:Disturbance regulation　　

]ds)T (1

s)Ts)(1T(1[1

s)T(1Ks)exp(-L

rsT1s)exp(-L

y 2c

cc

cc

c

c

c

λα

λ +++

−+

++

=

2c

cc

s)T(1s)T s)(1T(1

Q(s)λ

α+

++=

sT1sT 1

c

c

αλ

++

Design steps(continued)Design steps(continued)

APC2004APC2004


0 20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

2 responces

PV SV

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

2

time

MV D

V

1=?

50=? .

51=? .

1=?

51=? .

50=? .

SV

DV

ses

sG 1051

1)( −

+=

dT

esTsTK

er

sTe

yc

sLc

cc

sL

c

sL ccc

+

+−

++

+=

−−−

2)1()1(

1)1(1 λ

αλ

Adjustable response speed by λ

APC2004APC2004


0 20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

2 responces

PV

SV

0 20 40 60 80 100 120 140 160 180 200-0.5

0

0.5

1

1.5

time

MV

DV

SV

1=a

3=a

DV

751=a .

3=a

751=a .1=a

ses

sG 1051

1)( −

+=

dT

esTsTK

ey

c

sLc

cc

sL cc

+

+−

+=

−−

2)1()1(

1)1( λ

α

Adjustable Disturbance regulation speed by α

APC2004APC2004


Nyquist curves

s7.281s)21(exp714.0

G(s)

4.0F(s)s501

s)20(expP(s)

+−

=

=+

−=

Robustness

APC2004APC2004


＋－

+

sTK

cc

11

r u y)( sP

0,1,0 ===== cff LTK αλPI Control：

＋－

+

sTK

cc

11

r u y)( sP

0,1,0 ===== cff LTK αλPI Control：

＋－

+

sTK

cc

11

r u y)( sP＋－

+

sTK

cc

11

+

sTK

cc

11

r u y)( sP )( sP

0,1,0 ===== cff LTK αλPI Control： PI-PD Control： 0,1 === cLαλ

sT

sTK

f

ff

κ+

+

1

)1(

＋－

+

sTK

cc

11

r u y)( sP＋－

PI-PD Control： 0,1 === cLαλPI-PD Control： 0,1 === cLαλ

sT

sTK

f

ff

κ+

+

1

)1(

＋－

+

sTK

cc

11

r u y)( sP＋－

sT

sTK

f

ff

κ+

+

1

)1(

sT

sTK

f

ff

κ+

+

1

)1(

＋－

+

sTK

cc

11

+

sTK

cc

11

r u y)( sP )( sP＋－

sL

c

cesT

−

+11

cKr u y)( sP＋

－

＋＋

1,0 ==== αλff TKPIDτd Control：

sL

c

cesT

−

+11

cKr u y)( sP＋

－

＋＋


sL

c

cesT

−

+11

cKr u y)( sP＋

－

＋＋

sL

c

cesT

−

+11 sL

c

cesT

−

+11

cK cKr u y)( sP )( sP＋

－

＋＋


＋－ sT

sT

c

c

λ++

11

sL

c

cesT

−

+11

cKr u y)( sP

＋＋

1,0 === αff TKIMC：

＋－ sT

sT

c

c

λ++

11

sL

c

cesT

−

+11

cKr u y)( sP

＋＋

1,0 === αff TKIMC：

＋－ sT

sT

c

c

λ++

11

sL

c

cesT

−

+11

cKr u y)( sP

＋＋＋

－ sTsT

c

c

λ++

11

sTsT

c

c

λ++

11

sL

c

cesT

−

+11 sL

c

cesT

−

+11

cK cKr u y)( sP )( sP

＋＋

1,0 === αff TKIMC： 1,0 === αff TKIMC：

cK

sL

c

cesT

−

+11

Model

Q Filter Gain

r v + -

+

+

Main Controller

2)1()1)(1(

sTsTsT

c

cc

λα

+++

sTsT

c

c

αλ

++

11

Set Point Filter

sT

sTK

f

ff

κ+

+

1

)1(

)(sPProcess

PD Feedback

u y - +

d

+ +

)(sG

Upper compatibility

APC2004APC2004


Summery of Properties

1. Wide Applicability PD feedback

2. Two degree of freedom characteristicsKc=1/K Tc=T Lc=L

λ tuning;Response speed, α tuning:Disturbance regulation speed

3. Robustness can be examined by well-known nyquistchart

4. Upper compatibility from conventional PID control systems

s)T? (1s)T(1K

F(s) s T 1

) s L Kexp() s G(

f

ff

++

=+

−≅

APC2004APC2004


Control performance - PV distribution -

-5 -4 -3 -2 -1 0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Before

AfterOld SV

New SV

Reported reduce operator’s over-riding actions and fuel cost, obtain high quality of product though some field applications.

APC2004APC2004


1r

2r

＋

－

－

＋

sTsT

cc

cc

11

11

11

αλ

++

sTsT

cc

cc

22

22

11

αλ

++ ＋

=

2221

1211

dd

dd

KKKK

K

)1( 11 sTK ff +

Decoupler

PD Feedback2

)1( 22 sTK ff +

－

－＋

＋

sTe

c

sLc

11

1

+

−

211

111

)1()1)(1(

sTsTsT

c

cc

λα

+++

222

222

)1()1)(1(

sTsTsT

c

cc

λα

+++

sTe

c

sLc

21

2

+

−

＋

Model1

Model2

Q1

Q2

PD Feedback1

2y

1y

MIMO Process

)(sP

＋

＋1cK

2cK

Multivariable Model Driven PID Control SystemMultivariable Model Driven PID Control System

APC2004APC2004


１．Decoupler（Kdec）

the control process

1

2221

12111

22

22

2221

21

21

12

12

1211

11

11

)0(

11

11)(−

−

−−

−−

==⇒

++

++=KKKK

PKe

sTK

esT

K

esT

Ke

sTK

sP decsLsL

sLsL

２．Other MD control systems

=

2221

1211

ˆˆˆˆ

)(PPPP

sPKdec

Design stepsDesign stepsDesign steps

A decoupler

Designed for the diagonal element of KdecP(s)

APC2004APC2004


0 200 400 600 800 10000

1

2

3

4

5

6

G11

0 200 400 600 800 10000

1

2

3

4

5

6G

12

0 200 400 600 800 10000

1

2

3

4

5

6

G21

0 200 400 600 800 10000

1

2

3

4

5

6

G22

SimulationSimulationSimulationControlled object ： Shell heavy oil fractionator

++

++=−−

−−

ss

ss

es

es

es

essP

1418

2827

60127.5

50139.5

60177.1

50105.4

)(

IEEE Control System MagazineShell heavy oil fractionator

By Daniel E. Rivera

Step responses

APC2004APC2004


１．Distributed MD PID Control

Design resultsDesign resultsDesign results

−

−=

3431.04567.01500.04465.0

Decoupler

ss es

es

1427

6011

model2,5011

model1 −−+

=+

=

２．Decoupling PID Control by Model-matching method by Kitamori

=

−

−=

6909.581015.516909.471015.45

7372.03455.02618.02982.0

I

p

T

K

APC2004APC2004


0 200

400

600

800

1000

1200

1400

1600

1800

2000

-0.50

0.51

1.52

0 200

400

600

800

1000

1200

1400

1600

1800

2000

-0.20

0.20.4

0.60 200

400

600 800 1000 1200 1400 1600 1800 2000-0.5

0

0.5

1

1.5

2

0 200 400 600 800 1000 1200 1400 1600 1800 2000-1

-0.5

0

0.5

time

SV1 Step

DV1 Step

SV2 Step

DV2 Step

1y

2y

1u

2u

Green：Decoupling PIDBlue：ＭＤ-ＰＩＤ

Modelling error 0%

APC2004APC2004


0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.5

0

0.5

1

1.5

2

出力

１

0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.4

-0.2

0

0.2

0.4

0.6

入力

１

0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.5

0

0.5

1

1.5

2

出力

２

0 200 400 600 800 1000 1200 1400 1600 1800 2000-1

-0.5

0

0.5

1

入力

２

time

Modelling error 25%

SV1 Step

DV1 Step

SV2 Step

DV2 Step

Green：Decoupling PIDBlue：ＭＤ-ＰＩＤ

APC2004APC2004


ConclusionsConclusions

PID

MD-PID

Large L/TSmall L/TUnstableIntegralOscillationZero

Delay with dead time

★We discussed a Model Driven PID control system,its properties and a multivariable application.

★PD feedback give us wide applicability of controlled processes:

★MD-PID control system shows Good control performances like a TDOF control system with easy tuning.

★ MD- PID control system has upper compatibility from conventional PI, IMC, PIDτdand PI-PD

★ Multivariable MD PID Control system shows useful results in spite of simple control structure.

model-driven pid control system, its properties and ...apc2004apc2004 toshiba toshiba it & control...

Documents