2020/07/11Advanced Topics in PID Control System Design, Automatic Tuning and Applications

@IFAC WC 2020 Workshop

Toru YAMAMOTOHiroshima University

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Global competition in industrial world

・Reduction of production costs・Energy-saving and labor-saving・Improvement of the quality of products

High-performance control systems

are required in industries.

Introduction(1)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

PID Controllers 80％ or more in industrial systems

t

DI

c dt

tdeTde

Ttektu

0

)()(

1)()(

current past future

proportional integral derivative

PIDController

Plant±r

uy

e

PID controllers have a simple structure. PID controllers are simple to maintain and tune. Physical meaning in sense of the control engineering is clear.

Introduction(2)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Introduction(3)Systems have usually uncertainties.

In order to overcome these problems,

Data-Driven PID(DD-PID) Controller（PID parameters are updated using a database）

system changesnonlinearities

This work was cooperated withOMRON Co. Ltd.

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Data-Driven PID ControllerLocal control parameter tuning

[step 0] Create initial data-base by operating data

[step 1] Get an information request (query)

[step 2] Calculate distance between query & Information vectors

[step 3] Select neighbors with small distance

[step 4] Calculate PID parameters and generate control input

[step 5] Update PID parameters using gradient method

[step 6] Remove redundant data

Algorithm

Data-Driven PID(1)

Data-Driven PID(2)[Step 0] Create initial data-base by operating data

')](),(),([:)( tKtKtKt DIPKData-base

data datadata

datadata

data

PIDController

Plantr u y

-

r

u y

)]'1(,),2(),1(),2(),1(),(),([:)( dtutututytytytrt

information vector

+ PID parameter vector

↓

]')'(,)'([:)( tKtt Φ

・・・

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

[Step 1] Given an information request (query)

t

y(t))]'1(,),2(),1(),2(),1(),(),([:)( dtutututytytytrtq

query (information request)

Data-Driven PID(3)

・・・

[Step 2] Calculate distance between query & information vectors

t

y(t)

Data-Base

data

query

datadata

datadata

[Distances between and ])(tq )(i

Data-Driven PID(4)

)]'1(,),2(),1(),2(),1(),(),([:)( dtutututytytytrtq ・・・

))()(())'()(()( itqitqid or

|)()(|)( itqid

e.g.

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

[Step 3] Select neighbors with small distance

t

y(t)

Data-Basequery

data datadata datadata

)](),(),([:)( jKjKjKj DIPK

kj ,.....,2,1

selected PIDparameter vectors

Data-Driven PID(5)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Review

)]'3(),3(),3([)3(]'),2(,),3(),3([:)3( DIP KKKuyr K・・・・・・

)]'2(),2(),2([)2(]'),1(,),2(),2([:)2( DIP KKKuyr K・・・・・・

)]'1(),1(),1([)1(]'),0(,),1(),1([:)1( DIP KKKuyr K・・・・・・

)]'(),(),([)(]'),1(,),(),([:)( NKNKNKNNuNyNrN DIP K・・・・

・・・

・・・

]'),1(,),(),([:)( ・・・・・・ tutytrtq

Distance

0.36

0.11

0.18

query

Data-base

0.22

PID parameter vectors are selected

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

[Step 4] Calculate PID parameters and generate control input

k

ii

k

ii wiwt

11

1),()( KK

Neighbors

k

iiiiii vvwdv

1

, //1

data

data

data

e.g.

)())()()(()( 2 tetKtKtKtu DIP [PID control]

system

Data-Driven PID(6)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Review(cont.)

)]'3(),3(),3([)3(]'),2(,),3(),3([:)3( DIP KKKuyr K・・・・・・

)]'2(),2(),2([)2(]'),1(,),2(),2([:)2( DIP KKKuyr K・・・・・・

)]'1(),1(),1([)1(]'),0(,),1(),1([:)1( DIP KKKuyr K・・・・・・

)]'(),(),([)(]'),1(,),(),([:)( NKNKNKNNuNyNrN DIP K・・・・

・・・

・・・

]'),1(,),(),([:)( ・・・・・・ tutytrtq

Distance

0.36

0.11

0.18

query

Data-base

0.22

PID parameter vectors selected

Weight

0.4730.290

0.237

)(*237.0)3(*290.0)2(*473.0)(

)(*237.0)3(*290.0)2(*473.0)(

)(*237.0)3(*290.0)2(*473.0)(

NKKKtK

NKKKtK

NKKKtK

DDDD

IIII

PPPP

)(tu

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

[Step 5] Update PID parameters

[Steepest descent method]

2))1()1((2

1)1(

)(

)1()()(

tytytJ

t

tJtt

r

oldoldnew

KηKK

12

11

1

1

1

1:)(

modelreference desied:)()(

)1(:)(

rateleaning:],,[:

ztztzT

trzT

Tztyr

DIP η

Data-Base

)(tq +

new data vector

]')'(,)'([:)( ttqt newKΦ

Data-Driven PID(7)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

[Step 6] Remove redundant data

In order to avoid excessive increase of stored data

[First condition]

)))()(())'()(()((

)( 1

itqitqid

id

[Second condition]

)()(),()(),()(

})(

)()({

321

22

3

1

iKiiKiiKi

t

ti

DIP

lnew

lnew

l

l

KKK

K

KK

Data-Driven PID(8)

・・・

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Simulation Example 1 (1)

)()1(148.0

)273)1((exp10739.5)1(804.0)( 15

ttu

tyREtyty a

01986.0,240

01.0varianceandmeanwithnoiseGaussianwhite:)(

RaE

zerot

Polystyrene polymerization reactor model

reactorjacket

heater

cooler

control valueReactor temperatureOutline Figure

70yStrong nonlinear property

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

[Fixed PID controller] [Proposed method]

Trajectories of PID parameters

8856.1,5522.1,5422.6 DIP KKK

CHR tuning scheme

Simulation Example 1 (2)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

)()()1()(1

]5.2)()[1()()1(

22ttu

tyty

tytytyty

0001.0varianceandmeanwithnoiseGaussianwhite:)( zerot

[Static property]

This system has Hysteresisbetween y=0 and y=2.0

(by K.S.Narendra)

Simulation Example 2 (1)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

327.0,028.0,654.0 DIP KKK

Using fixed PID parameters (CHR)

Simulation Example 2 (2)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

[Proposed method]

Control result Trajectories of PID parameters

Simulation Example 2 (3)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Trajectories of Kold and Knew

Simulation Example 2 (4)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

With STEP 6Number of data

406 89

The number of data is decreased drastically

Without STEP 6Number of data = initial data + Control interval

406 = N(0) = 6 + 400[step]

Simulation Example 2 (5)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

The learning speed of the DD-PID control scheme is very fast

DD-PID method145.0)1( ep

NN-PID method145.0)39( ep

][400][1)(

)(1:)(

2

1

stepepoctr

t

Nepoc

N

tep

Evaluation of control performancesIn this case

Simulation Example 2 (6)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Temperature Control System

Fan

Power Conditioner

Solenoid

Heater Part

Solenoid: On

Heater Part Steel plate

Generate periodic disturbances

Experimental Example (1)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

)(

)23002200(

)21002000(

)18001700(

)15001400(

)12001100(

)900800(

)600500(

)(

otherwiseOff

tOn

tOn

tOn

tOn

tOn

tOn

tOn

tD

Experimental Example (2)

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Implementation 1×

Electronic Thermal Regulator （E5CD）Release date: 2017. 4. 3

OMRONHP: http://www.fa.omron.co.jp/products/family/3668/

Time

150℃152℃

148℃

Time

150℃152℃

148℃

before after

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

【Conventional Scheme】

Improved!

Database24 [s] 12 [s]

Flow rate of rice follows the reference signal

“accurately” and “quickly”

Purpose

【Database-driven control scheme】

Adaptively tuned

Implementation 2×

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

DD-PID algorithm has been mounted on a hydraulic excavator in joint project with KOBELCO Construction Machinery.

System properties change by the attachment and/or the temperature.

Implementation 3 ×

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

Summary of DD-PID Controller（1/2）New Design of a PID Controller

Based on Database

Deal with nonlinear systems Robustness by knowledge stored in data-base Adaptability by adjusting PID parameters

[Features]

Advanced Topics in PID Control System Design, Automatic Tuning and Applications @IFAC WC 2020 Workshop

T.Yamamoto, K.Takao and T.Yamada : Design of a Data-Driven PID Controller, IEEE Trans. on Control Systems Technology, Vol.17, No.1, pp.29 -39 (2009)

[Reference]

Summary of DD-PID Controller（2/2）

S.Wakitani, T.Yamamoto and B.Gopaluni :Design and Application of a Data-driven PID Controlwith Data-Driven Updating Algorithm,Industry & Engineering Chemistry Research,Vol.58, No.26, pp.11419-11429 (2019)

Off-line leaning

[Correspondence] Toru Yamamoto ( yama@hiroshima-u.ac.jp )