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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 ( [email protected] )