PREDICTIVE FUNCTIONAL

CONTROL

                                           J.Richalet 2015

WHO INVENTED

PREDICTIVE CONTROL ?

 ERGONOMY OF FLIGHT CONTROL

•  In the fifties : •  How the pilot manages his aircraft ? •  What operating image ? •  Comparison between: •  Human control and Automatic control : SURPRISE ! ….    

 Jean Piaget (1896 / 1980)

•  Swiss Grand Father of Cognitive Psychology

•  How the child learns and controls his environment . Four phases ….!      

4 PIAGET BASIC PRINCIPLES

–  OPERATING IMAGE –  TARGET – Sub TARGET –  ACTION –  COMPARISON BETWEEN

PREDICTED AND ACHIEVED RESULT

–  INTERNAL MODEL –  REFERENCE TRAJECTORY –  STRUCTURATION OF THE MV

–  ERROR COMPENSATION

• NATURAL CONTROL : “ YOU DO NOT DRIVE YOUR CAR WITH A PID SCHEME”

PREDICTIVE CONTROL

IS NOT

AN INVENTION

BUT A DISCOVERY ….!

PrH(C - (n)) (1 - ) (n)yy Mu(n) + H GMGM(1 - )

λ

α=

P = G - se1 + Ts

M yu

θ

= =

y(n) = α y(n-1) + (1- α) . u(n-1-r) . G α = e -TsampT

θ = Tsamp . r

ELEMENTARY TUTORIAL EXAMPLE

Trajectory expo. : λ

1 coincidence point: H

1 Base function: step Target : ΔP(n+H) = (C - yPr) (1 - λH)

Processus with delay : yPr (n) = yP (n) + yM (n) - yM(n-r)

Model :

Free mode Forced mode (Liebniz 1674)

My (n) HαHu(n) . GM 1 - α

⎛ ⎞⎜ ⎟⎝ ⎠

Model increment :

M MPH H H(C - (n)) (1 - ) (n) + u(n) GM(1 - ) - (n)y y yr λ α α=

Control equation : P(n +H) M(n + H)Δ Δ=

Increment = Free(n+h) + Forced(n+h)- ymodel(n) The only mathematical problem for trainees …!

BAYER reactor

0 20 40 60 80 100 1200

20

40

60

80

100

120TEMPERATURE DE MASSE

d°

min

92°

Tmax=108.4°

Tinit=42°

Figure 4

ON LINE ESTIMATOR of DISTURBANCES

Pert

R1

R2

Cons1 MV1 P SP

SP*M≡PMV2

Cons2=SP

+

+

B

+

+

Pert*-

+

0 10 20 30 40 50 60 70 80

0

20

40

60

80

100

120 ESTIMATION DE L‘EXOTHERMICITE

Tmasse/ Tmasseestimée

TS-TE

TS

EXOTHERMICITE

min

Figure 3

31

ReactantFlow

T1 Reactor

Cooler

Steam

T2

T4

T3Heat

Exchanger

BASFBASFBASF

B A S F

15

R

T M F i , T i T e

R Reagent

¥

r M

C P M V

M d T

M dt

= UA T e - T

M + D H x

r e C P e V e d T e dt = r e F i T i - T e + UA T M - T e

q ( F i ) T M + T M = T i .

1) Fi =ct /MV= Ti CV=TM / level 0 =Ti ? :PFC

2) Ti =ct (!) MV=Fi Parametric Control non linear :PPC

3) MV : Ti and Fi : Enthaplic control (power) :PPC+

4) MV : Pressure of reactor :PFC

4 CONTROL STRATEGIES OF BATCH REACTORS

Batch Reactor : MV=Qf / CV= TM DEGUSSA EVONIK

Qf

Tif

Tof

TM

 Control PID Degussa / EVONIK

Datum | Name der Präsentation Seite | 17

time

tem

per

atu

re [

°C]

+/- 2 °C

39 different batches with PID

Control PFC Degussa / EVONIK

Datum | Name der Präsentation Seite | 18

time

tem

pera

ture

[°C]

32 different batches with PPC

+/- 0,2 °C

CONTINUOUS CASTING

poche de 335 t d’acier liquide à 1550 °C

distributeur de 60 t

lingotière à largeur variable 850-2200 mm,refroidie à l’eau

capteurradio-actif

consigne=70%PFCPFC

mesure de niveau

cages d’extraction

consigne de poids

tquenouillePFC

PI vérin

mesure de position

busette rotative

busette à 2 ouïesA

A

mesure de poids

amplificateurde puissance

  IDENTIFICATION    -­‐    Ultra-low level test signals ! ! ….      «    I do want to see your test signal on the level ..!«                  -­‐  Set of harmonics signals Eigen function  -­‐  High level Parallel filtering  .-­‐  Different metal alloys    

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

x 104

-20

-10

0

10

20

30

40

50

60

70

BULGING COMPLEX CONTROL

without with

STOPPER

Amp sinus

Bmp cosinus

Frequency reference

N*0.025 sec

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

x 104

-20

-10

0

10

20

30

40

50

60

70

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

x 104

-20

-10

0

10

20

30

40

50

60

70

BULGING COMPLEX CONTROL

without

BULGING COMPLEX CONTROL

without with

STOPPER

Amp sinus

Bmp cosinus

Frequency reference

N*0.025 sec

COMPLEX ALGEBRA PREDICTIVE CONTROL ?!

     -­‐ Bench test of pump gaskets  -­‐      Flow : 35000 m3/h ….! ? - Pressure : 17.50 MPa - Temperature : 330 d°  

PFC controller

PUMP

CONTROL ENVIRONMENT

Pressuriser

REACTOR

Steam generatorr

PFC control joints

Engine

Pump

: " Size : 10 m " Mass : 100 tons " Flow: ~35000 m3/h

Support

PFC CHAUD

Convexité Echangeur Chaud

TEQ = L x T31 + ( 1 – L ) x T0

Prise en tendance de la température d’entrée

F(T0)

PFC FROIDConvexité Echangeur Froid

TEQ = L x T30 + ( 1 – L ) x T51

Prise en tendance de la température d’entrée

F(T51)

Logique de choix de l’action

(Chaud ou Froid)

T5 T0 T31

T5 T51 T30

Consigne de température

Régulation débit chaud

Régulation débit froid

Débit source chaude

Débit source froide

T0

T51

T5

T31

T30

PID

Essai A2si du 17 avril 2012 (673)

15,0

25,0

35,0

45,0

55,0

65,0

18:14:24 18:21:36 18:28:48 18:36:00 18:43:12 18:50:24 18:57:36 19:04:48

Temps (heures)

Tem

péra

ture

(°C

)po

sitio

n va

nne

(%)

PFC

Essai A2si du 18 avril 2012 (676)

0,0

20,0

40,0

60,0

80,0

100,0

14:31:12 14:45:36 15:00:00 15:14:24 15:28:48 15:43:12 15:57:36 16:12:00 16:26:24

Temps (heures)

Tem

péra

ture

(°C)

posi

tion

vann

e (%

)

T Inj

Consigne

retard +3 mn

F1, T1

F2, T2

F, T

F.T =F1.T1+F2.T2 (enthalpic balance)

T=λ.T1 +(1- λ).T2 with 0 ≤ λ ≤ 1

Hyperbolic function ! λ = F1/(F1+F2)

Convexity Theorem

tsf

qf, tef

qp, teptsp

)]11(.exp[1

)]11(.exp[1)(

FfFpAU

FfFp

FfFpAU

Qf−−−

−−−=Γ

Fp, Ff : Thermal flows

Fp = (ρ.Cp)p.Qp Ff = (ρ.Cp)f.Qf.

 SANOFI  

   

VERTOLAY VITRY sur SEINE ARAMON MONTPELLIER KÖLN Training of staff: Transfer of Know How

DIFFUSION  and  PROMOTION  

•  Training  in  many  countries  •  Universi@es,  technical  schools  (IRA  in  France)  •  Training  of  professors  •  Con@nuous  educa@on  of:  

–   Teachers  of  technical  schools  –   Industrial    operators  

•  Documenta@on:  “Techniques  de  l’ingénieur”  

Prac@cal  implementa@on  with  Scilab  

•   The  Scilab  PFC  book:  Text  +  Diagram  +  Program  Code  

•  45  programs  in  Scilab  implemen@ng  PFC  control:  – Elementary  – Ordinary  – Advanced  

Elementary  example:  control  of  an  integrator  process  with  delay  

// E_com_intg12 // process H(s) :integrator with delay : H(s)=exp(-R.s)/s clear; xdel(winsid());clc tf=1200;w=1:1:tf; u=zeros(1,tf); MV=u;CV=u; SP=u;sm=u;DV=u; tech=1;//sampling period r=50; // dealy R=r*tech G=0.01; // proportional gain tau=1/G; // closed loop time constant am=exp(-tech/tau); bm=1-am; //model parameters trbf=250; lh=1-exp(-tech*3/trbf); SP=100; // set point for ii =2+r:1:tf, // perturbation if ii>600 then DV(ii)=-0.2; end // MV proportional loop ec(ii)=MV(ii-1-r)-CV(ii-1); // error MVp(ii)=G*ec(ii); CV(ii)=CV(ii-1)+MVp(ii)+DV(ii); // pfc sm(ii)=sm(ii-1)*am+bm*MV(ii-1); // model spred=CV(ii)+DV(ii)*1+sm(ii)-sm(ii-r); d=(SP-spred)*lh+sm(ii)*bm; MV(ii)=d/bm; // MV pfc end scf(0) plot(w,SP*ones(w),'k',w,CV,'r',w,DV*100, 'k',w,MV,'b') a=gca(); a.grid=[1,1]; a.tight_limits="on"; a.data_bounds=[1,-40;tf,140]; xlabel('sec'); xtitle('Control of a process : integrator + delay CV r / MV b / DV*100 k')

Ordinary  example:  control  of  a  loop  with  constraint  transfer  

// O_pfc_transparent // back calculation, transparent control of level clear,xdel(winsid()),clc tf=1000; //duration of test w=1:1:tf; //time; tech=1;//sampling period u=zeros(1,tf); CV=u;//process output MVp=u; MV=u;//manipulated variable eps=u; //error sm=u; //output of model k=0.1; // gain of integrative process level Kp=0.07; // gain of P(ID) tau=143; // =1/(k*Kp) am=exp(-tech/tau); bm=1-am; //time constant of internal closed loop system by P(ID) trbf=200; //desired closed loop system by PFC: only tuning factor h=1; lh=1-exp(-tech*3*h/trbf); fl=input('fl (1 with back calculation / 0 without back calculation) = '); MVmax=5; //maxvalue of mv SP(1:tf)=100; for ii=2:1:tf, eps(ii)=MV(ii-1)-CV(ii-1); // error of P(ID) MVp(ii)=Kp*eps(ii); // manipulated variable of P(ID) if MVp(ii)>MVmax then MVp(ii)=MVmax;end // constraint on the mvp mvbc=(MVp(ii)/Kp)+CV(ii-1); // back calculation CV(ii)=CV(ii-1)+k*MVp(ii-1);// output of process sm(ii)=sm(ii-1)*am+bm*(fl*mvbc+(1-fl)*MV(ii-1));// internal model of PFC with/without transfer of constraint d =(SP(ii)-CV(ii))*lh+sm(ii)*bm; // computation of mv MV(ii)=d/bm; // computation of mv end scf(0) plot(w,SP','k',w,MVp*10,'m',w,CV,'r',w,MV,'b'); a=gca(); a.grid=[1,1]; a.tight_limits="on"; a.data_bounds=[2,0;tf,230]; xlabel('sec') if fl==0 then title('without back calculation SP k / MVp*10 m / CV r / MV b'),end if fl==1 then title('with back calculation SP k / MVp*10 m / CV r / MV b'), end

Conclusion  •  Dissemination? : where is the problem? •  The technical and economic efficiency of

PFC is clearly demonstrated on many different processes World Wide

•  Implementing PFC: the Scilab PFC book