"Predictive Functional Control" By Jacques Richalet for ScilabTEC 2015

1. PREDICTIVE
FUNCTIONAL
CONTROL
J.Richalet 2015

2. WHO INVENTED
PREDICTIVE CONTROL ?

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

4. Jean Piaget (1896 / 1980)
• Swiss Grand Father of Cognitive Psychology
• How the child learns and controls his
environment
. Four phases ….!

5. 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”

6. PREDICTIVE CONTROL
IS NOT
AN INVENTION
BUT A DISCOVERY ….!

7. Pr
H(C - (n)) (1 - ) (n)yy Mu(n) +
H GMGM(1 - )
λ
α
=
P =
G - se
1 + Ts
M
y
u
θ
= =
y(n) = α y(n-1) + (1- α) . u(n-1-r) . Gα = e
-Tsamp
T
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) Hα
Hu(n) . GM 1 - α
⎛ ⎞
⎜ ⎟
⎝ ⎠
Model increment :
M MP
H 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 …!

8. BAYER
reactor

9. 0 20 40 60 80 100 120
0
20
40
60
80
100
120
TEMPERATURE DE MASSE
d°
min
92°
Tmax=108.4°
Tinit=42°
Figure 4

10. ON LINE ESTIMATOR of
DISTURBANCES
Pert
R1
R2
Cons1 MV1
P SP
SP*
M≡P
MV2
Cons2=SP
+
+
B
+
+
Pert*
-
+

11. 0 10 20 30 40 50 60 70 80
0
20
40
60
80
100
120
ESTIMATION DE L‘EXOTHERMICITE
Tmasse/ Tmasse
estimée
TS-
TE
TS
EXOTHERMIC
ITE
min
Figure 3

12. 31
Reactant
Flow
T1 Reactor
Cooler
Steam
T2
T4
T3
Heat
Exchanger
BASFBASFBASF

13. B A S F

15. 15
R
TM
Fi, Ti Te
R Reagent
¥
r
M
C
P
MV
M
dT
M
dt
= UA T
e
- T
M
+ DHx
reCPe Ve
dTe
dt
= reFi Ti- Te + UA TM- Te
q(Fi) TM+ TM= Ti
.
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

16. Batch Reactor : MV=Qf / CV= TM
DEGUSSA EVONIK
Qf
Tif
Tof
TM

17. Control PID Degussa / EVONIK
Datum | Name der
Präsentation
Seite | 17
time
temperature[°C]
+/- 2 °C
39 different batches with PID

18. Control PFC Degussa / EVONIK
Datum | Name der
Präsentation
Seite | 18
time
temperature[°C]
32 different batches with PPC
+/- 0,2 °C

20. CONTINUOUS CASTING

21. 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
capteur
radio-actif
consigne=70%
PFCPFC
mesure de niveau
cages d’extraction
consigne de poids
tquenouille
PFC
PI
vérin
mesure de position
busette rotative
busette à 2 ouïes
A
A
mesure de poids
amplificateur
de puissance

22. 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

23. -10
0
10
20
30
40
50
60
70
BULGING COMPLEX CONTROL
without with
STOPPER
Amp sinus
Bmp cosinus
Frequency reference
-10
0
10
20
30
40
50
60
70
-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
COMPLEX ALGEBRA PREDICTIVE CONTROL ?!

24.
-­‐
Bench test of pump gaskets
-­‐
Flow : 35000 m3/h ….! ?
- Pressure : 17.50 MPa
- Temperature : 330 d°

25. PFC controller
PUMP
CONTROL ENVIRONMENT
Pressuriser
REACTOR
Steam generatorr

26. PFC control joints
Engine
Pump
:
" Size : 10 m
" Mass : 100 tons
" Flow: ~35000 m3/h
Support

27. PFC CHAUD
Convexité Echangeur Chaud
TEQ = L x T31 + ( 1 – L ) x T0
Prise en tendance de la
température d’entrée
F(T0)
PFC FROID
Convexité 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

29. 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)
Température(°C)
positionvanne(%)

30. 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)
Température(°C)
positionvanne(%)
T Inj
Consigne
retard +3 mn

31. 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

32. tsf
qf, tef
qp, teptsp
)]
11
(.exp[1
)]
11
(.exp[1
)(
FfFp
AU
Ff
Fp
FfFp
AU
Qf
−−−
−−−
=Γ
Fp, Ff : Thermal flows
Fp = (ρ.Cp)p.Qp Ff = (ρ.Cp)f.Qf.

33.
SANOFI
VERTOLAY
VITRY sur SEINE
ARAMON
MONTPELLIER
KÖLN
Training of staff: Transfer of Know How

36. 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”

37. 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

38. 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')

39. 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

40. 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