AUTOMATIC ADVANCED CONTROLOF A DI8TILLATION PLANT

Didier Dumur, Patrick Boucher

Supélec, Plateau de Mouton, F 91192 Gíf-sur-Yvette Cedex, FrancePhone: +33 (0)1 69851375 Fax: +33 (0)1 69851389 Email: Didier.Dumur@supelec.fr

Distillation is not as simple as is generally believed. Given the very high nuinber of components inwine, the phenomena involved are infinitely complex, The lack of precise mies and the initiativeIeft up to each distiller mean that Distillation is an Art rather than a technique.

The distillation method used at MARTELL in COGNAC, a finn founded in 1715, follows the mainprincipies of Charente Distillation. It is the outcome of years of observation and countless triaIs .This vast experience has always been guided by the best tasting specialists.

Distillation lasts from November 1st to March 31st• The "eau-de-vie" is obtained after twodistillations or "heats" . First the wine is distilled to produce the "brouillis" and then the larter isdistilled in tum to produce the "eau-de-vie". The two "heats" are done in different boilers (the firstwith a125 hl capacity and the second 25 hl). Nevertheless, the operating principie is similar in thetwo cases, as illustrated in the flow chart given on Figure 1.

St:d<(I\:ir,Tdr)

Ibd

111><_ inlnodrsprib-

'Rne:Sbd<_ 11m:Sbd<larJl'I1lIlnTd.:1i:Ild1l!rrp!r1lbftTat::SMnd<"""""""

AIatdanrtby\dllT<"lhe cbolI'

Q!:cw_ftown* 11(:CW_lmpnOlnQ1: 1JlliI*1ow....Td:I-.1mpnIlnTAVd:Alatdanrtby_lnlhe.-Thp

Fig.l - Distillation flow chart ("brouillis" and "eau-de-vie")

698

1. Introduction: Distillation in the Charente tradition

The first "heat" may be broken down into four stages, as summed up on the flow chart ofFigure 2.

J "Mise au Courant", the first stage, lasting roughly an hour and a half, during which theliquid is brought to a boil.

J First run, lasting roughly fifteen minutes , during which the initial product may be removedifthe wine's quality is doubtful.

J "Brouillis" run, lasting eight hours on an average, through to the cut (stage at which thealcohol content reaches 2%). The "brouillis" will be the charge in the "good heat",

J Cut stops the distillation and the remaining content in the boiler is removed .

W: ,---- - - -- --- -- r -ines Boilers 125 hl

__

Boilers 25 hl

Mise aucourant

mmmFirst run Brouill is '" 50hl

--1----r Boilers 25 hl

"Goodheat" J "Good

heat"

_,I First run "Hearts'U'Seconds" First run "Hearts" "Seconds"-I-+-__ - I I__.. -1- .. J ..J

Fig.2 - Flow chart of double distillation process (MARTELL distilleries)

The "good heat" may be broken down into four stages as summed up on the flow chart Figure 2.

J "Mise au courant", the first stage, lasting roughly an hour and three quarters, during whichthe liquid is brought to a boil. -

J First run, lasting thirty to thirty-five minutes . These runnings will be reinjected into the winefor another first "heat" ,

699

,f "Hearts" run, lasting five and a haIf hours on an average, through to the cut at 60 (stage atwhich the alcohol content reaches 60%). The "hearts" make up the spirits which the distillerwill use to make "cognac".

,f "Seconds" run, consists of running the rest of the charge, for as short a time as possibIe,until the cut at 2. (the alcoho1 content reaches 2%). The "seconds" are reinjected into thewine and the first runnings to undergo a whoIe new distillation.

2. Towards a computerised management of the process controI

There were aIready two distilleries at the Gallienne site in Javrezac, one of them older (which wasshut down in 1996) composed of small 18 hl boilers and the other, more modem, installed at thebeginning ofthe 70's. The new project was located in the prolongation ofthe rnost recent distillery.

The innovations in the Gallienne distillery lie in the nature of both the distillation automationprocess and the auxiliary shops. For example, the coId water production circuit (closed loop) islocated outside the buildings, but is an essentiaI link in the good operation of the distillery. Anyfailure at this leveI wouId have an immediate impact on the regularity of the run temperature andthus on the quality ofthe "cognac".

The main innovation in the distillery invo1ves the procedure to automate the stills. The project ledto MARTELL's developing an in-house process computing department. The ·obj ective of theautomation approach implemented was to determine the most effective still controI system possible,whileat the same time developing a tool to observe, describe and better understand the phenomenainvolved in the running cycles. This approach had .a twofold objective: to acquire a rationaItechnical observa-tory capable of modifying the distillation parameters on-line; and to compile atechnical data base on distillation that can provide research guidelines. The final quality of theproduct has been one of the constant concems underlying this endeavour.

The [mal focus of the research was to achieve better control over distillate running. The principIebehind MARTELL'S distillation method imposes very precise flow rates and temperatures throughoutthe entire running phase. The initial idea was to succeed in controlling the operation of the bumerand the cooling water circuit on the basis of real-time measurement of the running rate and distillatetemperature.

Until now, the gas pressure and cooling water flow rate commands were set at the beginning ofthe"heat". Those curves, the result of experience, were set according to the amount of distillate to berun and the alcohol content by volume of the "brouillis" to be distilled. These commands were thenapplied by the operators to the actuators in chronological arder, with the flow rates and temperatureread and compared to the distillers' objectives.

The approach taken was to reverse the problem, by defining the distillate flow rate and temperaturecurves desired by MARTELL and then by adapting the commands to be applied on-line so as toobtain the specified result. In automation, this is known as switching from an open to a closed loop.This was made possible by acquiring real-time measurements on system inputs and outputs andstoring those measurements in a monitoring system. In particular, the distillate flow rate was notmeasured, so the necessary instruments had to be installed. Finding the right flowmeter for theproduct and the flow rates was a problem; many different sensors were tested before onecompatible was found.

700

3. Systems approach to automation: Modelling and identification

The first stage, typi cal of any advanced process control study, was to build a mathematical model ofthe system ' s behaviour. A simple behavioural model, of the input-output type, was chosen torepresent the processo However, the multivariable aspect of the system (two inputs - gas pressureand cooling water flow rate, and two outputs - distilled product flow rate and temperature)complicated the representation (Figure 3) and, more importantly, made obtaining. the modeIexperimentally more difficult. .

This identification phase was conducted for several distillation campaigns, without disrupting theplant's operation, simpIy by anaIysing the signals registered, with a sampling period Te = I min ,during the different "heats".

Distillate flow-

temperature Td

'essure Pg rate Dd...• DistilIation ...process ....

ng water DistillafeCooliflow-rate De

Gas pr

Fig. 3 - MultivariabIe input-output modelling

Model definition . With the objective of implementing control techniques on this system, whichparticularIy require the definition of an input-output numerical modeI, this model was identifiedunder the following MIMO transfer function:

A(q - I )y(t) =B(q - I )u(t - d) (1)

with:[Y I (t)] [Dd ]Y(t ) : vector of the 111 sys tem ou tputs y(t) = = ;Y2 (t) Td

[

U I (t)] [Pf!;]u(t): vector ofthe m controI signals applied to the system u(t) = = ;. U2(t) De

where it is assumed that det A is not equal to zero and d corresponding to the deIay time of thesystem is chosen equaI to 1.

701

Method. The best prediction of the system outputs at time t +1, using data up to time i, is obtainedfrom Eq. 1 under the foIlowing vector form [13] (Ê>i is the estimate ofthe parameters vector Si):

with:

j\(t + 1/ t)= Ê>T (t) for 1s i 2

(t) =[-YI (r), ... ,- Yl (t +1- na )'''':'Y2(t), "',-Y2(t +1- na),uI (t), ""UI (t - nb),u2(t), ... ,U2(t - nb)Y

SJ =rail 1, ··· , a il ll ,ai21, ..·,ai2ll ,bilQ, ... ,billlb,bi2Q, ... ,bi2n], a , , a' , . ' , b

(2)

The ê i vector is then obtained through a recursive least squares algorithm with forgetting factors,according to the classical set of equations [8],[9]: .

êi(t + 1) = Ê>i(t)+ F(t i(t + 1)

F(t+1)=_1_[F(t)- ]111(t)

c .(t+1)=Yi(t +1)-êJI

(3)

(4)

(5)

The identification of a simple model but including sufficient information (mainly dealing with thecoupling terms) has been performed with the tuning: na = 2; nb = 1 ; 111 (t) = 0.95 ; 112 (t) = I.

Validation. A parameters set has been first estimated using a particular data file, then the quality ofthis rnodel has been tested comparing the estimated and real outputs using another data file . Theresults of Figure 4 show that the estimated and real outputs completely agree. Other tests looking atthe evolutions of the estimated parameters, the a posteriori errors, bode diagrams and step responsesof the transfer functions have been performed and enable to validate the adopted approach.

,-'-,,

Time (min) 1

25 - - --l - - - - l - - - - l- - -- -l - - - - r - -- u l -I I Distillatc tempernturc (DC, II I I I • II I I I I I- - - t - - - - .- - - - - I - - - - I - - -. - .-I I I I Ir 1 I I I

15 - - - _1 - _ h _ • .1 _ _ _ _ _ •• .J _ _ _ L _ _ II I ' I II ' I I

t I I r I10 - -- - -1 - - - - + - - - - 1- - - - '"" - - . - I- - - - l -

I I I I II r I I I II I , r I I

5 -- -· ··.---- - T "----'- - - - -, - - --r - - -r -'I I I I I I1 I I I I

O . - - .- -: - - - --+- - - -;- .... - -;- -I I 1 I, , ,

Distillatc flow-ratc (Iih)2CO

150

250

. . .- I - - - .. .- - - - - , -, ,, ,-1- - - ---1-

I r I 1I I 1 1 1

- - - 1- •• - - T - - - - - _. - "I - - . - 1- - - - -

i 1 1 1 t II I 1 I I I

SO - - - - 1- - .- - , --- .. ,-- - -' - .. -r-- - r "I I 1 1 I I

O - - - -: n - - - T - - - -:- - - - "l - - I-I=:===r...l'ti l I 1 II 1 1 1 I I

- - - -' .- - - - r .- - - - 1- - - - , - - - r - - - ·-1 -I 1 1 1 1 1I 1 1 I I 1

-100 - -- -1- - - - r -- - -,-- - - .- - - Time(min)-l -

100 200 300 400 500 600 100 200 300 400 500 600

Fig. 4 - Comparison between the estimated and measured outputs(with identification coming from another data file)

Thus the models derived from Eq. (1):

y(t) =H(q-I)u(t -d) (6)

702

representing the different boilers of same capacity, showed a superimposable behaviour in thefrequency band useful for controI. Figure 5a shows the Bode plots of distillate flow rate and gaspressure identified transfer functions for different boilers. Bode plots of distilled producttemperature and cooling water flow rate transfer functions for different boilers are given Figure 5b.

. Fig. 5a - Frequency-response.gas pressure => distillate flow rate

Fig. 5b - Frequency-responsewater flow rate => distillate temperature

This analogy provided the foundations for robust control, that is, the use of a single controllerstructure for all MARTELL's boilers of same capacity, moreover identical for the"hearts" or"seconds" runs.

4. Distillate flow-rate and temperature P.I. control

In light of the available equipment, and as a first experience in control, a structure as simple aspossible was chosen to make it easier to implement on site.

Basic PID theory. A desired form of response (in terms of stability, rapidity and accuracy) isgenerally attained by incorporating some form of controller in the loop, namely acting on the errorsignal to generate an appropriate input signal for the processoThe general structure of such acontroller is called the Proportional Integral Derivative (PID) structure [11], [12], which includesthree complementary actions: .

,f The proportional action Up(t) = Ke(t) , or Up (8) = Ke(s) (with s the Laplace variable),which aims at increasing the transient velocity when increasing the proportional gain, butmay damage stability, .

t

,f The integral action Ui(t) =K fe(t)d't, or Ui(s) = K e(s),whiçh cancels the steadyT t:»1 o I .

state error when the input signal is constant, which is commonly a system requirement, buttends to destabilize the system,

703

./ The derivative action ud(t)=KTd de(t) , or Ud(S) =KTd sc(s), which may increasedtstability but aIso amplify any high frequency noise present in the signal.

Globally, the transfer function of such a PID controller is given by the following relation:

IRp/D(s) =K(l +- + Td s)li s

(7)

where K is the proportional gain, li is the integral time constant (in sec) and Td the derivativetime constant (in sec).

From this relation, and with Te as sampling period. :the discrete form of (7) can be derivedconsidering the Euler approximation for the derivative action and the rectangular approximation forthe integral action, leading to:

Finally, the controllaw can be rewritten under a RST form, Ieading to the difference equation:

(8)

with:

S(q -I) u(t) = -R(q -\) y (t ) +T(q -I) w(t)

S(q-l) = l-q-I

R(q-I)= T(q-l) =K(I + Te + Td ) _ K q-I (I +2Td ) +K Td q-2li Te Te Te

(9)

(10)

where u(t) is the controI applied to the system, y (t ) the system output and w(t) the setpoint.

Experimental results for the "Good heat" case. Using only the diagonal terms of the H(q -I)matrix, two single-variable P.I. controllers were synthesised (with Td =O), one controlling the gaspressure depending on the distillate flow-rate, and the other controlling the cooling water valvedepending on the distillate temperature, as indicated on Figure 6.

Equivalent flow-rate .. polynomial control1er ,-----,

f--------------,

T"

Fig. 6 - Monovariable PI control ofthe distillation process

704

The supervision showed that ramp demands as flow rate setpoints seemed more fitting than stepsetpoints as initially planned. In fact, such setpoints avoid sudden variations in gas pressure, knownas "gunshots", and at the same time any major disturbances in the distillate temperature.

However, this structure which is appropriate for the "hearts" runs, must be modified during the"seconds". In that phase, a phenomenon specific to the product arose. The charge, as its alcoholcontent fell, modified the behaviour of the overall system, inducíng a flow-rate drift in the system(actually a derivative effect), causing a closed-loop static error which increased constantly as thedistillation continued.The solution chosen was to opt for an adaptive controller, to compensate for that error by increasingits gain over time, í.e. as a function of the alcohol content by volume.

This approach, tested and validated on a numerical simulator of the instaIlation designed on thebasis of the modeIling made, was successfully implemented on the real system. Experimentalresults given on Figures 7 ando8 correspond to lhe foIlowing tunings:

i. For the "hearts " runs:

.t Distillate flow-rate P.I.:

.t DistilIate temperature P.I.:

ii. For the "seconds'':.t DistilIate flow-rate P.I.:00.1 DistilIate temperature P.I.:

K =1.23;1';= 3minK = - 750; 1';= 10min

K =1.23up to 6;1';= 3minK = - 5000;1';= 10min

H----- --- - --- ------- o--

Fig. 7a - Distillate flow-rate controlled by PI /RST (during the "hearts"),

Flow-rate setpoint (litre/h), distillate flow-rate(Iitre/h) and gas pressure (gram) versus time

(min)

0'-_- 0_

lSo:JO O 0_l

- .- -- -+---,--

Fig. 7b - Distillate temperature controIled by PI / oRST (during the "hearts" and "seconds").Temperature setpoint (100 x "C), distilIate

temperature (100 x "C), cooling water flow-ratesetpoint (litre/h) and measured cooling water

flow-rate (Iitrelh) versus time (min)

We can see on Figure 7b that the control leeway is not as broad and that some of the setpointsrequested cannot be reached: for example, as when t < 75min , distilIate is toa cold, even thoughlhe water valve is c1osed.

705

Chaudiàre 25 - Distillatian du3OAl1l1996, • , , , I , • •Si " . ., . I , ,

"'"'i5

'"

o O ,...340 3liO 380 400 420 440 460 480 500

tempsenminules

Fig. 8a - Flow-rate control without an adaptívegain (during the "seconds")

Chaudiére25 - Dislillatian du llill3Il996

Fig. 8b - Flow-rate controI with an adaptive gain(during the "seconds")

As it can be seen on Figure 8, the static error is Iower as Iong as the actuator is not saturated (inother words, as long as the maximum gas pressure has not been reached). However, once the vaIveis open full (roughly t =:= 430 min), we retum to the preceding problem, since we run up against thesystem's constraints. Efforts must be made to define the ideal controI strategy whíle taking theinstallation's constraints into consideration,

Experimental results for lhe "Brouillis" case. After solving the probIem of the "good heat", thestudy then focused on the "brouillis" run: the first "heat" 125 hl capacity boiler were identified, themodels of the different 125 hl capacity boilers show similar behaviours of those used for 25 hIboilers. Thanh to this simiIarity, the use of P.I. controllers was tested on the numerical simulatorand the experimental results of Figure 9 prove the excellent behaviour of this distillation phase.

.'

Fig. 9 - Distillate flow-rate and temperature controlled by PI / RST.Temperature setpoint (100 x,°C), distillate temperature (100 x 0C), flow-rate setpoint (litrelh),

distillate flow-rate (litre/h) versus time (min)

5. Predictive Control

5.1 Monovariable GPC controllers

A Generalised Predictive Control structure (OPC) [1], [4], [5] and [6] has been studied, to improveperformances obtained with P.I. control previousIy developed.

706

Basic ideas. Predictive Control philosophy ean be summarised in five main ideas, whieh areeommon to alI methods:

I) Definition of an anticipative effeet by using the explicit knowledge of the evolution of thetrajeetory to be followed in the future (this knowledge is at Ieast neeessary over a few pointshorizon from present time) .

2) Definition of a numerieal model of the system, used to predict the future behaviour of thesystem. This discrete time mode! is often obtained through a preliminary off-lineidentification. This main feature enables to include Predictive ControI within the 'ModelBased ControI' family.

3) Minimisation of a quadratic cost function over a finite future horizon, using future predictederrors , difference between predicted system outputs and future setpoint values or values of areference trajeetory which is in fact a filter of the setpoint.

4) Elaboration of a sequence of future controI values, optimaI according to the previous costfunction, but only the first value is applied both on the system and on the mode!.

5) Repetition of the whole procedure at the next sampling period according to the recedinghorizon strategy.

Output j :

Setpoint IV

Future control values

The polynomiaI predietive controllerperformed through the minimisation ofthe cost function and modelIed in a RSTform enables the predicted output totend toward the setpoint or the referencetrajectory over a prespecified predictionhorizon.

Fig. 10 - Predietive Control strategy

Past Future t + h

. Due to the receding horizon strategy,only the first control value u(t) isapplied to the system. Thus it will bepossible to decrease the number ofcomputed controI values in thesequence.

Some elements 01 resolution. Taking only the diagonal terms of the MIMO representation Eq. 1,the mono-GPC law uses a SISO externai representation form, under the polynomiaI form [3]:

(11)

II is the controI signal applied to the system, y the output of the system, Ll(q -\ ) =I - q -I thedifferenee operator, A and B polynomials in the backward shift operator «' . of respective orderna and nb' ç, an uncorrelated zero-mean random sequence.

From the previous model Eq. 11, a polynomial optimaI predictor is designed:

y(t+j / t) =Fj (q-l)y(t) +Hj(q-l)LlU(t -1) +Gj(q-I )Llu(t + j -1)+Jj(q-l )ç,(t+ j) (12)• v I \ v '

free response forced response

707

Unknown polynomiaIs Fj , Gj' H j and J j are derived soIving Diophantine equations, withunique soIutions. In the further developments, the term related to future disturbances is taken equaIto zero, corresponding to the best prediction of (t + j).

The criterion is a weighted sum of square predicted future errors and square controI signaIincrements:

N 2 NII

J= :L (jJ(t + j)-w(t+ j)f+À:L.ó.u(t+ j_l)2j=N1 j=1

With the matrix form ofthe predictor Eq. 12:

y=Gõ + if y(t) + ih .ó.u(t -1)

the minimisation ofEq. 13 written in a matrix form provides the future controI sequence:

(13)

(14)

õ = M [w -if y(t) - ih .ó.u(t -1)] (15)with:

if = [FN1(q-l) FNz(q-I)]'

ih = [HN1(q-I) HN/q-l»)'

õ = [.ó.u(t) ... .ó.u(t+Nu -1»)'

y = [y(t+NI ) y(t + N2»)'w= [w(t+NI ) w(t+N2»)'

N1 N1gN, gNt-1N1+I N1+1

G= gN1+I gN1

N2 N2 Nzg N2 gNrl gN2-NII 1-1

M =[G'G+ÀINII ]-IG' dim V, x(N2 +1)

The GPC controller is implemented under a RST form through the same difference equation Eq. 9as defined for the P.I. controI, with:

S(q-I) =1+ml ihq"":lR(q-I) =ml ifq-I

T(q) =m, [qN1 qN2 ]

dO[S(q-I)]=

dO[R(q-J)]= dO[A(q-I)]

é[T(q)] = N 2

Autotuning strategy. With the polynomial model of the controller and the definition of transferfunctions, the stability of the controlled loop may be examined for specific parameter values. Fromthis frequency study in the Bode and Black planes, a method which generates sets of parameters(N I ,N2' Nu'À) assuring closed Ioop stability can be elaborated. These results offer the nonspecialists a method to compute these parameters in a transparent way. The main points of themethod, completely developed in [2], [3], are the following.

708

./ The selection process for the RST parameters is accomplished by generating a large parameter set(N1 ' N 2'N ú ' Â. ) assuring closed-loop stability. This set is denoted as admissible parameter values.The proposed approach considers a restricted area in the Black plane, which ensures a minimalstability requirement. Thus a set of parameters is admissible if the frequency curve of the loopgain remains outside the restricted area illustrated in Figure 11.

25 ,-- - - .,--- - - ,--- - - -,-- - ----,Module [dB] : :

I I

20 -- -- .. - -- : - - .I II I

III

• _ I .. . _

III

I

I Phase [degree)

I

5

o

10

15 - .. Complementary sensitivity funct ion 3 dB ..

\

-210 -180 - 150 - 120

Fig. 11 - Restricted area in the Black plane

This area is the region outside where the direct sensitivity function is greater than 6 dB:

cr -d

and outside where the complementary sensitivity function is grea ter than 3 dB:-IBRo =--q..::....-_-

C

(16)

(17)

In particular, this restricted area ensures a minimal phase margin of 45° and a minimal gainmargin of 6 dB. The delay margin is also examined .

./ Systematic studies and observations of different stable, monovariable, non derivative systemswithin the automatic control field has lead to the following remarks or empirical generalizationrelated to the evolution of the phase and gain margins as functions of the tuning parameters:

i) The parameter N 1 is fixed, equal to the deadtime of the system.ii) N induces small evolution of the phase and gain margins, thus choosing large values of

/I

this parameter increases the complexity of the algorithm without improving the stability.iii) For a particularN 2 ' there exists values of Â. providing a maximum phase margin.

Based on these remarks or observations, two relations can be established:

i) N is chosen equal to one due to its fair influence on the stability margins:li

N =1li

(18)

ii) The 'optimal' Â. is bound to the gain of the system through the relat ion:

709

(19)

This fundamental relation decreases the range of admissible values and hence, search canbe carried out over a smaller range of values. In particular, the search range is one decadeabove and below the nominal values, Eqs. (18) and (19).

J The search phase is perfotmed according to stability and robustness, considering the variationsofonly two parameters, as follows:

N = dead - time of the system =11 sampling period

N 1 Nresponse time of the system+ S S

1 2 sampling periodN =1

/I

0.1 Àopt =0.1 tr(GTG) S À S 10 Àopt =10 tr(GTG)Simulation results. This GPC law was designed only on the "good heat", which is considered as the. most important distillation phase, and during which the trajectories are more precise and difficult tofoIlow. This controllaw has been first tested in simulation.

Parameters Description Choice

N, Minimal prediction horizon 1N z Maximal prediction horizon 5N Controlhorizon 1

/I

'A Control weighting factor 0.125Sampling period 1 min

Umin'umax Control signal constraints 50, 1000 gram

Table 1 - Definition of the distillate flow-rate 100pGPC parameters

Parameters Description Choice

N 1 Minimal prediction horizon 1N 2 Maximal prediction horizon 5N ControI horizon 1

11

À Control weighting factor 0.1T Sampling period 1 mine

Umin ' Umax Control signal constraints O,lOV

Table 2 - Definition of the temperature 100pGPC parameters

Two monovariable GPC controllers, one for the distillate flow-rate, another for the temperature, aredesigned using the polynomial approach and the RST structure, this form being well adapted to areal time implementation and making a simple transition from the P.I. controllaw. To obtain a very

710

simple controller, easy to implement in the current numericaI environment of the plant, the choiceofthe maximum prediction horizon N 2 was chosen equaI to 5 (TabIes I and 2).

The results obtained in simulation, with two mono-Gl'C controllers for the distillate flow-rate andthe temperature, presented on Figure 12, are very interesting and extremely encouraging. Incomparison with the P.I. controllers of section 4, the flow-rate trajectory is strictly followed,without tracking error and the temperature behaviour is more nervous, with better decoupling,specifical1y at the end ofthe "hearts" and the beginning ofthe "seconds".This controI allows a partiaI decoupling, and so a better tracking of trajectories, thus a morenervous controI of the two Ioops is possibIe, without disturbance on control signaIs or pIantdestabilisation.These simulation results obtained with predictive controI seem to be very attractive in terms of rapi-dity, tracking error, stability, smoothness ofcontroI signals and decoupling effects ofthe two Ioops.

500Time (mn)

400300200100

2

20 , ,Temperalure (0C) : : , ,18 J i. - , - - - - - - -' - -

" ,t I I I

16 , .- - ,, - -' - ----- - " -- - - - -,- - --- --<--I I I I II I I I I

14 - - - - - - 1- - - - _ • . oi - - - - - - - - - - - - 1- - - - - - -i - -I I I I 1I I I I I12 - - - - - - ,- - - - - - 't - - - - - - - - - - - -, - - - - - - - .., - -I I I I II I ! I10 - - - - - -,- - - - - - -- - - -- - -- - t- - - - • .. - - - - - -, - -

Waler flow rale (volt) I : :8 - - - - - - ,- - - - - - "1 - - -- - - - r - - - - - - , _ .. - - - ., . .. .

, I I I I

6 - - - - - - - - - _ .. - - - - - - - - - - - - : - - -: - -. ,, ,_.. -- - - - -_. - - - - - - - - -,.. -I I

. . _ _ .... _ L __ .• , . _ I _ • •, ,,500400300200100

20

I I I I ,I I I I I

180 - u - - - - ,- - - - - - • • -- -- - -- - - " - - - . • .. - - - - - •••• - -

I I I I I1 I I I

160 - - - - - -,.. - - - - - -l - - - - - - - - -- - - , - - - - - .. -

Flow-rate (litre / hour) : : :140 - - - .. - - ,- - - - - - 1 - - - - - - r- -- - - - -t r- - - - - - - -I I I I II I I I I120 -- - - - - - r- - - - r - -- - . - - '.- - - - - -- , - .. "I I I I I100 - - - - -,- - - - - - , - -- - -- r -- - -- ,- - - -- - -, - ..I I I I II I I I I

- - - - - , -- - - - - 1 - - - -- - -. r - - - - ,- - - - - - -, - -I . t I , II I I I I- - - - - - , - - .- - - - -; - _ .. - - - I - - - - - -,- - _. - - - , - --, ,

- - - - __ - - - __ - - - - - - - - - _!.. - - - - - 1- •. _I _ _I I I I, "

_ 1 .' L . . .. 1_ I ..

: ' : : Time (mn)

Fig. 12 - DistilIate flow-rate and temperature with two Gl'C control1ers (simulation)

Experimental results. The proposed structure, very simple and easy to implement, withouthardware modification and few software developments, has been tested on site and resuItspresented on Figure 13, obtained with these two controIlers, are very cIosed to simuIation.

Fig. 13 - Experimental distillate flow-rate and temperature controlled by OPC I RST (hearts)Left pIot: FIow-rate setpoint (litre/h), distilIate flow-rate (litre/h) and gas pressure (gram)

versus time (min)Right plot: Temperature setpoint (100 x "C), distillate temperature (100 x 0c), cooIing water flow-

ratesetpoint (litre/h) and measured cooling water flow-rate (litre/h) versus time (min)

711

5.2 Multivariable GPC controllers

Without loss of generality, the multivariable GPC theory [2], [7] is presented here in the case of a minputs-m outputs multivariable system (with m =2 for the considered application).

Basic notations. The numericaI modeI ofthe system is defined under the CARIMA form Eq. 1. Thecost function to be minimised is a weighted sum of squares of predicted outputs errors and controIsignaIs increments:

with:

and:

Su, (t+ j) =O for j N ui

Wi (t + j) : the setpoints at time f + j ;)li(f + j) : the predicted outputs at time f + j;Su, (f + j - 1) : the future controI increments at time f + .i-1 ;N li , N2i : minimum and maximum prediction horizons;N ui ' À; : controI prediction horizons and controI weighting factors .

(20)

(21)

In our further developments, it will be considered that the prediction horizons N 1; , N 2i and N uihave the same value on each channeI, respective1y N 1, N 2 and Nu .

Similarly to the monovariab1e reso1ution, the predictor takes the po1ynomiaI matrix form:

y(t + j /f) =Fj(q-I)Y(f) + II j(q-I)L\U(f -1) +G j(q-I)L\u(t + .i-1) + J + j) (22)\ v I , V I

free response forced response

with: y(t) = [YI (t)U(f) = [UI(f)

Ym(t)Y;. ]Tum(t) .

where the F j ,Gi> II j ,J j are m xm matrix po1ynomia1s:

na

Fj(q-l) = IF;q-i;=0j

G .(q-I) ='"c'q-;j I

;=0

soIutions ofDiophantine equations:

I1b-2

II j (q-I) =I lI:q-ii=Oj-IJj (q -I) =I J:«'i=O

712

The optimal predictor defmed between N1 and N2 assumes that the best prediction of thedisturbance signal in the future equals zero, thus:

(23)

The minimisation of Eq. 20 provides the RST matrix form ofthe optimal controIler (Figure 14):

(24)

(25)

oA=

S(q-') =r, +q-IM 1IHR(q-I)=M1IF

T(q)=M1 [qN11m 0' 0 qNZ1mY

w(t) = [WI (t) 00 o wm(t)Y

[

FNI(q-I)] [F;J J [HNI (q-I)]IF- : - . : IH-: - :

- FN - FNz+o.;FNZq-lla · - H (q-I) - HNz q-nb+2Z O na Nz O nb-Z

OO

OG NzNz

I T )-1 TM 1 first line of \G G+A G

with:

In the G matrix, the coefficients are in fact equal to the Gj step response coefficients at time)of the m inputs-m outputs muItivariable system, so that:

G j =[gfi ... gf"J. 0 0 0 gmm

where is the step response coefficient at time} for the transfer between the eh• input and thei/h output. ConsequentIy the G matrix is oi' dimension m(N2 - N 1+1)x (mNu ) and explicitIyconsiders the coupling terms ofthe system.

Equivalent polynomialmatrix controIler

u(t)

Fig. 14 - Equivalent polynomial matrix controlIer.

713

Some elements for an autotuning strategy. In this part and further developments, the particularvalue m =2 will be chosen corresponding to the Cognac distillation case. Similarly to the approachdeveloped in the monovariable case [2], an automatic design of the tuning parameters has beenimplemented to help non-specialist users . In the multivariable case however, an autotuning strategyappears much more complex to elaborate. In fact, if N1 keeps the same meaning and may 15echosen looking at the delay time of the system, if it may be easily assumed that N 2 can be here thesame for the two channels, the autotuning approach consists now in a four dimensional researchphase, during which N2 ,Nu, 1..1 and 1..2 will vary. The developed approach is the following:

./ N1 remains constant and with the same value for the two channels:

with d, delay time of channel i (26)

< The user must choose a value for the N z parameter (same value for each channel), looking atthe response time of the system, in a similar way as in the monovariable case.

v' Generally speaking, the choice of Nu (same value for each channel) depends on the systemorder, and this parameter choice is not as simple as in the monovariable case. Successive valuesof Nu, with NJ Nu s Nz,must be analysed.

v' For ·NJ Nu N 2 ' a two-dimensional research phase is developed, considering 1..1 and 1..2variations. With this configuration , the influence of these two parameters on the stabilitymargins (input and output phase margins,input and output positive and negati ve gain margins)is examined, within the framework of unstructured and structured uncertainties, from theconcepts ofunstructured and structured singular values, with u-analysis techniques.Furthermore, to decrease the research range, "optimal" values (in tenns of stability) of the À.j

parameters may be found for a particular Nz and Nu parameters set, according to thefollowing relation, which is in fact an extension of the monovariable case to a multi channelssystem:

(G j step response coefficients matrix for channel i) (27)

A two dimensional research is thus performed from one decade around these 'optimal' values.

.Simulations results. To eliminate the strong coupling effect which appeared using themonovariable GPC, the MGPC algorithm, with the autotuning strategy, has been applied to themultivariable modeI of the Cognac distillation identified in section 2. Two GPC parameters havebeen fixed a priori: NJ =I,N2 =5 to reach an easy implementation (polynomial of small degrees).

In the monovariable case, the robustness and stability of a system are studied looking at thesensitivity functions, and the gain and phase margins. The generalisation to the multivariable case isachieved through the concept of structured and unstructured singular values under structured orunstructured uncertainties, using u-analysis techniques [14]. From thecomputation of thesesingular values, input and output stability margins can then be deduced [10], representative of thesystem performance. Only results with structured singular values, which are less restrictive (lesspessimistic case), will be presented above.

714

Figure 15 disp1ays the evolution of the stability margins for the particular value Nu =2 , showingthe input and output stability margins, as a function of the control weight ing factors /...1 and /...2 .These contro1weighting factors variations are plotted in a logarithmic scale with norma1ised valuesin comparison with the optimal term ofEq. 27.

AXeX -> logUam1/11nl 11n=0 .001514 <: AXeY logUam2 /I2nl 12n=1.041e-00G

o·1 ·1

1r,put phase

_-- -----7... -... -2 _ - - I I ;-- "' _ ...

t _ ..J.. I .

1 _ - - - - - - - - : ... ... ... "';-... ... :I Io J

1

o-1 ·1

Inputposl tive and negative ga in

___ - - - - - 7 ..... ... __0.4 _ - - I I I - _

_- ----} ...... ... ...:...0.2 - - - I I

I

o-1 -1

Outputphase

_-- ---7.........--- , ...-

------- -;- - ... _-4 _ - - - I I -

2 - - - I I

o1

o-1 -1

Outputposltive and negative gain

o1

20

4

o1

__- - - - 7 ... ...... __I I I '"

II

--- ...0.4 _ - - - - : ...... ...;- .........

I _..I..1. _ - - - J ... ...

0.2 - - - I II

Fig. 15 - Input and output stability margins evoIution (structured uncertainties) functionof the control weighting factors /...1 and /...2 for Nu =2

In a general way, the autotun ing strategy has provided the resuIts of table 3, showing for severalvalues of Nu the maximum input and output stability margins e input phase margin , eminand minimum and maximum input gain margins, output phase margin, and

minimum and maximum output gain margins), as a function of the controI weightingfactors /...1 and /"'2'

N = 2 N = 3 Nu = 4 Nu = 5li 11

Case I Case 2 Case I Case 2 Case 1 Case 2 Case I Case 2/...1 = 1,5 10-4 /..., = 1,5 10-4 /...1 = 4,5 10-3 /...1 =8,110- 5 /...1 = 4,9 10-3 x, = 9,3 10- 5 /...) = 3,2 10-3 /...1 = 8,9 10-5

/...2 = 1,0 10-5 /...2 = 1,0 10- 6 /...2 = 2,7 10-7 /...2 = 1,2 10-6 /...2 =1,3 10-7 1-2 = 1,3 10--6 /...2 =.7,5 10-8 /...2 =1,3 10--6

(0) 0.23 1.69 0.228 1.45 0.16 1.44 0.26 1.45.6.Gemin (dB) -0.649 -0.639 -0.400 -1.578 -0.418 -0.247 -0.658 -0.318

(dB) 0.652 0.620 0.407 1.378 0.424 0.248 0.676 0.315(0) 17.94 17.05 17.69 10.70 15.86 9.75 14.22 9.6(dB) -60 -47.96 -24.58 -6.411 -24.88 -7.64 -5.78 -50.45(dB) 15.78 9.568 14.49 12.11 14.34 13.30 12.26 13.24

Table 3: Stability margins for several Nu values within the structured uncertainties frameworkcase 1: maximum output phase margin - case 2: maximum input phase margin

715

From the previous results, it can be noticed that the autotuning strategy provides "optimal" stabilityfor Nu =2, greater values decrease the phase margins, a smalIer value gives an unstable controller,even if the closed-loop is stable. Case I which gives maximum output phase margins with toaimportant control weighting factors lead to slow temporal responses and must be left out. Case 2realises the best compromise between input and output stability margins, with less importantcontrol weighting factors, thus with a better rapidity.

With the particular tuning N I = I;N 2 = 5;Nu = 2;À.[ = 0.00015;À.2 = 0.000001, selected in table 3,the results of figure 16 shows that the temperature and flow-rate trajectories are correctly folIowed,almost without overshoot and track.ing errors. '

_ _ _ _ L- _

,Gas pressure (gram / 10) :

I

Distillate tlow-rate (litre / h) .. :__.... .. ,, ,, ,-. _ .j ._ • • _ • - 1 _,,,

50 - - - .. - - - -: - - - - .-- - _ 1_ - - - - -- - - •. - - - '--- - - - - 1- - -

150

100

500400

II, , ,

1000l-..-----'-----'-----.l..-.-.:...----'-----1----JO

20

500400300200

Waterflow-rate (vol t)

100

Distillate temperature (0C)

oL-__---'- ...L..<'---__1 ---'- -1----J

O

15 - - - - - - - .1 .• - - - .. - - _I - - - - .. - - - . • . • - - .. - - - - - - - - - - ;- -- - •

I I, II - • - .• - .- - - 1- . - .. -,10

5

Fig. 16 - Distillate flow-rate and temperature. Gas pressure and cooling water flow-rate

These results , compared to monovariable ones, proved that this control law takes into accountcoupling effects. As shown on Figure 16, at the beginning of the seconds, the temperature transientdue to the increase of distillate flow-rate setpoint is partialIy compensated by an anticipative action,not only on the cooling water flow-rate, but aiso onthe gas pressure,which is exactly the behaviourperformed by manual operators.

6. Organoleptic validation and energy savingsWhile all the curves in the world could follow setpoints correctly, the only test capable ofvalidatingthis new system or not is a blind taste test. The sensors we rely on at this point are humans,MARTELL'S Master of Spirits and his staff are the only people qualified to give a real verdictconcerning this innovation.

The tests have already shown that the "eaux-de-vie" obtained are of an excellent quality.

Energies savings were not a priority goal. However, a more rational management of the boilersresulted in "controlled heats" saving lOto 20% more energy in the "seconds" runs.

This is indeed a promising result, since it was achieved even before the setpoint profiles wereoptimised.

716

7. Conclusions and prospectsThe successes that have already been achieved open up numerous prospects in the field of processcontrol.One noteworthy outcome of this study was that it provided MARTELL with an opportunity toreexamine a number of questions regarding, for example, the strategy used during certain runningphases.Even though it has preserved some of the mystery and time-honoured tradition, CharenteDistillation has undeniably made a leap forward within three years, notably with respect to the .distillation control processes, supervision and behaviour model!ing.In short, MARTELL now has an effective tool that will help it perpetuate the impeccable quality ofits "cognac".

8. Acknowledgements

The authors would like to thank ENSIA , ODF and MARTELL for their support during the studies.

9. References

[1] Bitmead, R.R., M. Oevers, and V. Wertz (1990). Adaptive Optimal Control. The Thinking man'sGPe. Prentice Hall International, Systems and Control Engineering.

[2] Boucher, P., D. Dumur, and S. Daumüller (1993). Autotuned Predictive Control. MutualImpact ofComputing Power and Control Theory, pp. 277-287.

[3] Boucher, P., and D. Dumur (1996). La Commande Prédictive. Editions Technip, CollectionMéthodes et Pratiques de 1'Ingénieur, Paris.

[4] Clarke, D.W., e. Mohtadi, and P.S. Tuffs (1987a). Oeneralized Predictive Control Part I "TheBasic Algorithm. Part li Extensions and Interpretation". Automatica, voI.23-2, pp. 137-160,March.

[5] Clarke, D.W., and C. Mohtadi (1987b). Properties ofGeneralized Predictive Control. 10thWorldCongress IFAC'87, VoI.9, pp. 63-74,Munich, July.

[6] Clarke, D.W. (1988). Application ofOeneralized Predictive Control to Industrial Processes. IEEEControl Systems Magazine, pp. 49-55, April.

[7] Codron, P., and P. Boucher (1993). Multivariable O.P.C. with multiple reference model. Aflexible arm application. 12lh World Congress IFAC, Sydney, vol. 8, pp. 253-256, July.

[8] Landau L D. (1988). Identification et commande des systêrnes. Editions Hermes, Paris.[9] Ljung L. and T. Sõderstrõm (1983). Theory and Practice of Recursive Identification. MIT

Press.[10] Postlethwaite, L, and S. Skogestad (1993). Robust multivariable control using (MATH) methods :

Analysis, design and industrial applications. Essays on control: Perspectives in the theory and itsapplications, Progress in Systems and control theory, Birkhãuser, pp. 269-337.

[11] Rachid A. (1996). Systêmes de régulation. Editions Masson, Paris.[12] Sinskey, F.G. (1967). Process control systems. Me Graw Hill.[13] Sõdcrstrôm, T., and P. Stoica (1989). System Identification. Prentice Hal!.[14] Zhou, K., I.C. Doyle, and K. Glover (1995). Robust and optimal control. Prentice Hal!, New

Jersey.

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