Non interacting multivariable paper machine headbox control: Some comparisons with classical loops

PAPER: COMPUTER AND MODELLING Copyright © IFAC PRP 4 Automation, Ghent, Belgium 1980

NON INTERACTING MULTIVARIABLE PAPER MACHINE HEADBOX CONTROL: SOME COMPARISONS WITH CLASSICAL LOOPS B. Lebeau*, R. Arrese**, S. Bauduin*, R. Grobet* and C. Foulard**, *** *Centre Technique du Papier, BP 7110, 38020 Grenoble Cedex, France **Laboratoire d'Automatique de Grenoble, BP 46, 38042 Saint Martin d'Heres, France ***Ecole FraTl,faise de Papeterie, BP 3, 38400 Saint Martin d'Heres, France

Abstract: A non interacting multivariable papermachine headbox control is discussed and compared with some classical loops. The control design is based on quadratic optimization criterion with a discrete state variable process model. Two reference models are used in this control structure: Tracking model and Perturbation model. Integrators have not been used to remove steady state error. Different results are obtained on an experimental headbox, controlled by a process control computer. Keywords : Papermachine - Headbox control - Multivariable control - Optimal control - State variables - Time delay - Non interacting control - Reference model. 1. INTRODUCTION Papermachine digital control systems have been developed with a lot of success during the last ten years. On many industrial processes the return on investment is obtained by maximizing the production : this is now incorporated in many available papermachine control systems (or dedicated packaging control systems). In order to maximize the production of paper machines we must control their speed, in accordance with the evaporating capabilities of the drying section. These running conditions require good headbox control. The controlled variables are : the level in a pressurised headbox (or the level in a surge tank or a stand pipe,for hydraulic headboxes), and the total head at the slice ; the latter being used for the jet speed, wire-speed ratio control. Two single loops (PI controllers) are generally used for these controls, but it is well known that a strong interaction exists between the two loops. Moreover it is strictly necessary to control the consistency (in order to monitor the dry line position on the wire or the formation of the sheet, etc.) and the substance flowrate at the slice (in order to monitor the basis weight). For example, in order to change the machine speed, we must change the total head. This is generally created by a modification of the total flow in the headbox at constant slice opening. Consistency and substance flowrate are thus modified (there is also an interaction between these two outputs). This disturbance will of course be deleted by the basis weight

227

controller. We can see therefore that it would be necessary to decouple this multivariable system to increase the performances of the machine during the speed change. On the other hand head box substance flowrate control gives better results on basis weight than the classical basis weight controller because of the reduction in dead time in the loop. So, this paper shows a linear multivariable control system based on quadratic criterion optimization. We have introduced two reference models : the first deals with tracking problems and the other with regulating problems. This control deals not only with the classical hydraulic variables but also with the consistency and the substance flowrate. Low consistency sensors are known for poor long term performance but we shall show that this drawback can be overcome in a supervisor control structure (using the conventional basis weight control loop). The whole control system has been applied on an experimental head box using a process control computer. We show comparative results with classical monovariable controllers. Experimental results are shown both in singlevariable and multivariable cases and for different working conditions of the process (control, set point chaITge, production optimization).

B. Lebeau et al.

228

2. MULTIVARIABLE CONTROL ALGORITHM

- regulating process disturbances

We consider a simplified scheme of the head circuits of a paper machine on the figure 1.

- tracking for operating point transition.

We shall now present the linear multivariable controller we have established and studied extensively. Air Multivariable linear control have been pressure successfully applied to control the moisture and basi"s: weight in the paper machine (2), (3). The multivariable reference model with quadratic criterion minimization controller Slice headbox has the advantage of specifying the pening level Y1 behaviour of the controlled process explicity Thick stock flow through a reference model. jet speed Moreover if we consider the control of an Stock Y2 internal model in parallel with the process valve we can introduce a second reference model u3 Substance for the disturbancEE (4). To establish the controller, we assume the flow rate Y3 u2 White system to be stable. Speed An internal model, in parallel with the Fan pump water process, takes into account the control inputs : Air

~

t

~

Fig. 1

Simplified scheme of head circuits

The different variables that we take into account in the mathematical model are the following

X(k+1)

A.X(k) + B.u(k)

Y (k)

C.X(k)

A second internal model in parallel to the process takes into account the measurable perturbations

- Control variables (Inputs)

Ap • Xp ( k) + Bp. up (k)

Air valve

Cp. Xp (k)

Fan pump speed Stock valve

Headbox level

The tracking reference model is X (k + 1 ) a

Ca· Xa (k)

Jet speed Y3

Substance flow rate. The regulation reference model is

- Measurable disturbance : uP1 : Thick stock pulp consistency The slice opening could be considered as a measurable disturbance. But for the time being we consider it as a non measurable disturbance. We come back later on this point. A general non-linear dynamic continous model for pressurized headboxes without overflow has been established (1). A discrete state variable linear representation based on this knowledge model was obtained and validated on an experimental headbox circuit. It can be noticed that an important characteristic of this process is the time delay between stock valve and Substance flowrate. The essential objective of the control system are : - decoupling the multivariable system

Ys(kJ is the output of the process at time k Moreover, we introduce a new concept to overcome the steady state error. Generally, the state variable representation is increased and integrators are added on the system output. But in the case where we have some constraints on the inputs, it is well known that the integrato~ drift to the saturation. So there are some problems when the inputs come out of the constraints. In our case, we can not use integrators. As we control an internal model of the process, we decompose the control action signal in two components : U

::

0

+

u

229

Multivariable Paper Machine Headbox Control

where :

o will

be determined by optimal control

u is t he part whi ch eliminates the steady state error so that u(k)

Finally the control structure based on this control law can be seen on Fig. 2. First of all. this .control system was applied to a simulation of the headbox process on a minicomputer with a sampling period of 2 seconds.

M.Zp(k)

with M :: G- 1 (0)

The different matrix L1 Pa ... Nr are obtained by integration of Riccati and linear equations (3).

inverse static gain matrix of the model.

For process where G is not a square matrix it is necessary to compute the pseudo inverse as follow : l

Fig. 3 shows a set point change on the jet speed of 0 15 m/sec. One can see the perfect decoupling on the level and substance flowrate outputs, according to the choice of non-interacting reference model both in tracking and regulation conditions. As it can be see~ to decouple the outputs it is necessary to change the three inputs. l

So the entire system which comprises process models tracking reference model and regulation reference model can be written as follow : l

X( k+ 1)

A

Xa (k+ 1)

0

Aa

Xp (k+ 1)

0

0

Xr (k +1 )

0

0

0

0

X( k)

0

0

Ap

0

0

Ar

Xa ( k) X (k) p Xr(k)

0

3. SINGLE VARIABLE CONTROL STRUCTURE ON PAPER MACHINE We summarize here the control system which is presently used on many industrial paper machines. GenerallYI we find10n one hand local single variable controllers such as PI controllErs for the following loops : l

+

- headbox level - total head pressure - steam pressure

B 0

B.M.Z p (k)

consistencYI flow 1 etc ...

Ba·Z(kJ

+

u(k)

- speed of the machine

0

Bp' up (k)

0

Br. e( k)

We consider the following output :

on the other hand1a centralized digital control system for the following control routines : - non-interacting moisture and basis weight control (via single-variable techniques) - jet speed-wire speed ratio control

E (k)

[- C

Ca - Cp

-

Cr] .

X(kJ Xa (kJ X p

[kJ

Xr ( k)

The classical quadratic criterion optimization problem

N-1 J == L k==o

wi t h 0

ET(kJ.O.E(kJ + uT(k).R.u(kJ ~ 0

an d R> 0

gives the optimal control law U( k) :: - L. X ( k) - P a X (k) a

P,

p Xp (k J - P r Xr (k)

- product yield optimization and set points optimization.

B. Lebeau

230

et al.

+

Ym +

Fig. 2

Multivariable control system

Jet speed m/sec ".-----------

1,00

o pO 0,20

__ I

D,O

/

0,02 0,01

/

------------

0,00 -0,01

-0,40

-0,02

-0,80

-1 ,00

Substance flowrate kg/sec

0,03

Time 0

100

10

20

30

40

10

0

SO

Level cm

60

Time

-0,03

50 (sec)

20

30

40

SO Air valve Fan pump

Actuators %

- - - Stock valve

30 10 D

2

0-2

-so -100 0

10

20

Fig. 3

30

40

Time

50

Multivariable control

0

10

20

30

40

50

Time

jet sQeed step response

231

Multivariable Paper Machine Headbox Control If we look at the running conditions of such control structure on a industrial paper machine with respect to the headbox subsystem we can consider the two following cases a/ Paper machine producing a paper at a constant basis weight but with a production at either constant rate (e.g. constan~ machine speed) or variable rate ( e.g. to maximize the production rate) b/ Grade change (usual basis weight change) at either constant production rate (drying limit) or variable rate (speed limit). In the first case, it is interesting to study the effect on the basis weight of a machine speed change. Obviously, the ideal change is obtained when there is no effect on the basis weight. In the second case, when the machine is running at a constant production rate, it is interesting to change the basis weight (for grade change) with the same substance flowrate at the headbox. On the other hand, the classical basis weight control contains a significant deadtime in the loop. Moreover the 8 gauge which delive~ -~e basis weight measurement is generally permanently traversing across the machine to give informations on the profile and to avoid interactions between cross and machine direction. (Basis weight measurements are filtered or mean averaged according to the traversing time). So, such a control cannot pratically eliminate a high frequency disturbances spectrum (typically more than 0,01 Hz).

But, with a control system which will have no deadtime and a measurement available at any time, it would be possible to remove more disturbances (typically more than 1 Hz). It is not possible to exceed this frequency because of the time response of industrial sensors and actuators (e.g"valve). It is one of the objectives of the multivariable control with a consistency measurement. In this case, we cannot completely remove t~e daadtime but we reduce it at least 4 times, depending on the machine. The classical papermachine control system (based on single-variable design) is shown on the fig. 4. To evaluate our new multivariable control system, we must compare it with the classical one. We only use an experimental headbox whi ch has neit her pap er she e t forma t ion part nor dryer section. So, we simulate in the minicomputer the lacking process part (gain factor and deadtime between the substance flowrate at the slice and the basis weight at the end of the machineJ. The 8 gauge is assumooto be permanently traversing and the measurement mean-averaged on the travelling period.

Furthermore, it is well Known that a deadtime control loop can amplify a given part of the spectrum and, to reduce this trouble,one must reduce the performances of the loop (for example time response).

8

Dryers

--0 asis

speed white water ~__.-~eed

Feed-forward control

change set point

weigh - set point

rig. 4 : Classical paper-machine control system

weight

232

B. Lebeau

J35 000 Pascal

et al.

Speed jet

Total Head

130 000 (

~

l.

20 000 15 000

Level

~ ,_5_m/_s~r

\ ...

--------

6,5 6

Level 32 cm 2B

26

Fan pump

S(j bstan ce flowrate

g/l

__

l~

.~~~~_'5_%_ {

100 ~

~

Fan pump

Air valve

75

52,5 50

"-""-----Air valve

o 73 68

'0

Stock valve

---J,,6-.....~.....---~~---------~..-.....-..~----

1

58 53

St.ock valve

1o.122k,{S

Substance flowrate

~;.J.)~ ~"'~~"r(-~,,~~, ~ .•(:-~i\.f'\A. I : . r· f~.~ "V''N~)iA~Av~~UI~ p,-T,

I

r'

I

0, 104

~ig.

~=t3l

~ead

set point change

Basis weight single-variable system

Fig. 6

lr~

s~eed

set point change

Multivariable system

Multivariable Paper Machine Headbox Control

233

4. COMPARATIVE RESULTS ON AN EXPERIMENTAL HEADBOX Here. we show a set of experimental results for differents running conditions as previously described. We must emphasize that for these e xp er i men t 5 the model is known. So. the single variable controllers are adjusted at the~optimal values. Total head

• Pascal

fDDDD

\...

J

~~§~§-~~~g~~

.20 000 J15 000 m I

When the machine is on product optimization control the speed is permanently modified to adj L!S t the production leve 1 to the constreint capacities (generally evaporation capacity). It is necessary to control in the same way the jet speed at the slice to maintain constant the effux ratio. So the jet speed is also permanently modified but at the same time basis weight must not be modified.

Level

0~32 ~

j 0 ~28 0~26

~ 14 ~ 5,8

_

~

72 'i 4 ~ 44 ~

•

Fig. 5 shows two set point changesof the total head (jet speed) for the classical control. As it can be seen during this change, substance flowrate and consequently basis weight are disturbed.

Consistency

/l

\

.

,/~t..J~.1~'It

V-

~j~5;_~5_( SS

Fan pump

~'------

52~5

50

t%

J75

Air valve ~

~ o

1.'(;

1

68

1 minute ~

]~!_~p~~~_§§!_e~~~!_~~~~g~_~!_~_~~~§!~~~

~

Stock valve _

.r....~

Fig. 6 shows the same changes with multivariable control. We can see the perfect decoupling with the substance flowrate. To have a better idea on the multi-variable structure~ we also compare it with a single-variable structure taking into account the same output (level. speed jet and substance flowrate at the rleadbox). Fig. 7 shows the same changes. It gives an idea of the decoupling effect of the multi-variable structure. In this case substance flowrate is much disturbed.

~-.

J 58

I 53

Fig. 7

Total head set point change Substance flowrate single-variable control

Fig. 8 and Fig. 9 show other speed changes. One can see the basis weight signal,which is disturbed in the single variable case and perfectly decoupled with multi-variable control. In this case. it is necessary to change two outputs in a coordinated way. jet speed: and substance flowrate. Obviously~ the three inputs are modified.

-

~~~~§_~~~g~!_~~~~g§_~!_~_~~~§!~~!_e~~-

duction level In this part. we shall see a particular grade change, where the basis weight and the machine speed (hence jet speed) are changing so that the substance flowrate remains constant (hence production level). This is easily realized by a substance flowrate set po~nt change.

234

B. Lebeau et al.

Pascal Total Head

J Pascal

-~-L-5-4=1~oA~~~-----/

---./-----------..-----

2500

1500

~

m

20000 15000

4m

Level

{0,32

Level

1 U,32 m

I ~ ' 30

-- ~~...,.or,~3".rrr-----------------------..-------..,-

J

JO,28

0,28

10,26 .kg/s -10 , 11 6

0,26 0kg/s , 122

~ ~~ ~.~ !!"l~ Sub s tan ce ~..... - 'W ~ r r .. N-.. ~ .~'fl ~ ~ ~ ~w~')~ . flovrtate

~ ,

Total Head

I 30000

3500

Substance flowrate

0,104

g/l

Consistency

Consistency

!5,28

t~"tV·~~~ 5 4 1 ,72

j ~o ~;;H;~ ,~5 __ :

4,72

Fan pumo

---f

. .....

"\

'--____

i 52,5 % 75

i

Fan pump

~

Ijo

57 ,5

_----------__._

(

J--5~5-----~

-1 52 ,5

Air valve

.t\ir valve

5

,25

i

25

0

% 73 68 63 58

Stock valve

Basis weight ~

I

1

0

% 73 68 63 58

Stock valve

;. g/m2

Basis weight

45 42 3 , 36 33

36

1

Fig. 8

J9t speec set point change at constant basis weight Molti-variable control

J3t speed set point chang3 at constant ~asis wei~ht 3ingle-v~riable control

"----

Multivariable Paper Machine Headbox Control

Total head

Total head

Pascal

~...c::.~.c.~o~o~;.+--_ _. r - - - - - - - - - - - " " " " " - - - - - - -

l~OOOO

__

_--------

~~~--..;------------'\ ....

Level Level

15000 ~

235

~~

. ._...--__

~-

.".J------

Substance flowrate

g/l

..,...~~' ~ .44 Consistency

Ir~

,28

.72

l

~O

57,5 55

52,5

Fan pump

I

5~~6

11... ~ 14.;~ .~~~ ~~~ Consistency

5,28

%

Fan pump

5· \"------- ii-525 ,5

Air valve

57,5

r--~-----'l

---------

150

Air valve

%

1 minute %

..-----...

Stock valve

73

68 63 58

g/m2 42

., ~/m2 Basis weight BaSls w e l g h t .~~~,....~~ ~ 1~.

~ ~36 ~~ ., 33

Fig. 10

Basis weight change at constant production Multi-variable structure

~36

~

....

_.L

_

1 33

Fig. 11

I ....

r····-r~"""'v_~,...."

~........~

Basis weight change at constant production Single-variaBle structure

236

et al.

B. Lebeau

Speed jet

~

Speed jet

~m/s

8 m/s 7,5

----------------------

6,5 6

7,5

~7~----------------------~

6,5

16

Level

m

.,....--.

~ 0 , 32

Level

"'f'lOt-,~"3rP1eJ----------------..---~-

0,28 0,26 0,116

,56 g/l 5,28

i

Consistency ~-aA.

~/l

5

flowrate

Consistency

8

4~·-~~4.n·~~~ 14 ,44

4,44

i

7, 5 5

~

Fan pump

0

52,5 50 s

Fan pump

55 --01--.1-----------------------

52,5 50

~ 5

~ 57,5

%

.

Air valve

. ,~~~

~~

%

Air valve

~2~V'r'~~~~"'""'-~~~~~~-r".....,..,.""""'~----"-

0 1 0

Stock valve

~3%

Stock valve

~ ~_ _\ 6 e ~ ~ ~

8 3

1 minute

f1~o 50

-------. 1 minute

~~~o Thik stock .consistency ~~J.--,.It"~~_.A ' ._J~ -..,~~-----. y- ""' , 1 700 --- ~ ' --~ 650

E-00

58 53

Fig. 12

Thik stock consistency • ... ---

1

Thik stock consistency change multi-variable control with unmeasured disturbance

Fig. 13

Thik stocK consistency change Multi-variable control with measured disturbance

Multivariable Paper Machine Headbox Control

t7 • S m/s

l~ .r

Speed jet ~

j~.s

-------~------

Level 0,32 m

Consistency

Fan

pump

~----

.l

~

Slice opening 9mm

le

Fig. 14

I--~---

~

I~

Slice opening change Multi-variable control

-

237

238

B. Lebeau et al.

Fig. 10 and Fig. 11 show this change for both structures. Here, we must look at the substance flowrate signal. On ce more we obtain a decoup1ed response in the multivariable case.

taken into account by the headbox system (for example retention ... ). Furthermore, the use of a knowledge model improves the control system starting phase. It gives a first model used to obtain a controller. An adjustment of this model can be done in a second phase. For example, if we observe a non perfect decoupling control then we can adjust parameters. This kind of procedure is generally more efficient than input-output identification : the machine normally runs to produce saleable paper. We are currently working on physical and economical studies to estimate the economic returns of this system.

We show two classical disturbances in the multi-variable case. Fig. 12 and Fig. 13 show the responses of the control system to a change in this stock consistency. On Fig. 12, the dist urban ce is not meas ured. Whereas, on Fig. 13, the disturbance is measured by a consistency sensor and taken into account as a measurable disturbance. We can see the improvment of the sUbstance flowrate. We must say that the disturbance is also taken into account in a single-variab~ REFERENCES structure. And in this case. Wp obtain the same results with both structures. But, we (1) A. NADER, B. LEBEAU, J.P. GAUTHIER, wish m emphasize that we can also consid8r meaC. FOULARD and A. RAMAZ surable disturbancesin the multi-variable control structure. New developments in multi-variable control The Fig. 14 shows a change in the slice opeof paper machine headboxes ning. In this case, the disturbance is not International Symposium Paper Machines measured. This case corresponds to a headbox Headboxes - Mc Gill University Montreal consistency change at a constant jet speed June 3-5 1979. and basis weight. It is generally called dry line control on the wire. We can see that (2) J.P. SANDRAZ, C. FOULARD, A. RAMAZ during the change jet speed and substance Commande multidimensionnelle d'une unite flowrate are disturbed. To reduce (and may pilote de fabrication de papier be completely eliminate) this, it would be 4th IFAC/IFIP International Conference on necessary to consider slice opening as a meaDigital Computer Applications to process surable disturbance. But in this case, control - Zurich 1974. it is necessary to reduce the sampling period (2 sec) because a slice opening change modi(3) C. FOULARD, S. GENTIL, J.P. SANDRAZ fies the outputs with a very fast time response. Commande et regulation par calculateur This improvment is in progress and we have numerique. De la Theorie aux Applications not yet new results. Eyrolles 2eme edition 1979.

5. CONCLUSION This study aimed at showing the feasability of multi-variable control strategies for the headbox system. We can notice that we have introduced a structure which eliminates the use of integrators for steady state precision. The application on an experimental headbox pilot has shown that it was possible to obtain a complete non-interacting system. Moreover, the use of a consistency sensor improves the performances of the control as compared wi th classi cal basis weight controls. For industrial applications, the headbox multivariable control system will not run alone but will have ID beSupervised by a modified basis weight controller. In fact, the new basis weight controller will give the substance flowrate set point of a multi variable headbox control, The stock valve itself will be controlled by the headbox control. This must be realized for two main reasons : first of all, it is well known that low consistency sensors have poor long term performancec and basis weight control allows to remove this trouble,and finally, the more important thing is to control the final paper quality (~e.basis weight). Moreover basis weight loop is necessary to compens at e for the di s turban ces whi ch are not

(4) G. BORNARD, J.P. GAUTHIER Commande dynamique multivariable des systemes industriels de production. Internal Report - Laboratoire d'Automatique de Grenoble nO 77-29, 1977.