Learning control of a batch reactor

Com~ukw r&m. Engag. Vol. 13, No. I I/12, pp. 1273-1276, Printed in Great Britain. All rights reserved

LEARNING of Chemical

KATOH,

Engineering,

009% 1354189 $3.00 + 0.00 Q 1989 Pergamon Press plc

Copyright

CONTROL N.

Department

1989

K.

OF A BATCH NAKAO

Kogakuin

and

University,

M.

REACTOR

HANAWA

I-24-2, Nishi-Shinjuku,

Tokyo

160, Japan

(Received for pubifcarion 19 June 1989) Abstract-Nowadays, batch process operations are growing important in the chemical industry and more precise tracking or programmed control techniques are required for batch process operations. However, control techniques for batch processes seem to be still unestablished. It is clearly difficult for a simple PID control to show good performance of’ batch process with exothermic/endothermic reactions. To improve the quality of control, learning control theories were applied to the batch reactor operation. The operation of the batch process is naturally repetitive. Therefore, learning control or repetitive control aiming to improve the quality of control with each trial is quite suitable for the batch reactor control. In fact, a learning control experiment of a cellulose pyrolysis process with exothermic/endothermic reactions showed that the reaction temperature trajectory could almast perfectly coincide with the desired trajectory after several trials. It is obvious that the learning control is applicable not only to the cellulose pyrolysis process but also to various types of batch processes.

Recently, batch chemical reactors are paid attention to because of the industrial structure change from a

large amount of few products to a small amount of various products with high added value (Takamatsu, 1984). However, it is well known that batch chemical reactors are highly nonlinear and time varying. To realize high value-added products, batch reactors have to be operated as precisely as possible. In order to overcome this difhcult problem of the batch reactor operation, it is indispensable to use advanced control theories. Empirically speaking, we cannot expect precise control of the highly nonlinear and time-varying batch reactor only by conventional PID control. or In this work, three types of learning control

r =k,,exp(-E/Ry)*m,

OF CELLULOSE

PYROLYSIS

(11

dmfdt = -r,

(2)

(mC,tM)dy/dt=hA~,--)+(--L)N)r+q.

(3)

Reaction rate, mass balance and heat balance are expressed by (l-3), respectively. Heat of reaction, (-DH) 2: 2093. 4 J g-’ is given by Reed (1978). Other constants such as ko, E and hA are determined experimentally.

repetitive control theories are adopted and compared for the batch reactor control problem. Furthermore, a cellulose pyrolysis reactor is used as an example of the nonlinear and time-varying batch reactor and is experimentally controlled based on the learning control theories. DYNAMICS

operation of the system are provided by Thurner and Mann (1981). An example of experimental results is shown in Fig. 2. From the results, we built a simple cellulose pyrolysis reactor model as follows:

REACTOR

As a typical example of a batch reactor, we adopt the cellulose pyrolysis reactor which has an important role in the field of energy and resources. To analyze and model the batch cellulose pyrolysis reactor, we used the experimental apparatus shown in Fig. 1. The system consists of a reactor and a cooler. The reactor size is 15 mm i.d. and 150 mm long. A sample boat can insert the cellulose sample into the reactor of which temperature is kept constant and can withdraw it into the cooler at the end of a run. Details on the

SIMULATION

OF PYROLYSIS

REACTOR

CONTROL

In this section, PID and three types of learning control theories are compared by simulation of batch cellulose pyrolysis process control. The objective of the control is to maintain a constant heating rate which determines the quality of products (Reed, i 978). In Fig. 3, an example of PID control is shown. Heating rate is 10 K min-‘. Clearly, due to the highly nonlinear characteristics of the cellulose pyrolysis process, the results are quite unfavorable. It is well known that the Internal Model Control (Arkun et nl., 1986) is more robust than PID control. So we examined the validity of Internal Model Control (IMC) to the cellulose pyrolysis process control. The result also shows unfavorable control, Thus, it is obvious that the control theories based on linear process dynamics such as PID and IMC

1273

1274

N.

KATOH

ef ul.

-+P

2.

?.4eter

1.

FiOW

3.

React”?

cootet aoac

4.sampie 6.

5.ThPrmOCOUPLe

Tar

Trap

Fig. 1. Pyrolysis reactor.

Fig. 3.

cannot obtain favorable control results against highly nonlinear processes. In order to overcome these difficulties we adopted learning control theories. It is noticeable that the batch process and the learning control are both repetitive. in other words, by the idea of application of the learning control to the batch process, we can expect good control performance through iterative operations. Three types of learning control were considered. These are introduced briefly as follows: First, simple learning control (LC) for the cellulose pyrolysis reactor is expressed by (4): 4,+,(“)=9~(t)fRLLVd(t)--,(t)l,

(4)

where i indicates the ith trial, g, is learning gain and y, designates the desired temperature. Secondly, the betterment process (BP) proposed by Kawamura 4~ cal. (1986) is expsessed by (5) and (6): si,i(I)=rji(r)-tgB*dPi(t)/dt,

e,(f)

=

Yd(fl

(5)

-YAP>-

ccl

It is proved that reaction temperature yi converges to a desired temperature yd at large i by using an appropriate value of ga. reference learning control Lastly, the model (MRLC) proposed by Shin and Kitamori (1986) is introduced as follows:.

6, ith * . . * &At% y(t) = ri-rtr).u(t) + gti)f’fr).

8@0 1ZW TIM5 I 5ec I

1600

Fig. 2. Typical example of kinetic experiments.

2888

(IO)

Parameters L:(r) and d,(r) are online estimated values of k7i/) and g(t), respectively. Decrease of e{(t) through control trials is also proved. The above three learning: control theories are all at the open-loop type. From a practical standpoint, the proportional control term Ic,f(r,(t) -y,(i)] may be effective so t&t learning control plus proportional control are also examined. In order to examine three types of learning control, simulation of the heating rate control of the cellulose pyro@sis reactor was carried out. The objective of the control is to maintain a heating rate 10 K min 1from 423 to 623 K during whose temperature range the pyrolysis reaction occurs. Simulation results are summarized in Table 1. The increase of the initial amount of cdtulose tn(#> means the increase of nonlinearity of the process dynamics. Simple learning control (LC) cannot show good results in the case of m(0) = 2 and 3 and selection of the value of g, is difficult because the suitable range of gL for convergence of e:‘(I) is very narrow. The betterment process (BP) shows good performance. This scheme is based on nonlinear dynamics so that the trial number required is not dependent on Table

4BB

f%

Plant dynamics are expressed by ( 10):

m CO> (8)

0

Simulation of PID control.

1. Simulation

resolrs

of learning

LC

BP

I

174

15

2

..._

3

-

control NlRLC

VP

36 (3) -

ct:, 16 (15)

(4) (17)

“The number n~eans the iteration number required for max,,je,(r)l< 10 K. bThe number in parentheses means leaning control plus prc~portion-al controi The objective ofcontrat IS to maintuin heating rate. IO K mm” from 423 to 673 K.

Learning

control

of a batch reactor

1275

0

588

1Elm TII’E

I.

Flow

3.

Reactor

Meter

S.Ampllfler 7.

2.

Thermocouple

4.

Heater

Fig. 6. Learning

control

t sea

(MRLC)

I

of the batch reactor.

e.7‘tlyristor

Tar

l-rap

computer

8.

Fig. 4. Experimental

apparatus of cellulose pyrolysis reactor control system.

the value of m (0). It is clearly recognized that proportional control is effective for rapid convergence. However, proportional gain, k,, should be suitably selected as small as possible or should be reduced in each iteration. Model reference learning control (MRLC) looks inferior to the betterment process because MRLC is based on the linear process dyanmics. However, it is noticeable that MRLC plus proportional control shows favorable results. In other words, MRLC can be effective when an initial guess of q,(t) is appropriate. Thus, it is obvious that both the betterment process and model reference learning control can be practical by adding proportional control. LEARNING

CONTROL

EXPERIMENTS

In order to examine practical aspects of the learning control theories, heating rate control experiments of the cellulose pyrolysis process were carried out. The experimental apparatus is shown in Fig. 4. The reaction temperature is measured with a thermocouple inserted within the reactor and controlled by the microcomputer. Argon supplied from a high-pressure cyclinder is used as the inert gas. Experimental conditions are similar to the simulation in the

preceding section. However, the initial amount of cellulose, m(O), is set at 2 g. Results of PID control and simple learning control showed unfavorable controls which correspond to the simulation results. As for the betterment process, we obtained rather favorable control results which are recognized in Fig. 5. As seen in the previous section, control performance of the betterment process is quite sensitive to the value of grammes in (5), and the sampling time DT should be small enough in order to approximate the derivative of e,(t) in (5). In the result in Fig. 5, grammes = 3 and DT = 1 s were used, and proportional control added was effective to the reduction of the trial number and to the compensation for disturbance. In contrast to the betterment process, model reference learning control (MRLC) has no sensitive parameters such as gs. However, the initial guess of q(t) in (IO) has to be suitably selected in order that the linearization of the highly-nonlinear process is valid. Proportional control added is also effective to the suitable selection of q(f). A typical result of MRLC is shown in Fig. 6. Sampling time DT = 5 s and n = 2 are used in this result. Control performance is similar to the case of the betterment process. Acknowiedgemenrs-The authors wish to thank K. Nakamichi and H. Sakurai of this department for their experimental contributions and theoretical suggestions.

NOMENCLATURE A

888

40aT 0

”

”

”

”

1020 TIE

Fig. 5. Learning

=

C,, = (-DH) = E = e =

/

control

1

SBC

(BP)

15m

I

of the batch reactor.

g g, gL & h k k, k,

= = = = = = = =

Area

for heat transfer

Specific heat of cellulose Heat of reaction Activation energyError (desired temperature - reaction temperature) Plant parameter Learning gain of the betterment process Learning gain of the simple learning control Estimated plant parameter Heat transfer coefficient Plant parameter vector Frequency factor Proportional gain

l = Estimated plant parameter vector M = Heat capacity of the reactor without

cellulose

I276

N.

KATOH

= Mass of cellulose q = Heat supply R = Gas constant r = Reaction rate / = Reaction time _r = Reaction temperature _vd= Desired temperature ,v, = Environmental temperature

m

et al

Kawamura S., F. Miyazaki and S. Arimoto, Proposal of betterment process: a learning controi method for dynamical systems (in Japanese). Keisoku Jido Scig_ro-Gokkoi Ronbuns_vu 22, 56 (1986). Reed T. B., Survey of pyroconversion processes for biomass. AiChE Swy~. SW. No. 18.’ 74. 38 (1978). Shin S. and T. Kitamori. Model reference learning control for discrete-time linear time varying systems (in Japanese). Keisoku Jido .Seix+w-Gakk-ai Ronhunsyu 22, 835 (1986).

REFERENCES

Arkun Y.. J. Experimental

Hollett, W. M. Canney and M. Morari, study of internal model control. Ind. Engng C’hern. Process Des. Der. 25, 102 ( 1986).

Takamatsu T., Present engineering. Proc. Modeling

and future aspects

of batch

int. Cmi_ OH Indusrvial and Conrrai. Hangchou. China (1984).

process

Process

Thurner F. and U. Mann, Kinetic investigation of wood pyrolysis. Inti, &gng C,‘terr. Pr0ce.s.s Des. Der. 20, 482 (1981).