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Supervision and Control of an Exothermic Batch Process
Copyright © IFAC Artifi<:.ial Intelligence in Real-Time Control, Delft, The Netherlands, 1992
SUPERVISION AND CONTROL OF AN EXOTHERMIC BATCH PROCESS R.Perne Process ConJro/ Systems, Bayer AG, Leverkusen, Germany
Abstact- A mode I based superv i s ion and contro I system has been des i gned for exotherm i c chem ica I reactions, and batch processes inparticular. Adaptive, extendedKalman fi Iters reconstuct process states aswell as reaction parameters and a Bayes-Markov process allows to discrim inate between normal and unwanted process states. The new concept considerably reduces the time for one batch and warns of hazardous states at avery early stage, leavingenough time for counter act ions.
Keywords' Exotherm ic React ion, Fault Detect ion, KalmanFi Itering
I ntroduct 1on The example, presented in this paper, is the supervision and control of an exotherm ic process with a potent ia Ily hazardous autocata lyt ic decomposition.Here it is essential to detect the onset of an autocatalytic decomposition at avery early stage, in time to take counter act ions. Mult i-KalmanFi Iter techniques as proposed by King, Schuler & Gi lies [2-3) are app l ied and suitably modif i ed allow ing a detect ion of unwanted process states hours before a runaway of the react ion. Furthermore, with the informat ion from the fi Iters contro l1er parameters optimally adapted to the processdynam ics reducing considerably the time needed forone batch. This concept has resulted in time-opt imal and safe operat ion of the chem ical reactions under a II process condi t ions.
Uniform qual ity, high product yields, low energy consumption and m inimal effects on the environment are the main demands on superv i sion and control systems forchemical reactions. lnexpensive process computers are increasingly being used to fulfil these demands. Such computers perm i t not only the implementat i on of a PlO contro I algorithm equ ivalent to analog contro l1ers but allows the app I icat ion of advanced process contro I technology. Th i s techno I ogy i nc Iudes observers, extended Ka 1man fi Iters and adapt ive control algorithms. As shown in practice, the use of these control processes is successful i f chem ical engineering know ledge of the react ion concerned is included in the contro I concept as a prior i know ledge [I J. In the applicationpresentedhereapriori information is provided to the control by simulat ing mathematical models of the nonl inearprocess dynam ics paralle l to the actual process on acomputer. This al10ws the online estimation of significant processvariables, such as concentrat ions of the reactants or reaction rate, which are difficult or impossible to measure onl ine. The informati on of these estimates form the basis for an improved supervis i on and contro I performance: rep l acement of unmeasurablevariables by estimated variables or adapt ion of control1er parameters according to the estimated process states.
The
Problem
Theprocessinthecaseathand i sanexothermic chem ica I react ion, described by the fo Ilow ing simp le stoichiometry:
[A)
+
[B]
( 1)
and a macrok inetic react ion rate k: k = k o* exp(-Eo/(R*T»)*[A]~I*[B]]l2 247
(2)
with A, B : reactants, C : product, 6h R: react ion
Furthermore, a short local temperature peak in some small part of the reactor can start the autocatalytiC decomposition which has hardly any effect on the controlled temperature and may go by unnot iced. Once started, the decomposit ion will not ext inguish in the normal operat ion mode and eventually lead to a runaway of the reaction. Thus, a supervis ing system is needed for the early detection of a beginning autocatalytic decomposition.
enthalpy , ko : pre-exponentialfactor,Eo : activat i on energy, R: gas constant, T : react ion temperature, [A) and [B) .. . concentrat ions of A and Band the exponents III and 112, which are allowed to be rational numbers. lncludingenergyandmassbalances one arrives at the follow ing mathematical mode 1of the process dynam ics :
The New Control Concept d[A)/dt
=
(3)
-k
To improve the control behaviour of the exotherm ic batch process, a new contro 1strategy w as deve loped contro 11 ing the react ion power dQreac/dt
(M : the total react ion mass, c p : the specific heat,
k F : the heat transfer coefficient between the reac-
rather than product temperature. React ion power, the most sensitive variable for safe operation is then under direct contro 1.
t ion vesse 1and the jacket coo 1ing, F the area of heat exchange and TM : the temperature of the coo 1ing medium.) Beside the normal react ion, product Cmay decompose autocata lyt ically:
C -) D
+
E + (-6h ) s
C+D - ) 2D + E+(-6h A )
start react ion exothermicdecomposit i on
Simulation tests demonstrated the disadvantages and inadequacy of a fixed param eter contro 11 er and showed, that the dynam ic response of the system changes markedly with the varyingheat production within the reactor. With a PI contro 1structure for the reactionpower controller, computer simulations showed that the control loop maintains its characteristics only if the gain is changed in accordance with the chang ing dynam ics.
The start of autocatalyt ic decomposit ion is favoured by high temperatures. To avo i da dangerous runaway of the exothermic decompositionof the react ion product C, an upper 1im i t is set for the r eact ion temperature T and care has to be taken to ensure eff icient rem ova 1of react ion heat so that the crit ica 1temperature is never reached. In the convent iona 1contro 1concept tem perature was controlled by a PID regulator with fixed parameters act ing on the jacket coo 1ing system . Even si ight changes in process parameters, however, have significant effect on the overa 11 behaviour of this chem ical plant, due to the high ly nonl inear dependence of the reactor behav iour on the process state. As a consequence, a regulatorwith fixed parameters does not work optimal ly in a 11 process states.
Again-scheduling strategy is therefore adopted whereby the value of the gain-scheduling factor is adjusted so as to keep the overall loop gain constant:
(5)
where kp and kc represent the gain of the process Because of this di ff icul ty, the slope of the temperature set point ramp was taken to be very small in order to avoid unwanted rapid changes in the react i on power. On the other hand, th is measure leads to a large increase inreaction time and a subsequent lossof product ivity without being sufficient to e1im inate totally the occurrence of dangerous peaks in reaction power followedby temperal shut-down of the reaction. Thus a new control concept wascalled for, using advanced process control technology.
248
and the contro llerrespect ively. The gain has then the fo llow ing form:
= o(dQreac/dt)1 oT * oT / oT M
(6)
High Temperature State
As shown by equat ion 4, react ion power is a funct ion of unknown concentrat ions [A) and [B). To provide the control with a value of the react ion power these var i ab I es are est i mated by an extended Kalman fi Iter based on the mathematical model of the process as described by equat ion 3. The overall block diagram for the control loop inquestion is shown in Fig. 1.
a
I
O-Aotu. Value 0-8etpolnt
Normalized Time
Low Temperature State
a
:;.;,:.00-----... . . .... . Q-Actu. Value 0-6etpolnt
Normalized TIme
100%
Fig.2: Transient behaviour of the react ion power control loop
Typical exper1mental results are shown in Fig. 3 and 4. The product temperature trajectory followedby the conventional control d1ffers sign1ficantly from the more efficient trajectory of reaction powercontrol.
Fig. I : Overall Block Diagram
As an integral part of the control design process, simulat ion tests of the control system must be performed to ensure that transient performance specificat ions are met. Fig. 2 shows reactions to set point changes for two different temperatures: in the upper diagram the react ion temperature is close to the lower limit and in the lower diagram it close to the higher I im it of the allowed temperature range. The results demonstrate that, in contrast to the earl ier temperature contro I, the re levant variab le for safe operation, thereact ion power, is now contro lied direct Iy ensuring sat isfactory transient behaviour for all process state.
line
Fig. 3 : Product temperature trajectories for convent i ona 1and advanced contro I strategy
249
c::J _
The abi 1ity of the Bayes-Markov formal ism to detect unwanted process states depends crucially on the choice of the covariance matrix of process noise Q. Whereas the covariance matri x of measurement noice R is chosen such that it corresponds to the actual measurement noise, Q and the init ial values of the covariance matrix of the states Po are
convent. Control Reactlon Power Control
considered as designvariab les for the Kalman fi 1ter. Po is chosen such that the desired speed and
ie-
necessary degree of mode 1adapt ion is achieved at the start of each batch. Q for the normal react ion is a comprom ise between speed of process track ing and accuracy of est imat ion. Care has to be taken choosing this variable for the adapt ive fi lter which i nc 1udes the decom pos i t i on and param et ers to be est imated along with process states.
ll.
87...
Normalized Time
For the normal react ion both models should be equivalent and give sim i larresults.1 t has been observed, however, that the higher dimension of the second mode 1leads to a much broader est imated probabi 1ity density distribut ion p for the measured variab les effect ing the abi I ity of the subsequent decision logic todiscrim inatebetween the two cases.
Fig. 4: Frequency of normal ized product ion time
Early Detect Ion of a Hazardous Secondary React I on
The detect ion principle appl ied here is based on propositions of King & Gilles [3] and Gilles & Schuler[ 21, who suggest to construct extended Kalman Fi lters for the normal react ion and each typeof disturbed process. Adecision stage based on a Bayes-Markov process discrim inates between the di fferent process states: normal and type of disturbance. Thereby, probabi 1it ies derived from the Ka lman filters (Fig.5) are used to update a Markov process which models the probabi 1it ies to be in one of the different process states and givesa priori est imates for these probabi 1it ies. This mode 1contains rates for the transit ion between the different process states - an example is the transit ion rate from norma 1react ion to autocatalyt ic decomposit ion which is a funct ionof temperature and concentrat ions.
f
.~
i...
Tt
Fig. 5: Probabi 1ity density distribut ion Pi for twomodels
In contrast to King and Gi lles, on ly two models are used: one for the normal react ion and one for disturbed processes. The second mode 1contains parameters, which are est imated along with the process states and can describe different types of disturbances at the same time. Much of the effort gained by reducing the number of fi lters has to be reinvested in construct ing and calculat ing a more compl icated fi lter. However, this approach wi 11 automatically deal w ithcommonly observed model deviations.
Fig: 5 shows the probabil ity density distribut ion for two models. Eland E2 are expected values, To is the observed va lue. Pi is a funct ion of the innovationYi(k)=Ei-T 0 and the error covariance matrix Pi(klk-l) of the Kalman filter ( H: Jacobian of measurement equat ion, m: dimension of R):
250
Conclusion
The situat ion shown in the Fig. 5 has to be avoided. Although the observed temperature is much closer to the expected value of model2 including decomposit ion, for the given probabi 1ity densit ies the decision logic will choose model 1. A steeper probabi 1i ty densi ty distribut ion can be obtained by assum ing smallervalues for the "process noise", which, however wi 11 reduce the speed of model adaptat ion. The opt imum Q of the Kalman filter is a comprom ise bet ween speed of detect i ng autocata 1ytic decomposit ionon one side and certainty of discrim inat ion and accuracy of estimat ion on the other side.
l
t
The performance of the supervision and control system for exotherm ic batch react ion is encouraging for further pract ica 1app 1icat ions. 1t should be mentioned, however, that models accurate enough to discriminate between different process states are not readi ly avai lable and often difficult to establ ish 1imit inga straightforward extension of this approach to other react ions. These restrict ions are not as stringent for the react ion power control where somet imes agood model of thereactor without an explicit model of the react ion can lead to considerable improvement.
References [1]
ModerneMethoden der Mef3- und Automat is ierungstechni k und ihre Bedeutung fur die Automat isierung verfahrenstechnischer Prozesse [hem log Tech 55, pp, 437-446
l
/ "'"""......
Gilles,E.D, (1983)
t [2]
Gilles, E.D,,5chuler,H. (1981)
Zur fruhzeit igen Erkennung geUihrl icher Reakt ionszustande in chem ischen Reak toren, Chem Ing Tech 53, pp. 673-682
.... [3]
King, R., Gilles, E.D, (1986)
Early detection of hazardous states in chem ical reactors, Preprints of the IFAC Workshops "Fault Detect ion and Safety inChem ical Plants", Sept. 1986, pp, 137-143
-..... N...."
1In.
Fig. 6 : Test results from an industrial plant
Thisdetectionmechanism has been implemented in a process with a react ion mechanism sim i lar to the one shown above. Fig. 6 shows results for different batch sam pies: 1n the first case, the react ion proceeded normally, in the second case, deviat ion of the start concentrat ions required the addit ion of one component during the heat ing phase. The resulting he.at of m ixing is interpreted by the detect ion mechanism as an addit ional potent ially dangerousheat source and a warning Is given. At this point the temperature is st i lllow anda autocatalyt ic decomposit ion not very probab le.
251
SUPERVISION AND CONTROL OF AN EXOTHERMIC BATCH PROCESS R.Perne Process ConJro/ Systems, Bayer AG, Leverkusen, Germany
Abstact- A mode I based superv i s ion and contro I system has been des i gned for exotherm i c chem ica I reactions, and batch processes inparticular. Adaptive, extendedKalman fi Iters reconstuct process states aswell as reaction parameters and a Bayes-Markov process allows to discrim inate between normal and unwanted process states. The new concept considerably reduces the time for one batch and warns of hazardous states at avery early stage, leavingenough time for counter act ions.
Keywords' Exotherm ic React ion, Fault Detect ion, KalmanFi Itering
I ntroduct 1on The example, presented in this paper, is the supervision and control of an exotherm ic process with a potent ia Ily hazardous autocata lyt ic decomposition.Here it is essential to detect the onset of an autocatalytic decomposition at avery early stage, in time to take counter act ions. Mult i-KalmanFi Iter techniques as proposed by King, Schuler & Gi lies [2-3) are app l ied and suitably modif i ed allow ing a detect ion of unwanted process states hours before a runaway of the react ion. Furthermore, with the informat ion from the fi Iters contro l1er parameters optimally adapted to the processdynam ics reducing considerably the time needed forone batch. This concept has resulted in time-opt imal and safe operat ion of the chem ical reactions under a II process condi t ions.
Uniform qual ity, high product yields, low energy consumption and m inimal effects on the environment are the main demands on superv i sion and control systems forchemical reactions. lnexpensive process computers are increasingly being used to fulfil these demands. Such computers perm i t not only the implementat i on of a PlO contro I algorithm equ ivalent to analog contro l1ers but allows the app I icat ion of advanced process contro I technology. Th i s techno I ogy i nc Iudes observers, extended Ka 1man fi Iters and adapt ive control algorithms. As shown in practice, the use of these control processes is successful i f chem ical engineering know ledge of the react ion concerned is included in the contro I concept as a prior i know ledge [I J. In the applicationpresentedhereapriori information is provided to the control by simulat ing mathematical models of the nonl inearprocess dynam ics paralle l to the actual process on acomputer. This al10ws the online estimation of significant processvariables, such as concentrat ions of the reactants or reaction rate, which are difficult or impossible to measure onl ine. The informati on of these estimates form the basis for an improved supervis i on and contro I performance: rep l acement of unmeasurablevariables by estimated variables or adapt ion of control1er parameters according to the estimated process states.
The
Problem
Theprocessinthecaseathand i sanexothermic chem ica I react ion, described by the fo Ilow ing simp le stoichiometry:
[A)
+
[B]
( 1)
and a macrok inetic react ion rate k: k = k o* exp(-Eo/(R*T»)*[A]~I*[B]]l2 247
(2)
with A, B : reactants, C : product, 6h R: react ion
Furthermore, a short local temperature peak in some small part of the reactor can start the autocatalytiC decomposition which has hardly any effect on the controlled temperature and may go by unnot iced. Once started, the decomposit ion will not ext inguish in the normal operat ion mode and eventually lead to a runaway of the reaction. Thus, a supervis ing system is needed for the early detection of a beginning autocatalytic decomposition.
enthalpy , ko : pre-exponentialfactor,Eo : activat i on energy, R: gas constant, T : react ion temperature, [A) and [B) .. . concentrat ions of A and Band the exponents III and 112, which are allowed to be rational numbers. lncludingenergyandmassbalances one arrives at the follow ing mathematical mode 1of the process dynam ics :
The New Control Concept d[A)/dt
=
(3)
-k
To improve the control behaviour of the exotherm ic batch process, a new contro 1strategy w as deve loped contro 11 ing the react ion power dQreac/dt
(M : the total react ion mass, c p : the specific heat,
k F : the heat transfer coefficient between the reac-
rather than product temperature. React ion power, the most sensitive variable for safe operation is then under direct contro 1.
t ion vesse 1and the jacket coo 1ing, F the area of heat exchange and TM : the temperature of the coo 1ing medium.) Beside the normal react ion, product Cmay decompose autocata lyt ically:
C -) D
+
E + (-6h ) s
C+D - ) 2D + E+(-6h A )
start react ion exothermicdecomposit i on
Simulation tests demonstrated the disadvantages and inadequacy of a fixed param eter contro 11 er and showed, that the dynam ic response of the system changes markedly with the varyingheat production within the reactor. With a PI contro 1structure for the reactionpower controller, computer simulations showed that the control loop maintains its characteristics only if the gain is changed in accordance with the chang ing dynam ics.
The start of autocatalyt ic decomposit ion is favoured by high temperatures. To avo i da dangerous runaway of the exothermic decompositionof the react ion product C, an upper 1im i t is set for the r eact ion temperature T and care has to be taken to ensure eff icient rem ova 1of react ion heat so that the crit ica 1temperature is never reached. In the convent iona 1contro 1concept tem perature was controlled by a PID regulator with fixed parameters act ing on the jacket coo 1ing system . Even si ight changes in process parameters, however, have significant effect on the overa 11 behaviour of this chem ical plant, due to the high ly nonl inear dependence of the reactor behav iour on the process state. As a consequence, a regulatorwith fixed parameters does not work optimal ly in a 11 process states.
Again-scheduling strategy is therefore adopted whereby the value of the gain-scheduling factor is adjusted so as to keep the overall loop gain constant:
(5)
where kp and kc represent the gain of the process Because of this di ff icul ty, the slope of the temperature set point ramp was taken to be very small in order to avoid unwanted rapid changes in the react i on power. On the other hand, th is measure leads to a large increase inreaction time and a subsequent lossof product ivity without being sufficient to e1im inate totally the occurrence of dangerous peaks in reaction power followedby temperal shut-down of the reaction. Thus a new control concept wascalled for, using advanced process control technology.
248
and the contro llerrespect ively. The gain has then the fo llow ing form:
= o(dQreac/dt)1 oT * oT / oT M
(6)
High Temperature State
As shown by equat ion 4, react ion power is a funct ion of unknown concentrat ions [A) and [B). To provide the control with a value of the react ion power these var i ab I es are est i mated by an extended Kalman fi Iter based on the mathematical model of the process as described by equat ion 3. The overall block diagram for the control loop inquestion is shown in Fig. 1.
a
I
O-Aotu. Value 0-8etpolnt
Normalized Time
Low Temperature State
a
:;.;,:.00-----... . . .... . Q-Actu. Value 0-6etpolnt
Normalized TIme
100%
Fig.2: Transient behaviour of the react ion power control loop
Typical exper1mental results are shown in Fig. 3 and 4. The product temperature trajectory followedby the conventional control d1ffers sign1ficantly from the more efficient trajectory of reaction powercontrol.
Fig. I : Overall Block Diagram
As an integral part of the control design process, simulat ion tests of the control system must be performed to ensure that transient performance specificat ions are met. Fig. 2 shows reactions to set point changes for two different temperatures: in the upper diagram the react ion temperature is close to the lower limit and in the lower diagram it close to the higher I im it of the allowed temperature range. The results demonstrate that, in contrast to the earl ier temperature contro I, the re levant variab le for safe operation, thereact ion power, is now contro lied direct Iy ensuring sat isfactory transient behaviour for all process state.
line
Fig. 3 : Product temperature trajectories for convent i ona 1and advanced contro I strategy
249
c::J _
The abi 1ity of the Bayes-Markov formal ism to detect unwanted process states depends crucially on the choice of the covariance matrix of process noise Q. Whereas the covariance matri x of measurement noice R is chosen such that it corresponds to the actual measurement noise, Q and the init ial values of the covariance matrix of the states Po are
convent. Control Reactlon Power Control
considered as designvariab les for the Kalman fi 1ter. Po is chosen such that the desired speed and
ie-
necessary degree of mode 1adapt ion is achieved at the start of each batch. Q for the normal react ion is a comprom ise between speed of process track ing and accuracy of est imat ion. Care has to be taken choosing this variable for the adapt ive fi lter which i nc 1udes the decom pos i t i on and param et ers to be est imated along with process states.
ll.
87...
Normalized Time
For the normal react ion both models should be equivalent and give sim i larresults.1 t has been observed, however, that the higher dimension of the second mode 1leads to a much broader est imated probabi 1ity density distribut ion p for the measured variab les effect ing the abi I ity of the subsequent decision logic todiscrim inatebetween the two cases.
Fig. 4: Frequency of normal ized product ion time
Early Detect Ion of a Hazardous Secondary React I on
The detect ion principle appl ied here is based on propositions of King & Gilles [3] and Gilles & Schuler[ 21, who suggest to construct extended Kalman Fi lters for the normal react ion and each typeof disturbed process. Adecision stage based on a Bayes-Markov process discrim inates between the di fferent process states: normal and type of disturbance. Thereby, probabi 1it ies derived from the Ka lman filters (Fig.5) are used to update a Markov process which models the probabi 1it ies to be in one of the different process states and givesa priori est imates for these probabi 1it ies. This mode 1contains rates for the transit ion between the different process states - an example is the transit ion rate from norma 1react ion to autocatalyt ic decomposit ion which is a funct ionof temperature and concentrat ions.
f
.~
i...
Tt
Fig. 5: Probabi 1ity density distribut ion Pi for twomodels
In contrast to King and Gi lles, on ly two models are used: one for the normal react ion and one for disturbed processes. The second mode 1contains parameters, which are est imated along with the process states and can describe different types of disturbances at the same time. Much of the effort gained by reducing the number of fi lters has to be reinvested in construct ing and calculat ing a more compl icated fi lter. However, this approach wi 11 automatically deal w ithcommonly observed model deviations.
Fig: 5 shows the probabil ity density distribut ion for two models. Eland E2 are expected values, To is the observed va lue. Pi is a funct ion of the innovationYi(k)=Ei-T 0 and the error covariance matrix Pi(klk-l) of the Kalman filter ( H: Jacobian of measurement equat ion, m: dimension of R):
250
Conclusion
The situat ion shown in the Fig. 5 has to be avoided. Although the observed temperature is much closer to the expected value of model2 including decomposit ion, for the given probabi 1ity densit ies the decision logic will choose model 1. A steeper probabi 1i ty densi ty distribut ion can be obtained by assum ing smallervalues for the "process noise", which, however wi 11 reduce the speed of model adaptat ion. The opt imum Q of the Kalman filter is a comprom ise bet ween speed of detect i ng autocata 1ytic decomposit ionon one side and certainty of discrim inat ion and accuracy of estimat ion on the other side.
l
t
The performance of the supervision and control system for exotherm ic batch react ion is encouraging for further pract ica 1app 1icat ions. 1t should be mentioned, however, that models accurate enough to discriminate between different process states are not readi ly avai lable and often difficult to establ ish 1imit inga straightforward extension of this approach to other react ions. These restrict ions are not as stringent for the react ion power control where somet imes agood model of thereactor without an explicit model of the react ion can lead to considerable improvement.
References [1]
ModerneMethoden der Mef3- und Automat is ierungstechni k und ihre Bedeutung fur die Automat isierung verfahrenstechnischer Prozesse [hem log Tech 55, pp, 437-446
l
/ "'"""......
Gilles,E.D, (1983)
t [2]
Gilles, E.D,,5chuler,H. (1981)
Zur fruhzeit igen Erkennung geUihrl icher Reakt ionszustande in chem ischen Reak toren, Chem Ing Tech 53, pp. 673-682
.... [3]
King, R., Gilles, E.D, (1986)
Early detection of hazardous states in chem ical reactors, Preprints of the IFAC Workshops "Fault Detect ion and Safety inChem ical Plants", Sept. 1986, pp, 137-143
-..... N...."
1In.
Fig. 6 : Test results from an industrial plant
Thisdetectionmechanism has been implemented in a process with a react ion mechanism sim i lar to the one shown above. Fig. 6 shows results for different batch sam pies: 1n the first case, the react ion proceeded normally, in the second case, deviat ion of the start concentrat ions required the addit ion of one component during the heat ing phase. The resulting he.at of m ixing is interpreted by the detect ion mechanism as an addit ional potent ially dangerousheat source and a warning Is given. At this point the temperature is st i lllow anda autocatalyt ic decomposit ion not very probab le.
251