Plant wide Tenesee Eastman Prblem

8/7/2019 Plant wide Tenesee Eastman Prblem

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e Pergamon Computers chem. Engng Vol. Ie}. No.3, pp. 321 331. IWSCopyright !e}e}S Elsevier Science LtdPrinted in Great Britain. All rights reserved0098-1354(94)00057-3 IK)'JR13541e}5 $e}. SO + 0 (K)PLANT-WIDE CONTROL OF THE TENNESSEE EASTMANPROBLEM

P, R, LYMAN and C. GEORGAKtstChemicalProcessModelingand Control Research Center and Department of ChemicalEngineering,LehighUniversity, Bethlehem, PA 18015-4732, U.S.A.(Received 6 May 1993; final revision received 15 February 1994; received for publication 16 May 1994)Abstract-This study focuses on thedevelopmentand performanceof four p l a n t - w i d e c o n t ~ o l structuresfor theTennesseeEastman challenge problem.The control structures are developedto a tiered fashionand without the use of a quantitativesteady state or dynamicmodelof the process.The throughput orproduction rate manipulator is selected first so. t h a ~ it is located on the major process path. Theinventory controls are arranged in an outward direction from this throughput m a O l p u l a t o ~ . The fourstructures are describedand commentsare givenon their effective handlingof the defineddisturbancesand setpoint changes, One structure provideseffectivecontrol under all circumstances for 50 hoursofprocesstime, The effectivedynamicperformanceof these structures supports the strengthof the tieredplant-wide control designmethodology used.

l. INTRODUCTION AND BACKGROUNDThe purpose of plant-wide control is to provide anoverall structure for the coordinated control ofseveral important variables of a multi-unit process,including the overall plant throughput and the product quali ty control . The main incentive for thisapproach is the coordination of the different localcont rol tasks so that one can achieve substantialreduction of costly intermediate storage facilities,The classical aproach to the plant-wide control problem has consisted in the past of the breaking down ofthe over-all problem into a series of smaller controlproblems around the individual unit operations ofthe process, Fo r this approach to work effectively,the designer must provide sufficient material inventories between units which serve to isolate one fromthe dynamic characteristics of the others, Theseinventories might need to be large and are costly inmany ways, They contribute to a high capital cost,increase the overal l holdup of valuable processingmaterial and occupy valuable plant space. Largestorage of possibly hazardous material also poses asafety and an environmental hazard and the possibledegradation and contamination could significantlyaffect the product quality, Furthermore, the existence of such large material hold-ups make requiredproduction shifts between different products or product grades difficult and time consuming, The use ofan effective plant-wide control structure may lead toa significant reduction in the size of these intermediate inventories or possibly their elimination fromthe plant designt To whomall correspondenceshould be addressed.

The synthesis of plant-wide control structures hasbeen the topic of recent research by Price andGeorgakis (1993), They have provided a systematicmethod and a set of guidelines which enable the userto develop a plant-wide s tructure which providestight and effective control of the overall plant. Thiscan be extremely valuable, especially in a systemwhich includes large recycle s treams which oftenpropagate and amplify process variation and theeffect of disturbances. The proposed method consists of a t iered framework in which control loopsare classified and ordered according to their importance for the plant as a whole. The categories whichcompose the tiered framework are production andinventory control , product specification control ,equipment and operating constraints, and economicperformance enhancement, respectively in the orderin which they are developed. One of the majorrecommendations of the cited references is to designthe structure so that the inventory control loops arear ranged in an outwardly fashion away from thelocation of the production rate manipulator. Controlstructures which possess this characteristic are called"self-consistent" .In this paper, atten tion is focused on the plant

wide control of the Tennessee Eastman (TE) challenge problem, defined in Downs and Vogel (1993).They have also made available an open-loop dynamic simulat ion of the already designed process buthave refrained from providing even the simplestSISO controllers. The primary solution to the challenge problem described in the present paper is a setof SISO loops, labelled structure 2, Three additionalcontrol structures, labelled structures I . ' and 4, will

321


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322 P. R. LYMAN and C. GEORGAKISalso be briefly described and compared to the primary solution. All these control structures have beendescribed in great detail byLyman (1992).We focushere on structure 2 because this has been able tosuccessfully handle all of the process disturbancesdescribed in the posed problem. The other structures are also of interest because they provide alternative structures that handle the great majority ofthe defined disturbances. The paper is organized asfollows. The development procedure which wasused to synthesize the control structure is describedin Section 2. The three additional structures, resulting from alternate locations of the variable thatmanipulates the production rate, are described inSection 3. The response performance of the mainstructure to the applied disturbances and setpointchanges and its comparison with the other structuresis described in Section 4. Finally the conclusions ofthis work are provided in Section 5.

2. SYNTHESIS OF A PLANT-WIDE SISO CONTROLSTRUCTURE

In the following discussion we will describe howthe tiered framework method proposed byPrice andGeorgakis (1993), leads to a plant-wide SISOcontrol structure for the TE process. For completeness, the Appendix details the tuning approach usedfor the different control loops. The description ofthe control structures starts with the selection of thevariable that willmanipulate the production rate ofthe plant and with the design of the inventorycontrol loops. The last ones are to be located alongthe primary process path and oriented in an outwarddirection from the location of the manipulationvariable for the production rate. This arrangementof inventory controllers follows the recommendations made by Price and Georgakis (1993) whocalled it a self-consistent structure through the primary process path. Consequently, it is important tofirst identify the primary process path.The primary process path for the TE process

starts at the raw material feeds to the reactor, goesthrough the reactor, condenser, and separator, goeson to the stripper, and through the liquid stream ofthe stripper to the liquid outflow from the stripper,the product stream. The next step is to locate theproduction rate manipulator. A second recommendation from the same references is to locate theproduction rate manipulator near the center of theprocess flow path. With such a choice, the production rate changes will propagate in both directionssimultaneously and thus faster. Although it mightnot be obvious on first sight, the condenser coolingwater valve (valve 11) can be considered to be onthe major process flow path. The control structure

which uses valve 11 as the production rate manipulator, shown in Fig. 1, will be called control structure 2.As valve 11is being closed, the temperature of the

reactor product stream at the exit of the condenserrises and a lesser amount of the G and H productsare condensed and separated. More of G and Haresent back to the reactor where they cause a rise inthe reactor level. The reactor level iscontrolled withthe flowrate of stream 4. This stream has a substantial effect on the reactor level because it is thelargest feed stream and contains both A and C whichtake part in both product producing reactions. Theseparator and stripper levels are controlled by theliquid efflux stream flow rates from each vesselfollowingthe rules defined previously. For example,as the condenser cooling water flow rate is reducedin response to a reduction in the product flow ratesetpoint, the separator and stripper efflux valvesclose to maintain their corresponding vessel levelsresulting in a reduction in the finalproduct flowrate.This sequence illustrates the action of a self consistent structure.The one inventory which has not been addressed

is the gas content in the reactor/recycle system,indicated by any of the different but interrelatedpressure values. In all of the structures described inthis paper, the reactor pressure is left uncontrolledand is allowed to float. Although the reactor pressure can cause large variations in reaction rates, itseffective control would require the simultaneousand coordinated manipulation of the many factorswhich can influence the reactor pressure. This listincludes the raw material flow rates, the recycle flowrate and the reactor temperature and level. Becausethere are substantial interactions between the different variables, one should consider the design of amultivariable controller for this reactor. Such acontroller was not considered here for two primaryreasons. First we wished to consider the simplestcontrol structure possible and we chose to restrictthe problem solution to SISO structures with PIDtype controllers. The second reason that restrainedus from considering a multivariable controller is itsrequirement for a dynamic process model. We considered it of interest to investigate what type ofcontrol performance one could obtain without theuse of a process model. This completes the description of the inventory control tier of the developmentof control structure 2.Additional tiers in the structure development

must provide for reactor temperature control,inventory control of individual species in the recycleloop and final product purity. The reactor temperature is controlled through a cascade controller by


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Fig. 1. TE processcontrol structure 2.


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324 P. R. LYMAN andC. GEORGAKISmanipulating in the master loop the set point of theoutlet temperature of the coolingwater in the reactor. In the inner or slave loop the outlet coolingwater temperature is controlled by manipulating thecoolingwater flowrate. This minimizesdisturbancesto the reactor temperature from the cooling waterinlet temperature. A number of additional loops areused to control the overall material balance of someindividual components from the reactor/recyclesystem. Stream 1 is used to maintain a constantcomposition of A in the reactor feed stream. Thiscontroller is required to compensate for a variableamount of A which might enter the system fromstream 4. Stream 3, whichisnearly pure E, is used inorder to maintain the proper product ratio which ismeasured at the product stream. The purge flowrateismanipulated in order to maintain a constant composition of the inert component B in the recyclestream. The purity of the product at the bottom ofthe stripper is related to the composition of E, theheaviest of the impurities. It is controlled throughthe outer loop in a cascade structure by manipulation of the set point of an inner temperature controlloop. The temperature controller manipulates thesteam flow rate.

The performance characteristics of this controlstructure will be examined in the section after thenext and are also detailed by Lyman (1992).

3. ADDITIONAL PLANTWIDE CONTROL STRUCTURESThis section briefly describes three additional

structures which result from the use of the tieredapproach mentioned above. These structures differin the location of the manipulated variable for theproduction rate. They are all self-consistent andhave several of the samecontrol loops as structure 2.Figure 2 shows the location of the production ratemanipulated variable for the structure already described and for the three additional structures.Detailed information about these additional controlstructures is presented elsewhere (Priceet al., 1994).Structure 1 sets the production rate bymanipulatingthe feed flow rate of D into the reactor. In order toreduce the production rate the flow rate of D isreduced. This lowers the production rate of G andcauses a drop in the level within the reactor. In thisstructure, the condenser cooling water valve is usedto maintain the reactor liquid level.It closes in orderto condense less product vapor and return it to thereactor as part of the recycle gas. The reduction incondensate flow to the separator is carried downstream by the separator and stripper level controllers resulting in a reduction in the product flowrate.

Structure 3 controls the production rate by manipulating the outflowfrom the separator tank. As thisvalve is closed the flowinto the stripper is reducedand the level within the separator will rise. Theoutflow from the stripper isthen reduced in order tomaintain the stripper bottoms level as in structures 1and 2. The condenser cooling water flow is used tocontrol the separator level in this structure. As theseparator level rises the condenser cooling watervalve closes in order to maintain this level. Thiscondenses less reactor product and sends it back tothe reactor where it causes a temporary increase inreactor level. The reactor level is maintained bymanipulating the flow rate of stream 4 as instructure 2.

Structure 4 controls the production rate by manipulating the stripper underflow valve. A closure ofthis valve will cause the stripper level to rise. Thestripper level is controlled with the separator outflow, and the separator level is controlled with thecondenser cooling water valve. The level in thereactor is controlled as described for structures 2and 3. The above description illustrates the differences between the four control structures studied.Several controllers are identical in all control

structures. These include control of the reactor temperature by the use of the coolingwater flowand thecontrol of the composition of the inert component Bwith the flowrate of the purge stream. The productquality control loop described above is also commonto all control structures examined and the composition of A in the reactor feed iscontrolled using thefeed rate of A to avoid accumulation of this component. The composition of the components D and Eare controlled in structures 2, 3 and 4 in a similarmanner to prevent their accumulation. Lastly andvery importantly, the recycle flowrate ismaintainedat a constant value in structures 2, 3 and 4 using thecompressor recycle valve. This valve is kept at aconstant position in structure 1 to avoid interactionwith the reactor level control loop. None of the fourstructures include control of the reactor pressure forreasons explained earlier.

4. CLOSED LOOP PERFORMANCE OF PLANTWIDECONTROL STRUCTURES

In this section we will concentrate on the performance of structure 2 and we will make some comparisons between structure 2 and the other ones withrespect to their response performance to theprovided disturbances and the recommended setpoint changes. The discussion of the control structure's performance is divided into three segments:operating costs, some disturbance response resultsand the responses to the defined setpoint changes.


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Fig. 2. TE process-locations of the production rate manipulated variable for four SISO contr


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326 P. R. LYMAN and C. GEORGAKIS

*These runs include a 15% reduction in the production rate andcan be expected to have lower operating costs. SDdenotes processshutdown at the simulation time given.

4,1. Operating costThe total process operating costs calculated from

the simulation runs that lasted 50 hours and representing each control structure's response to thedifferent disturbance upsets and setpoint changesare presented in Table 1. The operating cost isa sumof costs associated with the purge stream, the product stream, the recycle compressor and steamusage and has been defined in the problem definingpaper (Downs and Vogel, 1993). At the base caseprovided, about two-thirds of the total operat ingcost can be att ributed to the purge stream. Sinceeach structure incorporates identical purge streamcontrollers the operating cost does not show largedifferences between structures. Disturbance 2 whichis an increase of component B in stream 4 results invery high operating costs for all structures becauseof the high purge rate needed to maintain a lowconcentration of B in the system. Disturbance 6, lossof stream 1, also gives high operating costs since onemechanism utilized to remove excess C from thesystem is a higher purge flow rate. This is implemented with the use of an override controller on thepurge stream flow rate. The override responds to anexcess of C in the sytem by purging more material tocontrol the composition of C instead of B in therecycle stream. Entries denoted with a (*) symbolare runs in which the product ion rate is decreasedand they should be compared only with other entriesof the same type. The problem statement suggestsusing disturbances 14through 20 in conjunction with

Table I. Total operating costControl structure2 3

4.2. Disturbance 12Disturbance 12 provides some interesting results

since it occurs in the center of the main process path.The control structures described above can beexpected to respond very differently to this disturbance since the production rate manipulated variable is in a different location for each structure.Disturbance 12, random variation in the condensercooling water temperature, has the effects on production rate and reactor pressure shown in Figs 3and 4. Control structures 1 and 2 transmit thevariation out through the primary process flowstream resulting in variation of the product flowrate. This is contrasted to control structures 3 and 4which maintain a nearly constant product flow rateby rejecting the disturbance's effect and propagatingit back to the feed flow rates, through the recyclestream, resulting in increased reactor pressure variation, eventually causing the process to shutdown. Inthis case, it is preferable to transmit the disturbanceout of the process as quickly as possible in order tominimize its effect upon the reactor system. Controlstructures 3 and 4 could be made more robust byeither reactor pressure control such that the pressure variation could be removed from the process orby relaxing the production rate control in appropriate situations to allow specific disturbances to betransmitted out of the process. To summarize, thelocation of the production rate manipulated variablerelative to a specific disturbance to a large extent

another disturbance or setpoint change. In order tosatisfy this recommendation, a 15% setpoint reduction in the production rate, was selected since itrepresents a plant-wide shift and therefore providesa rigorous test for these plant-wide control structures.The results shown in Table 1 indicate that all four

structures are capable of rejecting the majority ofthe disturbances and Structure 2 is capable of controlling the TE process simulation for 50 handresponds efectively to all disturbances and set-pointchanges postulated, A total of six process shutdownsoccur in the other three structures all of them due tohigh pressure. Control structure 1 has a slightlylower operat ing cost at steady state but will shutdown with disturbance 6. Control s tructure 3 hastwo shutdowns: disturbances 12 and 18. Controlstructure 4 has three shutdowns: disturbances 12, 13and 18. Detai led descriptions of the results fromeach of the four structures with each disturbance isprovided by Lyman (1992). For clarity and brevity,only selected plots will be presented here.Disturbance 12 and the setpoint changes are described in more detail below.

48472822814,037847284728475

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DisturbanceNone123456789101112131415161718192021222324


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Control of the Tennessee Eastman problem 327Product Flowrate, Disturbance 12

3 0 r - - - . . . . , . . . - - - - , r _ _ - - r - - ~ - - . . , _ - . . . . , . . - - r _ - . . . . , . . . - - r _ _ - _ _ ,

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- Structure 1- - Structure 2

. . Structure 3. - . - Structure 4

21

2 4 6 8 10 12time (hrs) 14 16 18 20

Fig. 3. Closed loop response of product flowrute to disturbance 12 for each controlstructure.

determines the ability of the structure to reject thatdisturbance. In the example provided above, it isbetter to pass the disturbance through the processquickly using structures 1 and 2 rather than hold thedisturbance in the recycle loop as with structures 3and 4.

4.3. Setpoint changesThe following setpoint changes are defined In the

postulation of the problem to allow comparisonsbetween structures and test their ability to move theprocess to alternate operating points.

Reactor Pressure, Disturbance123000r---,----r---r---,----r---r---,----r------,

2900

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2500- Structure 1- - Structure 2

2400 Structure 3. - - Structure 4

1864223000'- -- ....J...- - -'-- - - - ''- -- ....J...- - -' -- - - - 'L-- ......L-- - -'-- - - J8 10time (hrs)Fig. 4. Closed loop response of reactor pressure to disturbance 12 for each control

structure.


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328 P. R. LYMAN and C. G EORGAKISincludes the dynamic lag of the stripper columnwhile structure 4 could be retuned to give a fasterresponse. Figure 5(B) shows the response of theflowof D, the most expensive raw material, with thesame setpoint change . Control structure 1 turnsdown the flow rate of raw material s the fastest asexpected while the other three structures are aboutthe same. In short , control structure 1 wastes thefewest raw materials in a production rate reduction.The impact on the reactor can be seen in Fig. 5(C).Control structure 2 affects the reactor pressure first.Although control structure 1 turns down the flow ofD and the other raw materials faster this has a muchmore gradual impact on the reactor pressure sincethe flows are small compared to the recycle flow.The reactor pressure also equil ibrates at the newreaction rate sooner for structure 2. A productionrate reduction is easily accomplished using any ofthe four structures. Those structures in which theproduction rate is controlled towards the end of theprimary process path give a faster turn down of theproduction rate as could be expected.

4.3.2. Setpoint change 2 . Setpoint change 2 is ashift in the product ratio of G/H from 1.0 to 0 .67 inmass units . The ratio of products is plotted forcontrol structure 2 in Fig. 6. The setpoint change ismade directl y in the reactor feed composition loopsas a step change. The change in operating conditionsiscomplete after 15h. All four control structures areable to move the process to produce this new product ratio. The shift in operating points takes about15h using structure 2.

4.3.3. Setpoint change 3. The reactor pressure iss tepped down in setpoint change 3. Since all fourstructures are designed to let the pressure float, thepressure can only be adjusted by changing anothervariable which is controlled. The reactor temperature was found to be the best variable to use for thispurpose. A temperature shift of + l OC gives approximately a 50 kPa reduction in reactor pressure. Thisshift in reactor temperature was used with controlstructure 2 giving the results shown in Fig. 7. Thepressure reduction per C change in the reactortemperature setpoint is greater for structures 2. 3and 4 than for structure I (not shown). This effect isa result of recycle flow rate control differencesbetween the control schemes. For instance. in structure I the recycle flow rate is uncontrolled; thehigher temperature gives a higher molecular weightrecycle mixture however control structures 2. 3 and4 hold the molar flow rate constant despite pressurechanges and the density shift. In the case of structur e I. the molecular weight shift and the newoperating pressure cause the recycle flow rate todrop . This reduced flow rate lessens the impact of

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Fig. 5. Closed loop response of product fiowrate, flowrateof 0 and reactor pressure to se tpo in t change I for eachcontrol structure.4.3.J. Setpoint change I. The first setpoint

change , which is a 15% reduction in productionrate, is described by Fig. 5(A-C). Figure 5(A)shows the response of the stripper underflow to aproduction rate change at 1 h . Control structure Igives the slowest response, as expected, since theproduction rate is controlled at the start of theprocess . Control structure 3 is actually slightly fasterat turning down the production rate than controlstructure 4. This is surprising because structure 3


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Control of the Tennessee Eastman problemRatio01 GIHin Product. Setpoint(2)

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Closed loop response of reactor pressure to setpoint change 4 for eachcontrol structure.

505050 25 30time (hrs)

ReactorPressure, Setpolnt(4)

15

P. R. LYMAN andC. GEORGAKIS

10

, NAII , t \ , i ~ ~ i ' ; ' : ,!i,/ fl ~ ~ ll. , I , ~ i ! t;p r : ~ :: : t ~ } ; / ( ! ' V ~ ~ ' A ! v ~ N ~ ~ . t r \ f : J : \ H t i ~ Y : : < l N ~ r ~ I U W ~ :f! ;"0: (;11;;iW \ n ' j ~ F > j',!;,I . _ Structure1 1 :' il - - Structure2

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pressure than the other structures. Since the recyclestream is now lighter (B is a noncondensible and lowmolecular weight component) the recycle flow rateis higher. The additional flow of a lighter streamgives a much higher reactor pressure. In the case ofthe other control structures, the recycle flowrate isheld constant by loop 5 despite the shift in therecycle stream molecular weight. This results in alower pressure rise compared to control structure 1.Control structure 3 gives significantlymore variationin reactor pressure than any of the other structures.The same behavior was observed with structure 3without any disturbances present and isattributed tointeraction between the separator level control loopand the recycle flowrate control loop. In structure 3,the separator level is controlled using the condensercooling water flowrate and recycle flow rate loop isthe same as shown in Fig. 1. In light of this evaluation of control structure performance, controlstructure 2 isselected as the best of the four studied.This control structure has reasonable operating costsand more importantly is able to withstand all of thedisturbances and setpoint changes without experiencing a process shutdown. Control structure 1 isthe second structure of choice since it only shutsdown with disturbance 6, the most severe disturbance. Also, structure 1 has a lower operating costwith no disturbances. The reactor pressure can bemanipulated by changing the reactor temperature incontrol structures 2, 3 and 4. This could also be used

in control structure 1 if the recycle flow rate werecontrolled.

S. CONCLUSIONSThe TE process was found to be particularly

difficult to control because the recycle stream andthe reaction characteristics introduce the potentialfor excessive interaction between reactor temperature, reactor pressure, reaction or production rateand reactor level. Despite these difficulties, fourplant-wide SISO control structures were developed.The development of these structures is consistentwith the tiered structure development framework.In this method, the production rate manipulator ischosen first and located on the primary process path.The inventory control loops function in an outwarddirection from the production rate manipulator.This ensures that production rate and inventorycontrols are self consistent as described in Price andGeorgakis (1993) and Price (1993). Control structure 2 offers the best control system of those studiedfor the TE process. This structure weathers alldisturbances and setpoint changes without experiencing a process shutdown. It has the further benefit of being composed of a simple set of SISO loopsand a few cascade systems. This would enable it tobe easily implemented and understood by operatingpersonnel. If additional complexity could be tolerated a supervisory level of control may allow for


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Control of the Tennessee Eastman problem 331indirect control of the reactor pressure. The feasibility of this algorithm was shown by the use of thereactor temperature setpoint to change the reactoroperating pressure in setpoint change 3. The development of the supervisory algorithm is left forfuture work.Acknowledgements-The authors would like to acknowledge William L. Luyben for helpful discussions during thecourse of this study.

REFERENCES

Downs J. and E. Vogel, A plant-wide industrial processcontrol problem. Computers chern. Engng 17, 245-255(1993).Lyman P. , Plant-wide control structures for the TennesseeEastman process. Master's thesis, Lehigh University(1992).Price R. , Design of plant-wide regulatory control systems.Ph.D. dissertation, Lehigh University (1993).Price R. and C. Georgakis, Plantwide regulatory controldesign procedure using a tiered framework. Ind. EngngChern. Res. 32,2693-2705 (1993).Price R. , P. Lyman and C. Georgakis, Throughput manipulat ion in plantwide control structures. Ind. EngngChern. Res. 33,1197-1207 (1994).Tyreus B. and W. Luyben, Tuning PI controllers forintcgrator/deadtime processes. Ind. Engng Chern. Res.31,2625-2628 (1992).

CACE 19-3-F

APPENDIXControl lers and tuning decis ions are based on the following criterion. Level controllers for the separator tankand the stripper column bottoms use proport ional actiononly with a dimensionless gain of one. The range of thevalve is set such that a maximum allowable level corresponds to a fully opened or closed valve depending on ifthe valve is located downstream or upstream of the vessel.

respectively_ Series cascade arrangements arc used forreactor level or composition cont ro l. In these cases. theslave portion is a very simple flow control ler. Thc slavecontroller uses proportional action only while the masterloop uses proportional-integral action. The slave controlleris tuned such that the closed loop time constant is one halfthe open loop time constant. The ult imate gain and periodfor the master loop are calculated from an integratordeadtime model of the open loop response of thecontrolled variable to a step change in the manipulatedvariable. In this arrangement the manipulated variable 01the master loop is the setpoint of the slave loop. During theidentification procedure. the step change isimplemented inthe manipulated variable of the slave loop and not themanipulated variable of the master loop. This differencemay be neglected if one assumes that the dynamics of theslave loop are sufficiently fast as to be negligible. The uscof propor tional only control for the slave loop helps toensure that this is the case. Once the ul timate propert iesare obtained. the controller tuning is calculated usingsettings described in Tyreus and Luyben (1992). Thesesettings are referred to as TL settings and are less oscillatory than Ziegler-Nichol settings. The remaining loops uscproportional -integral action and arc tuned in the samemanner described above for the master controllers.

Plant wide Tenesee Eastman Prblem

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