I n d . Eng. C h e m . Res. 1993,32, 2693-2705
2693
Plantwide Regulatory Control Design Procedure Using a Tiered Framework Randel M. Price+and Christos Georgakis' Chemical Process Modeling and Control Research Center and Department of Chemical Engineering, Lehigh University, Iacocca Hall, 111 Research Dr., Bethlehem, Pennsylvania 18015
Two frameworks for process control design have been identified, and they are used to structure the control design decision sequence in a way which preserves the "plantwide" character of the problem and solution. A CSTR/column process example has been studied in depth, and a procedure for the design of the coupled system regulatory control structure (throughput, inventory, and product quality controls) has been developed. The procedure is based on a tiered framework for plantwide control system design and is justified and supported by an extensive set of dynamic simulations. Specific guidelines for designing inventory control structures are presented. The best-performing structures are shown to be those which are "self-consistent" and designed t o minimize the propagation of disturbances through the system. The design procedure for throughput and inventory control design is believed t o be fully applicable to other processes. Results from specific application examples will be presented in forthcoming publications (Price et al., 1993). 1. Introduction
The systematic design of plantwide regulatory control structures for today's highly integrated and interconnected chemical processes is an often neglected area of current process control research and practice. Many of the techniques which are proposed focus on higher level application objectives, such as process optimization or the design of multivariable product quality control strategies. These generally assume that a structure controlling production rate and process inventories is already in place. Rarely considered is the impact of the assumed structure on higher level control tasks. Process control systems for chemical plants have typically been designed using what has been called a "unit operations" approach (Stephanopoulos, 1983). Individual control systems are designed for each unit operation or piece of equipment in a plant, after which any conflicts between control loops are reconciled. Implicit in this approach is the assumption that both the static and dynamic behavior of the unit operations are independent of the way in which they are connected. Such an assumption was relatively safe as long as a sufficient amount of intermediate storage was available between units, so that the surge capacity could be readily employed to dynamically decouple process equipment. In recent years, the complexity and intensity of the interaction between processing units have increased as a consequence of several historical factors. The energy cost spiral of the 1970sand 1980sled to process design strategies where energy integration is the rule, rather than an exception. Today's tighter focus on a customer's needs requires plants with substantial production flexibility. In such situations, excessive inventory is a liability, so designers tend to minimize the storage capacity between operations. These developments violate the basic assumption which underlies the unit operations approach to plant control design and require a new methodology for the design of plantwide control systems. The plantwide design process is a sequence of choices. Furthermore, the order in which the decisions are made
* To whom correspondence should be addressed. E-mail:
[email protected]. t Present address: Department of Chemical Engineering, University of Mississippi, University, Mississippi 38677. Qaaa-5885/93/2632-2693$04.00/0
is itself a variable which influences the final result, for once a process variable is assigned a task, it typically becomes unavailable for other tasks. I t is thus important that the decision sequence be conducted in a rationally ordered manner. A design framework is a formal guide for ordering the sequence. The concept of a design framework is based on the belief that the smaller design problems resulting from decomposition of a plant are more readily solved than the original monolithic problem. The frameworks provide guidelines and structure for the division of the plant and its control system into subsets. The overall plantwide control procedure is thus a three-part effort: (1)Decompose the plant control problem into smaller subproblems. (2) Design the subset control systems. (3) Combine and reconcilethe control system subsets into a single plantwide regulatory control structure. This paper presents two frameworks for the decisions made while designing a plantwide regulatory control system. Regulatory control refers to the first level control hierarchy which interacts directly with the process. Optimization, shutdown, scheduling, and similar tasks are performed by a higher level supervisory or independent parallel control structure. 2. Frameworks for Control Design
Current plantwide control practice has been assessed by reviewing the literature and through meetings with industrial practitioners. From this background, two general frameworks for plantwide control have been identified. It is believed that one of these, or some combination of the two, can provide overall guidance for a control designer. Moreover, most current practice, as well as most of the techniques discussed in the literature, can be represented as special cases of these approaches. Within a framework, additional guidance can be offered in the form of design guidelines. These are more specific rules for control system design, but they are not absolute. Instead, they are suggestions for use in most cases which must always be applied using sound engineeringjudgement and with the aid of process specific knowledge. Although two frameworks have been identified and will be presented, the bulk of this paper will elaborate and apply only one, the tiered framework. 0 1993 American Chemical Society
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2694 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
IV Economic Performance Enhancement I n Equipment t Operating Constmints 11 Product Specification Control Inventory Control ----------_---___-______________________-----Production Rate Control
Figure 1. Modular control design framework.
Figure 5. Tiered design framework.
-
I
t Figure 2. Material recycle module.
Process
I Figure 3. Feed/effluent heat-exchange module.
D
Reactor
Separator
I
-
t Figure 4. Reactor/separator module.
2.1. Modular Framework. Process systems are typically represented as sets of interconnected unit operations. For most applications, such a representation has proven convenient, justifiable, and accurate; however, when attempting to develop dynamic models of complex processes for use in control system design, it has been shown that the unit operations approach is sometimes inadequate-particularly when recycle streams are present. This suggests using a larger “building block” in the control design process. These “modules” might consist of several linked unit operations which recur in the same grouping in a variety of processes. Ideally, these modules have little or no dynamic effect on each other and can be combined in series, parallel, or nested sequences. Control systems can then be designed separately for each module and later combined and reconciled into a plantwide system. A control design framework based on interconnection modules is represented in Figure 1. If the modules are defined to be unit operations, this framework reduces to the unit operations method of control design. Candidate modules have been identified by reviewing a number of process flow sheets from the series of design studies coordinated by Washington University (for example, Bolles, 1968). The flow sheets were successively abstracted and recurring equipment groups identified. The abstraction procedure used was similar to the hierarchical decomposition procedure discussed by Douglas (1988) as a preparatory step in conceptual plant design. The flow-sheet review yielded three strong candidates for use in a modular control decision framework material recycle, feedleffluent heat exchange, and the reactor/ separator (Figures 2, 3, and 4). These combinations of operations are fairly common, and it is hoped that their
dynamic behavior is consistent wherever they occur. It is believed that these modules, used in series and/or parallel connection, can be combined to simulate most common process flow sheets. 2.2. Tiered Framework. The second design framework is a direct descendant of Buckley’s (1964) “dynamic process control”. His arguments that the plantwide design problem could be broken into two phases-material balance control and product quality control-are extended, as it seems useful to subdivide the problem still further. This framework leads the control designer to address the control problem in stages corresponding to the goals and tasks of the control system. Eachgoal defines a subset of control loops, and these control subsets are designed one at a time. A schematic representation of the framework is shown in Figure 5. The control tasks are presented in a tier, where the task at the bottom of the diagram is the first to be considered. The ordering of the tasks is based upon the importance of a goal in the operation of the plant. Fundamental control loops essential to all forms of operation are addressed before those needed only under special circumstances or for improved, rather than basic, operation. Papadourakis et al. (1987) observe that decisions concerning inventory control should be made prior to or at the same time as the relative gain array calculations used in the selection of composition controllers. This observation seems to support the use of a tiered strategy for plant control design, where each tier depends upon those before. If control design tools, like manipulator selection, are dependent on the sequence in which loops are designed, a structured order should be employed during the design process. It has been suggested that the tiers within the framework correspond to certain economicorders of magnitude within a plant. Control failure a t lower tiers probably would incur greater cost penalties than a similar failure at a higher layer. As an example, the cost penalty if a plant is unstable and inoperable is much greater than if it operates stably but produces product of marginal quality. The tiers which interact with the process most frequently are considered “lowlevel”and often are prerequisites to satisfactory design of higher tiers. In each tier, the control designer must make a set of decisions. Often, several alternatives of equal quality will be available. In this situation, the designer can carry forward a set of alternatives to the next design tier, where subsequent decisions or loop conflicts may eliminate some of the candidates. A significant advantage of the tiered framework over the modular version, as well as many previous plant control design strategies, is that it preserves the “plantwide”nature of the design problem. Because the implied decomposition of the control system is based on function rather than loop locations or the unit controlled, the subproblems which result are each plantwide problems. 2.3. Design Tiers. Five stages are proposed within the tiered framework. The stages, listed in the order of consideration, are as follows:
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2695 ProductionRate Control: The throughput of the plant must be regulated to correspond to sales or usage demand. Inventory Control: Inventory within the plant is controlled to maintain material balance. These controls consist primarily of liquid level, solid weight, and vapor pressure controllers. These stages (production rate and inventory control) are jointly concernedwith the material balance of the plant and are more closely linked with each other than any two subsequent stages. As a result, it is preferable to think of these two tasks as a single design tier. Product Specification Control: The products of a process must meet specifications if they are to be sold. Often these specifications take the form of restrictions on product composition and are measured by analyzers or inferred from temperature measurements. Typical examples might include distillate and bottoms composition controls on distillation columns and reactor temperature controllers. Equipment and Operating Constraints: Sometimes, disturbances may tend to drive the process into a region where equipment constraints are encountered. For example, changes in a distillation column’sfeed composition may require increased reflux to meet the product specification; however, excessive reflux can result in column flooding. Instruments may have limited operating regions. Controls designed at this stage are intended to anticipate and compensate for such constraints. In some cases, these requirements may force recalculation or rearrangement of lower layers. It should be noted that sometimes a piece of equipment pushed beyond its constraint can fail catastrophically and result in danger to operating personnel. Controlloops designed to prevent such occurrences will be primarily subjects of the safety controls, not the regulatory control structure. Other control decisions are motivated by basic common sense or legal restrictions which transcend economic motivations. These restrictions have been called “noneconomic”constraints, because they must be met without regard for their impact on the economic performance of the process. Examples might include restrictions on the release of chemicals to the environment or limitations on operating regions set as a consequence of a hazards analysis. Economic Performance: Once a process is operating, additional controls are often used to maximize its economic performance. Such control loops might be designed to minimize production of a byproduct, losses of product in a waste stream, or energy consumption to meet a target imposed by an off-line optimizationor a supervisory control hierarchy. 2.4. Combined Tiered Modular Framework. It seems likely that a combination of the tiered and modular frameworkscan be developed,combining strengths of each. Most likely, this would involve using modular concepts to address the problems of the product quality and subsequent design tiers. 3. Study of a CSTR/Column
To examine the effectiveness of the framework concept and to identify guidelines for use by designers using the frameworks,the dynamic behavior of a CSTR/column has been studied by simulation. This system is a common example of the reactor/separator module identified for use within the modular control design framework. It has been studied by several previous researchers (Gilliland et al., 1964;Verykios and Luyben, 1978;Papadourakis, 1985). The initial purpose of the simulations was to provide insight into the design and tuning of control structures for
m h
D , xd
FO, xo V
I
-1
0 xb
Figure 6. CSTR/column. Table I. Characteristics of the CSTR/Column System Flows 3.99mol/min, 100% A 8.33mol/min, 50% A 4.34 mollmin, 95% A 3.99mol/min, 1 % A
fresh feed column feed overhead product bottoms product Column number of trays feed tray inside diameter tray spacing
20 12 6 ft 24 in.
Reactor residence time reaction rate constant
0.20 h 0.079h-l
Holdups reactor column base column accumulator total column
100 mol 89.4mol 69.4mol 226.9 mol
a representative process. It soon became apparent that the CSTR/column control problem was effectively addressed by applyingtiered concepts, and hence subsequent work has focused on plantwide application of the tiered design framework. 3.1. Process Description. The study system chosen for this effort was the CSTR/column (Figure 6): a CSTR containing an isothermal A B reaction followed by a distillation column, with recycle of unreacted feed component A. Basic physical characteristics of the system are shown in Table I. Probable measured variables include the final product (column bottoms) composition Zb, the column overhead (recycle)compositionxd, and the reactor outlet (column feed) composition xr. Potential manipulators include the fresh feed flow Fo, the reactor outlet flow F, the column overhead D, reflux R, vapor boilup V, and final product B. A FORTRAN program for time domain simulation of the system was developed. The simulation assumed constant relative volatility, rigorously modeled the tray liquid hydraulics, and neglected vapor hydraulics. 3.2. Enumeration of Control Structures. As a first step in the detailed study of the CSTR/column, it was necessary to enumerate the set of control structures to be examined. The enumeration employs tiered concepts by first identifying the possible inventory control structures. Then, for each inventory structure, the additional controls which might be implemented to manipulate product quality are examined. An inventory control structure is defined by selecting a process variable for use in manipulating the production rate and then selecting a set of manipulators for control of the material inventories (levels and pressures) within the process. To limit the extremelylarge number of control structures which might result from an indiscriminate
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2696 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
choice of manipulators, it is useful to apply intuitive rules. One is the "proximity rule", which can be found in the literature. Stephanopoulos (1984, p 468) offers one statement of this rule: "Choose the manipulation that has a direct and fast effect on a controlled variable." The same basic idea is given a more specific form by Morari (1983): "Choose systems where the manipulated variable is 'close' to the controlled variable. Physical closeness usually implies short time constants and small deadtimes and thus superior control performance." These rules have the same effect; they eliminate potential control structures which are expected to show poor dynamic behavior. The proximity of the potential manipulator to the expected controlled variable is a factor in this decision, and it is possible to formulate a general statement of this proximity rule which is useful in the development of plantwide control structures. Development of level control structures for the simulation study is guided by basic proximity rules; hence, reactor level can be controlled using F, Fo, or D;reflux drum level by D , R, or V; and column base level by B, F , or V. One convenient way to summarize the proximity rules for these cases is to use a set notation, x E (a,b,c), which is read "x is an element of the set containing a, b, and c". The proximityrules for level control in the CSTR/ column system then become
where the abbreviations RLM, ALM, and BLM stand for reactor level manipulator, accumulator level manipulator, and column base level manipulator, respectively. Individual designers may prefer to use proximity rules which are more liberal or more restrictive than those stated above; they might then obtain a different set of control structures for the same process. Similarly, a designer will wish to adapt the proximity rules to fit the design characteristics of the specific process under consideration. For example, the feed to a column may not be acceptable as a base level manipulator because of the dynamic lag between the feed tray and the column base. In such cases, the proximity rule can be modified to BLM E (B,VJ,and the list of possible control structures will be different. This study did not consider the use of flow ratios or calculated variables as manipulators. Adding even a limited number of ratios to the list of acceptable manipulators markedly increases the number of structures which must be examined. A complete inventory control structure for a process consists of both inventory and throughput (production rate) controls. The options for controlling the production rate of the CSTR/column system are the fresh feed Fo,the reactor product/column feed F , the column distillate/ recycle D , and the final product B. When these four options are combined with the level control proximity rules, 36 different inventory control structures are possible. These are shown in Table 11. In the table, the inventory control structures are presented in descriptive form as an ordered sequence of manipulators of the form TPM; RLM,ALM,BLM, where T P M stands for throughput manipulator and RLM, ALM, and BLM represent the level manipulators as defined above. Each structure has also been given an identifier of the form ISxx.
Table 11. Descriptive Key to Inventory Control Structures for the CSTR/Column System. IS01 = Fo;F,D,B IS11 = F;Fo,D,B IS02 Fo;F,D,V IS12 F;Fo,D,V IS03 = Fo;F,R,B IS13 F;Fo,R,B IS04 = Fo;F,R,V IS14 = F;Fo,R,V IS05 Fo;F,V,E IS15 = F;Fo,V,B IS06 = Fo$I,R,F IS16 = F,D,R,B IS07 = Fo;DJ(,B IS17 F,D,R,V IS08 Fo$I,R,V IS18 = F,D,V,B IS09 = Fo;D,V;F IS19 = D;Fo,V;F IS10 = Fo$I,V,B IS20 D;Fo,V,B
IS21 = D;Fo,R,V IS22 D;Fo,R,F IS23 D;Fo,R,B IS24 = D;F,R,B IS26 = D;F,R,V IS26 = D;F,V,B IS27 B;Fo,D,F IS28 = B;Fo,D,V IS29 B;Fo,R,F IS30 = B;Fo,R,V
IS31 B;Fo,V,F IS32 = B;F,L),V IS33 = B;F,R,V IS34 B;D,R,F IS36 = B;D,R,V IS36 B;D,V,F
Structures are designated by an identifying key of the form ISxx and described by a sequence of manipulators: TPMRLM,ALM, BLM.
These inventory control structures can be complemented by adding additional loops for the control of process stream compositions. Adding these loops transforms an inventory control structure into a full control structure. Control structures will be given an identifier of the form S x x . It should become clear that a single inventory structure can lead to zero, one, or more control structures. Consider first the case where only one composition control loop, regulating the composition of the final (distillation bottoms) product, is used. The acceptable manipulators for Xb can be stated in a proximity rule as BCM E (B,F,VJ,where BCM stands for bottoms composition manipulator. When this rule is combined with the inventory control structures, 34 single-endcomposition control structures result. The single-end structures developed are listed in descriptive form as SO1 to S34 in Table 111. SO1is given as Fo;F,D,B;V,-,-. The two dashes are space holders, indicating that the structure does not control either the column overhead composition or the reactor outlet composition, and so neither a top composition manipulator (OCM) or reactor composition manipulator (RCM) is listed. One might note that IS36 does not lead to an acceptable control structure because the manipulators which are proximate to the bottoms composition are all assigned to inventory control tasks. On the other hand, IS06 can lead to two different control structures: SO5 if B is chosen or SO6 if Vis chosen as the BCM. After product composition control is in place, enough manipulators remain free to control one additional composition. The logical alternatives are the intermediate streams-the column overhead composition (Xd) and the reactor outlet composition (xr). If one chooses to control distillate composition, the control variable choices can be restricted by the proximity rule OCM E {D,R,v). Using this rule, 20 double-end, overhead-bottoms control structures can be developed from the single-end structures. These are listed in Table I11 as 535 to S54. If, instead, it is decided to control the reactor outlet composition, the proximity rule for composition control becomes RCM E (D$,Fo). This produces an additional 16 structures, shown in Table 111 as 555 to ,570. There are thus a total of 70 structures for the control of composition of the CSTR/column system. These have been listed descriptively in Table I11 and are presented in another form, more convenient for comparison, in Table IV. In the latter table, each numbered line represents an inventory control structure and the composition structures associated with it. The manipulators and structure identifier codes are provided for reference. 3.3. Implementing t h e Control Structures. A control designer must decide more than the control structure to be used. The type of controller used in each loop and its tuning must also be determined. In this work,
Ind. Eng. Chem. Res., Vol. 32, No. 11,1993 2697 Table 111. Descriptive Key to Composition Control Struatures for the CSTR/Column System.
501 FO;F,DB;V,-,-
S26 D;F&B;V,-,- S51= B;Fa,D,F;V,R,502 Fo;F,D,V;B,-,- 527 D;F,R,B;V,-,552 B;Fo,D,V;F,R,so5 FO;F,R,B;V,-,- 528 D;F,R,V,B,-,- 553 BJa,RAV,D,504 Fo;F,R,V,B,-,- S29 = B;Fo,DAV,-,- 554 = B;Fa,R,V,F,D,506 = F@,RP;B,-,S30 = B;Fo,D,V;F,-,- 555 Fa;F,RB,V,-,D so8 F@,RzV,-,531 B;Fo,RfiV,-,556 Fa;F,R,V;B,-,D 501 3 F@,RB;F,-,532 B;Fo,R,V;F,-,- 557 Fa;D,R,B;V,-,F SO8 = F@,RB;V,-,- 533 B;D,RP,V,-,558 = Fa;D,R,V;B,-P SOB F@,R,V;F,-,534 B;D,R,V;F,-,559 F;F&,E;V,-,D S10 F@,R,V,B,-,535 = Fo;F,D,B;V,R,- 560 = F;Fo,R,V;B,-,D Sll F@,VP;B,-,536 Fa;F,D,V;B,R,- 5 6 1 F,D,R,B;V,-,Fo ~ 512 Fo;D,V,B;F,-,- 537 = Fo;F,R,B;V,D,- 562 = F,D,R,V;B,-,Fo S13 F;Fo,D,B;V,-,- S38 Fo;F,R,V;B,D,- 563 D;Fa,R,V;B,-,F 514 F;Fo,D,V;B,-,S39 = Fo;D,RP;B,V,- 564 = D,Fo,R,B;V,-P 515 = F;Fo,RB;V,-,S40 Fo;D,R,B;F,V,- 565 = D;F,RB;V,-,Fo S16 F;Fo,R,V;B,-,541 = Fo;D,VP,B,R,- 566 = D;F,R,V;B,-,Fa 517 = F,D,R,B;V,-,- 542 = Fo;D,VB;F,R,- 567 = B;Fa,RAV,-P 518 F,D,R,V$,-,-543 = F;Fa,D,B;V,R,- 568 B;Fa,R,VJ,-,D 519 D;Fa,VP;B,-,- 544 F;Fo,D,V;B,R,569 = B,D,RAV,-+Fo 520 D;Fa,V&F,-,- S45 = F;Fa,RB;V,D,- S70 B,D,R,V;F,-;Fa S21= D;Fa,R,V;F,-,- 546 = F;Fa,R,V;B,D,S22 D;Fa,R,V$,-,- 547 = D;Fa,VP;B,R,523 D;Fo,RP;B,-,- 548 D;Fa,VB;F,R,524 D;Fa,RAV,-,- 549 D;Fa,RP;B,V,525 D;Fa,R,B;F,-,550 = D,Fo,RB;F,V,0 Structures are designated by an identifier of the form Sxx and a string of manipulators in the order TPM;RLM,ALM,BLM; BCM,TCM,RCM. A dash indicates that no manipulator is used.
a control structure with ita associated controller types and tunings will be referred to as an “implementation”. In the CSTR/column study, implementations were differentiated by the tunings used for the level controllers and by the type of controller used in the intermediate composition control loops. All levels were controlled with proportional-only controllers. These were tuned in three ways. The first set, described as “loose”,used a P-only dimensionless gain of 1.0 for all three level controllers. The “tight” set used a dimensionless gain of 20.0. The third set of level controls was a “mixed” set. This was based on rules of thumb for level control: Reactor Level: Loose if D or F is used; tight if FOis used. Loose is selected so that adisturbance is not abruptly passed to downstream unit operations. Accumulator Level: Loose if D or V is used; tight if R is used. Tight tuning of a loop using R is not disadvantageous, as the flow remains internal to the column. Column Base Level: Loose if B or F is used; tight if V is used. V is also a column internal flow. Each of the 70 control structures was examined with all three level tuning patterns. The bottoms composition controller is always PI. Two options were examined for the intermediate composition controllers; both proportional-only and proportional integral controllers were used. In all cases, Ziegler-Nichols tunings were used. Implementations will be designated by adding the level controller tuning and intermediate composition controller type to the structure identifier. Thus, S35:M-PO describes structure 35 with mixed level tunings and a proportionalonly controller on the loop controlling the intermediate composition (in this example, the distillate). 4. Simulation Study
Ziegler-Nichols (ZN) settings were used for the composition controllers. The relay test method (Astrom and Hagglund, 1983) was the primary tool used to obtain the ultimate gain and frequency values required for tuning
(as in Luyben 1990, pp 519-521). This approach uses a simple relay controller to induce sustained oscillationabout the set point of a loop. The amplitude ( A )and period (P) of this oscillation are related to the ultimate gain and period by
P, = P K , = 4m/ AT where m is the relay magnitude. When two compositions are controlled, interaction between the loops becomes a factor in the tuning process. The tuning parameters change depending on the loops which are closed. Typically, allowance is made for interaction in one of two ways-detuning or sequential tuning. Both seek to achieve what has been called “implicit decoupling” (Ryskamp, 1982) of the control loops. If the detuning approach is selected, each loop is first tuned with all others in manual. The resulting settings are then “detuned” (gains reduced, reset times decreased) to compensate for interaction. Several authors have suggested detuning approaches incorporating the relative gain interaction method (on relative gain analysis, see Bristol (1966); for a detuning example, see Shinskey (1988));Luyben has provided a more general alternative, dubbed “BLT tuning” (Luyben, 1990). The second approach for compensating tuning parameters for loop interaction is based on tuning the loops in sequence. After a loop is tuned, it is left in automatic as subsequent loops are tuned. This way, as loops are commissioned, the tuning includes the effects of ita predecessors (McMillan, 1983, p 181). Often, the tuning order is based on loop speed (fastest first) or independence (least subject to interaction first). Sequential tuning is conceptually similar to the approach taken when tuning any mixture of inventory and quality control loops. Level control loops are almost never tuned at the same time as composition control loops. Instead, the levels are tuned first so that controller effects are included in the tuning of the composition loops. In this study, the number of cases which were to be considered suggested the use of sequential tuning to reduce the required calculations. Since the bottom composition loop was considered most critical, it was tuned first and the intermediate loop second. This does not guarantee stability of the system should the bottoms composition loop fail. All of the control structures shown in Table IV were simulated. Two different inputs were studied: a 5 % decrease in feed composition and a 2% decrease in throughput. The actual manipulator change required to produce the throughput decrease depended on the throughput manipulator used. In bothcases, the integral absolute error is calculated and presented for the final product composition (Xb). The error is referenced to the composition controller set point. All simulations were run for 12 h (720 min). Error summation begins at 80 min to ensure the absence of initiation effects, and the step input is introduced at 100 min. The complete simulation set examined 318 different control implementations. The results can be ranked by IAE to allow comparison. Complete rankings for each phase of the study and for both inputs will be provided elsewhere (Price, 1993);the 16 implementations with the least IAE for a given input and selected others for comparison are included in Tables V and VI. The highest ranked implementations for the feed composition input, S64:M-PO and S64:T-PO, are P-only
2698 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 Table IV. List of CSTR/Column Control Structures Examined in the Simulation Study and Their Relationships to Inventory Control Structures. inventory control line 1 2
3 4
5 6 6A 7 7A 8 8A 9 10 11 12 13 14 15 16 17 18 19 20 21 21A 22 22A 23 23A 24 25 26 27 28 29 30 31 32 33 34 35 36
TPM
Fo Fo Fo Fo Fo Fo Fo Fo FO Fo Fo Fo Fo F F F F F F F F D D D D D D D D D D D B B B B B B B B B B
LMs
composition control IS-id IS01 IS02 IS03 IS04 IS05 IS06 IS06 IS07 IS07 IS08 IS08 IS09 IS10 IS11 IS12 IS13 IS14 IS15 IS16 IS17 IS18 IS19 IS20 IS21 IS21 IS22 IS22 IS23 IS23 IS24 IS25 IS26 IS27 IS28 IS29 IS30 IS31 IS32 IS33 IS34 IS35 IS36
BCM V B V B
V B F V F B B F V B V B
S-id
so1
so2 SO3 SO4
B&OCMs
S-id s35 S36 s37 S38
B&RCMs
S-id
BP
VP
555 S56
VP
557
BP
558
BP
VP
ss9 S60
VJO BA
S61 562
BP
S63
VP
564
VPO
B A
S65 S66
VP FP
567 568
VPO FPO
S69 S70
SO5
SO6 SO7
s39 540
SO8
so9 s10 s11 s12 S13 S14 S15 S16
541 542 s43 544 545 S46
V B
517 S18
B F F B V B V F V B
s19 s20 s21 s22 S23 S24 S25 S26 S27 S28
s47 548
V F V F
529 S30 S31 S32
551 552 s53
V F
s33 s34
549
550
s54
a Table Key: TPM, throughput manipulator; LM, level manipulator; IS-id, inventory control structure ID; BCM, bottoms composition manipulator; B&OCMs, bottoms and overhead compositionmanipulators, respectively;B&RCMs, bottomsand reactor compositionmanipulators, respectively.
reactor bottoms versions of IS23; these rank eighth and ninth for the throughput input. Highest ranked for the throughput input are S59:M-PO and S59:T-PO, P-only reactor bottoms versions of IS13; these rank 13th and 14th for the composition input. The implementation with the highest aggregate ranking is S37:M-PI, a double-end P I version of IS03, which ranks fourth in the composition rankings and third in the throughput rankings. 5. Discussion of Simulation Results
The highest ranked implementations tend to share certain characteristics. This section of the paper aims to elucidate these characteristics, motivating the synthesis of a set of design guidelines. One way to demonstrate common characteristics is to look at the prevalence of a selected characteristic among the top 10,20,30,40, or 50 structures in the IAE rankings. Starting with Table VII, a series of “prevalence tables” is presented. Each of these shows the number of implementations within a set which share a characteristic. The characteristics to be examined can be divided into two main areas-those related to inventory control and those related to composition control. Within each area,
there are several general characteristics worthy of note. These will be presented in the form of propositions and supported by prevalence tables and other evidence. Checks on the results were provided by two additional seta of simulations. In one, the IAE results were calculated for inputs of varying size. The relationship between the error values and the input size appears to be basically linear. The ranking tables were also compiled using integral squared error instead of integral absolute error. Although the two sets of rankings showed some differences, the general conclusions presented in the propositions were not changed. Details on these matters are presented in Price (1993). 5.1. Inventory Structures. The best-performing CSTR/column control implementations are characterized by the arrangement of the inventory structure, the chosen manipulators, and controller tuning. 5.1.1. Inventory Control Paths. Proposition 1: The control structure implementations which produce the smallest IAE in response to disturbances in either throughput or feed composition are those whose inventory control structure is self-consistent and directed along the primary process path. To properly interpret this proposition, it is first nec-
Ind. Eng. Chem. Res., Vol. 32, No, 11,1993 2699 Table V. Input Composition IAE Ranking. rank
implementation
TPM
CMs
S64M-PO SMT-PO S65T-PO S37:M-PI S45M-PO S45T-PO S13T S65 M-P0 S37:M-PO S43:T-PO S43:T-PI S43:M-PO S59:M-PO S59T-PO S 43:M-PI S37:T-PI
D D D
FR5 FR6 FR7 FR8 FR9 FRlO FRll FR12 FR13 FR14 FR15 FR16
0.001 687 0 0.001 691 6 0.003 298 0 0.004 959 3 0.005 458 4 0.005 477 0 0.005 669 1 0.006 389 8 0.006646 5 0.0068156 0.0070608 0.007 219 4 0.007 471 3 0.007 503 0 0.0080084 0.008013 8
F D Fo F F F F F F Fo
VP VP VPO VP VP VP V VPO VP VJi VJi VJi VP VP VJi VP
FR99 FRl00 FRlOl
0.037866 0.038 20 9 0.038 44 2
S35:T-PI S32L S40L-PI
Fo B Fo
VJi F F,V
FR199 FR200 FR201
0.202 75 0.20356 0.209 29
S66:L-PI S49:L-PI S39L-PO
D D
BPo
FR1
FR2 FFi3
FR4
m
b
Fo F
F
Fo
B,V B,V
a Ranking of control implementations based on the IAE of the final product composition in response to a 5% step decrease in fresh feed composition.
Table VI. Throughput IAE Ranking. rank W b imdementation TRl 0.002 970 1 S59M-PO 0.002 982 9 TR2 S59T-PO 0.003 187 8 TR3 S37:M-PI 0.003 936 2 TR4 S37:M-PO TR5 0.004 806 8 S57:M-PI 0.005 100 6 TR6 S45M-PO 0.005 132 9 TR7 S45:T-PO 0.005 516 7 TR8 S64:M-PO 0.005 540 2 TR9 S64:T-PO 0.0059647 TRlO S37:T-PI 0.0060988 TRll S53:M-PI 0.0063000 TR12 S57:M-PO 0.0065375 TR13 S55:T-PI 0.0065687 TR14 S08M 0.0067385 TR15 S35T-PO 0.0068456 TR16 S37:T-PO
TPM
CMs
F F
Fo
VP VP VP VP VP VP VP V 3 VP VP VP VP VP V VJi VP
Fo Fo Fo F F D D Fo B Fo
Fo Fo
Fo
TR99 TRl00 TRlOl
0.052 248 0.052800 0.054 799
S58L-PI S38L-PO S13:M
Fo Fo F
BP BP V
TR199 TR200 TR201
2.1493 2.1604 2.1622
S38:T-PI S31:T S07:T
Fo B Fo
BP V
F
a Ranking of control implementation based on the IAEof the final product composition in response to a 2 % step decrease in throughput.
essary to examine the definitions of “self-consistency”and “primary process path”. An inventory control structure is said to be “self-consistent” if it is able to propagate a production rate change throughout the process and in particular if such a change produces changes in the flow rates of major feed and product streams. The CSTR/ column has only one feed (Fo) and one product ( B )stream. Consequently, a self-consistent inventory control structure must use both FO and B as either the throughput manipulator or as level manipulator(s). For example, IS01 is self-consistent while IS34 is not self-consistent (“inconsistent”) because a change in the throughput manipulator ( B )does not result in a change in the main feed flow (Fo). Of the 36 inventory control structures listed in Table 11, only 14 (ISO1, 03, 05, 07, 10, 11, 13, 15, 20, 23, 27, 28, 29, and 31) are self-consistent, Only one of the inconsistent
structures (IS24) produces an implementation (S65:M,TPO) ranked among the first 20 structures for either input. When an inventory control structure is inconsistent, it cannot operate effectively by itself without additional control loops to supplement the action. Return to the example of IS34 and consider the structure (S69) which results from the addition of composition control loops on the column bottoms composition and the reactor outlet composition. FO is now used to control the reactor composition. Consequently, when a change in throughput is made by changing the value of B, an eventual change will be made in FO by the action of the composition controller. I t can then be said that the composition control loops in S69 have “remedied the inconsistency” in IS34 or that S69 has a “remedied inconsistency”. This idea could play an important role in the study of the resiliency of control structures like S69 when it is necessary to place the reactor composition controller into manual operation. It should also be stressed that an inconsistent inventory control structure cannot always be remedied by the addition of composition control loops. This can be seen by examining S33, another control structure which might be developed from IS34. Here, a single composition loop is employed, manipulating V. FOis not involved in the control structure and remains fixed, so the control structure retains the inconsistency of the underlying inventory structure. A structure with a retained inconsistency may be able to respond to feed composition disturbances but fails to respond effectively to changes in throughput (see Table XVII and the accompanying discussion in a subsequent section). An equivalent approach to the self-consistency of a level control structure is to examine the direction in which a level controller operates. The significance of such directional chains has been known for many years (Buckley, 1964). These chains are typically developed “in the direction of flow” (using outlet flows) or “in the direction opposite to flow” (using inlet flows). In the formulation presented here, controls in the direction of flow imply the use of the feed flow as the throughput manipulator (as in IS03); control in the direction opposite to flow implies the selection of product flow as the throughput manipulator (as in IS29). Implicit in both is the concept of a “primary process path” proceeding from the major feed streams to the major products. Such a path exists in most processes, and this concept will be used extensively in this work. For the CSTR/column, the primary path begins with the feed stream Fo, follows the reactor outlet F, and ends with the product stream B. Not all inventory control structures will manipulate production rate using feed or product flows. One might select an intermediate flow, such as the reactor effluent (F)or the recycle (D), as the throughput manipulator. In such cases, and in the general case of intermediate flows as throughput manipulators, the chain of level controls needs to be constructed to radiate outward from the throughput manipulator. This implies that level controllers between the feed and the throughput manipulator are in the direction opposite to flow, while those between the throughput manipulator and the main products are in the direction of flow. Additionally, level controllers on streams branching off of the primary path also need to be arranged in such an outward direction. An example of an inventory control structure with an outward arrangement is IS13. Here, throughput is manipulated by F. The upstream, reactor inventory is controlled using the inlet flow (Fo),while the downstream inventory in the column base is controlled using an outlet flow (B). A quick review
2700 Ind. Eng. Chem. Res., Vol. 32,No. 11,1993 Table VII. Prevalence of Consistent Inventory Control Structures in Feed Composition IAE Ranking
no. of implementations 10 20 30 40 50
all (295)
self-consistent primary alternate no. 6 16 23 28 32 69
%
60 80 77 70 64 23
no. 2 2 5 8 11 66
%
20 10 17 20 22 22
inconsistent no. 2 2 2 4 7 172
%
20 10 7 10 14 58
Table VIII. Prevalence of Consistent Inventory Control Structures in Throughput IAE Ranking
no. of imdementations 10 20 30 40 50 all (230)
consistent primary alternate no. 7 13 18 22 23 69
%
70 65 60 55 46 30
no. 3 7 11 16 20 66
5% 30 35 37 40 40 29
inconsistent no. 0 0 1 2 7 95
% 0
0 3 5 14 41
of the structures in Table I1showsthat inventory structures ISO1, 03, 05, 11, 13, 15, 27, 29, and 31 have outwardly arranged level controls tracing the primary process path. Outward chains can also be constructed along paths through the process other than the primary one. Consider IS07, where a change in the throughput manipulator, Fo, is passed by way of the distillate and reflux streams to the column product. Such “alternate process path” structures and 28. If these 5 structures are include IS07,10,20,23, added to the 9 which use the primary process path, the result is the set of 14 self-consistent structures identified previously. The significance of self-consistency in the performance of a control implementation can be seen by examining Tables VI1 and VIII. These show the number and percentage of implementations which have self-consistent inventory structures and are ranked near the top of the set of all implementations ranked by IAE. For example, consider the line for the top 30 implementations in Table VII. Of the 30 implementations, 28 have self-consistent inventory structures, while only 2 are inconsistent. Of the 28 consistent implementations, 23 are organized along the primary process path. Contrast these numbers to the totals in the bottom line of the table. Less than half of all implementations considered (135of 295,or 46% ) use self-consistent inventory structures, yet 94% of the top 30 do. Clearly, self-consistency correlates with good IAE rankings. A similar observation can be made of the importance of path selection. Those using the primary path supply 77% of the best 30,but only 23 % of the total. Table VI1 might suggest that self-consistency along alternate paths is not important; after all, such implementations are equally represented in the best structures and the total pool. Table VI11 suggests otherwise. This table contains the same categories of information, but for the IAE ranking based on the throughput disturbance. Two points should be made about this table. First, note that most of the inconsistent implementations do not appear-these were structurally unable to make any throughput change at all. This is why there are only 230 implementations ranked instead of the 295 for the feed composition disturbance. The inconsistent structures which remain are those whose inconsistencies are remedied by the addition of composition control loops. Second, note that alternate path
structures provide better implementations than inconsistent structures but are inferior to primary path structures. Clearly, control designers should concentrate on consistent inventory control structures directed along the primary path. 5.1.2. Throughput Manipulator Location. Proposition 2 I f all else is equal, throughput manipulators internal to the process tend to produce smaller IAE than external throughput manipulators. When the concept of a primary process path was introduced, a differencewas suggestedbetween flowswhich are external to the process (feeds and products) and those which are internal (intermediate streams). In the CSTRI column,there are four alternative TPMs. Two are external the others (Dand F)are internal flows flows ( B and Fo); which transfer material between processing operations. From an intuitive standpoint, internal flows would seem to offer certain advantages with respect to the patterns of disturbance propagation through a process. If the throughput adjustment is made internal to the plant, the change in production rate will need to propagate outward through only part of the plant before the feed flow is affected, and this change is simultaneously working through the other portion of the plant to change the product flows. In contrast, when an external flow is used to control throughput, the change must propagate through the entire plant from beginning to end (or vice versa). This observation suggests that internal flows should be somewhat more effective as throughput manipulators. If the prevalence of the throughput manipulator choices for the CSTR/column are examined (Tables IX and X), it is possible to draw conclusions about the relative value of internal and external manipulators. Table IX clearly shows that implementations using F as the throughput manipulator are preferred by the feed composition disturbance IAE ranking. Nearly one-third of all the TPM = F implementations fall within the 50 highest ranked. If both internal manipulators (F and D) are considered together, they compose 75% of the best 20 implementations versus only 46% of the total. Results for the throughput IAE ranking (Table X) are less clear. Here, the preference for internal throughput manipulators only extends about 10implementations deep. This table also shows a large number of implementations using FOas the throughput manipulator. B is clearly the least effective manipulator-when it is selected for throughput control, the variables which remain for use in base level and bottoms composition control (F and V) generally lead to poor implementations. D performs less well than either F o r Fo. This can be ascribed, at least in part, to the fact that D is not on the primary process path, and so changes must take a more roundabout route before their impact is felt. Additional support for proposition 2 will appear as part of the example in section 5.3. 5.1.3. Recycle Loop Inventory Controls. Proposition 3 For the CSTRlcolumn, the better IAE rankings are obtained for implementations which use reflux to control the accumulator level, thus preventing the return of disturbances to the primary process path. Prevalence arguments are less effective in supporting this proposition, since the vast majority of the implementations considered (214of 295) use R as the accumulator level manipulator. With this in mind, it is still worth noting that less than one-third of the 30 top implementations in the feed composition ranking use D to manipulate accumulator level, while the first to use V is ranked
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2701 Table IX. Prevalence of Throughput Manipulators in Feed Composition IAE Ranking TPM no. of implementations no. ofB %B no. ofD %D no.ofF %F no.ofF0 4 40 4 40 10 0 0 2 4 20 11 55 3 20 2 10 3 10 5 17 14 27 8 30 4 10 6 15 16 35 14 40 10 40 20 32 50 4 8 16 61 21 74 25 61 21 99 all (295)
%Fo 20 15 21 35 32 34
internal, % 80 75 63 55 60 46
external, % 20
internal, % 60 40 33 35 34 41
external, % 40 60 67 65 66 59
25
31 45 40 54
Table X. Prevalence of Throughput Manipulators in Throughput IAE Ranking TPM no. of implementations 10 20 30 40 50 all (230)
no.ofB 0 2 4 4 4 43
%B 0 10 13 10 8 19
no.ofD 2 4 6 8 9 51
%D 20 20 20 20 18 22
no.ofF 4 4 4 6 8 43
%F 40 20 13 15 16 19
no.ofFo 4 10 16 22 29 93
%Fo 40 50 53 55 58 20
Table XI. Prevalence of Level Tuning Patterns in Feed Composition IAE Ranking L M T no. of imdementations no. % no. % no. % 0 0 5 5 0 5 50 10 0 0 11 55 9 45 20 3 10 16 53 11 37 30 3 8 22 55 15 38 40 21 42 5 10 24 48 50 106 36 83 28 106 36 all (295)
Table XIII. Prevalence of Composition Manipulators i s Feed Composition IAE Ranking.
Table XII. Prevalence of Level Tuning Patterns in Throughput IAE Ranking L M T no. of implementations no. % no. % no. % 0 0 6 6 0 4 4 0 10 0 0 12 60 8 40 20 16 53 13 43 1 3 30 16 40 4 10 20 50 40 9 18 23 46 18 36 50 84 36 62 27 a4 36 all (230)
'Manipulators given in sequence BCM, OCM, RCM. Dash indicates an uncontrolled composition.
55th. The pattern is even more pronounced for the throughput input-37 of the 40 top structures use R. The preference for R can also be examined by studying the 1 2 pairs of structures which are the same except for the accumulator level manipulator. One such pair is SO1 (Fo$,D,B;V,-,-) and SO3 (F&,R,B;V,-,-). In 8 of the 12 pairs, the structure using R to manipulate the accumulator level ranks higher for the composition input. Of the 12 pairs, 6 are based on self-consistent inventory control structures. In 5 of these 6, the structure using R ranks higher than that using D. 5.1.4. Level Tunings. Proposition 4: A self-consistent inventory control structure performs less well when all level control loops are tuned loosely than when mixed or tight tunings are employed. The validity of this proposition can be seen by examining Tables XI and XII, where mixed or tight level control tunings are clearly preferred. Less than 10% of the 50 highest ranked implementations use loose tunings, even though such tunings comprise about one-third of the total. The highest ranked loosely tuned implementations are in 20th place for the composition input and 27th place for the throughput input. It should be stressed, however, that choice of tuning is dependent on the choice of inventory control structure. Later in this section, in the discussion of Table XVII it will be seen that for selected structures loose tunings outperform their mixed or tight counterparts. Many of
no. of V,-,F V,D,-or V,-,D implemen- tations no. % no. % 10 2 20 4 40 20 2 10 11 55 30 5 1 7 14 47 16 40 40 6 15 17 34 50 7 14 45 15 all(295) 18 6
V,R,V,-,V,-A no. % no. 7% no. 1 10 1 10 2 4 20 1 5 2 7 2 3 2 1 2 7 18 9 22 2 7 14 17 34 2 24 8 6 2 21
%
20 10 1 5 4 9
these are RV column-level structures where the loose tuning will help reduce the impact of the positive feedback effects. A requirement that all structures be self-consistent would serve to eliminate such cases from consideration. 5.2. Composition Control. The simulation study indicates that the product composition of the process should be controlled using column vapor boilup as the bottoms composition manipulator and that an intermediate composition should be controlled using a proportional-only controller. The nature of the composition control problem makes these observations specific to the CSTRlcolumn and hence less suitable for extension to other systems. 5.2.1. Composition Manipulators. When composition manipulators are selected for a control system, it is desirable that the manipulator be close to the controlled variable. This suggests the following: Proposition 5: Vapor boilup should be used to manipulate the product composition of the CSTRlcolumn. The simulation results confirm the proposition. Table XI11 shows that all of the first 50 implementations in the feed composition ranking use boilup to manipulate the bottoms composition, as do the 28 of the first implementations in the throughput rankings (Table XIV). It should be emphasized that almost all of the bestperforming inventory structures will almost by default use V as the bottoms composition manipulator. Proposition 1 (self-consistency) will produce CSTRlcolumn inventory control structures which use B to manipulate column base level. In concert with the proximity rules used for composition manipulator selection,this will ensure the choice of V as the bottoms composition manipulator. 5.2.2. Control of Intermediate Compositions. Proposition 6 The best-performing CSTRlcolumn control implementations measured by IAE ranking are those
2702 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 Table XIV. Prevalence of Composition Manipulators in Throughput IAE Ranking. ~~
no. of implementations 10 20 30 40 50 all (230) 0
V,-P no. 3 7 10 13 13 18
V,D,- or V,-,D no. % 7 70 12 60 17 57 20 50 21 42 45 20
%
30 35 33 32 26 8
V3,no. % 0 0 1 5 1 3 2 5 2 4 24 10
F ,V,no. % 0 0 1 3 4 18
0 0 3 2 2 8
0 0
0 0
1
3
1 1
2 2
18
8
Fa,-
BP,-
B, V,no. %
no.
%
0
0
0 0 1 6 33
0 0 2
12 14
no. 0
%
0
0
0 0 3 24
0 0 6 10
0
Manipulators given in sequence BCM, OCM,RCM. Dash indicates an uncontrolled composition.
Table XV. Prevalence of Intermediate Control and Controller Type in Feed Composition IAE Ranking. no. of implementations 10 20 30 40 50 all (295)
B 1 1 2
9 17 95
B0:PO 4 5 9 9 10 55
B0:PI 1
7 8 8 8 55
BRPO 4 7 10
BR:PI
11 12
3 3 45
45
0 0 1
% BO
% BR
50 60 57 42 36 37
40 35 37 35 30 30
%PO 80 60 63 50 44 34
%PI 10 35 30 28 22 34
0 B, only column base controlled; BO, column base and overhead controlled; BR, column base and reactor outlet controlled; PO, proportionalonly controller used for intermediate; PI, proportional integral controller used for intermediate.
Table XVI. Prevalence of Intermediate Control and Controller Type in Throughput IAE Ranking. no. of implementations 10 20 30 40 50 all (230)
B 0 1
7 13 18 66
B0:PO 3 5 6 8 9
55
B0:PI 2
3 3 3 7 55
BRPO 4 7 8 9 9 27
BR:PI 1
4 6 7 7 27
% BO
% BR
50 40 30 28 32 48
50 55 47 40 32 23
%PO 70 60 47 42 36 36
%PI 30 35 30 25 28 36
0 B, only column base controlled; BO, column base and overhead controlled; BR, column base and reactor outlet controlled; PO, proportionalonly controller used for intermediate; PI, proportional integral controller used for intermediate.
which control an intermediate composition (either the distillate or the reactor outlet). The highest ranked single-end structure for the feed composition input is S13 in 7th place; for throughput, it is SO8 in 14th place. These are the only single-end structures in the top 20. This provides a basis to assert that controlling intermediate values is beneficial. It may be confirmed by consulting Tables XV and XVI, which show the prevalence of the various types of structure. Consider the 30 highest ranked structures for the feed composition input. Ninety-four percent (28) of these control two compositions. This is in contrast to the total set of control implementations examined, where only 67 % control two compositions. The type of disturbance considered seems to have an impact on the decision of which intermediate to control-feed composition disturbances seem to be best rejected when the column overhead composition is controlled and throughput disturbances when the reactor outlet composition is controlled. The prevalence tables do not provide a clear indication as to which intermediate composition to control; however, a slight preference for the reactor outlet seems indicated. Looking directly at the rankings confirms this preference, as implementations which control the reactor composition sit atop both ranking tables. These same prevalence tables also support a second proposition. Proposition 7 Proportional-only controllers are the preferred means for controlling intermediate compositions. This is readily confirmed by a quick examination of Table XV, where 44% of the 50 highest ranked ,
implementations use a P-only controller for the intermediate versus only 34% of the total. Table XVII offers another way of examining the questions of intermediate composition control, controller type, and level controller tuning. In this table, one line is devoted to each possible inventory control structure, and the best-performing implementation for each of the two disturbance inputs is listed. Thus, if ISOl is taken as an example, it can be seen that, regardless of the disturbance input S35:T-PO, a tightly tuned bottoms plus overhead composition control implementation performs best. This implementation ranks 21st on the feed composition IAE ranking and 15th on the throughput IAE ranking. All other implementations derived from ISOl are ranked below these positions. Other inventory structures show different results for different disturbances. Take IS08 as an example. The best-performing implementation of this inventory control structure for the feed composition input is a bottoms plus reactor composition controlled structure employing loose level tunings (S58:L-PI, ranked 146th). For the throughput input, a single-end loosely tuned structure (SlO:L, ranked 90th) is preferred. In only two cases (S37:M-PI, S53:M-PI) is PI control of the intermediate composition clearly the best variant of a control structure. These are both VD structures controlling column overhead, as is S45. The two which prefer PI are those which use external throughput control; that which prefers PO does not. Focusing on disturbance propagation provides an explanation for the difference. Using an internal TPM restricts the propagation of disturbances between the unit operations much the same as the tight control of Xd provided by PI control in the other two cases. A limited number of other structures
Ind. Eng. Chem. Res., Vol. 32, No. 11,1993 2703 Table XVII. Bert Implementation (Determined by IAE) by Inventory Structure. FC TP
Table XVIII. Comparison of IAE Rankings for Selected CSTR/Column Control Implementations IS-id TPM
LMs
S-id CMs FCrank TPrank ranksum
~~
IS-id IS01 IS02 IS03 IS04 IS05 IS06 IS07 IS08 IS09 IS10
IS11 IS12 IS13 IS14 IS15 IS16 IS17 IS18 IS19 IS20 IS21 IS22 IS23 IS24 IS25 IS26 IS27 IS28 IS29 IS30 IS31 IS32 IS33 IS34 IS35 IS36
implementation S35T-PO S02M S37:M-PI S38L-PO
***
rank FR21 FR81 FRO4 FR142
implementation S35T-PO S36M-PO S37:M-PI S56T-PI
***
rank TR15 TR40 TR03 TR82
S05M S5'I:M-PO S58L-PI S11:L S12L S13:T S14:T S45:M-PO s46:L-P0
FR52 FR28 FR146 FR197 FR90 FRO6 FR51 FRO5 FRlll
S06:L S57:M-PI S10L S11:L S12L S13:T S14T S59M-PO S46:L-PO
S17:T S18M
FR46 FR154
none none
S19T S20L S21:L S24:T SMM-PO S65:T-PO S28M
FR58 FR55 FR104 FR57 FRO1 FRO2 FR160
S19T S20L S63L-PO S24T S64M-PO none none
TR44 TR120 TR68 TR29 TR08
S29M S30T S53M-PI S54L-PO
FR87 FR125 FR19 FR77
S29M S52:M-PO S53:M-PI S32L
TR58 TR88 TRll TR59
FR53 FR219
none none
*** ***
***
*** *** ***
***
***
*** *** ***
*** S33:M S34:L
***
TR114 TR05 TR90 TR119 TR43 TR91 TR42 TROl TR67
***
a Asterisks are used in both columns when an inventory control structure does not permit any acceptable composition control structures to be developed. The word *none* signifies a structure where either the feed or the product flow is fixed, and hence a throughput change cannot be accomplished.
show a partial preference for PI control, but generally single-end or P-only control of intermediates is preferred. Table XVII also provides support for proposition 4 (level tuning). Each of the self-consistent inventory control structures arranged along the primary path is best represented by a mixed or tightly tuned variant. This is not true for structures arranged along alternate paths or inconsistent structures. The latter generally seem to produce smaller IAE values when tuned loosely. This seems justified, as the loose tunings tend to mask the problems caused by inconsistency. 5.3. Unifying Observations. As a final step in evaluating the propositions, consider several alternative control structures for the CSTR/column. Beginning with the three potential throughput manipulators on the primary process path (Fo,F, and B ) , construct selfconsistent inventory control structures. Control the accumulator inventory using reflux. The results are inventory structures IS03, IS13, and IS29. Each of these can be transformed into three different composition control structures. Table XVIII shows the nine structures and lists the first appearance of each in the IAE rankings. Also provided is a composite ranking, formed by adding the two individual ranks. To begin with, note that the three structures with the worst ranking, for either input or composite, are those which control the bottoms composition only. Next,
IS03
Fo
IS13
F
IS29
B
F,R,B
SO3 s37 s55 Fo,R,B S15 s45 s59 Fo,R,F 531 s53 S67
36 4 30 40 5 13 32 19 20
22 3 13 33 6
58 7 43 73
1
14 57 30 39
25 11
19
11
compare the rankings for each set of controlled compositions. Only when a single composition is controlled is B the best choice for the throughput manipulator, and then only by a small margin. This confirms the arguments of proposition 2 that B is a poor choice of throughput manipulator. What if all of the propositions presented are applied? Two implementations of structures S45 and S59 result. These have good composite rankings, falling second and third in the Table XVIII rank sum, and provide more than a fifth of the top 20 implementations. The best composite ranking goes to an implementation of 537. This satisfies all of the propositions except that suggesting the use of an internal throughput manipulator. Hence, when guidelines for control design are derived from the propositions, the selection of an internal throughput manipulator will be less critical than application of the other rules-particularly that requiring self-consistency. When all of the propositions, excluding the recommendation of an internal throughput manipulator, are applied, four structures are produced: S37, S45, S55, and 559. Three of these are the best alternatives for this example; the fourth (S55) is only sixth of the nine considered. If all of the propositions are applied, the two structures which are produced-S45 and S59-are the second- and third-best alternatives. A key observation in interpreting the results is the role of the control structure in restricting the propagation of disturbances. The ideal structure appears to be one which combines control of the final product composition with control of a flow and/or composition of a transfer stream between the reactor and column. 6. Control Design Using the Tiered Framework
The tiered design framework provides a way for a control designer to structure the decisions made during the design procedure. An experienced designer will often find this structure to be more than adequate. Less experienced users might require additional help in making design choices. The tiered design framework addresses this desire by including a set of guidelines which add detail to the more general design tiers. No set of guidelines can possibly substitute for judgement or process knowledge, but some assistance can be provided. Guidelines for use within the tiered framework have been developed based on the observations of other designers and the results of the CSTR/column study. Additional guidelines have been proposed based on consideration of more examples, including an extractive distillation system (Grassi, 1991),a toluene hydrodealkylation plant (Douglas, 19881, and the Tennessee Eastman test problem (Downs and Vogel, 1990). Production Rate Control: (i) Identify the primary process path. It will begin with major feed streams and progress to the primary product. The path will not split or branch unless two or more equally
2704 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
important products are made. Streams connecting unit operations within the process will be referred to as “process internal streams”; streams entering or leaving the process as “process external streams”. (ii) Evaluate options for measuring and manipulating the production rate. Typically, this requires measurement of a flow or flows along the primary path; sometimes a more accurate measurement can be made by combining these with compositionmeasurements. Generally, streams which are product rich or feed streams which are substantially converted should be preferred. (iii) Consider stoichiometry and conversion. In many reacting systems, there will be components which are “limiting” on the reactions and others which are in excess. Limiting components are preferable for manipulating throughput, since their impact is typically more immediate. Knowledge of factors influencing conversionmay be useful in identifying nonflow throughput manipulators and the primary process path. (iv) List candidates for use as throughput manipulators (TPMs). There are two basic categories of TPMs. The majority are flows of material along the primary process path and are manipulated explicitly. The second category includes cases where the property being manipulated is a heat duty, etc., which affects conversion and/or product separation. These manipulators are usually implicitly controlled by adjusting a utility flow. For convenience, these two types of TPM will be referred to as “explicit” and “implicit” manipulators, respectively. It is useful to track several TPMs during the early stages of a control design, so all possibilities not invalidated during the design process are available for final evaluation. (v) Eliminate candidate TPMs which are “small”. The definition of small will reflect the desired turndown, since it must be possible to adjust the TPM enough to produce the required change in production rate. It is particularly important to consider the gain between the proposed TPM and the product flow when implicit TPMs are used. (vi) It is generally recommended that process internal flows be used as TPMs because they impede the propagation of disturbances through the system. The recommendation is based on evidence from the CSTR/column and anecdotal evidence from industrial practitioners. Inventory Controls: Inventory controls have a dual role. They must ensure that inflow equals outflow when the process is at steady state. Second, flows through the system must be adjustable to meet changes in product demand. (i) Identify those inventories which may require control. The number of inventories is not necessarily the same as the number of unit operations or vessels (a binary distillation column has two liquid and one vapor inventory). Inventories may be measured as liquid level, vapor pressure, or solid weight or level. (ii) Use proximity rules to identify the manipulators suitable for adjusting each inventory. Special consideration should be given to how strictly the proximity rules should be enforced. In particular, using distillation column feed flow to control column base level seems prone to cause some dynamic problems when used as part of an inventory control structure. (iii) The choice of a TPM will demarcate at least two subsystems of the process, one upstream and one downstream of the TPM. If a change in throughput is to result from a change in the TPM, at least one external stream on each end of each subsystem must be able to vary to transmit the change in TPM. Variation can be ensured
by setting the selected external streams on direct throughput control or on inventory control. (iv) Use a test of the “degrees of dynamic freedom” (Tyreus, 1992) to help determine how many inventories associated with each unit operation may be controlled. (v) Consideringeach inventory along the primary process path, construct a consistent chain of controls. These will radiate outward from the TPM. When freedom is insufficient to control all inventories within a unit operation, a choice of which to control must be made. Rules of thumb are useful in this decision. For example, if the liquid leaving a drum must be pumped, it is essential to ensure an adequate level in the drum to prevent cavitation, and so the liquid level should be selected as a controlled inventory. It is often adequate to control the pressure of the vapor in an entire section of the process by using a single manipulator at a single location and allowing the remaining vapor inventories to equilibrate or “float” on the pressure-controlled processing step. (vi) Once the inventory controls along the primary process path are completed, construct inventory controls for side chains. Work outward and direct disturbances away from the primary process path. (vii) Construct additional inventory control chains along any recycle paths. When working with recycle loops, inventory manipulators should be chosen to reduce or eliminate disturbance backpropagation via the recycle streams. This generally means manipulating inventories using flows which do not return disturbances to the primary path. (viii) If additional inlet or outlet flows remain uncontrolled, assign control loops to govern them. Often these are best satisfied by using the flow to control a composition or flow ratio or some other process specification. (ix) Check component entrance and exit points. All components required by the process must be able to enter the system on demand. Similarly, components produced or passing through must be able to leave. As the inventory control structure is completed, the designer should check that appropriate entrances and exits are available and supported by the control system. This check will often help decide how to control makeup and purge streams and supplementary feeds and producta. Exit points for trace Components are of particular importance in recycle systems. If not provided, these can accumulate in the recycle loop and cause system pressure or composition problems. Joshi and Douglas (1992)have recently suggested rules for including exit point considerations in the design of a process. During the inventory control structure design, it is not uncommon to discover that freedom limitations or other restrictions may invalidate a particular TPM choice and its corresponding inventory control structure. Similarly, product quality and other higher level tiers may require modification of a throughputlinventory structure by the addition of overrides or cascade controllers or by occasional rearrangement of an inventory control structure. 7. Conclusion
Design frameworks are a convenient way to structure the complicated sequence of decisions which must be made during the design of a plantwide regulatory control system. Specifically, a tiered framework based on a decomposition of the control system by task is suggested. Using this tiered framework offers several advantages. It is generally applicable to a variety of processes. It is readily adapted to make use of the designer’s individual experience or the particulars of corporate in-house design specifications.The
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2705 framework does not require a detailed mathematical model of the process and so can be used during the conceptual design stage before all design details of a process are fully known. The tiered control design framework provides an effective reference point for interpreting the results of a detailed simulation study of a CSTR/column system. Thirty-four inventory control structures were developed for the system. These were in turn transformed into 70 control structures. Controller type and tuning choices led to a total of 318 control structure implementations. The response of each implementation was studied for both a feed composition and a throughput change. The integral absolute error of the final product composition was compared for all implementations studied. The results of the study have been summarized in seven general propositions relating IAE performance to control structure. The best performing control structures were shown to be those which were self-consistent. Selfconsistency appears to be the single most important characteristic governing the impact of the inventory control structure on system performance. The results of the CSTR/column simulation study have been generalized to obtain a set of guidelines for the design of production rate and inventory control structures. These guidelines are used in conjunction with the tiered framework to provide more specific guidance for the first control design tier. The guidelines are generic and applicable to a variety of processes. A formal approach to plantwide control design also will be helpful to engineers seeking to design plants suitable for operation at several different production capacities. The CSTR/column study suggests this advantage by including a change in production rate among the inputs considered.
Nomenclature ALM = accumulator level manipulator B = column bottoms product flow rate BCM = column base composition manipulator BLM = column base level manipulator CMs = composition manipulators CSTR = continuous stirred tank reactor D = column distillate (recycle stream) flow rate FO = fresh feed flow rate F = reactor outlet (column feed) flow rate IAE = integral absolute error ISxx = inventory control structure identification number LMs = level manipulators OCM = column overhead composition manipulator PI = proportional integral P-only = proportional only R = column reflux flow rate RCM = reactor outlet composition manipulator RLM = reactor level manipulator Sxle = control structure identification number TCM = column overhead composition manipulator TPM = throughput manipulator
V = column vapor boilup flow rate = fresh feed composition xb = column bottoms composition Xd = column overhead composition xr = reactor outlet (column feed) composition leg
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* Abstract published in Advance ACS Abstracts, October 1, 1993.
