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Garcia, C. E.; Morari, M. Internal Model Control. 1. A Unifying Review and Some New Results. Ind. Eng. Chem. Process Des. Dec. 1982,21, 308-323. Garcia, C. E.; Morari, M. Internal Model Control. 3. Multivariable Control Law Computation and Tuning Guidelines. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 484-494. Li, S.; Lim, K. Y.; Fisher D. G. A State Space Formulation for Model Predictive Control. AIChE J . 1989, 35, 241-249. Marquis, P.; Broustail, J. P. SMOC, a bridge between State Space and Model Predictive Controllers: Application to the automation of a hydrotreating unit. In Model-Based Process ControlProceedings of the 1988 IFAC Workshop;McAvoy, T . J., Arkun, Y., Zafiriou, E., Eds.; Pergamon Press: Oxford, 1989; pp 37-46. Morari, M.; Doyle, J. A Unifying Framework for Control System Design Under Uncertainty and its Implications for Chemical Process Control. Chemical Process Control-CPC III; Morari, M., McAvoy, T. J., Eds.; Elsevier: New York, 1986; pp 5-52. Morari, M.; Zafiriou, E. Robust Process Control: Prentice-Hall: Englewood Cliffs, NJ, 1989. Navratil, J. P.; Lim, K. Y.; Fisher, D. G. Disturbance Feedback in Model Predictive Control Systems. In Model-Based Process Control-Proceedings of the 1988 IFAC Workshop; McAvoy, T. ,J., Arkun, Y., Zafiriou, E., Eds.; Pergamon Press: Oxford. 1989; pp 63-68. Prett, D. M.: Garcia, C. E. Fundamental Process Control; Butterworth: Stoneham, MA, 1988. Ricker, N.L. The Use of Quadratic Programming for Constrained Internal Model Control. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 925-936. Ricker, N. L.; Sim, T.; Cheng, C.-M. Predictive Control of a Multieffect Evaporation System. Proc. 1986 Am. Control Conf. ( S e attle) 1986, 1, 355-359. Ricker. N. L.: Subrahmanian, T.; Sim, T. Case Studies of ModelPredictive Control in Pulp and Paper Production. In Model-
Based Process Control-Proceedings of the 1988 IFAC Workshop; McAvoy, T. J., Arkun, Y., Zafiriou, E., Eds.; Pergamon Press: Oxford, 1989; pp 13-22. Richalet, J. A.; Rault, A.; Testud, J. D.; Papon, J. Model Predictive Heuristic Control: Applications to Industrial Processes. Automatica 1978, 14. 413-428. Rivera, D. E.; Skogestad, S.; Morari, M. Internal Model Control. 4. PID Controller Design. Ind. Eng. Chem. Process Des. Deu. 1986, 25, 252-265. Rouhani, R.; Mehra, R. K. Model Algorithmic Control (MAC); Basic Theoretical Properties. Automatica 1982, 18, 401-414. Skogestad, S.; Morari, M. Implications of Large RGA Elements on Control Performance. Ind. Eng. Chem. Res. 1987,26,2323-2330. Skogestad, S.; Morari, M. Understanding the Dynamic Behavior of Distillation Columns. Ind. Eng. Chem. Res. 1988a, 27, 1848-1862. Skogestad, S.; Morari, M. LV-Control of a High-Purity Distillation Column. C'hem. Eng. Sei. 198813, 43 ( l ) ,33-48. Subrahmanian, T. M.S. Thesis. University of Washington, Seattle, 1988. Svoronos, S. Disturbance Rejection Through Model Dependent Control. Proc. 1986 Am. Control Conf. (Seattle) 1986,2,664-668. Wellons, M. C.; Edgar, T. F. A Generalized Analytical Predictor for Process Control. Proc. 198.5 Am. Control Conf. (Boston) 1985, 2, 637-645. Yuan, P.; Seborg, D. E. Predictive Control Using an Observer for Load Estimation. Proc. 1986 Am. Control Conf. (Seattle) 1986, 2, 669-675. Zafiriou, E.; Morari, M. Setpoint Tracking vs. Disturbance Rejection for Stable and Unstable Processes. Proc. 1987 Am. Control Coni. (Minneapolis) 1987, 1 , 649-651. Received for reuiew December 28, 1988 Reuised manuscript received August 4, 1989 Accepted October 30, 1989
Expert Multivariable Control. 1. Structure and Design Methodology Vassilios K. Tzouanas, William L. Luyben,* Christos Georgakis, and Lyle H. Ungart Chemical Process Modeling a n d Control Center a n d D e p a r t m e n t of Chemical Engineering, Lehigh Cniuersity, 111 Research Drive. Bethlehem, Pennsylvania 28015
This is the first of a series of three papers that present the methodology and demonstrate the application of an approach to the design of control systems that overcome the fragility of many control structures when applied to multivariable processes. This methodology is called expert multivariable controller (EMC). The EMC determines and implements on-line the appropriate controller structure that should be used under normal and abnormal operating conditions (sensor failure, valve saturation, and process constraints). It is fundamentally a generalization of conventional override control to complex multivariable control systems. The implementation of EMC has been facilitated by using Artificial Intelligence and Expert Systems techniques. Part 1 presents the generic structure and design methodology. Part 2 demonstrates the application to linear and nonlinear binary distillation columns where the system is 4 X 4: two levels and two compositions. Part 3 illustrates the extension of the method to a higher order system, a 5 X 5 side-stream distillation column. Most early applications of process control dealt with single-input-single-output (SISO) processes that could be controlled by using linear single-loop control theory. Hardware limitations, economic cost, and the lack of adequate control theory precluded anything more complex than simple control schemes. Simple control schemes were usually adequate because of the use of large intermediate surge tanks between process units and little energy integration. In recent years, however, the economic need to operate industrial processes as close as possible to optimum
* Author t o whom correspondence should be addressed. Present address: Department of Chemical Engineering, University of Pennsylvania, Philadelphia, PA 1910.1.
0888-5885/90 / 2629-0382$02.50/0
specifications with minimum energy consumption while safety and environmental constraints are not violated has produced processes that are more complicated and multivariable. The extensive use of heat integration and material recycle has led to complex control configurations and difficult control problems. Simple control schemes are not always adequate for controlling processes when the requirements for disturbance rejection and set-point response are strict, the interactions between control loops are severe, and nonlinear behavior and time-varying characteristics are present. These complex plants are currently controlled by using either conventional multiloop SISO controllers (diagonal structure) or multivariable controllers (Garcia and Morari, 1982; Cutler, 1982). A number of complex control schemes C 1990 A m e r w a n Chemical Society
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economics, product specifications, and dynamic performance of the controlled process. Similar problems arise when one of the manipulated variables becomes saturated. In this case, control over one of the outputs is lost. In order to retain control of the most important controlled output variable, changes in the controller structure and controller tuning may be necessary. The importance of the valve saturation problem is illustrated by considering a binary distillation column. During normal operating conditions, control of both the distillate composition (xD) and the bottoms composition ( x g ) is achieved by manipulating the flow rates of reflux (R) and steam (S). If the reflux valve becomes wide open, perhaps because of a feed flow rate increase, control of XD would be lost. If the purity of the distillate product is more important than the purity of the bottoms, it may be desirable to modify the control structure in order to control x D : use steam S to control xD and let x g float. The distillate composition controller would probably have to be retuned. The difficulty of designing a control system that is capable of making the necessary changes in controller structure and tuning increases rapidly with increasing problem complexity. Picking the best control action to be taken under a particular set of process operating conditions is not an easy task when controlling high-order multivariable processes. This is true for any type of controller: diagonal or multivariable.
0bjective The purpose of this work was to develop a methodology for designing a controller than can guarantee safe, effective operation for multivariable processes under a wide range of abnormal conditions like sensor failure, valve saturation, and process constraints. The controller must be able to select manipulated and controlled variables according to desired priorities, make structural changes in controller configurations, select appropriate control algorithms, and tune controllers. The decision-making process must be 4 done on-line in real time. The design of such a controller requires a large amount of knowledge about the controlled process (process structure, process equipment, control objectives and priorities among them, process economics, process dynamics, and process constraints) and control theory (control algorithms, loop selection methods, and tuning methods) as well as experience in how to use all this information. The process information and the control information are both quantitative and qualitative in nature. Therefore, the design of the EMC controller is facilitated by using Artificial Intelligence (AI) and Expert System (ES) techniques (Tzouanas et al., 1988).
Previous Applications of Expert Systems in Process Control Most of the work on closed-loop control using expert systems has been in the adaptive control area (Astrom and Anton, 1984) and has dealt with SISO systems that are nonlinear and time variant. Astrom’s expert system does not account for sensor failure, valve saturation, or process constraints. It assumes normal operating conditions. The work on EMC reported in this series of papers is applicable to MIMO processes and accounts for normal as well as abnormal operating conditions. The EMC does not use adaptive control methods in the classical sense: updating model parameters. The EMC is adaptive in the sense that it restructures control loops. Expert systems have been developed for the off-line design of control structures for distillation columns under
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normal operating conditions (Shinskey, 1986; Umeda and Niida, 1986; Birky et al., 1988). In addition to designing the control loop for normal operation, the EMC designs new control loops for a number of process abnormalities and implements the newly designed loops along with any necessary changes in control algorithms and controller tuning. Structure of EMC The fundamental components of the EMC are shown in Figure 2. The EMC observes the state of the process by accepting data from sensors. By use of this information along with the knowledge that is contained in its knowledge base, the EMC decides what actions must be taken and applied to the process because of the observed process state. Since the EMC is an expert system, it consists of a knowledge base and an inference mechanism. The knowledge base is separated into two parts: a processrelated knowledge base and a control-related knowledge base. The process-related knowledge base has information about the controlled process and is process dependent. The control-related knowledge base has information about process control. Much of this control theory is process independent, but some parts are process specific. The inference mechanism, which is the driving force of any expert system, is used by the EMC to properly manipulate any information in its knowledge base and take actions. The operator (or control engineer) must provide information about the process and the control objectives. Figure 3 shows how the EMC is integrated into the closed-loop control system of a process. The EMC acts like a supervisory control system. It accepts information from the controlled process (sensor readings). It uses this information in order to redesign the control loops: select controlled variables, select manipulated variables, and determine controller structure, algorithms, and tuning. The structure of EMC is in some ways similar to that of an adaptive control system. The fundamental difference is in the way that process information is used. In classical adaptive control systems, this information is used for process model updating, and a set of new tuning parameters is fed to a controller with fixed structure but variable tuning parameters. In the EMC context, information from the process is used for control system restructuring in response to process abnormalities. So, the dashed line from the EMC block to the controller block in Figure 3
contains vectors of qualitative as well as quantitative information: controller structure, controller types, and tuning constants. The EMC applies the proper control actions to the controlled process by performing a number of tasks in real time within a control cycle: data acquisition, diagnosis, decision making, and implementation. Data acquisition is concerned with obtaining information from the process that is sufficient to describe the process state. Readings from all sensors are obtained: flows, temperatures, levels, pressures, compositions, etc. The diagnosis step uses the process information to detect process abnormalities. Sensor failure, valve saturation, and process constraints are the abnormalities considered in the design of the EMC. Detection of such abnormalities is an area of active research both in academia and industry. For the purposes of the present work, we assumed that detection techniques have been developed and are available for use by the EMC. The decision-making step is the central problem in EMC that this work addresses. It is concerned with determining the appropriate actions needed to maintain the process in operation. For a given set of process abnormalities, the objective is to keep the process at the highest possible level of operation between fully automatic control and manual control. This usually requires reconfiguration of control loops. Figure 4 shows the reasoning paths of the EMC. Initially, the EMC must determine the control structure to be used under normal operating conditions (when no sensor failure, valve saturation, or process constraints are present). We call this structure the normal structure (NS). The EMC must determine what variables should be controlled, what manipulated variables should be used, and what controller to apply (both structure and tuning). The procedures for making these decisions will be discussed in more detail later in this paper. Once the normal structure has been determined, it is used if no process abnormalities occur. However, when abnormal operating conditions are encountered, the EMC has to determine how the controller structure must be revised. We separate process abnormalities into two types: (I) instrumentation abnormalities (sensor failure and valve saturation), these lead to the abnormal structure (AS); ( 2 ) process constraints, these lead to the constrained structure (CS). The constrained process variables must be controlled so that they do not violate certain limits. This usually means that we have to give up the control of some other variables. The implementation step is the application of the previously determined actions to the controlled process with all the appropriate considerations of bumpless transfer, reset windup, etc.
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A. Determination of Normal Structure. Figure 5 gives a logic diagram for deciding the normal structure. The tasks to be performed here are to determine (1)the variables to control, ( 2 ) the variables to manipulate, (3) the structure of the control system (diagonal or multivariable), (4) the types of controllers (for example, P, PI, or PID if diagonal) and (5) the controller tuning parameters (gains, reset times, and derivative times). When a diagonal controller structure is used, a variable pairing step is also required. When a multivariable controller structure is used, the variable pairing problem is not present because each of the controlled variables is used to determine the values for all of the manipulated variables. The current implementation of EMC uses the following procedures to perform these tasks. They w ill be illustrated in more detail in distillation applications in parts 2 and 3 of this paper. (1) Selection of Controlled Variables. The operator specifies the variables to be controlled and the priorities among them. The EMC will attempt to control as many of the high-priority controlled variables as possible, subject to the availability of suitable manipulated variables. (2) Selection of Manipulated Variables. The operator supplies a list of the available manipulated variables. Then the EMC selects the best group by using either heuristics (shallow knowledge) or control theory (deep knowledge). An example of heuristics is that reflux flow rate is used to control the reflux drum level in a high-reflux ratio distillation column. An example of control theory is the use of the Morari resiliency index (the minimum singular value of the open-loop plant-transfer function matrix) to find the best choice of manipulated variables (Yu and Luyben, 1986). (3) Controller Structure. The operator specifies the desired highest level structure: diagonal or multivariable. The EMC will attempt to implement the structure specified, but if abnormal conditions prevent it from doing so, it will implement the highest possible structure.
For example, if multivariable control is desired and if the process is 3 X 3, under normal conditions a 3 X 3 multivariable controller will be used. However, if a valve saturates or a sensor fails, the EMC will reduce the controller structure to a 2 X 2 multivariable controller (or perhaps a 2 x 2 diagonal controller structure if a multivariable controller cannot be implemented for some process or control reason). (4) Controller Types. For the multivariable structures, a number of types of multivariable controllers can be used. The appropriate algorithms and design procedures must be included in the multivariable controller design box shown in Figure 5 . Internal model control is used to demonstrate the application of multivariable controllers to a binary distillation column in part 2. For diagonal control structures, the choice of any procedure for pairing and tuning can be specified by the user. The necessary procedures must be inserted in the variable pairing and controller design box shown in Figure 5 . In the distillation applications presented in parts 2 and 3 of this paper, heuristics are used to select the types of controllers used in the composition loops (PI) and in the level loops (averaging proportional only when level changes a product flow but tight PI when level is controlled by reflux or heat input). (5) Controller Tuning. Tuning for the multivariable controllers is part of the design procedure. Tuning and variable pairing for the diagonal structure was implemented in the current version of EMC using the LACEY procedure (Yu and Luyben, 1986). The steps in this procedure are (a) use the Niederlinski index to eliminate unworkable pairings, (b) determine the controller tuning constants by detuning all diagonal controllers from the individual Ziegler-Nichols settings using the closeness of the multivariable Nyquist plot to the origin, and (c) select the pairing that provides the best load rejection. One important piece of information that the operator must provide the EMC is the importance of different sensors on the operation of a process. Several categories of sensors must be considered: (1)Essential sensors measure variables that are necessary to the operability of the process. The proper functioning of such a sensor is necessary for the safe operation of a process on either a short-term or long-term basis. Failure of such a sensor requires that immediate action be taken or that the operator be notified of a situation that cannot be tolerated for very long. For example, level sensors are usually essential sensors. (2) Nonessential sensors measure variables that are not critical to the safe operation of the process. In many cases, they may measure product quality. Failure of such a sensor does not mean that the process cannot continue to operate. For example, the composition sensors in a distillation column fall into this category. If these sensors fail, the column can continue to operate, but the purities of one or more of its products will not be maintained. (3) Replaceable sensors can be replaced by alternative measurements. An example is substituting a tray temperature for a composition analyzer in distillation. Another item of knowledge that the operator must provide the EMC is the effect of saturation of a control valve. Different manipulated variables have different effects on the controllability of a process, primarily from their impact on the degrees of freedom. The control valves can be 1-deg valves (saturation implies loss of control for only one controlled variable) or 2-deg valves (saturation implies loss of control for two controlled variables). For example, the distillate valve in a distillation column is a
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2-deg valve, while the steam valve is a 1-deg valve. This is discussed more fully in part 2 . The effect of a manipulted variable (valve) on a particular controlled variable (sensor) must also be known. A valve may have a direct or an indirect effect on a controlled variable. For example, in a distillation column, the reflux valve has a direct effect on the reflux-drum level and an indirect effect on the bottoms level. From the discussion above, it is apparent that the EMC determines the NS using process-dependent as well as process-independent knowledge. By using shallow knowledge first, the use of deep, computationally intensive control knowledge is minimized. There is no claim that the solution obtained by using shallow knowledge is necessarily the optimum. It is a characteristic of expert systems that they provide not necessarily an optimum solution to the problem but an acceptable one. Use of shallow knowledge leads to higher efficiency from a running time point of view. However, the use of deep knowledge increases the applicability of the EMC to a number of processes. The basic structure of the design methodology that the EMC follows to determine the NS is independent of a specific process and independent of specific control knowledge. The control engineer is at liberty to incorporate any type of process or control knowledge in the appropriate boxes in Figure 5. B. Determination of Abnormal Structure. When valves saturate, sensors fail, or process constraints are encountered, the EMC must decide what new control structure to implement, how to reconfigure the control loops, how to change the type of controllers, and what new tuning constants should be used. The design of such a system is complex because any combination of process abnormalities must be handled. In order to meet these requirements, a three-dimensional design problem must be solved, as illustrated in Figure 6. The three dimensions of the cube denote different kinds of abnormalities. The S axis represents sensor failure, the V axis valve saturation, and the C axis process constraints. The EMC must account for any operating point ( S , V , C ) within this cube. The size of the cube, which indicates the magnitude arid the complexity of the design problem, depends on the order of the controlled process and the number of the process constraints. If we want to account for five sensors, five valves, and two process constraints, the EMC must be able to handle 100 operating points that result from any combination of failed sensors, saturated valves, and process constraints.
Of course, the number of combinations increases drastically if we consider which particular sensors have failed or which valves are saturated. For example, in a distillation column, one could have two failed sensors. They could both be composition sensors, or they could both be level sensors, or one could be a level sensor and the other a composition sensor. In order to solve this three-dimensional design problem, we decompose it into two subproblems. First, instrumentation abnormalities (sensor failure and valve saturation) are considered. This is schematically shown in Figure 7 where the sensor-valve plane is considered. For a given set of failed sensors and saturated valves, the EMC determines what the control structure should be. This is the abnormal structure (AS). This structure can lie anywhere between fully automatic and fully manual control. The number of the intermediate structures, between fully automatic and manual control, is determined by the order of the controlled process and the type of failure. The second subproblem of handling process constraints will be discussed in the following section. There are a number of tasks that must be completed in order to determine the AS. Basically, we want to reconfigure the control loops, change the type of controllers, and retune them. This sounds almost the same as the tasks involved in the determination of the NS. However, there is the additional task of determining the level of operation. By this we mean that we must find the highest possible structure at which control of the process can be maintained when some sensors have failed or some valves are saturated. One way to determine the level of operation is to find solutions to each of the operating points represented by the squares in Figure 7 and to include all of these solutions in the data base of the EMC. However, a very large number of cases would have to be evaluated and stored since we must know which particular sensors have failed and which particular valves have saturated. The EMC methodology determines the level of operation by developing a set of rules. To generate these rules, a number of process abnormaiities are examined in order to determine what actions must be taken under these particular conditions. These abnormalities correspond to the points ( S , V )of the sensor -valve plane. It is obvious that a particular point (S,V ) is not unique since it can represent any of the process sensors (SI,S,, ..., S,) and any of the control valves (V,. V,, etc.). For a given set of abnormalities, a number of actions are determined. These actions are then expressed in an abstract form in the EMC’s data base using rules. Since the rules are based on properties assigned to sensors
Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990 387 and valves, no enumeration of all operating points is required. Examples of rules are
IF any essential sensor has failed THEN the level of operation is manual control IF one nonessential, nonreplaceable sensor has failed T H E N the level of operation is reduced to one-product composition control How this methodology of determining the rules is applied to distillation process control along with a more detailed set of rules needed for the determination of the level of operation are presented in parts 2 and 3. The first rule given above is based on the need to take some fairly prompt action when an essential sensor fails because of operability and safety considerations. For example, in the distillation process, level sensors are considered essential. The operator must take some action if a base level or reflux-drum level sensor fails. Several alternative actions could be taken, but for purposes of illustration, we have chosen the most simple, Le., put all loops on manual. In a specific process application, it may be more appropriate to take other actions. For example, in a chemical reactor, the failure of a temperature sensor would normally require immediate shutdown of the system to prevent a temperature runaway. From an execution point of view, the different rules are grouped according to the level of operation they lead to. Groups of rules that lead to the most elementary levels of operation, for example, manual control, have the highest priority of execution. This is done so that safe operation of the process is guaranteed before quality control is attempted. Once a rule from a particular group fires, this completes the determination of the level of operation, and no rules in groups of lower priority have to be checked for execution. Once the level of operation has been determined, the remaining tasks are performed in the same way as in the determination of the NS. Manipulated variables are selected by using heuristics or the Morari resiliency index. Controller structure and tuning is determined by using either a multivariable controller or a diagonal controller. C. Determination of Constrained Structure. If process constraints are detected, the control system must be modified. Instrumentation abnormalities are considered before process constraints because instrumentation abnormalities can lead to manual control. If the level of operation is manual control, the EMC should not and cannot deal with process constraints. According to the EMC methodology, the previously implemented control structure (normal or abnormal) is modified in such a way that process constraints are not violated. For example, if a maximum pressure-drop constraint is detected (to prevent flooding in a distillation column), the reboiler steam valve would be used to control the pressure drop at its limit. The controlled variable that had been controlled by the steam valve would no longer be controlled. More detailed examples are presented in parts 2 and 3. Knowledge Representation and Reasoning The following section presents a brief description of some of the AI techniques used in the EMC implementation. From the above discussion of the general structure of the EMC, it should be clear that different types of information must be contained in its knowledge base so that the normal, abnormal, and constrained structures can be determined. Two types of information must be used: process information and control information. Both types
have process-specific as well as generic components. Both types contain both shallow (heuristic) and deep (algorithmic or theoretical) knowledge. Examples of processspecific shallow knowledge include normal operating conditions, control objectives and priorities, available measurements, available manipulated variables, and simple constraints. Examples of process-specific deep knowledge include a specific transfer function model, complex operating and safety constraints, physical properties, and thermodynamic data. Examples of generic deep knowledge include multivariable controller design procedures, diagonal controller pairing and tuning methods, and rigorous steady-state and dynamic models of a generic process. Normal operating conditions are useful in the selection of the normal or the abnormal structures. For example, the information that the column has a high reflux ratio can be used to eliminate any control structure that uses reflux to control compositions from the list of candidates for the normal structure. Knowledge about the priorities among the controlled variables is necessary during the selection of structures. Knowledge about transfer function models and knowledge about rigorous dynamic models of the process are useful in making certain controller design decisions. The EMC can use simple rules in order to eliminate candidate normal or abnormal structures. An example is the rule
IF the phase of the side stream is vapor THEN any control structure that involves the side stream to control the bottoms composition or base level cannot be selected Despite the fact that this rule is referred to as part of the shallow control knowledge, it is generic enough to be applicable to any distillation process (with side stream) and control structure. A. Knowledge Representation. All the previous types of information must be represented in the EMC’s knowledge base in an organized manner so that it is easy to access and apply. Knowledge has been defined as a set of syntactic and semantic conventions that make it possible to describe things. The syntax of a representation specifies a set of rules for combining symbols and arrangements of symbols to form expressions in the representation language. The semantics of a representation specify how expressions so constructed should be interpreted. In the field of expert systems, knowledge representation implies some systematic way of codifying what is known about a domain (Jackson, 1986). Expert systems designers have favored the use of rules and frames in representing knowledge. In representing knowledge in the EMC’s knowledge base, the following techniques have been used: (1) Facts. Facts are based on the classical object-attribute-value (0-A-V) formalism for representing knowledge. Facts can be static or dynamic. For instance, the fact that the design steady-state feed flow rate to the column is 10000 kg/h is static in nature. In contrast, the fact that the name of the current control structure is one-end composition control is dynamic because it changes in response to the operating conditions. The previous facts when represented in the EMC knowledge base using the ART (automated reasoning tool) formalism are (deffacts operating-conditions “Some operating conditions” (feed-flow rate 10000)) (deffacts current-state “Current control structure” (current-control-structure one-end-composition))
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Although facts can be used to describe information in a system’s data base, they are not the best way, particularly when the same information is applicable to similar entities. (2) Frames. Frames are a way of grouping information in terms of a record of “slots” and “fillers” (Minsky, 1975). A frame is a data structure that represents an entity type. A frame consists of a collection of named “slots”. Each slot can be filled by values. When the slots of a frame are filled, the frame is said to be “instantiated” and then represents a particular entity of the type represented by the unfilled frame. For example, the frame sensor-1 is an instantiation of the generic frame sensor. (a) Sensor-1: (defschema sensor-1 “Instantiated frame of sensor-1” (instance-.of sensor) (type essential) (replaceable n) (measured _variable reflux-drum-level)) (b) Generic Frame Sensor (defschema sensor “Generic frame of a sensor” (measured__variable) (type) (replaceable) (failure-status n ) ) Through the “inheritance” mechanism, all of the properties of a generic frame are inherited by its instances. In the previous example, the instantiated frame sensor-1 inherits the named “generic value” or “generic property” (failure-status n ) from the generic frame sensor. But this is not the only thing inherited by a member of a class of objects from the generic object of the class. It inherits all the rules that are applicable to the entire class of objects. For example, the rule given below is applicable to all of the sensors that are essential. IF an essential sensor has failed THEN the level of operation is manual control In summary, frames are used to represent common information about similar objects such as control configurations, control valves, sensors, and controllers. By identifying similarities among the different entities, procedures and rules can be written that are applicable to a class of them. This significantly reduces the programming effort, but most importantly, it increases the generality of the system. This is an advantage of using AI techniques. (3) Rules. Rules are mainly used to encode associations between patterns of data presented to the system and actions that the system should perform as a consequence. In the expert systems literature, rules are also called “condition-action rules”. The general structure of a rule is IF (condition) T H E N (action) The conditions are usually 0-A-V triples. A typical rule in the knowledge base of the EMC could be IF the top level sensor has failed THEN the level of operation is manual control This rule implies that, whenever the top level sensor fails, the EMC must use manual control. Although the action dictated by this rule is correct, this rule is not generic enough since it only applies to the top level sensor. The following rule, which does not denote a particular sensor, can be applied to all sensors that are essential. IF any essential sensor has failed
THEN the level of operation is manual control The rules represented in the EMC’s knowledge base fall into several categories: control rules, process specific rules, and procedural rules. Control rules are used to describe the strong and weak points of different control techniques. Examples are IF a 2-deg valve is used to control a level THEN the type of the controller should be P IF a control configuration has a negative RGA index THEN this configuration cannot be selected Process specific rules are used to describe the expert’s knowledge about the controlled process. An example is IF the reflux ratio is greater than five THEN do not use a control configuration that manipulates reflux in order to control a composition Procedural rules are used to activate numerical techniques in order to calculate the value of a variable i p it is not known. An example is IF the RGA of a control configuration is unknown and the process gains of the configuration are known THEN calculate the RGA by using the RGA function (4) Functions. Functions are used to describe algorithmic knowledge. For instance, the RGA is described by a function. Functions are executed by procedural rules in the data base of the EMC. Information described by a function is generic and applicable to different processes. B. Reasoning within EMC. The data contained in the data base of the EMC are used by the “interpreter” in order to “drive” the rules in the sense that the presence or absence of data elements in the data base will trigger some rules by satisfying their activation patterns. The interpreter can be described in terms of what is known as the “recognize-act cycle“ consisting of the following steps: (1) Evaluate the conditions in all rules with respect to the current data base state, thereby identifying a set of applicable rules. ( 2 ) Choose one of the applicable rules and execute its action part. (3) Return to the beginning of the cycle if the goal is not achieved. This procedure of “firing” rules is c d e d a “data-driven”, “forward chaining”, or “antecedent reasoning“ approach. The EMC is based on a set of data, and it uses rules to find new facts. The EMC selects control structures by performing the tasks of determining the level of operation, selecting controlled and manipulated variables, and selecting controller structures, types, and tuning. These tasks are usually performed in a sequential manner. This allows us to determine groups of rules dedicated to specific tasks. The different groups of rules are executed according to priorities determined by the task they perform. Within a given group, rules that represent shallow knowledge are executed first without any priorities among them. Rules that call for the use of deep knowledge are executed next.
Conclusions Part 1 has discussed the general structure of the EMC. It handles multivariable processes. It accounts for normal as well as abnormal operating conditions. In response to different operating conditions, the EMC determines the level of process operation, selects the controlled and manipulated variables, determines the proper types of controllers, pairs variables in the diagonal structure, and calculates controller tuning parameters. The on-line determination and implementation of the abnormal and constrained structures are unique contributions of the present work.
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Facts, frames, rules, and functions have been used to represent knowledge. Identification of common information between similar objects allows the writing of rules that are applicable to many objects. This significantly reduces the programming effort and increases the generality of the resulting system by allowing reasoning at a higher level of abstraction. From a reasoning point of view, the EMC is a data-driven system.
Literature Cited Astrom, K. J.; Anton, J . J . Expert Control. Tech. Report TERT7271; Lund Institute of Technology: Lund, Sweden, 1984. Astrom, K. J.; Wittenmark, B. Adaptive Control; Addison-Wesley: Reading, MA, 1989. Birky, G. J.; McAvoy, T. J.; Modarres, M. An Expert System for Distillation Control Design. Comput. Chem. Eng. 1988, 12 (9/10), 1045-1063. Buckley, P. S.; Luyben, W. L.; Shunta, J. P. Design of Distillation Column Control Systems; ISA: New York, 1985. Cutler, C. R. Dynamic Matrix Control-An Optimal Multivariable Control Algorithm with Constraints. Ph.D. Dissertation, University of Houston, Houston, T X , 1982. Edmunds, J. M. Digital Adaptive Pole-Shifting Regulators. Ph.D. Dissertation, Control Systems Centre, UMIST, Manchester, England, 1976. Elaahi, A.; Luyben, W. L. Control of an Energy-Conservative Com-
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plex Configuration of Distillation Columns for Four-Component Separations. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 368-376. Garcia, C. E.; Morari, M. Internal Model Control-A Unifying Review and Some New Results. Ind. Eng. Chem. Process Des. Deu. 1982, 21, 308-323. Jackson, P. Introduction to Expert Systems; Addison-Wesley: Reading, MA, 1986. Koivo, H. N. A Multivariable Self-Tuning Controller. Automatica 1980, 16, 351-366. Minsky, M. A Framework for Representing Knowledge. In The Psychology of Computer Vision; Winston, P. H., Ed.; Wiley: New York, 1975. Shinskey, F. G. An Expert System for the Design of Distillation Columns. In Chemical Process Control-CPC III; Morari, M., McAvoy, T. J., Eds.; Wiley: New York, 1986. Tzouanas, V. K.; Georgakis, C.; Luyben, W. L.; Ungar, L. H. Expert Multivariable Control. Comput. Chem. Eng. 1988, 12, (9/10), 1065-1074. Umeda, T.; Niida, K. Process Control System Synthesis by an Expert System. Control Theory Adu. Technol. 1986, 2, 385-398. Yu, C. C.; Luyben, W. L. Design of Multiloop SISO Controllers in Multivariable Processes. Znd. Eng. Chem. Process Des. Deu. 1986, 25, 498-503. Received for review M a y 8, 1989 Revised manuscript received October 10, 1989 Accepted October 27, 1989
Expert Multivariable Control. 2. Application of EMC to Two-Product Distillation Columns Vassilios K. Tzouanas, William L. Luyben,* Christos Georgakis, and Lyle H. Ungart Chemical Process Modeling and Control Center a n d D e p a r t m e n t of Chemical Engineering, Lehigh University, 111 Research Drive, Bethlehem, Pennsylvania 18015
In part 2, the expert multivariable controller (EMC) is applied to two-product distillation columns. Details of the design of the controller and computer-simulation studies of its effectiveness are presented. Two columns are studied: a linear transfer function model and a rigorous nonlinear model. Results for both diagonal controller structures and multivariable controller structures (IMC) are presented. An operational control system should be able to handle problems like sensor failure, valve saturation, and process constraints. These problems appear both in single-input-single-output (SISO) as well as multiinput-multioutput (MIMO) processes. However, it is more difficult to handle such problems in the MIMO case because of the very large number of different actions that can be taken and the interaction effects among the control loops. The need for having a control system that is capable of making the necessary structural changes in the existing control configuration increases rapidly with increasing problem complexity. The conventional approach to handling problems like sensor failure, valve saturation and process constraints is to use override control systems. The usual objective is to provide protective controls that permit the process to operate close to constraints without exceeding them. Overrides can be designed to provide gradual corrective action. Although efficient for simple systems, override control systems become quite complex for high-order
* Author to whom correspondence
should b e addressed. address: Department of Chemical Engineering, University of Pennsylvania, Philadelphia, P A 19104. t Present
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multivariable systems. Override control systems can be devised that can choose among different alternative control structures, but design of new control loops, selection of new manipulated and controlled variables, accounting for priorities among controlled variables, and retuning to meet dynamic performance specifications can become very complex. In part 1, the general structure of the EMC was discussed. As pointed out, the structure of the EMC is independent of the controlled process and of a particular control technique. Obviously, in order to make the EMC work for a particular process, the appropriate “boxes” must be filled in. These boxes include both process knowledge and control knowledge that the user wishes to employ. In this paper, we will illustrate the application of the EMC to a specific process: a two-product distillation column. In the distillation process, there are a number of variables that must be controlled in order to guarantee safe and effective operation. For safety and operability reasons, the reflux-drum level and the bottoms level must be controlled. Therefore, the level sensors will be essential sensors. From a product-quality point of view, the distillate composition and bottoms composition should be controlled. However, the column can be operated with one 0 1990 American Chemical Society
