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Synthesis of control systems for chemical plants
Pergamon
Computers chem. Engng Vol. 20, Suppl., pp. $999-SI004,1996 Copyright © 1996 Elsevier Science Ltd S0098-1354(96)00174-3 Printed in Great Britain. All rights reserved 0098-1354/96 $15.00+0.00
SYNTHESIS OF CONTROL SYSTEMS FOR CHEMICAL PLANTS Christine S. Ng and George Stephanopoulos Laboratory for Intelligent Systems in Process Engineering, Dept. of Chemical Engineering Massachusetts Institute of Technology, Cambridge, MA 02139
Abstract - Synthesis of plant-wide control structures involves identifying control objectives that are consistent with the overall production goals and formulating control strategies in a multivariate environment. This is a complex task. A hierarchical framework is proposed in which the plant is vertically decomposed into a set of representations of different degrees of abstraction. Starting from the input-output level, we develop a control structure for the overall plant. Then, we move onto the next level where the model, the control objectives and the control strategies are being refined. This procedure is repeated until all levels of the plant have been analyzed. The hierarchy of control strategies can be integrated to form a multi-horizon control system. In this paper, the key conceptual steps of the methodology are being demonstrated.
INTRODUCTION Operation of a chemical plant is a multifaceted task. First, ideally, the plant should be steered to track the product demands driven by market forces at the minimum operating cost. Second, the plant should also be maintained at the desired steady-state in the presence of continuously varying external influences, like changes in ambient temperature or compositions of feed streams. In addition to the above "operational" objectives, the plant must always be maintained within the safe operating region and must not violate the regulations imposed by the government. Some of these objectives are explicitly related to specific process variables in the plant, while some are only implicitly defined by the overall process. The accomplishment of all these objectives falls within the domain of tasks of an automated plant-wide control system. The job of the control system designer is to identify specific controlled variables in the plant, formulate control strategies using the available manipulated variables and derive appropriate control laws. The current direction of research in this area (Banerjee and Arkun, 1995; Lyman and Georgakis, 1995; McAvoy and Ye, 1994) recognizes that the once popular unit-based design approach (Umeda et al., 1978) does not provide design viewpoints which can capture the broad range of objectives that are involved in the operation of the plant and so a plant-wide viewpoint is being advocated. We believe that the perspective of the plant can be further enhanced by developing control strategies using multiple viewpoints via hierarchical decomposition of the process into representations of various degrees of abstraction: an input-output model, a series of generalized reaction-separation systems and a detailed representation (Morari and Stephanopoulos, 1980; Ng and Stephanopoulos, 1994; Ponton and Laing, 1993). The use of a hierarchy of representations reduces the complexity of the problem by allowing the designer to separately address process goals which are significant in various ranges of time-horizon. The objective of this paper is to illustrate how a plant-wide control system can be synthesized within the hierarchical framework. In the next section, we will give an overview of the proposed design framework, which will be followed by a demonstration of the key conceptual steps of the methodology on the hydrodealkylation of toluene (HDA) plant. METHODOLOGY OVERVIEW Figure 1 gives a conceptual description of our methodology. In the hierarchical framework, we begin the synthesis with a simple representation of the process, like the input-output plant. This model is a unique viewpoint of the overall purpose of the plant, that is, to transform the available feed streams to the desired products with the available resources of utilities. The input-output plant represents the longest time-scaie of operation. Based on the overall production goals, we identify control objectives which are relevant for this level of the design and develop a control structure for the input-output plant. Then, we move down one level of $999
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European Symposiumon Computer Aided Process Engineering---6.Part B
the hierarchy and refine our model into one which describes a shorter time-horizon of operation. Control objectives and constraints from the previous level are propagated to the new model. In a representation with added details, we can identify refined control objectives for the plant and develop a control strategy that is suitable for a shorter time-horizon of operation. This process is repeated until we reach the most detailed level of representation which models the shortest time-horizon of operation in the plant. The set of plant abstractions form a hierarchy of modeling levels. Each of the control strategies that we develop is suitable for a particular range of time-scale of operation and thus, together, they form a hierarchy of control strategies for different time-scales. This hierarchy of control strategies can be judiciously integrated to form a multi-horizon control system for the complex plant.
y
OVERALLPRODUCTIONGOALS
M~e-~, Hydrogen
7
3
r q m i i
CONTROLSTRATEGIES
1
I_..
T
CONTROLSYSTEM R~'~leT d t ~
Figure 1. Synthesis of Control Structures for Complete Plants
Figure 2. Rowsheet of the Hydrodealkylation of Toluene Plant
CASE STUDY: HYDRODEALKYLATION OF TOLUENE PLANT The HDA plant produces benzene from the hydrodealkylation of toluene (Douglas, 1998). A process flowsheet is given in Figure 2. The basic reactions are : toluene(T) + hydrogen(H) ---> benzene(B) + methane(M) [R1] 2(benzene) --> diphenyl(D) + hydrogen [R2] With the given flowsheet of the process, the overall material and energy balances, the overall production objectives of the plant, and some idea about the type of disturbances that are expected for the plant, a control structure can by synthesized through the methodology described in the subsequent sections of this paper.
Preliminary Analysis To begin, we examine the characteristics of the process. Step 1: Identify overall production objectives, process constraints and sources of external disturbances The goal of the operation is to produce benzene at 265 lbmol/hr with 0.9997 purity. It is also expected that there will be variations of temperatures of coolants, temperatures and pressures of toluene and hydrogen feed, pressures of steam lines and purity of hydrogen in the make-up stream. The only operational/safety constraints are the following (a) the temperatures at the inlet, outlet and interior of the reactor must not exceed 1300°F; (b) the hydrogen/toluene ratio must be at least 5:1 at the inlet of the reactor to prevent coking. It is also desired to minimize the operating cost of the process. Step 2: Examine the open-loop stability of the process Plants which contain unstable dynamics are generally harder to control. Without the implementation of a sufficient process control strategy on an open-loop unstable plant, the temperature or pressure of a part of the plant might build up and this might eventually cause violations of the operational and safety limits and lead to a plant runaway. Instability in a chemical process plant is typically caused by either (1) the presence of an inherently unstable unit-operation, like a continuous-stirred tank reactor being operated at an unstable operating point or (2) the circumstantial interconnections of the plant through the material recycle loops or
European Symposium on Computer Aided Process Engineering--6. Part B
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heat-integration which generate positive feedback in the system (Morud and Skogestad, 1994).These are the items in the plant we need to examine. In the HDA plant, the distillation columns, coolers, heaters and compressor are all inherently stable unitoperations. The reactions occur in an adiabatic tubular reactor. As long as there is sufficient coolant to quench the effluent, the process should also be stable. Local numerical sensitivity analysis shows that the material recycle loops in the HDA plant are stable. Step changes of the flows of toluene and hydrogen produce step changes in the amounts of the various materials in the output streams (Ng, 1995). The energy in the HDA plant is partially integrated. A qualitative simulation of the heat loop in the plant shows that the heat integration system in the HDA plant creates a positive feedback loop in the system and energy in the system would accumulate if there is a step increase in the temperature of the feed streams (Ng, 1995). Thus, somewhere in this loop, we must select a manipulated variable to control the inventory of energy in the system. We will assign fuel to control the temperature of the feed stream to the reactor. The above analyses can be and have been formalized through systematic procedures, which use qualitative propagation of causes through a cause-and-effect diagram describing the behavior of a plant (Ng, 1995). Phase I: Long-horizon Analysis With that understanding of the process in mind, we proceed to develop a hierarchy of control structures for the plant. In the first phase of the design, we focus on the aspects of the plant which are caused by long-term changes in the process.
Step 3: Perform overall system analysis Figure 3 displays the input-output representation of the system which uniquely represents the overall process. Fuel , steam
1 2
HDA Product By-product
Figure 3. lnpubOutput representation of the HDA plant
In the long-horizon, at steady-state, this model is described by a set of independent material and energy balances. In general, each abstract block can be defined by one energy balance (EB) and a number of material balances (MBs). The number of material balances required is given by: no. of independent material balances = no. of components involved in the reactions - no of independent reactions + no. of inert components in the system [1] For the HDA plant, writing one energy balance and material balances for toluene, hydrogen and methane will completely define the input-output block. The material balance for toluene (MB-T) is given by : F2X2,T = FsXs,a + F3X3,a + 2F6X6,t) + F3X3,T + FsXs.T + F6X6,T [2] where Fi represents the mole flow of stream i , where i is the stream number indicated in Figure 3. Xi.n is the mole fraction of component n in stream i. Other material balances can be written in a similar manner. The energy balance of the abstract block is given by: H1 + H2 + AHFael+ AI-IcoolingWater+ AHst~ + AW = H 3 + H4 + H5 + H6 [3] where Hi is the rate of the enthalpy entering from stream i and AW and AHj is work and heat done on the system respectively. Step 4: Identify the process objectives At each abstract level of the hierarchical framework, we focus our attention on the aspect of the plant that is relevant to that particular representation. This means, only objectives that could be defined by the observable process variables would be within the scope of our design at that level. Constraints on the temperatures of the inlet and outlet streams of the reactor are not visible at the input-output level. At this level, we would like to: (a) meet product specifications; (b) ensure that materials and energy are balanced and (c) minimize the operating cost of the plant. Step 5: Prioritize the process objectives There are multiple objectives that we wish to accomplish and not all of them are of equal importance. Prioritization of overall production objectives can be accomplished via a paired comparison method (Morris, 1964). Objectives which are related to the product specifications have the highest priorities. Energy balances are not as important as material balances because disturbances which affect the energy balances can usually be
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localized by adjusting the utility flows. A material balance is of high priority if the expected rate of change of that material is high. The expected rate of change of a material is indicated by the expected amount/frequency of variations of the inventory of that material caused by external process disturbances or setpoint-changes. The set of criteria used for ranking of material balances have been formalized and they can be analysed via qualitative propagation of causes using cause-and-effect diagrams of the process (Ng, 1995). In the HDA plant, we expect the amount of hydrogen coming into to system to vary as the content of methane in that stream changes so we rank our goals to form the following hierarchy of objectives : (1) maintain the stability of the process; (2) maintain the production of benzene at the desired level; (3) maintain the purity of benzene product at the desired level; (4) maintain hydrogen balance (MB-H); (5) maintain methane balance (MB-M); (6) maintain toluene balance (MB-T); (7) maintain energy balance (EB); (8) minimize operating cost. Note that the above are objectives which are implicitly defined as they cannot be directly related to some specific process variables in the input and output streams of the abstract block. Step 6: Synthesize long-horizon control structure Our model is an abstract representation of a multi-input, multi-output (MIMO) unit block. We begin the synthesis by analyzing how changes in each of the process variables affect the most important objective. We have previously assigned fuel to maintain the stability of the heat integration loop. Fs and Fs.B have the most direct effects on the product specifications (production level, purity). Note that these are "notional" control assignments which have to be refined to specific control strategies at a later stage of the design. Row 1 of Table 1 gives the gains of the accumulation of the inventory of hydrogen in the system for each of the visible variables. These gains have been estimated through perturbation analysis on the system of equations. As shown, Fj (hydrogen make-up stream) gives the largest gain on the inventory of hydrogen. A control strategy which regulates the inventory of hydrogen by adjusting FI gives a better performance than those which adjusts other process variables, so we associate F1 with MB-H. Having assigned a manipulated variable (MV) to our most important objective, we estimate the gain of the second objective (MB-M) for each of the remaining process variables, while MB-H is being maintained by F1. Results are shown in row 2 of Table 1. In this case, F3.M is the best choice. Using F3.M will also help to divert the variations of the inventory of methane in the system out to the environment. A similar analysis shows that MB-T can be best controlled by F2 (toluene feed). Table 1: Input-output plant : Summary of Gains (lb mol / hr) MB-H MB-M
FI 4.1169 N/A
F3,a -0.0327 0.0344
F3,M 0 -2.7525
F31H
F4rB
-I.426 0.0750
-0.0090 0.0095
F4,M 0 -0.1893
F4,H -0.0134 0.0007
F5,8 N/A N/A
F6,D -0.0466 0.0957
Our next objective is to maintain the energy balance. The energy balance equation indicates that AHFuel, AHcooJi,gwat~r and AHst~m are potential manipulated variables. We have previously selected fuel to be used to maintain the stability of the heat integrated loop of the plant. Cooling water is a relatively cheap utility so we assign cooling water to be used to maintain the energy balance of our abstract model. The remaining free manipulated variables can be used for cost optimization of the plant. The control structure that we have developed attempts to satisfy the control objectives in order of decreasing importance, by assigning the best manipulated variable for the most important objective in the plant before allocating manipulations to the less important objectives. In general, the criteria used in allocating the primary manipulated variables (MVs) to each of the control objectives are : (1) the magnitude of the gain caused by changes in the MV; (2) the economic sensitivity to the usage of the particular MV; (3) the character of the MV as a "disturbance sink"; (4) robustness of the selection (whether the sign of the gain changes). The theoretical details of the lexicographic allocation of MVs to the given hierarchy of control objectives can be found in Meadowcroft et ai. (1992) and Ng et al. (1994; 1995). Step 7: Refine process representation The next step of the design is to refine the previous abstraction into a model which represents a shorter timehorizon of the plant. Models at the coarse and refined levels must be internally consistent. Material and energy balances and control objectives must also be refined into sub-goals to reflect the added details in the new representation. These sub-goals are allocated to one or more refined sub-blocks at the lower level. Process specifications which become visible through the streams in the refined model also need to be included in the analysis. As one moves to a more detailed level of plant representation, existing objectives are (a) propagated, (b) refined or/and new objectives are spawned. The control strategy developed at a detailed level must be upwardly compatible with the one developed at a coarser level. All of these tasks are guided by specific algorithmic procedures which can be found in Ng (1995).
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European Symposiumon Computer Aided Process Engineering---6.Part B
Step 8: Repeat steps 4 to 7 until the dynamics of the plant becomes dominant in the representation At each subsequent level, analysis similar to that for the input-output plant is performed. Figures 4 and 5 show the control strategies that have been developed for the HDA plant. Notice that in the strategies that we have developed, variations of the inventories caused by external disturbances are being diverted to the feed streams and the purge stream. This approach minimizes variations in the product stream. At Level 2, we spawn an objective to minimize the loss of benzene from the separation section as part of the cost minimization strategy. At Level 3, we realize that to reduce the loss of benzene from the purge, the temperature of the separator could be judiciously chosen to reflect the variations of materials in the system. A more detailed description of the refinement of the cost optimization strategy can be found in Ng (1995). 3
2:L:
7
~:
12r
aration
~
~, Wae tr~
9
Figure4. ControlStructureat Level2 of the HDAPlant
5 6
Figure 5. ControlStructureat Level3 of the HDAPlant
Phase H: Short.horizon Analysis When we reach a level at which the overall time-horizons of the sub-blocks are comparable to the fastest dynamics within the sub-blocks, we switch to Phase II of the design and perform short-horizon analysis on the plant. For the HDA plant, this happens when we reach Level 5 (Figure 6). Step 9: Refine model and process objectives The goal of this phase of the design is to develop a control structure that is to be used for fast dynamic feedback control. We require that all objectives be refined into measurable process variables in the plant. Balances of materials around the same unit form a group. The general rule is to identify the key indicator(s) of build-up of materials or energy in the unit. If the inventory of these materials exists in the liquid phase, refine the set of MBs to the amount of liquid in that unit. If the inventory of these materials also exist in the gas phase, also refine the set of MBs to the pressure of the unit. Energy build-up is usually manifested in the temperature of the system. For units with gaseous materials, energy may also manifest in the pressure of the system. Whenever there are alternative indicators, choose the process variables which can be easily accessed by some manipulated variables or those variables which are along the pathways of the propagation of disturbances in the plant.
Figure 6. Control Structure at Level5 of the
HDAplant(notthecompletecontrolstructure)
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European Symposium on Computer Aided Process Engineering--6. Part B
For each of the refined objectives; study the interconnections of the plant to determine if they are selfregulating. Self-regulating objectives are less crucial and can be demoted in the ranking of the objectives. If variations of those self-regulating objectives can be tolerated, their controls are optional. Step 10: Synthesize short-horizon control structure The methodology for the synthesis of control structure in the short-horizon case is very similar to the analysis done in Phase I (step 6). The criteria to use in the selection of MVs are : (I) speed of the response; (2) invertability of the process; (3) the economic sensitivity with the usage of that MV; (4) the character of the MV as a "disturbance sink". Figure 6 depicts the control structure at Level 5 of the HDA plant. For more details on the allocation of MVs to short-horizon objectives and its relationship to robust control lexicographic ideas, see Ng (1995).
Multi-horizon Control Strategies In our design, we arrive at a hierarchy of control strategies. Control structure at Level 5 is primarily being used to maintain the plant at its desired operating point in the immediate time-horizon. Control strategies from higher levels which are not covered by the Level 5 control structure are added to the overall control scheme. Strategies at different levels are being controlled at different rates. At Level 2, we identified that the composition of methane in the purge be adjusted to help maintain the inventory of methane in the system, while at Level 3, the recycle toluene composition has been chosen to maintain the inventory of toluene in the generalized separation system. These suggest that controlling those compositions at their respective levels can supplement the overall control scheme. SUMMARY AND CONCLUSION We have briefly introduced a hierarchical approach to the synthesis of plant-wide control structures. The scope of this paper has been confined, due to space limitations, to the illustration of the key conceptual steps of the design. The theoretical framework and analysis of quantitative arguments are given in significant detail in Ng (1995) where the reader can also find application of the methodology to other plants. Our methodology allows one to systematically identify the specific control objectives in the plant and the level at which their variations are the most significant. By maintaining a "plant-wide" view at all times, our control strategies are consistent with the overall production objectives. Also, our approach respects the multiobjective nature of the design problem and take into account the propagation of disturbances in the process. REFERENCES Banerjee, A. and Y. Arkun, "Control Configuration Designing Applied to the Tennessee Eastman Plant-wide Control Problem," Comp. Chem. Engng, 19, (4), 453-480 (1995). Douglas, J. M., Conceptual Design of Chemical Processes, McGraw-Hill, (1988). Lyman, P.R. and C. Georgakis, "Plant-wide Control of the Tennessee Eastman Problem," Comp Chem Engng, 19, (3), 321-331 (1995). McAvoy, T.J. and N. Ye, "Base Control for the Tennessee Eastman Problem," Comp. Chem. Engng, 18, (5), 383-413 (1994). Meadowcroft, T., G. Stephanopoulos and C. Brosilow, "The Modular Multivariable Controller I: Steady-State Properties," AIChE J., 38, 1254 (1992). Morari M, and G. Stephanopoulos, "Studies in the Synthesis of Control Structures for Chemical Process. Part I", AIChE J., 26, 220 (1980). Morris, W.T.,The Analysis of Management Decisions, Homewood, I1. : Richard D. Irwin, 1964. Morud, J, S. Skogestad, "The Dynamic Behavior of Integrated Plants," Proceedings of the Process System Engineering Conference, Korea, 1994. Ng, C.S. and G. Stephanopoulos, "A Hierarchical Approach to the Synthesis of Plant-wide Control Structures," 1994 Annual AIChE meeting, San Francisco (1994) Ng, C.S., MIT-LISPE Technical Report, Dept. of Chemical Engineering, MIT, (1995). Ponton, J.W. and D.M.Laing, "A Hierarchical Approach to the Design of Process Control Systems", Trans. 1Chem. E., 71, Part A, 181, (1993). Umeda, T., T. Kuriyama, and A. Ichidawa, "A Logical structure for Process Control System Synthesis," Proc. IFAC Congress, Helsinki, (1978).
Computers chem. Engng Vol. 20, Suppl., pp. $999-SI004,1996 Copyright © 1996 Elsevier Science Ltd S0098-1354(96)00174-3 Printed in Great Britain. All rights reserved 0098-1354/96 $15.00+0.00
SYNTHESIS OF CONTROL SYSTEMS FOR CHEMICAL PLANTS Christine S. Ng and George Stephanopoulos Laboratory for Intelligent Systems in Process Engineering, Dept. of Chemical Engineering Massachusetts Institute of Technology, Cambridge, MA 02139
Abstract - Synthesis of plant-wide control structures involves identifying control objectives that are consistent with the overall production goals and formulating control strategies in a multivariate environment. This is a complex task. A hierarchical framework is proposed in which the plant is vertically decomposed into a set of representations of different degrees of abstraction. Starting from the input-output level, we develop a control structure for the overall plant. Then, we move onto the next level where the model, the control objectives and the control strategies are being refined. This procedure is repeated until all levels of the plant have been analyzed. The hierarchy of control strategies can be integrated to form a multi-horizon control system. In this paper, the key conceptual steps of the methodology are being demonstrated.
INTRODUCTION Operation of a chemical plant is a multifaceted task. First, ideally, the plant should be steered to track the product demands driven by market forces at the minimum operating cost. Second, the plant should also be maintained at the desired steady-state in the presence of continuously varying external influences, like changes in ambient temperature or compositions of feed streams. In addition to the above "operational" objectives, the plant must always be maintained within the safe operating region and must not violate the regulations imposed by the government. Some of these objectives are explicitly related to specific process variables in the plant, while some are only implicitly defined by the overall process. The accomplishment of all these objectives falls within the domain of tasks of an automated plant-wide control system. The job of the control system designer is to identify specific controlled variables in the plant, formulate control strategies using the available manipulated variables and derive appropriate control laws. The current direction of research in this area (Banerjee and Arkun, 1995; Lyman and Georgakis, 1995; McAvoy and Ye, 1994) recognizes that the once popular unit-based design approach (Umeda et al., 1978) does not provide design viewpoints which can capture the broad range of objectives that are involved in the operation of the plant and so a plant-wide viewpoint is being advocated. We believe that the perspective of the plant can be further enhanced by developing control strategies using multiple viewpoints via hierarchical decomposition of the process into representations of various degrees of abstraction: an input-output model, a series of generalized reaction-separation systems and a detailed representation (Morari and Stephanopoulos, 1980; Ng and Stephanopoulos, 1994; Ponton and Laing, 1993). The use of a hierarchy of representations reduces the complexity of the problem by allowing the designer to separately address process goals which are significant in various ranges of time-horizon. The objective of this paper is to illustrate how a plant-wide control system can be synthesized within the hierarchical framework. In the next section, we will give an overview of the proposed design framework, which will be followed by a demonstration of the key conceptual steps of the methodology on the hydrodealkylation of toluene (HDA) plant. METHODOLOGY OVERVIEW Figure 1 gives a conceptual description of our methodology. In the hierarchical framework, we begin the synthesis with a simple representation of the process, like the input-output plant. This model is a unique viewpoint of the overall purpose of the plant, that is, to transform the available feed streams to the desired products with the available resources of utilities. The input-output plant represents the longest time-scaie of operation. Based on the overall production goals, we identify control objectives which are relevant for this level of the design and develop a control structure for the input-output plant. Then, we move down one level of $999
S1000
European Symposiumon Computer Aided Process Engineering---6.Part B
the hierarchy and refine our model into one which describes a shorter time-horizon of operation. Control objectives and constraints from the previous level are propagated to the new model. In a representation with added details, we can identify refined control objectives for the plant and develop a control strategy that is suitable for a shorter time-horizon of operation. This process is repeated until we reach the most detailed level of representation which models the shortest time-horizon of operation in the plant. The set of plant abstractions form a hierarchy of modeling levels. Each of the control strategies that we develop is suitable for a particular range of time-scale of operation and thus, together, they form a hierarchy of control strategies for different time-scales. This hierarchy of control strategies can be judiciously integrated to form a multi-horizon control system for the complex plant.
y
OVERALLPRODUCTIONGOALS
M~e-~, Hydrogen
7
3
r q m i i
CONTROLSTRATEGIES
1
I_..
T
CONTROLSYSTEM R~'~leT d t ~
Figure 1. Synthesis of Control Structures for Complete Plants
Figure 2. Rowsheet of the Hydrodealkylation of Toluene Plant
CASE STUDY: HYDRODEALKYLATION OF TOLUENE PLANT The HDA plant produces benzene from the hydrodealkylation of toluene (Douglas, 1998). A process flowsheet is given in Figure 2. The basic reactions are : toluene(T) + hydrogen(H) ---> benzene(B) + methane(M) [R1] 2(benzene) --> diphenyl(D) + hydrogen [R2] With the given flowsheet of the process, the overall material and energy balances, the overall production objectives of the plant, and some idea about the type of disturbances that are expected for the plant, a control structure can by synthesized through the methodology described in the subsequent sections of this paper.
Preliminary Analysis To begin, we examine the characteristics of the process. Step 1: Identify overall production objectives, process constraints and sources of external disturbances The goal of the operation is to produce benzene at 265 lbmol/hr with 0.9997 purity. It is also expected that there will be variations of temperatures of coolants, temperatures and pressures of toluene and hydrogen feed, pressures of steam lines and purity of hydrogen in the make-up stream. The only operational/safety constraints are the following (a) the temperatures at the inlet, outlet and interior of the reactor must not exceed 1300°F; (b) the hydrogen/toluene ratio must be at least 5:1 at the inlet of the reactor to prevent coking. It is also desired to minimize the operating cost of the process. Step 2: Examine the open-loop stability of the process Plants which contain unstable dynamics are generally harder to control. Without the implementation of a sufficient process control strategy on an open-loop unstable plant, the temperature or pressure of a part of the plant might build up and this might eventually cause violations of the operational and safety limits and lead to a plant runaway. Instability in a chemical process plant is typically caused by either (1) the presence of an inherently unstable unit-operation, like a continuous-stirred tank reactor being operated at an unstable operating point or (2) the circumstantial interconnections of the plant through the material recycle loops or
European Symposium on Computer Aided Process Engineering--6. Part B
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heat-integration which generate positive feedback in the system (Morud and Skogestad, 1994).These are the items in the plant we need to examine. In the HDA plant, the distillation columns, coolers, heaters and compressor are all inherently stable unitoperations. The reactions occur in an adiabatic tubular reactor. As long as there is sufficient coolant to quench the effluent, the process should also be stable. Local numerical sensitivity analysis shows that the material recycle loops in the HDA plant are stable. Step changes of the flows of toluene and hydrogen produce step changes in the amounts of the various materials in the output streams (Ng, 1995). The energy in the HDA plant is partially integrated. A qualitative simulation of the heat loop in the plant shows that the heat integration system in the HDA plant creates a positive feedback loop in the system and energy in the system would accumulate if there is a step increase in the temperature of the feed streams (Ng, 1995). Thus, somewhere in this loop, we must select a manipulated variable to control the inventory of energy in the system. We will assign fuel to control the temperature of the feed stream to the reactor. The above analyses can be and have been formalized through systematic procedures, which use qualitative propagation of causes through a cause-and-effect diagram describing the behavior of a plant (Ng, 1995). Phase I: Long-horizon Analysis With that understanding of the process in mind, we proceed to develop a hierarchy of control structures for the plant. In the first phase of the design, we focus on the aspects of the plant which are caused by long-term changes in the process.
Step 3: Perform overall system analysis Figure 3 displays the input-output representation of the system which uniquely represents the overall process. Fuel , steam
1 2
HDA Product By-product
Figure 3. lnpubOutput representation of the HDA plant
In the long-horizon, at steady-state, this model is described by a set of independent material and energy balances. In general, each abstract block can be defined by one energy balance (EB) and a number of material balances (MBs). The number of material balances required is given by: no. of independent material balances = no. of components involved in the reactions - no of independent reactions + no. of inert components in the system [1] For the HDA plant, writing one energy balance and material balances for toluene, hydrogen and methane will completely define the input-output block. The material balance for toluene (MB-T) is given by : F2X2,T = FsXs,a + F3X3,a + 2F6X6,t) + F3X3,T + FsXs.T + F6X6,T [2] where Fi represents the mole flow of stream i , where i is the stream number indicated in Figure 3. Xi.n is the mole fraction of component n in stream i. Other material balances can be written in a similar manner. The energy balance of the abstract block is given by: H1 + H2 + AHFael+ AI-IcoolingWater+ AHst~ + AW = H 3 + H4 + H5 + H6 [3] where Hi is the rate of the enthalpy entering from stream i and AW and AHj is work and heat done on the system respectively. Step 4: Identify the process objectives At each abstract level of the hierarchical framework, we focus our attention on the aspect of the plant that is relevant to that particular representation. This means, only objectives that could be defined by the observable process variables would be within the scope of our design at that level. Constraints on the temperatures of the inlet and outlet streams of the reactor are not visible at the input-output level. At this level, we would like to: (a) meet product specifications; (b) ensure that materials and energy are balanced and (c) minimize the operating cost of the plant. Step 5: Prioritize the process objectives There are multiple objectives that we wish to accomplish and not all of them are of equal importance. Prioritization of overall production objectives can be accomplished via a paired comparison method (Morris, 1964). Objectives which are related to the product specifications have the highest priorities. Energy balances are not as important as material balances because disturbances which affect the energy balances can usually be
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European Symposium on Computer Aided Process Engineering---6. Part B
localized by adjusting the utility flows. A material balance is of high priority if the expected rate of change of that material is high. The expected rate of change of a material is indicated by the expected amount/frequency of variations of the inventory of that material caused by external process disturbances or setpoint-changes. The set of criteria used for ranking of material balances have been formalized and they can be analysed via qualitative propagation of causes using cause-and-effect diagrams of the process (Ng, 1995). In the HDA plant, we expect the amount of hydrogen coming into to system to vary as the content of methane in that stream changes so we rank our goals to form the following hierarchy of objectives : (1) maintain the stability of the process; (2) maintain the production of benzene at the desired level; (3) maintain the purity of benzene product at the desired level; (4) maintain hydrogen balance (MB-H); (5) maintain methane balance (MB-M); (6) maintain toluene balance (MB-T); (7) maintain energy balance (EB); (8) minimize operating cost. Note that the above are objectives which are implicitly defined as they cannot be directly related to some specific process variables in the input and output streams of the abstract block. Step 6: Synthesize long-horizon control structure Our model is an abstract representation of a multi-input, multi-output (MIMO) unit block. We begin the synthesis by analyzing how changes in each of the process variables affect the most important objective. We have previously assigned fuel to maintain the stability of the heat integration loop. Fs and Fs.B have the most direct effects on the product specifications (production level, purity). Note that these are "notional" control assignments which have to be refined to specific control strategies at a later stage of the design. Row 1 of Table 1 gives the gains of the accumulation of the inventory of hydrogen in the system for each of the visible variables. These gains have been estimated through perturbation analysis on the system of equations. As shown, Fj (hydrogen make-up stream) gives the largest gain on the inventory of hydrogen. A control strategy which regulates the inventory of hydrogen by adjusting FI gives a better performance than those which adjusts other process variables, so we associate F1 with MB-H. Having assigned a manipulated variable (MV) to our most important objective, we estimate the gain of the second objective (MB-M) for each of the remaining process variables, while MB-H is being maintained by F1. Results are shown in row 2 of Table 1. In this case, F3.M is the best choice. Using F3.M will also help to divert the variations of the inventory of methane in the system out to the environment. A similar analysis shows that MB-T can be best controlled by F2 (toluene feed). Table 1: Input-output plant : Summary of Gains (lb mol / hr) MB-H MB-M
FI 4.1169 N/A
F3,a -0.0327 0.0344
F3,M 0 -2.7525
F31H
F4rB
-I.426 0.0750
-0.0090 0.0095
F4,M 0 -0.1893
F4,H -0.0134 0.0007
F5,8 N/A N/A
F6,D -0.0466 0.0957
Our next objective is to maintain the energy balance. The energy balance equation indicates that AHFuel, AHcooJi,gwat~r and AHst~m are potential manipulated variables. We have previously selected fuel to be used to maintain the stability of the heat integrated loop of the plant. Cooling water is a relatively cheap utility so we assign cooling water to be used to maintain the energy balance of our abstract model. The remaining free manipulated variables can be used for cost optimization of the plant. The control structure that we have developed attempts to satisfy the control objectives in order of decreasing importance, by assigning the best manipulated variable for the most important objective in the plant before allocating manipulations to the less important objectives. In general, the criteria used in allocating the primary manipulated variables (MVs) to each of the control objectives are : (1) the magnitude of the gain caused by changes in the MV; (2) the economic sensitivity to the usage of the particular MV; (3) the character of the MV as a "disturbance sink"; (4) robustness of the selection (whether the sign of the gain changes). The theoretical details of the lexicographic allocation of MVs to the given hierarchy of control objectives can be found in Meadowcroft et ai. (1992) and Ng et al. (1994; 1995). Step 7: Refine process representation The next step of the design is to refine the previous abstraction into a model which represents a shorter timehorizon of the plant. Models at the coarse and refined levels must be internally consistent. Material and energy balances and control objectives must also be refined into sub-goals to reflect the added details in the new representation. These sub-goals are allocated to one or more refined sub-blocks at the lower level. Process specifications which become visible through the streams in the refined model also need to be included in the analysis. As one moves to a more detailed level of plant representation, existing objectives are (a) propagated, (b) refined or/and new objectives are spawned. The control strategy developed at a detailed level must be upwardly compatible with the one developed at a coarser level. All of these tasks are guided by specific algorithmic procedures which can be found in Ng (1995).
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European Symposiumon Computer Aided Process Engineering---6.Part B
Step 8: Repeat steps 4 to 7 until the dynamics of the plant becomes dominant in the representation At each subsequent level, analysis similar to that for the input-output plant is performed. Figures 4 and 5 show the control strategies that have been developed for the HDA plant. Notice that in the strategies that we have developed, variations of the inventories caused by external disturbances are being diverted to the feed streams and the purge stream. This approach minimizes variations in the product stream. At Level 2, we spawn an objective to minimize the loss of benzene from the separation section as part of the cost minimization strategy. At Level 3, we realize that to reduce the loss of benzene from the purge, the temperature of the separator could be judiciously chosen to reflect the variations of materials in the system. A more detailed description of the refinement of the cost optimization strategy can be found in Ng (1995). 3
2:L:
7
~:
12r
aration
~
~, Wae tr~
9
Figure4. ControlStructureat Level2 of the HDAPlant
5 6
Figure 5. ControlStructureat Level3 of the HDAPlant
Phase H: Short.horizon Analysis When we reach a level at which the overall time-horizons of the sub-blocks are comparable to the fastest dynamics within the sub-blocks, we switch to Phase II of the design and perform short-horizon analysis on the plant. For the HDA plant, this happens when we reach Level 5 (Figure 6). Step 9: Refine model and process objectives The goal of this phase of the design is to develop a control structure that is to be used for fast dynamic feedback control. We require that all objectives be refined into measurable process variables in the plant. Balances of materials around the same unit form a group. The general rule is to identify the key indicator(s) of build-up of materials or energy in the unit. If the inventory of these materials exists in the liquid phase, refine the set of MBs to the amount of liquid in that unit. If the inventory of these materials also exist in the gas phase, also refine the set of MBs to the pressure of the unit. Energy build-up is usually manifested in the temperature of the system. For units with gaseous materials, energy may also manifest in the pressure of the system. Whenever there are alternative indicators, choose the process variables which can be easily accessed by some manipulated variables or those variables which are along the pathways of the propagation of disturbances in the plant.
Figure 6. Control Structure at Level5 of the
HDAplant(notthecompletecontrolstructure)
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European Symposium on Computer Aided Process Engineering--6. Part B
For each of the refined objectives; study the interconnections of the plant to determine if they are selfregulating. Self-regulating objectives are less crucial and can be demoted in the ranking of the objectives. If variations of those self-regulating objectives can be tolerated, their controls are optional. Step 10: Synthesize short-horizon control structure The methodology for the synthesis of control structure in the short-horizon case is very similar to the analysis done in Phase I (step 6). The criteria to use in the selection of MVs are : (I) speed of the response; (2) invertability of the process; (3) the economic sensitivity with the usage of that MV; (4) the character of the MV as a "disturbance sink". Figure 6 depicts the control structure at Level 5 of the HDA plant. For more details on the allocation of MVs to short-horizon objectives and its relationship to robust control lexicographic ideas, see Ng (1995).
Multi-horizon Control Strategies In our design, we arrive at a hierarchy of control strategies. Control structure at Level 5 is primarily being used to maintain the plant at its desired operating point in the immediate time-horizon. Control strategies from higher levels which are not covered by the Level 5 control structure are added to the overall control scheme. Strategies at different levels are being controlled at different rates. At Level 2, we identified that the composition of methane in the purge be adjusted to help maintain the inventory of methane in the system, while at Level 3, the recycle toluene composition has been chosen to maintain the inventory of toluene in the generalized separation system. These suggest that controlling those compositions at their respective levels can supplement the overall control scheme. SUMMARY AND CONCLUSION We have briefly introduced a hierarchical approach to the synthesis of plant-wide control structures. The scope of this paper has been confined, due to space limitations, to the illustration of the key conceptual steps of the design. The theoretical framework and analysis of quantitative arguments are given in significant detail in Ng (1995) where the reader can also find application of the methodology to other plants. Our methodology allows one to systematically identify the specific control objectives in the plant and the level at which their variations are the most significant. By maintaining a "plant-wide" view at all times, our control strategies are consistent with the overall production objectives. Also, our approach respects the multiobjective nature of the design problem and take into account the propagation of disturbances in the process. REFERENCES Banerjee, A. and Y. Arkun, "Control Configuration Designing Applied to the Tennessee Eastman Plant-wide Control Problem," Comp. Chem. Engng, 19, (4), 453-480 (1995). Douglas, J. M., Conceptual Design of Chemical Processes, McGraw-Hill, (1988). Lyman, P.R. and C. Georgakis, "Plant-wide Control of the Tennessee Eastman Problem," Comp Chem Engng, 19, (3), 321-331 (1995). McAvoy, T.J. and N. Ye, "Base Control for the Tennessee Eastman Problem," Comp. Chem. Engng, 18, (5), 383-413 (1994). Meadowcroft, T., G. Stephanopoulos and C. Brosilow, "The Modular Multivariable Controller I: Steady-State Properties," AIChE J., 38, 1254 (1992). Morari M, and G. Stephanopoulos, "Studies in the Synthesis of Control Structures for Chemical Process. Part I", AIChE J., 26, 220 (1980). Morris, W.T.,The Analysis of Management Decisions, Homewood, I1. : Richard D. Irwin, 1964. Morud, J, S. Skogestad, "The Dynamic Behavior of Integrated Plants," Proceedings of the Process System Engineering Conference, Korea, 1994. Ng, C.S. and G. Stephanopoulos, "A Hierarchical Approach to the Synthesis of Plant-wide Control Structures," 1994 Annual AIChE meeting, San Francisco (1994) Ng, C.S., MIT-LISPE Technical Report, Dept. of Chemical Engineering, MIT, (1995). Ponton, J.W. and D.M.Laing, "A Hierarchical Approach to the Design of Process Control Systems", Trans. 1Chem. E., 71, Part A, 181, (1993). Umeda, T., T. Kuriyama, and A. Ichidawa, "A Logical structure for Process Control System Synthesis," Proc. IFAC Congress, Helsinki, (1978).