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The role of computers in simulation, optimization and control
Analytica Chimica Acta, 210 (1988) 109-114 Elsevier Science Publishers B.V., Amsterdam -
THE ROLE OF COMPUTERS AND CONTROL
109 Printed in The Netherlands
IN SIMULATION,
OPTIMIZATION
DJORDJIJA PETKOVSKI Faculty of Technical Sciences, Veljka VlahouZa 3,210OO Novi Sad (Yugoslavia) (Received 20th July 1987)
SUMMARY The impact of recent achievements in computer technology on the simulation, optimization and control of chemical systems is discussed.
The past fifteen years have seen a major change in the practice of chemical industry. The need for improved productivity, improved quality, and lowered cost of production has caused the industry to re-examine the need for new methods of production. The initial steps taken to develop these new methods were based on the traditional methods of economic analysis. The next steps towards the improvement of production efficiency are the introduction of integrated, advanced control systems. The computer has played and will play a major role in this improvement. Advanced technologies in the hardware and software of computer systems have had dramatic effects on the practice of chemical engineering. Process modelling, design, optimization and control are areas that will play a leading role in the forthcoming transformation of process industry. The increased complexity of applications of technological systems and control engineering has forced dependence on large computer resources in the simulation, control and optimization. Computer technology has progressed so far that combinational interdisciplinary problems that took many hours to solve only a decade ago, can now be handled within a few minutes. Solving almost any significant problem in chemical engineering requires finding a framework for identifying subsystems which interact with each other in an easily described way. Computers will be used not only to improve a particular step in the process by automation but also to provide the interconnections which permit communication between related steps in the process. Advances in computer technology, both hardware and software, provide a major, but as yet only partially achieved, positive means of obtaining such inte-
0003-2670/88/$03.50
0 1988 Elsevier Science Publishers B.V.
110
gration. Integration needs to be accomplished by progress in the development of efficient methods for monitoring and controlling complex systems such as those involved in the process industry. Computers of all kinds have become indispensable, both as design aids and as elements in the implementation of control algorithms, designs or schemes. In process control, where systems may contain hundreds of control loops, even a small improvement in yield can be quite significant economically. Advanced, multivariable control algorithms are now being implemented by several large chemical companies. Moreover, improved control algorithms also permit inventories to be reduced, which is a particularly important consideration in processing dangerous material. MODELLING
The goal of much of science is to obtain quantitative descriptions of natural phenomena. Systems and control engineering depend critically on mathematical models. The first step in the analysis, design and synthesis of real complex technological systems is the development of a “mathematical model”, which can be substituted for the real problem. A great deal of intellectual activity has been motivated by attempts to construct models of chemical processes. A model is an abstract generalization of an object or system. Any set of rules and relationships that describes something is a model of that thing. It is essential that the underlying model is both realistic and correct, that it is easy to set and change parameters, that the running time is not too slow, and that the results are presented in a clear and easily interpretable fashion. A common use of a model is to provide the designers or the decision-makers with a “laboratory” for exploring the probable consequences of a wide range of alternative plans or designs. In addition, a typical result of modelling is the opportunity to see a system from several viewpoints, to polarize thinking and to pose sharp questions. One of the most important challenges to system and control theory brought forth by present-day technology is to overcome the increasing size and complexity of the mathematical models. Because the amount of computational effort required to analyze these processes increases much more swiftly than the size of the corresponding system, the problems arising in complex technological systems may become either impossible or uneconomical to solve, even with modern computers. It is common procedure in practice to work with mathematical models that are simpler, but less accurate, than the best available model of a given technological system. In going from the most complex to the most simplified model, the trade-off is between computational convenience and modelling adequacy [l-3]. Also, not only should a model be faithful in terms of the physical reality
111
that it represents, but it should also provide the designer, planner or the analyst with enough information to enable him to act on the system in a knowledgeable way. In other words, a satisfactory model is one that provides a good aid to the designer or analyst, and at the same time achieves the right level of trade-off between accuracy and computational convenience. In many practical situations, mathematical models cannot provide all the required answers, but there cannot be good answers without mathematical models. Therefore, in the examination and design of complex processes in chemical industry, the methods of analysis and design should somehow take advantage of special features in the physical system, leading to simplification of the computing requirements. One important class of special features is the system structure. Lack of understanding of the structure of the underlying system can often lead to wrong conclusions regarding problem solution. Theoretical models used for the design of control systems are most often simplified by neglecting non-linearities, time-varying parameters and higherorder dynamics. Thus, the practicing engineer is always confronted with the problem of mismatch between the approximate model and the real plant, which he has to address carefully during the design of controllers. The critical point is that the controller is designed from the model but implemented on the real plant. If the controller design does not take into account the modelling errors, the closed-loop performance of the plant deteriorates from that produced by the model and often the onset of instability prevails. As is known, the ability of a given system to maintain its important properties, such as stability, optimality, controllability, etc., despite modelling uncertainties is referred to as the robustness [ 4-61 of the system with respect to these properties. Design of robust controllers is a pressing problem and it is now receiving more and more recognition in control theory. SIMULATION AND OPTIMIZATION
Simulation, a system analysis approach, can provide a comprehensive view of a complex technological system. In essence, simulation is an iterative problem-solving process which involves problem formulation, mathematical modelling, refinement and testing of the resulting model, and creative design and execution of simulation experiments intended to provide the answer to the questions posed. This approach requires specialized knowledge from various professions and disciplines, i.e., creative interaction among systems analysts, computer specialists, chemical engineers and other specialists. In many real-life situations, planners and decision-makers are forced to make important decisions on the basis of a wide range of alternative plans and management strategies. In these cases, especially when large-scale technological systems are considered, the simulation approach can be time-consuming and not very efficient. Brute-force simulation often generates so much information
112
and so many possible alternatives that it is difficult to know how to begin the analysis. Therefore, a systematic way is often required to find the “best” solution. With current computing technology and methodology, simulation models can also be used in an optimization mode. Development of mathematical programming and optimal control theory has focused attention on more precise statements of design problems, i.e., design criteria. This approach presupposes some criterion (index performance) to be maximized or minimized. Therefore, it is usually necessary to decide on a selection on the basis of which a choice can be made from among the many alternatives that are normally possible. In other words, in this mode, the model is programmed to search automatically for a solution which optimizes the selected criterion, such as time, energy, profit, cost, etc. In addition, in many cases, an optimal policy is one that minimizes or maximizes the performance criterion without violating any chosen constraints. However, it should be emphasized that optimal implies neither “good” nor “bad” but may simply be a way of selecting one policy from a number of satisfactory scenarios. Another point is also very important. Once the optimization problem has been posed in a satisfactory way, its solution may be difficult because of the size (i.e., dimensionality ) of the complex technological system considered. Various simplifications of the optimization methodology have been proposed. However, in the strictly mathematical sense, what is optimal in a simplified scheme, will not generally be an optimal solution to the original problem. Adequate experience is sadly lacking in this area and a great deal of further work is needed. Simulation is also widely used for verification of new control schemes. The complexity and variety of processes in chemical industry renders standard mathematical analysis of the designs often impractical. In that case, the only resource for testing and verification is simulation, whether exclusively on a computer or in a test bed. The latter combines computer simulation of some subsystems and functions with actual components and software. These largescale simulation systems with their many degrees of freedom have raised serious technical problems about the design of experiments and the sequence in which they should be conducted in order to obtain the maximum relevant information. CONTROL SYSTEMS
The process industries have historically recognized the importance of process control in order to achieve successfully functioning production. In engineering systems, the paradigm of feedback control addresses the problem of using the information about the output to design or modify the input for a given task. The central motivation for using feedback in control systems arises from its ability to reduce the impact of uncertainties present in the process and its
113
environment. (Here, uncertainties mean external disturbances and variations in process parameters, as well as differences between the mathematical design model and the corresponding physical system.) One of the goals of control theory has been to capture major elements of the engineering process of feedback design under the umbrella of a formal problem in mathematical synthesis. The motivation for this goal is self-evident. Once formulated under such an umbrella, the elements of engineering art become rigorous tools which can be applied more or less automatically to every more complex design situation. Today, chemical engineers are considerably interested in the use of modern, optimal control theory. The application of this theory requires an adequate definition of the problem in physical terms and a translation of this physical description into mathematical terms [7]. Similarly, the aim of the physical process must be mathematically tractable. The subsequent search for the control mechanism to attain the desired goal constitutes the fundamental problem of optimal control theory. However, the problem in using the state-space mathematical models in the design of control systems is that relatively complicated calculations are required. Moreover, in many practical situations, the specifications of the behaviour of the control system are not quite clear in terms of the performance index. An even greater drawback is that the use of the criterion function optimization allows the designer to pick out only one optimal solution. In process control, there are reasons, mainly practical, which require change in the controller parameters. Four examples illustrate this: (a) the control system has to be applicable to other similar processes which do not have wellknown models; (b) subsequent changes of the controller parameters by the operators must be possible; (c) if the parameters of the controllers have to be found by experiments, some starting points and directions for search should be known in advance; and (d) because of lack of vital information on what the designer will have to pay, in engineering terms, for the various aspects of the desired performance of the final system, he may be unable, at the beginning of the investigation, to specify what he wants in terms of the desired final behaviour. Therefore, besides the use of a criterion function optimization, additional aspects must be considered in the feedback designs. This emphasizes the necessity for further analysis and trial-and-error “hedging” about the nominal solution [8]. No matter how powerful the design methodology is, a typical application requires several iterations. Hence, it is imperative that the procedures for control design are transparent and are conducive to educated trialand-error design iterations, and that the number of design parameters be kept at an absolute minimum. The theory of controllability, observability and feedback stabilization of linear state-space models answers the question of whether or not a linear model,
114
if unstable, can be stabilized and whether it can perform a given tracking or regulation task. However, models of realistic chemical systems are seldom known completely and, if known, they are seldom linear. Control theorists are now challenged to expand their horizons and to extend their concepts and methods to be applicable to incompletely modelled systems and to systems which have initially poorly defined models. Developments in computer technology have made possible a whole range of new approaches and applications. Thanks to faster and cheaper computers, the new control laws can incorporate adaptation leading to on-line learning and to better control. However, computer-aided procedures for off-line design of multivariable control laws can involve a more comprehensive experienceguided search for robust and fault-tolerant control structures. Therefore, control engineers need systematic design procedures for designing high-performance feedback control systems for both single-input/singleoutput (SISO ) and multi-input/multi-output (MIMO ) systems. It is also essential that readily available and reliable computer-aided design software be used for the design process. From the viewpoint of the practicing engineer, the availability of first-generation computer-aided control engineering software (LOGALPHA, MATLAB, MATRIX-X, CTRL-C, Program CC, to mention a few) has vastly accelerated the progress of applications. This research was supported in part by the U.S./Yugoslav Joint Fund for Scientific and Technological Cooperation, in cooperation with DOE under Grant PP-727.
REFERENCES 1 2 3 4 5 6 7
M. Aoki, IEEE Trans. Automat. Control, 13 (1968) 246. Dj. Petkovski, Comput. Chem. Eng., 2 (1978) 123. Dj. Petkovski, Int. J. Control, 30 (1979) 661. Dj. Petkovski, Automatika, 24 (1983) 103. Dj. Petkovski and M. Athans, Elec. Power Syst. Res., 9 (1985) 253. Dj. Petkovski, IEE Proc., Part D, 134 (1987) 53. B.D.O. Anderson and J.B. Moor, Linear Optimal Control, Prentice-Hall, NJ, 1971. 8 Dj. Petkovski, Proc. World. Con. Chem. Eng. Tokyo, 1986, p. 634.
Englewood Cliffs,
THE ROLE OF COMPUTERS AND CONTROL
109 Printed in The Netherlands
IN SIMULATION,
OPTIMIZATION
DJORDJIJA PETKOVSKI Faculty of Technical Sciences, Veljka VlahouZa 3,210OO Novi Sad (Yugoslavia) (Received 20th July 1987)
SUMMARY The impact of recent achievements in computer technology on the simulation, optimization and control of chemical systems is discussed.
The past fifteen years have seen a major change in the practice of chemical industry. The need for improved productivity, improved quality, and lowered cost of production has caused the industry to re-examine the need for new methods of production. The initial steps taken to develop these new methods were based on the traditional methods of economic analysis. The next steps towards the improvement of production efficiency are the introduction of integrated, advanced control systems. The computer has played and will play a major role in this improvement. Advanced technologies in the hardware and software of computer systems have had dramatic effects on the practice of chemical engineering. Process modelling, design, optimization and control are areas that will play a leading role in the forthcoming transformation of process industry. The increased complexity of applications of technological systems and control engineering has forced dependence on large computer resources in the simulation, control and optimization. Computer technology has progressed so far that combinational interdisciplinary problems that took many hours to solve only a decade ago, can now be handled within a few minutes. Solving almost any significant problem in chemical engineering requires finding a framework for identifying subsystems which interact with each other in an easily described way. Computers will be used not only to improve a particular step in the process by automation but also to provide the interconnections which permit communication between related steps in the process. Advances in computer technology, both hardware and software, provide a major, but as yet only partially achieved, positive means of obtaining such inte-
0003-2670/88/$03.50
0 1988 Elsevier Science Publishers B.V.
110
gration. Integration needs to be accomplished by progress in the development of efficient methods for monitoring and controlling complex systems such as those involved in the process industry. Computers of all kinds have become indispensable, both as design aids and as elements in the implementation of control algorithms, designs or schemes. In process control, where systems may contain hundreds of control loops, even a small improvement in yield can be quite significant economically. Advanced, multivariable control algorithms are now being implemented by several large chemical companies. Moreover, improved control algorithms also permit inventories to be reduced, which is a particularly important consideration in processing dangerous material. MODELLING
The goal of much of science is to obtain quantitative descriptions of natural phenomena. Systems and control engineering depend critically on mathematical models. The first step in the analysis, design and synthesis of real complex technological systems is the development of a “mathematical model”, which can be substituted for the real problem. A great deal of intellectual activity has been motivated by attempts to construct models of chemical processes. A model is an abstract generalization of an object or system. Any set of rules and relationships that describes something is a model of that thing. It is essential that the underlying model is both realistic and correct, that it is easy to set and change parameters, that the running time is not too slow, and that the results are presented in a clear and easily interpretable fashion. A common use of a model is to provide the designers or the decision-makers with a “laboratory” for exploring the probable consequences of a wide range of alternative plans or designs. In addition, a typical result of modelling is the opportunity to see a system from several viewpoints, to polarize thinking and to pose sharp questions. One of the most important challenges to system and control theory brought forth by present-day technology is to overcome the increasing size and complexity of the mathematical models. Because the amount of computational effort required to analyze these processes increases much more swiftly than the size of the corresponding system, the problems arising in complex technological systems may become either impossible or uneconomical to solve, even with modern computers. It is common procedure in practice to work with mathematical models that are simpler, but less accurate, than the best available model of a given technological system. In going from the most complex to the most simplified model, the trade-off is between computational convenience and modelling adequacy [l-3]. Also, not only should a model be faithful in terms of the physical reality
111
that it represents, but it should also provide the designer, planner or the analyst with enough information to enable him to act on the system in a knowledgeable way. In other words, a satisfactory model is one that provides a good aid to the designer or analyst, and at the same time achieves the right level of trade-off between accuracy and computational convenience. In many practical situations, mathematical models cannot provide all the required answers, but there cannot be good answers without mathematical models. Therefore, in the examination and design of complex processes in chemical industry, the methods of analysis and design should somehow take advantage of special features in the physical system, leading to simplification of the computing requirements. One important class of special features is the system structure. Lack of understanding of the structure of the underlying system can often lead to wrong conclusions regarding problem solution. Theoretical models used for the design of control systems are most often simplified by neglecting non-linearities, time-varying parameters and higherorder dynamics. Thus, the practicing engineer is always confronted with the problem of mismatch between the approximate model and the real plant, which he has to address carefully during the design of controllers. The critical point is that the controller is designed from the model but implemented on the real plant. If the controller design does not take into account the modelling errors, the closed-loop performance of the plant deteriorates from that produced by the model and often the onset of instability prevails. As is known, the ability of a given system to maintain its important properties, such as stability, optimality, controllability, etc., despite modelling uncertainties is referred to as the robustness [ 4-61 of the system with respect to these properties. Design of robust controllers is a pressing problem and it is now receiving more and more recognition in control theory. SIMULATION AND OPTIMIZATION
Simulation, a system analysis approach, can provide a comprehensive view of a complex technological system. In essence, simulation is an iterative problem-solving process which involves problem formulation, mathematical modelling, refinement and testing of the resulting model, and creative design and execution of simulation experiments intended to provide the answer to the questions posed. This approach requires specialized knowledge from various professions and disciplines, i.e., creative interaction among systems analysts, computer specialists, chemical engineers and other specialists. In many real-life situations, planners and decision-makers are forced to make important decisions on the basis of a wide range of alternative plans and management strategies. In these cases, especially when large-scale technological systems are considered, the simulation approach can be time-consuming and not very efficient. Brute-force simulation often generates so much information
112
and so many possible alternatives that it is difficult to know how to begin the analysis. Therefore, a systematic way is often required to find the “best” solution. With current computing technology and methodology, simulation models can also be used in an optimization mode. Development of mathematical programming and optimal control theory has focused attention on more precise statements of design problems, i.e., design criteria. This approach presupposes some criterion (index performance) to be maximized or minimized. Therefore, it is usually necessary to decide on a selection on the basis of which a choice can be made from among the many alternatives that are normally possible. In other words, in this mode, the model is programmed to search automatically for a solution which optimizes the selected criterion, such as time, energy, profit, cost, etc. In addition, in many cases, an optimal policy is one that minimizes or maximizes the performance criterion without violating any chosen constraints. However, it should be emphasized that optimal implies neither “good” nor “bad” but may simply be a way of selecting one policy from a number of satisfactory scenarios. Another point is also very important. Once the optimization problem has been posed in a satisfactory way, its solution may be difficult because of the size (i.e., dimensionality ) of the complex technological system considered. Various simplifications of the optimization methodology have been proposed. However, in the strictly mathematical sense, what is optimal in a simplified scheme, will not generally be an optimal solution to the original problem. Adequate experience is sadly lacking in this area and a great deal of further work is needed. Simulation is also widely used for verification of new control schemes. The complexity and variety of processes in chemical industry renders standard mathematical analysis of the designs often impractical. In that case, the only resource for testing and verification is simulation, whether exclusively on a computer or in a test bed. The latter combines computer simulation of some subsystems and functions with actual components and software. These largescale simulation systems with their many degrees of freedom have raised serious technical problems about the design of experiments and the sequence in which they should be conducted in order to obtain the maximum relevant information. CONTROL SYSTEMS
The process industries have historically recognized the importance of process control in order to achieve successfully functioning production. In engineering systems, the paradigm of feedback control addresses the problem of using the information about the output to design or modify the input for a given task. The central motivation for using feedback in control systems arises from its ability to reduce the impact of uncertainties present in the process and its
113
environment. (Here, uncertainties mean external disturbances and variations in process parameters, as well as differences between the mathematical design model and the corresponding physical system.) One of the goals of control theory has been to capture major elements of the engineering process of feedback design under the umbrella of a formal problem in mathematical synthesis. The motivation for this goal is self-evident. Once formulated under such an umbrella, the elements of engineering art become rigorous tools which can be applied more or less automatically to every more complex design situation. Today, chemical engineers are considerably interested in the use of modern, optimal control theory. The application of this theory requires an adequate definition of the problem in physical terms and a translation of this physical description into mathematical terms [7]. Similarly, the aim of the physical process must be mathematically tractable. The subsequent search for the control mechanism to attain the desired goal constitutes the fundamental problem of optimal control theory. However, the problem in using the state-space mathematical models in the design of control systems is that relatively complicated calculations are required. Moreover, in many practical situations, the specifications of the behaviour of the control system are not quite clear in terms of the performance index. An even greater drawback is that the use of the criterion function optimization allows the designer to pick out only one optimal solution. In process control, there are reasons, mainly practical, which require change in the controller parameters. Four examples illustrate this: (a) the control system has to be applicable to other similar processes which do not have wellknown models; (b) subsequent changes of the controller parameters by the operators must be possible; (c) if the parameters of the controllers have to be found by experiments, some starting points and directions for search should be known in advance; and (d) because of lack of vital information on what the designer will have to pay, in engineering terms, for the various aspects of the desired performance of the final system, he may be unable, at the beginning of the investigation, to specify what he wants in terms of the desired final behaviour. Therefore, besides the use of a criterion function optimization, additional aspects must be considered in the feedback designs. This emphasizes the necessity for further analysis and trial-and-error “hedging” about the nominal solution [8]. No matter how powerful the design methodology is, a typical application requires several iterations. Hence, it is imperative that the procedures for control design are transparent and are conducive to educated trialand-error design iterations, and that the number of design parameters be kept at an absolute minimum. The theory of controllability, observability and feedback stabilization of linear state-space models answers the question of whether or not a linear model,
114
if unstable, can be stabilized and whether it can perform a given tracking or regulation task. However, models of realistic chemical systems are seldom known completely and, if known, they are seldom linear. Control theorists are now challenged to expand their horizons and to extend their concepts and methods to be applicable to incompletely modelled systems and to systems which have initially poorly defined models. Developments in computer technology have made possible a whole range of new approaches and applications. Thanks to faster and cheaper computers, the new control laws can incorporate adaptation leading to on-line learning and to better control. However, computer-aided procedures for off-line design of multivariable control laws can involve a more comprehensive experienceguided search for robust and fault-tolerant control structures. Therefore, control engineers need systematic design procedures for designing high-performance feedback control systems for both single-input/singleoutput (SISO ) and multi-input/multi-output (MIMO ) systems. It is also essential that readily available and reliable computer-aided design software be used for the design process. From the viewpoint of the practicing engineer, the availability of first-generation computer-aided control engineering software (LOGALPHA, MATLAB, MATRIX-X, CTRL-C, Program CC, to mention a few) has vastly accelerated the progress of applications. This research was supported in part by the U.S./Yugoslav Joint Fund for Scientific and Technological Cooperation, in cooperation with DOE under Grant PP-727.
REFERENCES 1 2 3 4 5 6 7
M. Aoki, IEEE Trans. Automat. Control, 13 (1968) 246. Dj. Petkovski, Comput. Chem. Eng., 2 (1978) 123. Dj. Petkovski, Int. J. Control, 30 (1979) 661. Dj. Petkovski, Automatika, 24 (1983) 103. Dj. Petkovski and M. Athans, Elec. Power Syst. Res., 9 (1985) 253. Dj. Petkovski, IEE Proc., Part D, 134 (1987) 53. B.D.O. Anderson and J.B. Moor, Linear Optimal Control, Prentice-Hall, NJ, 1971. 8 Dj. Petkovski, Proc. World. Con. Chem. Eng. Tokyo, 1986, p. 634.
Englewood Cliffs,