mit symposium 2040 visions of process systems engineering...

MIT Symposium2040 Visions of Process Systems Engineering

George’s Impact

Manfred MorariElectrical & Systems EngineeringUniversity of Pennsylvania

June 1, 2017

George’s Formative Years

1965 1974 1977

MIT Symposium2040 Visions of Process Systems Engineering

George’s Impact

Manfred MorariElectrical & Systems EngineeringUniversity of Pennsylvania

June 1, 2017

Outline• My Time with George at U of MN• Past Attempts to Predict the Future• Predicting the Future

Outline

• My Time with George at U of MN• Past Attempts to Predict the Future• Predicting the Future

My advisors at the U of Minnesota 1975-77

George Stephanopoulos

Rutherford “Gus” Aris 1929-2005

Accompanying Note ~ 1995

Technology: Digital Control ComputerIBM 1800 (introduced 1964)

[wikipedia]

Computer Control ~1968Standard Oil of California

Courtesy: Chevron

Advanced Process Control Textbookswith Origins at U of Minnesota

1969 1981

Critique of (Process) ControlJOURNAL CRITIQUE

Critique of Chemical Process Control Theory A. S. FOSS

Department of Chemical Engineering University of California, Berkeley, California 94720

When it is stated, as it has been in more than one recent publication, that there is a wide gap between the theory of process control and its application, one is left with the unmistakable impression that those who conceive the theory are in some sense leagues ahead of those who would use it. That the contrary is the case is the thesis of this essay. Indeed, the theory of chemical process control has some rugged terrain to traverse before it meets the needs of those who would apply it.

PROBLEMS OF CHEMICAL PROCESS CONTROL

The needs are intimately related to the problems, and the problems, as usual, wear a sometimes effective camou- flage. Superficially the pioblem of chemical procesy control appears to involve the regulation of complex, often poorly understood physicochemical processes in the face of many unknown and uncharacterized disturbances. The word regulation has several interpretations when applied to industrial processes, but it usually implies the desire to hold constant certain states or perhaps a time-average of the states. Disturbances may consist of slow drifts such as those originating in diurnal temperature changes, of monadnocks illustrated by the explosive vaporization of a slug of water in the feed to a crude still, or of persistent random upsets such as the step-like fluctuation in pressure in utility headers. Sometimes disturbances result from a purposeful change in the level of operation, but with the exception of batch operations, these changes are infre- quent. In addition to the continuous regulation tasks, there are the tasks of start-up and shut-down. In all of these activities, there is the dominating necessity for safe operation in the event of malfunction or failiue of any part of the process or control system.

But there is much beneath the surface. One finds that the processes possess dynamic components and that in the design of control systems attention must be given to this characteristic. In one view the dynamic characteristics are seen to affect adversely the controllability of the process owing to lagging of process states to corrective commands. In another view the dynamic characteristics are welcomed as fortunate endowments that lend a degree of stability to processes and that sometimes can be ex- ploited for useful purposes. And because the dynamics of a process are directly influenced by its design, the control system designer finds that his sphere of responsibility encompasses process design as well. Indeed, m a o r j contributions to effective control system performance often derive from perceptive and clever modifications of the process itself.

But perception is difficult to acquire in this field because the dynamic behavior of chemical processes is not simple. There are many variables whose dynamic behavior is of consequence. The behavior of any one variable is influenced by many others through the innumerable physical and chemical interactions found in these processes. The interactions in a modern methanol process, for

instance, are complex enough to tax one’s ability to untangle the relationships even at steady conditions (Shah and Stillman, 1970). ‘The inert level in the synthesis loop may be regulated by manipulation of the purge rate, but since the purge constitutes a large fraction ok the reformer fuel flow, one finds that such an adjustment influences the temperature and methane content of the reformer process effluent stream. Steam production in the waste heat boilers is thus upset and so too are the compressors driven by that steam. The compressors are also upset by the change in recycle rate in the synthesis loop. The resultant flow changes influence temperature rises in the synthesis reactor, leading perhaps to higher temperatures at which the side reactions that produce ether and methane contribute significantly to the total heat libera- tion and to reduction in methanol production. Further, the upsets in the reformer lead to concentration disturbances in the synthesis loop makeup gas , which also disturbs the methanol production rate.

Now add to these static interactions the influence of a 20-minute thermal lag in the reformer, the composition and thermal lags in the carbon dioxide absorber-stripper system, the treacherous feed-effluent heat exchange in a synthesis reactor that can exhibit wrong-way (nonmini- mum phase) temperature effects, and the long-lived composition transient in the synthesis loop. Even were the process well understood, the dynamic cause-effect relationships would be difficult to untangle.

But such processes are not completely understood. The coke level on the reformer catalyst is likely unknown, different from furnace to furnace, and drifting; the firing distribution of the burners in the reformer changes in an undefined way with fuel flow changes; and the carbon dioxide separation efficiency is a poorly understood function of changing flows and absorbent concentrations. Uncertainties in other processes are, for example, the course and rate of the solid reactions in cement kilns, the reactions and their dependence on the hydrodynamics in multiphase hydrocracking reactors, and the dependence of conversion on the flow regime in fluid bed reactors. And it is well recognized that no amount of detailed study will ever replace all uncertainties with certainties. Rather, it is for the control system designer to recognize the significant uncertainties and to conceive controls that function effectively nonetheless.

While it is the presence of coupling among many variables that is primarily responsible for the near in- scrutable complexity of dynamic processes, the nature of the coupling as well often plays a significant role. By nature and by design the coupling among most variables in chemical processes is nonlinear: temperature-reaction rate, feed enthalpy-vapor/liquid split, temperature- equilibrium conversion, boilup rate-overhead concentration, and on and on. Such effects often need direct attention; indeed, the stability of exothermic chemical reactors may be assured only through consideration of the nonlinear dependence of the chemical reaction rate

March, 1973 Page 209 AlChE Journal (Vol. 19, No. 2)

JOURNAL CRITIQUE

Critique of Chemical Process Control Theory A. S. FOSS

Department of Chemical Engineering University of California, Berkeley, California 94720

When it is stated, as it has been in more than one recent publication, that there is a wide gap between the theory of process control and its application, one is left with the unmistakable impression that those who conceive the theory are in some sense leagues ahead of those who would use it. That the contrary is the case is the thesis of this essay. Indeed, the theory of chemical process control has some rugged terrain to traverse before it meets the needs of those who would apply it.

PROBLEMS OF CHEMICAL PROCESS CONTROL

The needs are intimately related to the problems, and the problems, as usual, wear a sometimes effective camou- flage. Superficially the pioblem of chemical procesy control appears to involve the regulation of complex, often poorly understood physicochemical processes in the face of many unknown and uncharacterized disturbances. The word regulation has several interpretations when applied to industrial processes, but it usually implies the desire to hold constant certain states or perhaps a time-average of the states. Disturbances may consist of slow drifts such as those originating in diurnal temperature changes, of monadnocks illustrated by the explosive vaporization of a slug of water in the feed to a crude still, or of persistent random upsets such as the step-like fluctuation in pressure in utility headers. Sometimes disturbances result from a purposeful change in the level of operation, but with the exception of batch operations, these changes are infre- quent. In addition to the continuous regulation tasks, there are the tasks of start-up and shut-down. In all of these activities, there is the dominating necessity for safe operation in the event of malfunction or failiue of any part of the process or control system.

But there is much beneath the surface. One finds that the processes possess dynamic components and that in the design of control systems attention must be given to this characteristic. In one view the dynamic characteristics are seen to affect adversely the controllability of the process owing to lagging of process states to corrective commands. In another view the dynamic characteristics are welcomed as fortunate endowments that lend a degree of stability to processes and that sometimes can be ex- ploited for useful purposes. And because the dynamics of a process are directly influenced by its design, the control system designer finds that his sphere of responsibility encompasses process design as well. Indeed, m a o r j contributions to effective control system performance often derive from perceptive and clever modifications of the process itself.

But perception is difficult to acquire in this field because the dynamic behavior of chemical processes is not simple. There are many variables whose dynamic behavior is of consequence. The behavior of any one variable is influenced by many others through the innumerable physical and chemical interactions found in these processes. The interactions in a modern methanol process, for

instance, are complex enough to tax one’s ability to untangle the relationships even at steady conditions (Shah and Stillman, 1970). ‘The inert level in the synthesis loop may be regulated by manipulation of the purge rate, but since the purge constitutes a large fraction ok the reformer fuel flow, one finds that such an adjustment influences the temperature and methane content of the reformer process effluent stream. Steam production in the waste heat boilers is thus upset and so too are the compressors driven by that steam. The compressors are also upset by the change in recycle rate in the synthesis loop. The resultant flow changes influence temperature rises in the synthesis reactor, leading perhaps to higher temperatures at which the side reactions that produce ether and methane contribute significantly to the total heat libera- tion and to reduction in methanol production. Further, the upsets in the reformer lead to concentration disturbances in the synthesis loop makeup gas , which also disturbs the methanol production rate.

Now add to these static interactions the influence of a 20-minute thermal lag in the reformer, the composition and thermal lags in the carbon dioxide absorber-stripper system, the treacherous feed-effluent heat exchange in a synthesis reactor that can exhibit wrong-way (nonmini- mum phase) temperature effects, and the long-lived composition transient in the synthesis loop. Even were the process well understood, the dynamic cause-effect relationships would be difficult to untangle.

But such processes are not completely understood. The coke level on the reformer catalyst is likely unknown, different from furnace to furnace, and drifting; the firing distribution of the burners in the reformer changes in an undefined way with fuel flow changes; and the carbon dioxide separation efficiency is a poorly understood function of changing flows and absorbent concentrations. Uncertainties in other processes are, for example, the course and rate of the solid reactions in cement kilns, the reactions and their dependence on the hydrodynamics in multiphase hydrocracking reactors, and the dependence of conversion on the flow regime in fluid bed reactors. And it is well recognized that no amount of detailed study will ever replace all uncertainties with certainties. Rather, it is for the control system designer to recognize the significant uncertainties and to conceive controls that function effectively nonetheless.

While it is the presence of coupling among many variables that is primarily responsible for the near in- scrutable complexity of dynamic processes, the nature of the coupling as well often plays a significant role. By nature and by design the coupling among most variables in chemical processes is nonlinear: temperature-reaction rate, feed enthalpy-vapor/liquid split, temperature- equilibrium conversion, boilup rate-overhead concentration, and on and on. Such effects often need direct attention; indeed, the stability of exothermic chemical reactors may be assured only through consideration of the nonlinear dependence of the chemical reaction rate

March, 1973 Page 209 AlChE Journal (Vol. 19, No. 2)

Design Concepts for Process Control

A. Kestenbaum,’ R. Shinnar,*l and F. E. Thau2

Depadments of Chemical Engineering and Electrical Engineering, The City College of The City University of New York, New York. New York 10031

Six criteria are offered for the evaluation of the performance of process controllers. Classical techniques for the design of PID controllers and modern control theoretic techniques for controller design are reviewed. It is shown that modern optimal control algorithms often do not lead to useful controller designs. They are useful only as tools in heuristic design methods. Their main problem is sensitivity to the nature of the process transfer function and the lack of conservative design methods. The problems faced in developing better algorithms are outlined.

1. Introduction In recent years there has been a growing literature on the

applications of optimal control techniques in the process industries (Bryson, 1967; Cegla, 1969; Denn, 1972; Doug- lass, 1972; Gould, 1969; Lim, 1970; Lapidus, 1967; Lueck, 1968). However, it is generally felt that these methods have not made the expected impact on the industrial practice of process control, a problem which was the subject of panel discussions a t several recent AIChE meetings (National Science Foundation Workshop, 1973; Foss, 1973).

Often the hypothesis is raised that the lack of applications is due to the lack of sophistication of the practitioner and might be the result of the normal time lag between the conception of modern control system design techniques in the academic community and their industrial application. Some are less generous and claim that the problems dealt with in the academic world are too far removed from reality to lead to useful results. One of the authors (R.S.) has been involved in industry for many years and has often tried to apply some of these optimal control techniques with rather limited success and reluctantly has come to the conclusion that in the present state of the art it is quite difficult to apply optimal control theory to an industrial problem. I t is not that the techniques are not useful. In fact, they often contribute significantly to our understanding of the problem. I t is rather that they are often not in a state where their application is straightforward enough to allow their use in a reasonable amount of time without extensive study and research, and where straightforward application might even lead to serious troubles.

We therefore need to rethink our approach to the problem, and this paper is intended to be a first start in this direction. We will try to present a critical review of the application of modern control theory techniques to process control, and, although the paper contains considerable amounts of heretofore unpublished work of our own, it is not a regular research paper, but rather a special type of review.

We do not intend to cover the whole spectrum of process control, but we choose to concentrate on a rather simple and almost trivial problem: the design of analog controllers for single-input single-output systems, and specially over- damped systems. An example of such a system is the transfer function

Department of Chemical Engineering. Department of Electrical Engineering.

2 Ind. Eng. Chem., Process Des. Dev., Vol.

(1.1)

15, No. 1, 1976

It is trivial in the sense that classical frequency response methods lead to satisfactory designs. Interestingly enough, a considerable part of our optimal control literature deals with examples of this type (Lim, 1970; Lueck, 1968; Cegla, 1969; Koppel, 1968; Kalman, 1960).

We started our own research with the same type of problem for the reason that a well understood example is the best test for any algorithm. If the algorithm fails to produce reasonable process performance we can thoroughly analyze the example system and hopefully understand why.

We are fully aware that the interesting problems are far more complex and that optimal control has been applied to multiple-input, multiple-output problems. We will show, however, that our approach and conclusions also apply to those cases.

An important feature of a good control system design algorithm is that it provides the practicing engineer with a framework within which to cast his problem and provides a systematic design procedure which can be applied to a larg- er number of similar problems. If, however, an algorithm gives unsatisfactory results, we have to understand why, and put proper safeguards into the design algorithm. Hence, in section 2 below we state our interpretation of the principal desirable characteristics that should be achieved by a process controller. In section 3 we describe and compare various design methods for the classic PID controller in terms of their achieving these goals. In section 4 we describe some approaches to the design of process controllers using frequency-domain and time-domain optimization procedures. Section 5 contains an evaluation of three com- peting process controller designs for a simplified problem. Our conclusions are summarized in section 6.

2. Design Criteria for Process Control Before discussing in detail the advantages or disadvan-

tages of specific controllers, let us restate the aims and goals of process control and the specifications that such a controller must fulfill. We will list them first without any intention of ranking them. Again, we are referring here to a simple continuous feedback controller, as discussed in the optimal control literature (Horowitz, 1963; Hougen, 1964; Ziegler, 1942; Cohen, 1952), which may be part of a more complex system but which can be designed separately.

I t is important to remember that in process control we seldom totally rely on such controllers, and that they nor- mally are part of a more complex scheme which is managed by an operator who achieves the desired control of the total process by adjusting the set-points of individual controllers. Interestingly, contrary to quality control in mass production by machine tools, there has been little systematic research on the way an operator should or does control a

Design Concepts for Process Control

A. Kestenbaum,’ R. Shinnar,*l and F. E. Thau2

Depadments of Chemical Engineering and Electrical Engineering, The City College of The City University of New York, New York. New York 10031

Six criteria are offered for the evaluation of the performance of process controllers. Classical techniques for the design of PID controllers and modern control theoretic techniques for controller design are reviewed. It is shown that modern optimal control algorithms often do not lead to useful controller designs. They are useful only as tools in heuristic design methods. Their main problem is sensitivity to the nature of the process transfer function and the lack of conservative design methods. The problems faced in developing better algorithms are outlined.

1. Introduction In recent years there has been a growing literature on the

applications of optimal control techniques in the process industries (Bryson, 1967; Cegla, 1969; Denn, 1972; Doug- lass, 1972; Gould, 1969; Lim, 1970; Lapidus, 1967; Lueck, 1968). However, it is generally felt that these methods have not made the expected impact on the industrial practice of process control, a problem which was the subject of panel discussions a t several recent AIChE meetings (National Science Foundation Workshop, 1973; Foss, 1973).

Often the hypothesis is raised that the lack of applications is due to the lack of sophistication of the practitioner and might be the result of the normal time lag between the conception of modern control system design techniques in the academic community and their industrial application. Some are less generous and claim that the problems dealt with in the academic world are too far removed from reality to lead to useful results. One of the authors (R.S.) has been involved in industry for many years and has often tried to apply some of these optimal control techniques with rather limited success and reluctantly has come to the conclusion that in the present state of the art it is quite difficult to apply optimal control theory to an industrial problem. I t is not that the techniques are not useful. In fact, they often contribute significantly to our understanding of the problem. I t is rather that they are often not in a state where their application is straightforward enough to allow their use in a reasonable amount of time without extensive study and research, and where straightforward application might even lead to serious troubles.

We therefore need to rethink our approach to the problem, and this paper is intended to be a first start in this direction. We will try to present a critical review of the application of modern control theory techniques to process control, and, although the paper contains considerable amounts of heretofore unpublished work of our own, it is not a regular research paper, but rather a special type of review.

We do not intend to cover the whole spectrum of process control, but we choose to concentrate on a rather simple and almost trivial problem: the design of analog controllers for single-input single-output systems, and specially over- damped systems. An example of such a system is the transfer function

Department of Chemical Engineering. Department of Electrical Engineering.

2 Ind. Eng. Chem., Process Des. Dev., Vol.

(1.1)

15, No. 1, 1976

It is trivial in the sense that classical frequency response methods lead to satisfactory designs. Interestingly enough, a considerable part of our optimal control literature deals with examples of this type (Lim, 1970; Lueck, 1968; Cegla, 1969; Koppel, 1968; Kalman, 1960).

We started our own research with the same type of problem for the reason that a well understood example is the best test for any algorithm. If the algorithm fails to produce reasonable process performance we can thoroughly analyze the example system and hopefully understand why.

We are fully aware that the interesting problems are far more complex and that optimal control has been applied to multiple-input, multiple-output problems. We will show, however, that our approach and conclusions also apply to those cases.

An important feature of a good control system design algorithm is that it provides the practicing engineer with a framework within which to cast his problem and provides a systematic design procedure which can be applied to a larg- er number of similar problems. If, however, an algorithm gives unsatisfactory results, we have to understand why, and put proper safeguards into the design algorithm. Hence, in section 2 below we state our interpretation of the principal desirable characteristics that should be achieved by a process controller. In section 3 we describe and compare various design methods for the classic PID controller in terms of their achieving these goals. In section 4 we describe some approaches to the design of process controllers using frequency-domain and time-domain optimization procedures. Section 5 contains an evaluation of three com- peting process controller designs for a simplified problem. Our conclusions are summarized in section 6.

2. Design Criteria for Process Control Before discussing in detail the advantages or disadvan-

tages of specific controllers, let us restate the aims and goals of process control and the specifications that such a controller must fulfill. We will list them first without any intention of ranking them. Again, we are referring here to a simple continuous feedback controller, as discussed in the optimal control literature (Horowitz, 1963; Hougen, 1964; Ziegler, 1942; Cohen, 1952), which may be part of a more complex system but which can be designed separately.

I t is important to remember that in process control we seldom totally rely on such controllers, and that they nor- mally are part of a more complex scheme which is managed by an operator who achieves the desired control of the total process by adjusting the set-points of individual controllers. Interestingly, contrary to quality control in mass production by machine tools, there has been little systematic research on the way an operator should or does control a

84 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. AC-20, NO. 1, FEBRUARY 1975

Perspectives

Superiority of Transfer Function Over State-Variable Methods in Linear Time-Invariant

Feedback System Design ISAAC M. HOROWITZ, FELLOW, IEEE, AND URI SHAKED

Abstm-The objectives and achievements of state-variable methods in linear time-invariant feedback system synthesis are examined. It is argued that the philosophy and objectives associated with eigenvalne realization by state feedba&, with or without observers, are highly naive and incomplete in the practical -ontext of control systems. Furthermore, even the objectives undertaken have not really been attained by the state-variable tedmiques which have been developed. The extremely important factors of sensor noise and loop bandwidths are obscured by the state-variable formnlalion and have been ignored in the state-variable literature. The basic fundamental problem of sensitivity in the face of significant plant p%rameter uncertainty has hardly received any attention. Instead, the literatme bas concentrated primarily on differential sensitivity functions and even those results are so highly obscured in the state-variable formation as to lead to incorrect conclusions.

In contrast, the important practical considerations and constraints have k n clearly revealed and considered in the -fer function formulation. Differentid sensitivity results are simple and transparent. For single input-utput systems, there exists an exact design technique for achieving quantitative sensitivity speeircations in the face of signircant parameter

problem is mu& more difficult and bas not been completely solved for multivariable systems, but it has at least been realistidy attacked by some transfer function methods.

Finally, the concepts of controllability and observability so much emphasized in the state-variable literature are examined. It is argued that their importance in this problem class has been greatly exaggerated. On the one hand, transfer function methods can be nsed to check for their existence. On the other hand, nothing is lost when they are ignored, if the synthesis problem is lreated as one witfi parameter uncertainty by transfer function methods.

uncertainty, which is optimum in an important practical sense. This

I. INTRODUCTION

S TAT€-VARIABLE formalism was introduced in feedback control theory primarily in the study of nonlinear

system stability by Lyapunov’s method and in optimal control theory. Kalman used state-variable formalism for

recommended by S . J. Kahne, Chairman of the IEEE S-CS Urban and Manuscript received September 18, 1973; revised July 26, 1974. Paper

Social Systems Committee. This work was supported in part by the National Science Foundation under Grant GK-33485 A-1 at the Un- iversity of Colorado, and in part by the European Office of Aerospace Research (AFSC) under Grant AFOSR 73-2549 at the Weizmann Insti- tute.

I. M. Horowitz is with the Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel, and the Department of Electrical Engineering, University of Colorado, Boulder, Colo. 80302.

mann Institute of Science, Rehovot, Israel. He is now with the Engineer- U. Shaked was with the Department of Applied Mathematics, Weiz-

ing Department Control Group, Cambridge University, Cambridge, En- gland.

his work on controllability and observability. State variables are the natural formulation for these problems. However, since then there has been an enormous literature on linear time-invariant feedback system design using the state-variable formalism. This paper reviews the topics which have received a great deal of attention by state- space methods: eigenvalue realization by state feedback, observers for states which may not be sensed, and de- coupling theory (Section II), sensitivity theory (Section III), and controllability and observability (Section V). While these problems are very interesting from the mathematical viewpoint, it is argued here that some of them are not significant from the feedback control engineering viewpoint. In others, the state-variable formalism greatly obscures the problem, whereas much more transparent results are obtained by transfer function methods. A review is given (Section IV) of transfer function methods for satisfying system response specifications over a range of plant parameter uncertainty. This is the central basic problem in feedback system design to which state-variable methods have made essentially no significant contributions.

The following fairly standard state-variable system description is used. with the bracketed subscripts giving the number of rows and columns of the matrix. The system states are denoted by x , the plant input control vector by u. and the system output by y , with the relations

= A (nn)X + B(nm)u(ml ) ( 1 4

Y ( p l ) = C(pn)X (1b)

giving the “plant” matrix of transfer functions

Y ( p I ) = P ( p m ) U ( m l )

P ( s ) = C ( s I - A ) - ’ B

= CAdj(s1-A)B/det(sl-A) N ( s ) / d ( s ) (2b)

where Y , U, R denote the respective vectors of transforms.

84 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. AC-20, NO. 1, FEBRUARY 1975

Perspectives

Superiority of Transfer Function Over State-Variable Methods in Linear Time-Invariant

Feedback System Design ISAAC M. HOROWITZ, FELLOW, IEEE, AND URI SHAKED

Abstm-The objectives and achievements of state-variable methods in linear time-invariant feedback system synthesis are examined. It is argued that the philosophy and objectives associated with eigenvalne realization by state feedba&, with or without observers, are highly naive and incomplete in the practical -ontext of control systems. Furthermore, even the objectives undertaken have not really been attained by the state-variable tedmiques which have been developed. The extremely important factors of sensor noise and loop bandwidths are obscured by the state-variable formnlalion and have been ignored in the state-variable literature. The basic fundamental problem of sensitivity in the face of significant plant p%rameter uncertainty has hardly received any attention. Instead, the literatme bas concentrated primarily on differential sensitivity functions and even those results are so highly obscured in the state-variable formation as to lead to incorrect conclusions.

In contrast, the important practical considerations and constraints have k n clearly revealed and considered in the -fer function formulation. Differentid sensitivity results are simple and transparent. For single input-utput systems, there exists an exact design technique for achieving quantitative sensitivity speeircations in the face of signircant parameter

problem is mu& more difficult and bas not been completely solved for multivariable systems, but it has at least been realistidy attacked by some transfer function methods.

Finally, the concepts of controllability and observability so much emphasized in the state-variable literature are examined. It is argued that their importance in this problem class has been greatly exaggerated. On the one hand, transfer function methods can be nsed to check for their existence. On the other hand, nothing is lost when they are ignored, if the synthesis problem is lreated as one witfi parameter uncertainty by transfer function methods.

uncertainty, which is optimum in an important practical sense. This

I. INTRODUCTION

S TAT€-VARIABLE formalism was introduced in feedback control theory primarily in the study of nonlinear

system stability by Lyapunov’s method and in optimal control theory. Kalman used state-variable formalism for

recommended by S . J. Kahne, Chairman of the IEEE S-CS Urban and Manuscript received September 18, 1973; revised July 26, 1974. Paper

Social Systems Committee. This work was supported in part by the National Science Foundation under Grant GK-33485 A-1 at the Un- iversity of Colorado, and in part by the European Office of Aerospace Research (AFSC) under Grant AFOSR 73-2549 at the Weizmann Insti- tute.

I. M. Horowitz is with the Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel, and the Department of Electrical Engineering, University of Colorado, Boulder, Colo. 80302.

mann Institute of Science, Rehovot, Israel. He is now with the Engineer- U. Shaked was with the Department of Applied Mathematics, Weiz-

ing Department Control Group, Cambridge University, Cambridge, En- gland.

his work on controllability and observability. State variables are the natural formulation for these problems. However, since then there has been an enormous literature on linear time-invariant feedback system design using the state-variable formalism. This paper reviews the topics which have received a great deal of attention by state- space methods: eigenvalue realization by state feedback, observers for states which may not be sensed, and de- coupling theory (Section II), sensitivity theory (Section III), and controllability and observability (Section V). While these problems are very interesting from the mathematical viewpoint, it is argued here that some of them are not significant from the feedback control engineering viewpoint. In others, the state-variable formalism greatly obscures the problem, whereas much more transparent results are obtained by transfer function methods. A review is given (Section IV) of transfer function methods for satisfying system response specifications over a range of plant parameter uncertainty. This is the central basic problem in feedback system design to which state-variable methods have made essentially no significant contributions.

The following fairly standard state-variable system description is used. with the bracketed subscripts giving the number of rows and columns of the matrix. The system states are denoted by x , the plant input control vector by u. and the system output by y , with the relations

= A (nn)X + B(nm)u(ml ) ( 1 4

Y ( p l ) = C(pn)X (1b)

giving the “plant” matrix of transfer functions

Y ( p I ) = P ( p m ) U ( m l )

P ( s ) = C ( s I - A ) - ’ B

= CAdj(s1-A)B/det(sl-A) N ( s ) / d ( s ) (2b)

where Y , U, R denote the respective vectors of transforms.

1973

1976

1976

1975

Theory-Practice Gap

Main theme of CPC I in 1976

Explosive development of theory had taken place

• Industry did not understand theory• Academia had no clue about

real controller design

Exceptions: Åström, Gilles, Balchen,…

George’s Research Theme in the 1970s

“The research community is studying the wrong problems”

Importance of Timing and a Good Start

If you are to do important work then you must work on the right problem at the right time and in the right way. Without any one of the three, you may do good work but you will almost certainly miss real greatness. An important aspect of any problem is that you have a good attack, a good starting place, some reasonable idea of how to begin.

A Stroke of Genius: Striving for Greatness in All You Do R. W. Hamming October 1993

Socratic Method: Learning by Debate

Success is a journey, not a destination. The doing is often more important than the outcome.

Arthur Ashe

Major Themes of George’s Research Program in the 1970s

“The research community is studying the wrong problem”

• Architectures– Control Structure– Decomposition for optimization

• Design for Control

Decomposition

Solubilization and Microemukions, Vol. 2, Plenum, New York ( 1976).

Ruckenstein, E. and J. C. Chi, “Stability of Microemulsions,” J. Chem. SOC. Faraduy Trans. I I , 71, I690 (1975).

Ruckenstein, E., “Stability Phase Equilibria, and Interfacial Free Energy in Microemulaions,” pp. 755ff in K. L. Mittal ( ed. ), Micellization, Solubilization and Microemulsions, Vol. 2, Plenum, New York ( 1976).

Ruckenstein, E., “The Origin of Thermodynamic Stability of Microemulsions,” Chem. Phys. Letters, 57, 517 (1978).

Ruckenstein, E., “On the Thermodynamic Stability of Micro- emulsions,” J. C d l . Interface Sci., 66, 369 (1978).

Saito, H. and K. Shinoda, “The Stability of w/o Type Emul- sions as a Function of Temperature and of the Hydrophilic Chain Length of the Emulsifier,” J. Coil. Interfoce Sci., 32, 647 ( 1970).

Salter, S. J., “The Influence of the Type and Amount of Al- cohol on Surfactant-Oil-Brine Phase Behavior and Proper- ties,” Soc. Petrol. Eng., Preprint 6843, Annual Meeting, Denver ( 1977).

Schulman, J. H., W. Stroeckenius, and L. M. Prince, “Mech- anism of Formation and Structure of Microemulsions by Electron Microscopy,” J. Phys. Chem., 63, 1677 (1959).

Schulman, J. H. and J . B. Montagne, “Formation of Microemul- sions by Amino Alkyl Alcohols,” Ann. New York Acad. Sci., 92,366 ( 1961).

Scriven, L. E., “Equilibrium Bicontinuous Structures,” Nature, 263,123 (1976).

Talmon, Y. and S. Prager, “Statistical Mechanics of Micro- emulsions,” Nature, 267, 333 ( 1977).

Talmon, Y. and S. Prager, “Statistical Thermodynamics of Phase Equilibria in Microemulsions,” J. Chem. Phys., 69, 2984 ( 1978 ),

Winsor, ‘P. A.,’ “Hydrotropy, Solubilization, and Related Emul- sification Processes,” Trans. Faraday SOC., 44, 376 ( 1918 ).

Manuscript receieed April 11 , 1979; reoision received July 26, and uccepted August 30, 1979.

Studies in the Synthesis of Control Structures for Chemical Processes Part I: Formulation of the Problem. Process Decomposition and the Classification of the Control Tasks. Analysis of the Optimizing Control Structures.

Part I of this series presents a unified formulation of the problem of synthesizing control structures for chemical processes. The formulation is rigorous and free of engineering heuristics, providing the framework for generalizations and further analytical developments on this important problem.

Decomposition is the underlying, guiding principle, leading to the classification of the control objectives (regulation, optimization) and the partitioning of the process for the practical implementation of the control structures. Within the framework of hierarchical control and multi-level optimization theory, mathematical measures have been developed to guide the decomposition of the control tasks and the partitioning of the process. Consequently, the extent and-the purpose of the regulatory and optimizing control objectives for a given plant are well defined, and alternative control structures can be generated for the designer’s analysis and screening.

In addition, in t h i s first part we examine the features of various optimizing control strategies (feedforward, feedback; centralized, decentralized) and develop methods for their generation and selective screening. Application of all these principles is illustrated on an integrated chemical plant that offers enough variety and complexity to allow conclusions about a real-life situation.

SCOPE During the last ten years, numerous works have dealt with

the design of control systems to regulate specific unit operations (e.g., distillation), to bring a system (e.g., a reactor) back to the desired operating point in some optimal fashion, to guarantee optimal profiles in nonhomogeneous reactors, etc. The interactions between different pieces of equipment in a chemical plant are complex, and do not allow us to regard plant

All correspondence \huuld be addressed to M . Morari, Department of Chemical

Present address for Arkun: Department of Chemical Engineering, Hensselaer Engineering, University of Wixonsin, Madison, Wscconsin, 5.3706

Polytechnic Institute, Troy, New York, 12181

OOO 1- IS4 I-X0-3238-O220-$0 1.45. RThe American Institute of Chemical Engineers, 1980.

MANFRED MORARI YAMAN ARKUN

GEORGE STEPHANOPOULOS Department of Chemical Engineering

and Materials Science University of Minnesota

Minneapolis, Minn. 55455

control as a simple extension of unit operations control. These interconnections decrease the number of degrees of freedom, and great care must be taken not to over- or under-specify the cmtrol objectives in a process.

All available control theories assume that measured and manipulated variables have been selected, thus not answering one of the basic questions an engineer is facing when designing a plant. Rules of thumb and experience guide the designer’s choice of measured and manipulated variables. Naturally, without a systematic procedure, there is no guarantee that all the feasible alternatives are explored, and even less that the best possible structure is chosen. The lack of sound techniques for solving those problems has been criticized frequently, and

Page 220 March, 1980 AlChE Journal (Vol. 26, No. 2)































































found the framework of the multilayer-multiechelon concept to be very meaningful, convenient, and having the potential for further development. Let us elaborate further on this, and on how it affects the synthesis of control structures.

Multiloyer Decomposition

During chemical plant operation, the basic goal is to optimize an economic measure of the operation (e.g. minimize operating cost, maximize profit), while at the same time satisfying certain equality or inequality constraints (quality and production specifications, environmental regulations, safety etc.). This optimization must be achieved in the presence of external disturbances which enter the plant. Thus, we formulate the optiqization problem to reflect these attitudes during the operatio; of a chemical process

m subject to

f = g’ (x, m, 4 state equations (2) x(0) = xo g”(x, m, d) 5 0 feasibility constraints (3) y = h(x, m, 6) outputs from the process. (4)

where x E Rn is the vector of state (dependent) variables m E R‘ is the vector of manipulated (independent) variables d E Rm is the vector of external disturbances y, E R‘ is the vector of process outputs. @ is the operating cost (performance function) of the process.

Plant control is required because of external disturbances d. Their stochastic nature makes solving the resulting nonlinear stochastic control problem (1) an impossible task. If we partition the disturbance vector in the following fashion (which can always be done by an appropriate change of the coordinate system), a manageable degree of complexity can be reached

and

d , eRml such that lim E { d J = d, # 0, d,(O) = d,o 1-m

& E RmZ such that lim E { & = d, = 0, &(O) = 4 0 t-r

where

d T = idf, 4.

This partition into a stationary (d2) and a nonstationary (d , ) disturbance component is discussed in more detail in Part 111.

The disturbance model underlying d l has its poles on the imaginary axis, while the poles of the model ford, lie strictly in the left half plane. This strict partition into d,, d, is rarely possible from experimental observations alone. A suitable criterion is to assume the poles of the disturbance model, which are several times slower than the time constant of the system, to be effectively zero. The partition defines implicitly two-time scales, the basis of the “temporal hierarchy” (Findeisen 1976) in the control activities on a chemical plant. The disturbance components d, are “fast” varying. They are irrelevant for the long term optimization of the process, because their predicted value is essentially zero after a short time. Regulatory control is used to suppress their influence.

On the other hand, d , contains persistent and/or periodic disturbances which have to be included in the long term optimization. Without much error, we can neglect the time averaging of the objecive function (1) and reformulate it in mathematical terms employing a pseudo steady state assumption.

1) Optimizing Control:

m subject to

I

1 t ‘

1 ADAPTATION

DISTURBANCES d ~ OPTIMIZATION

t REGULATION G REGULATION G c PROCESS

Figure 1. Multiloyer decomposition of the control tosks.

-

g”(x, m, d,) 5 0

Y = h(x, m, 4) -

where d1 = E{dl(T,)}; d l (0 ) = dlo and the time period, To, is large enough for the prediction to be approximately constant and the plant dynamics to be negligible. The optimum solution of the problem (Pl) is

x* = x(m*, d l ) -

Y* = y(m*, 4) 2) Regulatory Control:

m

s.t.

Minimize ./$ {(y - y*)W,(y - y*) + (m - m*)Wz(m - m*)}dt

where W1 andWz are positive definite and symmetric weighting matrices. A natural definition would be

a2 cp u=u*

m=-m* d=d 1

m=m* d=dl

Note that 0 to t , To, i.e. the time horizon for regulation is significantly shorter than for optimization.

The previous discussion indicates that the “multilayer structure” is a natural element of the control activities in a chemical plant and leads to a vertical decomposition of the control tasks. The first (lower) layer takes care of the regulation and allows the process to be considered at pseudo steady state. The second (higher) layer is responsible for determining the optimal set points under the influence of changing disturbances. For a general system, more layers can be realized (Figure l), but they will not be discussed here.

Multiechelon Decomposition

The second type of decomposition is done horizontally, developing multiple echelons for control action in the chemical process. The plant is divided into interacting groups of processing units, for which the optimization is carried out separately. These are coordinated from time to time by a coordinator (see

AlChE Journal (Vol. 26, No. 2) March, 1980 Page 223

JCOORDINATOR I,

SUBSYSTEM 5

CONTROL SYSTEM I

SUBSYSTEM I SUBSYSTEM 2

- - - - - - - - U I

Figure 2. Multiechelon decomposition of the control tasks.

S T W r n , I I \\ I I I

I \ \

, ?rLm8:;o:m::emd 1 ~ j;03:R;;;l;r S y n r h e r i s - Shi f t Converter

i onr ~ ___ it I I P r v r e o r R"

I

Figure 3. One possible decomposition of an ammonia plant.

Figure 2). This multiechelon decomposition is also a natural element arising from the structure of a chemical process.

Decomposing the process under steady state assumptions is necessary for the following reasons:

1. Developing an optimizing control strategy for an integrated plant often goes contrary to the designer's or the operator's intuition, which is to think in terms of groups of units with a common functional goal. Further, different aggregates of operating units will have different functional goals.

2. Solution of the on-line optimization problem every time an important disturbance enters the system can be over- whelming; decomposition facilitates its solution.

3. Synthesis of- the regulatory control structure is also simplified, since it is concentrated within a group of units (subgroup. echelon) with a common functional goal.

As an example, consider an ammonia plant (Figure 3) , where one possible process decomposition for optimization is dernon- stratcd. Note that each subgroup of units has a very well specified and well understood operational objective. Thus, the operational goal of the first subgroup (the primary and secondary reformer and the shift converter) is to provide the hydrogen necessary for the ammonia synthesis. The goal of the second subgroup is to prepare the reaction feed of nitrogen and hydrogen at the desired stoichiometry, by removing the undesired components. The third subgroup is to achieve the desired conversion of the H z and N 2 to ammonia.

The decomposition of the process should be made in such a way that an involved coordination among the subgroups is not required every time a disturbance enters the system. Qther- wise, it loses its attractive features. This, along with our desire to develop processing groups with functional uniformity, consti- tute the two basic design guidelines in decomposing the process for the optimizing control structure.

Bcfbre we proceed with the mathematical formulation of the multiechelon decomposition, let us simplify the notation of (P1). Some of the inequality constraints, g", will be active at thc optimum. Since all our considerations will be of a local nature, we hypothesize that the set of active inequality constraints does not change with changing disturbances. Then, we can combine the steady-state transformation equations (i.e. g ' = 0) and the active inequality constraints into one vectorfand upon substitu- tion for we obtain

min @(x, m, d) m (PI') (5)

s.t. Ax, m, d) = 0 where

f '= [g", g;"] with g"' = [gYT, gg'] and gi < 0 .

Wealso omitted the subscript and superscript of dl for simplicity because we will be dealing with non-stationary disturbances only. For the decomposition, we assume the function of the overall plant to be the sum ofthe operatingcosts ofall processing units, that is,

(6)

We have s processing units in the plant, and the subscript i denotes the states (x i ) , manipulated variables (mi) and disturbances (di) associated with processing unit i. Further, the set of constraints is assumed to be decomposable

5

@ = x @i(xi , m,, ui,d) i=l

fi(xi, mi, ut, di) = O for i 1, 2, . . ., s (7) The inputs ui result from the interconnections of unit i with the other units of the processing system

(8)

where Q i is the incidence matrix describing the interconnection ofuniti with the other units. (PI') reflects the extreme situation of completely centralized data acquisition and decision making (control action). On the other hand

P

~i = x ( I i j y i = QiY j=l

F

Min @ = x Min Q ( x i , mi, ui, d;) (P2) i=l m ml

s.t. (7), (8)

represents complete decentralization down to the basic operating unit. (PI') suffers from too much complexity, while in (P2) the extensive coordination between the subunits may be undesirable. The multiechelon decomposition criteria to be developed later supply quantitative means for judging the attrac- tiveness of the different decompositions.

CLASSIFYING DISTURBANCES AND DECOMPOSING THE CONTROL TASK:

Formalizing the discussion in the last section we can state for Disturbance Classifiation 1 : (a) the nonstationary "slowly varying" disturbances d , are candidates for optimizing control action, and (b) only regulatory action will bc taken to deal with the remaining disturbances dz.

Not all the slow disturbances will affect seriously the optimum economic performance of the process. It is therefore impcrtant to realize which disturbances are of economic interest and to act appropriately. Here, we establish a measure to classify the disturbances from an economic point of view and thus establish the optimization requirements for the control structure. Since the external disturbancesd,, i = 1, . . . s are considered constant in a particular optimization step, we can regard them as additional constraints on the process, i.e. d i = d:, i = 1, , . . s. If we let A, be the Lagrange multipliers associated with the interconnections (8) and rj the multipliers associated with the constraints d, = d: then the sub-Lagrangian associated with unit i is defined as

li = Qi(xi , mi, ui, d,) - ATui + ~ A ~ Q i i y i - .rrTddi (9)

The stationarity condition at the optimum, with respect to the disturbance di, yields

I


George Arguing about Decomposition

George’s Dissertation with Art Westerberg

• Lagrangian decomposition• Method to resolve the dual gap destroying the separability of

separable systems

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. t5, No. 3, 1975

The Use of Hestenes' Method of Multipliers to Resolve Dual Gaps

in Engineering System Optimization 1

G . STEPHANOPOULOS 2 AND A. W . WESTERBERG 3

Communicated by R. Jackson

Abstract. For nonconvex problems, the saddle point equivalence of the Lagrangian approach need not hold. The nonexistence of a saddle point causes the generation of a dual gap at the solution point, and the Lagrangian approach then fails to give the solution to the original problem. Unfortunately, dual gaps are a fairly common phenomenon for engineering system design problems.

Methods which are available to resolve the dual gaps destroy the separability of separable systems. The present work employs the method of multipliers by Hestenes to resolve the dual gaps of engineering system design problems; it then develops an algorithmic procedure which preserves the separability characteristics of the system. The theoretical foundations of the proposed algorithm are developed, and examples are provided to clarify the approach taken.

Key Words. Decomposition methods, duality theory, engineering design, method of multipliers, nonconvex programming, mathematical programming.

I , Introduction

The Lagrangian approach, representing a dual method, has often been proposed for solving optimization problems. In many engineering design problems, the system to be optimized comprises several fairly conlplex subsystems or units which are connected together by sets of 1 T h i s work was suppor ted by N S F Gran t No. GK-18633. 2 Gradua te Student , D e p a r t m e n t of Chemica l Engineer ing , Un ive r s i ty of Flor ida,

Gainesvil le , Florida. a Associate Professor, D e p a r t m e n t of Chemica l Eng ineer ing , Univers i ty of Florida,

Gainesvit le , Florida.

285 © 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of tMs publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by arty means, eleetronle, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. t5, No. 3, 1975

The Use of Hestenes' Method of Multipliers to Resolve Dual Gaps

in Engineering System Optimization 1

G . STEPHANOPOULOS 2 AND A. W . WESTERBERG 3

Communicated by R. Jackson

Abstract. For nonconvex problems, the saddle point equivalence of the Lagrangian approach need not hold. The nonexistence of a saddle point causes the generation of a dual gap at the solution point, and the Lagrangian approach then fails to give the solution to the original problem. Unfortunately, dual gaps are a fairly common phenomenon for engineering system design problems.

Methods which are available to resolve the dual gaps destroy the separability of separable systems. The present work employs the method of multipliers by Hestenes to resolve the dual gaps of engineering system design problems; it then develops an algorithmic procedure which preserves the separability characteristics of the system. The theoretical foundations of the proposed algorithm are developed, and examples are provided to clarify the approach taken.

Key Words. Decomposition methods, duality theory, engineering design, method of multipliers, nonconvex programming, mathematical programming.

I , Introduction

The Lagrangian approach, representing a dual method, has often been proposed for solving optimization problems. In many engineering design problems, the system to be optimized comprises several fairly conlplex subsystems or units which are connected together by sets of 1 T h i s work was suppor ted by N S F Gran t No. GK-18633. 2 Gradua te Student , D e p a r t m e n t of Chemica l Engineer ing , Un ive r s i ty of Flor ida,

Gainesvil le , Florida. a Associate Professor, D e p a r t m e n t of Chemica l Eng ineer ing , Univers i ty of Florida,

Gainesvit le , Florida.

285 © 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of tMs publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by arty means, eleetronle, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher.

Literature from the 1970s

Decomposition and Optimization

Current revival because

• Suitable hardware has become available• Problems have become too large, e.g. machine learning

Control Structures

Edgar, 1’. F., “Status of Design Methods for Multivariable Control” in Chemical Process Control, AIChE Symp. Ser. 159, 72 (1976).

Findeisen, W., “Lectures on Hierarchical Control Systems,”Center for Control Sciences, U. of Minnesota, Minneapolis (1976).

Findeisen, W . , F. N. Bailey, M. Brdys, K. Malinowski, P. Tatjewski, and A. Wozniak, Control and Cuordination in Hierurchical Systems, Intern. Inst. for Applied Systems Anal., Laxenburg, Austria (1979).

Foss, A. S., “Critique of Chemical Process Control,”AIChEJ., 19, 209, (1973).

Foss, A. S., and M . M. Denn, (eds.), ChemicalProcessControl, AIChE Symp. Ser. 159, 72 (1976).

Friedman, P., and K. L. Pinder, “Optimization ofaSiniulation Model of aCheinical Plant,”lnd. Eng. Chenz. Proc. Des. Deo., 11, 512 (1972).

Gaines, L. D., and J . L. Gaddy, “Univ. of Missouri-RollaPROPS Users Guidc,” Rolla, MO (1974).

Gaines, L. D., and J. L,. Gaddy, “Process Optimization by Flowsheet Simulation,” Ind. Eng. Chem. Proc. Des. Deo., 15, 206 (1976).

Govind, R., and 6. J. Powers, “Control System Synthesis Strategi AIChE 82nd National Meeting, Atlantic City N J , (1976).

Johns, W. R. , “Asscssing the Effect of Uuccrtainty on the Probable Performance of Chemical Processra,” Symp. on Uncertain Systems, Cambridge, July (1973).

Kestcvbauni, A,, R. Shinnar, and H. E. Thau, “Design Concepts for Process Control,” Ind. Eng. Chcm., Proc. Dcs. Dee., 15, 2 (1976).

Lasdon, L. W., Optimizution Theory for Large Systems, Macmillan, Ncw York, (1970).

Lee, W., and V. W. Wwkinan, Jr,. “Advanced Control Practice in the Chemical Industry,” AIChE J., 22, 27 (1976).

Lefkowitz, I . , “Multilevc~l Approach Applied to Control System Dr- sign,” ASME Truns., J. Basic Eng. , 392 (June, 1966).

Lrfkowitz, I., “Systcins Control of Chemical and Related Process Sys- tems” Proc. 6th IFAC Congress, Boston, 38.2 (1975).

Lottkin, M . , and R. Rcimage, “Scaling and error analysis for matrix inversion hy pnrtitioning.” A n n Math. Stutist., 24, 428 (1953).

Maarleveld, A , , and J. E. Hijnsdorp, “Constraint Control on Distillation Columns,” Proc. 4th IFAC Congress, Warsaw (1969) (also iiuto- matica, 6 , 61 (1970)).

Masso, A. H. , and D. F. Rudd, “The Synthesis of System Design, 11. Heuristic Structuring,” AIChE J., 15, 10 (1969).

Mesarovic, M., D. Macko, and Y. Takahara, Theory of Hierarchical Multiletjel Sgstems, Academic Press, (1970a).

Mesarovic, M., “Multilevel Systems and Concepts in Process Control,” I E E E Proc., 58, 111 (1970b).

Mordri, M., “Studies in the thesis of Control Structures for Chemi- cal Processes,” Ph. D. th

Motard. R. L., H. M . Lee, R. W. Barkley. D. M . Ingels, C H E S S , Chem. Eng. Simulation System System’s Guide, Technical Publ. Co., Houston (1968).

Rudd, D. F., “The Synthesis of Systems Design I. Elementary Decom- position Theory,” AIChE J . , 15, 343 (1968).

Schoeffler, J . D., and L. S . Lasdon, “Decentralized Plant Control,” Proc. 19th Ann. ISA Conference, lS(III), 3.3-3-64, (1964).

Tinnis, V., “An Optimum Production Control System,” ISA Trans., 13(1), 70 (1974).

Umeda, T., T. Kuriyama, and A. Ichikawa, “A Logical Structure for Process Control System Synthesis,” Proc. IFAC Congress, Helsinki, (1978).

Westerherg, A. W., “Decomposition Methods for Solving Steady State Process Design Prohlems” in Decomposition of Large-Scale Prob- lems, D. M. Hiinmelblau (Ed.), North Holland Publishing Co., (1973).

Wismer, D. A. (Ed.), Optimization Methods for Large-Scale Systems, McGraw Hill, New York, (1971).

Univ. Minnesota (1977).

Monrracript receibed Februury 6 , 1979: rwi,sion r r re i r rd August 26, und U C L epted August 27, 1879.

Part I I : Structural Aspects and the Synthesis of Alternative Feasible Control Schemes

MANFRED MORARI The classification of control objectives and external disturbances in a chemical

plant determines the extent of the optimizing and regulatorv control structures (see Part I). In this article we discuss the structural design of alternative regulatory control schemes to satisfy the posed objective. Within the framework of hierarchical control, criteria are developed for the further decomposition of the process subsystems, reducing the combinatorial problem while not eliminating feasible control structures. We use structural models to describe the interactions among the units of a plant and the physicochemical phenomena occurring in the various units. The relevance of controllability and observability in the synthesis of control structures is discussed, and modified versions are used to develop all the alternative feasible regulatory structures in an algorithmic fashion. Various examples illustrate the developed concepts and strategies, including the application of the overall synthesis method to an integrated chemical plant.

SCOPE In Part I, the control tasks were divided into those of the

regulatory and of the optimizing type. The first can always be expressed in the form of functions of operating variables, which have to be kept a t desired levels through the use manipulated variables. The same is possible for the second, if certain conditions derived in Part I are satisfied. The structure of the feedback controllers used for that purpose is developed here on a sound theoretical basis, The fnllowing problems are addressed:

1. Development of a suitable type of system representation (model), requiring a minimal amount of information.

GEORGE STEPHANOPOULOS and

Department of Chemical Engineering and Materials Science

University of Minnesota Minneapolis, Minn. 55455

2. Formulation of mathematical criteria to be satisfied by

3. Development of guidelines for decomposing the overall problem into manageable subproblems.

4. Algorithmic procedure to develop alternative control structures.

The approach adopted in this work is based on the structural characteristics describing (a) the interactions among the units of a chemical process and (b) the logical dependence (of the Boolean type) among the variables used to model the dynarnic behavior of the various units. Thus, detailed dynamic model- ling at an early stage is avoided. The mathematical feasibility criteria for the generated alternative control structures are

every feasible control structure.

Page 232 March,- 1980 AlChE Journal (Vol. 26, No. 2)



























































































based on the concepts of controllability and observability. But they go far beyond the general textbook definitions, which are demonstrated to be too weak in certain cases and too strong in others.

The process decomposition developed in Part I for the synthesis of decentralized optimizing control structures can be

extended for the design of the regulatory structures. Within the above framework, we develop an algorithmic procedure to generate alternative control structures for a given steady-state chemical process design. We demonstrate the synthesis strategies in a series of examples.

CONCLUSIONS AND SIGNIFICANCE

A method for synthesizing control structures is presented. Systems are represented as structured matrices and the method uses extended versions of the conditions for structural controllability and observability as feasibility criteria. Mainly, feedback control structures are addressed, and feedfonvard compensation is developed as a logical extension. Numerous examples show the various characteristics of the synthesis method. A hypothetical plant (Williams and Otto 1960) demon- strates the applicability of the method.

The significance of the paper is twofold: First, it presents a theory-based method for developing alternative control structures-excluding the possibility of singularities, overspec- ifications and undetectable local instabilities. Engineering

heuristic criteria can enter at any stage of the synthesis procedure, and thus, the method should be suitable for industrial applications. Second, the usefulness and implication of the properties, controllability and observability, have been only incompletely covered and understood in the chemical engineering literature. Here a unified representation is given, explaining the physical meaning of those concepts.

The results are by no means final, but they are a first step to bridge the discontinuity between the employed completely heuristic structuring procedures and the available sophisti- cated detailed design techniques for multivariable control loops.

In Part I we presented the general philosophy for the synthesis of control structures for chemical processes. The steps are summarized in Figure 5 of Part'I. Specification of the control objectives is the first step, and dictates that the control task be composed of a regulatory part and an optimizing part. Classifica- tion of the expected disturbances determines the extent of each of these control parts.

Part I concentrated further on optimizing controllers after developing the proper decomposition of the process. The implicit assumption made at that point is that the regulatory controllers would he designed for each subsystem develooed from the decomposition, but no guidelines were established on how to develop these regulatory structures. It is this question that we mainly address here.

Regulatory control structures for a chemical process are designed to keep certain processing variables at desired set points. These set points might be the results of product quality specifications, safety considerations, environmental regulations etc. or from feedback optimizing structures. These objectives should be satisfied almost continuously, and indicate the set of measurements that should be made in the process. In case these measurements cannot be made for various reasons-because of undesirable large time lags or low reliability, we select secondary measurements in conjunction with an estimation scheme (Part 111).

As a first step we have to determine what variables have to be measured and controlled to guarantee smooth plant operation. Before the actual control algorithms can be designed, the alternative sets of manipulated variables which can be used in a feedback arrangement must be developed.

Whenever we approach a design problem, establishing suitable process models offers great difficulties. The underlying philosophy is to make initial decisions based on a crude model, and refine the model appropriately after each design step. The use of a simple model at the start is adopted here. The most primitive model for control purposes is one which displays the structural dependencies of the variables only, showing if the time derivative of one variable depends on another or not. For initial structural considerations, this turns out to be sufficient.

We found that the most efficient way to determine feasible sets of measured and manipulated variables, and to keep the

model as simple as possible, is to use criteria of structural controllability and observability (Lin 1976). These properties, however, are neither necessary nor sufficient for a control system to work in practice. Extended concepts of output structural controllability and observability have been formulated to rem- edy these deficiencies

MODELING ASPECTS

Most results of the current systems theory are based on linear or linearized system models

i = A(t)x + B(t)u (1) y = C(t)x (2)

(x E A", u E R", y E A' and A@), B ( t ) , C(t) are compatible matrices). Consequently, the linearized description of a nonlinear system will be accurate in an infinitesimal region around the point of linearization only. A compromise would be to use a linear model which is approximately valid in a finite region ofthe state space. Most ofthe elements in the matricesil, B andC will vary from one linearization point to another, but some of the elements will always be zero. This suggests a structural representation of the system, where A, B and C consist of elements which are generally nonzero and others which are always zero. The model of a double effect evaporator (DEE) (Figure 1) is

0 2

Figure 1. The double effect evaporator.

AlChE Journal (Vol. 26, No. 2) March, 1980 Page 233

3 2 r r

x x x X x x x X

Y

x x X

x x x x x x x

w - 2 ' u Figure 2. The digraph for the double effect evaporotor.

used as an illustrative example at this point. Developing the structural linearized equations is quite straightforward, and is given by Newell and Fisher (1972).

Wi =fi(Cl,hl;F,BJ

Ci =f3(Cl,hi;F,C~) yz =fdC 1,C*,h 1 ;B I ,B 2 )

c, = f,(C 1,Cz,h,;B 1 )

h, = f5(C 1 ,h 1;F ,TF3 1 where:

W1 Wz C I C2 h , F feedflowrate Cp concentration in feedstream T F feed temperature S1 steam rate B 1 B 2

holdup in the first effect holdup in the second effect concentration in the first effect concentration in the second effect enthalpy in the first effect

outlet flowrate of first effect outlet flowrate of second effect

The structural matrix of this system is

1 W1 W2 C1 C, hi I F CV T P Si B1 B2

wx I X x l x x w; Cl

h'l

cz

The first part corresponds to the system matrix A , the controller matrix B will consist of a subset of the columns of the second part (e.g., B l , B z , F ) while the remaining columns indicate the influence ofdisturbances. We can associate a graph with the system matrix which shows the mutual influence of the variables. The system variables form the state-nodes of the graph. There is a directed edge from node i to node i, if the structural system matrix has a nonzero entry in the ith row and thejth column. The graph corresponding to the structural matrix above is shown in Figure 2. Each manipulated variable and disturbance can be represented by a node, and its influence on the state variables shown graphically. The structural representation ofa staged system gives rise to large matrices with repeated common structural elements. This observation has been used to reduce the size of the representation of complex staged systems, without losing the fundamental information about the system structure (see Appendix C).

In connection with structural matrices and their associated graphs, we define the generic rank pu of a structural matrix to be the maximal rank a matrix achieves as a function of its free parameters, e.g., the matrix

has a generic rank of 2 despite the fact that one of the diagonal

Page 234 March, 1980

elements could be zero as a special case and then the rank would be 1.

We define a node i to be nonacessible from a nodej if there is no possibility of reaching node i starting from nodej and going to node i only in the direction of the arrows along a path in the graph.

Govind and Powers (1976) used a steady-state cause and effect graph as their basic modeling for the synthesis of control structures and accessibility, as one of the feasibility criteria that a control structure should satisfy. We show this later to be in- sufficient, i.e., additional modeling is needed and further feasibility criteria should be imposed.

FEASIBILITY ANALYSIS OF CONTROL STRUCTURES

Apart from the available engineering rules of thumb, we would like to establish rigorous mathematical critieria to decide the feasibility of a suggested control structure. Every regulatory control structure should achieve the following two objectives: (i) Be it a regulation or a servo problem, the goal is to bring several outputs of the system from an undesired state to the desired one in some tolerable fashion, under the influence of disturbances entering the system. (ii) On the other hand, we would like to monitor the process almost continuously by observing all those outputs which are critical for system performance.

The concepts of complete state controllability and observability are generally believed to provide the necessary and sufficient conditions for a control structure to achieve the above two objectives. This is not so, and in the following paragraphs, WP discuss the shortcomings of these concepts.

CONTROLLABILITY AND OBSERVABILITY IN RELATION TO PROCESS CONTROL STRUCTURES

The concept of controllability was introduced by Kalman (1960) and states that a linear system with the state differential equation

i(t) = A(t) x ( t ) + B ( t ) u(t) (1)

is said to be completely controllable if the state of the system can be transferred from the zero state at any initial time, to any terminal state x(tJ = x i within a finite time t l - t o , through the use of a piecewise continuons control input u(t).

IfA and B are constant matrices, it is well known that the pair (A ,B) is completely controllable if and only if

rank (B , AB, A2B, . . . , A"-'B) = n (3) The mathematical implications of controllability with respect to existence and uniqueness of an optimal feedback control, eigenvalue assignment using state variable feedback etr. are available in any textbook (Kwakernaak and Sivan 1972). We would like to explore the usefulness of controllability for the synthesis of control structures. To avoid common misunderstandings, let us clarify the deficiencies of the definition and theorem above for our purposes:

1. The path for going from xo toxl is not completely arbitrary. Any practical control input might result in intolerably large deviations before we reach x, from xo.

2. If the control u is bounded, we might not be able to reach x i in the specified amount of time, or not at all.

3. We have no information concerning regulation, ~ e . , what to do when disturbances enter the system. 4. Assuming that we are just interested in keeping a subset of

the outputs at their setpoints in the face of disturbances by constructing feedback loops using the available manipulated variables, we cannot deduce if and how this can be achieved.

5. The rank test gives us no quantitative clues as to "how controllable" a system is.

6. The rank test might fail because of some unfortunate parameter choice. In reality, most of the system parameters are determined experimentally and not known exactly. An arbi- trarily small variation in some of the parameters might make the system controllable.

AlChE Journal (Vol. 26, No. 2)

Control Structures

!This paper was not presented at any IFAC meeting. This paper wasrecommended for publication in revised form by Editor ManfredMorari.

*Corresponding author. Tel.: #31-40-2472784; fax: #31-40-2461418.

E-mail addresses: [email protected] (M. van de Wal),[email protected] (B. de Jager).

!http://www.wfw.wtb.tue.nl/english/research/control/

marcw/.

Automatica 37 (2001) 487}510

Survey Paper

A review of methods for input/output selection!

Marc van de Wal!"!, Bram de Jager""*!Philips CFT, Mechatronics Motion, P.O. Box 218, SAQ-2116, 5600 MD Eindhoven, Netherlands

"Faculty of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands

Received 11 June 1998; revised 3 July 2000; received in "nal form 6 September 2000

Abstract

Control system design involves input/output (IO) selection, that is, decisions on the number, the place, and the type of actuators andsensors. The choice of inputs and outputs a!ects the performance, complexity, and costs of the control system. Due to thecombinatorial nature of the selection problem, systematic methods are needed to complement one's intuition, experience, and physicalinsight. This paper reviews the currently known IO selection methods, which aids the control engineer in picking a suitable method forthe problem at hand. The methods are grouped according to the control system property that is addressed and applications aregrouped according to the considered control systems. A set of criteria is proposed that a good IO selection method should possess. Itis used to assess and compare the methods and it could be used as a guideline for new methods. The state of the art in IO selection issketched and directions for further research are mentioned. ! 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Control system design; Structural properties; Input signals; Output signals; Controllability; Observability; Relative gain array; Robustcontrol

1. Introduction

Control system design could be split into the followingsix steps. First, the control goals are formulated. Thisinvolves choosing and characterizing the exogenous vari-ables w and choosing and imposing requirements on thecontrolled variables z, see Fig. 1. The control goalsshould be quanti"ed in the time and/or frequencydomain. The choice of z may be a!ected by the outcomeof the other steps of control system design, like the choiceof the plant model G in the second step of control systemdesign. The techniques used in other steps also determinethe model type, e.g., linear or nonlinear, time-invariant ortime-varying, physical principles or black box. In thethird step, the control structure is selected. Fourth, thecontroller K is designed. The choice of the design method

(PID, LQG, adaptive control, H#

optimization, etc.)depends on aspects like the control goal, model accuracy,and restrictions on the implementation. Fifth, theclosed-loop system is evaluated via simulations or pilotplant experiments. In the last step, the controller andhardware like sensors, actuators, and control processorsare implemented in the real plant. Iterative re"nements ofthese steps are often necessary, e.g., meeting the controlgoal might call for a more accurate model or a modi"ca-tion of controller parameters.

The third step of control system design, i.e., controlstructure selection, is usually split into two separateproblems which are then solved successively: input/out-put (IO) selection, which is the focus of this paper, andcontrol con"guration (CC) selection. Approaches tosolve IO and CC selection jointly are seldomly encoun-tered in the literature. Here, the IO selection problem isposed as follows:

Select suitable variables u to be manipulated by thecontroller (plant inputs) and suitable variables y to besupplied to the controller (plant outputs).

Both the inputs and the outputs of G are divided into twoclasses, but in this paper the terms `inputsa and `out-putsa are reserved for u and y. Each combination of

0005-1098/01/$ - see front matter ! 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 5 - 1 0 9 8 ( 0 0 ) 0 0 1 8 1 - 3

Control structure design for complete chemical plants!

Sigurd Skogestad +

Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway

Abstract

Control structure design deals with the structural decisions of the control system, including what to control and how to pair thevariables to form control loops. Although these are very important issues, these decisions are in most cases made in an ad hocfashion, based on experience and engineering insight, without considering the details of each problem. In the paper, a systematicprocedure for control structure design for complete chemical plants (plantwide control) is presented. It starts with carefully definingthe operational and economic objectives, and the degrees of freedom available to fulfill them. Other issues, discussed in the paper,include inventory and production rate control, decentralized versus multivariable control, loss in performance by bottom-up design,and a definition of a the ‘‘complexity number’’ for the control system.# 2003 Elsevier Ltd. All rights reserved.

Keywords: Control structure design; Chemical plants; Plantwide control; Process control

1. Introduction

A chemical plant may have thousands of measure-ments and control loops. In practice, the control systemis usually divided into several layers, separated by timescale, including (see Fig. 1):

. scheduling (weeks),

. site-wide optimization (days),

. local optimization (hours),

. supervisory (predictive, advanced) control (minutes),

. regulatory control (seconds)

Here, we consider the lower three layers.The local optimization layer typically recomputes new

setpoints only once an hour or so, whereas the feedbacklayers operate continuously. The layers are linked by thecontrolled variables , whereby the setpoints are computedby the upper layer and implemented by the lower layer.An important issue is the selection of these variables.

Control structure design deals with the structuraldecisions that must be made before we start the

controller design, and involves the following tasks(Foss, 1973); (Skogestad & Postlethwaite, 1996):

1. selection of manipulated variables m (‘‘inputs’’);2. selection of controlled variables (‘‘outputs’’; vari-

ables with setpoints);3. selection of (extra) measurements (for control

purposes including stabilization);4. selection of control configuration (the structure of

the overall controller that interconnects the con-trolled, manipulated and measured variables);

5. selection of controller type (control law specifica-tion, e.g. PID, decoupler, LQG, etc.).

Control structure design for complete chemical plantsis also known as plantwide control . In practice, theproblem is usually solved without the use of existingtheoretical tools. In fact, the industrial approach toplantwide control is still very much along the linesdescribed by Buckley in 1964 in his chapter on Overallprocess control . The realization that the field of controlstructure design is underdeveloped is not new. Foss(1973) made the observation that in many areasapplication was ahead of theory, and stated that:

The central issue to be resolved by the new theoriesis the determination of the control system struc-ture. Which variables should be measured which

! Extended version of this paper ‘‘Plantwide control: towards asystematic procedure’’ from ESCAPE 12 Symposium, Haag, May2002.

* Tel.: !/47-7349-4154; fax: !/47-7349-4080.

E-mail address: [email protected] (S. Skogestad).

Computers and Chemical Engineering 28 (2004) 219"/234www.elsevier.com/locate/compchemeng

0098-1354/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.compchemeng.2003.08.002

Major Themes of George’s Research Program in the 1970s

“The Research Community is studying the wrong problem”

• Architectures– Control Structure– Decomposition for optimization

• Design for Control

Design for Control

Predicting the future in 1990Digital Equipment Corp. (DEC) and DuPont

Voice ControlFinger Print IDVideo PhoneOperator Screen

Status Assessment and Trends• Interest in control is at an all-time high

Graduate Course Enrollments ETH

2008 2009 2010 2015/16

MPC 32 44 67 149

Linear Systems 34 42 59 63

Dynamic Programming 72 101 140 218

Status Assessment and Trends• Interest in control is at an all-time high• Interest in computer science is at an all-time high

CS Majors at Caltech

Status Assessment and Trends• Interest in control is at an all-time high• Interest in computer science is at an all-time high• Interest in traditional positions in “hot” areas is low

Raff D’AndreaPhD students & Post-Docs since moving to ETH

Federico AugugliaroMark MullerPhilipp ReistLuca GherardiGajamohan MohanarajahMarkus WaibelMarkus HehnSergei Lupashin Raymond OungSebastian TrimpeAngela SchoelligMichael SherbackFrederic BourgaultGuillaume DucardOliver Purwin

startupassistant professor (Berkeley)startupstartup startup (founder)startup (founder)startup (founder)startup (founder)startupgroup leader (Max Planck)assistant professor (U. of Toronto)startupstartupassistant professor (U. of Nice)startup

Status Assessment and Trends• Interest in control is at an all-time high• Interest in computer science is at an all-time high• Interest in traditional positions in “hot” areas is low• Interest in predictive control is at an all-time high

American Control Conference 2017

• 65 / 900 papers on MPC

10

Example problem

● Hit back a thrown ball

● Implicit feedback law updated at 20ms– Try 10’000 trajectories

● Sample different ways to hit the ball

– Apply first 20ms of the best one

Mark W. MuellerPhD Thesis, ETH(w/ Raff D’Andrea)

11

Evaluation

● Algorithm evaluated in the Flying Machine Arena

● System limits

MPC@MHzMotivationProve feasibility of online optimization@MHz sampling rate

Setup- Algorithms: first-order methods (FGM, ADMM)- Implementation: hand-crafted fixed-point VHDL design

on high-end FPGA (Xilinx Vertex 7)

Case studyControl of Piezo-electric plate actuator in high-speed AFM (provided by IBM Zurich)

Objective: Maintain constant loading force

deflection signal

actuation signal

Piezo plate actuator

sample

scan direction

Jerez, Goulart, Richter, Constatinides, Kerrigan, Morari, IEEE TAC 2014

Status Assessment and Trends• Interest in control is at an all-time high• Interest in computer science is at an all-time high• Interest in traditional positions in “hot” areas is low• Interest in predictive control is at an all-time high• Trends in software and hardware

– Optimization software– Data and Connectivity– Validation and Verification

Speedup of software for MIPsProgress in MIP Solvers MILP Speedups

Calculations

Improvement in MIP Software from 1988-2017

Algorithms: 147650x

Machines: 17120xhttp://preshing.com/20120208/a-look-back-at-single-threaded-cpu-performance/

NET: (Algorithm ⇥ Machine): 2,527,768,000x

What Does This “Mean”?

A “typical” MILP that would have taken 124 years to solve in 1988will solve in 1 second now.

This is amazing, but your mileage may vary

Linderoth (UW ISyE) Quo Vadis MIP FOCAPO 12 / 58

Control and Optimization

Abundance of Data and Connectivity The New Opportunity

• 2020: 50 billion devices connected to the internet• 2020: 800 million smart meters deployed => 1 million smart meters generate 1.3 TB data over 90 days.

Price of sensors that make up the IoT will keep falling

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renewal. I love the depth of the articles and the business focus.”— Jeffery Nelson

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HBR subscribers have enhanced their careers and grown theircompanies with articles like these:

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• Model checking of safety properties for Simulink Models• Avionics distributed control system complexity:

– 10K-250K simulink blocks– 40k-150K binary raw variables– Hundred to few thousand bin’s after simplification/abstraction

• Automotive single controller complexity:– 5K-80K simulink blocks– Few thousand bin’s after simplification/abstraction

• FormalSpecsVerifier tool environment (NuSMV)

Formal Verification of Embedded Software inModel Based Design

Advanced Laboratory on Embedded Systems S.r.l.A Research and Innovation Company

Source: Alberto Ferrari

Status Assessment and Trends• Interest in control is at an all-time high• Interest in computer science is at an all-time high• Interest in traditional positions in “hot” areas is low• Interest in predictive control is at an all-time high• Trends in software and hardware

– Optimization software– Data and Connectivity– Validation and Verification

Dear George:

Thank you!Happy Birthday!

Happy Retirement!

mit symposium 2040 visions of process systems engineering...

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