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Decentralized Control Systems for Chemical Plants. Issues and Approaches
CoplTight © I F.-\C 10th Triennial \\"orld C()I1~ress. \!linich. FR(;. 19~7
DECENTRALIZED CONTROL SYSTEMS FOR CHEMICAL PLANTS. ISSUES AND APPROACHES V. Manousiouthakis Chl'll/im! t."lIgilll'l'rillg Dl'jJllrlllll'lll. [·lIi'·l'l".Iily of C({!tjllmill. LII.\ .·llIg,·!,·\. C.-I 'J1){)2-J. LS4
Abstract: This work concentrates on three tasks that a control systems engineer is faced with, when attempting the design of a decentralized control system. These are: a. Selection of measurements to be used for control purposes. b. Selection of manipulated variables to be used for control purposes. c. Selection of the control structure (i.e. the interconnections between measurements and manipulated variables). The issues to be addressed, in relation to these tasks, are then presented and approaches through which they can be addressed are proposed. More specifically, the related issues are: 1. Minimization of closed-loop interactions resulting from decentralization. 2. Assessment of the effects that decisions related to tasks a, b, and c have on the robustness characteristics of the system. 3. Assessment of the effects that decisions related to tasks a, b, and c have on the reliability characteristics of the system. Key Words:
Decentralized control, control structures, Block Relative Gain, Robustness
INTRODUCTION Synthesis of control systems for chemical plants can be decomposed into five tasks. First, the designer must specify the control objectives. Second, the measurements to be used for control purposes must be selected. Third, the manipulated variables must be chosen. Fourth, the control structure (i.e. the interconnections between meas urements and manipulations) must be constructed. Fifth, a control law must be designed which governs the relations between system outputs and system inputs. In this work, we concentrate on tasks 2, 3, 4 in an effort to present recent developments in control systems rather than controller design. F~ more, new challenges related to the resolution of tasks 2, 3, 4, are identified in an effort to stimulate research in this area. PREVIOUS WORK A brief review of plant control strategies and interaction analysis methods is provided next, in hope that it will help streamline the presentation Of material in the subsequent sections. A widely accepted control system design strategy was developed by Buckley (1964). Plant control was decomposed into material balance control and pro~ duct quality control. The first, material balance control, utilized intermediate storage tanks to reduce the interactions among process units and minimize the propagation of disturbances throughout the plant, thus leading to smooth plant operation. The second, product quality control, utilized local controllers to dampen fluctuations of process stream properties and maintain product specifications. However, this control strategy requires significant plant overdesign. To overcome this problem, Govind and Powers (1982) proposed the generation of alternative control configurations using only process flowsheet information. The large number of possible controller structures is limited
using simple heuristics and design experience. The remaining alternatives are then tested for interaction problems based on such information as steadystate gains, time delays and dominant time con~ stants. The disadvantages of this procedure stem from the highly integrated nature of chemical plants and the "curse of dimensionality" associated with large scale systems. To avoid these problems many researchers (Umeda et al., 1978; Morari et al., 1980, Morari and Stephanopoulos, 1980) proposed plant decomposition as the appropriate COntrol systems deSign strategy. By decomposing the process (either for optimizing or regulatory control purposes) into subsystems and designing control systems for each process subsystem, they were able to simplify the design procedure and develop decentralized control systems. A critical element in the success of this approach was the need for the subsystems to interact as little as pcssible with each other. To achieve that, Umeda et a •. concentrated first on the control of process units and then on the coordination of the process unit control systems. Morari and Stephano~ poulos, on the other hand, proposed the creation of subsystems by precedence ordering and grouping of the system (Sargent and Westerberg, 1964). Variable matchings were then made giving preference to matches within subsystems and attempting to minim~ ize interactions among subsystems. Since the level of subsystem interactions is always an important criteriOn for control structure selec~ tion, interaction analysis has become an integral part of control system design. The main interac~ tion measures have been Bristol's (1966) Relative Gain Array and Rosenbrock's (1974) Nyquist Array methods and related Gershgorin and Ostrowski bands. However, these techniques were developed to assess interactions among single~input single·output loops and therefore fell short of the researchers expec. tations.
206
\ '. \ Ltnollsiolllil;lkis
To resolve the problem of subsystem interactions, we recent l y introduced the concept of Block Rela L tive Gain (Manousiouthakis et al. , '985). This concept is briefly reviewed next .
1.
The diagonal elements of the BRG are equal to the row sums of the corresponding RGA ele~ ments.
2.
THE BLOCK RELATIVE GAIN (BRG) Given a square openLloop transfer function matrix G, consider the following system partitioning:
CONTROL STRUCTURE SYNTHESIS
m
with
G-
[~:1 .
G
(1)
Working with the decentralized feedback system given in Fig. " the fo ll owing relations can be derived . ay, au,- l u 2 =0
G" (2)
F~O
ay, au1y , 2 ~O F,
~
The eigenvalues of the BRG are scaling independent. The use of this concept and its properties for decentra l ized control structure synthesis are outlined in the next section.
([G - ' J "
t'
~O
F2~I
Within this section, the assumption is made that tasks 2 and 3 (i . e. selection of measurements and manipulations) are a l ready complete . Some ideas on how these tasks can be addressed will be presented in the next section. The main idea behind the proposed control structure synthesis procedure is that one should not seek to decompose the process but rather decompose the sets of measurem~d mani~ pulations into subsets thatwill be assigne<1t-o- each other and create control subsystems (instead of process subsystems) . There are many criteria that can be used to achieve that. The one used here is the minimization of closed-loop interac L tions among subsystems. The Block Relative Gain is used as an interaction measure. It has been shown (Manousiouthakis et al., '985) that when BRG is "close" to identity, closed loop interactions are expected to be minimal. Capitalizing on the BRG properties presented in section Ill , one can in fact proceed towards synthesis (rather than analysis) of control structures using initiall y on l y Relative Gain Array information. SELECTION OF MEASUREMENTS AND MANIPULATIONS
where [G
~1
J"
~1
is the first mxm block of G =
-, J" -, [G J ,
[
There are many criteria that can be used for the selection of these variables . Economic considera L tions, interaction levels, process uncertainty and reliability play an important role during this decision making process. Although economic considerations are difficult to quantify, the other criteria are amenable to mathematical formulation.
:
[G
2
According to (2) G'l denotes the ~ gain between y and u, when_~ll tQl loops are open i.e. F = o. Similarly, ([G J ) is the block gain between y, 11 and u, when the flrst m lOOps are open i . e. F, - 0, the last nLm loops are closed i.e . F2 = I and under perfect control i.e . Y2 = O. We can now define the mLdimensional Block Re l ative Gain
.. ,
ay, BRG =
au,-IY2=0 F=O
ay, au1y , 2 =0 F,=O F2=I
(5)
For the first one, interaction, the control struc ~ ture synthesis method discussed in section IV is ap:'lied for various sets of measurements and mani " pulations. The best control structure and the interaction levels associated with it are then found for each alternative . The alternatives with the smallest interaction levels are further inves. tigated. Is is well known rpalazogllJ et al., 1985) that the winimal (over all scalings) condition number (E ) of an open-loop plant is an indicator of the closed ~ loop system's rObujtness characteristics. Since the evaluation of E entails a very difficu l t optimization problem it cannot be used for screening purposes. However , recent results (Nett and Manousiouthakis, '986) connect the Relat~ve Gain Array and the Block Relative Gain with E. More specifically it is shown in the above reference that
(/+11 2
£
*
+
Note that the 1-dimensional BRG is Bristol's relative gain . Thus the relative gain array is the collection of all possible 1Ldimensional BRGs. Furthermore, the following hold:
p (BRG'
(p(')
is spectral radius)
'* E
2
~
max
I
i
j
IRGA(i,j'l
It is apparent from these two inequalities that the mathematical tools (RGA, BRG) used for control structure synthesis , provide also information on the effect that the choice of measurements and manipulations has on the robustness characteristics of the closedLloop system.
~07
RESEARCH CHALLENGES It must be clear by now that control systems design cannot become a dry mathematical exercise . The issues are too many and the approaches even more. We feel that in the last few years, a number of significant advances have occurred but the problem is far from being solved . I n thi3 section, we will briefly present some areas in which increased research effort3 3hould be 3pent. 1.
2.
3.
Mathematical development of interaction meas~ ures for systems that are nonsquare in nature, i.e. the number of outputs is dif~ ferent than that of the inputs at the system and/or subsystem level. Mathematical development of interaction meas~ ures for systems whose variables (inputs and/or outputs) belong to more than one subsystem. Incorporation of robustness considerations in the control structure synthesis procedure.
An analytical approach that can resolve all the control system design issues, is the repeated use of H~ optimization . It is well known that such problems as sensitivity minimization, set point tracking and disturbance rejection can be formu· lated as H optimization problems . Their robust counterparts are formulated a3 Hu optimization problems. When an external optimization over all possible open~loop plants (e . g. the ones resulting from the use of different measurements) is employed then a comprehensive treatment of control system design can be achieved . The main difficulties associated wi th this comprehensive approach are two: a.
Structural constraints on the controller can not be easily incorporated in the procedure.
b.
There are hardly any synthetic elements in this procedure. CONCLUSIONS - SUMMARY
In this work, we presented a review of past work related to control system design and more specifically to the selection of measurements, manipula~ tions and control structures. Recent developments in these areas were presented and new research directions were outlined. REfERENCES Bristol, E. (1964). On a new measure of interac~ tion for multivariable process control", IEEE Trans. Aut. Con., AC-:!.2., 133-134 . Buckley, P. s. (1964). Techniques of Process Control. John Wiley & Son3, New YOr -k-.----Govind, R., and Powers, G. (1982). Control system synthesis strategies. AIChE ~., 28, 60 - 73 . Manousiouthakis, V., Savage, R., and Arkun, Y. (1987) Synthesis of decentralized control structures and the block relative gain con cept . AIChE J. lin press) .
b
Morari, M., Ark~n, Y., and Stephanopoulos, G., (1980 1 . Studies in the synthesis of control structures for chemical processes, Part I. AIChE ~., 26, 220-232. Morari, M., and Stephanopoulos, G. (1980). Struc ~ tural aspects and the synthesis of alterna tive feasible control schemes. AIChE ~., 26,
Nett, C., and Manousiouthakis , V. (1987). On the Euclidean condition and the relative gain array: connections, conjectures and clarifi· cations. IEEE Trans. ~.~., to appear. Palazoglu, A., Manousiouthakis, V., and Arkun, Y. ( 195) . Design of chemical plants with improved dynamic operability in an environ. ment of uncertainty. Ind. Eng. Chem. Proc. Des. Dev ., 24 , 802-813-.-- --Rosenbrock, H. (1974). Computer Aided Control tern Design . Academic Press, New ~
Sys~
Sargent, R., and Westerberg, A. (1964). SPEED~UP in chemical engineering design", Trans. Inst. Chem. Eng., ~, T190. Umeda , T., Kuriyama, T., and Ichikawa, A. (1978). A logical structure for process control sys tem synthesis . Proceedings IFAC Congress, Helsinki.
DECENTRALIZED CONTROL SYSTEMS FOR CHEMICAL PLANTS. ISSUES AND APPROACHES V. Manousiouthakis Chl'll/im! t."lIgilll'l'rillg Dl'jJllrlllll'lll. [·lIi'·l'l".Iily of C({!tjllmill. LII.\ .·llIg,·!,·\. C.-I 'J1){)2-J. LS4
Abstract: This work concentrates on three tasks that a control systems engineer is faced with, when attempting the design of a decentralized control system. These are: a. Selection of measurements to be used for control purposes. b. Selection of manipulated variables to be used for control purposes. c. Selection of the control structure (i.e. the interconnections between measurements and manipulated variables). The issues to be addressed, in relation to these tasks, are then presented and approaches through which they can be addressed are proposed. More specifically, the related issues are: 1. Minimization of closed-loop interactions resulting from decentralization. 2. Assessment of the effects that decisions related to tasks a, b, and c have on the robustness characteristics of the system. 3. Assessment of the effects that decisions related to tasks a, b, and c have on the reliability characteristics of the system. Key Words:
Decentralized control, control structures, Block Relative Gain, Robustness
INTRODUCTION Synthesis of control systems for chemical plants can be decomposed into five tasks. First, the designer must specify the control objectives. Second, the measurements to be used for control purposes must be selected. Third, the manipulated variables must be chosen. Fourth, the control structure (i.e. the interconnections between meas urements and manipulations) must be constructed. Fifth, a control law must be designed which governs the relations between system outputs and system inputs. In this work, we concentrate on tasks 2, 3, 4 in an effort to present recent developments in control systems rather than controller design. F~ more, new challenges related to the resolution of tasks 2, 3, 4, are identified in an effort to stimulate research in this area. PREVIOUS WORK A brief review of plant control strategies and interaction analysis methods is provided next, in hope that it will help streamline the presentation Of material in the subsequent sections. A widely accepted control system design strategy was developed by Buckley (1964). Plant control was decomposed into material balance control and pro~ duct quality control. The first, material balance control, utilized intermediate storage tanks to reduce the interactions among process units and minimize the propagation of disturbances throughout the plant, thus leading to smooth plant operation. The second, product quality control, utilized local controllers to dampen fluctuations of process stream properties and maintain product specifications. However, this control strategy requires significant plant overdesign. To overcome this problem, Govind and Powers (1982) proposed the generation of alternative control configurations using only process flowsheet information. The large number of possible controller structures is limited
using simple heuristics and design experience. The remaining alternatives are then tested for interaction problems based on such information as steadystate gains, time delays and dominant time con~ stants. The disadvantages of this procedure stem from the highly integrated nature of chemical plants and the "curse of dimensionality" associated with large scale systems. To avoid these problems many researchers (Umeda et al., 1978; Morari et al., 1980, Morari and Stephanopoulos, 1980) proposed plant decomposition as the appropriate COntrol systems deSign strategy. By decomposing the process (either for optimizing or regulatory control purposes) into subsystems and designing control systems for each process subsystem, they were able to simplify the design procedure and develop decentralized control systems. A critical element in the success of this approach was the need for the subsystems to interact as little as pcssible with each other. To achieve that, Umeda et a •. concentrated first on the control of process units and then on the coordination of the process unit control systems. Morari and Stephano~ poulos, on the other hand, proposed the creation of subsystems by precedence ordering and grouping of the system (Sargent and Westerberg, 1964). Variable matchings were then made giving preference to matches within subsystems and attempting to minim~ ize interactions among subsystems. Since the level of subsystem interactions is always an important criteriOn for control structure selec~ tion, interaction analysis has become an integral part of control system design. The main interac~ tion measures have been Bristol's (1966) Relative Gain Array and Rosenbrock's (1974) Nyquist Array methods and related Gershgorin and Ostrowski bands. However, these techniques were developed to assess interactions among single~input single·output loops and therefore fell short of the researchers expec. tations.
206
\ '. \ Ltnollsiolllil;lkis
To resolve the problem of subsystem interactions, we recent l y introduced the concept of Block Rela L tive Gain (Manousiouthakis et al. , '985). This concept is briefly reviewed next .
1.
The diagonal elements of the BRG are equal to the row sums of the corresponding RGA ele~ ments.
2.
THE BLOCK RELATIVE GAIN (BRG) Given a square openLloop transfer function matrix G, consider the following system partitioning:
CONTROL STRUCTURE SYNTHESIS
m
with
G-
[~:1 .
G
(1)
Working with the decentralized feedback system given in Fig. " the fo ll owing relations can be derived . ay, au,- l u 2 =0
G" (2)
F~O
ay, au1y , 2 ~O F,
~
The eigenvalues of the BRG are scaling independent. The use of this concept and its properties for decentra l ized control structure synthesis are outlined in the next section.
([G - ' J "
t'
~O
F2~I
Within this section, the assumption is made that tasks 2 and 3 (i . e. selection of measurements and manipulations) are a l ready complete . Some ideas on how these tasks can be addressed will be presented in the next section. The main idea behind the proposed control structure synthesis procedure is that one should not seek to decompose the process but rather decompose the sets of measurem~d mani~ pulations into subsets thatwill be assigne<1t-o- each other and create control subsystems (instead of process subsystems) . There are many criteria that can be used to achieve that. The one used here is the minimization of closed-loop interac L tions among subsystems. The Block Relative Gain is used as an interaction measure. It has been shown (Manousiouthakis et al., '985) that when BRG is "close" to identity, closed loop interactions are expected to be minimal. Capitalizing on the BRG properties presented in section Ill , one can in fact proceed towards synthesis (rather than analysis) of control structures using initiall y on l y Relative Gain Array information. SELECTION OF MEASUREMENTS AND MANIPULATIONS
where [G
~1
J"
~1
is the first mxm block of G =
-, J" -, [G J ,
[
There are many criteria that can be used for the selection of these variables . Economic considera L tions, interaction levels, process uncertainty and reliability play an important role during this decision making process. Although economic considerations are difficult to quantify, the other criteria are amenable to mathematical formulation.
:
[G
2
According to (2) G'l denotes the ~ gain between y and u, when_~ll tQl loops are open i.e. F = o. Similarly, ([G J ) is the block gain between y, 11 and u, when the flrst m lOOps are open i . e. F, - 0, the last nLm loops are closed i.e . F2 = I and under perfect control i.e . Y2 = O. We can now define the mLdimensional Block Re l ative Gain
.. ,
ay, BRG =
au,-IY2=0 F=O
ay, au1y , 2 =0 F,=O F2=I
(5)
For the first one, interaction, the control struc ~ ture synthesis method discussed in section IV is ap:'lied for various sets of measurements and mani " pulations. The best control structure and the interaction levels associated with it are then found for each alternative . The alternatives with the smallest interaction levels are further inves. tigated. Is is well known rpalazogllJ et al., 1985) that the winimal (over all scalings) condition number (E ) of an open-loop plant is an indicator of the closed ~ loop system's rObujtness characteristics. Since the evaluation of E entails a very difficu l t optimization problem it cannot be used for screening purposes. However , recent results (Nett and Manousiouthakis, '986) connect the Relat~ve Gain Array and the Block Relative Gain with E. More specifically it is shown in the above reference that
(/+11 2
£
*
+
Note that the 1-dimensional BRG is Bristol's relative gain . Thus the relative gain array is the collection of all possible 1Ldimensional BRGs. Furthermore, the following hold:
p (BRG'
(p(')
is spectral radius)
'* E
2
~
max
I
i
j
IRGA(i,j'l
It is apparent from these two inequalities that the mathematical tools (RGA, BRG) used for control structure synthesis , provide also information on the effect that the choice of measurements and manipulations has on the robustness characteristics of the closedLloop system.
~07
RESEARCH CHALLENGES It must be clear by now that control systems design cannot become a dry mathematical exercise . The issues are too many and the approaches even more. We feel that in the last few years, a number of significant advances have occurred but the problem is far from being solved . I n thi3 section, we will briefly present some areas in which increased research effort3 3hould be 3pent. 1.
2.
3.
Mathematical development of interaction meas~ ures for systems that are nonsquare in nature, i.e. the number of outputs is dif~ ferent than that of the inputs at the system and/or subsystem level. Mathematical development of interaction meas~ ures for systems whose variables (inputs and/or outputs) belong to more than one subsystem. Incorporation of robustness considerations in the control structure synthesis procedure.
An analytical approach that can resolve all the control system design issues, is the repeated use of H~ optimization . It is well known that such problems as sensitivity minimization, set point tracking and disturbance rejection can be formu· lated as H optimization problems . Their robust counterparts are formulated a3 Hu optimization problems. When an external optimization over all possible open~loop plants (e . g. the ones resulting from the use of different measurements) is employed then a comprehensive treatment of control system design can be achieved . The main difficulties associated wi th this comprehensive approach are two: a.
Structural constraints on the controller can not be easily incorporated in the procedure.
b.
There are hardly any synthetic elements in this procedure. CONCLUSIONS - SUMMARY
In this work, we presented a review of past work related to control system design and more specifically to the selection of measurements, manipula~ tions and control structures. Recent developments in these areas were presented and new research directions were outlined. REfERENCES Bristol, E. (1964). On a new measure of interac~ tion for multivariable process control", IEEE Trans. Aut. Con., AC-:!.2., 133-134 . Buckley, P. s. (1964). Techniques of Process Control. John Wiley & Son3, New YOr -k-.----Govind, R., and Powers, G. (1982). Control system synthesis strategies. AIChE ~., 28, 60 - 73 . Manousiouthakis, V., Savage, R., and Arkun, Y. (1987) Synthesis of decentralized control structures and the block relative gain con cept . AIChE J. lin press) .
b
Morari, M., Ark~n, Y., and Stephanopoulos, G., (1980 1 . Studies in the synthesis of control structures for chemical processes, Part I. AIChE ~., 26, 220-232. Morari, M., and Stephanopoulos, G. (1980). Struc ~ tural aspects and the synthesis of alterna tive feasible control schemes. AIChE ~., 26,
Nett, C., and Manousiouthakis , V. (1987). On the Euclidean condition and the relative gain array: connections, conjectures and clarifi· cations. IEEE Trans. ~.~., to appear. Palazoglu, A., Manousiouthakis, V., and Arkun, Y. ( 195) . Design of chemical plants with improved dynamic operability in an environ. ment of uncertainty. Ind. Eng. Chem. Proc. Des. Dev ., 24 , 802-813-.-- --Rosenbrock, H. (1974). Computer Aided Control tern Design . Academic Press, New ~
Sys~
Sargent, R., and Westerberg, A. (1964). SPEED~UP in chemical engineering design", Trans. Inst. Chem. Eng., ~, T190. Umeda , T., Kuriyama, T., and Ichikawa, A. (1978). A logical structure for process control sys tem synthesis . Proceedings IFAC Congress, Helsinki.