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Coordinated Decentralised Control Design and Distillation Pilot Plant Application
Copyright © IFAC Automatic Control ill Petrole um , Pe trochemica l and Desalill(ltioTl Industries, Kuwait, I 'ISO
COORDINATED DECENTRALISED CONTROL DESIGN AND DISTILLATION PILOT PLANT APPLICATION Z.
J.
Binder and R. A. Perret
ill'
GmlObil' (CXRS -L'A 228), t;,\'SIEG-INPG, BP -16 , 38-1{)2 Sailll-.\[arlill-D'Hnfs, FrtllI(I'
La/lOrtI/oirl' r/'.J..II/01ll1lIiljllf
Abstract. The COOrdinated Decentralised Control forms a useful approach to control a complex industrial process. It enables the design of a multi level control system in the form of a hierarchical network of control and decision centers. The vertical information transfer help for the coordination in a hierarchical control and the horizontal information transfer is used for the cooperation in decentralised control. The relations between the control centers are expressed by the tracking of the used process models. The aggregated model situated on the upper level of the hierarchy is tracked by the detailed models of the lower level. Eventually a multiple model could be introduced to caracterise a process part in its various operating conditions . On the base of linear state variable models and the input-output quadratic tracking cost function, a Coordinated Decentralized Control Algorithm in the form of matrix modular computing blocs is presented. The stability study gives the condition to be satisfied for the interconnection of these centers. The application of the proposed approach to the experimental pilot plant with two distillation columns controled by a micro-computer distributed system is presented. Xeywords: Hierarchical control I Distributed system; Tracking multivariable control Multimodel control ; Distillation column.
Control methods are based on the tracking algorithm illlplemented in these centers. The proposed method leads to easier implrnnentat;'on of a distributed microcomputer network. The internal structure of the deciSion centers may be multiple, function of the number of models representing the system.
The development of the domain of distributed control systems using computer networks in creases the interest in the hierarchical and decentralised control methods for complex systems . Several new problems arise from these applications. The control system organisation, decentralised control methods and information exchanges are the most important aspects in the design and realization of the distributed control system. A common methodological approach in the design of particular parts could increase the efficiency and reduce the cost of the process control applications. Unfortunately there are very few workS taking into account simultaneously algorithm, information, hardware and software point of view.
An industrial process is composed of different systems characterized by their behaviour and particular situation. The structure of the industrial process is determined by the interconnections between its composing systems. This structure can be modified in conjunction with the global goals. The role of a control system is to organize and control the ensemble to realise these goals which concern the production quality, energy and material consumption and disturbances compensation.
The other problem comes from the complexity of the industrial processes and their modelling . The classical hierarchical and decentralised control methods aid to solve the problem of the control of large scale system due to the decomposition on several interconnected subsystems. The quality of results of these applications depends on the satisfaction of the mathematical hypotheSiS used for the method development. The large domain of the process operating conditions is usualy incompatible with linear hypotheSiS, consequently the classical methods do not give good results. There are no general methodology to control a non-linear or time-varying large scale systems. A multimodel representation could be proposed to overcome the limits of classical methods based on linear models.
To aide a progressive implementation of the hierarchical control system we propose a multilevel network with nets formed by "Control and Decision canters· ( CDC ) ( Binder, 1977 ) structured as knowledge based systems. The functional relation between the neighbouring centers on the same or on different levels and redundancy of corresponding information exchange contributes to the rObustness of the proposed structure .
The architecture of a multi-level control system consisting of several centers is presented in fig .1. A control and decision center, often of multiple representation, is assigned to each system to control it in its different operating situations (Binder and others, 19844). The centers located at a lower level are guided by those in the higher level whose role is similar except that they affect a group of systems. The highest center of the hierarchy takes decision following a global criteria and, through the different levels, controls the whole industrial
OUr contribution to solve the above problems consists in the methodological approach in the hierarchical control systetD design. The Control and Decision canters (CDC) formes the basic modular elements of the control system network. The COOrdinated Decentralized Control (CODECO) method and the loLlltimodel
135
Z. J. Binde r and R. A. Pe rret
136
process. Every center has the knowledge concerning that part which it controls. This knowledge is either in the font of analytical model or data baBe stored in the aaaory of this center. The limited size of this aaaory gives rise to a compromise between the precision and the extent of the stored model. So, the models on the low levels are more precise than those of the higher levels . On observing the hierarchy it is noticed that the number of centers is increasing going down in the hierarchy. Each center simulates one part of the process . The set of models of the centers located at the same level simulate the whole industrial process. The hierarchy of the models and the precision of the Simulation are related to the hierarchy of the criteria considered to elaborate the decisions in each center . The higher level centers consider globally the economical criteria, while the centers located near the process act on the physical characteristics. (Perret, 1983) . The control strategy of each control and decision
center is elaborated using a model or group of models and the corresponding criterion, which expresses the relations with center environment . The strategy consists of a realization of the goals issued by the center situated on the higher level of the control hierarchy. The neighbouring centers on the same level realize the goals independently of each other and in general their interaction constraints are not satisfied. Then the cooperation between these centers are proposed. It consists of modifying the original goals and consequently the interaction variables to respect their constraints. A multiple representation can be used in the different centers. The centers connected to the processes dispose several models concerning, for example, the different operating points. Also, the higher level models can represent several types of interconnections or structures among which , one is chosen to satisfy a desired production . The realization of the centers and the construction of multi- level control network may be easily done by multi-microcomputer &yst_ . To do this and to define the communication rules between the computers, standard functional relations between the centers should be established .
we
propose a tracKing approach to syntheSize a class of real time algorithms . This approach offers the capability of progressive implementation of such type of systems. Also, the dialog on the baBe of trajectory tracKing with any center allow an operator intervention at any point of the industrial process .
L&2WfRALIZIID CDftR)L 1InB
CDm'IIRM'Ioa (CXlmICD)
Descending in the hierarchy, the models in control are more detailed and act on saaller parts of the industrial process. The centers try to achieve the Objectives issued by those of the higher levels . and decision centers
centers using a Single model. The model at the level (n+1) is a Simplified model of the ensemble, but keepe the structure of three systems connected in series. The evolution of this model is determined by the reference variables supplied by the level (n+2). The variables (zn) of the models at the level (n) tracK the reference variables (Zn+1) from the level (n+1). This tracKing may be measured as a distance (D) between the models, expressed in terms of the deviation between their corresponding variables. The distance between each model and the corresponding part of the higher level model could be minimized by optimal tracKing min 0 (f(zn+1 - zn» u
COOperation between interconnected systems. (HAgras, Binder, 1983 ). Each model has an ensemble of reference variables, supplied by a higher level model which may be incoherent. This is because of the difference between the simplified models or, because of the local constraints which are not considered by the higher level. Also, the form of the distance may be different for the different decision centers . Consequently, tracKing the same reference variable may lead to different values by the different models. For example consider the interaction variables of the neighbouring models Vj and wi' To equate their values, a cooperation between the centers j and i is suggested and produced by the correction lJ.Zv j and lJ.ZWi of the reference variables ZVj and zwi issued by a higher level. This correction increases the distances (Dj + .AD j ) which may lead to a definition of cooperation strategy for the N centers of the same level. One of the possible cooperation strategy (F) is based on the minimisation of the sub-optimality mesured by increasing (.AD) of the distances (and the costs). N
min F
r:
I:J.
0i
i=1
The relation between models may be represented by the quadratiC tracKing cost function baBed on the deviation of model variables. The input and output variables of each model tracK the reference variables given by a higher level models (Fig . 2) . For linear models and quadratic criterion, the solution of tracKing is a function of the reference variables evolution during an optimisation horizon. One step horizon gives an acceptable results due to the simultaneous input/output tracKing of the coherent reference variables issued at the same origin, the upper level model. In this case a real time control algorithm is independent of the position of the center in the hierarchy. The basic algorithmic solution for the Single model center is a classical one . (Ray, 1978) . The linear model (M) has the form :
TracKing coordination. A solution for this probl_ is to test the satisfaction of the Objectives by a simplified simulating model . By this Simulation, variables of the models in a higher level center are supplied to be tracKed by those of the models in a lower level center . To realize the tracKing approach a correlation between the models of different levels, for exa.ple between their variables, is needed . In fact, this condition is always satisfied since the models describe the same industrial process. The models can represent the dynamic evolution of the processes or can be limited to the static characteriBtics only. An exaIIPle of a
coordin4ted decentralised control (OODEOO) is illustrated in fig . 2. It represents the relations between the models belonging to different
x(k+1) y(k)
A x(k) C x(k)
+
B u(k)
where
y
and v represent the interaction variables of appropriate dimensions. The input (u) and the output (y) track the refBL'Bnce variables (zu) and (zy) issued by the higher level model W
137
Coo rdinated Dece ntralised Control Design
zv
zu -
[
ZU
zy -
L
zy
L
'!'he track.i.ng cost function is
T-l I: [(zu(k) - u(k»T R (zu(k) - u(k»]
Ji -
k-o
+ [(zy(k) - Y(k»T
Q (zy(k) - y(k»]
Taking a one step optilllization hori zon, the model input is given by u(k) - - L x(k) + "1 zu(k) -
~
zy(k)
-
S BT J( A
"1-
S BT (GT -
~_
S BT (GT - 1)-1
+
S R
cT Q
(R+BTJ(B)-l
S G J(
I )-1 LT R
-
A-BL
steady state solution of Riccati equation .
input variable (u) including the interaction (w) is a function of the reference variables (zu) and (zy) . The modification of interactions (w) and also ( v) could be realized by a correction of corresponding reference variables, (6zw , Azv). In figure 2 the three models (":l' Kt, ",,) connected in series track a higher level model. The interaction constraints may be not satisfied.
'!'he
To achieve the equality of interactions, the correction of reference variables could be calculated as a function of the cooperation matrix (") which expresses a relative effort of each element to aatisfy these interactions
Vj(k)--Wi(k)
A -i(k)
-1 "i
P'Unctional structure. The presence of several models to control physical process gives an additional degree of freedom . TWo fundu.ntal points should be considered I the quality measure of the lDOdels and the control 1_. The analysis of these points leads to a propoeition of an algorithmiC structure consisting of two parts (Monnier , 1977) (fig . 3) I Location models process and/or goals, . Synthesis of the control .
with L
strategy and depends on the observed evolution of the process . The different models and also the corresponding control algorithms may be different in nature and .achaniBID . Even if this affects the internal structure of the center., it should not modify the relations with the other center.. Tracking of reference variables can be used in different cases even in the presence of different model natures. Also, the multiple-<:enter may be integrated in the propoeed modular hierarchical structure without difficulties. This control canter realizes the objectives supplied by the other center. or given by the operator to control the process . ( Badr and other., 1984).
$
The location (or the classification) of the models uses as reference the control goals and process evolution. The respective _ight of these information depend on the position of the center in the control hierarchy. To simplify the explenation _ consider only the autonomous 1DU1tilDOdel center directly connected to one part of a real process . Location . It means poeitioning the models close to the process using the data obtained from the process. Then, the models are classified according to their capabilities to approximate the behaviour of the process . This classification is enabled by a quality index associated to each model. Positioning . It can be ensured by tracking the process by the models which are in competition to approximate the process behaviour. The variables of the process (Zp) are considered as reference variables to be tracked by those of each model (;.) . Thus , every model tries to be close to the process and its evolution follows that of the process. The optimal positioning can be achieved by finding a minilllulll distance between the process and every model
um
i
vi(k+l)--wk(k+l)
A zVi(k)
min ("li )w
- ("2i)v
(C i Bi Nli)v
- (C i Bi "2i)v
Ni
with (
0i (f(Zp - Zmi)}
u.u
where
)w '
)v
as sullalatricies of
d~n-
sions of the interactions between the neighbouring elements and
o
The existing algorithms take into accound either the difference be~en the model and process outputs through the optimal filtering (Lainiotis, 1976 I P'erreira-Magalhaes, 1983), or the difference in both inputs and outputs using the tracking optillliaation (Monnier, 1977) I (Badr and other., 1985). Classification. Usually, the distances used for positi oning are used to classify the candidate models. The model which gives a minilllllm value for 0i is chosen as the best one
° - inf( ( 01 ..•. . , several models could be used for the representation of one part of the process. The corresponding lDOdelbaBe formes a groundwork of 1DU1tiple control and decision centers. Each part of a center amploies one model with an appropriate mechaniBID of decision or control. '!'he coaa.ttation between the different parts of a multiple-<:enter is function of the control
0i' . . .. )
If the model i is identical to the process, its quality index will be null and, from this point of view the process will be exactly represented by this model. Control . Based on the results of the location stage, the control of the process is elaborated . It consists of basic control and control synthesis.
z..r. Binde r a nd R. A. Perrel
1 :~8
Basic control. The first problem of control is to generate control signals based on each model supposing that the representation of the process by these models is valid. This is called the basic control. The goal. is to make the model traclt the reference variables ( Zo ) which characterize the desired process evolution. The control will be calculated so as to IlliniIDize the distance.
Control BYBthesis. Its goal is to obtain the control Signals applicable to the process. This takes into account the goals, and the process approx1lllation. The control may be the one issued by the best model (Lainiotis, 1976 I Monnier, 1977) . Also it can be a combination of the different controls of the different models using weighting coefficients depending on the clasSification of the models (FerreiraMagalhaes, 1983) . The process control is
where
ai is function of the quality of the model
i
"M and "a being respectively the lIIl.n:unum and max:i.mum eigenvalues of matrix Qi Bi and AT ij . Atj '
This test has the advantage of reducing the problem to the study of a matrix of order n, if n subsysteII\B are interconnected, whatever the order of these subsyst8II\B is.
The application of new methods on industrial plants is generaly preceded by tests on pilot plants . In our case , the distillation pilot plant of "Laboratoi re d' Autexnatique de Grenoble" was used for the experimentation . Pour units compose this process I two binary distillation column, mixing and remixing unit. The units may be interconnected to form d i fferent configurations (series , parallel). The glass columns had 9 and 15 tray of 150 mm diameter. water methanol mixture feds the columns (2 tonnes/day) . The control action on each column are the heating power QB of the boiler and the reflux rate R. The mesured characteristics of the top product of each column are the quality (concentration) XD and the quantity (flow rate) ID . experimental results are presented : multi-model control and coordina tion of two column i nterconnected in serie. other results are presented in (Acquadro and others, 1982 I Badr and others, 1985) .
Two
The proposed multilnodel control structure is gener al and the corresponding traclting algorithms (Badr and others, 1984) can be easily adjusted to any center of the multilevel control system.
Multilnodel Multivariable Dynamic Control
For checlting the stability of the proposed control method, we can notice that the different subsystems, submitted to traclting control through the use of classic quadratiC optilllization, are stable . The problem is then reduced to the study of the stability of an interconnected system of stable subsystell\B . A sufficient condition of stability, to be published later, has been used, while testing a Lyapunov function made of the sum of local Lyapunov functions associated to the different subsyst8ll\B . Let us consider an interconnected linear system of n subsyst9II\B of equation n
d
i=l, . . . ,n
The stability of a subsystem gives the possibility to associate to this subsystem a Lyapunov function
with
Bi
solution of
Qi being an arbitrary positive definite matrix. A global Lyapunov function can be tested under the form
This test is satisfied if the square matrix G of order n is positive definite. I n G diagonal elements gi' and non diagonal elements gij have the values I
9
i
~
The quality of the control of real system depends largely on the representation of the models. The models based on physical and chemical laws are generally nonlinear and of large dimensions. They may be non applicable to a real time dynamic control. Usually the classical control methods requier the linear state-variable models for the syntheSis of feedbaclt control . In our case the identification of the first distillation column around several operating points give several linear state variables models. The control aim is to change the operating point of the column. The traclting of the reference variables g i ves the transition between the operating points . The experimental results of the multilnodel control algorithm (Perreira-Magalhaes, 1983) show (figure 4) a good performance and efficiency of this method . Dynamic Tracking Coordination. The aim of the experiment is the dynamic coordination of the two distillation column connected in series . That is , knowing the feed of the first column how can the efforts be partitioned between the two columns ; and how to partition the efforts for each column so as to satisfy the second column output product characteristics, taking into account the energy consumption (heating power) (Binder , 1984). The solution of this problem involves searching a compromise between the production and the consumption of the process as a wholl. Using a simplified state variable coordinator model, the partitioning of the increasing production is proposed to each column . These informations are used, by the control center, as reference variables to the control (QB , R) and output (XD,ID) variables of each column . The detailed model (6 state variables) of the column is used in the way that the column models traclt a part of coordinator model so as to minimise the traclti ng performance index , interaction constraint are solved by cooperation . The control variable of the column model is applied
Coo rdin ated Dece ntralised Co ntrol Design to the real process. The lIIOdelling error and non mesurable disturbances are caapensated by the traCking corrector working on the s~ bases as the traCking controlller (Ray, 1978) . In figure 5 the evolution of the coordinator DIOdel variables and local lIIOdel variables and real process evolution are presented . The correct evolution of the process ~s from the production goals lIIOdification.
139
traCking, an easy and natural dialogue with the h.-in operator. The general aspects of the traCking relations allows to build an open system for the futur developments not only on the function of the process control requirements, but also to be oompleted by new control and decisions techniques. The recent developments in the artificial intelligent can be introduced to the multimodel control structure in order to construct an expert control systems.
Hardware - SOftware Architecture REEEiEiiC&i
The traCking approach leads to the development of the lIIOdular control algorithms and consequently analogous hardware architecture. The Control and Decision center network is realised using microcomputers . The centers are built around one or several microprocessors. They are differentiated by their hardware architecture and software, depending on their level. In our application we distinguish three different levels instrumentation , local control and coordination . (Acquadro and others, 1982) . Instrumentation level , It was necessary at this level to be able to assure the acquisition and processing of measurements, and to achieve local controls of type P . I . D. At this level we made use of the multiprocessor instrumentation and control system called SKIRE . This system includes a treatment processor, a processor of C
Acquadro J . P., Binder Z., Pranco A, Rey D. (1983) . "Coordinated Decentralized Control (CODECO) Method, Implementation on Microcomputers and Experimentation on a Physical Process". In Binder-Perret , coaponents and Instruments for Distributed Control Systems, Pergamon Press, 1983, pp.37-44. Badr A. , Binder Z., 8agras A. N . , Perret R. (1984). " A mu It i-lIIOde 1 traCking controller for distributed control systems" , Conqress 1. P . A. C . , Budapest, Hungary. Badr A. , Binder Z . , Pranco A., Ray D. (1985). "TraCking Multimodel Control of Distillation Processes". WOrkshop LP' . A. C . Adaptive Control of Chemical Process, P'rankfurt, octobre 85 . Binder Z. (1977) . "Sur l'organisation et la conduite des systemes Complexes" . These de OOcteur-esSCiences, Grenoble. Binder Z . (1984). "Commande multimodele et cc::mnande coordonn"". RAIRO Automatique, vol. 18, n 2, p. 173 a 189. d~entraliHe
Binder Z. , Hagras A.N., perret R. (1984&). "Coordinated decentralised control (CODECO) with multimodel representation in S.G. Tzafestas (ed) Multivariable ~, p . 343- 358, Riedel Pub. Corp . Binder Z., p'erreira-Magalhaes M. and Rey D. (19841» . "Multivariable control of distillation columns" . Congres IP'AC, Budapest, Hungary . Perreira--Magalhaes M. (1983). "Sur une repr~sen tation multi-modele Etude d ' une technique de localisation et !pplication a la commande d ' une colonne a distiller. Thesis Docteur-In~nieur, INP Grenoble , P'rance. Hagras A.N. and Binder Z. (1983). "A decentralized cooperative control method" . Journal of Large Scale Systems , Theory and Applications. Vo1.4, n 3, 263277 . Lainiotis D.G. (1976). "Partitioning , a unifying framework for adaptive systems I . Estimation, II. Control". Proceeding of IEEE, vol. 64, n 8. Monnier B. (1977). "Contribution a la cc::mnande d'une classe de prOC4ki~s dynamiques industriels dans de grands domaines de fonctionnement" . Thesis OOcteurIng~nieur INP Grenoble, P'rance. Olaiwan Z. , Binder Z. (1978). "Algorithm processing unit for automatic control" . Proceeding IEEE camp. ~ n 78 , pp. 139-145 .
The control system organisation proposed in this paper forma a framework for the deSign of the control system and the methodology of its industrial application. The DIOdularity and standardization of control and decision centres facilitate the progressive implementation of the system in the industrial areas. The traCking approach aids the algorithmic development and permits, through the reference variables
Perret
R.
(1983). "Sur une ~e de COImlIilnde Bulletin ASSPA/SGA - Zurich n 3, pp .
hi~rarchis"".
3-10. Ray
D.
(1978). "Sur la COmmande DEcentral1~ Thesis Docteur-In~n1eur, INP Grenoble,
COordo~" .
Prance .
Z. J. Binder and R. A. Perret
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COORDINATED DECENTRALISED CONTROL DESIGN AND DISTILLATION PILOT PLANT APPLICATION Z.
J.
Binder and R. A. Perret
ill'
GmlObil' (CXRS -L'A 228), t;,\'SIEG-INPG, BP -16 , 38-1{)2 Sailll-.\[arlill-D'Hnfs, FrtllI(I'
La/lOrtI/oirl' r/'.J..II/01ll1lIiljllf
Abstract. The COOrdinated Decentralised Control forms a useful approach to control a complex industrial process. It enables the design of a multi level control system in the form of a hierarchical network of control and decision centers. The vertical information transfer help for the coordination in a hierarchical control and the horizontal information transfer is used for the cooperation in decentralised control. The relations between the control centers are expressed by the tracking of the used process models. The aggregated model situated on the upper level of the hierarchy is tracked by the detailed models of the lower level. Eventually a multiple model could be introduced to caracterise a process part in its various operating conditions . On the base of linear state variable models and the input-output quadratic tracking cost function, a Coordinated Decentralized Control Algorithm in the form of matrix modular computing blocs is presented. The stability study gives the condition to be satisfied for the interconnection of these centers. The application of the proposed approach to the experimental pilot plant with two distillation columns controled by a micro-computer distributed system is presented. Xeywords: Hierarchical control I Distributed system; Tracking multivariable control Multimodel control ; Distillation column.
Control methods are based on the tracking algorithm illlplemented in these centers. The proposed method leads to easier implrnnentat;'on of a distributed microcomputer network. The internal structure of the deciSion centers may be multiple, function of the number of models representing the system.
The development of the domain of distributed control systems using computer networks in creases the interest in the hierarchical and decentralised control methods for complex systems . Several new problems arise from these applications. The control system organisation, decentralised control methods and information exchanges are the most important aspects in the design and realization of the distributed control system. A common methodological approach in the design of particular parts could increase the efficiency and reduce the cost of the process control applications. Unfortunately there are very few workS taking into account simultaneously algorithm, information, hardware and software point of view.
An industrial process is composed of different systems characterized by their behaviour and particular situation. The structure of the industrial process is determined by the interconnections between its composing systems. This structure can be modified in conjunction with the global goals. The role of a control system is to organize and control the ensemble to realise these goals which concern the production quality, energy and material consumption and disturbances compensation.
The other problem comes from the complexity of the industrial processes and their modelling . The classical hierarchical and decentralised control methods aid to solve the problem of the control of large scale system due to the decomposition on several interconnected subsystems. The quality of results of these applications depends on the satisfaction of the mathematical hypotheSiS used for the method development. The large domain of the process operating conditions is usualy incompatible with linear hypotheSiS, consequently the classical methods do not give good results. There are no general methodology to control a non-linear or time-varying large scale systems. A multimodel representation could be proposed to overcome the limits of classical methods based on linear models.
To aide a progressive implementation of the hierarchical control system we propose a multilevel network with nets formed by "Control and Decision canters· ( CDC ) ( Binder, 1977 ) structured as knowledge based systems. The functional relation between the neighbouring centers on the same or on different levels and redundancy of corresponding information exchange contributes to the rObustness of the proposed structure .
The architecture of a multi-level control system consisting of several centers is presented in fig .1. A control and decision center, often of multiple representation, is assigned to each system to control it in its different operating situations (Binder and others, 19844). The centers located at a lower level are guided by those in the higher level whose role is similar except that they affect a group of systems. The highest center of the hierarchy takes decision following a global criteria and, through the different levels, controls the whole industrial
OUr contribution to solve the above problems consists in the methodological approach in the hierarchical control systetD design. The Control and Decision canters (CDC) formes the basic modular elements of the control system network. The COOrdinated Decentralized Control (CODECO) method and the loLlltimodel
135
Z. J. Binde r and R. A. Pe rret
136
process. Every center has the knowledge concerning that part which it controls. This knowledge is either in the font of analytical model or data baBe stored in the aaaory of this center. The limited size of this aaaory gives rise to a compromise between the precision and the extent of the stored model. So, the models on the low levels are more precise than those of the higher levels . On observing the hierarchy it is noticed that the number of centers is increasing going down in the hierarchy. Each center simulates one part of the process . The set of models of the centers located at the same level simulate the whole industrial process. The hierarchy of the models and the precision of the Simulation are related to the hierarchy of the criteria considered to elaborate the decisions in each center . The higher level centers consider globally the economical criteria, while the centers located near the process act on the physical characteristics. (Perret, 1983) . The control strategy of each control and decision
center is elaborated using a model or group of models and the corresponding criterion, which expresses the relations with center environment . The strategy consists of a realization of the goals issued by the center situated on the higher level of the control hierarchy. The neighbouring centers on the same level realize the goals independently of each other and in general their interaction constraints are not satisfied. Then the cooperation between these centers are proposed. It consists of modifying the original goals and consequently the interaction variables to respect their constraints. A multiple representation can be used in the different centers. The centers connected to the processes dispose several models concerning, for example, the different operating points. Also, the higher level models can represent several types of interconnections or structures among which , one is chosen to satisfy a desired production . The realization of the centers and the construction of multi- level control network may be easily done by multi-microcomputer &yst_ . To do this and to define the communication rules between the computers, standard functional relations between the centers should be established .
we
propose a tracKing approach to syntheSize a class of real time algorithms . This approach offers the capability of progressive implementation of such type of systems. Also, the dialog on the baBe of trajectory tracKing with any center allow an operator intervention at any point of the industrial process .
L&2WfRALIZIID CDftR)L 1InB
CDm'IIRM'Ioa (CXlmICD)
Descending in the hierarchy, the models in control are more detailed and act on saaller parts of the industrial process. The centers try to achieve the Objectives issued by those of the higher levels . and decision centers
centers using a Single model. The model at the level (n+1) is a Simplified model of the ensemble, but keepe the structure of three systems connected in series. The evolution of this model is determined by the reference variables supplied by the level (n+2). The variables (zn) of the models at the level (n) tracK the reference variables (Zn+1) from the level (n+1). This tracKing may be measured as a distance (D) between the models, expressed in terms of the deviation between their corresponding variables. The distance between each model and the corresponding part of the higher level model could be minimized by optimal tracKing min 0 (f(zn+1 - zn» u
COOperation between interconnected systems. (HAgras, Binder, 1983 ). Each model has an ensemble of reference variables, supplied by a higher level model which may be incoherent. This is because of the difference between the simplified models or, because of the local constraints which are not considered by the higher level. Also, the form of the distance may be different for the different decision centers . Consequently, tracKing the same reference variable may lead to different values by the different models. For example consider the interaction variables of the neighbouring models Vj and wi' To equate their values, a cooperation between the centers j and i is suggested and produced by the correction lJ.Zv j and lJ.ZWi of the reference variables ZVj and zwi issued by a higher level. This correction increases the distances (Dj + .AD j ) which may lead to a definition of cooperation strategy for the N centers of the same level. One of the possible cooperation strategy (F) is based on the minimisation of the sub-optimality mesured by increasing (.AD) of the distances (and the costs). N
min F
r:
I:J.
0i
i=1
The relation between models may be represented by the quadratiC tracKing cost function baBed on the deviation of model variables. The input and output variables of each model tracK the reference variables given by a higher level models (Fig . 2) . For linear models and quadratic criterion, the solution of tracKing is a function of the reference variables evolution during an optimisation horizon. One step horizon gives an acceptable results due to the simultaneous input/output tracKing of the coherent reference variables issued at the same origin, the upper level model. In this case a real time control algorithm is independent of the position of the center in the hierarchy. The basic algorithmic solution for the Single model center is a classical one . (Ray, 1978) . The linear model (M) has the form :
TracKing coordination. A solution for this probl_ is to test the satisfaction of the Objectives by a simplified simulating model . By this Simulation, variables of the models in a higher level center are supplied to be tracKed by those of the models in a lower level center . To realize the tracKing approach a correlation between the models of different levels, for exa.ple between their variables, is needed . In fact, this condition is always satisfied since the models describe the same industrial process. The models can represent the dynamic evolution of the processes or can be limited to the static characteriBtics only. An exaIIPle of a
coordin4ted decentralised control (OODEOO) is illustrated in fig . 2. It represents the relations between the models belonging to different
x(k+1) y(k)
A x(k) C x(k)
+
B u(k)
where
y
and v represent the interaction variables of appropriate dimensions. The input (u) and the output (y) track the refBL'Bnce variables (zu) and (zy) issued by the higher level model W
137
Coo rdinated Dece ntralised Control Design
zv
zu -
[
ZU
zy -
L
zy
L
'!'he track.i.ng cost function is
T-l I: [(zu(k) - u(k»T R (zu(k) - u(k»]
Ji -
k-o
+ [(zy(k) - Y(k»T
Q (zy(k) - y(k»]
Taking a one step optilllization hori zon, the model input is given by u(k) - - L x(k) + "1 zu(k) -
~
zy(k)
-
S BT J( A
"1-
S BT (GT -
~_
S BT (GT - 1)-1
+
S R
cT Q
(R+BTJ(B)-l
S G J(
I )-1 LT R
-
A-BL
steady state solution of Riccati equation .
input variable (u) including the interaction (w) is a function of the reference variables (zu) and (zy) . The modification of interactions (w) and also ( v) could be realized by a correction of corresponding reference variables, (6zw , Azv). In figure 2 the three models (":l' Kt, ",,) connected in series track a higher level model. The interaction constraints may be not satisfied.
'!'he
To achieve the equality of interactions, the correction of reference variables could be calculated as a function of the cooperation matrix (") which expresses a relative effort of each element to aatisfy these interactions
Vj(k)--Wi(k)
A -i(k)
-1 "i
P'Unctional structure. The presence of several models to control physical process gives an additional degree of freedom . TWo fundu.ntal points should be considered I the quality measure of the lDOdels and the control 1_. The analysis of these points leads to a propoeition of an algorithmiC structure consisting of two parts (Monnier , 1977) (fig . 3) I Location models process and/or goals, . Synthesis of the control .
with L
strategy and depends on the observed evolution of the process . The different models and also the corresponding control algorithms may be different in nature and .achaniBID . Even if this affects the internal structure of the center., it should not modify the relations with the other center.. Tracking of reference variables can be used in different cases even in the presence of different model natures. Also, the multiple-<:enter may be integrated in the propoeed modular hierarchical structure without difficulties. This control canter realizes the objectives supplied by the other center. or given by the operator to control the process . ( Badr and other., 1984).
$
The location (or the classification) of the models uses as reference the control goals and process evolution. The respective _ight of these information depend on the position of the center in the control hierarchy. To simplify the explenation _ consider only the autonomous 1DU1tilDOdel center directly connected to one part of a real process . Location . It means poeitioning the models close to the process using the data obtained from the process. Then, the models are classified according to their capabilities to approximate the behaviour of the process . This classification is enabled by a quality index associated to each model. Positioning . It can be ensured by tracking the process by the models which are in competition to approximate the process behaviour. The variables of the process (Zp) are considered as reference variables to be tracked by those of each model (;.) . Thus , every model tries to be close to the process and its evolution follows that of the process. The optimal positioning can be achieved by finding a minilllulll distance between the process and every model
um
i
vi(k+l)--wk(k+l)
A zVi(k)
min ("li )w
- ("2i)v
(C i Bi Nli)v
- (C i Bi "2i)v
Ni
with (
0i (f(Zp - Zmi)}
u.u
where
)w '
)v
as sullalatricies of
d~n-
sions of the interactions between the neighbouring elements and
o
The existing algorithms take into accound either the difference be~en the model and process outputs through the optimal filtering (Lainiotis, 1976 I P'erreira-Magalhaes, 1983), or the difference in both inputs and outputs using the tracking optillliaation (Monnier, 1977) I (Badr and other., 1985). Classification. Usually, the distances used for positi oning are used to classify the candidate models. The model which gives a minilllllm value for 0i is chosen as the best one
° - inf( ( 01 ..•. . , several models could be used for the representation of one part of the process. The corresponding lDOdelbaBe formes a groundwork of 1DU1tiple control and decision centers. Each part of a center amploies one model with an appropriate mechaniBID of decision or control. '!'he coaa.ttation between the different parts of a multiple-<:enter is function of the control
0i' . . .. )
If the model i is identical to the process, its quality index will be null and, from this point of view the process will be exactly represented by this model. Control . Based on the results of the location stage, the control of the process is elaborated . It consists of basic control and control synthesis.
z..r. Binde r a nd R. A. Perrel
1 :~8
Basic control. The first problem of control is to generate control signals based on each model supposing that the representation of the process by these models is valid. This is called the basic control. The goal. is to make the model traclt the reference variables ( Zo ) which characterize the desired process evolution. The control will be calculated so as to IlliniIDize the distance.
Control BYBthesis. Its goal is to obtain the control Signals applicable to the process. This takes into account the goals, and the process approx1lllation. The control may be the one issued by the best model (Lainiotis, 1976 I Monnier, 1977) . Also it can be a combination of the different controls of the different models using weighting coefficients depending on the clasSification of the models (FerreiraMagalhaes, 1983) . The process control is
where
ai is function of the quality of the model
i
"M and "a being respectively the lIIl.n:unum and max:i.mum eigenvalues of matrix Qi Bi and AT ij . Atj '
This test has the advantage of reducing the problem to the study of a matrix of order n, if n subsysteII\B are interconnected, whatever the order of these subsyst8II\B is.
The application of new methods on industrial plants is generaly preceded by tests on pilot plants . In our case , the distillation pilot plant of "Laboratoi re d' Autexnatique de Grenoble" was used for the experimentation . Pour units compose this process I two binary distillation column, mixing and remixing unit. The units may be interconnected to form d i fferent configurations (series , parallel). The glass columns had 9 and 15 tray of 150 mm diameter. water methanol mixture feds the columns (2 tonnes/day) . The control action on each column are the heating power QB of the boiler and the reflux rate R. The mesured characteristics of the top product of each column are the quality (concentration) XD and the quantity (flow rate) ID . experimental results are presented : multi-model control and coordina tion of two column i nterconnected in serie. other results are presented in (Acquadro and others, 1982 I Badr and others, 1985) .
Two
The proposed multilnodel control structure is gener al and the corresponding traclting algorithms (Badr and others, 1984) can be easily adjusted to any center of the multilevel control system.
Multilnodel Multivariable Dynamic Control
For checlting the stability of the proposed control method, we can notice that the different subsystems, submitted to traclting control through the use of classic quadratiC optilllization, are stable . The problem is then reduced to the study of the stability of an interconnected system of stable subsystell\B . A sufficient condition of stability, to be published later, has been used, while testing a Lyapunov function made of the sum of local Lyapunov functions associated to the different subsyst8ll\B . Let us consider an interconnected linear system of n subsyst9II\B of equation n
d
i=l, . . . ,n
The stability of a subsystem gives the possibility to associate to this subsystem a Lyapunov function
with
Bi
solution of
Qi being an arbitrary positive definite matrix. A global Lyapunov function can be tested under the form
This test is satisfied if the square matrix G of order n is positive definite. I n G diagonal elements gi' and non diagonal elements gij have the values I
9
i
~
The quality of the control of real system depends largely on the representation of the models. The models based on physical and chemical laws are generally nonlinear and of large dimensions. They may be non applicable to a real time dynamic control. Usually the classical control methods requier the linear state-variable models for the syntheSis of feedbaclt control . In our case the identification of the first distillation column around several operating points give several linear state variables models. The control aim is to change the operating point of the column. The traclting of the reference variables g i ves the transition between the operating points . The experimental results of the multilnodel control algorithm (Perreira-Magalhaes, 1983) show (figure 4) a good performance and efficiency of this method . Dynamic Tracking Coordination. The aim of the experiment is the dynamic coordination of the two distillation column connected in series . That is , knowing the feed of the first column how can the efforts be partitioned between the two columns ; and how to partition the efforts for each column so as to satisfy the second column output product characteristics, taking into account the energy consumption (heating power) (Binder , 1984). The solution of this problem involves searching a compromise between the production and the consumption of the process as a wholl. Using a simplified state variable coordinator model, the partitioning of the increasing production is proposed to each column . These informations are used, by the control center, as reference variables to the control (QB , R) and output (XD,ID) variables of each column . The detailed model (6 state variables) of the column is used in the way that the column models traclt a part of coordinator model so as to minimise the traclti ng performance index , interaction constraint are solved by cooperation . The control variable of the column model is applied
Coo rdin ated Dece ntralised Co ntrol Design to the real process. The lIIOdelling error and non mesurable disturbances are caapensated by the traCking corrector working on the s~ bases as the traCking controlller (Ray, 1978) . In figure 5 the evolution of the coordinator DIOdel variables and local lIIOdel variables and real process evolution are presented . The correct evolution of the process ~s from the production goals lIIOdification.
139
traCking, an easy and natural dialogue with the h.-in operator. The general aspects of the traCking relations allows to build an open system for the futur developments not only on the function of the process control requirements, but also to be oompleted by new control and decisions techniques. The recent developments in the artificial intelligent can be introduced to the multimodel control structure in order to construct an expert control systems.
Hardware - SOftware Architecture REEEiEiiC&i
The traCking approach leads to the development of the lIIOdular control algorithms and consequently analogous hardware architecture. The Control and Decision center network is realised using microcomputers . The centers are built around one or several microprocessors. They are differentiated by their hardware architecture and software, depending on their level. In our application we distinguish three different levels instrumentation , local control and coordination . (Acquadro and others, 1982) . Instrumentation level , It was necessary at this level to be able to assure the acquisition and processing of measurements, and to achieve local controls of type P . I . D. At this level we made use of the multiprocessor instrumentation and control system called SKIRE . This system includes a treatment processor, a processor of C
Acquadro J . P., Binder Z., Pranco A, Rey D. (1983) . "Coordinated Decentralized Control (CODECO) Method, Implementation on Microcomputers and Experimentation on a Physical Process". In Binder-Perret , coaponents and Instruments for Distributed Control Systems, Pergamon Press, 1983, pp.37-44. Badr A. , Binder Z., 8agras A. N . , Perret R. (1984). " A mu It i-lIIOde 1 traCking controller for distributed control systems" , Conqress 1. P . A. C . , Budapest, Hungary. Badr A. , Binder Z . , Pranco A., Ray D. (1985). "TraCking Multimodel Control of Distillation Processes". WOrkshop LP' . A. C . Adaptive Control of Chemical Process, P'rankfurt, octobre 85 . Binder Z. (1977) . "Sur l'organisation et la conduite des systemes Complexes" . These de OOcteur-esSCiences, Grenoble. Binder Z . (1984). "Commande multimodele et cc::mnande coordonn"". RAIRO Automatique, vol. 18, n 2, p. 173 a 189. d~entraliHe
Binder Z. , Hagras A.N., perret R. (1984&). "Coordinated decentralised control (CODECO) with multimodel representation in S.G. Tzafestas (ed) Multivariable ~, p . 343- 358, Riedel Pub. Corp . Binder Z., p'erreira-Magalhaes M. and Rey D. (19841» . "Multivariable control of distillation columns" . Congres IP'AC, Budapest, Hungary . Perreira--Magalhaes M. (1983). "Sur une repr~sen tation multi-modele Etude d ' une technique de localisation et !pplication a la commande d ' une colonne a distiller. Thesis Docteur-In~nieur, INP Grenoble , P'rance. Hagras A.N. and Binder Z. (1983). "A decentralized cooperative control method" . Journal of Large Scale Systems , Theory and Applications. Vo1.4, n 3, 263277 . Lainiotis D.G. (1976). "Partitioning , a unifying framework for adaptive systems I . Estimation, II. Control". Proceeding of IEEE, vol. 64, n 8. Monnier B. (1977). "Contribution a la cc::mnande d'une classe de prOC4ki~s dynamiques industriels dans de grands domaines de fonctionnement" . Thesis OOcteurIng~nieur INP Grenoble, P'rance. Olaiwan Z. , Binder Z. (1978). "Algorithm processing unit for automatic control" . Proceeding IEEE camp. ~ n 78 , pp. 139-145 .
The control system organisation proposed in this paper forma a framework for the deSign of the control system and the methodology of its industrial application. The DIOdularity and standardization of control and decision centres facilitate the progressive implementation of the system in the industrial areas. The traCking approach aids the algorithmic development and permits, through the reference variables
Perret
R.
(1983). "Sur une ~e de COImlIilnde Bulletin ASSPA/SGA - Zurich n 3, pp .
hi~rarchis"".
3-10. Ray
D.
(1978). "Sur la COmmande DEcentral1~ Thesis Docteur-In~n1eur, INP Grenoble,
COordo~" .
Prance .
Z. J. Binder and R. A. Perret
140
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:
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i
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~ ____ J
ll/h l
V
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:
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360
Multi-level control structure
Fig.1 zu
REFERENCE
VARIABLES
zy
Fig.4
,, leve 1 n + '--.:--f-ih::f--tr--:f-II--'- _ - - - - - -- - - - - - - - - - - ,
' I
31 :0 L_'_ _-=---=-=,.,""'-"-"",,--;-n o 24 1012 2022 x lO' 1[51
08
Multimodel Control of Distillation Column Set point coordinator model
~
~oc:al model proce ••
~~f
0_
R
-7
~ 12
M.
Fig.2
5
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4 \
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~
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Coordinated Decentralised Control (CODECO)
LD
-5
.
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fj U
~ MO~~~E~,'
CONTROL ""."
TY
BASIC CONTROL
MODEL
,/ /
.' CONTROL
7 "
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-
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Fig.S
Tracking Coordination of Distillation Plant
'
'\ ftodule
MODEL CLASSIFICATION Admin istT'-Itive
,
interface
lEJ~ tt IA~'Ir\I; I "em. '-I
I
I
'ieac.
Fig.3
~
-5
u
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e
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Multimodel Control Structure
Fig.6
Ring multi-microprocessor structure