Integrating expert knowledge into industrial control structures

Computers in Industry 52 (2003) 235–251

Integrating expert knowledge into industrial control structures Sylvie Galichet*, Laurent Foulloy Laboratoire d’Informatique, Syste`mes, Traitement de l’Information et de la Connaissance, Universite´ de Savoie, BP806, Annecy 74016, France

Abstract This paper is concerned with the improvement of existing industrial control structures by the integration of human experience and expertise. Through two case studies concerning mechanical and petrochemical industries, it is illustrated that conventional control techniques and knowledge-based strategies can complement each other. The objective is to derive maximum profit from available materials and equipment by combining them efficiently. From a concrete point of view, linguistic fuzzy systems (LFS) are used to achieve a collaboration between numeric and expert processing. Three distinct architectures are proposed to combine conventional regulators and knowledge-based procedures in a unified control structure. All of them are based on a context-oriented decomposition of the control problem under consideration. The choice of a particular architecture is then related to existing industrial installations and is finally dependent on company strategy. # 2003 Elsevier B.V. All rights reserved. Keywords: Knowledge-based control; Conventional control; Co-operative approach; Linguistic fuzzy systems

1. Introduction Industrial processes are often so complex that their automation calls for sophisticated control techniques, particularly in the presence of non-linearities, parameter variations and disturbances. Unfortunately, since most ‘‘modern’’ control methods depend upon an accurate model of the process, their use in industry is still limited. Indeed, industrial processes are usually ill-defined and explicitly modelling them is a considerably difficult task. Induced costs are often so high that most types of industrial processes are still manually supervised, or even controlled. Much knowledge might be available in many forms, such as operator experience, reports, recorded data. Knowledge-based *

Corresponding author. Tel.: þ33-450-09-65-42; fax: þ33-450-09-65-59. E-mail address: [email protected] (S. Galichet).

control that can capture human experience and other forms of ‘‘soft’’ knowledge and use them in a reasoning framework would be quite desirable for many control process applications. In this context, Mamdani’s pioneering work [1] has shown that linguistic fuzzy controllers were able to emulate or duplicate human control behaviour. Based on fuzzy set theory introduced by Zadeh [2], Mamdani-type fuzzy controllers interpolate between discrete control rules, usually obtained from human operators. Nowadays, Mamdani style controllers are used in most commercial applications of fuzzy control (air-conditioners, washing machines, etc.). In industry, the success of fuzzy control is essentially due to low development cost. However, the empirical nature of fuzzy controller design does not allow any performance guarantee. Actually, knowledge-based approach implicitly assumes that human beings are ‘‘good’’ controllers. This strong assumption

0166-3615/$ – see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0166-3615(03)00129-5

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is not always true, especially in nominal context when automatic control is generally more precise than a human operator. In other words, fuzzy expert control should not replace model-based crisp control but they can complement each other. Even if desirable, the development of a co-operative strategy is seldom tackled in a direct way. In other words, the question ‘‘How does an engineer integrate a conventional and an expert control design?’’ remains an open problem. This paper will address this key point with direct reference to industrial applications. The proposed methodology is based on the decomposition of the global control problem. However contrary to hierarchical control that relies on a taskoriented decomposition (e.g., [3]), a context-oriented decomposition is considered. Available controllers (fuzzy expert controllers, conventional controllers (CCs), etc.) are then classified with respect to the decomposition. Given a specific identified context, control action is determined by selecting the optimal available controller. Different practical architectures are proposed for implementing the multi-controller structure. Especially, when the initial context-oriented decomposition is fuzzy rather than crisp, fuzzy mixing of different control contributions is preferred instead of classical switching which may induce bumps in the resulting control signal. This paper is organized as follows. In Section 2, the computation mechanism associated with linguistic fuzzy systems is summarized, as this is necessary to understand possible co-operation between different controllers. Section 3 is devoted to fuzzy controller design with the purpose of collaborating with other controllers. Different control architectures are proposed and practical guidelines are given for synthesizing linguistic fuzzy systems. Then, Section 4 presents two different industrial applications in which fuzzy and crisp controllers complement each other. The last section gives some conclusions regarding advantages and drawbacks of presented implementations.

2. Linguistic implementation of fuzzy systems As exhibited in the typology of fuzzy controllers developed by Foulloy and Galichet [4], Mamdani-type fuzzy systems can be implemented in four different ways depending on the nature of fuzzy subsets handled

by the inference unit. Indeed, according to the chosen fuzzifier, the inference procedure has to deal with input fuzzy subsets which can be defined on numerical universes or linguistic term sets. In the same way, the inferred result can be expressed in numerical or linguistic forms, leading to the use of an appropriate defuzzifier. Finally, depending on whether the fuzzy inputs and output are numerical or linguistic, the inference scheme can take four different forms. Among those, one is of particular interest because it allows pure linguistic reasoning, numerical interfacing being achieved by fuzzification and defuzzification units. This implementation results in what we call linguistic fuzzy systems (LFS) and will be used in all applications that are considered. The remainder of this section is devoted to a detailed presentation of LFS implementation. For the sake of simplicity, LFS are introduced for dealing with two inputs, x and y, and one output z. The extension to more inputs is straightforward. LFS are described using fuzzy rules whose form is similar to Mamdani-type rules. The single difference resides in the possibility to assign a weight to each rule, as expressed in the following generic rule: If x is Ai and y is Bj z is Ck with weight aijk ;

then (1)

where LX ¼ fAi gi¼1;...;I , LY ¼ fBj gj¼1;...;J and LZ ¼ fCk gk¼1;...;K represent the sets of words, i.e. the vocabularies, associated with the considered variables. Each rule, indexed by a triple (i, j, k), can be viewed as a relationship linking input words Ai and Bj with output word Ck. The weight aijk 2 ½0; 1 defines the strength of the link between Ai, Bj and Ck, that is mR ðAi ; Bj ; Ck Þ ¼ aijk :

(2)

A Mamdani rule base represents a special case of weighted rules since each rule has a weight equal to 1. Using weighted rules, several rules can have identical premises but different conclusions. In this case, they can be regrouped in a single compact rule expressed as: X aijk If x is Ai and y is Bj then z is ; C k¼1;k k (3) where aijk ¼ 0 when the corresponding rule does not exist.

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x0 ∈X

D

Ex ∈F(LX) I

D

y0 ∈Y

237

Ey ∈F(LY)

H

Fz∈ F(LZ)

z ∈Z

Fig. 1. LFS implementation for two inputs.

Let us assume the input pair (x0, y0). The output z is then computed according to the fuzzy mechanism illustrated in Fig. 1, where D, I and H represent the fuzzification, inference and defuzzification steps respectively. F(LX) (resp. F(LY) and F(LZ)) denotes the set of all fuzzy subsets defined on LX (resp. LY and LZ). The fuzzifier transforms a numeric input value into a linguistic fuzzy subset using the fuzzy description D introduced by Zadeh [5], that is Ex ¼ Dðx0 Þ ¼

X mA ðx0 Þ i

i¼1;I

Ey ¼ Dðy0 Þ ¼

j¼1;J

Bj

8Ck 2 LZ; mFz ðCk Þ ¼ maxAi 2LX;Bj 2LY minðmEx ðAi Þ; mEy ðBj Þ; aijk Þ ¼ maxAi 2LX;Bj 2LY minðmDðx0 Þ ðAi Þ; mDðy0 Þ ðBj Þ; aijk Þ ¼ maxAi 2LX;Bj 2LY minðmAi ðx0 Þ; mBj ðy0 Þ; aijk Þ:

8Ck 2 LZ; (4)

8Ck 2 LZ; mFz ðCk Þ ¼ maxAi 2LX;Bj 2LY minðmEx Ey ðAi ; Bj Þ; mR ðAi ; Bj ; Ck ÞÞ:

(7)

where ? stands for a t-conorm and T1, T2 for t-norms that, respectively, implement combination and cartesian product operations. Finally, the defuzzification interface H has to determine a crisp value z from the inferred linguistic fuzzy subset Fz. In order to apply classical defuzzification methods that are commonly used in numerical framework (e.g., [6]), Fz first has to be transformed into a numeric fuzzy subset. One way to avoid this conversion step consists in choosing a specific defuzzification method whose implementation only requires the knowledge of the degree of applicability attached to each possible conclusion Ck. In what follows, a fuzzy mean method is chosen, which leads to PK mFz ðCk Þzk z ¼ HðFz Þ ¼ Pk¼1 ; (8) K k¼1 mFz ðCk Þ

The notation mAi(x0) (resp. mBj(y0)) represents the membership degree of x0 (resp. P y0) in the fuzzy meaning of Ai (resp. Bj). Signs and / are used to express linguistic fuzzy subsets as proposed by Zadeh [2]. Fig. 2 illustrates Eq. (4) when x0 ¼ 23. Then, the inference I consists in determining the image of Ex Ey by the relation R built from the rules. This is done by directly applying Zadeh’s compositional rule of inference at the linguistic level

(5)

Linguistic fuzzification of x0 = 23

Fuzzy partition of X 1

mFz ðCk Þ ¼?Ai 2LX;Bj 2LY T1 ðT2 ðmAi ðx0 Þ;

mBj ðy0 ÞÞ; aijk Þ; :

A1

A2

A3 A4

0

10

17 20 25 x0 = 23

A5

0

(6)

From a more general point of view, inference I can be expressed as

and

Ai

X mBj ðy0 Þ

When using t-norm min to implement the cartesian product, Eq. (5) becomes

Ex = D(23) = 0.4/A4 + 0.6/A5

X

A1

Fig. 2. Linguistic fuzzification.

A2

A3

A4

A5

LX

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with conventional control techniques. On the contrary, it serves as a tool for developing a collaboration between numeric control and expert control. For complex processes, it is often difficult to build a single control law which is able to take into account all situations that can be encountered. On the other hand, it is generally possible to design controllers for dealing efficiently with specific cases. The strategy developed in this paper is based on this state of the facts. It simply consists in applying a ‘‘divide and rule’’ policy. The global control problem is thus decomposed into elementary problems which can be solved more easily. For implementing such a strategy, different control structures can be devised as illustrated in Fig. 3. A LFS is included in the three considered architectures. However, depending on the chosen configuration, the objective of the LFS is completely different and the knowledge required for its synthesis has to be in accordance. In the first structure, called parallel combination (Fig. 3a), two controllers are included in the global architecture. The underlying principle consists in using a CC that responds satisfactorily in most cases, while keeping in the background a fuzzy controller (LFS) which is ready to take over from the former

where zk is a characteristic numerical value associated with symbol Ck. In the case of a triangular partitioning of Z, zk will be chosen so that mCk ðzk Þ ¼ 1. In other words, zk represents the modal value of Ck. Such a selection results in the height defuzzification method used by Bouslama and Ichikawa [7].

3. Fuzzy controller design 3.1. Control architectures This section introduces different control architectures that include LFS. In order to tackle LFS synthesis, it is essential to gather all information that can be merged into the fuzzy strategy. Not only expert knowledge has to be considered but also numeric information such as process models and control laws. This means that process engineers and control practicians should contribute to the development of a global strategy. Actually, our propose is simply to take the best advantage of distinct available competencies. In this framework, the use of LFS provides an unified formalism for handling information of different types. The fuzzy approach must not be viewed as being in opposition

EK

Implemented component Incorporated knowledge

LFS EK CC SS LFS P C

Expert Knowledge Conventional Controller Switching Strategy Linguistic Fuzzy System Process Controller

SS

+

P

CC (a) Parallel combination EK

CC EK

SS

C2

+ +

LFS

P

SS

C1 LFS

P

-

Cn

(b) Integrated combination

(c) Supervised combination

Fig. 3. Co-operative control architectures.

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when a specific situation occurs. Both controllers concurrently deliver the evaluated control action and a switching strategy (SS) is implemented using a crisp decision-making algorithm. In the second architecture (Fig. 3b), the three previously introduced components (CC, LFS, SS) are merged into a single fuzzy controller. The considered CC can be represented, or at least approximated, by a LFS which can be built automatically by applying modal equivalence principle (see [8]). Then, the switching strategy is based on linguistic fuzzy variables, specially introduced in the rule premises for this purpose. Indeed, in this integrated combination, a rule of the form ‘‘If x is Ai and y is Bj and s is Sl then z is Ck’’ is viewed as implementing a fuzzy selection according to variable s among L fuzzy controllers where L is the number of symbols used to describe s. The last structure (Fig. 3c) is a generalization of the two previous ones in the sense that many different controllers can be handled simultaneously. The LFS acts as a fuzzy supervisor that implements the switching strategy in a fuzzy way. The provided fuzzy decision is no longer crisp and a defuzzification-like algorithm determines the final control action by mixing control contributions according to their activation degree. A similar result is obtained with structure (b) which is however restricted to the combination of fuzzy expert controllers. In the supervised architecture (c), any type of controller C can be exploited. 3.2. General methodology As illustrated in the previous paragraph, different architectures can be chosen for implementing a particular control strategy. Under certain conditions, the three presented configurations can be strictly equivalent from a numeric point of view. In such cases, there are no scientific arguments for making an objective choice. It means that technical considerations become preponderant in the decision making. Moreover, induced economical and strategic orientations are of great importance for concerned companies. Incidentally, the latter point is often at the source of the choice of an expert approach. In this context, a complete formalization of control design procedure becomes very difficult or even impossible. In what follows, some key points are however exhibited. They form a kind of applied

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methodology for LFS-based control structure development. 3.2.1. Listing existing equipment and knowledge Facing a real automation problem, the first step consists in compiling an inventory of available means. This task has to be carried out at same time in terms of knowledge (model, control law, expertise, data) and industrial devices (regulators, sensors, actuators). 3.2.2. Determining the exact purpose of the fuzzy system According to existing environment, LFS contribution has to be precisely defined. Actually, this step consists in choosing a global architecture into which the LFS will have to fit. 3.2.3. Verifying the adequacy between available expert knowledge and defined LFS objective Expert knowledge is rarely available in the form of written rules. Its existence is however guaranteed when a human being is able to solve considered problem. Here, it should be noticed that fuzzy control is not panacea. In other words, it does not apply to complex or ill-defined problems when these cannot be tackled with a human-based approach. 3.2.4. Selecting and constructing influential variables In order to get a satisfying reproduction of expert know-how, all quantities preponderantly involved in the human reasoning process have to be used as LFS input variables. This means that they must be accessible, i.e. measured or at least estimated. This key point emphasizes the necessity of equipping the automated system with appropriate sensors. Actually, the success of most industrial fuzzy applications is essentially related to the introduction of new sensors, such as, for example, turbidity sensors in washing machines. 3.2.5. Building the rule base Whatever the technique used (direct synthesis or CC mimicking), experts should be closely associated in the rule generation process. In a fuzzy framework, the rule base replaces the transfer function. It is thus an essential element whose interpretability has to be kept in order to allow final validation by expert.

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3.2.6. Partitioning input and output universes of discourse into labelled fuzzy subsets This task allows the assignment of a numeric fuzzy meaning to words involved in the linguistic rule base. Actually, it corresponds to the definition of numericto-linguistic and linguistic-to-numeric interfaces, which are needed for implementing fuzzification and defuzzification according to Eqs. (4) and (8). From a conceptual point of view, it can be put in the same category as the identification of the parameters associated with a specified transfer function. 3.2.7. Fine tuning using rule weights This ultimate step consists in adjusting the final rule base for improving LFS performance. Assigning a degree of importance to each elementary rule amounts to a constrained adjustment of numeric outputs. When simulation is not possible, rule weights must be adapted on line according to a trial and error procedure.

However, preliminary calibration can often be achieved off line using recorded process data.

4. Applications This section reviews three different industrial applications that exploit LFS-based control structures. The three co-operative architectures introduced in Fig. 3 are successively illustrated. 4.1. An expert fuzzy controller for continuous casting mould level control The process under consideration is illustrated in Fig. 4 (for details, see [9]). Essentially, a casting machine consists of

a liquid metal reservoir, the ladle;

a distribution system, the tundish;

Fig. 4. Mould level control: (a) continuous cating machine; (b) clogging/unclogging cycle of the nozzle.

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a water-cooled mould;

a rolls system to drive and bend the semi-finished steel product. Liquid steel is delivered in a ladle to the casting floor and then poured at a controlled rate into the tundish. At the bottom of the tundish, the molten metal flows through several submerged entry nozzles and fills the mould. Solidification of the liquid steel starts in the water-cooled mould and progressively continues as the strand moves through the casting machine. It is now widely acknowledged that surface quality of the final product highly depends on steel level in the water-cooled mould. That is the reason why steel producers pay particular attention to mould level control. The control objective simply consists in maintaining the height of liquid steel in the mould at a constant desired level. In the application presented, the flow of liquid metal from the tundish to the mould is controlled by a stopper rod mechanism driven by an electric jack and the steel level is measured by an eddy current sensor. Under normal circumstances, PID control performs quite well, but abnormal conditions, particularly nozzle uncloggings as illustrated in Fig. 4b, require manual intervention. Indeed, when the flow of matter into the mould increases suddenly, the PID controller is not able to prevent large level variations that can even lead to mould overflow. A fuzzy controller is thus designed for rejecting effects of nozzle uncloggings. The global control architecture includes both controllers, i.e. PID and fuzzy, that concurrently deliver a control action (see Fig. 3a). The one that will be effectively applied to the process is selected in

241

accordance with the process state. In order to ensure bumpless switching between both controllers and thus smooth control, an additional tracking PI block is introduced in the control structure (for details, see [10]). The choice of parallel combination of both involved controllers has been based on the existing technical environment. Indeed, the control architecture of Fig. 3a has not been specifically developed for integrating the fuzzy controller but was already in use for dealing with the switching from manual to PID control. The fuzzy controller synthesis is directly based on the know-how of the operators who habitually control the process during disturbed phases. The rule design has been divided into three steps according to the following decomposition:

Writing of general rules.

Specification of anticipative rules.

Tuning of the LFS. During the first step, general rules that describe the expert control strategy are generated. According to the expert formulation, three situations can be distinguished for the mould level: ‘‘Above’’, ‘‘Around’’ and ‘‘Under’’ the setpoint. By defining the regulation error as the difference between the measured level and the desired one, ‘‘Above’’, ‘‘Around’’ and ‘‘Under’’ can be translated in terms of ‘‘Positive’’, ‘‘Zero’’ and ‘‘Negative’’ errors. In the same way, a ‘‘Positive’’, ‘‘Zero’’ or ‘‘Negative’’ change in error characterizes an increasing, stable or decreasing mould level. For a given process state, i.e. a given mould level and a given evolution, the expert can express how he would act if he was controlling the system. By coding the expert strategy in a linguistic table, the rule base given

Fig. 5. General rules.

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Fig. 6. Anticipative rules.

in Fig. 5 is obtained. The notations ‘‘Nothing’’, ‘‘Open’’, and ‘‘Close’’ correspond to the possible control actions defined by the expert. The cells where two different conclusions are specified correspond to cases for which the operator is unable to decide. In the second step, new rules describing how to reject disturbances are added to the rule base. It consists in introducing anticipatory actions that allow preventive reactions when sudden and important variations occur in the process behaviour. As illustrated in Fig. 6, two anticipatory rules have been defined. They are based on the reaction of the experts when unclogging occurs. Thus, the stopper is closed down when the level is rising even if the level is below the setpoint. Similarly, the stopper is opened when the level is decreasing even if the level is above the setpoint. It can be noticed that the definition of the two anticipatory rules requires the definition of two new linguistic terms (NS and PS) for the error description.

They, respectively, represent subclasses of N(egative) and P(ositive) errors. The third and last step consists in tuning the fuzzy controller. Indeed, once the rule base is defined, the link between the linguistic and numeric representations has to be established. This is done by defining the fuzzy meaning attributed to each linguistic term. The fuzzy controller tuning also requires balancing anticipatory actions with natural actions. This was done by assigning a weight to each expert rule. Furthermore, the introduction of rule weights makes it possible to keep in a single rule base several rules with the same antecedent but different conclusions without any contradiction. The control strategy described earlier was successfully implemented in January 1996 on a French slab caster. A data-logger allows an accurate analysis of the control performance. Fig. 7 shows the behaviour of the fuzzy control strategy during a real nozzle unclogging. Without the introduction of the LFS,

Fig. 7. Experimental results of the expert fuzzy control strategy.

S. Galichet, L. Foulloy / Computers in Industry 52 (2003) 235–251

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the unclogging occurrence would have led to a manual intervention. 4.2. An expert fuzzy numeric controller for floating level control in a refinery tank This section is concerned with the synthesis of a fuzzy controller for maintaining a floating level in a tank on top of the atmospheric distillation unit of a refinery (see [11]). The designed fuzzy controller, developed in collaboration with ELF Solaize research centre, takes advantage of a non-linear algorithmic controller that was in use prior to the present study. Indeed, the original controller, whose performance was satisfactory during normal behaviour phases, was used for building the initial fuzzy controller. By introducing expert knowledge in the initial rule base, the fuzzy controller has then been improved so that manual intervention can be avoided when disturbances occur. Generally speaking, the proposed design strategy can be decomposed into two steps

fuzzy controller initialization by copying an existing controller,

fuzzy controller improvement by local rule modification or generation. This kind of procedure makes possible the integration of numerical and expert knowledge in a single fuzzy controller possible. It leads to the choice of an integrated combination of different available information as advocated in the control architecture of Fig. 3b. This implementation is all the more natural because the prior control structure was already computer-based (no specific analog device). In the present case, the process under consideration is illustrated in Fig. 8. The level in the tank has to be maintained between Lmin and Lmax by acting on output flow. In this framework, the implemented algorithmic controller estimates the required change in output flow (dF) according to the following equations: ðdLÞ2 if dL  0; Lmax  L (9) 2 ðdLÞ dF ¼ K if dL  0; Lmin  L where dL represents the change in level and K is a numerical constant value that depends on tank dF ¼ K

Fig. 8. Floating level control.

characteristics and the sampling period. A saturation procedure is finally applied so that jdFj  G:

(10)

This controller is transformed into an initial fuzzy controller by applying the modal equivalence principle (see [8]). Input variables are chosen according to Eq. (9). It is thus reasonable to make direct use of the variable L in the fuzzy rules. On the other hand, as dL2 is the single occurrence of the change in error in Eq. (9), it is possible to square the considered variable before it enters the fuzzy controller. This procedure requires that information concerning the sign of dL be preserved and leads to the choice of sign(dL) dL2 as the fuzzy system’s second input. Applying the modal equivalence principle, Table 1 is obtained for Lmin ¼ 0, Lmax ¼ 100 and K ¼ 1. Symbols Ai, i ¼ 0; . . . ; 4, (resp. Bj, j ¼ 3; . . . ; 3) correspond to triangular fuzzy subsets whose membership functions are regularly distributed on [0, 100] (resp. [100, 100]). It can be noticed that generated rules are expressed using zero-order Sugeno formalism, that is rule conclusions are numerical values. Symbols A0 and A4 have 0 and 100 as modal values, respectively, i.e. Lmin and Lmax, which results in fuzzy rules whose conclusion is undefined (1 according to the sign of dL). However, by introducing the saturation step of Eq. (10) into the fuzzy controller, infinity can be replaced by G in Table 1. The fuzzy cells (A0, B0) and (A4, B0) illustrate the existence of a discontinuity in the algorithmic control law (9). If a good representation of the latter is desired, the symbol B0 has to be split into B0 and B0þ. In the present case, the initial rule base will be modified according to expert opinions. Hence, the quality of the equivalence between the control law (9) and its fuzzy implementation (Table 1) is judged sufficient and no further advanced processing is developed.

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Table 1 Synthesized flizzy rule base L 2 ½Lmin ; Lmax 

A0 A1 A2 A3 A4

Sign(dL) dL2 B3

B2

B1

B0

B1

B2

B3

1 4 2 1.33 1

1 2.67 1.33 0.89 0.67

1 1.33 0.67 0.44 0.33

1/0 0 0 0 0/þ1

0.33 0.44 0.67 1.33 þ1

0.67 0.89 1.33 2.67 þ1

1 1.33 2 4 þ1

Fig. 9. Control surfaces.

Fig. 9 illustrates the control surfaces associated, respectively, with the algorithmic controller of Eq. (9) and the fuzzy controller described by Table 1 (choice of a zero control action when two antagonist conclusions are identified and G ¼ 10). Concerning the fuzzy implementation, the distribution of the considered modal points is shown in Fig. 9b. It can be noticed that the choice of sign(dL) dL2 as input variable has induced a quadratic distribution of the modal values associated with dL. In order to facilitate knowledge integration, it is convenient to transform the generated Sugeno rules into linguistic rules. This preliminary step can be done simply by fuzzifying rule conclusions with respect to a fuzzy partition of the output universe of discourse. For better interpretability, the latter can be chosen by concerned experts. In the present case, nine linguistic values, respectively, denoted N(egative)V(ery)B(ig), NB, NM(edium), NS(mall), Z(ero), P(ositive)S, PM, PB and PVB, are defined according to expert suggestions. Associated membership functions are triangular

and form a strict partition.1 Corresponding modal values are set to 10, 2, 1, 0.25, 0, 0.25, 1, 2, 10, where extreme value 10 represents the saturation threshold G (see Eq. (10)). Using the so-defined output partition, rule base of Table 1 is transformed into rule base of Table 2 (restricted to positive values of dL because of original symmetry). The resulting linguistic rules are weighted and their use is based on the LFS implementation described in Section 2. For example, the gray cell in Table 2 corresponds to two distinct rules with different weights, merged into a single compact rule of form (3) L is A0

If

and

signðdLÞ dL2 is B1

dF is PS with weight 0:89 1

then (11)

Let LX ¼ fAi gi¼1;...;I be a set of linguistic terms. If the associated membership functions are defined so that X mAi ðxÞ ¼ 1; 8x 2 X; i¼1;...;I

the corresponding fuzzy partition is said to be strict.

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245

Table 2 LFS rule base L 2 ½Lmin ; Lmax 

A0 A1 A2 A3 A4

Sign(dL) dL2 B0

B1

B2

B3

1/Z 1/Z 1/Z 1/Z 1/Z

0.89/PS þ 0.11/PM 0.74/PS þ 0.26/PM 0.44/PS þ 0.56/PM 0.67/PM þ 0.33/PB 1/PVB

0.44/PS þ 0.56/PM 0.15/PS þ 0.85/PM 0.67/PM þ 0.33/PB 0.92/PB þ 0.08/PVB 1/PVB

1/PM 0.67/PM þ 0.33/PB 1/PB 0.75/PB þ 0.25/PVB 1/PVB

If L is A0 and signðdLÞ dL2 is B1 dF is PM with weight 0:11:

then (12)

It can be also noticed that output linguistic fuzzy subsets have been obtained by fuzzifying the numerical conclusions of Sugeno rules using the fuzzy description advocated in Eq. (4). For the rule previously considered, this procedure is illustrated by the following equation: Dð0:33Þ ¼

mPP ð0:33Þ mPM ð0:33Þ 0:89 0:11 þ ¼ þ : PS PM PS PM (13)

Thanks to rule weights introduced in the generated LFS, the numerical precision of Sugeno fuzzy rules is kept. Actually, when appropriate fuzzy operators are chosen in the LFS implementation (7), a strict equivalence with zero-order Sugeno mechanism is guaranteed. However, different levels can be considered when interpreting a LFS. Indeed, when computational aspect is left out, a better understanding may be achieved by considering condensed rules. For example, the rule ‘‘If L is A0 and sign(dL) dL2 is B1 then dF is between PS and PM’’ is probably more meaningful than its weighted counterpart of Table 2. A more synthetic rule base can even be derived by simply

restricting each rule conclusion to the more representative linguistic term, that is the one associated with the largest weight. In the present application, such a synthetic representation has been chosen to make interaction with experts easier. Then, the rule base of Table 3 serves as a basis for further integration of expertise. First, experts point out the importance of being in a favourable situation when possible disturbances appear. It means that level stabilization close to authorized limits Lmin and Lmax should be avoided. Actually, stabilization should be allowed only around central level values, which leads to the modification of column B0 in Table 3 as illustrated in Table 4. Another expert modification concerns control actions that have to be applied when the level is close to bounds Lmin and Lmax (rows A0 and A4 in Table 3). In such cases, according to safety requirements, strong actions are advocated whatever the observed change in level. By taking into account both expert recommendations, the modified rule base given in Table 4 is finally obtained. The next step in the proposed improvement process consists of integrating a new input variable in the rule premises. The latter is built using data measured above the considered tank which reflect future process behaviour. Actually, it represents the predicted amplitude

Table 3 Synthetic initial rule base L 2 ½Lmin ; Lmax 

A0 A1 A2 A3 A4

Sign(dL) dL2 B3

B2

B1

B0

B1

B2

B3

NVB NB NB NM NM

NVB NB NM NS NS

NVB NM NM NS NS

Z Z Z Z Z

PS PS PM PM PVB

PM PM PM PB PVB

PM PM PB PB PVB

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Table 4 Modified rule base L 2 ½Lmin ; Lmax 

A0 A1 A2 A3 A4

Sign(dL) dL2 B3

B2

B1

B0

B1

B2

B3

NVB NB NB NM PVB

NVB NB NM NM PVB

NVB NM NM NS PVB

NVB NS Z PS PVB

NVB PS PM PM PVB

NVB PM PM PB PVB

NVB PM PB PB PVB

of disturbances that may plausibly occur and thus allows the development of an anticipative strategy. Indeed, if a positive disturbance is forecast (increase in level), effective processing requires that the level be low when it happens. Preventive decreasing of the level is thus desirable. It is obtained by applying a positive control value whose amplitude depends upon the importance of the predicted disturbance. The introduction of a new variable in the rule premises leads to new rules whose qualitative form can be illustrated by the following example: ‘‘If level is high and strongly increasing and predicted disturbance is positive large then control is positive very big’’. From a practical point of view, seven linguistic terms are defined for characterizing predicted disturbances according to their amplitude. The rule base of Table 4 is kept but only used in the case when no disturbance is predicted. Six new rule bases with similar structure are added to deal with other situations. They were generated with human operator aid by applying some kind of translation in the initial rule base of Table 4 according to the previously described anticipative strategy. Finally, the generated LFS implements a disturbance-driven fuzzy switching strategy between seven elementary fuzzy controllers. The designed fuzzy controller, industrialized by Elf under the name FLOUNIV, was first introduced in a refinery as far back as 1994. Since that time, about ten other industrial sites have been equipped with FLOUNIV.

disturbances such as nozzle uncloggings. Based on the supervised architecture of Fig. 3c, a more general control structure is now proposed for taking into account other disturbance types. Generally speaking, the process behaviour is characterized by the presence or the absence of disturbances. Furthermore, two kinds of disturbances can be distinguished, inducing distinct elementary situations. The first category corresponds to sudden uncloggings of the nozzle as already studied in Section 4.1. The second situation is concerned with periodic oscillations of steel level whose origin is linked to different factors like geometry defaults of the extraction rolls or flow dynamics in the mould. When no disturbance is detected, the process behaviour is considered as being normal. According to this decomposition, three controllers were developed. The first one, denoted CN, is able to carry out the control task in a non-disturbed context. The two others were designed to deal with specific disturbances. So, controller CU is suitable to reject sudden large disturbances, such as nozzle uncloggings. Finally, the last available controller CO aims at reducing periodic oscillations. Any type of controllers can be used to implement CN, CO and CU. In particular, CN and CU can be implemented using the specific controllers previously introduced in Section 4.1 (PID and LFS, respectively). According to these considerations it is reasonable to derive the following switching rules: If

unclogging ¼ yes

then

controller ¼ CU

4.3. An expert fuzzy supervisor for continuous casting mould level control

If

oscillations ¼ yes

then

controller ¼ CO

If

unclogging ¼ no

This last application is concerned again with mould level control in continuous casting machines. Section 4.1 focused on the rejection of sudden abrupt

then

and

oscillations ¼ no

controller ¼ CN

In the first two rules, the occurrence of oscillations is considered independently of the unclogging one.

S. Galichet, L. Foulloy / Computers in Industry 52 (2003) 235–251

247

Fig. 10. Switching rules.

It means that a conflict appears when both phenomena exist simultaneously. One way to solve this problem consists in handling the preponderant disturbance in priority. As uncloggings result in steel level variations much larger than the ones caused by oscillations, their rejection is the most urgent thing. The controller CU is thus chosen as soon as an unclogging is detected. Final switching rules are given in Fig. 10. Actually, the applied decision strategy is based on a characterization of the global situation by means of a fuzzy conjunction between each elementary situation. This information fusion is implemented by the and operator involved in the rule premise. The implementation of the developed switching strategy then requires disturbance detection. This is done using two specific fuzzy sensors (see [12,13]), each of them delivering a degree associated with the existence of the considered disturbance. Fuzzy sensor design for unclogging detection is based on the study of the trajectory followed by the

system when unclogging occurs. Fig. 11 gives an illustration of such a trajectory in the phase plane. The error is defined as the difference between the measured level and the desired one. In spite of instantaneous abnormal behaviours due to noisy measurement, three areas can be easily distinguished. The first one, centred on the origin, corresponds to a normal behaviour around the setpoint. The second one is formed by the left half plane with the exception of the previous central rectangle. As a nozzle unclogging induces a level increase, that is a positive error, it can not happen in this left area. Finally, uncloggings can only occur in the third zone which complements the two other ones. The developed sensor is based on a translation of these remarks in terms of fuzzy rules (see Fig. 12). The required numeric inputs are the error and the change in error. These are fuzzified according to the defined fuzzy partitions using the fuzzy description (Eq. (4)). The inference process is then achieved using the rule base

Fig. 11. Trajectory in the phase plane during unclogging.

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S. Galichet, L. Foulloy / Computers in Industry 52 (2003) 235–251

Fig. 12. Fuzzy sensor for unclogging detection.

of Fig. 12 in which the three areas identified in the phase plane can be easily recognized. The result is a fuzzy symbolic subset which describes the linguistic variable ‘‘Unclogging occurrence’’ using words Yes and No, for example 0:2=Yes þ 0:8=No. As the proposed switching strategy (Fig. 10) is able to handle fuzzy linguistic inputs, a defuzzification procedure can be avoided. In other words, there is no need to defuzzify for fuzzifying later again when underlying operations are dual (see [14]). The second fuzzy sensor is concerned with the detection of oscillations whose period T0 is approximately known. Indeed, for each plant it is possible to roughly determine the frequency of oscillations that may happen. This piece of information is thus used to distinguish between undesired mean level oscillations and harmless surface waves. In order to identify a periodic behaviour, the level signal has to be studied during several periods. The proposed strategy is thus decomposed into two steps. The first one consists in analysing the level signal by using a moving temporal window. The developed algorithm returns the amplitude (Ad) and period (Td) of the oscillations that are detected (zero if no periodic behaviour is identified). These values are then transmitted to a fuzzy system responsible for the final detection process. This second step is carried out using the rule base of Fig. 13 which simply translates the definition of undesired oscillations. Indeed, those are characterized by a Good period (around T0) and an amplitude Large enough.

In all other cases, the detected oscillations do not coincide with the ones sought after. By linking both developed fuzzy sensors to the decision making process associated with switching rules of Fig. 10, a fuzzy supervisor (see [15]) is finally obtained as illustrated in Fig. 14. The decision provided by the system is a fuzzy linguistic subset which must be transformed into a numeric control value. This task is achieved by the fuzzy mixer, which acts as a linguistic defuzzifier (see Eq. (8)). Indeed, let D be the fuzzy decision. It is expressed in the form D¼

a CN a C O a CU þ þ CN CO CU

(14)

where ai denotes the degree associated with controller i. The final control is assessed according to the following equation: u¼

a CN u CN þ a C O u CO þ a C U u CU a CN þ a CO þ a CU

(15)

where uCN , uCO and uCU represent the outputs delivered by the different controllers. It should finally be noticed that Fig. 14 is nothing else that a detailed illustration of the generic architecture of Fig. 3c. The implemented LFS is based on a hierarchical distribution of the components that carry out fuzzification (fuzzy sensors), inference (decision making process) and defuzzification (fuzzy mixer). The performance of the developed strategy has been evaluated using a knowledge-based process model

Fig. 13. Fuzzy sensor for oscillation detection.

S. Galichet, L. Foulloy / Computers in Industry 52 (2003) 235–251

Fig. 14. Supervised combination of controllers.

(see [10]) whose non-measurable parameters were identified on-line for a specific caster. The first results (Fig. 15) correspond to the simulation of a nozzle unclogging, which can be viewed as a perturbation added to the stopper position (magnitude 10 mm). In the three plots of Fig. 15, the simulation conditions are identical, and only the implemented control law varies. In the first (resp. second) case, the control value is delivered by controller CN (resp. CU). It is clear that controller CU is much more efficient than controller CN in rejecting the generated disturbance. With the supervised control structure (last plot), the performances are almost similar to the ones achieved with the ‘‘optimal’’ controller (CU). Similar tests have been carried out in the case of periodic oscillations. In both simulated situations, fuzzy supervision allows a gradual switching between different controllers and no bump appears in the applied control as it can be seen in Fig. 15. In return, this transition smoothing together with the latency period due to the detection of a periodic phenomenon restrict the efficiency of the specialised controller. In spite of this limitation, the global behaviour of the supervised structure remains satisfactory. Although the entire supervision has not been installed yet, on site partial implementations have exhibited interesting properties. A major advantage of such a supervised strategy is the possibility of benefiting from existing regulators. In particular, any

Fig. 15. Nozzle unclogging simulations.

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controller implemented on a specific casting machine can be easily merged in the proposed supervised structure. This feasibility is obtained because the supervisory output is determined independently of controller outputs. Actually, this can be done owing to the linguistic nature of the fuzzy decision. The link between the fuzzy decision and the computed control values is established by the fuzzy mixer which acts as an interface between linguistic and numeric worlds.

5. Conclusion We have investigated an empirical adhoc approach to control structure design through industrial applications. The proposed architectures make the integration of human operator experience and conventional control techniques into co-operative control structures possible. In this framework, the fuzzy formalism associated with LFS has two major advantages. On the one hand, it guarantees the readability of the designed rule base. Even when automatic building is achieved by duplicating a known numeric controller, the resulting fuzzy system can be understood and then improved according to available expert knowledge. This property is essential, especially when the integrated combination is chosen. On the other hand, LFS formalism is suitable for a distributed architecture as advocated in the case of supervised combination. By making a clear distinction between interfaces and inference units, flexibility is introduced in the fuzzy system. Furthermore, the use of fuzzy symbolic subsets allows the propagation of linguistic information without loss of the graduality naturally present in numeric representation. The chosen strategy has proven to be effective on the industrial applications that have been considered. By avoiding the cost for producing an accurate model, the knowledge-based approaches are economically satisfying. Even if optimal control is not achieved, substantial improvements are obtained at ‘‘low’’ prize.

Acknowledgements The authors wish to thank their industrial partners, especially M. Chebre and M. Dussud who are responsible for project development at Elf Solaize Research

Centre and SERT (Scocie´ te´ d’Etudes et de Re´ alisations Techniques). References [1] E.H. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller, International Journal of Man-Machine Studies 7 (1975) 1–13. [2] L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems Man and Cybernetics 3 (1) (1973) 28–44. [3] C.W. Silva, Considerations of hierarchical fuzzy control, in: H.T. Nguyen, M. Sugeno, R. Tong, R.R. Yager (Eds.), Theoretical Aspects of Fuzzy Control, Wiley, New York, 1995, pp. 183–234. [4] L. Foulloy, S. Galichet, Typology of fuzzy controllers, in: H.T. Nguyen, M. Sugeno, R. Tong, R.R. Yager (Eds.), Theoretical Aspects of Fuzzy Control, Wiley, New York, 1995, pp. 65–90. [5] L.A. Zadeh, Quantitative fuzzy semantics, Information Science 3 (2) (1971) 159–176. [6] W. Van Leekwijck, E.E. Kerre, Defuzzification: criteria and classification, Fuzzy Sets Systems 108 (1999) 159–178. [7] F. Bouslama, A. Ichikawa, Fuzzy control rules and their natural control laws, Fuzzy Sets and Systems 48 (1992) 65–86. [8] S. Galichet, L. Foulloy, Fuzzy controllers: synthesis and equivalences, IEEE Transactions on Fuzzy Systems 3 (2) (1995) 140–148. [9] Association of iron and steel engineers, continuous casting of semi-finished steel products, in: W.T. Lankford, N.L. Samways, R.F. Craven, H.E. McGannon (Eds.), The Making Shaping and Treating of Steel, Herbick and Held, Pittsburgh, 1985 (Chapter 21). [10] M. Dussud, S. Galichet, L. Foulloy, Application of fuzzy logic for continuous casting mold level control, IEEE Transactions on Control Systems Technology 6 (2) (1998) 246–256. [11] S. Galichet, L. Foulloy, M. Chebre, J. Beauchene, Fuzzy Logic Control of a Floating Level in a Refinery Tank, in: Proceedings of the Third IEEE International Conference on Fuzzy Systems, FUZZ-IEEE’94, Orlando, USA, 1994, pp. 1538–1542. [12] L. Foulloy, S. Galichet, Fuzzy sensor for fuzzy control, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 2 (1) (1994) 55–66. [13] G. Mauris, E. Benoit, L. Foulloy, The aggregation of complementary information via fuzzy sensors, Measurement 17 (4) (1996) 235–249. [14] J.V. De Oliveira, Design methodology for fuzzy system interfaces, IEEE Transactions on Fuzzy Systems 3 (4) (1995) 404–414. [15] M. Dussud, S. Galichet, L. Foulloy, Fuzzy Supervision for continuous casting mold level control, in: Proceedings of the Second Conference IFAC/IFIP/IEEE on Management and Control of Production and Logistics (MCPL2000), Grenoble, France, CDROM P361, 2000.

S. Galichet, L. Foulloy / Computers in Industry 52 (2003) 235–251 Sylvie Galichet graduated in 1986 and received the PhD degree in 1989, both from the Universite´ de Technologie de Compie`gne (France). Since 1991, she has been an Assistant Professor of Electrical Engineering at the Universite´ de Savoie and a Researcher at the Laboratoire d’Automatique et de Micro-Informatique Industrielle (LAMII). She is currently a visiting researcher at the Institut de Recherche en Informatique de Toulouse (IRIT), France. Her main topics of interest are the representation of knowledge and rule-based reasoning with applications to process control and modelling.

251

Laurent Foulloy graduated from the Ecole Normale Supe´ rieure de Cachan in 1980. He received the PhD degree in 1982 and the DSc degree in 1990, both from the Universite´ de Paris XI (France). He is Professor of Electrical Engineering at the Universite´ de Savoie. From 1992 to 2000, he was Director of the Laboratoire d’Automatique et de MicroInformatique Industrielle. Since 2000, he has been Vice President for Research at the Universite´ de Savoie. His research interests include intelligent components and fuzzy techniques for process control and measurements.