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Problems of Classifications in Diagnostics and Control of Complex Systems
CopHi~llI
©
Budapt'i;t,
Illlll ~an.
IF .- \<: ~llh 1 rit"lllli.d \\"olld
(:
( " r H':lt'"
1 ~1."q
PROBLEMS OF CLASSIFICATIONS IN DIAGNOSTICS AND CONTROL OF COMPLEX SYSTEMS J.
Spa) and L. Madanisz
Abstract. Situational control is an elfectiye means in the control of complex systems. The respective decision processes require the solu tion of problems of luzzy classification, which may be readily solved by methods of modified fuzzy sets. The application to the problems 01 operative control of power systems and to the design control of robotic manufacturing lines has given promising results. Keywords. Complex system; situational control; luzzy classilication fuzzy decision; power system control; robotic line.
system is submitted to substantial limitations.
THEORETICAL FOUNDATIONS OF THE CONTROL OF COMPLE)' SYSTEMS
Ihe basic problem of control of a complex system is the solution 01 the discrepancy between the immense number of possible situations and the limited number of disponible strategies of control.
There are two kinds of large-scale systems : The properties of a composed system are described in the way 01 decomposition. Its dynamic properties are completely determined by its structure and by the dy namic properties of its parts. in spite of the lact that the dynamic properties of any part may be altered by its incluaion into the composed system.
The control of a complex system is ade quately lormulated in the sense ot situational control (Benei. 1981; XlykoY, 11)74; Klykov, Gorkov. 1980) as a problem 01 classilication. Control strategies are assigned to classes 01 situations Parameters and operands ot these strategic algorithms are derived trom the descriptive vector of the complex system.
The properties of a complex system are based on the properties and interconnections of its parts, but they are no more completely determined in this way. Sub atantial properties, especially the in teractions with the environment. get lost in the process of decomposition. The starting point of description is here the situation, comprising the global effect of the external and internal factors and expressing the relation of the complex system towards its environment.
Ihe classilication of situations in the process of situational control requires a generalized lorm 01 classification, the so-called fuzzy classification (Spal, 1980), abandoning the requirement of uniqueness 01 assignation ot a given situa tion to one class only. Ihe classes of classilication may overlar. at least some situations simultaneously belonging to several classes.
A multicomponental descriptive vector serves a. indicator of the situation • though its arplicability as an operand in the algorithmization of the complex
1205
120 6
J. Spa l and L. Madarasz
FUZZY SEIS AS ~EAN~ OF FUZZY CLASSIFICATION The well-known and widely discussed fuzzy sets (Zadeh, 1965) form a suitable tool in fuzzy classification. A modification, the modified fuzzy sets (~-fuzzy sets) , has been developed (Spal, 1981. 1982) showing the following features 1. The membership function of the fuzzy sets with the interval of values (0,1) has been replaced by the criterial func~ with an arbitrary interval of values. While the membership function indicates the measure of affiliation of the respective element to the fuzzy set, thus expressing the result of the process of classification, the criterial function indicates the level of the respective criteria of classification, thus forming the basis for the subsequent process of classificati on. 2. ~-fuzzy set is defined as a mapping from the values of the criterial function on a system of subsets of the basic set 3. A ~-fuzzy set and its complementary M-fuzzy set ar€ derived from the same criterial function. The mapping takes place on the system of level sets for the M-fuzzy set and on the system of complements of the level sets for the respective complementary M-fuzzy set. Ihus complete validity of all axioms of the classical theory of "crisp" sets is obtained, including the axiom of complementarity. 4. In spite of a certain formal simila rity between the random variable and the W-fuzzy set, there exists a prinCipal difference. The random variable assigns a value of probabilistic measure to a preselected subset of the basic set, thus showing a descriptive character. - Ihe M-fuzzy set assigns a subset of the basic set to a preselected value of the crite rial function, having thus a normative significance. It is interesting to note that there does not exist any inverse mapping, either in the case of random variables or in the case of M-fuzzy sets.
ArplICAIIO~ OF FUZZY SlTUAIlONAl COHROl
ClASSIFICAIIO~
TO
Ihe application takes in two phases : 1. Ihe definition of a system of criterial parameters as a basis of multicri terial classification. 2. Ihe specification of the levels of the preselected criterial parameters. A system of strategies (algorithms) produces a mapping of the descriptive vector of the system under control on the space of controlling vectors. Ihe prinCiple is shown in Fig. 1. The scales of Singular criterial parameters are co-ordinated in the case of multicriterial classification in such a way as to obtain one common criterial parameter S expressing the significance of the respective level for any of the applied criteria. The co-ordination of the levels of significance of individual criteria provides a substantial step in the formation of an appropriate control system. The starting point in establishing a system of criterial functions is a cer tain crisp classification of the values of the parameter A, partitioning the basic set into a complete system of non overlapping classes at the chosen level. Ihe basic level is S = 1 in the given example.
A system of criterial functions
AI' Aa'
AJ , A4 is defined over this crisp partitioning of the basic set. Ihe choice of the form and height of the criterial functions provides the designer of the system with another possibility of in fluencing the process of fuzzy classification. Ihe establishment of such a system of criterial functions is a specific problem of any application, reflecting th€ aim of the process of control and the properties of the system under control, thus expressing the philosophy in the given case of application.
Dia gnosti cs and Control of Complex Systems
Lowering the level of the criterial significance, for example to the value S = = 0.6, causes the overlapping of the neighbouring classes (as marked by thick lines). The respective elements of the basic set may be assigned to anyone of the corresponding criterial functions and thus any of the corresponding strategies is applicable. The final choice of the strategy is then performed by means of a separate decision process. A further lowering of the level may bring about the overlapping of even more than two intervals. The rise of the criterial significance over the level of the crisp partitioning, e.g. to the level S = 1.2 , leaves some subsets of the basic set uncovered by any criterial function. Here the fuzzy classification does not provide any motivation for assigning the respective elements to any of the classes such as defined by the system of criterial functions, thus bringing about a failure of the respective criterion. The decision is obtained with the use of another criterion (e.g. B) with defined criterial functions 8 1 ,B , •. 2
REALIZATION OF SlTUATIONAL CONTROL IN COMPLEX TECHNICAL SYSTEMS
Situational control makes possible the consideration of normal operating conditions, as well as of abnormal situations (disturbances, recoveries etc.) occurring in t€chnical systems (Madarasz. 1982). The control of complex technical or organizational systems takes place in two phases : a) Scheduling of the process of control which is accomplished separately from the process under control. The result is a plan of the control process and a set of algorithms for its realization. b) Operational control performing cur rently, in real-time conditions, the suppression of deviations from tht plan and of the effects of other imperfections of
1207
the process of scheduling, thus having as its result the adaptation of the plan to the real-world conditions. The situational control is connected with current solution of two problems of fUZZy classification : 1. It performs the classification of situations in order to assign adequate strategies to any class of situations. 2. It creates effective and applicable decision procedures. There are three main groupes of criteria used in the control of complex technical systems ; a) Aspects of b) Aspects of relations c) Aspects of terconnections
reliability and security quality, quantity and time economy, representing into the social environment.
The performance of situational control in complex aystems proceeds in two phases , the decision phase and the control phase, each further subdivided into activities of selection and action. The situation to be processed is analyzed in the selective period of the decision phase. According to the result of the analysis it is allotted to one of prepared standard strategies, performing the processing of the respective normal or emergency situation. A certain set of algo rithms is stored in the memory of the computer for any standard situation. The most suitable selection of these algo rithmA is activated during the action period of the decision phase for the pro cessing of the given situation. These algorithms are adapted in the course of the selective period of the control phase (para.etrization and further adap tations). The realization of the control process takes place in the action period of the control phase. The design consists of the following steps ;
1208
J. Spal and L. Ma dar a s z
1. Establi.baent et a .tructural and tunctional .odel ot the co.plex system. 2. Detinition ot the ai. ot control 3. Cla.sitication ot situations and ot their causes 4. Classitication and description ot standard classes ot situations, assigned to indiyidual emergency situations 5. Algorithmization et control .trate gies in the tor. ot subopti.al strategies
SItUAtIONAL CONtROL OF ELECtRIC POWER SYStEWS Large electric power systems, with their .arked decentralized hierarchical structure and decisiye partiCipation ot the hu.an tactor, are typical examples ot complex systems suitable tor the application ot situational control. A thorough analysis ot their control under consideration ot emergency situations is giyen in (Zaborsty and others, 1980). the aim ot control can be summed up by the tollowing criteria 1. Reliability ot the power supply 2. CoYering ot the power demand in the desired ti.e, quantity and quality 3. Generation, distribution and consumption with lowest global costs (aspects ot economy).
the decomposition ot the problem (Madarasz 1982) was detined as tollows : a) Normal operating conditions 'emergency 0) b) Nor.al conditions with structural detects (e.ergency 1) c) Nor.al conditions with security detects (emergency 2) d) Stability crisis (e.ergency 3) e) Viability crisis (emergency 4) t) Integrity crisis (emergency 5) the adYantages ot preliminary scheduling ot .mergency situations in application ot situational control become yery eYident in power systems. the priority ot the global criteria Yaries tor ditferent leYels ot emergency. The aspect at economy preyails in normal operation (emerlenoy 0),
the aspects ot reliability lacking uraency under these conditions. - On the contrary, the aspects at reliability become para.ount at high e.ergency leyels, the criteria ot econo.y retreating to the background. The need at recoyery (restoration) ot the syste. is a co. .on per.anent task of control in any situation ot non-zero emergency.
SITUATIONAL CONTROL OF ROBOlIC MA~UFACTURING SYSTEWS The economic design and operation at robotic .anutacturing lines requires consideratioD not only of normal operation , but at emergency situations, too. Prob lems at this kind baye been paid atten tion in the design ot a crankshatt manutacturing line (13 handling deyices, 27 technological equipments and 14 processing machines) and a global algorithm ot situational control has been elaborated (Madarasz, 1982). Tbe control ot the robotic subsystem was aimed at the reduction at idle times, at the elimination at the necessity ot i . proYisation under occurrence ot abnormal (emergency) conditions and at the requirement ot a prompt recoyery ot the syste& A marked improyement ot the general arrangement and a reduction at the inyestment costs haYe been obtained. The tollowing points ot Yiew were taken into account in the design ot the system at control : A) Emergency leyels 1. Nor. . l operating conditions (e.ergency 0) 2 • • ormal operatioR wit~ structural de tects (emergency 1) 3. Alert operation ot subsystems (emer gency 2) 4. Alert operation ot the whole manutacturing system (emergency 3) B) Location ot the detect 1. Failure ot tbe technological subsystem 2. Failure at the subsystem ot material handling
Diagnost ics and Control of Compl ex Sys t ems
3. Failure of the subsystem of control C) Significanc! 01 the def~ct 1. Partial failure {equipment capable of operation witb decreased parametric .alue~ 2. Complete failure (equipment unable of any productive operation) D) Extent of tbe defect 1. Failure of one or several partial workplaces 2. Failure of one complete subsystem 3. Failure of several subsystems E) Duration of tbe emergency situation 1. Quickly reparable failures (duration 01 tbe failure Tf sborter than the line cycle T) 2. Failure of short duration {longer than tbe line cycle T, but shorter than th~ interval of complete run-out of the inte~ operational container (magazine» 3. Failure of long duration (the failure brings about complete run-out of the interoperational magazine of the subsequent operation, thus pro.oking a secondary standstill of the subsequent equipment) {(T f > Tc )" °f>1O·T». The general strategy of situational control of the robotic line is shown in Fig. 2. Sets of algorithms (regimes of control) were defined, aimed at the recovery 01 the system from any emergency situation. The main contribution of the applied methodology consists in building-up a syst.m of emergency control algorithms. The impor tance of this task increases with the pr~ gressing de.elopment and complexity of the automation of production processes, namely in connection with the application of robotic systems. The methodology of si tuational control requires the develop ment and solution of many connected problems, such as : 1. Classification of situations, namely in the sense of fuzzy classificatioD 2. Methods of identilication of situa tions under operational conditions 3. Means (suitable languages) for the description of situations and 01 classes of situations 4. Establishment of an adequate system of strategies, capable of co.ering the whole
1209
field of expected situations by means of a reasonable number of strategies 5. Procedures of a practical assignation of strategies to the given situation under operational conditions 6. Procedures 01 acti.ization of the selected chain of strategies.
C ONC L. US I ONS 1. Situational control is an effective method of control of complex systems 2. It is based on fuzzy decisionmaking with the application of modilied fuzzy sets and fuzzy classification 3. Effecti.e control 01 complex t~chnical systems should invol.e control algorithms for abnormal (emergency) situations 4. Application to electric power system operation and to the control of a robotic line has given promising results.
REFERENCES Benei, J. (198l). Control of Extensi.e Systems. (In Czech). SNTL, Praha (Czechoslovakia). 301 pp. 11ykov, Yu. I. (1974). Situational Con trol of Large-Scale Systems. (In Russian). Energija, Moskva. 11ykov, Yu. I., and L. M. Gorkov (1980). Data Banks 10r Decision Making. (In Russian). So.jetskoje Radio, Mosk.a. Madar'sz, L. (1982). prinCiples of Situational Control and 01 Formalization of Decision Processes in the Control of Complex Systems. (In Slovak). Dissertation. TU Koiice. 95 pp. Spa1, J. (1980). Fuzzy classilication. (In Slo.ak). Informa~ne systemy. Bratisla.a. Vol. 9, No. 5, pp. 413-429. Spal, J. (1981). Modified fuzzy sets. Problems 01 Control and Information Theory. Budapest. Vol.lO, No. 6 pp. 375-386 Spal, J. (1982). Fundamentals of a mathematical theory of luzzy sets. Aplikace matematiky. Vyda.atelst.i CSAV, Praha. Vol. 27, pp. 326-340.
J. Spal and L. Madarasz
1210
Zaborszky, J., K. Prasad, and K. I. Whang (1980). Operation of the large interconnected power system by deciaion and control. IEEE Trans. on Power Apparatur and Systems, Vol. PAS-99, No. 1, pp. 37-45. Zadeh, L.A. (1965). Fuzzy sets. Information and Control, Vol. 8, pp. 338-353
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I PRODUC TI V ITY
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Fig. 1.
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Fuzzy classification according to criteria A,B with signi!icanceS
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INQUIRY OF THE 01 SPACHER ABOUT THE STATE OF MANUFACTURING SYSTEM AT OCCUR RENCE OF ABNORM AL SITUATION
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General algorithm of situational control of a robotic line tor crankshaft manufacture
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©
Budapt'i;t,
Illlll ~an.
IF .- \<: ~llh 1 rit"lllli.d \\"olld
(:
( " r H':lt'"
1 ~1."q
PROBLEMS OF CLASSIFICATIONS IN DIAGNOSTICS AND CONTROL OF COMPLEX SYSTEMS J.
Spa) and L. Madanisz
Abstract. Situational control is an elfectiye means in the control of complex systems. The respective decision processes require the solu tion of problems of luzzy classification, which may be readily solved by methods of modified fuzzy sets. The application to the problems 01 operative control of power systems and to the design control of robotic manufacturing lines has given promising results. Keywords. Complex system; situational control; luzzy classilication fuzzy decision; power system control; robotic line.
system is submitted to substantial limitations.
THEORETICAL FOUNDATIONS OF THE CONTROL OF COMPLE)' SYSTEMS
Ihe basic problem of control of a complex system is the solution 01 the discrepancy between the immense number of possible situations and the limited number of disponible strategies of control.
There are two kinds of large-scale systems : The properties of a composed system are described in the way 01 decomposition. Its dynamic properties are completely determined by its structure and by the dy namic properties of its parts. in spite of the lact that the dynamic properties of any part may be altered by its incluaion into the composed system.
The control of a complex system is ade quately lormulated in the sense ot situational control (Benei. 1981; XlykoY, 11)74; Klykov, Gorkov. 1980) as a problem 01 classilication. Control strategies are assigned to classes 01 situations Parameters and operands ot these strategic algorithms are derived trom the descriptive vector of the complex system.
The properties of a complex system are based on the properties and interconnections of its parts, but they are no more completely determined in this way. Sub atantial properties, especially the in teractions with the environment. get lost in the process of decomposition. The starting point of description is here the situation, comprising the global effect of the external and internal factors and expressing the relation of the complex system towards its environment.
Ihe classilication of situations in the process of situational control requires a generalized lorm 01 classification, the so-called fuzzy classification (Spal, 1980), abandoning the requirement of uniqueness 01 assignation ot a given situa tion to one class only. Ihe classes of classilication may overlar. at least some situations simultaneously belonging to several classes.
A multicomponental descriptive vector serves a. indicator of the situation • though its arplicability as an operand in the algorithmization of the complex
1205
120 6
J. Spa l and L. Madarasz
FUZZY SEIS AS ~EAN~ OF FUZZY CLASSIFICATION The well-known and widely discussed fuzzy sets (Zadeh, 1965) form a suitable tool in fuzzy classification. A modification, the modified fuzzy sets (~-fuzzy sets) , has been developed (Spal, 1981. 1982) showing the following features 1. The membership function of the fuzzy sets with the interval of values (0,1) has been replaced by the criterial func~ with an arbitrary interval of values. While the membership function indicates the measure of affiliation of the respective element to the fuzzy set, thus expressing the result of the process of classification, the criterial function indicates the level of the respective criteria of classification, thus forming the basis for the subsequent process of classificati on. 2. ~-fuzzy set is defined as a mapping from the values of the criterial function on a system of subsets of the basic set 3. A ~-fuzzy set and its complementary M-fuzzy set ar€ derived from the same criterial function. The mapping takes place on the system of level sets for the M-fuzzy set and on the system of complements of the level sets for the respective complementary M-fuzzy set. Ihus complete validity of all axioms of the classical theory of "crisp" sets is obtained, including the axiom of complementarity. 4. In spite of a certain formal simila rity between the random variable and the W-fuzzy set, there exists a prinCipal difference. The random variable assigns a value of probabilistic measure to a preselected subset of the basic set, thus showing a descriptive character. - Ihe M-fuzzy set assigns a subset of the basic set to a preselected value of the crite rial function, having thus a normative significance. It is interesting to note that there does not exist any inverse mapping, either in the case of random variables or in the case of M-fuzzy sets.
ArplICAIIO~ OF FUZZY SlTUAIlONAl COHROl
ClASSIFICAIIO~
TO
Ihe application takes in two phases : 1. Ihe definition of a system of criterial parameters as a basis of multicri terial classification. 2. Ihe specification of the levels of the preselected criterial parameters. A system of strategies (algorithms) produces a mapping of the descriptive vector of the system under control on the space of controlling vectors. Ihe prinCiple is shown in Fig. 1. The scales of Singular criterial parameters are co-ordinated in the case of multicriterial classification in such a way as to obtain one common criterial parameter S expressing the significance of the respective level for any of the applied criteria. The co-ordination of the levels of significance of individual criteria provides a substantial step in the formation of an appropriate control system. The starting point in establishing a system of criterial functions is a cer tain crisp classification of the values of the parameter A, partitioning the basic set into a complete system of non overlapping classes at the chosen level. Ihe basic level is S = 1 in the given example.
A system of criterial functions
AI' Aa'
AJ , A4 is defined over this crisp partitioning of the basic set. Ihe choice of the form and height of the criterial functions provides the designer of the system with another possibility of in fluencing the process of fuzzy classification. Ihe establishment of such a system of criterial functions is a specific problem of any application, reflecting th€ aim of the process of control and the properties of the system under control, thus expressing the philosophy in the given case of application.
Dia gnosti cs and Control of Complex Systems
Lowering the level of the criterial significance, for example to the value S = = 0.6, causes the overlapping of the neighbouring classes (as marked by thick lines). The respective elements of the basic set may be assigned to anyone of the corresponding criterial functions and thus any of the corresponding strategies is applicable. The final choice of the strategy is then performed by means of a separate decision process. A further lowering of the level may bring about the overlapping of even more than two intervals. The rise of the criterial significance over the level of the crisp partitioning, e.g. to the level S = 1.2 , leaves some subsets of the basic set uncovered by any criterial function. Here the fuzzy classification does not provide any motivation for assigning the respective elements to any of the classes such as defined by the system of criterial functions, thus bringing about a failure of the respective criterion. The decision is obtained with the use of another criterion (e.g. B) with defined criterial functions 8 1 ,B , •. 2
REALIZATION OF SlTUATIONAL CONTROL IN COMPLEX TECHNICAL SYSTEMS
Situational control makes possible the consideration of normal operating conditions, as well as of abnormal situations (disturbances, recoveries etc.) occurring in t€chnical systems (Madarasz. 1982). The control of complex technical or organizational systems takes place in two phases : a) Scheduling of the process of control which is accomplished separately from the process under control. The result is a plan of the control process and a set of algorithms for its realization. b) Operational control performing cur rently, in real-time conditions, the suppression of deviations from tht plan and of the effects of other imperfections of
1207
the process of scheduling, thus having as its result the adaptation of the plan to the real-world conditions. The situational control is connected with current solution of two problems of fUZZy classification : 1. It performs the classification of situations in order to assign adequate strategies to any class of situations. 2. It creates effective and applicable decision procedures. There are three main groupes of criteria used in the control of complex technical systems ; a) Aspects of b) Aspects of relations c) Aspects of terconnections
reliability and security quality, quantity and time economy, representing into the social environment.
The performance of situational control in complex aystems proceeds in two phases , the decision phase and the control phase, each further subdivided into activities of selection and action. The situation to be processed is analyzed in the selective period of the decision phase. According to the result of the analysis it is allotted to one of prepared standard strategies, performing the processing of the respective normal or emergency situation. A certain set of algo rithms is stored in the memory of the computer for any standard situation. The most suitable selection of these algo rithmA is activated during the action period of the decision phase for the pro cessing of the given situation. These algorithms are adapted in the course of the selective period of the control phase (para.etrization and further adap tations). The realization of the control process takes place in the action period of the control phase. The design consists of the following steps ;
1208
J. Spal and L. Ma dar a s z
1. Establi.baent et a .tructural and tunctional .odel ot the co.plex system. 2. Detinition ot the ai. ot control 3. Cla.sitication ot situations and ot their causes 4. Classitication and description ot standard classes ot situations, assigned to indiyidual emergency situations 5. Algorithmization et control .trate gies in the tor. ot subopti.al strategies
SItUAtIONAL CONtROL OF ELECtRIC POWER SYStEWS Large electric power systems, with their .arked decentralized hierarchical structure and decisiye partiCipation ot the hu.an tactor, are typical examples ot complex systems suitable tor the application ot situational control. A thorough analysis ot their control under consideration ot emergency situations is giyen in (Zaborsty and others, 1980). the aim ot control can be summed up by the tollowing criteria 1. Reliability ot the power supply 2. CoYering ot the power demand in the desired ti.e, quantity and quality 3. Generation, distribution and consumption with lowest global costs (aspects ot economy).
the decomposition ot the problem (Madarasz 1982) was detined as tollows : a) Normal operating conditions 'emergency 0) b) Nor.al conditions with structural detects (e.ergency 1) c) Nor.al conditions with security detects (emergency 2) d) Stability crisis (e.ergency 3) e) Viability crisis (emergency 4) t) Integrity crisis (emergency 5) the adYantages ot preliminary scheduling ot .mergency situations in application ot situational control become yery eYident in power systems. the priority ot the global criteria Yaries tor ditferent leYels ot emergency. The aspect at economy preyails in normal operation (emerlenoy 0),
the aspects ot reliability lacking uraency under these conditions. - On the contrary, the aspects at reliability become para.ount at high e.ergency leyels, the criteria ot econo.y retreating to the background. The need at recoyery (restoration) ot the syste. is a co. .on per.anent task of control in any situation ot non-zero emergency.
SITUATIONAL CONTROL OF ROBOlIC MA~UFACTURING SYSTEWS The economic design and operation at robotic .anutacturing lines requires consideratioD not only of normal operation , but at emergency situations, too. Prob lems at this kind baye been paid atten tion in the design ot a crankshatt manutacturing line (13 handling deyices, 27 technological equipments and 14 processing machines) and a global algorithm ot situational control has been elaborated (Madarasz, 1982). Tbe control ot the robotic subsystem was aimed at the reduction at idle times, at the elimination at the necessity ot i . proYisation under occurrence ot abnormal (emergency) conditions and at the requirement ot a prompt recoyery ot the syste& A marked improyement ot the general arrangement and a reduction at the inyestment costs haYe been obtained. The tollowing points ot Yiew were taken into account in the design ot the system at control : A) Emergency leyels 1. Nor. . l operating conditions (e.ergency 0) 2 • • ormal operatioR wit~ structural de tects (emergency 1) 3. Alert operation ot subsystems (emer gency 2) 4. Alert operation ot the whole manutacturing system (emergency 3) B) Location ot the detect 1. Failure ot tbe technological subsystem 2. Failure at the subsystem ot material handling
Diagnost ics and Control of Compl ex Sys t ems
3. Failure of the subsystem of control C) Significanc! 01 the def~ct 1. Partial failure {equipment capable of operation witb decreased parametric .alue~ 2. Complete failure (equipment unable of any productive operation) D) Extent of tbe defect 1. Failure of one or several partial workplaces 2. Failure of one complete subsystem 3. Failure of several subsystems E) Duration of tbe emergency situation 1. Quickly reparable failures (duration 01 tbe failure Tf sborter than the line cycle T) 2. Failure of short duration {longer than tbe line cycle T, but shorter than th~ interval of complete run-out of the inte~ operational container (magazine» 3. Failure of long duration (the failure brings about complete run-out of the interoperational magazine of the subsequent operation, thus pro.oking a secondary standstill of the subsequent equipment) {(T f > Tc )" °f>1O·T». The general strategy of situational control of the robotic line is shown in Fig. 2. Sets of algorithms (regimes of control) were defined, aimed at the recovery 01 the system from any emergency situation. The main contribution of the applied methodology consists in building-up a syst.m of emergency control algorithms. The impor tance of this task increases with the pr~ gressing de.elopment and complexity of the automation of production processes, namely in connection with the application of robotic systems. The methodology of si tuational control requires the develop ment and solution of many connected problems, such as : 1. Classification of situations, namely in the sense of fuzzy classificatioD 2. Methods of identilication of situa tions under operational conditions 3. Means (suitable languages) for the description of situations and 01 classes of situations 4. Establishment of an adequate system of strategies, capable of co.ering the whole
1209
field of expected situations by means of a reasonable number of strategies 5. Procedures of a practical assignation of strategies to the given situation under operational conditions 6. Procedures 01 acti.ization of the selected chain of strategies.
C ONC L. US I ONS 1. Situational control is an effective method of control of complex systems 2. It is based on fuzzy decisionmaking with the application of modilied fuzzy sets and fuzzy classification 3. Effecti.e control 01 complex t~chnical systems should invol.e control algorithms for abnormal (emergency) situations 4. Application to electric power system operation and to the control of a robotic line has given promising results.
REFERENCES Benei, J. (198l). Control of Extensi.e Systems. (In Czech). SNTL, Praha (Czechoslovakia). 301 pp. 11ykov, Yu. I. (1974). Situational Con trol of Large-Scale Systems. (In Russian). Energija, Moskva. 11ykov, Yu. I., and L. M. Gorkov (1980). Data Banks 10r Decision Making. (In Russian). So.jetskoje Radio, Mosk.a. Madar'sz, L. (1982). prinCiples of Situational Control and 01 Formalization of Decision Processes in the Control of Complex Systems. (In Slovak). Dissertation. TU Koiice. 95 pp. Spa1, J. (1980). Fuzzy classilication. (In Slo.ak). Informa~ne systemy. Bratisla.a. Vol. 9, No. 5, pp. 413-429. Spal, J. (1981). Modified fuzzy sets. Problems 01 Control and Information Theory. Budapest. Vol.lO, No. 6 pp. 375-386 Spal, J. (1982). Fundamentals of a mathematical theory of luzzy sets. Aplikace matematiky. Vyda.atelst.i CSAV, Praha. Vol. 27, pp. 326-340.
J. Spal and L. Madarasz
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Zaborszky, J., K. Prasad, and K. I. Whang (1980). Operation of the large interconnected power system by deciaion and control. IEEE Trans. on Power Apparatur and Systems, Vol. PAS-99, No. 1, pp. 37-45. Zadeh, L.A. (1965). Fuzzy sets. Information and Control, Vol. 8, pp. 338-353
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