Methodological bases of building of dynamic models of hybrid systems using principles of a «block» modelling are exposed on the basis of the E-network formalism. The presented methods are based on use of mechanisms of hierarchical interaction of dynamic model elements. Principles of organization of E-network hierarchical circuits with use of rigid and flexible structures are shown. The mechanism of interaction of static and dynamic components is specified

Tarakanov, D. V.

Tsapko, G. P.

Tsapko, S. G.

Electronic archive of Tomsk Polytechnic University

Bulletin of the Томsк Pоlyтеchnic University. 2006. V. 309. № 4140At the present an essential complication of the automated control systems of various technological processes is occurring. It places new, more rigid requirementsto training of the attendants of the given systems. Thecomplete use of multipurpose computer simulators(MCS) is possible only in the case if its software is capable to function in real time or accelerating processwhich is simulated.To solve the given problem it is necessary to developthe general approaches to organization of the Enetwork [1] analyticalimitating model (AIM).The important question in building of analyticalimitating model (AIM) of the system to be researched isdevelopment of the general approaches in the organization of Enetwork model. The methodology of buildingof AIM for complex systems is based on the objectiveapproach to the organization of the model to be researched and consists of the following basic positions:1) Any model represents the set of the unidirectionalobjects (further the term – component Comp is used), interacting each with other, that allows to realize the cause and effect approach in building of themodel;2) Components of the model are chosen taking into account the minimal number of interrelations betweencomponents of the model and the minimum level ofinteraction (i.e. intensity of data exchange) betweencomponents;3) Data exchange occurs with help of connectionchannels;4) Components of model are built by a hierarchicalprinciple;5) Some processes being independent from each othercan be executed in the model, i.e. components canfunction in parallel and independently from eachother;6) Model components can correspond both to concrete technical objects of system and its elements, andto abstract mathematical objects, for example, transformation operators.AIM of the technical system Σ0 to be researched arepresented as integration of components with the certaininterrelation. The quantity of components of the modelis defined by mode of MCS operation and degree of detailed elaboration of the system. Every component ofthe technical system model, realized on the Enetworkimitating apparatus, can be presented by hierarchicalstructure «an input – a condition – an output». Functioning of model component is considered in theEnetwork apparatus, on accounting set of the time moments T={t0,t1,...,t?,...}.As a result of interaction of model components witheach other and processings of a data stream from an environment model the set of events E=E'∪E" is occurred, where E' – is a subset of external events,E'={E'1,E'2,…,Eμ' }, characterizing occurrence of inputsignals {Xμ}, E" – is a subset of internal events,E"={E"1,…,E"K }. As internal events the beginning, the ending of computing process, as well as sending of themessage (chip) to other components can act. Action ofmodel makes change of the system state vectorZ(tν)⎯z∈R. Generally the system state can have hierarchical structure. The state of any object is characterized by phase variables Zl(tν)⎯,{zl,l=1,L⎯} at the time moment tν∈T. The state vector Zl(tν)⎯ is formed due toprocessing of external (input) influences and inner stateof the component in tν–1. Data exchange between objectsas it was already marked above, is carried out on a connection channels by moving of chips Vi on the network.Value is assigned  X(tμ)⎯,{xμ,μ=1,M⎯⎯} to input signals only«from the outside», i. e. at reading of components ofchip attributes. Value to output signals Y(tξ)⎯,{yξ,ξ=1,Ξ⎯⎯}can be assigned only «inside» the model componentunit. An input/output is presented by managing commands, including service, physical characteristics of thecomponents, as well as the data on an environment.At building of an AIM it is proposed to define modelas set of static Stci, i={1,...,N}, and dynamic Dcj,j={1,...,M} components Stc∪Dc⊂MD. The subset of static components Stc={Stci} of technical system modelcontains the elements which are constantly physicallypresented in the technical system and do not depend ona phase of the technological process proceeding at present moment of time, and carry out beforehand certainfunction, i. e. are a constant resource of system. Staticcomponents (SC) are characterized by certain structureStruc, algorithm of functioning Alg, the operator of transformation of variables H:X⎯Δt→Y and duration of reaction of the system Δt. Thus, the static components of themodel are elements of the control system of technological processes (control PC, executive mechanisms, gauges etc.), as well as elements of the object of control itUDC 629.783:5233+519.7+6269BASIC PRINCIPLES OF BUILDING OF ENETWORK MODEL OF A COMPLEX TECHNICAL SYSTEMG.P. Tsapko, S.G. Tsapko, D.V. Tarakanov*Tomsk Polytechnic University*Surgut state universityEmail: serg@aics.ruMethodological bases of building of dynamic models of hybrid systems using principles of a «block» modelling are exposed on the basisof the Enetwork formalism. The presented methods are based on use of mechanisms of hierarchical interaction of dynamic model elements. Principles of organization of Enetwork hierarchical circuits with use of rigid and flexible structures are shown. The mechanismof interaction of static and dynamic components is specified.Technical sciences141self. Dynamic components (DC) of the model are variable resources in the technical system and are characterized by the fact that they have qualitative and quantitative change of physical (information) parameters independence on TP phase. Dynamic components intechnical systems are material (fuel, heatcarriers, electric current etc.) and information streams with the givenset of parameters over which the SC makes actions. Inthe apparatus of Enetworks DC is presented by chip VDCwith the structured set of attributes: X, Z, Y, Ind, whereInd∈N is identification parameter of the chip.To form the model taking into account the causeand effect relationships it is necessary to enter the following kinds of components: control components andcomponents to be controlled. Objects which make actions (technological, control operations etc.) over otherobjects of the system (dynamic), or these actions havedominant character, are named the control components– Contr_C. Objects of the system over which the actionsare made, or this process is prevailing, are named thecomponents to be controlled – Dir_C.During functioning of the model each componentcan be either active, or passive object. The active component has ability to initiate action i. e. to change its data and to send messages irrespective of an external environment. Passive components change data value only atpresence of external influence. Active components ofthe model are:1) generators of an environment;2) generators of malfunctions of devices and elementsof the system model;3) the simulator of activity of the operator.Data exchange between components of the model ismade by means of transfer of the message where a datacarrier in the Ecircuit is the chip.The block diagram of interaction of the system components is presented on Fig. 1 where each static component of the model has the following structure:1) the set of input XL(i)stc(k) and output YL(i)stc(k) channels of thekth component of the model, where Li – is connection between kth and ith objects;2) the set of input XMk and output YMk channels betweenexternal elements of the model (subsystems of profiling, giver of external influences) and kcomponent;3) a level of hierarchy gk∈NGk.Fig. 1. The block diagram of interaction of the static and dynamic components of the system. . .???????????????????????????Stc2 (Zstc2(t?))???????????????????????????StcN (Zstc2(t?))Dc1??????????????????????Dc1Dc1?????????????? g?????????????????????Stc1 ????? ??????? ????????? ????????????????????? ??????????? ???????? ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? Inter????? ??????????? ????????????????????????????????????????????????????Stc1 (Zstc1(t?))XM2 YM2XDc1YDc1ZDc1(t?)ZDc1(t?-1) ZDc1(t?+1)g=1g=Gstc1YL1stc2XL1stc2. . . YL2stc1XL2 stc1????? ?????L2,NYM1XM1YMN YMN Dynamic components also have input, output variables: XDc, YDc and the state vector ZDc.Process of interaction of the model components in ageneral view is wrote in the following form:Inter(Stc1({x1,x2,…,xl}), Stc2({y1,y2,…,yp}),Δt,Alg), where Inter – is a rule of interaction of the two components of themodel according to given algorithm Alg on the time interval Δt; Stcn({x1,x2,…,xl}) – is the nth component of the model with parameters x1,x2,...,xl;; Stcm({y1,y2,...,yp})  is the mthcomponent of the model with parameters y1,y2,...,yp.The interrelation between the static and dynamiccomponents is shown on Fig. 1 by dashed lines, andthickness of lines reflects a level of an information stream between the system components. Process of interaction between SC and DC can be illustrated on the following example: network water (Dc) which is set in themodel by a stream of chips, has a set of characteristics:temperature z1(t)=T and concentration of impurity(salts) in the heatcarrier z2(t)=Ns. At flowing of the heatcarrier on the pipeline (Stc) the physical generalizedcharacteristics – pressure of water, velocity of water,turbulent/laminar current, pressure difference an inputand an output, temperature on an output – are formedat dynamic components in process of interaction withthe static element of the model. By consideration ofphysical processes in a long time interval (days,months), i. e. modelling of long time interaction of thetwo considered component, occurs increase of hydraulic resistance of the pipeline due to deposition of salts.At excess of hydraulic resistance over critical one thecomponent [pipeline] state accepts new value{«MALFUNCTION» P>Pmax_out }.Realization of the static components of the model isbased on use of a set of ENelements: transitions, positions, turns with a structure being constant in time. It isexpediently to realize the dynamic components with thehelp of chips which provide property of changeability ofthe presence in the system by means of moving on Enetwork scheme with calculation of endogenous parameters.At creation of AIM in ЕNbasis it is expedient to assign the following functions onto Enetwork transitions/macrotransitions:1. realization of events E, i. e. transition Cj makes action of some element of the system.2. generation of external influences;Accordingly the positions of Enetwork model executes the following functions:1) define a condition of transition operation, i. e. execute function of protective predicate of transition;2) define a qualitative condition of the system, forexample presence of a chip in the position tells thatthe device is switched on etc.Bulletin of the Томsк Pоlyтеchnic University. 2006. V. 309. № 4142Fig. 2. Realization of the model component with concentrated or conditionally – concentrated time characteristicFig. 3. Realization of the components of the model with the distributed time characteristics. . .V.Atr(…,Par(ex_var))?-?????????????????????????????????????????????,??????????????????????????????V.Atr(ed_var)(????????????????????)?????????????????????????????????????? (????????) ?????????????????? ??????????Par(ed_var)=F(Par(ex_var)) V.Atr(…,Par(ex_var))?t – ????? ???????? ???????????? ?????????t=0 – ??????????????? ????????? ??????????t?0 – ???????-?????????????? ????????? ?????????A chip is an information carrier of the system sate,its objects, as well as internal and external commands.The chip attributes contain the following data: exogenous and endogenous variables, identifiers of physicalvalue, parameters of the model components etc.In addition to presentation of AIА as the interactingspace hierarchical components between them, themethod of simulating of the system is based on the important principle of decomposition of processes in time[2]. In relation to a simulation time all the model components are divided on three categories: concentrated,conditional – concentrated and distributed. The concentrated components in the simulation time always are executed instantly. Execution of anyone of other elementsusually has nonzero duration and can be distributedbetween some consecutive imitation steps. Conditionally– concentrated and the distributed elements differ fromeach other by modes of occurrence in the time of the results as which it is necessary to understand new values ofany phase variables. For conditional – distributed element they are defined only at the moment of its ending,and this component generated no data which appear onintermediate steps for immediate use the by other modelcomponents. At work of the distributed component calculations are carried out at the intermediate stages.Realization of the concentrated process in the simplest case can be created with the help of Т transition(Fig. 2). At the established zero delay of operation of Тtransition transformation of the chip attributes and recording of exogenous variables in the attributes.On Fig. 3 Enetwork algorithmic computing structure carries out process of calculation of required outputvariables and conditions of the system, i. e. allows to realize the components working in the mode distributedin simulation time.Technical sciences143Fig. 4. The generalized function scheme of components of the dynamic model of the technical system?????????????????????Stc1?????????????????????Stc2. . .......?????????????????????StcN???????????????????? N+1(????????????????????????–g)R1R2x[N+1,1]x[N+1,2]x[N+1,m]Cy[N+1]Cx[N+1]y[N+1,H]????????? ?????????????? ????????????????????????? ?????????N+1-??????????][1 nZN??????? ????? ????????????????? ??????????????????????? ?????????????????? g–1 ????????????????????? N+1 EN-????????????????????????????y[N+1,2]y[N+1,L+1]?1????????????,???????????????????????????? ??????CH[N+1]x[N+1,H]Bulletin of the Томsк Pоlyтеchnic University. 2006. V. 309. № 4144If intermediate output channels not to use in algorithmic structure (see Fig. 3) the given scheme can beused as conditionally – distributed time components.The generalized Enetwork function chart of the logicaldynamic model of some components of the system is shown on fig. 4. In the model any component ispresented even by one level of hierarchy, as a rule, logic.The low levels contain Enetwork algorithmic schemes of imitation of dynamic processes [3, 4] for example schemes of solution of ordinary differential equations, the Lagrange interpolation schemes etc, i. e. thepresented level is necessary to reproduce dynamic processes in any moment. Semantic sense of transitions ofthe component, presented on Fig. 4, is following:C1,...,Cn – are generators of the vector of the ith objectstate, i = {1, ..., n};Cy[N+1] – is a processor of the obtained data on the ith object state;CH[N+1] – carries out calculation of endogenous variables;Cx[N+1] – forms the vector of the state of the N+1th objectof the system.Semantic sense of positions:b(x[n+1,1]),...,b(x[n+1,m]) correspond to presence of applications on the state of adjacent static objects of the ith object;b(y[n+1,1]) – the application from ith object is served;b(y[n+1,2]),...,b(y[n+1,m+1]) – positions of the global conditions of the system.The description of transitions:Cy[n+1]=(Y(R1,b(x[n+1,1]),...,b(x[n+1,H])),(t1,t2,...,tn→0),)input of information streams from static and dynamicobjects;CH[n+1]=(the hierarchical organization of transition) –executes process of calculation of endogenous variableswith use of the algorithmic scheme of modeling;Cx[n+1]=(X(R2,b(yn+1,H),...,b(y[n+1,m+1])),(Δt *),) – a choiceof the global state of the N+1th static component of thesystem and/or change of physical parameters of the dynamic component. L1={1,...,l1} is the number of globalstates of the object;Δt *: is the delay of operation of transition Cx[n+1,2] is defined by velocity of N+1th component and the operationmode of the object (for example, switching on of theObject – 2 s, switching off – 0,9 s). At simulation ofprocesses in the required time scale Δt *M is calculated bythe formula:Δt *M=Δt *Mt,where Mt – is the time scale, Mt=[s/(unit of measurement of a variable)].The chip Vi of the network contains the informationon a state object Vi(v1,v2,...,vn). At change of the state ofthe i components a transfer of the chip Vi to the inputposition x[N+1,i] takes place. If the chip is absent in a position x[N+1,H], functioning of transition Cy[N+1] occurs. Calculation of a new global state of the N+1thcomponents ismade basing of analysis of the ith component state Zi[tv]and ZN+1[tv]. It is proposed to pin process of calculation ofendogenous variables on the algorithmic scheme of simulation [5] realized with the help of macrotransition CH.Process of activity АСМ has, as a rule, the distributedcharacter in time and allows to approximate functionalaction with required detailed elaboration. Further thechip stream is processed by transition Cx[N+1], which carries out record Vi in the position y[n+1,l], l={2,...,L+1} whereL is number of states in the N+1th component, which corresponds to the global state of the components (b(R2)=l).After that transfer of a chip (information) from objectN+1 to adjacent components of model occurs.The presented architecture of building of analyticalimitating model allows to simulate functioning of technical objects taking into account complex relationships ofcause and effect connections and the diverse spacetimeorganization of the system components. As the analysis ofbuilding of the model components by the Enetwork apparatus shows, the majority of schemes is realized byprinciple CУ–СH–СX, where СH – is macrotransition, realizing a hierarchical sublevel of the model component.Literature1. Sovetov B.Ya., Yakovlev S.A. Modeling of systems. 2nd Ed., reshaped and added. [in Russian]. – M.: Vysshaya Shkola, 1998. – 319 p.2. Technology of system modeling. [in Russian] / E.F. Avramchuk,A.A. Vavilov, S.V. Emelyanov et al.; S.V. Emelyanov et al. (Edits). –M.: Machine building; Berlin: Теchnik, 1988. – 312 p.3. Guig J. van. The applied general theory of systems. Transl. fromEngl. – M.: Mir, 1981. – 336 p.4. Goldaev S.V., Lyashkov B.A. Fundamentals of mathematical modelingin the heat engineer. [in Russian]. – Tomsk: Izd. TPU, 1999. – 106 p.5. Questions of algorithmic modeling of complex systems. [in Russian]// Col. of scient. works / V.V. Ivanishchev (Editorinchief). – L.:LIIAN, 1989. – 235 p.

Basic principles of building of E-network model of a complex technical system

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