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Engineering Applications of Artificial Intelligence 13 (2000) 741750Structural analysis in control systems design of hydraulic drives$Benno Steina,*, Elmar VierbaDepartment of Mathematics and Computer Science, University of Paderborn, D-33095 Paderborn, GermanybDepartment of Measurement and Control, University of Duisburg, D-47048 Duisburg, GermanyAbstractThe design of hydraulic control systems is a complex and time-consuming task that, at the moment, cannot be automatedcompletely. Nevertheless, important design subtasks like simulation or control concept selection can be e ciently supported by acomputer. Prerequisite for a successful support is a well-founded analysis of a hydraulic systems structure. This paper provides asystematics for analyzing a hydraulic system at different structural levels and illustrates how structural information can be usedwithin the design process. Another important point of this paper is the automatic extraction of structural information from a circuitdiagram by means of graph-theoretical investigations. # 2000 Elsevier Science Ltd. All rights reserved.Keywords: Algorithms and knowledge-based methods for CACSD; Structural analysis of hydraulic systems; Graph theory1. IntroductionHydrostatic drives provide advantageous dynamicproperties and therefore represent a major drivingconcept for industrial applications. Large-scale hy-draulic systems such as plants in marine technologyas well as drives for machine tools possess a largenumber of actuators. Consequently, sophisticated inter-dependences between single components or entiresubsystems may occur, which leads to a variety ofchallenging and demanding design and control tasks. Asa representative example with respect to complexity anddimension, Fig. 1 shows the circuit diagram of a cold-rolling plant (Wessling, 1995; Ebertsha user, 1994). Here,more than 20 actuators work on the coiled steel strips.Designing such large hydraulic control systemsimplies a systematic procedure. In practice, this is donerather implicitly based on the intuition and theexperience of the human designer. This paper introducesa systematics of hydrostatic drives which reveal theirunderlying structures, as well as relations and depen-dencies among substructures. This approach allows athorough structural analysis from which fundamentalconclusions for the automation of the design process canbe drawn.The concepts of this paper have been realized andintegrated withinartdeco, a knowledge-based system forhydraulic design support (Stein, 1995). Currently,artdeco combines basic CAD facilities tailored to fluidics,checking and structure analysis algorithms, simulationmethods, and basic design rule processing.The operationalization of hydraulic design knowledgerequires a formal definition and automatic extraction ofstructural information from a circuit diagram. Thepaper contributes within these respects; it is organized asfollows. Section 2 describes both conceptually andexemplarily the structural levels at which a hydraulicsystem can be investigated. Section 3 briefly discussesthe benefits that go along with a structural analysis.Section 4 precisely defines different types of couplingsbetween the functional units of a hydraulic system,hence establishing a basis for a computer-based analysis.Moreover, it is outlined how a structural analysis isautomated. Section 5 outlines the exploitation ofstructural information withinartdeco.2. Structural analysis of hydraulic systemsThe majority of hydraulic systems is designed byexploiting the experience and intuition of a singleengineer. Due to the lack of a structural methodology,$The authors acknowledge support of the Deutsche Forschungs-gemeinschaft, DFG, Germany.*Corresponding author. Tel.: +49-5251-603-348; fax: +49-5251-603-338.E-mail address: steinuni-paderborn.de (B. Stein).0952-1976/00/$-see front matter # 2000 Elsevier Science Ltd. All rights reserved.PII: S0952-1976(00)00043-9a thorough analysis of the system structure is not carriedout. Instead, a limited repertory of possible solutions isused, making the result highly dependent on thecapabilities of the individual. Such an approach issuitable only for recurring design tasks with littlevariation.In the following, a systematics of the structural set-upof hydraulic plants is introduced which leads to aproblem-oriented system analysis. Its application to ahydrostatic drive given as a preliminary design facilitates a consequent and purposive derivation ofstructural information, which is necessary to make thesystems behavior meet the customers demands.2.1. Structural levels of hydraulic systemsThe systematics developed here is based on threelevels of abstraction (Vier et al., 1996). The differentia-tion between functional structure, component structure,and system-theoretical structure corresponds to systemdescriptions of different characteristics (Fig. 2). Fromthis distinction results an overall view of how toinfluence the systems behavior.To illustrate the concept of structural levels, we willconcentrate on a sample subsystem of the cold-rollingplant, the four-roll stand is sketched in Fig. 3(Ebertsha user, 1994).The functional structure shows the fundamentalmodes of action of a hydraulic circuit by analyzing thedifferent tasks (functions) the plant has to fulfill. Itrepresents some kind of qualitative system description.A key element within the functional structure is the so-called hydraulic axis, which is defined as follows.Definition 2.1 (Hydraulic axis). A hydraulic axis Arepresents and fulfills a subfunction f of an entirehydraulic plant. A defines the connections and theinterplay among those working, control, and supplyelements that realize f (Vier, 1996).Fig. 1. Hydraulic circuit diagram of a cold-rolling plant.Fig. 2. Structural levels of hydraulic systems.Fig. 3. Setup of a four-roll stand of the cold-rolling plant.B. Stein, E. Vier / Engineering Applications of Artificial Intelligence 13 (2000) 741750742The hydraulic actuators of the four-roll stand performtwo tasks each of which defined by a directional loadand motional quantities:function1FT1;xT1; _xT1;fC127xT1;.T;function2FT2;xT2; _xT2;C127xT2;.T:A representation of the roll stand at the functional levelis given in Fig. 4. The detection of hydraulic axes andtheir interdependences admits far-reaching conclusions,which are stated in Section 3.On the level of the component structure the chosenrealization of a function is investigated. The arrange-ment structure comprises information on the hydraulicelements (pumps, valves, cylinders, etc.) as well as theirgeometric and physical arrangement (Figs. 5a and b). Bythe switching-state structure the entirety of the possiblecombinations of switching positions is characterized: Avalve, for instance, can be open or closed (Figs. 5c andd). Fig. 6 depicts the representation of the roll stand atthe component level.The system-theoretical structure contains informationon the dynamic behavior of both the hydraulic drive as awhole and its single components. Common ways ofdescribing dynamics are differential and differenceequations or the state-space form (Schwarz, 1991)XN:_x t f x t ;u t ;x0x t08t t0y t h x t ;u t ;x2Rn;y;u2R:The system-theoretical view comprises information onthe controlled quantities, as well as the dynamicbehavior of the controlled system. The block diagramin Fig. 7 reveals the system-theoretical structure of theroll stand.By comparing analysis and simulation results with theperformance demands at the drive, a decision can bemade for each hydraulic axis whether open- or closed-loop control concepts are adequate. In a further step, anappropriate control strategy (linear, nonlinear, etc.) canbe assigned (Fo llinger, 1992; Unbehauen, 1994).Remarks. While the functional structure yields a qua-litative representation, the system description becomesmore quantitative at the component and system-theoretical level, respectively. Moreover, the analysisof the structural set-up shows in which way the behaviorof a hydraulic plant can be influenced (cf. Fig. 2): (1) atfirst, the functional structure must be considered asinvariant, because it results from the customersdemands. Only if the given structure proves to beunsatisfactory, a modification resulting from aFig. 4. The roll stand described at its functional level.Fig. 5. Examples for arrangement structures (a, b) and switching-statestructure (c, d).Fig. 6. Description of the roll stand at the component level.Fig. 7. Description of the roll stand at the system-theoretical level.B. Stein, E. Vier / Engineering Applications of Artificial Intelligence 13 (2000) 741750 743heuristic analysis approach is advisable; (2) notethat at the component level, a combination ofheuristic and analytic methods is required for thevariation or exchange of hydraulic elements, whichform the controlled system; (3) the system-theoreticallevel facilitates the investigation of the dynamic be-havior: control theory provides an analytic approach forthe selection of a suitable control strategy, parameter-ization, etc.2.2. Hydraulic axes and their couplingsFocusing on the investigation of the functionalstructure of hydraulic systems, the detection andevaluation of hydraulic axes is of central interest. Theiranalysis contributes to a deeper understanding of theinner correlations of the plant and provides an overviewof the energy flows with respect to the functions to befulfilled.The definition of the hydraulic axis given in Section2.1 is based on the criterion of elements workingtogether in order to fulfill a single function. Note thatseveral actuators (hydraulic motors/cylinders) maycontribute to the same function, thus forming a singlehydraulic axis (Fig. 8). This situation is given for(a) identical sub-circuits that are controlled by onesingle control element,(b) synchronized movements that are carried out byopen or closed loop control, or(c,d) mechanical couplings such as guides and gearunits that enforce a unique behavior.Beyond the consideration of isolated hydraulic axes, itis necessary to investigate their interdependences. Thefollowing coupling types have been worked outLevel 0(No coupling.) Hydraulic axes possess nocoupling, if there is neither a power nor an informa-tional connection between them.Level 1(Informational coupling.) Hydraulic axeswhich are connected only by control connections arecalled informationally coupled.Level 2(Parallel coupling.) Hydraulic axes whichpossess their own access to a common power supply arecoupled in parallel.Level 3(Series coupling.) A series coupling connectsthe hydraulic axes whose power supply (or disposal) isrealized via the preceding or the following axis.Level 4(Sequential coupling.) A sequential couplingis given, if the performance of a following axisdepends on the state variables, e.g. the pressure or theposition of the preceding one in order to work in asequence.Applying the concept of functional structure to thecold-rolling plant of Fig. 1, 15 hydraulic axes along withtheir couplings can be found. The left-hand side of Fig. 9envisions the membership of the components in thediagram to the axes, the right-hand side shows the entirecoupling scheme in the form of a tree.3. Benefits of a structural analysisA structural analysis of hydraulic systems revealsbasic design decisions. Especially the functional analy-sis, which is based on the detection of a systemshydraulic axes, will simplify the modification, theFig. 8. Hydraulic axes with multiple actuators.Fig. 9. Overview of the hydraulic axes in the cold-rolling plant (left) and the coupling scheme (right).B. Stein, E. Vier / Engineering Applications of Artificial Intelligence 13 (2000) 741750744extension, and the adaptation of the system (Stein,1996). The separate treatment of hydraulic axesremarkably reduces the design effort within the follow-ing respects:Smart simulation. Smart simulation is a humanstrategy when analyzing a complex system: subsystemsare identified, cut free, and simulated on their own. Thisstrategy reduces the simulation complexity and simpli-fies the interpretation of its results. Hydraulic axesestablish suited subsystems to be cut free, since theyperform an indivisible but complete subtask.Static design. Information on the hydraulic axesdriving concept (open/closed center, load sensing,regenerative circuit, etc.) allows the selection of compu-tation procedures relating the static design (Walter,1981; Paetzold and Hemming, 1989). Moreover, theapplication of modification knowledge has to considerthe axes coupling levels.Control concept selection. The consideration ofcouplings between input and output variables suppliesa necessary decision basis for the selection of controlconcepts. Analyzing the decouplability matrix D(Schwarz, 1991) yields a common approach here. Notethat the system order that can be tackled is limited. Thefunctional structure analysis provides a separation into(1) SISO systems, to which standard methods ofcontroller design can be applied, and (2) coupledsubsystems of a reduced order, for which decouplabilitycan be investigated more e ciently or even becomespossible at all.Diagnosis. Having a hydraulic circuit decomposedinto its hydraulic axes, the diagnosis process canfocus onto a single axis according to the followingworking hypothesis: if symptoms are observed merelyat a single hydraulic axis, then the defect compo-nent(s) must be amongst the components of this axis.If symptoms are observed at several axes, the axescoupling type will give further answers with respectto defect components. Hesse and Stein (1998)describe a system where this idea has been set intooperation.Note that a smart classification of the coup-lings between hydraulic axes forms the rationale ofwhether a decomposition of a hydraulic designproblem is permissible. While subsystems with level 0or level 1 couplings can always be cut free, additionalinformation is required for parallel, series, andsequential couplings. Example: Let A, B be twohydraulic axes.IF couplingA,B is parallelAND NOT time-overlapprocessA,processBTHEN separate_designA,B ispermissibleIF couplingA,B is parallelAND time-overlapprocessA,processBTHEN separate_designA,B isprohibitedVier (1999) provides a more detailed description of amethodology to assess the separability of the design ofparticular hydraulic axes.4. Graph-theoretical analysis of hydraulic drivesKey objective of the topological analysis of ahydraulic drive is the automatic detection of its under-lying functional structure, which is reflected by thehydraulic axes along with their couplings.Note that within the usual design process, hydraulicaxes are not used as explicit building blocks. Thereasons for this are twofold: (1) it is not always possibleto design a hydraulic system in a top-down manner,starting with hydraulic axes, which are refined withinsubsequent steps; (2) both the experience and the abilityof a human designer to automatically derive functionfrom structure enable him to construct a hydraulicsystem at the component level.As an aside, the main working document for adesigner is the technical drawing, and there is notradition or standardized method to additionally specifythe functional structure of a hydraulic system. Thissituation emphasizes the need for an automatic detectionof the desired structural information.The topological analysis as pursued here is a matter ofgraph theory, and, in the following, we will fall back onsome basic graph-theoretical concepts such as multi-graph, path, or connected component. These conceptsare used in a standard way, and the main idea of ourelaborations can be understood without being an expertin graph theory. At the readers convenience Section 4.3provides a short introduction of the used definitions.4.1. A hierarchy of coupling typesFor the coupling types introduced in Section 2.2 wenow develop a precise mathematical formulation. In thisconnection hydraulic circuits are abstracted towardsordinary graphs. The following definition provides amapping rule which assigns to each circuit C its relatedhydraulic graph GhC .Definition 4.1 (Related hydraulic graph). A relatedhydraulic graph GhC of a circuit C is a multigraphhVC;EC;gCi whose elements are defined as follows.(1) VCis a set of points, and there is a mapping from theset of non-pipe components in C onto VC. (2) ECis a setof edges, and there is a mapping from the set of pipeB. Stein, E. Vier / Engineering Applications of Artificial Intelligence 13 (2000) 741750 745components in C onto EC. (3) g : EC!2VCis a functionthat maps an e2EConto vi;vj22VC, if and only ifthere is a pipe between the components associated withvi;vj, and if e is associated with this pipe.Fig. 10 contrasts a hydraulic circuit and its relatedhydraulic graph. The labels in the graph shall underlinethat there is a one-to-one mapping between the elementsof the graph and the components of the hydrauliccircuit.Remarks. for each circuit C there exists exactly onehydraulic graph GhC . Multigraphs instead of graphsmust be used here since components of a hydraulicsystem may be connected in parallel. Notice thefollowing topological simplifications of C: (1) substruc-tures within (directional) valves are contracted to onesingle point v, hence making all connected pipes incidentto v; (2) variations of the topology coming along withvalve switchings are neglected; (3) directional informa-tion that results from the behavior of the particularhydraulic components is dropped. These simplificationshave no effect on the classification of hydraulic axescouplings.Definition 4.2 (Coupling types). Given is a hydrauliccircuit C containing two sub-circuits A, B, which realizetwo different hydraulic axes. Moreover, letGhC : hVC;EC;gCi, GhA : hVA;EA;gAi, andGhB : hVB;EB;gBi denote the related hydraulicgraphs of C, A, and B, respectively.Level 0(No coupling.)IfGhC is not connected, and ifGhA and GhB are subgraphs of different conn