減速器-圓錐圓柱齒輪減速器設(shè)計(jì)【鏈?zhǔn)捷斔蜋C(jī)傳動(dòng)裝置】【F=2500M V=0.67ms D=445 L=800mm】,鏈?zhǔn)捷斔蜋C(jī)傳動(dòng)裝置,F=2500M V=0.67ms D=445 L=800mm,減速器-圓錐圓柱齒輪減速器設(shè)計(jì)【鏈?zhǔn)捷斔蜋C(jī)傳動(dòng)裝置】【F=2500M,V=0.67ms,D=445,L=800mm】,減速器 Engineering Applications of Artificial Intelligence 13 (2000) 741750 Structural analysis in control systems design of hydraulic drives $ Benno Stein a, *, Elmar Vier b a Department of Mathematics and Computer Science, University of Paderborn, D-33095 Paderborn, Germany b Department of Measurement and Control, University of Duisburg, D-47048 Duisburg, Germany Abstract The design of hydraulic control systems is a complex and time-consuming task that, at the moment, cannot be automated completely. Nevertheless, important design subtasks like simulation or control concept selection can be e ciently supported by a computer. Prerequisite for a successful support is a well-founded analysis of a hydraulic systems structure. This paper provides a systematics for analyzing a hydraulic system at different structural levels and illustrates how structural information can be used within the design process. Another important point of this paper is the automatic extraction of structural information from a circuit diagram 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 theory 1. Introduction Hydrostatic drives provide advantageous dynamic properties and therefore represent a major driving concept for industrial applications. Large-scale hy- draulic systems such as plants in marine technology as well as drives for machine tools possess a large number of actuators. Consequently, sophisticated inter- dependences between single components or entire subsystems may occur, which leads to a variety of challenging and demanding design and control tasks. As a representative example with respect to complexity and dimension, 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 systems implies a systematic procedure. In practice, this is done rather implicitly based on the intuition and the experience of the human designer. This paper introduces a systematics of hydrostatic drives which reveal their underlying structures, as well as relations and depen- dencies among substructures. This approach allows a thorough structural analysis from which fundamental conclusions for the automation of the design process can be drawn. The concepts of this paper have been realized and integrated within art deco, a knowledge-based system for hydraulic design support (Stein, 1995). Currently, art deco combines basic CAD facilities tailored to fluidics, checking and structure analysis algorithms, simulation methods, and basic design rule processing. The operationalization of hydraulic design knowledge requires a formal definition and automatic extraction of structural information from a circuit diagram. The paper contributes within these respects; it is organized as follows. Section 2 describes both conceptually and exemplarily the structural levels at which a hydraulic system can be investigated. Section 3 briefly discusses the benefits that go along with a structural analysis. Section 4 precisely defines different types of couplings between the functional units of a hydraulic system, hence establishing a basis for a computer-based analysis. Moreover, it is outlined how a structural analysis is automated. Section 5 outlines the exploitation of structural information within art deco. 2. Structural analysis of hydraulic systems The majority of hydraulic systems is designed by exploiting the experience and intuition of a single engineer. 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)00043-9 a thorough analysis of the system structure is not carried out. Instead, a limited repertory of possible solutions is used, making the result highly dependent on the capabilities of the individual. Such an approach is suitable only for recurring design tasks with little variation. In the following, a systematics of the structural set-up of hydraulic plants is introduced which leads to a problem-oriented system analysis. Its application to a hydrostatic drive given as a preliminary design facilitates a consequent and purposive derivation of structural information, which is necessary to make the systems behavior meet the customers demands. 2.1. Structural levels of hydraulic systems The systematics developed here is based on three levels of abstraction (Vier et al., 1996). The differentia- tion between functional structure, component structure, and system-theoretical structure corresponds to system descriptions of different characteristics (Fig. 2). From this distinction results an overall view of how to influence the systems behavior. To illustrate the concept of structural levels, we will concentrate on a sample subsystem of the cold-rolling plant, the four-roll stand is sketched in Fig. 3 (Ebertsha user, 1994). The functional structure shows the fundamental modes of action of a hydraulic circuit by analyzing the different tasks (functions) the plant has to fulfill. It represents 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 A represents and fulfills a subfunction f of an entire hydraulic plant. A defines the connections and the interplay among those working, control, and supply elements 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) 741750742 The hydraulic actuators of the four-roll stand perform two tasks each of which defined by a directional load and motional quantities: function 1 F T 1 ;x T 1 ; _x T 1 ;fC127x T 1 ;. T ; function 2 F T 2 ;x T 2 ; _x T 2 ;C127x T 2 ;. T : A representation of the roll stand at the functional level is given in Fig. 4. The detection of hydraulic axes and their interdependences admits far-reaching conclusions, which are stated in Section 3. On the level of the component structure the chosen realization of a function is investigated. The arrange- ment structure comprises information on the hydraulic elements (pumps, valves, cylinders, etc.) as well as their geometric and physical arrangement (Figs. 5a and b). By the switching-state structure the entirety of the possible combinations of switching positions is characterized: A valve, for instance, can be open or closed (Figs. 5c and d). Fig. 6 depicts the representation of the roll stand at the component level. The system-theoretical structure contains information on the dynamic behavior of both the hydraulic drive as a whole and its single components. Common ways of describing dynamics are differential and difference equations or the state-space form (Schwarz, 1991) X N : _x t f x t ;u t ;x 0 x t 0 8t t 0 y t h x t ;u t ;x2R n ;y;u2R: The system-theoretical view comprises information on the controlled quantities, as well as the dynamic behavior of the controlled system. The block diagram in Fig. 7 reveals the system-theoretical structure of the roll stand. By comparing analysis and simulation results with the performance demands at the drive, a decision can be made for each hydraulic axis whether open- or closed- loop control concepts are adequate. In a further step, an appropriate control strategy (linear, nonlinear, etc.) can be assigned (Fo llinger, 1992; Unbehauen, 1994). Remarks. While the functional structure yields a qua- litative representation, the system description becomes more quantitative at the component and system- theoretical level, respectively. Moreover, the analysis of the structural set-up shows in which way the behavior of a hydraulic plant can be influenced (cf. Fig. 2): (1) at first, the functional structure must be considered as invariant, because it results from the customers demands. Only if the given structure proves to be unsatisfactory, a modification resulting from a Fig. 4. The roll stand described at its functional level. Fig. 5. Examples for arrangement structures (a, b) and switching-state structure (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 743 heuristic analysis approach is advisable; (2) note that at the component level, a combination of heuristic and analytic methods is required for the variation or exchange of hydraulic elements, which form the controlled system; (3) the system-theoretical level facilitates the investigation of the dynamic be- havior: control theory provides an analytic approach for the selection of a suitable control strategy, parameter- ization, etc. 2.2. Hydraulic axes and their couplings Focusing on the investigation of the functional structure of hydraulic systems, the detection and evaluation of hydraulic axes is of central interest. Their analysis contributes to a deeper understanding of the inner correlations of the plant and provides an overview of the energy flows with respect to the functions to be fulfilled. The definition of the hydraulic axis given in Section 2.1 is based on the criterion of elements working together in order to fulfill a single function. Note that several actuators (hydraulic motors/cylinders) may contribute to the same function, thus forming a single hydraulic axis (Fig. 8). This situation is given for (a) identical sub-circuits that are controlled by one single control element, (b) synchronized movements that are carried out by open or closed loop control, or (c,d) mechanical couplings such as guides and gear units that enforce a unique behavior. Beyond the consideration of isolated hydraulic axes, it is necessary to investigate their interdependences. The following coupling types have been worked out Level 0(No coupling.) Hydraulic axes possess no coupling, if there is neither a power nor an informa- tional connection between them. Level 1(Informational coupling.) Hydraulic axes which are connected only by control connections are called informationally coupled. Level 2(Parallel coupling.) Hydraulic axes which possess their own access to a common power supply are coupled in parallel. Level 3(Series coupling.) A series coupling connects the hydraulic axes whose power supply (or disposal) is realized via the preceding or the following axis. Level 4(Sequential coupling.) A sequential coupling is given, if the performance of a following axis depends on the state variables, e.g. the pressure or the position of the preceding one in order to work in a sequence. Applying the concept of functional structure to the cold-rolling plant of Fig. 1, 15 hydraulic axes along with their couplings can be found. The left-hand side of Fig. 9 envisions the membership of the components in the diagram to the axes, the right-hand side shows the entire coupling scheme in the form of a tree. 3. Benefits of a structural analysis A structural analysis of hydraulic systems reveals basic design decisions. Especially the functional analy- sis, which is based on the detection of a systems hydraulic axes, will simplify the modification, the Fig. 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) 741750744 extension, and the adaptation of the system (Stein, 1996). The separate treatment of hydraulic axes remarkably reduces the design effort within the follow- ing respects: Smart simulation. Smart simulation is a human strategy when analyzing a complex system: subsystems are identified, cut free, and simulated on their own. This strategy reduces the simulation complexity and simpli- fies the interpretation of its results. Hydraulic axes establish suited subsystems to be cut free, since they perform an indivisible but complete subtask. Static design. Information on the hydraulic axes driving 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, the application of modification knowledge has to consider the axes coupling levels. Control concept selection. The consideration of couplings between input and output variables supplies a necessary decision basis for the selection of control concepts. Analyzing the decouplability matrix D (Schwarz, 1991) yields a common approach here. Note that the system order that can be tackled is limited. The functional structure analysis provides a separation into (1) SISO systems, to which standard methods of controller design can be applied, and (2) coupled subsystems of a reduced order, for which decouplability can be investigated more e ciently or even becomes possible at all. Diagnosis. Having a hydraulic circuit decomposed into its hydraulic axes, the diagnosis process can focus onto a single axis according to the following working hypothesis: if symptoms are observed merely at 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 axes coupling type will give further answers with respect to defect components. Hesse and Stein (1998) describe a system where this idea has been set into operation. Note that a smart classification of the coup- lings between hydraulic axes forms the rationale of whether a decomposition of a hydraulic design problem is permissible. While subsystems with level 0 or level 1 couplings can always be cut free, additional information is required for parallel, series, and sequential couplings. Example: Let A, B be two hydraulic axes. IF couplingA,B is parallel AND NOT time-overlapprocessA,process B THEN separate_designA,B is permissible IF couplingA,B is parallel AND time-overlapprocessA,process B THEN separate_designA,B is prohibited Vier (1999) provides a more detailed description of a methodology to assess the separability of the design of particular hydraulic axes. 4. Graph-theoretical analysis of hydraulic drives Key objective of the topological analysis of a hydraulic drive is the automatic detection of its under- lying functional structure, which is reflected by the hydraulic axes along with their couplings. Note that within the usual design process, hydraulic axes are not used as explicit building blocks. The reasons for this are twofold: (1) it is not always possible to design a hydraulic system in a top-down manner, starting with hydraulic axes, which are refined within subsequent steps; (2) both the experience and the ability of a human designer to automatically derive function from structure enable him to construct a hydraulic system at the component level. As an aside, the main working document for a designer is the technical drawing, and there is no tradition or standardized method to additionally specify the functional structure of a hydraulic system. This situation emphasizes the need for an automatic detection of the desired structural information. The topological analysis as pursued here is a matter of graph theory, and, in the following, we will fall back on some basic graph-theoretical concepts such as multi- graph, path, or connected component. These concepts are used in a standard way, and the main idea of our elaborations can be understood without being an expert in graph theory. At the readers convenience Section 4.3 provides a short introduction of the used definitions. 4.1. A hierarchy of coupling types For the coupling types introduced in Section 2.2 we now develop a precise mathematical formulation. In this connection hydraulic circuits are abstracted towards ordinary graphs. The following definition provides a mapping rule which assigns to each circuit C its related hydraulic graph G h C . Definition 4.1 (Related hydraulic graph). A related hydraulic graph G h C of a circuit C is a multigraph hV C ;E C ;g C i whose elements are defined as follows. (1) V C is a set of points, and there is a mapping from the set of non-pipe components in C onto V C . (2) E C is a set of edges, and there is a mapping from the set of pipe B. Stein, E. Vier / Engineering Applications of Artificial Intelligence 13 (2000) 741750 745 components in C onto E C . (3) g : E C !2 V C is a function that maps an e2E C onto v i ;v j 22 V C , if and only if there is a pipe between the components associated with v i ;v j , and if e is associated with this pipe. Fig. 10 contrasts a hydraulic circuit and its related hydraulic graph. The labels in the graph shall underline that there is a one-to-one mapping between the elements of the graph and the components of the hydraulic circuit. Remarks. for each circuit C there exists exactly one hydraulic graph G h C . Multigraphs instead of graphs must be used here since components of a hydraulic system may be connected in parallel. Notice the following topological simplifications of C: (1) substruc- tures within (directional) valves are contracted to one single point v, hence making all connected pipes incident to v; (2) variations of the topology coming along with valve switchings are neglected; (3) directional informa- tion that results from the behavior of the particular hydraulic components is dropped. These simplifications have no effect on the classification of hydraulic axes couplings. Definition 4.2 (Coupling types). Given is a hydraulic circuit C containing two sub-circuits A, B, which realize two different hydraulic axes. Moreover, let G h C : hV C ;E C ;g C i, G h A : hV A ;E A ;g A i, and G h B : hV B ;E B ;g B i denote the related hydraulic graphs of C, A, and B, respectively. Level 0(No coupling.)IfG h C is not connected, and if G h A and G h B are subgraphs of different connected components in G h , then the hydraulic axes A and B are not coupled. A and B do not have any physical connection, and thus they can be investigated indepen- dently. Level 1(Informational coupling.) Letfe 1 ;.;e n gbe in E and each e i associated with a control line within C.If G h 0 : hV C ;E C nfe 1 ;.;e n g;g C i is not connected, and if G h A and G h B are subgraphs of different connected components in G h 0, then the hydraulic axes A and B are informationally coupled (cf. Fig. 11). Notice that control lines can be realized by means of electrical, hydraulic, or pneumatic lines. Level 2(Parallel coupling.) Let P w;s be the set of all paths from a working element w to a supply element s that use no edge associated with a control line. Then A and B are coupled in parallel if there exist two nodes, v a 2V A , v b 2V B , such that the following conditions hold: (1) v a ;v b are associated with a control element. (2)8 p2P w;s : v a 2pV A t v b 2pV B . From the engineering point of view this definition states that each of the axes A and B is controlled by its own control element (cf. Fig. 12). Level 3(Series coupling.) Let P w;s be the set of all paths from a working element w to a supply element s that have no edge associated with a control line. Then A and B are coupled in series, if an axis X2fA;Bgand a path p2P w;s exist such that the following conditions hold: (1) p is a subgraph of X. (2) 9v2pV Y ;Y 2fA;BgY 6 X: v is associated with a control element. If several axes are coupled in series, at least one axis controls the flow of all other axes (cf. Fig. 13). Level 4(Sequential coupling