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1.
A procedure is presented whereby the control volume equations for one-dimensional, compressible gas dynamics are cast into first-order, state variable form. These equations are interpreted using causal bond graphs. The resulting bond graph is shown to reduce to the classic I-C chain under acoustic constraints and to a more recently developed model of low speed thermal energy transport subject to associated constraints.Through example it is demonstrated that the control volume bond graph is easily coupled to an overall system model and thus can be digitally simulated as part of the overall nonlinear state space representation. The result is that a very accurate gas dynamic model can be coupled with an overall dynamic system model without requiring a prohibitively large number of equations.  相似文献   

2.
This paper addresses the modelling and control of switched systems with Boolean inputs. A generalization of Passivity Based Control (PBC) is proposed and fitted to bond graph formalism. The state equations of the equivalent average model are first deduced from the original bond graph using the notion of commutation cells and then interpreted according to Port Controlled Hamiltonian formalism. The whole approach is presented in a formal way. This method is then applied on a multicellular serial converter, which is widespread in power systems and of growing interest. The application of PBC associated to a modelling approach using commutation cells on a non-trivial example shows its efficiency to determine a generic controller, the number of elementary cells being considered as a parameter.  相似文献   

3.
Lumped parameter, undamped vibratory system models are studied starting from a vector bond graph representation which yields a symmetric set of equations of motion in terms of momenta and displacements. Four additional formulations are obtained depending upon the choices of displacement or impulse-momentum degrees of freedom including the classical formulation in terms of mass displacements. Differences in terms of forcing and response variables are found among the alternative formulations and differences in system order are explained. A new form of normal mode equations is developed using first order symmetric variables and a bond graph representation is given. Advantages in the use of the new model analysis for subsystem coupling are discussed.  相似文献   

4.
A recent communication has proposed a conjectural procedure for representing a category of optimal control problems in bond graph language [W. Marquis-Favre, B. Chereji, D. Thomasset, S. Scavarda, Bond graph representation of an optimal control problem: the dc motor example, in: ICBGM’05 International Conference of Bond Graph Modelling and Simulation, New Orleans, USA, January 23-27, 2005, pp. 239-244]. This paper aims at providing a fundamental theory for proving the effectiveness of this procedure. The class of problem that the procedure can deal with has been extended. Its application was formerly restricted to linear time invariant siso system. The systems considered now are linear time invariant mimo systems. The optimization objective is the minimization of dissipation and input. The developments concerning the optimal control problem are based on the Pontryagin maximum principle and the proof of the effectiveness of the procedure makes a broad use of the port-Hamiltonian concept. As a result, the bond graph representation of the given optimization problem enables the analytical system, which provides the optimal solution, to be derived. The work presented in this paper is the first step in research with perspectives towards formulating dynamic optimization problems in bond graph and, towards coupling this formulation with a sizing methodology using bond graph language and a state-space inverse model approach. This sizing methodology, however, is not the topic of this paper and thus is not presented here.  相似文献   

5.
The Graph-Theoretical Field Model provides a unifying approach for developing numerical models of field and continuum problems. The methodology examines the field problem from the first stages of conceptualization without recourse to the governing differential equations of the field problem; this is accomplished by deriving discrete statements of the physical laws which govern the field behaviour. There are generally three laws, and these are modelled by the “cutset equations”, the “circuit equations”, and the “terminal equations”. In order to establish these three sets of equations it is expedient first to spatially discretize the field in a manner similar to the finite difference method and then to associate a linear graph (denoted as the field graph) with the spatial discretization. The concept of “through” and “across” variables, which underlies the cutset and circuit equations respectively, enables one to define the graph in an unambiguous manner such that each “edge” of the graph identifies a pair of complementary variables. From a knowledge of the constitutive properties and the boundary conditions of the field it is possible to associate terminal equations with sets of edges. Since the resulting sets of equations represent the field equations, these equations provide the basis for a complete (but approximate) solution to the field or continuum problem. In fact, this system approach uses a two part model: one for the components and another for the interconnection pattern of the components which renders the formulation procedures totally independent of the solution procedure.This paper presents the theoretical basis of the model and several graph-theoretic formulations for steady-state problems. Examples from heat conduction and small- deformation elasticity are included.  相似文献   

6.
Dynamic systems containing particles and rigid bodies capable of movement in two- or three-dimensions may be represented by equations of motion in several basic forms. In all cases geometric nonlinearities are involved and terms arise in the equations which are difficult to understand and interpret. The equations often conceal the basic structure of the dynamic model of the system since only combinations of parameters and combined effects of various constraints finally appear.In this paper the basic relations for the dynamic elements as well as the transformations among internal forces and velocities are depicted using bond graphs. The energetic structure of the system is thus exhibited in multiport form. This aids in the exploration of alternative equation formulation and in understanding of the assumptions involved in any particular equation set. Further, a bond graph model is easily coupled with nonmechanical dynamic models through force or motion generators.  相似文献   

7.
Bond graphs are used to construct finite mode representations of inherently distributed systems. These systems are, perhaps, only part of an overall dynamic system. The “causal” information provided by the bond graph permits the derivation of an automatable algorithm which produces the state equations as well as all output variables associated with the finite modes. The procedure requires only the a priori knowledge of modal masses, frequencies, and associated mode shapes for general boundary conditions of the distributed parts of the system. Thus, the algorithm is applicable to any multidimensional distributed system which is representable by normal modes.  相似文献   

8.
A procedure is developed which uses bond graph modeling and a digital computer to determine if semi-active control can provide a suitable performance in an application where totally active control is considered. The application areas principally addressed are those in which the disturbance inputs to the system are of zero mean, i.e. shock and vibration control.The procedure is developed through examples and then generalized to systems of high order and large complexity. The procedure consists basically of designing a control strategy suitable for totally active control and then enforcing a passivity constraint on the actuating device. Experience has shown that semi-active control approaches that of totally active control in most vibration isolation applications.  相似文献   

9.
The dynamic effects of muscle strength, timing of muscle activations, and body geometry have been modeled for a wide variety of human activities. These types of models require the development of complex system equations that account for the effects of rigid-body dynamics, musculotendon actuators, passive and active resistance to motion, and other physiological structures. One way in which model refinement can be expedited is through the use of bond graph modeling techniques. While bond graph techniques have been used extensively in a broad variety of applications, they have been used only sparingly in the field of biomechanics, despite the potential suitability of a modular, multidomain approach to the modeling of musculoskeletal function. In the current paper, bond graph modules representing muscle function and rigid-body motions of underlying bone structures are introduced. The system equations generated with the use of these models are equivalent to those developed with more traditional techniques, but the modules can be more easily used in conjunction with control models of neuromuscular function for the simulation of overall dynamic motor performance.  相似文献   

10.
This paper is concerned with the global exponential stability for an original class called coupled systems of multi-group neutral delayed differential equations (MNDDEs). By employing Razumikhin method along with graph theory, sufficient conditions are established to guarantee the global exponential stability of MNDDEs, which are in the form of Razumikhin theorem. For the convenience of use, sufficient conditions in the form of coefficients are also obtained. Furthermore, coefficient-type criterion is employed to study the stability of coupled neutral delay oscillators which shows the applicability of our findings. Finally, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results.  相似文献   

11.
Bond graph modeling techniques yield state equations intimately related to energy storage in physical systems. The easy physical interpretation of the state variables from a bond graph model aids in the realization of modern automatic control schemes involving state variable feedback. When it is inconvenient or impossible or measure certain state variables, the useful device of an observer may be used to estimate the missing state variables. It is shown that the same bond graph used to model the system can be used to derive a complete or reduced order observer. The partial observers use derivative causality in a new way and in some cases, the effects of completely unknown disturbances may be accounted for.  相似文献   

12.
Classical modal analysis techniques for the prediction of vehicle-guideway dynamics are developed and interpreted with bond graph representations. Bond graphs are shown to allow easy generalization to multiple span guideways incorporating virtually any dynamic boundary conditions at the support locations. In addition, non-linear vehicle models can be used with any vehicle displacement-time history desired. Straightforward formulation procedures are also provided through the bond graph representation.The analysis procedure is demonstrated for a two-span Bernoulli-Euler Guideway with first-order dynamic boundary conditions. The results for a vehicle traveling at different speeds are shown to compare favorably with current literature.  相似文献   

13.
A procedure for approximating fractional-order systems by means of integer-order state-space models is presented. It is based on the rational approximation of fractional-order operators suggested by Oustaloup. First, a matrix differential equation is obtained from the original fractional-order representation. Then, this equation is realized in a state-space form that has a sparse block-companion structure. The dimension of the resulting integer-order model can be reduced using an efficient algorithm for rational L2 approximation. Two numerical examples are worked out to show the performance of the suggested technique.  相似文献   

14.
In a previous work an approach was presented for extracting information about the eigenvalues of a linear, time-invariant dynamic system directly from a graphical model. In this paper a generalization is given of the results previously obtained. For some particular cases we can give the entire spectrum. For these cases the spectrum is shown as a function of the structure of an abstract form of the bond graph model. For more general cases, we give upper limits on the imaginery part, and upper and lower limits on the real parts, of the eigenvalues. In contrast to most existing methods, the information about the eigenvalues is generated prior to deriving the state equations. When suitably automated, the results obtained here can provide a considerable reduction in the computational effort required to get information about eigenvalues. This feature is particularly useful in an interactive design context.  相似文献   

15.
In this paper, we provide a new insight into clustering with a spring–mass dynamics, and propose a resulting hierarchical clustering algorithm. To realize the spectral graph partitioning as clustering, we model a weighted graph of a data set as a mass–spring dynamical system, where we regard a cluster as an oscillating single entity of a data set with similar properties. And then, we describe how oscillation modes are related with eigenvectors of a graph Laplacian matrix of the data set. In each step of the clustering, we select a group of clusters, which has the biggest number of constituent clusters. This group is divided into sub-clusters by examining an eigenvector minimizing a cost function, which is formed in such a way that subdivided clusters will be balanced with large size. To find k clusters out of non-spherical or complex data, we first transform the data into spherical clusters located on the unit sphere positioned in the (k−1)-dimensional space. In the sequel, we use the previous procedure to these transformed data. The computational experiments demonstrate that the proposed method works quite well on a variety of data sets, although its performance degrades with the degree of overlapping of data sets.  相似文献   

16.
Holonomic systems can be represented by a bond graph in which inertial variables are related to generalized variables using a multiport displacement-modulated transformer structure. It is shown that the part of the generalized forces due to inertial elements can be found either by direct calculation or by the operations of Lagrange's equations. Although no gyrators are needed for the representation, gyrational coupling may exist. Alternative representations may involve gyrators explicitly and it is possible to construct kinetic co-energy functions for these gyrators for use in Lagrange's equations.  相似文献   

17.
It is shown that reinvestment and inventory effects can be described in 0431 0368 bond-graph terms. The associated differential equations in price and order-flow 0431 0368 V variables are bilinear forms. These effects are the fundamental inertia and compliance 0431 0368 V 3 of economic bond graph theory. Properties of the components and example market 0431 0368 V 3 graphs are discussed.  相似文献   

18.
A social choice procedure is modeled as a Nash game among the social agents. The agents are communicating with each other through a social communication network modeled by an undirected graph and their opinions follow a dynamic rule modelling conformity. The agents’ criteria for this game are describing a trade off between self-consistent and manipulative behaviors. Their best response strategies are resulting in a dynamic rule for their actions. The stability properties of these dynamics are studied. In the case of instability, which arises when the agents are highly manipulative, the stabilization of these dynamics through the design of the network topology is formulated as a constrained integer programming problem. The constraints have the form of a Bilinear Matrix Inequality (BMI), which is known to result in a nonconvex feasible set in the general case. To deal with this problem a Genetic Algorithm, which uses an LMI solver during the selection procedure, is designed. Finally, through simulations we observe that in the case of topologies with few edges, e.g. a star or a ring, the isolation of the manipulative agents is an optimal (or suboptimal) design, while in the case of well-connected topologies the addition or the rewiring of just a few links can diminish the negative effects of manipulative behaviors.  相似文献   

19.
Topological analysis of the signal flow graph associated with the hybrid system of equations for a linear active or passive electrical network for which the element admittance matrix exists and is diagonal is considered. First, the term cancellation which occurs in Mason's topological formulas is investigated. Necessary and sufficient conditions on the signal flow graph topology such that a term in the expansion of the graph determinant and cofactors either cancels out with another term in the expansion or does not cancel are established. Properties of the associated network which result in non-cancelling terms are given and the number of non-cancelling terms is determined. Second, new signal flow graph topological formulas for the graph determinant and cofactors are proven. These formulas are such that no term cancellation occurs and are readily adaptable to computer implementation. In addition, the number of terms in these formulas is independent of the network tree used to formulate the signal flow graph. Examples are given to illustrate the new formulas.  相似文献   

20.
The paper describes the preparation of a dynamic model required for simulation of a 30 kW electro-hydraulic system used to induce controlled vibration of a wide range of components, machines or structures. The vibrator system is associated with a 28 tonne seismic block. The model is highly detailed to allow study of the system to its dynamic performance limits of around 300 Hz. The model consists of nearly eighty equations some of them nonlinear and discontinuous. The paper describes the orderly development of the model emanating from the bond graph approach. Some simulation results, with limited experimental correlation, are included.  相似文献   

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