Research Of Multi-domain Modeling And Simulation Based On Bond Graph

Mechatronics has the characteristics of complexity,heterogeneity and merged information-physics,which integrating mechanical,eleltrical,hydraulic and control subsystems.Multi-domain modeling is the key technique which is suited for predicting,analyzing and optimizing the coupled effects among the different subsystems,thus provides the valid way to create innovative solutions and concurrent design for complex mechatronics products.Bond graph and object-oriented modeling are the most prevailing methods used for multi-domain modeling and simulation.The common component-based connection mechanism often leads to the problems of algebraic-loop and derivative-causality in derived mathematical model,which make it difficult to derivate the state-space equations and to solve the differential-algebraic equations(abbreviated as DAEs).Causality analysis is the exclusive characteristic in bond graph,and the problems of algebraic-loop and derivative-causality can be displayed based on causality path analysis.In the paper,two strategies for disposing of the difficulties caused by the problems of algebraic-loop and derivative-causality are proposed.Firstly,algebraic-loop and derivative-causality can be eliminated by modifying the bond graph models.Secondly,the non-standard bond graph models with algebraic-loop and derivative-causality can be dealt with the mixed symbolic/numerical algorithm directly.Furthermore,based on the object-oriented modeling language,Modelica,a simulation tool supporting non-standard bond graph model with algebraic-loop and derivative-causality was developed.The main contents and conclusions include:(1)The existence of algebraic-loop and derivative-causality can be displayed by analyzing the causality path in bond graph model,and the problems is caused by omitting the tiny storage when modeling the physical system,which make it difficult to derivate the state-space representation.Furthermore,based on field and junction structure methodology,different forms of differential-algebraic equations are deduced from bond graph model with algebraic-loop and derivative-causality.And the suggestions are proposed that the allowance of the existence of algebraic-loop and derivative-causality sometimes is rational,especially on the conditions of compex non-linear system.On the one hand,the bond graph model of the non-linear system can be set up straightforwardly,which avoiding the model modification,on the other hand,a group of simple DAEs can be obtained,which is easy for programming and suited for automated modeling and simulation.(2)From point of view of singular perturbation,the principle of Karnopp-Margolis method is discussed,which eliminating the algebraic-loop and derivative-causality by adding tiny parasitic elements.The limitations of the method based on frequency-domain analysis for parameterizing the tiny storage are explored.And a new method based on relative activity analysis is proposed,especially on the condition with several added storages,also the forcing input and the damper effects in the system can be taken into account when decoupled the fast subsystem from the slow subsystem by parameterizing the added storages.The proposed method has the features of simpler computaion and specific physical meaning,and the common energy-interactive characteristic make it ideally suited for bond graph modeling.Furthermore,the resistance parameter can be determined by transforming the fast subsystem to a critically damped subsystem,from which the numerical stiff problem can be alleviated,and the balance between the simulation precision and computation efficiency can be obtained.(3)From point of view of the field and junction structure in bond graph methodology,a method for derivating the fundemental equations based on the component characteristics and the topology structure constraints is proposed,which taking the power variables on external bond as system variables.The proposed method will lead to a DAEs with small redundancy and explicit algebraic contraint equation,which can simplify the subsequent index reduction procedure.Combining the benefits of displaying the algebraic-loop and derivative-causality problems in bond graph and the mixed symbolic/numerical algorithm used for object-oriented modeling,a new algorithms based on causality path analysis is proposed to determine a smaller amount of tearing variables,then the tearing information can be added to the bond graph model by controlled-sink,which can be dealt with by the mixed symbolic/numerical algorithms,thus,the high index DAEs deduced from bond graph models with algebraic-loop and derivative-causality can be solved.(4)From point of view of combining the benefits of bond graph methodology and object-oriented modeling methodolody,an object-oriented bond graph simulation tool,BGSim,is developed,which complying with the connection mechanism used for Modelica.BGSim is suited for non-causality bond graph model,non-standard bond graph model with algebraic-loop and derivative-causality,also compatible with the Modelica standard library.Furthermore,a novel load sensing hydraulic system with overriding differential pressure control is explored through system modeling,experimental validations and simulation analysis,to validate the effectiveness when modeling the complex mechatronics with the achievements in the research and BGSim tool.The research is belonged to the fundamental theory of multi-domain modeling and simulation,and has certain theoretical significance and application value to provide the theoretical basis and simulation tool for the dynamic analysis of complex mechatronics.