Modeling of dynamic systems by method of bond graph

Abstract

The various technical systems consist of separate parts, which are in a certain way organized as a whole and interact with each other. The interaction is due to the connections of the parts, the external influences and the anticipation of the desired consequences. One of the problems of such interaction is the study of the temporal evolution of the effects of action on objects of different nature. The methodology of the systematic approach to solving management problems is based on two basic principles of modeling and purposefulness. One of the effective methods in which the ideas of component modeling at the lower level (level of energy domains) are imple-mented is the method of bond graphs. The language of bond graphs allows to build models of dynamic systems in the state space. As a result of the analysis of existing researches and publi-cations, the purpose of research is set, namely: creating dynamic models of technical systems with using the method of the bond graph. In this work, the structural model of control of the harmonic oscillator, which is described by the system of equations in the state space, is present-ed. In addition to state equations, we obtain observation equations that connect the state with the initial parameter of the system. An oscillatory system with one degree of freedom in which the resistance R is a model for the transformation of mechanical energy into other forms is con-sidered. Also, the principle of constructing a control model in a state of space for a vibrational system with one degree of freedom is considered in the conditions that the system is not per-turbed by force, but by speed. The next stage of the complication of the model was the consider-ation of the case when the support of oscillator has velocity which not equal zero. In accord-ance with the symbols of the language of the bond graphs, the equations of the system state, transitional structures and observation were compiled. A practical value of the work is the pro-posed method of building models of control systems in the state space. The originality is that the models have generalizations in case of increasing the dimensionality of the system, as well as when using nonlinear elements of different types. In the language of bond graphs, we can con-struct a model of a control system in the form of a system of differential equations. Then the search for the output or consequences of the action on the system consists in solving the system of differential equations with a determine control, or action u(t), substituting the found state x(t) into the observation equation and determining y(t).