The CAMP-G/MATLAB Solution of Algebraic Loops in Dynamic Systems represented by Bond Graph Models

摘要

The presence of algebraic loops in dynamic systems models present difficulties in computer simulation. Algebraic loops result in an implicit set of system equations. This paper presents a description of the problem and its physical interpretation in electrical and mechanical systems. In a system with algebraic loops Internal variables used to calculate the derivatives can not be explicitly defined in order to produce a closed loop explicit set of differential algebraic equations. A solution of course is to attempt to solve the system as an implicit set. This approach can result in computational problems. This research examines the problem and proposes a solution which produces a state space representation of a system with algebraic loops in explicit form. The automated methodology used is presented using symbolic equations and system matrices. It is based on the important principle of causality. An algorithm has beep developed and implemented into CAMP-G (Computer Aided Modeling Program with Graphical Input), a software package designed to aid engineers and scientists to generate computer models of dynamic systems. The CAMP-G/MATLAB system is used to illustrate the solution. Implementation of this method has led to a computerized automated solution of dynamic system models with multiple algebraic loops. Combining the CAMP-G solution with MATLAB and the nonlinear capabilities of SIMULINK the system offers a general solution for dynamic systems with algebraic loops.