Research On Solving Methods For Differential Algebraic Models Oriented To Hardware In The Loop Simulation

Complex systems often involve mechanics, electrics, hydraulic, electromagnetic andother interdisciplinary. Due to the high nonlinearity of real physical systems withtime-consuming and costly development process, hardware in the loop simulation basedon Modelica language has become the main trend of current system design andoptimization techniques. Since Modelica describes the physical systems’ dynamicfeatures and behavior via differential algebraic equations, efficient algorithms for suchequations prove to be a necessary condition to achieve successful simulations consideringthe remarkable point, i.e. hardware in the loop.Facing the significant part of physical system modelling, intensive study on inlineintegration aimed at enhancing the solving efficiency substantially for differentialequations is conducted, and so is following proven solution. According to stiff differentialequations or not, the discrete formulas representing integral methods are combined withmodel equations and structural analysis, thus minimizing the number of coupled variables.Finally by means of computer algebra methods the augmented equation system is solved.Unavoidably, there still will be nonlinear equations after inline integration. Byresearch on nonlinear solution with plenty of project cases, the efficient solution ofnonlinear equations has been performed. First, an approximate update formula ofJacobian matrix and its inverse matrix are proposed to avoid inverse matrix calculation ofhigher time complexity. After that, to make it possible in applications, the indispensableconstraint that must be satisfied when using the formulas above is put forward. At last, asolution handling row rank reduction of Jacobian matrix is introduced via singularitydisturb algorithm.Research results above has improved the solving efficiency of differential equations,and met the real time performance of hardware in the loop simulation, and contributed tothe technical basis for platform of hardware in the loop simulation based on Modelica.