Inline Integration: A new mixed symbolic/numeric approach for solving differential-algebraic equation systems

Abstract

This paper presents a new method for solving di erential{algebraic equation systems using a mixed symbolic and numeric approach. Discretization formulae representing the numerical integration algorithm are symbolically inserted into the di erential{algebraic equation model. The symbolic formulae manipulation algorithm of the model translator treats these additional equations in the same way as it treats the physical equations of the model itself, i.e., it looks at the augmented set of algebraically coupled equations and generates optimized code to be used with the underlying simulation run{time system. For implicit integration methods, a large nonlinear system of equations needs to be solved at every time step. It is shown that the presented uniform treatment of model equations and discretization formulae often leads to a signi cant reduction of the number of iteration variables and therefore to a substantial increase in execution speed. In a large mechatronics system consisting of a six degree{of{freedom robot together with its motors, drive trains, and control systems, this approach led to a speedup factor of more than ten