This paper presents a new method for solving differential-algebraic
equation systems using a mixed symbolic and numeric approach. Discretization
formulae representing the numerical integration algorithm are symbolically
inserted into the differential-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
significant 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.