Adapting Power-Series Integration to Real-Time Simulation

power-series, real-time simulation, diferential equation, controller

Simulation of physical systems using digital computers continues to play an ever
increasing role in all aspects of today's technological society. In general the
basis for simulation resides in mathematical models of the systems being
simulated. In the case of continuous dynamic systems these models consist of
either nonlinear ordinary or partial differential equations. The simulation of
these systems and hence the simulation of the corresponding mathematical models
can be accomplished by numerical integration of the differential equations.
An original mathematical method which uses the Taylor series method for solving
differential equations in a non-traditional way has been developed. Even though
this method is not much preferred in the literature, experimental calculations
have shown and theoretical analyses have verified that the accuracy and stability
of the Taylor series method exceeds the currently used
algorithms for numerically solving differential equations.
It is the aim of the paper to adapt power-series integration (Taylor series) to
real-time simulation. In real-time digital simulation the numerical integration
step size h is almost always fixed. The same is expected from corresponding
power-series integration. Actually, it may be difficult to apply the power series
method to real time simulation, since the required higher derivatives of the
real-time inputs will not in general be available. Furthermore, many real-time
simulations involve derivative functions that are represented by multidimensional
data tables rather than analytic functions. In this case the required
state-variable derivatives do not exist.
Adapting power-series integration to real-time simulation in this paper is based
on a model representation. The real system is driven by the model and all the
control is specified in the model. Next step how to speed up simulation is to use
a special digital hardware.