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.