Reduction of Discretization Errors of Dynamics with Variable Structures and Its Realization using FPGA

Abstract

In order to discretize continuous dynamics with variable structures, Euler integrators are often used. However, Euler integrators include large discretization errors, so that they deteriorate performances of the discretized dynamics. Use of Richardson extrapolation (RE) and fractional delay (FD) can reduce the discretization errors. However, Euler integrators using RE and FD directly have infinite gains at their Nyquist frequencies, and they are unsuitable for integrations of the dynamics with variable structures. In this paper, we propose an improved integrator which is suitable for integrations of the dynamics with variable structures. The proposed method consists of a high forward gain and a feedback structure with a high-precision differentiator. To realize the high-precision differentiator, RE and a high sampling rate (HSR) instead of FD are used, and those are implemented by FPGA. Its effectiveness is verified by software simulations, hardware in the loop (HIL) simulations, and experiments.