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

Abstract

SUMMARYIn order to discretize continuous dynamics with variable structures, Euler integrators are often used. However, Euler integrators include large discretization errors, so that they reduce the performance in the discretized dynamics. The 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 the Nyquist frequencies, and they are unsuitable for integrations of dynamics with variable structures. In this paper, we propose an improved integrator that is suitable for the integration of 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) are used instead of FD, and these are implemented using a field programmable gate array (FPGA). The effectiveness is verified through software simulations, hardware in the loop (HIL) simulations, and experiments.