A new accurate discretization method for high-frequency component mechatronics systems

Abstract

Modern mechatronics systems are implemented digitally. However, the magnitude and phase errors caused in the discretization process severely restrain the control performance in systems with high-frequency components where only a few sampled data points are available per period. This paper presents a new accurate discretization method for mechatronics systems that provide good performance even when intrinsic frequency components are close to the Nyquist frequency which is one-half of the sampling frequency. The bilinear transform method is most commonly used, but it causes oscillations when the initial state error of the output is not zero or when rapid changes occur in the input signal. Several variations of the bilinear transform method have been proposed to improve these problems, but as a tradeoff, they introduce large magnitude and/or phase errors at high frequencies. In this paper, a more accurate discretization method is developed, which combines a modified bilinear transform method with a new method to compensate for the frequency and damping ratio warping caused by approximate discretization. The proposed method reduces the magnitude and phase errors over the entire frequency range. The proposed method is experimentally evaluated in a mechatronics system with a mechanical resonance frequency that is about 0.6 times the Nyquist frequency.