Analysis of unobservable residual vibration characteristics in sampled-data control systems using first-order holds

Abstract

In this study, we examined the effects of introducing a First-Order Hold (FOH) on the “unobservable residual vibrations caused by mechanical resonances near the sampling frequency” in sampled-data control systems. We compared three types of holds used in sampled-data control systems: Zero-Order Hold (ZOH), Causal First-Order Hold (CFOH), and Triangle-method based First-Order Hold (TFOH). First, we conducted an analysis of the Shock Response Spectrum (SRS) using a half-sine wave and demonstrated that changing from ZOH to FOH can suppress the occurrence of residual vibrations near the sampling frequency. Next, we performed SRS analysis using an acceleration polynomial that considers the characteristics of the hold, and obtained results similar to those from the half-sine wave analysis. Finally, we conducted simulation verification of feedforward control using a model that mimics a precision positioning device, demonstrating the validity of the SRS analysis results. From these results, it was clarified that the “unobservable residual vibrations caused by mechanical resonances near the sampling frequency” in sampled-data control systems can be reduced by employing FOH instead of ZOH. Furthermore, it was shown that the reduction effect is greater when TFOH is employed compared to CFOH.

Keywords

• sampled-data control system
• first-order hold
• unobservable amount
• shock response spectrum
• residual vibration