Frequency response analysis for reset control systems: Application to predict precision of motion systems

The frequency response analysis describes the steady-state responses of a system to sinusoidal inputs at different frequencies, providing control engineers with an effective tool for designing control systems in the frequency domain. However, conducting this analysis for closed-loop reset systems is challenging due to system nonlinearity. This paper addresses this challenge through two key contributions. First, it introduces novel analysis methods for both open-loop and closed-loop reset control systems at steady states. These methods decompose the frequency responses of reset systems into base-linear and nonlinear components. Second, building upon this analysis, the paper develops closed-loop higher-order sinusoidal-input describing functions for reset control systems at steady states. These functions facilitate the analysis of frequency-domain properties, establish a connection between open-loop and closed-loop analysis. The accuracy and effectiveness of the proposed methods are successfully validated through simulations and experiments conducted on a reset Proportional–Integral–Derivative (PID) controlled precision motion system. • Current Describing function and Higher-order Sinusoidal-Input Describing Function (HOSIDF) analysis for closed-loop reset control systems are inaccurate. • The new theory provides insights that outputs of open-loop and closed-loop reset control systems under sinusoidal inputs can be analytically separated into their base-linear outputs and pulse-based nonlinear elements. • The proposed HOSIDF analysis rectifies the conservative assumption in previous HOSIDF analysis. • The closed-loop HOSIDF enables sensitivity function analysis, including higher-order harmonics. • The relation between open-loop and closed-loop analysis provide frequency-domain tools for future reset control system design.