Frequency response analysis for reset control systems
Application to predict precision of motion systems
Xinxin Zhang (TU Delft - Mechatronic Systems Design)
M.B. Kaczmarek (TU Delft - Mechatronic Systems Design)
S.H. Hassan HosseinNia (TU Delft - Mechatronic Systems Design)
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Abstract
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.
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