Frequency Response Analysis for Reset Control Systems: Application to Predict Precision of Motion Systems

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, and enable the prediction of time-domain performance for reset systems. 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.

arXiv comment22 pages; 13 figures

References in corpus (5)

• 'Constant in gain Lead in phase' element - Application in precision motion control
• Loop-shaping for reset control systems -- A higher-order sinusoidal-input describing functions approach
• Fractional-Order Single State Reset Element
• Continuous reset element: Transient and steady-state analysis for precision motion systems
• Band-Passing Nonlinearity in Reset Elements