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.
Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset
Delft Center for Systems and Control, Delft University of Technology（代尔夫特系统与控制中心，代尔夫特理工大学）；Department of Precision and Microsystems Engineering, Delft University of Technology（精密与微系统工程学院，代尔夫特理工大学）
Koopman-Based Robust Model Predictive Control for Nonlinear Systems with Stochastic Intermittent Measurements
Harbin Institute of Technology（哈尔滨工业大学）；School of Astronautics, Harbin Institute of Technology（哈尔滨工业大学航天学院）；Nanyang Technological University（南洋理工大学）；Nanyang Environment and Water Research Institute (NEWRI)（南洋环境与水研究）
