Reliability Assessment and Performance Enhancement of Reset Control Systems

This paper develops a frequency-domain reliability assessment framework for reset control systems. The closed-loop higher-order sinusoidal-input describing function formulation is extended to explicitly include the reset-triggering signal generated through a shaping filter. Based on this signal, two metrics are introduced: \(\sigma_t\), which quantifies reset-time deviation, and \(\sigma_d\), which evaluates the tendency toward additional zero crossings. These metrics provide design-oriented indicators for identifying potentially unreliable reset behavior. To improve reset-triggering reliability, a first-order shaping filter is proposed for a generalized first-order reset element, increasing the low-frequency attenuation slope of the nonzero higher-order harmonics. The proposed analysis is evaluated on an industrial motion stage. The results show that the proposed metrics capture reliability issues that are not evident from the first-order closed-loop response alone and can therefore support the design of reset controllers with more reliable reset-triggering behavior.