Closed-Loop Frequency Analysis of Reset Control Systems

This paper introduces a closed-loop frequency analysis tool for reset control systems. To begin with sufficient conditions for the existence of the steady-state response for a closed-loop system with a reset element and driven by periodic references are provided. It is then shown that, under specific conditions, such a steady-state response for periodic inputs is periodic with the same period as the input. Furthermore, a framework to obtain the steady-state response and to define a notion of closed-loop frequency response, including high order harmonics, is presented. Finally, pseudo-sensitivities for reset control systems are defined. These simplify the analysis of this class of systems and allow a direct software implementation of the analysis tool. To show the effectiveness of the proposed analysis method the position control problem for a precision positioning stage is studied. In particular, comparison with the results achieved using methods based on the Describing Function shows that the proposed method achieves superior closed-loop performance.