Higher-Order Harmonics Reduction in Reset-Based Control Systems: Application to Precision Positioning Systems

Abstract: To address the limitations imposed by Bode's gain-phase relationship in linear controllers, a reset-based filter called the Constant in gain- Lead in phase (CgLp) filter has been introduced. This filter consists of a reset element and a linear lead filter. However, the sequencing of these two components has been a topic of debate. Positioning the lead filter before the reset element in the loop leads to noise amplification in the reset signal, whereas placing the lead filter after the reset element results in the magnification of higher-order harmonics. This study introduces a tunable lead CgLp structure in which the lead filter is divided into two segments, enabling a balance between noise reduction and higher-order harmonics mitigation. Additionally, a filtering technique is proposed, employing a target-frequency-based approach to mitigate nonlinearity in reset control systems in the presence of noise. The effectiveness of the proposed methods in reducing nonlinearity is demonstrated through both frequency domain and time-domain analyses using a simulated precision positioning system as a case study.