Higher-Order Sinusoidal Input Describing Function Analysis and Optimal Tuning of Hybrid Integrator-Gain Systems

The hybrid integrator-gain system (HIGS) is a nonlinear control element with significant potential to enhance controller performance in precise motion control. However, existing HIGS-based controller design methods typically rely on describing functions (DFs), which neglect higher-order harmonics. This paper proposes a novel HIGS-based constant in gain lead in phase (CgLp) element, allowing flexible adjustment of the induced phase lead and high-frequency distortion. Higher-order sinusoidal input describing functions (HOSIDFs) are employed as tools for frequency-domain analysis, providing a method to predict the closed-loop behavior of HIGS-controlled systems by connecting open-loop and closed-loop characteristics. Optimal tuning guidelines for HIGS-based controllers are developed using the proposed tools, accounting for the harmonic effects on closed-loop behaviors. Simulation and experimental results on an H-type precise air-floating motion control platform validate the accuracy of the proposed analysis tools and the effectiveness of the optimal tuning method.