Nonlinear Control Design Using Fractional-order Hybrid-integrator-gain Systems

Abstract

Precision engineering applications, such as atomic force microscopes and semiconductor motion stages, demand high accuracy in tracking and disturbance rejection, often limited by the waterbed effect and gain-phase constraints in linear control systems. This thesis introduces nonlinear control designs leveraging Fractional-order Hybrid-Integrator-Gain Systems (FO-HIGS) to overcome these limitations, providing tunable phase lead with reduced higher-order harmonics compared to traditional integer-order HIGS.

Two novel FO-HIGS-based controllers are proposed: (1) An enhanced CgLp filter integrated with PID control to improve low-frequency tracking by compensating phase lag through parameter tuning (e.g., fractional order α and corner frequency), minimizing parasitic nonlinear effects via simulation-based higher-order sinusoidal-input describing function (HOSIDF) analysis and pseudo-sensitivity evaluation. (2) A FO-HIGS-based LPF for superior high-frequency noise attenuation, achieving lower cumulative power spectral density than linear counterparts.

Simulations and experiments on a linear-motor-actuated motion stage validate the designs, demonstrating improved performance in reference tracking and disturbance rejection while maintaining stability.