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.