Discrete-Time H-Infinity Synthesis of Frequency-Shaped Sliding Mode Control for Suppression of Vibration With Multiple Peak Frequencies

Vibration with multiple large peaks at high frequencies may cause significant performance degradation and have become a major concern in modern high precision control systems. To deal with such high-frequency peaks, it is proposed to design a frequency-shaped sliding mode controller based on H_∞ synthesis. It obtains an ‘optimal’ filter to shape the sliding surface, and thus provides frequency-dependent control allocation. The proposed frequency-shaping method assures the stability in the presence of multiple-peak vibration sources, and minimizes the weighted H_∞ norm of the sliding surface dynamics. The evaluation is performed on a simulated hard disk drive with actual vibration sources from experiments, and the effectiveness of large vibration peak suppression is demonstrated.