Multi-rate Observer Based Sliding Mode Control with Frequency Shaping for Vibration Suppression Beyond Nyquist Frequency*

Nyquist frequency limits the frequency range of the continuous-time signals that can be reconstructed through the sampled discrete-time signals. In hard disk drives (HDDs), there exist resonance modes near and beyond the Nyquist frequency in the voice coil motor (VCM). Such resonance modes, if excited, may generate vibration beyond the Nyquist frequency which would seriously degrade the servo performance. To capture such vibration, a multi-rate extended observer is designed based on the nominal dynamic model of the excitation process. This observer estimates both the states and the vibration at a fast rate based on the sampled position error signal (PES) at a slow rate. The estimated states are utilized to design a sliding mode control algorithm at the fast rate with frequency shaping to suppress vibration beyond the Nyquist frequency. Meanwhile, the estimated vibration are incorporated in the control signal to further compensate the actual vibration. Simulation results demonstrate the benefits of the proposed algorithm: large off-track behaviors of the VCM are mostly detected and the vibration beyond the Nyquist frequency are suppressed.