Optimal $H_{\infty}$ Control Design and Implementation of Hard Disk Drives With Irregular Sampling Rates

Missing position error signal sampling data in hard disk drives (HDDs) results in their servo systems having irregular sampling rates (ISRs). With the natural periodicity of HDDs, which is related to the disk rotation, HDD servo systems with ISRs can be modeled as linear periodically time-varying systems. Based on our previous results, an explicit minimum entropy
H
_∞
controller for HDD servos with ISRs via discrete Riccati equations is first obtained. The resulting controller is subsequently demonstrated to be periodically time-varying and implementable. Simulation and experimental studies, which have been carried out on a set of hard disk drives, demonstrate that the proposed control synthesis technique is able to handle ISRs and can be used to conveniently design a loop-shaping track-following servo that achieves the robust performance of a desired error rejection function for disturbance attenuation. Experimental results on ten actual 2.5" hard disk drives show around 27% improvement of the 3σ PES was obtained by the proposed control algorithm.