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Periodicity frequently occurs in hard disk drives (HDDs) whose servo systems with periodic phenomena can be usually modeled as linear periodically time-varying (LPTV) systems. This paper discusses optimal H\infty control synthesis for discrete-time LPTV systems via discrete Riccati equations. First, an explicit minimum entropy H\infty controller for general time-varying systems is obtained. Subsequently, the developed control synthesis algorithm is applied to LPTV systems and it is shown that the resulting controllers are periodic. The proposed control synthesis technique is evaluated through both single and multirate optimal H\infty track-following control designs. The single-rate servo design shows that our proposed control synthesis technique is more numerically robust in calculating optimal H\infty controllers for discrete-time linear time-invariant systems than the MATLAB function of “hinfsyn,” while the multirate servo design validates its ability of synthesizing multirate controllers to achieve the robust performance of a desired error-rejection function. Moreover, an experimental study—in which the developed control synthesis algorithm on a real HDD with missing position error signal sampling data is implemented—further demonstrates its effectiveness in handling LPTV systems with a large period and attaining desirable disturbance attenuation. [ABSTRACT FROM PUBLISHER]

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\infty 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 3\sigma PES was obtained by the proposed control algorithm. [ABSTRACT FROM PUBLISHER]

This paper considers two novel controller synthesis methodologies using a feedforward control structure for performing concentric self-servo track writing in hard disk drives. In the first methodology, it is assumed that a conventional causal track-following controller has been designed and a non-causal feedforward controller, which utilizes the stored error signal from writing the previous track, is designed using standard H\infty control synthesis techniques, in order to prevent the track errors from propagating and to achieve good disturbance attenuation. In the second methodology, both the track-following feedback controller and the feedforward controller are simultaneously designed via a mixed H2/H\infty control scheme, which involves the solution of a set of linear matrix inequalities and achieves good disturbance attenuation while preventing the propagation of track errors from the previous tracks. Simulation results confirm that the two proposed control synthesis methodologies prevent error propagation from the previously written tracks and significantly improve concentric self-servo track writing performance. [ABSTRACT FROM AUTHOR]