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In this paper we employ a modified filtered-x least mean squares (MFX-LMS) method to synthesis an adaptive repetitive controller for rejecting periodic disturbances at selective frequencies. We show how a MFX-LMS algorithm can be utilized when the reference signal is deterministic and periodic. A new adaptive step size is proposed with the motivation to improve the convergence rate of the MFX-LMS algorithm and fade the steady state excess error caused by the variation of estimated parameters in a stochastic environment. A novel secondary path modeling scheme is proposed to compensate for the modeling mismatches online. We further discuss the application of this adaptive controller in hard disk drives that use Bit Patterned Media Recording. Finally we present the results of comprehensive realistic numerical simulations and experimental implementations of the algorithms on a hard disk drive servo mechanism that is subjected to periodic disturbances known as repeatable runout.

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This paper considers robust controller design for track-following in hard disk drives (HDD) with irregular sampling of the position error signal (PES) but regular (clock-driven) control updates. This sampling and actuation behavior is modeled by applying a novel discretization method to a continuous-time model of an HDD, resulting in a discrete-time linear periodically time-varying model. Then, the controller design is performed using optimal control for periodic systems and uses a generalization of the disk margin to quantify the robustness of the closed-loop system. To show the effectiveness of the proposed method, the design methodology is applied to a hard disk drive model and the resulting controller is validated by examining its nominal performance in terms of the root mean square of the standard deviation of the PES and robustness in terms of disk margin. Since the proposed controller has too many parameters to be implementable on an HDD due to memory limitations, we use a vector quantization method to approximate the entire parameter set of the designed controller by a smaller set of parameters.