Optimal H∞ Control for Linear Periodically Time-Varying Systems in Hard Disk Drives

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.