Robust Control Synthesis Techniques for Multirate and Multisensing Track-Following Servo Systems in Hard Disk Drives

This paper proposes controller design methods, specially for track-following control of the magnetic read/write head in a hard disk drive (HDD). The servo system to be considered is a general dual-stage multisensing system, which encompasses most of the track-following configurations encountered in the HDD industry, including the traditional single-stage system. For the general system, a robust track-following problem is formulated as a time-varying version of the robust $H2$ synthesis problem. Both dynamic and real parametric uncertainties, which are typical model uncertainties in track-following control, are taken into account in the formulation. Three optimal robust controller design techniques with different robustness guarantees are applied to solve the synthesis problem. These are mixed $H2/H∞$⁠, mixed $H2/μ$⁠, and robust $H2$ syntheses. Advantages and disadvantages of each method are presented. Multirate control, which is inherent to control problems in HDDs, is obtained by reducing multirate problems into linear time-invariant ones, for which there are many useful theories and algorithms available. Most of the techniques proposed in this paper heavily rely on efficient numerical tools for solving linear matrix inequalities.