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Research Papers

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

[+] Author and Article Information
Ryozo Nagamune

Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, V6T 1Z4, Canadanagamune@mech.ubc.ca

Xinghui Huang

Seagate Technology, 389 Disc Drive, Longmont, CO 80503xinghui.huang@seagate.com

Roberto Horowitz

Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740horowitz@berkeley.edu

Throughout this paper, we assume that, if a plant model is originally given in continuous-time, it has been discretized with the fastest sampling/hold rate.

Throughout this paper, we use bold capital letters to denote block-diagonal matrices.

J. Dyn. Sys., Meas., Control 132(2), 021005 (Feb 02, 2010) (10 pages) doi:10.1115/1.4000835 History: Received September 28, 2005; Revised June 30, 2009; Published February 02, 2010; Online February 02, 2010

## Abstract

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.

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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 1

A generalized plant with an uncertainty block Δ and a multirate controller HKS

Figure 2

A periodic time-varying system consisting of a time-invariant generalized plant, a multirate sampler S, and a multirate hold H

Figure 3

Uncertainty structure for mixed H2/H∞ synthesis

Figure 4

Frequency responses from uV to yLDV (upper figure) and from uM to yLDV (lower figure)

Figure 5

Block diagram

Figure 6

Block diagram with parametric uncertainties

Figure 7

Comparisons between the experimental and simulation frequency responses for PVCM

Figure 8

Comparisons between the experimental and simulation frequency responses for PMA

Figure 9

Sensitivity functions

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