26 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 10, NO. 1, FEBRUARY 2005 A Comparative Study of the Use of the Generalized Hold Function for HDDs Keitaro Ohno, Member, IEEE, Mitsuo Hirata, Member, IEEE, and Roberto Horowitz, Member, IEEE Abstract—This paper is concerned with the application of control with the generalized hold function (GHF) to track-fol- lowing control of hard disk drives (HDDs). In HDDs, the sampling frequency is limited primarily by the fact that a high sampling frequency tends to decrease the available data storage capacity of the devices, since the position error signal (PES) must be stored on the disk. Under such conditions, GHF provides a possible way to enhance servo performance without requiring more PES data. In this paper, we investigate its possibility, comparing the results with other conventional control design results, including continuous/discrete-time and single/multirate control. Our results show that this controller has better performance due to the nature of the control input of the GHF. Index Terms—Generalized hold function (GHF), control, hard disk drives (HDDs), multirate, positioning. I. INTRODUCTION M ANY algorithms have been proposed so far for head-po- sitioning control of hard disk drives (HDDs) in order to meet the tracking requirements that are necessary to achieve their ever-increasing track density requirements. Utilization of the control design method is one possible way of enhancing the performance and robustness of HDD servo systems. This is because it can explicitly specify closed-loop specifications and systematically treat the tradeoff between control perfor- mance and robust stability. An early attempt can be found in [1], which was based on a simple continuous-time mixed-sensitivity problem. Since then, much research has focused on the con- trol design framework. However, it basically assumes zero-order hold function (ZOH). In a continuous-time design, there is no way besides discretizing the resulting continuous-time con- troller at the sampling frequency. The effect of the jump in the measurement cannot be considered in this way, which induces a small step response at every sampling time. In a discrete-time design, although this effect can be dealt with, there is no way to handle the intersample behavior. Sampled-data de- sign [2] provides a possible way to handle both of these effects, and some researchers [3] have been trying to take advantage of this feature for HDDs. However, it still assumes ZOH. Thus, this Manuscript received January 3, 2003; revised January 27, 2004. K. Ohno is with the Autonomous System Laboratory, Fujitsu Laboratories, Ltd., Kanagawa 243-0197, Japan (e-mail: keitaro.ohno@nifty.com). M. Hirata is with the Department of Electrical and Electronic Engineering, Utsunomiya University, Tochigi 321-1717, Japan (e-mail: hirata@cc.ut- sunomiya-u.ac.jp). R. Horowitz is with Department of Mechanical Engineering, Univer- sity of California, Berkeley, CA 94720-1740 USA (e-mail: horowitz@ me.berkeley.edu). Digital Object Identifier 10.1109/TMECH.2004.842244 raises the issue of whether we can obtain better performance by introducing other types of hold functions. In industry, the so-called multirate technique has been suc- cessfully developed and widely used. The basic idea is to introduce faster ZOH than sampling frequency. By using a higher control input update frequency, we can get wider con- trol bandwidth. Multirate control itself was developed in the late 1950s, and an early application attempt to HDDs can be found in [4]. It proposed a way to design a multirate state esti- mator that is driven several times faster than the measurement sampling rate and yields open-loop estimation of intersample state so that the resulting control input becomes smoother. Hara and Tomizuka [5] extended their idea in order to achieve better estimation. Furthermore, recently, much effort has con- centrated on the development of multirate control techniques based on the control design framework, which include the discrete-time lifting technique-based [6] multirate control [9], the zero-interpolator-based multirate control [10], sam- pled-data multirate control [7] for the dual-stage actuated HDDs [8], and frequency dividing technique-based multirate control [11]. However, all the above design methods still assumed a ZOH as the hold function. In this paper, we investigate the possibility of obtaining better performance by introducing a generalized hold function (GHF) in control proposed by [12], which never assumes a ZOH. The basic idea of GHF is to generate control through a hold function that is optimized based on the dynamics of the con- trolled plant, while the output is sampled periodically. Thus, the GHF can yield continuous-time control input which jumps at the measurement sampling instant. This controller is derived so as to satisfy a given performance requirement, which is de- fined in terms of the continuous-time domain. Thus, intersample behavior can be taken into consideration in a similar manner as in the sampled-data control problem. We first elaborate on how to obtain the controller. Then, a design example will be demonstrated in such a way that we can compare our results with those obtained by several other methods, including the continuous/discrete-time single/multi- rate controllers. II. CONTROLLER WITH GENERALIZED HOLD FUNCTION In this paper, we consider the linear system of the form (1) 1083-4435/$20.00 © 2005 IEEE