Microsystem Technologies 9 (2002) 92–98 Springer-Verlag 2002 DOI 10.1007/s00542-002-0206-6
Tuning of a digital disk drive servo controller using fixed-structure H¥ controller optimization W. Niu, S. Ibaraki, M. Tomizuka
92 The head positioning control for an HDD has attracted considerable attention in the literature. In particular, optimal control techniques are useful tools to obtain the optimal control performance with no extra cost to introduce an additional actuator or sensor. For example, Hirata et al. [1] and Steinbuch and Norg [2] presented applications of the standard full-order H1 controller synthesis, and Hernandez et al. [3] applied the l-synthesis to this problem. In the H1 and l-synthesis approaches, the order of the designed controller tends to be high, Keywords Control and optimization, Disk drive servo, H1 which is always a major issue. Furthermore, it is often control, Fixed-structure controller optimization, Digital undesirable to implement a new controller structure due to control time and cost limitations. This paper presents a tuning method for a linear digital feedback controller based on 1 fixed-structure H1 controller optimization. The experiIntroduction mental case study illustrates the effectiveness of the proThe areal density of hard disk drives (HDDs) has been posed method to improve the performance of the original increasing at nearly 100% per year and the price per controller, which may have been finely tuned by an exmegabyte is dropping at by approximately 50% per year. perienced servo engineer. The head positioning servo system is one of critical The remainder of this paper is organized as follows. components of HDD for increasing the storage capacity. Section 2 describes the mathematical model of VCM Recently, a lot of efforts have been devoted to dual-stage actuator dynamics used in the optimization. Section 3 actuator designs. With this technique, the servo bandwidth provides an outline of the optimization scheme. The of HDD can be as large as 2 kHz comparing to 600–900 Hz simulation and experimental results on a prototype HDD for a typical bandwidth under single-stage actuation with a setup are given in Sect. 4. Conclusions are given in Sect. 5. voice coil motor (VCM). However, the dual-stage actuator technique is not yet mature for mass production, and, it’s 2 cost is still high. Therefore, it is a challenge to tune a Plant model and controller structure controller for a VCM actuator such that it achieves the Figure 1 shows a schematic view of a HDD setup. A optimal performance to meet the demand for higher areal simplified block diagram of the control feedback loop is densities. shown in Fig. 2. In the block labeled ‘‘actuator,’’ the power Abstract To address the problem of improving the positioning accuracy of the read write head of hard disk drives (HDDs), we present a tuning methodology for the HDD servo controller based on the fixed-structure H1 controller optimization. Since optimization is carried out under the fixed controller structure without any additional sensor, no extra cost is introduced. The effectiveness of the proposed method is demonstrated by simulation and experimentation.
Received: 13 September 2001/Accepted: 20 February 2002
W. Niu (&) Advanced Servo Technology, Storage Technology Division, IBM, 5600 Cottle Road, 0KB/28-2, San Jose, CA 95193, USA e-mail:
[email protected] S. Ibaraki Department of Precision Engineering, Kyoto University, Kyoto, Japan M. Tomizuka Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720, USA
amplifier and actuator are presented by the discrete-time transfer function PðzÞ. It is assumed that the power-amplifier is ideal and the actuator is perfectly rigid without any friction or mechanical resonances. In other words, the plant dynamics PðzÞ is approximated by a double-integrator model and is represented by the following discretetime state equations:
xp ðkÞ ¼ Wp xp ðk 1Þ þ Cp uðk 1Þ yðk 1Þ ¼ hp xp ðk 1Þ
ð1Þ
where uðkÞ 2 R and yðkÞ 2 R denote the control input to the VCM actuator and the measured position error signal (PES), respectively, and xp ðkÞ 2 R2 is the state vector, consisting of the position and velocity of VCM actuator as state variables. The matrices in Eq. (1) are given by
1 Ts ; Wp ¼ 0 1
Ts2 =2 Cp ¼ ; Ts
hp ¼ ½ 1 0
ð2Þ
conventional controller setting, denoted by Cold ðzÞ, has the following state feedback and estimator gain matrices:
Kold ¼ 6:52 102 4:35 101 ; 3 2 9:10 101 7 6 Lold ¼ 4 1:65 104 5 2:83 102
ð4Þ
3 Controller tuning by fixed-structure H¥ controller optimization
93
Fig. 1. Schematic view of a hard disk drive
Fig. 2. Simplified control loop diagram of the disk drive servo system
where Ts is the sampling time in second. The measured frequency response of the experimental VCM actuator is shown in Fig. 3. The block labeled ‘‘controller’’ in Fig. 2 represents the VCM controller. We have employed the well-known observer-based state feedback controller structure of the following state space representation [4].
xp ðkÞÞ x^p ðkÞ ¼ xp ðkÞ þ Lð yðkÞ h^ xp ðkÞ ¼ W^ xp ðk 1Þ þ Cuðk 1Þ uðkÞ ¼ ½ K where
W¼
Wp 01 2
ð3Þ
1 ^ xp ðkÞ Cp ; 1
C¼
Cp 0
and h ¼ hp
0
3.1 Controller tuning by using H¥ optimization In this section, we present a tuning method of the controller parameters ðK; LÞ in the controller (3). The controller design requirements are summarized as follows: (1) the open-loop cross-over frequency and gain/phase margins should be larger than the given certain levels to secure a sufficient bandwidth and the robustness of the closed-loop system, and (2) the gain of the closed-loop sensitivity transfer function should be as low as possible to achieve the desirable disturbance rejection performance. In particular, the gain at low frequencies should be reduced to reject external disturbances at low to middle frequencies. A too high peak gain around the cross-over frequency should be avoided not to induce vibrations. The objective is to re-tune the controller parameters ðK; LÞ to improve the control performance (with respect to the above design requirements) of the existing controller Cold ðzÞ. First, we interpret that the above design objectives are represented by the following H1 (sub-)optimization problem: TðzÞWu ðzÞ
