108 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 1, FEBRUARY 2003 A Gradient-Based Track-Following Controller Optimization for Hard Disk Drive Qi Hao, Ruifeng Chen, Guoxiao Guo, Member, IEEE, Shixin Chen, Member, IEEE, and Teck Seng Low, Senior Member, IEEE Abstract—This paper presents a gradient-based parameter op- timization method to find the optimal compensator that minimizes the standard deviation of the position error signal (PES) in a hard disk drive servo system. By using the plant response data and the PES gradient information based on the nominal plant model, optimal digital controllers that minimized the of a plant with uncertainty were selected within a pre-found robust stable region. As a result, an optimal track-following controller that minimized the standard deviation of the measured PES was able to be obtained without the prior knowledge of the disturbance and noise model. Furthermore, we proved that if the measurement noise is white, an optimal controller that min- imizes the also minimizes the . Both simulation and implementation results suggest that such a gradient-based search process is faster than nongradient optimization methods such as Random Neighborhood Search and genetic algorithms. Index Terms—Gradient method, hard disk drive (HDD) servo, optimization, track mis-registration (TMR). I. INTRODUCTION I MPROVING the servo system performance for lower track mis-registration (TMR) is one of the prerequisites of moving to higher recording density in hard disk drives (HDDs). To cope with the challenge of the actuator pivot nonlinearity, high-frequency uncertainty, the effects of various external disturbances and noises, many efforts on the spindle motor, air flow, and arm/suspension designs have been made to reduce disturbance level and increase the actuator resonance frequency [1]. In addition, the improved servo control designs, such as proportional–integral–derivative (PID), LQG/LTR [2], [3], multirate control [4], [5], disturbance observer [6], and mode-switching control [7] also have been studied extensively as a cost-effective way toward higher track density. However, due to the limitation of the accuracy and uncertainty of the plant and disturbance models, system sampling frequency, controller order, stable margin requirements, and plant input saturation, the real servo system could not increase its bandwidth to an arbitrarily high value and achieve the best disturbance rejection. Manuscript received March 19, 2001; revised May 6, 2002. Abstract pub- lished on the Internet November 20, 2002. The Data Storage Institute is a na- tional research institution funded by the Agency for Science, Technology and Research (A Star), Singapore, and affiliated with the National University of Singapore. Q. Hao, G. Guo, S. Chen, and T. S. Low are with the Data Storage Institute, National University of Singapore, Singapore 117608 (e-mail: guoxiao_guo@ieee.org). R. Chen is with Hydrogenics Corporation, Mississauga, ON L5R 1B8, Canada. Digital Object Identifier 10.1109/TIE.2002.807254 On the other hand, with the development of modern optimiza- tion theory, more and more control problems are solved by ap- plying optimization methods, in which certain control law struc- ture and dynamic order are prescribed and the parameters of control law are optimized considering both performance and ro- bustness of the system. In a practical sense, HDDs are mass pro- duced and, as such, the exact parameters of their servo systems are unknown in advance. Due to the rapid development of dig- ital signal processors, to remain cost effective while being per- formance competitive, various numerical optimization methods have been studied recently to get a fine-tuned controller for each drive rather than using a generic one which is likely to be con- servative [8]–[11]. Among those optimization methods, Random Neighborhood Search (RNS) [12], genetic algorithms (GAs) [13], [14], arti- ficial neural networks (ANN’s) [15] and some other random optimization methods incorporated with statistical techniques [13], [16] have been employed for their well-known robust- ness property to the error of objective function and ability of global search. Furthermore, Simplex method [4], and Sequen- tial Quadratic Programming (SQP) [17] were also used to find the optimal controller within a convex subregion of performance surface. However, all of them as well as other nongradient-ori- ented methods suffer from the disadvantage of huge time con- sumption. Therefore, it is appealing to incorporate some gra- dient information based on nominal model into the optimization algorithm to accelerate the search process [10], provided that the performance surface is convex within the allowable controller parameters region. Given the bound of plant uncertainty, there are several ways to determine the bounds of admissible set of controller parameters. For example, Guo et al. [19] employed Algebraic Riccati Equations (AREs) to check the robust stability of an observer-based state feedback controller. Ding et al. [20] pro- posed to check the structured singular value of corresponding interconnection functions for an output feedback controller ac- cording to theory. In [8] and [9], a series of linear inequalities and an ANN were used, respectively, to represent the robust stable region bounds based on phase margin, bandwidth, and gain margin requirements. Since the computation involved is quite complicated, such work has to be done offline. In this paper, we also employ several linear inequalities to represent the robust stable region bounds to satisfy 30 phase margin and 6-dB gain margin requirements as well as 1.5-kHz bandwidth limits. Since the major contributor of the TMR during track fol- lowing mode is the 3-standard deviation of the true 0278-0046/03$17.00 © 2003 IEEE