A Minimum Parameter Adaptive Approach for Rejecting Multiple Narrow-Band Disturbances with Application to Hard Disk Drives Xu Chen, Student Member, IEEE, and Masayoshi Tomizuka, Fellow, IEEE Abstract—Many servo systems are subjected to narrow- band disturbances that generate vibrations at multiple fre- quencies. One example is the track-following control in a hard disk drive (HDD) system, where the airflow-excited disk and actuator vibrations introduce strong and uncertain spectral peaks to the position error signal. Such narrow- band vibrations differ in each product and can appear at frequencies above the bandwidth of the control system. This paper presents a control scheme that adaptively enhances the servo performance at multiple unknown frequencies, while maintaining the baseline servo loop shape. A minimum pa- rameter model of the disturbance is first introduced, followed by the construction of a novel adaptive multiple narrow-band disturbance observer for selective disturbance cancellation. Evaluation of the proposed algorithm is performed on a simulated HDD benchmark problem. Index Terms—adaptive control, loop shaping, multiple narrow-band disturbances, disks drives I. Introduction In a modern hard disk drive (HDD), data/information is stored in circular patterns of magnetization known as data tracks or simply, tracks. During reading and writing of the data, the disk spins and the read/write head is controlled to follow the circular tracks. This creates the track-following problem, where the servo system per- forms regulation control to position the read/write head at the desired track, with as low variance as possible. This process is evaluated by the so-called Track Mis- Registration (TMR), which is three times the standard deviation of the position error signal (PES). One important source of TMR is the vibration/flutter of disks and actuators. This motion is caused by the turbulent air flow within the hard disk assembly or imperfections in the spindle bearing, and results in non-repeatable narrow-band disturbances [1]–[3], whose energy is highly concentrated at multiple unknown fre- quencies. Due to different operation environments and structures of HDDs, these disturbances differ from track to track and disk to disk. Moreover, frequencies of the narrow-band components can be higher than the Manuscript received Jan 13, 2011; revised Aug 17, 2011; accepted Oct 26, 2011. This work was supported by the Computer Mechanics Laboratory (CML) in the Department of Mechanical Engineering, University of California, Berkeley. X. Chen and M. Tomizuka are with the Department of Mechanical Engineering, University of California, Berkeley, CA 94720 USA, e- mails: {maxchen, tomizuka}@me.berkeley.edu bandwidth of the existing servo loop [1], [2]. The above characteristics of such disturbances lead to the difficulty of rejecting them using traditional loop-shaping meth- ods. Similar problems occur in many other systems, such as active suspensions [4], air-forced cooling systems [5], and acoustic systems [6]. Various control algorithms have been developed for narrow-band disturbance rejection. Adaptive Noise Can- cellation (ANC) [7] is a very popular feedforward com- pensation scheme that has been used to reject not only narrow-band vibrations but also wide-band noises. It applies a correlated version of the disturbance (usually measured by additional sensors) to adaptively tune (in general) a Finite Impulse Response (FIR) filter, using Least Mean Squares (LMS) based adaptation algorithms. ANC can be quite effective, and its design principle is simple to realize. Its relative drawbacks are the computa- tion load to adapt a high order FIR filter, the often slow convergence rate to maintain stability, approximations in the LMS convergence proof, and finally the increased cost for sensors, whose precision and bandwidth also greatly determine the compensation quality. Many more algorithms have been developed in the feedback control category, including: (i) Repetitive Con- trol (RC) and its adaptive versions [8], [9]. (ii) State space design using the Internal Model Principle (IMP) [10], [11]. (iii) Youla Parameterization with an adaptive FIR Q filter [4], [6], [12], [13]. (iv) Adaptive Feedforward Can- cellation (AFC) with a Phase-Locked Loop (PLL) [14]. (v) Peak filters [15], [16] and the disturbance observer (DOB) [17], [18]. Among the above algorithms, RC integrates an internal model 1/(1 − z −N ) to the closed-loop system, and compensates disturbances at integer multiplications of a base frequency. Internal models for sinusoidal signals, in the forms of differential/difference equations and direct transfer functions, are used in groups (ii) and (iii) to adaptively shape the loop. These IMP based approaches in general do not preserve a baseline loop shape and may change much of the closed-loop dynamics at other fre- quencies. With the magnitude and the phase responses of the plant (at the disturbance frequencies), AFC with PLL locally performs frequency estimation and disturbance cancellation. Algorithms in [15], [16] selectively increase the loop gain via add-on peak filters, whose coefficients are tuned as functions of the disturbance frequencies. Finally in [17], [18], disturbances are selectively observed