Improvement of HDD Tracking Performance using Nonlinear Compensation and RPT Control

Improvement of HDD Tracking Performance using Nonlinear Compensation and RPT Control Guoyang Cheng Kemao Peng Ben M. Chen Tong H. Lee Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576 email:(engp1496, elepkm, bmchen, eleleeth)@nus.edu.sg Abstract Pivot bearing friction and flex cable nonlinearity are the two major torque nonlinearities which lead to performance degradation in hard disk drive (HDD) servo systems. Based on a comprehensive model of typical voice-coil-motor (VCM) actuator, which explicitly captures the characteristics of pivot bearing friction and flex cable nonlinearity, this paper presents a design of a parameterized controller for HDD servo systems using the Robust and Perfect Tracking (RPT) technique combined with nonlinear torque compensation and integral enhancement. Simulation and experimental results show that the controller can achieve fast settling time and eliminate static errors in HDD track following task. Keywords: Hard disk drive, Servo systems, Nonlinearity, Robust and Perfect Tracking, Track following. 1 Introduction Current trend of the Hard Disk Drive (HDD) industry is towards smaller disk drives with higher capacity, for increasing applications in consumer electronics, which means higher track density. Track density is measured by TPI (Track Per Inch), and its reciprocal is the socalled track pitch. To ensure reliable data reading and writing, it is required that during track following stage, the deviation of R/W head from target track center, or the so-called Track Mis-Registration (TMR), should not exceed 5% of track pitch, that s about.25µm for a 5KTPI HDD. This is one of the objectives in HDDs servo design. To this end, various control techniques have been proposed, ranging from conventional PD/PID controller, Lead-lag compensators, notch filters, and Disturbance Observer (DOB) [1], to more advanced control techniques, such as Adaptive control [11], Linear Quadratic Gaussian (LQG) and/or LTR (loop transfer recovery) approach [1], H 2 and H control [6], Robust and Perfect Tracking (RPT) [4], Mode Switch Control (MSC) [9], Composite Nonlinear Feedback (CNF) control [2, 3], and etc. Although these control techniques have significantly improved the performance of HDD servo systems, more challenges still lie ahead as the new generation HDDs impose a more stringent TMR budget for track following. It is known that torque disturbances play an adverse role in HDDs track following task. The so-called torque disturbances, which include bias torque due to flex cable, pivot bearing friction and hysteresis, as well as other unmodeled dynamics, have conventionally been treated as a lumped disturbance or even ignored when a servo controller is being designed. This may be acceptable in those old HDDs with low track density. However, when we are working with high TPI HDDs, where the TMR budget is at the scale of nanometer, the adverse effects induced by torque disturbances become conspicuous, and performance degradation will occur. To solve this problem, torque disturbances, especially those dominant contributing factors, should be sufficiently modeled and identified at the modeling stage, and integrated into the controller design; For those residual and unmodelled disturbances, an appropriate controller design methodology should be used to minimize their effects on closed-loop performance. This is the basic idea of this paper. This paper is organized as follows. In Section 2, we present a comprehensive model for a micro hard disk drive, which explicitly captures the characteristics of flex cable nonlinearity and pivot bearing friction. Next, in Section 3, we apply the Robust and Perfect Tracking methodology combined with integral and nonlinear torque compensation to design a tracking controller for HDDs based on the presented model. Simulation and experimental results are given in Section 4. Finally, we draw some concluding remarks in Section 5. 2 Model of a Micro Hard Disk Drive Presently, HDD servo systems use a VCM motor to actuate the read/write (R/W) recording arm assembly(see Figure 1). The VCM motor is a typical DC motor that translates an input current into a force or acceleration. Its frequency domain response without considering friction and nonlinearities matches very well to

that of a double integrator at low medium frequency range, typically from DC to somewhere around 1.5 khz, and has many high frequency resonance modes. The double integrator model has been used for HDDs servo design for quite some time and it seems to work well so far. However, this approximate model is not good enough for capturing the dynamic characteristics of the new generation of hard disk drives with more noticeable nonlinear and frictional behavior. Some attempts have been made to model and compensate such nonlinearities in the VCM actuator, see e.g., [5, 12]. In [8], the so-called physical effect approach was utilized to determine the structures of nonlinearities and friction associated with the VCM actuator in a typical HDD servo system. Then, a Monte Carlo process was employed to identify parameters in the structured model. These procedures resulted in a comprehensive HDD actuator model which explicitly incorporates the nonlinear effects of the flex cable and the pivot bearing friction. This model (omitting high frequency resonant modes) is given as follows: ÿ = b(u T c ) T f, T n, ẏ, T f = T e, ẏ =and T e T s, T s sgn( T e ), ẏ =and T e > T s, T n = ( d1 buy + d 2 ẏ 2 ) + d3 sgn(ẏ)+d ẏ, T e = b[u T c (y)], T s = d 4 b u y + d 5, T c = a arctan (cy), (1) where u and y are respectively the control input voltage (in volts) and the displacement (in micrometers) of the R/W head; Tf is the friction torque and T s is the break-away friction torque with u and y being respectively the corresponding input voltage and the displacement for the case when ẏ =; Tc is the bias torque induced by the flex cable, which is dependent on the position/displacement of the R/W head and can be measured as the offset torque needed to maintain the R/W head at the corresponding position, i.e., the control input voltage when ẏ =andÿ =. Experiments show that T c can be matched pretty well by an arctan function of y (see Figure 2). An IBM microdrive (model DMDM-134) was used in the experimental test and its associated parameters have been identified as follows: b =2.35 1 8, a =.2887, c =.5886, d = 282.6, d 1 =.5, d 2 =.1, (2) d 3 =1.5 1 4, d 4 =.55, d 5 =1.65 1 4. Verification procedure has been carried out to confirm that the identified model characterizes very well the behavior of the actual system. For example, figure 3 and 4 show the frequency response of the actual system and that of the identified model have a close match. Figure 1: A typical HDD with a VCM actuator. Functional value (volts).3.2.1.1.2.3 Solid line: experimental Dashed line: matched 1 8 6 4 2 2 4 6 8 Displacement (micrometers) Figure 2: Nonlinear torque induced by the data flex cable. Phase (degs) Magnitude (db) 5 4 3 2 1 Solid line: experimental Dashed line: identified 1 1 1 1 2 5 5 1 15 2 25 1 1 1 1 2 Figure 3: Frequency responses of the VCM actuator (low frequencies). Magnitude (db) Phase (Deg) 4 2 2 4 6 2 3 4 5 6 7 8 9 Solid line: experimental Dashed line: identified 1 3 1 4 1 3 1 4 Figure 4: Frequency responses of the VCM actuator (high frequencies).

3 Design of an HDD Servo Controller The so-called Robust and Perfect Tracking (RPT) technique was proposed in [7] and has been successfully used in HDD servo design [4]. This technique enables control engineers todesignaverylow-order controller which still results in a closed-loop system with fast tracking speed and low overshoot as well as strong robustness. RPT considers a general linear system with external disturbances described by ẋ = Ax + Bu + Ew, Σ: y = C 1 x + D 1 w, (3) h = C 2 x + D 2 u where x, u, w, y, h are respectively the state vector, the control input, the external disturbances, the measurement output and the output to be controlled. The core of RPT is to design a parameterized controller of the following form: { ẋv = A Σ v () : v ()x v + B y ()y + B r ()r, (4) u = C v ()x v + D y ()y + D r ()r such that 1. The resulting closed-loop system is internally stable for all (, ], where is a positive scalar. 2. The controlled output h is capable of tracking the reference r with arbitrary fast settling time in faces of external disturbances and initial conditions, i.e., e p = h r p,as. The above RPT problem is solvable if and only if the following conditions are satisfied: 1. (A, B) is stabilizable and (A, C 1 ) is detectable; 2. (A, B, C 2,D 2 ) is minimum phase and right invertible; 3. Ker(C 2 ) C 1 1 {Im(D 1)} {v C 1 v Im(D 1 )}. In what follows, we are going to design an HDD tracking controller using the above mentioned RPT technique with some enhancements. To do this, we first need to recast the HDD servo problem into RPT framework. It is noted that the identified HDD model of (1) actually represents a second order system with nonlinear input disturbance. Experimental observation shows that flex cable nonlinearity is more influential than pivot bearing friction. As a natural practice and the first step of controller design, we compensate the term of flex cable nonlinearity which is already identified in clear form. Next, since the model of friction is somewhat messy, we choose to tick out the viscous friction component (the linear part) and incorporate it into the second order model while treating residual components (including other un-modeled torque disturbances) as an unknown lumped disturbance d i.to be specific, we introduce ū = u α arctan (βy) (5) where α and β are tuning parameters, then the HDD model is recast as ÿ = a 1 ẏ + a y + b(ū + d i ) (6) where a,a 1 are parameters introduced to cover general second order systems. We define the following state variables x 1 = y, x 2 =ẏ, x 3 = (y r)dt (7) where r is the reference input, or the desired position/track of the R/W head. Next, we define the controlled output as h = x 1 + λx 3 (8) where λ> is a weighting factor. Now the system can be formulated into the following RPT form: ẋ = Ax + Bū + Ew, Σ: ŷ = C 1 x + D 1 w, (9) h = C 2 x + D 2 ū with A = 1 a a 1,B = b,e = b, 1 1 [ ] [ ] 1 C 1 =, D 1 1 =, C 2 =[1 λ ], D 2 =[]. (1) and x =[x 1 x 2 x 3 ],w =[d i r ], ŷ =[x 1 x 3 ]. It can be verified that the solvability conditions of the above RPT problem are satisfied, hence the RPT methodology can be applied here. Note that in HDD servo systems, the dominant task is set point tracking, i.e., to move the R/W head to a desired track, which corresponds to a step reference input characterized by ṙ(t) =r δ(t). (11) Following the design procedure of RPT controller in [7], a reduced order measurement feedback controller can be obtained as { ẋv = A Σ v () : v ()x v + B y ()ŷ + B r ()r, (12) ū = C v ()x v + D y ()ŷ + D r ()r

with A v () = (a 1 + λ + L + 2ζω ), B y () = [(a 1 + λ + L)(a 1 + L + 2ζω ) 2, ω 2 λ 2 ], B r () = 2ζωλ 2, C v () = 1 b (a 1 + λ + 2ζω ), D y () = 1 b [a +(a 1 + λ)(a 1 + L) 2 +(a 1 + λ + L) 2ζω, ω 2 λ 2 ], D r () = 1 b (ω2 2 + 2ζωλ ). (13) where is the time scale factor which can serve as a tuning parameter; ζ and ω are respectively the damping ratio and natural frequency of the supposedly dominant closed-loop conjugate poles; L>isaparameter, which corresponds to the observer pole at L. Next, we will combine the above linear controller which is of first order with the augmented integral term x 3 and nonlinear compensation term to result in a second order hybrid controller. [ ] xv Define x c =, and combining (5) and (12), we x 3 arrive at the following final controller: [ ] y ẋ c = A c ()x c + B c (), [ r] Σ c () : y (14) u = C c ()x c + D c () r +α arctan (βy) with [ (a1 + λ + L + A c () = 2ζω ) ] ω2 λ 2, [ ] 2ζωλ Bc11 B c () = 2, 1 1 C c () = 1 [ a1 + λ + 2ζω b, ] ω 2 λ, 2 D c () = 1 [ ] Dc11, b ω2 2ζωλ 2, (15) B c11 = [(a 1 + λ + L)(a 1 + L + 2ζω )+ω2 2 ], D c11 = a +(a 1 + λ)(a 1 + L) 2 +(a 1 + λ + L) 2ζω. Remark 1: Controller Σ c () of (14) is a RPT controller combined with integral and nonlinear compensation, as shown in Figure 5, hence will be referred to as hybrid RPT controller (or HRPT, in short) hereinafter. Note that Σ c () is a closed form controller parameterized by, ζ, ω, λ, L, α and β. These parameters Disturbances + u y + HDD + + α arctan(β ) ū RP T Figure 5: Block diagram of the HDD servo system. can be tuned online to improve control performance. As, perfect tracking can be achieved. However, toosmallavalueof may not be feasible in real implementation, due to physical limitation, such as actuator saturation, flexible modes, and etc. Remark 2: With controller Σ c () in the closed-loop, the transfer function from reference r (the desired track) to output displacement y of R/W head is calculated as: ω(ω +2ζωλ) H yr (s) = 2 (s + L)(s + ωλ (16) (s + L)(s 2 + 2ζωs ω+2ζλ ) 2 )(s + λ) First, we notice there is a zero/pole cancellation at L; Next, there are three poles at λ, ζω ± j ω 1 ζ 2 respectively and one zero at ωλ ω+2ζλ ; As ω, ωλ ω+2ζλ λ, there will be a zero/pole cancellation at λ, and the closed loop system will behave like a second order system. Finally, it is easy to see, the static gain, H yr () = 1, which means zero steady-state error for set point tracking. 4 Simulation and Experimental Results Simulations and experiments were carried out to evaluate the performance of the above designed controller in HDD track following task. For experiments we used an open microdrive (IBM model DMDM-134), which is the same one as in the modeling stage in Section 2. In the experiments, the only measurable output is the relative displacement of the R/W head which is measured by a Laser Doppler Vibrometer (LDV). Control algorithm is implemented on a dspace DSP board installed in a personal computer. The sampling rate is 1kHz. For this specific microdrive with track density of 35KTPI, its track pitch is around.7µm, hence the so-called TMR budget, which is defined as 5% of track pitch, is about.35µm. A desirable controller is expected to bring the R/W head into the.35µm neighborhood of the target track as soon as possible. r

Since Σ c () is a parameterized controller, we can easily tune its parameters (, ζ, ω, λ, L, α, β) online to achieve satisfactory results. For this microdrive, we have b =2.35 1 8,a =,a 1 = 282.6 By online tuning, we found the following parameters which lead to a good controller: =1,ζ =.75,ω= 12π, λ = 4, L = 6,α=.2,β =.5886 The resulting controller is [ ] 1.1772 1 4 5.6849 1 ẋ c = 9 x c [ ][ ] 8.3781 1 7 1.6474 1 + 7 y, 1 1 r u =[ 2.4563 1 5 (17) [ 24.191 ] ] x c y +[.215.71 ] r +.2 arctan (.5886y) The above controller can achieve a settling time of.68ms and.75ms respectively for.5µm and 1µm tracking following in simulation (see Figure 6 and 7); While in experiments, the corresponding settling time are.8ms and.9ms respectively (see Figure 8 and 9). Here settling time is defined as the time it takes for the R/W head to enter and remain in the.35µm neighborhood of the target track center. It is observed that the nonlinear compensation term α arctan (βy) plays an important role in fast settling. Without this term in the controller, the settling process will be a lot more sluggish. Although in that case we may use a larger value of the integral weighting factor λ to facilitate settling, it is still hard to approach the same performance as achieved with nonlinear compensation. It should be pointed out that the parameters of nonlinear compensationtermneednotbeexactlythesamevalues of the identified model, since the un-cancelled nonlinearity can be handled by the robustness of the HRPT controller; and interestingly enough, slightly smaller parameters (which mean under-compensation) seem to lead to better performance than over-compensation. For comparison, we also design a conventional RPT controller, which does not include integral enhancement and nonlinear compensation. Note that VCM actuator has long been assumed to observe a double integral model as ÿ = bu, hence a pure RPT controller is proposed as follows: { ẋv = (L + 2ζω )x v (L 2 + 2ζωL )y 2 r, 2 u = 1 b [ 2ζω x v +( 2ζωL )y ω2 2 r] 2 Obviously, the above controller places closed-loop poles at L and ζω ± j ω 1 ζ2. By online tuning, we found the above RPT controller seems to work best with the following parameters : =1,ζ=.4, ω= 2π, L = 6 Control input in Volts.7.6.5.4.3.2.1.1.8.6.4.2.2.5 1 1.5 2 2.5 3 3.5 4 : :.4.5 1 1.5 2 2.5 3 3.5 4 Figure 6: Simulation result:.5µm track following. Control input in Volts 1.4 1.2 1.8.6.4.2.2.15.1.5.5 1 1.5 2 2.5 3 3.5 4 : :.5.5 1 1.5 2 2.5 3 3.5 4 Figure 7: Simulation result: 1µm track following. The performance discrepancy between the RPT controller and the HRPT controller for.5µm and 1µm tracking following are shown in Figure 6 and 7 for simulation, Figure 8 and 9 for implementation respectively. It is easy to see that in both simulation and experiments, the conventional RPT controller is not able to bring the R/W head into the.35µm neighborhood of the target track center, i.e., there is a significant bias at the steady-state output. Although we may try to reduce such bias by using a larger ω or smaller ζ and, which means higher closed-loop bandwidth, it is likely to activate the resonance modes. The reasons behind such performance discrepancy between these two controllers, are analyzed as follows: First, as mentioned before, there is a nonlinear compensation term in the HRPT controller, which directly cancels the flex cable nonlinearity and hence speeds the motion of the R/W head; Second, the integral enhancement of the HRPT controller serves as inner mode control for constant disturbance, which helps remove steady-state error at the output displacement y; Third, the conventional RPT controller resorts to larger feedback gains to compensate nonlinear disturbance, which is likely to trigger limit cycle.

Control input in Volts.7.6.5.4.3.2.1.8.6.4.2.2.5 1 1.5 2 2.5 3 3.5 4 4.5 5.4.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Figure 8: Experimental result:.5µm track following. Control input in Volts 1.4 1.2 1.8.6.4.2.25.2.15.1.5.5.5 1 1.5 2 2.5 3 3.5 4 4.5 5.1.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Figure 9: Experimental result: 1µm track following. 5 Concluding Remarks In this paper we design an HDD servo controller using the Robust and Perfect Tracking methodology enhanced with integral and nonlinear compensation, based on a comprehensive VCM actuator model which explicitly identifies the characteristics of pivot bearing friction and flex cable nonlinearity for a micro disk drive. Simulation and experiments show that this hybrid RPT controller can achieve fast settling and eliminate static bias in HDD track following tasks, which is a significant improvement over a pure RPT controller. Further researches are now under way to adapt this controller to track seeking tasks. linear systems with input saturation: Theory and an application, IEEE Transactions on Automatic Control, Vol. 48, No. 3, pp. 427-439, 23. [4]T.B.Goh,Z.Li,B.M.Chen,T.H.LeeandT. Huang, Design and implementation of a hard disk drive servo system using robust and perfect tracking approach, IEEE Transactions on Control Systems Technology, Vol. 9, No. 2, pp. 221-233, 21. [5] J. Q. Gong, L. Guo, H. S. Lee and B. Yao, Modeling and cancellation of pivot nonlinearity in hard disk drives, IEEE Transactions on Magnetics, Vol. 38, pp. 356-3565, 22. [6] Z. Li, G. Guo, B. M. Chen and T. H. Lee, Optimal control design to achieve highest track-per-inch in hard disk drives, Journal of Information Storage and Processing Systems, vol. 3, no. 1-2, pp. 27-41, 21. [7] K. Liu, B. M. Chen and Z. Lin, On the problem of robust and perfect tracking for linear systems with external disturbances, International Journal of Control, Vol. 74, No. 2, pp. 158-174, 21. [8] K. Peng, G. Cheng, B. M. Chen and T. H. Lee, Comprehensive modeling of friction in a hard disk drive actuator, Proceedings of the 23 American Control Conference, Denver, USA, pp. 138-1385, 23. [9] V. Venkataramanan, B. M. Chen, T. H. Lee and G. Guo, A new approach to the design of mode switching control in hard disk drive servo systems, Control Engineering Practice, vol. 1, no. 9, pp. 925-939, 22 [1] M. White, M. Tomizuka and C. Smith, Improved Track Following in Magnetic Disk Drives Using a Disturbance Observer, IEEE/ASME Transactions on Mechatronics, Vol. 5, pp. 3-11, 2. [11] D. Wu, G. Guo, and T. C. Chong, Adaptive Compensation of Microactuator Resonance in Hard Disk Drives, IEEE Transactions on Magnetics, vol. 36, pp. 2247-225, 2 [12] T. Yan and R. Lin, Experimental modeling and compensation of pivot nonlinearity in hard disk drives, IEEE Transactions on Magnetics, Vol. 39, pp. 164-169, 23. References [1] J. K. Chang, and H. T. Ho, LQG/LTR frequency loop shaping to improve TMR budget, IEEE Transactions on Magnetics, vol. 35, pp. 228-2282, 1999. [2] B. M. Chen, T. H. Lee and V. Venkataramanan, Hard Disk Drive Servo Systems, Springer-Verlag, New York, London, 22. [3] B. M. Chen, T. H. Lee, K. Peng and V. Venkataramanan, Composite nonlinear feedback control for