Hysteresis Compensation of Piezoelectric Actuators in Dual-Stage Hard Disk Drives

Transcription

1 Proceedings of 211 8th Asian Control Conference (ASCC) Kaohsiung, Taiwan, May 15-18, 211 TuB3.2 Hysteresis Compensation of Piezoelectric Actuators in Dual-Stage Hard Disk Drives Yan Zhi Tan 1, Chee Khiang Pang 2, Fan Hong 3, Sangchul Won 4, and Tong Heng Lee 2,5 Abstract In the magnetic disk drive industry, the demand for faster Hard Disk Drive (HDD) higher storage capacities had led to the use of a dual-stage servo system a piggyback microactuator. However, the microactuator is a piezoelectric device and hysteresis is an inherent characteristics of piezoelectric devices. Hysteresis behavior, reduces the accuracy of the actuator and thus limits the level of performance that can be achieved by the microactuator. In this paper, hysteresis compensation is included in the control of a Lead Zirconate Titanate (PZT) microactuator from the dual-stage actuation system of a commerical HDD. A Generalized Prandtl-Ishlinskii (GPI) model is used to model its hysteresis behavior and the inverse of the GPI model is used as the hysteresis compensator. The hysteresis compensator is included into a simple feedback control structure and the effect of the hysteresis compensator on the performance of the feedback control structure is demonstrated. Index Terms Hard Disk Drive (HDD), Dual-Stage, Lead Zirconate Titante (PZT), Microactuator, Hysteresis, Prandtl- Ishlinskii (PI). I. INTRODUCTION Hysteresis is a phenomenon that is encountered in many different areas of science [1]. For example, magnetic hysteresis hinders the accurate control of electromagnetic actuators [2] as well as magnetostrictive actuators [3], and mechanical hysteresis hinders the accurate control of mechanical parts such as the stiffness adjustable tendon which is commonly used in robot manipulators [4]. Hysteresis behavior is also present in piezoelectric materials that are used in piezoelectric actuators, which are increasingly being used in industries such as the semiconductor and precision-manufacturing industries due to the increasing demand for high precision and high performance devices. Examples of applications where piezoelectric actuators are used include microlithography systems [5], scanning probe microscope [6], and a more interesting example of an automated sperm injection system [7]. This work was supported in part by Singapore MOE AcRF Tier 1 Grant R Y. Z. Tan is National University of Singapore Graduate School for Integrative Sciences and Engineering (NGS), Centre for Life Sciences (CeLS), #5-1, 28, Medical Drive, Singapore , Singapore. yanzhi@nus.edu.sg 2 C. K. Pang and T. H. Lee are Department of Electrical and Computer Engineering, National University of Singapore, Singapore , Singapore. justinpang@nus.edu.sg, eleleeth@nus.edu.sg 3 F. Hong is Data Storage Institute, A*STAR, Singapore 11768, Singapore. HONG_Fan@dsi.a-star.edu.sg 3 S. Won is Department of Electronic and Electrical Engineering, POSTECH San 31 HyojaDong Pohang , Republic of Korea. won@postech.ac.kr 5 T. H. Lee is also National University of Singapore Graduate School for Integrative Sciences and Engineering (NGS), Centre for Life Sciences (CeLS), #5-1, 28, Medical Drive, Singapore , Singapore. In the magnetic disk drive industry, a current goal in the magnetic disk drive industry is to break the 1-Terrabit per square inch storage density barrier. With an increase in the track density, the track width is smaller and thus, the positioning accuracy of the read/write head has to be improved. To improve the positioning accuracy of the read/write head, a high bandwidth servo system is required and a dual-stage servo system that consists of the Voice Coil Motor (VCM) a piggyback microactuator is capable of expanding the servo bandwidth of the Hard Disk Drive (HDD). An example of a piggyback actuator used in the dual-stage servo system is the pushpull multi-layered Lead Zirconate Titanate (PZT) microactuator [8]. However, the PZT microactuator is a piezoelectric device and hysteresis is an inherent characteristic of piezoelectric devices. Hysteresis behavior reduces the accuracy of the microactuator and thus limits the level of performance that can be achieved by the microactuator. Hysteresis can be classified into dynamic and static hysteresis, of which static hysteresis is a non-linear phenomenon a characteristic known as rate independent memory effects [9]. Rate independent means that the hysteresis diagrams are stable respect to arbitrary changes of the time scale [1], and memory effects are demonstrated by the fact that the output signal of a system hysteresis depends on both the present value of the input signal as well as the past input values. In this paper, the term hysteresis shall refer to static hysteresis. The most widely used models for modeling the hysteresis behaviors can be classified into phenomenological based and physics based models. Examples of the phenomenological based models include the Presaich model [1] and the Prandtl- Ishlinskii (PI) model [1] while examples of the physics based models include the Duhem model [9] and the Bouc- Wen model [9]. Compared to the physics based models, the phenomenological based models allow a more precise modeling of the hysteresis behavior as they are created based on the collected input/output data for modeling of both the major and minor curves of the hysteresis behavior. The PI model is currently a popular model for modeling hysteresis behavior. It is a subset of the Preisach model and its main advantage over the Preisach model is that the PI model is less computationally demanding to implement and invert for feedforward control since an analytic inverse exists [11]. In this paper, hysteresis compensation is included in the control of a PZT microactuator from the dual-stage actuation system of a commerical HDD. A Generalized Prandtl- Ishlinskii (GPI) model is used to model its hysteresis behavior

2 and the inverse of the GPI model is used as the hysteresis compensator. The hysteresis compensator is included into a simple feedback control structure and the effect of the hysteresis compensator on the performance of the feedback control structure is demonstrated. The rest of the paper is organized as follows. Section II gives a short description of the classical PI model and introduces the GPI and inverse GPI model. Section III shows the use of the hysteresis compensator a feedback control scheme to compensate the hysteresis behavior in the PZT microactuator of a dual-stage servo system in a commercial 3.5 HDD so as to improve the positioning accuracy of the PZT microactuator. II. HYSTERESIS MODELING AND COMPENSATION This paper makes use of the PI model, which is an operator type model, for modeling hysteresis nonlinearity. Details about the PI model will be discussed in the subsections that follow. A. Classical Hysteresis Play Operator The use of the hysteresis play operator for modeling hysteresis nonlinearity is a direct mathematical approach out consideration for any underlying physical laws. The hysteresis play operator is continuous and rateindependent and is written as [1] w(t) =F r [v](t) for r. (1) For any piecewise monotone input function v :[,t E ] R, w(t) =F r [v](t) is given by w() = f r (v(), ), w(t) =f r (v(),w(t i )) (t i <t t i+1, i N 1), (2) f r (v, w) = max(v r, min(v + r, w)), (3) where = t < t 1 <... < t N = t E is a partition of [,t E ] such that the function v is monotone on each of the subintervals [t i,t i+1 ]. Fig. 1. Hysteresis play operator. The hysteresis play operator is shown in Fig. 1. According to (3), when input v increases/decreases and v r w v+r, output w of the play operator will assume the value of w and change along the a or c branch depending upon its previous values. When v increases and v r>wand w v + r, output w of the play operator will assume the value of v r and increase along the b branch. On the other hand, when v decreases and v r v+r <w, output w of the play operator will assume the value of v+r and decrease along the d branch. B. Classical PI Model The classical PI model makes use of the hysteresis play operator defined by (1) and it is described as [1] P (t) =qv(t)+ R p(r)f r [v](t)dr. (4) In (4), v(t) is the input and P (t) is the output. q is a positive constant and p(r) is a density function satisfying p(r). F r [v](t) is the hysteresis play operator as described in Section II-A. It can be seen that the PI model is an integral of many elementary play operators which are parameterized by the threshold value r. When more play operators different threshold values are used, a more complex hysteresis behavior can be modeled. C. GPI Model The shortcomings of the classical PI model are that it cannot be used to model either asymmetric hysteresis loops or saturated hysteresis output [11]. In [11], a GPI model is proposed in order that asymmetric hysteresis loops or saturated hysteresis output can be modeled, and it is based on the use of a generalized play operator. The GPI model is P (t) =qγ(v(t)) + R p(r)f γ r [v](t)dr, (5) { γu (v(t)) if v(t) γ(v(t)) = γ d (v(t)) if v(t) <. (6) The main difference in the GPI model is the addition of the envelope function γ, of which γ is made up of γ u and γ d.an increase in input v will cause the output P of the GPI model to depend upon the function γ u, and a decrease in input v will cause the output P to depend upon the function γ d. Both γ u and γ d are strictly increasing, continuous and odd. In discrete form, the GPI model will be n P (k) =qγ(v(k)) + p j (r j )Fr γ j [v](k)dr, (7) j=1 { γu (v(k)) if v(k) γ(v(k)) = γ d (v(k)) if v(k) <, (8) where v(k) is the discrete input k =[, 1, 2,...N] and N being the total number of discrete samples. In (7), n is the number of generalized play operator described as w() = Fr γ j [v]() = fr γ j (v(), ), w(k) =Fr γ j [v](k) =fr γ j (v(k),fr γ j [v](k 1)), (9)

3 fr γ j (v, w) = max(γ u (v) r j, min(γ d (v)+r j,w)). (1) From (1), it can be seen that the output of the generalized play operator is dependent upon the functions γ u and γ d. The density function p j (r j )and envelope functions γ u (v) and γ d (v) are p j (r j )=λe δrj, where r j = ρj and j =1, 2, 3,...n, γ u (v) =αv β, γ d (v) =ɛv η, (11) where λ, δ, ρ, α, β, ɛ, and η are constants. D. Inverse GPI Model With an open loop structure for compensation of the hysteresis effects in a PZT microactuator, an inverse hysteresis model will be used as the hysteresis compensator. An exact inverse of the GPI can be computed and the discrete form of the inverse GPI is expressed as [11] n P 1 (k) =γ 1 (q 1 v(k)+ ˆp j Fˆrj [v](k)), (12) j=1 { γ γ 1 1 u (v(k)) if v(k) (v(k)) =, (13) (v(k)) if v(k) < γ 1 d where v(k) is the discrete input k =[, 1, 2,...N] and N being the total number of discrete samples. n is the number of generalized play operators for obtaining the inverse GPI and is described as w() = Fˆrj [v]() = fˆrj (v(), ), w(k) =Fˆrj [v](k) =fˆrj (v(k),fˆrj [v](k 1)), (14) fˆrj (v, w) = max(v ˆr j, min(v +ˆr j,w)). (15) The parameters q 1, ˆr j, and ˆp j are obtained as q 1 = 1 q, j 1 ˆr j = qr j + p i (r j r i ), i=1 ˆp j = (q + j i=1 p i)(q + j 1 i=1 p i). (16) III. APPLICATION OF GPI MODEL TO PZT MICROACTUATOR IN DUAL-STAGE HDD SERVO SYSTEM In this section, the GPI model is used to model the hysteresis behavior of a PZT microactuator from the dual-stage servo system of a commercial 3.5 HDD a storage capacity of 2 TB. A hysteresis compensator is then designed to compensate for the hysteresis behavior using the inverse of the GPI model. In addition to the hysteresis compensator, a feedback control loop is included to reduce the tracking error of the PZT microactuator. Experiments are then carried out to determine the efficacy of the control scheme. p j A. Modeling of hysteresis behavior of PZT microactuator The PZT microactuator used in the experiment is obtained from the dual-stage servo system of a commercial 3.5 HDD. As the servo system has been removed from its original assembly, position feedback can only be obtained by the use of a Laser Doppler Vibrometer (LDV). The resolution of the LDV is set to.5 μm/v. To identify the hysteresis behavior of the PZT microactuator, regular sinusoidal waves of different frequencies and amplitude 6 V are used as input signals into the PZT microactuator. The input and output signals are given to and collected from the PZT microactuator respectively using a dspace 114 system a sampling frequency of 4 Hz. The hysteresis behavior of the PZT microactuator at different frequencies are shown in Fig. 2. To obtain a GPI hysteresis model as described by (7-11), the parameters are found by doing a curve fitting of the inputoutput data from the PZT actuator using the nonlinear leastsquare optimization toolbox in MATLAB. The input signal that consists of regular sinusoidal waves of different frequencies are put together as shown in the top half of Fig. 3 and the corresponding output signal obtained from the PZT microactuator are put together as shown in the bottom half of Fig. 3. This is done so as to organize the inputoutput data into a form that can be used the nonlinear least-square curve fitting algorithm. The number of generalized play operators, n, is chosen to be eight and the identified values of the parameters of the GPI model are shown in Table I. Fig. 4 shows a comparison between the measured hysteresis behavior consisting of the hysteresis behavior at different frequencies and the hysteresis behavior generated using the GPI model. Although the hysteresis behavior of the PZT microactuator is measured at different frequencies, the nonlinear least-square optimization algorithm is able to converge to a solution. This shows that the hysteresis behavior of the PZT microactuator at different frequencies does not differ significantly. In other words, hysteresis has a rate independent characteristic Frequency = 5Hz 5 5 Frequency = 16Hz Frequency = 1Hz 5 5 Frequency = 2Hz 5 5 Fig. 2. hysteresis behavior for different frequencies

4 Time (s) x Time (s) x 1 3 Fig. 3. Input and corresponding output displacement signal used for hysteresis modeling. TABLE I PARAMETERS OF GPI MODEL IDENTIFIED USING NONLINEAR LEAST-SQUARE OPTIMIZATION The open loop hysteresis compensation structure that will be used to compensate the hysteresis behavior in the PZT microactuator is shown in Fig. 5. The hysteresis compensator is designed by obtaining an inverse of the GPI model, of which the inverse GPI model is obtained using (12-16). The measured output signal shown in Fig. 3 is fed into the open loop scheme shown in Fig. 5 and the inverse of the hysteresis behavior which is generated using the inverse GPI model is shown on the left of Fig. 6. In simulation, the hysteresis behavior of the PZT microactuator is represented using the GPI model. With the measured output signal shown in Fig. 3 used as the input signal into the open loop scheme, the hysteresis behavior generated using the GPI model is as shown on the right of Fig. 6. The hysteresis behavior of the PZT microactuator can be completely compensated the hysteresis compensator in simulation, and the system consisting of the hysteresis compensator and the GPI model becomes linear as shown in Fig Parameters Identified Values α.765 β ρ.2889 λ.1116 δ.786 q.2181 ɛ.764 η.248 Model Output of inverse GPI model (V) Output from GPI model (V) Input into GPI model (V) Fig. 6. Inverse hysteresis behavior generated using inverse GPI model and hysteresis behavior generated using GPI model Fig. 4. Comparison of measured hysteresis and hysteresis generated from GPI model. B. Hysteresis Compensator Design Output from GPI model Representation of PZT (V) Fig. 7. Plot of simulated output against input signal for open loop hysteresis compensation structure. Fig. 5. Open loop hysteresis compensation scheme

5 Bode Diagram Frequency = 5Hz Frequency = 1Hz Gain (db) Controller Plant Open loop Frequency = 16Hz Frequency = 2Hz Phase (deg) Frequency (Hz) Fig. 8. Controller, plant and open-loop frequency response C. Feedback Controller Design The purpose of the feedback controller is to ensure that the reference signal given to the system can be tracked out steady state error and that tracking error caused by disturbance and noise can be reduced. The feedback controller consists of a lag compensator combined notch and peak filters discretized a sampling frequency of 4 khz. The dotted line in Fig. 8 shows the modeled frequency response of the PZT microactuator. The dashed-dotted line shows the simulated frequency response of the discrete time feedback controller and the solid line shows the resulting simulated open loop frequency response. D. Experiment validation In this subsection, the effectiveness of both the open loop hysteresis compensation structure shown in Fig. 5 and the closed-loop structure shown in Fig. 1 are validated in experiment using the dspace 114 system a sampling frequency of 4 khz. The open loop hysteresis compensation structure is given input signals that are regular sinusoidal signals of different frequencies amplitude of.1 V and the plots of output signal against input signal for the open loop hysteresis compensation structure are shown in Fig. 9. Using the same reference signals, simulation was carried out and the plots of simulated output signal against input signal for the open loop hysteresis compensation structure are also included in Fig. 9 for comparison. It can be observed that the hysteresis compensator, hysteresis behavior at different frequencies have been reduced significantly and the system consisting of the hysteresis compensator and the PZT microactuator becomes approximately linear. A comparison of the step responses of the closed loop system and out the hysteresis compensator is shown in Fig. 11. The size of the reference step signal is chosen to be 1 nm as the PZT microactuator is obtained from a 3.5 commercial HDD a storage capacity of 2 TB and a track density of about 24 ktpi, where TPI refers to Tracks Fig. 9. Plot of measured output against input signal for open loop hysteresis compensation structure. Per Inch. In a dual-stage servo system, the PZT microactuator functions as a fine actuator a small stroke [8]. However, the controller is designed such that the PZT microactuator is able to eliminate the steady state error for a step size of 1 nm because the PZT microactuator is used out the VCM in this experiment. It can be seen from Fig. 11 that the addition of the hysteresis compensator, rise time and settling time of the step response of the closed loop system are reduced. This is beneficial in HDD applications where a fast transient dynamics is required. In the magnetic disk drive industry, Position Error Signal (PES) is measured to obtain the deviation between the center of the read/write head and the center of the track. The tracking performance of a HDD servo system operating in the trackfollowing mode is commonly evaluated using 3σ PES, where σ PES is the standard deviation of the tracking error of the HDD servo system. As the servo system has been removed from its original assembly, measuring of the PES will require models of input and output disturbances that will be experienced by the servo system in its original assembly. These disturbance models are obtained from [12]. The closed system the disturbances models included is implemented using the dspace 114 system a sampling frequency of 4 khz and PES is measured using the LDV. Fast Fourier Transform (FFT) of the measured PES signals are carried out and the PES spectrums a resolution of 5 Hz are shown in Fig. 12. The cumulative sum of each PES spectrum, which will be used to obtain σ PES and 3σ PES, are also shown in Fig. 12. It can be observed from Fig. 12 that the use of the hysteresis compensator, the magnitude of the PES spectrum at low frequencies is lower than that of the PES spectrum of the closed-loop system out the hysteresis compensator. In addition, it can be observed from Table II that the 3σ PES

6 of the closed-loop system the hysteresis compensator is also smaller than that out the hysteresis compensator. These show that hysteresis compensation, the tracking performance or positioning accuracy of the PZT microactuator is improved. TABLE II COMPARISON OF TRACKING PERFORMANCE σ PES (nm) 3σ PES (nm) Without hysteresis compensator With hysteresis compensator Fig. 1. Feedback control structure hysteresis compensator. Displacement (nm) Reference Closed loop step response out hysteresis compensation Closed loop step response hysteresis compensation Time (s) Fig. 11. Comparison of step response of closed loop system and out hysteresis compensator. FFT of PES (nm) 1 5 PES spectrum w/o hysteresis compensation Cumulative sum w/o hysteresis compensation PES spectrum w hysteresis compensation Cumulative sum w hysteresis compensation Frequency (Hz) Fig. 12. Comparison of FFT of PES signals for closed loop system and out hysteresis compensator. IV. CONCLUSION With the use of the GPI model to model the hysteresis behavior of a PZT microactuator from the dual-stage actuation 5 Cumulative sum (nm) system of a commerical HDD as well as its inverse to compensate the hysteresis behavior in the PZT microactuator, the proposed-control scheme has been able to compensate for the hysteresis behavior in the PZT microactuator and results in the system having a step response reduced rise time and settling time. In addition, the positioning accuracy of the PZT microactuator is improved. While this paper demonstrates the application of the the GPI model to compensate for hysteresis behavior in the PZT microactuator of a dual-stage actuation system of a commercial HDD, this method of hysteresis compensation can in fact be applied to the different areas of science where hysteresis behavior is encountered as the modeling and compensation of hysteresis behavior using the GPI model is a mathematical approach out consideration for any underlying physical laws. REFERENCES [1] I. D. Mayergoyz, Mathematical Models of Hysteresis. Springer-Verlag, New York, [2] S. Rosenbaum, M. Ruderman, T. Strohla, and T. Bertram, Use of Jiles-Atherton and Preisach Hysteresis Models for Inverse Feed-Forward Control, in IEEE Trans. Magn., vol. 46, no. 12, pp , Dec 21. [3] A. Cavallo, C. Natale, S. Pirozzi, and C. Visone, Effects of Hysteresis Compensation in Feedback Control Systems, in IEEE Trans. Magn., vol. 39, no. 3, pp , May 23. [4] K. Haiya, S. Komada, and J. Hirai Tension Control for Tendon Mechanisms by Compensation of Nonlinear Spring Characteristic Equation Error, in Proceedings of 11 th IEEE International Workshop on Advanced Motion Control, pp , Mar 21. [5] K. Y. Tsai and J. Y. Yen, Servo System Design of a High-Resolution Piezodriven Fine Stage for Step-and-Repeat Microlithography systems, in Proceedings of IEEE IECON99, vol. 1, pp , [6] N. Tamer and M. Dahleh, Feedback Control of Piezoelectric Tube Scanners, in Proceedings of 33rd IEEE Conference on Decision and Control, vol. 2, pp , [7] K. K. Tan and A. S. Putra, Piezo Stack Actuation Control System for Sperm Injection, in Proceedings of SPIE - The International Society for Optical Engineering 648, no. 648, 25. [8] S. Nakamura, H. Numasato, K. Sato, M. Kobayashi, and I. Naniwa, A Push-Pull Multi-Layered Piggyback PZT Actuator, Microsystem Technologies, Vol. 8, No. 2 3, pp , 22 [9] A. Visintin, Differential Models of Hysteresis. Springer, Berlin, [1] M. Brokate and J. Sprekels, Hysteresis and Phase Transitions. Springer, New York, [11] M. A. Janaideh, S. Rakheja, J. Mao, and C. Y. Su, Inverse Generalized Asymmetric Prandtl-Ishlinskii Model for Compensation of Hysteresis Nonlinearities in Smart Actuators, in Proceedings of International Conference on Networking, Sensing and Control, pp , Mar. 29. [12] F. Hong, C. K. Pang, W. E. Wong, and T. H. Lee, A Peak Filtering Method Improved Transient Response for Narrow-Band Disturbance Rejection in Hard Disk Drives., in Preprints of the 5 th th IFAC Symposium on Mechatronic Systems, MECHATRONICS21-5, pp , Cambridge, MA, USA, September 13-15, 21 (invited)