A swing-arm/PZT dual-stage actuator is designed to provide high performance solution to realize precise tracking and focusing operation of miniaturize... Actuators - Focusing - Servomotors - Transfer functions - Bandwidth - Frequency response - Optical sensors - fault tolerance - optical disc storage - piezoelectric actuators - servomechanisms - tracking - adaptive ZPETC method - dual-stage actuator controller design - optical disc drive - servo system - zero phase error tracking controller - focusing

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Department of Mechanical Engineering, National Chiao-Tung University, Hsinchu , Taiwan, ROC Abstract- A swing-arm/PZT dual-stage actuator is designed to provide high performance solution to realize precise tracking and focusing operation of miniaturized optical disc drive (mini-ODD). Because of its dual-stage mechanical characteristics can perform the focusing action smoother and more precise for better fault and error tolerance, the servo system to control such a dual-stage system tends to be more effective than a conventional single-stage ODD system. However, it is not enough to restrain the unwanted outside disturbance. Therefore, the zero phase error tracking controller (ZPETC), as proposed by Tomizuka (1987), which is very sensitive to improve the modeling error in motion control is used for this dual-stage miniaturized actuator. This paper presents an adaptive ZPETC method in dual-stage actuator design to achieve better focusing performance.

I. INTRODUCTION Optical disk drive is one of the most popular systems of information storage. Such a high track density and accurate focusing operation requires a higher precision servo system [1][2]. The VCM limits the bandwidth extension in the single-stage servo system because of its mechanical resonances and high frequency uncertainties.[3] As such, dual-stage actuation is seen to be the solution for new generation of miniaturized ODDs. Referring Fig.1, the new servo mechanism of dual stage actuation in the mini-ODD, which places a small secondary actuator on the seesaw actuator head, has been proposed to perform the fine focusing for ultra-narrow track pitch.

Rotary Arm

Focusing

Piezo Plate

Tracking VCM

Pivot

Fig.1. seesaw swing-arm/PZT dual-stage actuator The secondary micro-actuator which holding the optical read/write head may be embedded in the arm of the seesaw suspension is placed in front of seesaw swing-arm. This secondary micro-actuator is made of piezo-electronic material (PZT).[4] In mini-ODD servo system, the PZT-actuator works for fine movement while the seesaw VCM performs the coast focusing [5]. From the control point of view, the track-following is an output regulation problem, while the trackseeking is related to the problem of reference seeking. A control problem is that the overshoot or oscillation may delay of the output signal and result in a long seeking time. Solving this problem can use the ZPET controller to compensate the phase error and delay. This paper is organized as follows. Section II gives a brief introduction on dual-stage servo system in mini-ODD. Section III used the new control method of adaptive ZPETC in the dual stage actuator. The performance of the proposed control scheme and experimental results are discussed in Section IV. The conclusion is discussed in Section V. II. DUAL-STAGE SERVO SYSTEM Referring Fig.2.1, the micro actuator performs the master and fast focusing motion due to its high bandwidth [3].

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Micro OPU location

Fig.2.1. dual-stage closed loop block diagram Although the displacement of the PZT actuator is smaller than the major (seesaw) actuator, it is mainly used in focusing following the data track to reduce outside disturbances.[4] When the seesaw focuses the optic axis of disc, the suspension produces a tilt to the horizontal plane. The PZT actuator can be effectively decreased the focusing time and correct the departure. The open loop transfer function form the input signal r(t) to the head displacement signal y(t) is

y (t )

CV PV CM PM CV PV CM PM r (t ).

by the basic performance. Therefore, it uses the open loop function to attain the stable phase margin and gain margin. The open loop function of the micro-actuator PZT is FPZT CM PM CM PM CV PV (6) ! The Eq (6) includes two parts, active motion and passive decoupling to the seesaw. The relative decoupling effect is conspicuous in the low frequency range and slight in the high frequency range. This advantage will ensure that the seesaw and PZT cooperate to reduce the sensitivity at all frequencies within the servo bandwidth. The PZT controller is designing by adjusting the seesaw’s outside disturbances. III. ADAPTIVE ZPET CONTROLLER IN DUAL STAGE SYSTEM

(1) !

In the Eq (1), the micro-actuator is decoupled the VCM actuator. Therefore, the feedback closed loop transfer function: CV PV CM PM CV PV CM PM r (t ). (2) ! y (t ) 1 CM PM 1 CV PV So the sensitivity function (error rejection function) is 1 . (3) Es 1 CM PM 1 CV PV

Fig.3.1. FF dual-stage model

Eq (1) shown the proposed actuator controller which has two following algorithms: 1. If the controller responses the feedback error position signals, it provides a useful feedback loop from the output micro-actuator PZT to the input major actuator. This loop is important to

establish decoupling the seesaw and the PZT. 2. The overall control block diagram is a twodegrees-of-freedom servo system. The sensitivity function to the major closed loop is 1 (4) ! ESEESAW 1 CV PV The open loop function is FSEESAW CV PV

(5) !

Referring the Eq (4) (5), to determine the stability of the dual actuator system when the PZT actuator is not activated, the seesaw feedback loop must be stable by itself. The major controller designs

Fig.3.2. FF in seesaw actuator control The basic feed-forward controller is shown in the Fig. 3.1 and Fig. 3.2. The memory is used to memorize the focusing error of seesaw focusing quake. M is the system memory steps to fit the actuator motion. This compensator reduces the periodic outside disturbances. In this closed loop, the focusing errors give an m step memories to pass the estimator block. The passing signal errors compare to the next signal errors then reduced in the adaptive

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system. The low-pass filter (LPF) can restrain high disturbance in high frequency.

method of identification in frequency domain. The System Identification experiments are performed on 1 the system. The step input signal data can give PV ( z ) G closed loop ( z 1 ) (7) 1 1 1 CV ( z ) PV ( z ) ! information about the dynamics characteristics. Rise time, overshoot and static gain are directly related to 1 Z ZPECT ( z 1 ) (8) 1 the step response of system. It has a significant G closed loop ( z ) influence on the resulting parameter estimates. Z ZPECT ( z 1 ) is the inverse transfer function of G closed loop Sometimes, the input signal must be introduced to to improveing the FB closed loop, but it considers the ! yield a reasonable identification results. A model is effect of the unstable zeros. fitted to the signal’s data by assigning accepted values The estimator designs for the feedback closed loop to the parameters of model. System identification is 1 the field of modeling dynamic systems from PV ( z ) E ( z 1 ) Gclosed loop ( z 1 ) (9) 1 1 experimental data of the LDV. 1 C (z )P (z ) V

V

!

But the actual system transfer function is very complex. It will be reduced to a fourth-order function and kept major resonant poles of the seesaw actuator.

! Fig.4.1. Parametric model

Fig. 3.3. FF-PZT The difference between the FF controller and the FFPZT controller is FF-PZT without the LPF. Because the PZT actives in the high frequency.[9][10] IV. EXPERIMENTAL RESULTS Analyzing System is an important task of which it would like to control and affect the behavior. A model is the knowledge of the properties of a system. It is necessary to have a model of the system in order to solve problems of control and system design. The ideal inverse model of the ZPETC controller is very important to design the closed loop of ODD. The system is controlled by the input signal u(t). But the nonlinear disturbance v(t) exist in the dynamical system, and the disturbance isn’t easy to reduce. A useful model should encompass essential characteristic without becoming too complex to control. In the experimental implementation, the LDV captures the overall displacement of the dual actuators. The Dynamic Signal Analyzer (DSA) performs the measurement of seesaw and PZT models with the

Referring Fig. 4.1, y(t) is the measurements of input signal. I(t) is a vector of known input values, and T is a vector of unknown parameters. The uncontrollable modeling error e(t) is in the dynamic system. The system identification method is to minimize the error e(t) between the y(t) and the model prediction yˆ(t ) . The measured frequency response is shown in Fig. 4.2 and Fig. 4.3, where the seesaw bandwidth is around 114.57Hz with stable phase margin. The bandwidth of the plant is 114.57Hz not enough to do a precise motion in the high frequency. The seesaw motion is perform a long distance focusing within 1000 Hz. The micro-actuator PZT is working in the high frequency of 1000 Hz to 4000 Hz to focus in a very fine displacement. This had a great effect upon shortening the response times.

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Fig.4.2 Plant frequency response of Seesaw Fig.4.5. System Identification of PZT micro-actuator Also, the transfer function of PZT micro-actuator via curve-fitting system identification is as following: 9.87e -80s14 2.15e -75s13 1.24e -68 s12 4.651e -64s11 5.459e -58s10 2.46e -53 s^9 9.866e - 48 s8 4.794e - 43s7 8.265e -38s6 3.628e -33s5 2.888e - 28s4 8.843e - 24s3

Fig.4.3. Plant frequency response of PZT

3.849e -19s2 3.523e -15s 1.97e -10 ª1.235e -74s14 6.026e -70s13 1.704e -63 s12 5.648e -59s11 º « » 10 9 8 7 «7.804e -53s 1.622e - 48s 1.449e - 42s 1.71e -38s » «1.145e -32s6 7.346e - 29s5 3.902e - 23s4 1.222e -19s3 » « » «¬4.767e -14s2 2.868e -11s 2.98e -06 »¼

! The Least Squares Method is the best method of the system identification. It can use a method that a sequence of model structures of increasing dimension to obtain the best fitted model within each of the model structures. Therefore, a better fit will be obtained with more free parameters in the high order model than in the sample order model. In determining the best model structure, the important thing is to investigate whether or not the improvement in the fit is significant. If a model is more complex than is necessary, the model may be over-parameterized. Therefore, the high order transfer function makes the Fig.4.4. System Identification of seesaw actuator design of feedback closed loop for the dual stage system very complex. To simplify the actuator’s The transfer function of seesaw actuator via model is very important. The fourth order transfer curve-fitting system identification is as following: function of both VCM and PZT actuator are 9.159e - 014 s 8.132e - 012 ! approached to reduce the actual high-order system, §1.788e - 48 s 9 8.236e - 44 s8 2.493e - 37 s 7 · and maintained the major dynamics characteristics.

¨ ¸ 6 5 4 ¨ 9.52e - 33 s 8.076e - 27 s 2.537e - 22 s ¸ ¨ 3.715e -18 s 3 6.76e -16 s 2 1.835e -12 s ¸ ¨ ¸ ¨ 1.766e -10 ¸ © ¹

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improves the bandwidth. The bandwidth is increased from 1065 Hz to 3853 Hz. Because the feed-forward controller comprises the ZPETC feed-forward controller, it increases the stable phase margin in the dual stage actuators.

Fig.4.6. System Identification of seesaw actuator The reduced-order transfer function of seesaw actuator is as following: 6.296e -14 s 4.288e -11 ! 1.642e - 21s 4 2.645e -18s 3 3.165e -15s 2 1.385e -12s 1.09e - 09

Fig.4.8. Plant frequency response of dual stage

Fig.4.7. System Identification of PZT micro-actuator Fig.4.9. Plant frequency response of dual stage with adaptive ZPETC

The reduced-order transfer function of PZT microactuator is:

§ 3.585e - 27 s 4 6.445e - 22 s 3 1.334e -17 s 2 · ¨ ¸ 3.402e -13s 1.937e - 08 © ¹! §1.63e - 21s 4 6.053e -18s 3 4.709e -12 s 2 · ¨ ¸ 2.635e - 09s 0.0003038 © ¹ The performance of controller is simulated with Simulink. The low pass filter of the FF controller must not exceed the active bandwidth of the microactuator PZT. This advantage would keep the ZPETC design away the negative effect of the subtle modes of PZT. Referring the Fig.4.8, the traditional servo control works a narrow bandwidth of 1065Hz, and the bandwidth is not enough to do the precise focusing. Shown in the Fig 4.9, the adaptive ZPETC controller

V. CONCLUSION We proposed an adaptive ZPETC method to design servo controller for dual-stage actuator for high speed focusing function in miniaturized ODD. The dual-stage actuator provides a fine biaxial focusing solution to overcome the signal actuator coarse focusing. An adaptive design technique is studied to inverse the transfer function of feedback closed loop and to use the ZPECT method to reduce the phase lag and delay. The feed-forward controller is added to seesaw and PZT controller input in addition to other servo input signals, and the effective adaptive ZPETC closed loop algorithm is established. The frequency response measurement of this dual-

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stage actuator, and the Least Squares Method for system identification with reduced-order transfer functions were established. Simulation results showed that the signal of the FF and FF-PZT controller is matched to the input signal and work well for controlling the seesaw/PZT dual-stage swing-arm actuator focusing operation in mini-ODD. Acknowledgment Research supported by TDPA project 95-EC-17-A07-S1-011, MOEA, Taiwan, ROC. Corresponding author E-mail: [email protected] REFERENCES [1] T. Hirano, L. S. Fan, W. Y. Lee, J. Hong, W. Imaino, S. Pattanaik, S. Chan, P. Webb, R. Horowitz, S. Aggarwal, and D. A. Horsley, “High-bandwidth high-accuracy rotary microactuators for magnetic hard disk drive tracking servos”, IEEE/ASME Trans. Mechatron., vol.3, pp. 156–165, Sept. 1998. [2] R. B. Evans, J. S. Griesbach, and W. C. Messner, “Piezoelectric micro-actuator for dual stage control,” IEEE Trans. Magn., vol. 35, pp. 977–982, Mar. 1999. [3]!D. A. Horsley, D. Hernandez, R. Horowitz, A. K. Packard, and A. P.Pisano, “Closed-loop control of a micofabricated actuator for dual-stage hard disk drive servo systems,” in Proc. Amer. Control Conf., 1998, pp. 3028–3032. [4]!S. J. Schorceck and W. C. Messner, “On controller design for linear time-invariant dual-input single-output systems,” in Proc. Amer. Control Conf., 1999, pp. 4122–4126. [5]! T. Yamaguchi, H. Numasato, and H. Hirai, “A modeswitching control for motion control and its application to disk drives: Design on optimal mode-switching conditions,” IEEE/ASME Trans. Mechatron., vol. 3, pp. 202–209, Sept. 1998. [6] Tomizuka, Y. 1987, " Zero Phase Error Tracking Algorithm for Digital Control", ASME Journal of Dynamic systems, Measurement, and Control, Vol.109, PP. 65-68. [7] Tomizuka, M. 1989, " Design of Digital Tracking Controllers for Manufacturing Applications", American Society of Mechanical Engineers. Manufacturing Review Vo1.2, No. 2, pp. 134-141. [8] Chia-Hsiang Heng, 1993, "Precision Tracking Control of Discrete Time Nonminimum-phase System", ASME. Journal of Dynamic System, Measurement, And Control, Vol. 115, pp. 238-245. [9] Gross, Eric, Tomizuka, Mesayoshi and Messner Willian. March,1994, " Cancellation of Discrete Time Unstable Zeros by Feedforward Control", ASME, Journal of Dynamic System, Measurement and Control, [10] Tung, E.D., 1993, " Feedforward Tracking Controller Design Based on the Identification Of Low Frequency Dynamics", ASME Journal of Dynamic Systems, Measurement, And Control, Vol. 115, pp. 348-355.

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