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1, FEBRUARY 2005. On the Tracking Performance Improvement of. Optical Disk Drive Servo Systems Using. Error-Based Disturbance Observer. Kwangjin Yang ...
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On the Tracking Performance Improvement of Optical Disk Drive Servo Systems Using Error-Based Disturbance Observer Kwangjin Yang, Youngjin Choi, Member, IEEE, and Wan Kyun Chung, Member, IEEE

Abstract—There are many control methods to guarantee the robustness of a system. Among them, the disturbance observer (DOB) has been widely used because it is easy to apply and the cost is low due to its simplicity. Generally, an output signal of the system is required to construct a DOB, but for some systems such as magnetic/optical disk drive systems, we cannot measure the position output signal, but only the position error signal (PES). In order to apply a DOB to such systems, we must use an error signal instead of an output signal. We call it the error-based disturbance observer (EDOB) system. In this paper, we analyze the differences between a conventional DOB system and EDOB system, and show the effectiveness of the proposed EDOB through simulations and experiments. Also, this paper proposes criteria to enhance the robustness of an EDOB system, and reveals the disturbance rejection property of the EDOB system. Finally, we propose a new method of a double system to improve the track-following performance. This is also verified through experiments for a DVD 12 optical disk drive system. Index Terms—Digital signal processor (DSP), error-based disturbance observer (EDOB), normalized coprime factorization, optical disk drive (ODD) system, robustness, tracking servo.

I. INTRODUCTION

T

HE optical disk drive (ODD) systems, such as CD and DVD players, are the media-of-the-day in data storage devices. Due to their large storage capacity and portability, CD and DVD players have been widely used and have gained popularity. However, reproducing data with high speed and high accuracy is not an easy task because the track to follow becomes very narrow. In the case of a DVD tracking servo, the optical spot must follow the track within 0.1- m residual tracking error in the face of disturbances [1], which are mainly generated from the eccentricity of disk in the player device. Since the magnitude of these disturbances is very large, the conventional feedback controllers are not enough to attenuate these disturbances. Several attempts have beeen made to improve the tracking servo performance. The first method is to use a zero Manuscript received March 11, 2002; revised June 7, 2004. Abstract published on the Internet November 10, 2004. This work was supported in part by the National Research Laboratory program from MOST and by the Ministry of Health and Welfare, Korea, under Grant 02-PJ3-PG6-EV04-0003. K. Yang is with the Department of Mechanical Engineering, Korea Air Force Academy, Chungju 363-842, Korea (e-mail: [email protected]). Y. Choi is with the Intelligent Robotics Research Center, Korea Institute of Science and Technology (KIST), Seoul 136-791, Korea (e-mail: [email protected]). W. K. Chung is with the Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea (e-mail: [email protected]). Digital Object Identifier 10.1109/TIE.2004.841069

phase error tracking (ZPET) control [2]. Actually, it is impossible to use a ZPET control in the ODD systems because the reference signal is required to implement a ZPET. The author of [2] implemented a ZPET by estimating the reference signal. The second method is to use a disturbance observer (DOB). The DOB has been widely used in the precision motion control field because of its good performance [3]–[7]. Only the position error signal (PES) is available in ODD tracking control systems instead of the position output signal. To overcome this problem, the authors of [8] achieved a conventional DOB by attaching an additional position sensor to the original system. As a matter of fact, it is possible to construct a DOB by using only an error signal without adding another sensor. In [9] and [10], good experimental results were obtained by using the error-based disturbance observer (EDOB), but its characteristics were not revealed. Actually, the DOB for a position error signal has a little bit different meaning from the conventional DOB applied to the position output signal. One of main objectives of this paper is to reveal the basic characteristics of an EDOB system by comparing it with a conventional DOB system. As will be shown later, the EDOB offers an additional feedforward control input to the conventional DOB system as its inherent characteristics. This feedforward controller acts as a compensator by assisting the actuator to follow the track. To begin with, we propose a robustness measure of the EDOB system when the binomial filter is used. Next, we characterize the disturbance rejection property of the EDOB system. Finally, we propose a new method to improve the tracking performance of ODD systems when the EDOB is used. This paper is organized as follows. Section II describes the ODD model and experimental equipment. Section III reveals the characteristics of the EDOB system. Section IV analyzes the robustness and disturbance rejection performance of the EDOB system. Section V suggests a new method to enhance the performance of the EDOB, and conclusions are drawn in Section VI. For future notation, the following will be used: Hardy space of stable and proper function; real plant; nominal plant; normalized coprime factors; coprime factor uncertainties; main controller output; external disturbance; plant perturbation; tracking error; sensor noise.

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(3) . where is the dc gain of real plant In Fig. 2, the lead–lead–lag compensator was used as the conventional fine tracking controller which is realized in a hardwired digital signal processor (“Hardwired DSP”). Its control frequency is 176.4 kHz. Also, the EDOB is realized as a TMS320C44 DSP chip (manufactured by TI Company). Its control frequency is 25 kHz. In other words, the control frequency of the conventional controller is approximately seven times faster than that of the EDOB. III. EDOB

Fig. 1.

Coarse/fine tracking motion of ODD systems.

II. EQUIPMENT: ODD SYSTEMS The DVD 12 ODD system (manufactured by Samsung Electronics Company) is used as a representative example for the analysis and experiment. Fig. 1 illustrates the schematic diagram of the DVD system. The step motor is used for the coarse tracking motion and the voice coil motor (VCM) for the fine tracking motion. Our major concern is the fine tracking motion by the VCM. Fig. 2 depicts the control loop of the ODD fine tracking system including EDOB. In this figure, the transfer function of VCM has the following form:

There exist many disturbances in ODD control systems. Among them, the most severe disturbance is generally caused by the eccentricity of the disk itself. In other words, the eccentric disk causes a very large disturbance affecting the control performance. In this case, the DOB can be a good alternative to reject the disturbance. However, as previously discussed, the position output signal cannot be measured directly in ODD systems; only the error signal can be measured. Therefore, we use an error signal instead of the position output signal. In this case, the structure of a DOB cannot be composed of the conventional form. To deal with these systems, we define the EDOB system as shown in Fig. 3. The transfer function of the EDOB system has the following form: (4) where

mm V is the undamped where is a damping ratio of the VCM and natural frequency of the VCM. Also, the RF amplifier generates the tracking error signal from the optical spot reflected on the optical disk and its transfer function has the following form: V mm The transfer function of the VCM driver is as follows: V V

Driver

Therefore, the real plant can be modeled as a fifth-order transfer function as follows: Driver

In (4), if we approximate in low frequencies, then the effect of disturbance can be rejected because goes to zero. It means that the EDOB system also has the disturbance rejection property just as the DOB system does. Here, let us defined as the difference consider the error signal between the reference and output signal, then we can decompose signal as follows: the

VCM

RF

V V

(1)

However, three poles of the driver and RF can be neglected because their dynamics disappear so quickly. Hence, the nominal plant used in the EDOB can be obtained as the following form: V V

(2)

Now, the EDOB system can be interpreted in the framework of a conventional DOB system with the feedforward controller as shown in Fig. 4 [11]. The basic difference between the DOB and EDOB systems can be seen from Fig. 4. The EDOB system preserves the DOB property. In addition, it brings a new feedforward control input. This feedforward controller acts as a dynamic compensator, and , it makes the actuator follow the reference signal. If then the feedforward controller improves the tracking performance for the reference signal like the perfect control, since it produces the effect of inverse dynamics.

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Fig. 2.

Schematic diagram for fine tracking servo system with EDOB.

Fig. 3.

EDOB structure I.

Fig. 5. EDOB system expressed by coprime factors.

eling for a real plant and it can be factorized as the following form: Fig. 4.EDOB structure II.

IV. ROBUSTNESS AND PERFORMANCE OF EDOB In this section, we analyze the characteristics of the EDOB. It is difficult to identify the real plant exactly because the system has many uncertainties. Let us consider the real plant expressed by normalized coprime factors and coprime factor uncertainties as the following form:

If we use the coprime factor representation, then the EDOB structure can be obtained as shown in Fig. 5. Let us consider the perturbation quantity in Fig. 5 as follows: (7) and assume that the bound of perturbation is

(5) Here, small means large perturbation. In general, it is very difficult to calculate the size of the perturbation directly. However, we can perceive the following relation from Fig. 5:

where

and are normalized coprime factors in [12]. The normalized coprime factorization is unique and has the following characteristics:

(8)

(6)

If the small gain theorem is applied to (8) by using (7), then the robustness bound of the EDOB can be obtained as following form:

Let us assume that the real plant of (5) is controllable and observable, then the nominal plant can be obtained through mod-

If the normalization characteristics for coprime factors are utiof lized for the above equation, in other words,

A. Robustness of EDOB

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TABLE I COEFFICIENTS b AND c

(6) is multiplied by both sides, then the above can be changed to the following form:

can be calculated by using the symbolic calculation software, e.g., MACSYMA, MATHEMATICA, etc., as follows:

(9) Since (9) means the degree of robustness of the EDOB system against the perturbation, we define it as the “robustness mea. In other words, if a small can be sure” denoted by filter for a given nomachieved by designing an adequate , then the DOB system can be stabilized in spite inal plant of the large perturbation or uncertainties. Hence, the robustness measure of (9) can guide the design of the filter to be a robust DOB. Actually, there are three important factors in designing a filter: the filter time constant, the numerator order, and denominator order (or relative degree) of the filter. Actually, the filter time constant and orders of filter should be designed so can be achieved for a good robustness. These that the small will be explained through the example of an ODD system in the following. Here, we utilize the filter suggested as the following form:

where

(11)

and the coefficients and are listed in Table I. To perceive the relation between the robustness and the characteristics (numerator order, denominator order, and filter time constant) of the filter, we assume that the damping ratio is very small, which is a reasonable assumption for ODD systems. Then, we can say that the maximum value of (11) is approximately ob, though the maximum value of (11) is extained at actly obtained at the resonance frequency for . At , the following coefficients are easily calculated:

(10) where the filter time constant;, binomial coefficients calculated as ; denominator order; numerator order . Also, most ODD systems can be described by the second-order transfer function as shown in (2). Using the suggested filter (10) and the nominal plant (2), the robustness measure (9)

Now, if we determine the filter time constant satisfying , then the maximum value can be approximately achieved for all frequencies as shown in (12), at the bottom of the page. means large robustness bound, we deBecause small rive the following relation by noting the relative degree and the denominator order from (12).

(12)

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(Criterion 1) (Robustness and the Orders of Filter): The robustness of the EDOB system can be better as the relative deof the filter decreases. Also, for the case of gree the same relative degree, the increase of denominator order makes the robustness better. As we can see in (12), the robustness of the EDOB is better as the relative degree becomes smaller. In case the relative degree filter is the same, the increase of denominator of order makes the robustness better. For example, the robustness filter than a of the EDOB system can be better if we use a filter. Also, the filter makes system more robust than the , and the filter makes the system more robust than filter. Fig. 6 shows the trend predicted by criterion 1. the B. Disturbance Rejection Property of EDOB Considering the transfer function from the disturbance to an error in Fig. 5, then it can be obtained as the following form:

and its magnitude is calculated as follows:

Also, its decibel magnitude is calculated as (13), shown at the bottom of the page. Since most disturbances exist at low frequencies, we can approximate the transfer function for low fre, its magnitude of quencies. At low frequencies such as (13) can be approximately calculated as follows:

(14) as shown in Table I. As the magnibecause is smaller, the disturbance rejection proptude of erty becomes better. Finally, we can derive the following relation from (14).

Fig. 6. Robustness according to Q filters, where y axis means  (j!). (a) Robustness and relative degree. (b) Robustness and denominator order.

(13)

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Fig. 8. Simulation results for disturbance rejection performance. (a) With EDOB and without EDOB. (b) According to the numerator order. Fig. 7. Disturbance rejection performance according to Q filter, where y axis means jG (j!)j. (a) Performance and numerator order. (b) Performance and filter time constant.

(Criterion 2) (Disturbance Rejection and the Orders of Filter): The disturbance rejection performance of the EDOB system can be improved as the numerator order of the filter increases. Also, for the case of the same numerator order, the decrease of denominator order makes the disturbance rejection performance better. If we would expect the disturbance rejection performance enhancement by using the EDOB, the filter time constant must be chosen so that can be satisfied. As the numerator order of the filter increases, the disturbance rejection performance of the EDOB system is improved as shown in Fig. 7(a). Also, for the case of the same numerator order, a larger denominator order brings worse performance in Fig. 7(a), because it brings a larger value in (14). For example, the disturbance rejection performance of the filter is better than the filter and the filter is better than the filter. If the numerator order of filter is the same, then the decrease of denominator order makes the disturbance rejection performance better as shown in Fig. 7(a), e.g., the filter shows better disturbance rejection performance than the filter.

(Criterion 3) (Disturbance Rejection and the Filter Time Constant): The disturbance rejection performance of EDOB system becomes smaller. can be improved as the filter time constant Since is smaller as the filter time constant is smaller as shown in Fig. 7(b), the disturbance rejection performance of the EDOB system can be improved as the filter time constant becomes smaller. However, as the filter time constant becomes smaller, the control input becomes more sensitive to the sensor noise. C. Simulations A computer simulation was carried out using MATLAB. The nominal model for the Samsung 12 DVD fine tracking system was given by (3). As shown in Fig. 8(a), the magnitude of error signal is attenuated to one-third when the EDOB is used. In Fig. 8(b), we can see that the disturbance rejection property of EDOB is improved as the numerator order of filter is increased just like criterion 2. D. Experimental Results As explained in Section II, the EDOB was realized by using a DSP as shown in Fig. 2. Also, the control frequency of the

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Fig. 9. Experimental results for disturbance rejection according to the numerator order (note that this DVD system has the 1.81 bias volt). (a) Without EDOB. ). (c) EDOB ( ). (d) EDOB ( ). (b) EDOB (

Q

L

NORM

Q

FOR

Q

TABLE II ERROR SIGNAL ACCORDING TO ORDER OF FILTER

Q

THE

NUMERATOR

example, the error was reduced about 42% when we used the filter and 53% in the case of the . These results confirm criterion 2. V. PERFORMANCE ENHANCEMENT OF EDOB

conventional controller was 176.4 kHz and that of the EDOB was 25 kHz. To introduce the external disturbance into EDOB system, we used a 150- m DVD eccentric disk (manufactured by Almedio Company). We obtained the experimental results as shown in Fig. 9. To see the average performance according to norm performance from the numerator order, we arranged experimental results in Table II. When we used the filter in the EDOB, the error was reduced about 22% compared to when we did not use the EDOB. Moreover, as the numerator order of the filter increases, the error was reduced much more. For

In this section, we suggest the new method defined from the modification of the EDOB system, which shows the better tracking performance than the EDOB system. When the EDOB of nominal plant (3) becomes is implemented, the dc gain a very large value; conversely, the dc gain of an inverse of the nominal plant becomes very small. In particular, it makes the almost meaningless in the EDOB system role of part rarely affects of Fig. 3. Actually, since the is very large, we the control system when the dc gain can replace with a new controller according to the with objective of the control system. Now, replacing , then the structure of double system can be a simple defined as shown in Fig. 10. In designing the double system,

YANG et al.: TRACKING PERFORMANCE IMPROVEMENT OF ODD SERVO SYSTEMS USING EDOB

Fig. 10.

Double

277

Q system.

we do not have to consider the causality unlike the EDOB system, however, one condition is required to improve the track-following performance of ODD systems. This condition will be obtained in the following section. A. Disturbance Rejection Property of Double

System

of Fig. 10 with the uncertain model (5), After replacing let us consider the whole structure of the double system of Fig. 10. Then, the transfer function from the disturbance to error is obtained as follows:

Fig. 11. Comparison of disturbance rejection property by using EDOB and double system (simulation).

Q

L

TABLE III NORM COMPARISON

FOR EXPERIMENTAL AND DOUBLE Q SYSTEM

RESULTS

OF

EDOB

(15) On the other hand, if we replace of Fig. 3 with the uncertain model (5), then the transfer function from the disturbance to error is obtained as follows: (16) Here, if we compare (15) with (16) after calculating their decibel magnitudes, the following equation can be obtained:

(17) where

If (17) is smaller than zero, then we can say that the disturbance rejection property of the double system becomes better than the EDOB. Thus, the following inequality should be satisfied to show the better tracking performance:

Moreover, since always, the above condition can be simplified as the following inequality: (18) To satisfy the above inequality at low frequencies, the dc gain of nominal plant (2) should be larger than 1 as follows: (19)

(Criterion 4) (Condition for Performance Enhancement of of the nominal plant Double Q System): If the dc gain is larger than 1 at low frequencies, then the disturbance rejection property of the double system is superior to that of the EDOB. B. Simulations and Experiments We suggested the performance enhancement condition of the double system as Criterion 4. As suggested in Criterion 4, if the DC gain of nominal plant is larger than 1, then we can say that the disturbance rejection property of double system is superior to that of EDOB. In this section, we can confirm Criterion 4 through simulations and experiments. To begin with, we carried out the computer simulation using MATLAB just as EDOBs, and then we experiment with the double system under the same experimental conditions as the EDOB system. As we can see in an (3), since SAMSUNG 12X DVD fine tracking system satisfies the Criterion 4, , the disturbance rejection performance of the double system will be better than that of the EDOB system. Firstly, we obtained Fig. 11 as the simulation result. As we can see in Fig. 11, the disturbance rejection property of the double system is better than that of the EDOB system. Also, we can confirm the same fact repeatedly through the experimental results of Fig. 12. The experimental conditions of the system are equal to that of the EDOB system exdouble plained in Section IV-D. To compare the effectiveness of the system with the EDOB one, we rearranged the exdouble perimental results of the EDOB [Fig. 9(b)–(d)] at Fig. 12(a), norms of the experimental results in (c), and (e). Also, the norms were calculated Fig. 12 were arranged in Table III (the from the deviation for 1.81 bias voltage). When we used the

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Fig. 12. Comparison of disturbance rejection property by using EDOB and double ( ). (d) Double ( ). (e) EDOB ( ). (f) Double ( ).

Q

QQ

Q

QQ

filter, the error of the double system was reduced about 32% compared to that of the EDOB. Also, the error was reduced 23%

Q system (experiments). (a) EDOB (Q

). (b) Double

Q (Q

in the case of the and 12% in the case of the can confirm the validity of criterion 4.

). (c) EDOB

. Thus, we

YANG et al.: TRACKING PERFORMANCE IMPROVEMENT OF ODD SERVO SYSTEMS USING EDOB

VI. CONCLUSION The characteristics of an EDOB were revealed in this paper. As a matter of fact, the difference between the DOB and EDOB systems is that the EDOB includes an inherent additional feedforward controller assisting the fine tracking. Also, we analyzed the robustness of the EDOB system quantitatively and derived the analytic design guidelines of the EDOB system. Finally, a new performance enhancement method was proposed for the filters. These were proved ODD systems by using double through simulation and experiments.

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[12] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1995.

Kwangjin Yang received the B.S. degree from Republic of Korea Air-Force Academy, Chungju, Korea, in 1996, and the M.S. degree in mechanical engineering from Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 2002, both in mechanical engineering. He is currently an Instructor in the Department of Mechanical Engineering, Republic of Korea Air-Force Academy. His research interests include robust control and discrete-time control.

REFERENCES [1] Y. Kaneda, “Advanced optical disk mastering and its application for extremely high-density magnetic recording,” IEEE Trans. Ind. Electron., vol. 42, no. 3, pp. 257–262, Jun. 2000. [2] M. Tomizuka, “Zero phase error tracking algorithm for digital control dynamic systems: Modeling and control,” Trans. ASME, J. Dyn. Syst., Meas. Control, vol. 109, no. 1, pp. 65–68, 1987. [3] C. J. Kempf and S. Kobayashi, “Disturbance observer and feedforward design for a high-speed direct positioning table,” IEEE Trans. Contr. Syst. Technol., vol. 7, no. 5, pp. 513–526, Sep. 1999. [4] H. S. Lee and M. Tomizuka, “Robust motion controller design for highaccuracy positioning systems,” IEEE/ASME Trans. Mechatronics, vol. 5, no. 1, pp. 32–38, Mar. 2000. [5] M. White, M. Tomizuka, and C. Smith, “Improved track following in magnetic disk drives using a disturbance observer,” IEEE/ASME Trans. Mechatronics, vol. 5, no. 1, pp. 3–11, Mar. 2000. [6] T. Umeno and Y. Hori, “Robust speed control of dc servomotors using modern two degrees-of-freedom controller desine,” IEEE Trans. Ind. Electron., vol. 38, no. 5, pp. 363–368, Oct. 1991. [7] T. Umeno, T. Kaneko, and Y. Hori, “Robust servosystem design with two degrees of freedom and its application to novel motion control of robust manipulators,” IEEE Trans. Ind. Electron., vol. 40, no. 5, pp. 473–485, Oct. 1993. [8] J. Ueda, A. Imagi, and H. Tamayama, “Track following control of large capacity flexible disk drive with disturbance observer using two position sensors,” in Proc. Int. Conf. Advanced Intelligent Mechatronics, 1999, pp. 144–149. [9] K. Fujiyama, R. Katayama, T. Hamaguchi, and K. Kawakami, “Digital controller design for recordable optical disk player using disturbance observer,” in Proc. Int. Workshop Advanced Motion Control, 2000, pp. 141–146. [10] K. Fujiyama, M. Tomizuka, and R. Katayama, “Digital tracking controller design for CD player using disturbance observer,” in Proc. Int. Workshop Advanced Motion Control, 1998, pp. 598–603. [11] K. Yang, Y. Choi, and W. K. Chung, “Robust tracking control of optical disk drive systems using error based disturbance observer and its performance measure,” in Proc. Amer. Control Conf., 2002, pp. 1395–1400.

Youngjin Choi (S’01–M’03) was born in Seoul, Korea, in 1970. He received the B.S. degree in precision mechanical engineering from Hanyang University, Seoul, Korea, in 1994, and the M.S. and Ph.D. degrees in mechanical engineering from Pohang University of Science and Technology (POSTECH), Pohang, Korea, in 1996 and 2002, respectively. He is currently a Research Scientist with the Intelligent Robotics Research Center, Korea Institute of Science and Technology (KIST), Seoul, Korea. From September 2002 to June 2003, he was a Postdoctoral Researcher at KIST. His research interests include robust control, auto-tuning control, humanoid walking control, and robotics.

Wan Kyun Chung (S’84–M’86) received the B.S. degree in mechanical design from Seoul National University, Seoul, Korea, in 1981, and the M.S. degree in mechanical engineering and the Ph.D. degree in production engineering from Korea Advanced Institute of Science and Technology (KAIST), Seoul, Korea, in 1983 and 1987, respectively. He is currently a Professor in the Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, Korea, where he has been a member of the faculty since 1987. During 1988, he was a Visiting Professor at the Robotics Institute, Carnegie-Mellon University, Pittsburgh, PA, and during 1995, he was a Visiting Scholar at the University of California, Berkeley. His research interests include localization and navigation for mobile robots, underwater robots, and development of robust controllers for precision motion control. He is a Director of the National Research Laboratory for Intelligent Mobile Robot Navigation.