APPLICATION OF MULTIVARIABLE CONTROL DESIGN TO DUAL-MODE DIGITAL VERSATILE DISC DRIVE

Transcription

1 Asian Journal of Control, Vol., No. 3, pp. 4-11, September 4 APPLICATION OF MULTIVARIABLE CONTROL DESIGN TO DUAL-MODE DIGITAL VERSATILE DISC DRIVE Myoung Soo Park, Hee Soo Lee, Seung-Ho Kim, Il-Yeong Roh and Yossi Chait ABSTRACT With the ever increasing demand for on storage media with more memory and faster speeds, Digital Versatile Disc (DVD) appears to eclipse Compact Discs (CD). Its denser track pitch and shorter minimum pit length allows for at least eight time more storage memory in the same area. However, smaller tracks increase the performance demands placed on control algorithms. Moreover, to achieve shorter read times, higher disc rotation speed is required, further increasing the demands on the controller. Classical single-loop control design techniques, the usual approach used in such applications, become less effective for DVDs and may even fail to yield a design for higher disc speeds and with increased coupling in the mechanism s dynamics. For this purpose, we employ the Quantitative Feedback Theory (QFT) and specialized graphical user interface to experimentally demonstrate that new design tools can accomplish the task. Specifically, we show that our multivariable design approach can cope with performance robustness issues and achieve backcompatibility for dual use (i.e. play both CD and DVD discs) in a single drive. Moreover, since QFT can be used with direct frequency response measurements to represent the dynamics, our control tuning procedure facilitates fast and efficient use in an industrial setting so as to minimize the time it takes to bring new products to market. KeyWords: Multivariable control, robustness, DVD, CD. Brief Paper I. INTRODUCTION The first optical data storage system has been standardized in 1981 by CD-DA Red-book [1,]. Since then, the rotation speed of optical data storage drives has been increased significantly [3]. In order to improve performance and stability robustness in these high speed systems, many control design techniques [3-1] have been applied Manuscript received August 17, 1999; revised November 6, 1999; accepted June 7,. Myoung Soo Park is with Amherst Applied Controls, 5 Porta Rossa Cir., Pleasanton, CA94588, USA. Hee Soo Lee and Il-Yeong Roh are with Samsung Electronics Co., Ltd., 416 Metan-3Dong, Paldal-Gu, Suwon City, Korea. Seung-Ho Kim is with Samsung Electronics Co., Ltd., San 4, Nongseo-Ri, Kiheung, Youngin City, Kyungki-Do, Korea. Yossi Chait is with Dept. of Mechanical & Industrial Engineering, University of Massachusetts, Amherst, MA13, USA. The rsearch is supported by a Samsung grant to Amherst Applied Controls. This support is greatly appreciated. to control the optical pickup s radial and vertical motion. In this paper, a multivariable QFT design technique is applied to a DVD drive to deal both with the coupled dynamics and robustness issues which are neglected by single-loop control design techniques. QFT [13-17] was popularized with the introduction of QFT Control Design Toolbox in MATLAB which replaced tedious manual designs with graphic user interface (GUI) programs [18] for mainly single-input single-output systems. In other to extend this program to a x multivariable system, Park [19] developed DQFT (direct QFT) design tool based on the DQFT. The DQFT design tool includes an option for translating standard optical device specifications into frequency-domain specifications. Together, these DQFT and GUI tools allow for efficient multivariable QFT design. This paper motivates this point via an industrial application. This paper is organized as follows. Section 1 describes the mechanism and the general control problem. Section describes the modeling problem. Section 3 presents the uncertainty description and the performance

2 5 M.S. Park et al.: Application of Multivariable Control Design to Dual-Mode Digital Versatile Disc Drive specifications of the system. Section 4 described application of our design technique to CD and DVD modes. Section 5 present the simulated sensitivity and the experimental sensitivity functions. II. THE MECHANISM AND CONTROL OBJECTIVES The optical data storage mechanism shown Fig. 1 is composed of a DC-motor (Motor 1) for the rotation of the compact disc, and Motor for a sled bar track following. An optical element is mounted at the pick-up unit. A diode located in this unit generates a laser beam that passes through a series of optical lenses to give a spot on the information layer of the disc. An objective lens, suspended by two parallel leaf springs, can move in a vertical direction for focusing action. Both the vertical and radial positions of the laser spot, relative to the track of the disc, have to be controlled actively. To accomplish this, the controller uses position-error information provided by four photo diodes. As input to the system the controller generates control currents to the radial and focus actuator, which both are permanent-magnet/coil systems. The control mechanism in an optical data storage system (Fig. ) can be represented by a linear, timeinvariant, x multivariable feedback system. To reflect uncertainties (see more details in Section 3), the plant P(s) is assumed to belong to, where is a family of linear, time-invariant transfer function matrices. The basic objective of this control system is to design robust controllers to satisfy performance specifications for two different usages (e.g., 4X CD-ROM and 4X DVD) in a single drive. Pick-up III. MODELING For control design, the dynamics from the plant input (actuator current) to plant output (positions) must be established. The only available signals for measurement are the differences between the pickup s vertical and radial positions and the laser spot position []. These are the radial error, ε rad, and the focus error, ε foc. Based on these measurements, the controller, G = diag(, ), feeds the system with the required control currents for each drive, ι rad and ι foc. Note that in this particular DVD system, even though the CD and the DVD modes are using different disc rotation speeds and have different performance specifications, the plant P(s) remains unchanged in theory. Due to limited memory in digital signal processor it is highly desired to have a single, robust control algorithm for both playing modes. To identify the x nominal plant, we use Siglab - [1] to measure input/output signals and then use GUI program DQFT to generate mathematical plant model. The identified nominal plant, P = {p ij }, by using the DQFT design tool consists of a common 18 th order denominator and four 17 th order numerators. where vertical error radial error = p 11 p 1 p 1 P = p p 11 1 p 1 p = (s p i ) Πi =1 17 Π i=1 17 Π i=1 vertical current radial current (s z i ) 11 (s z i ) 1 17 Π i=1 17 Π i=1 (s z i ) 1 (s z i ) Motor 1 Sled bar Motor and where p i and z i denote poles and zeroes. We use the term nominal to define the identified dynamics. The frequency response magnitudes of the nominal and measured plant are shown in Fig. 3. Note that the magnitude of p 1 is almost the same as the magnitude of p 11 implying strong off-diagonal interaction in the vertical direction. This interaction will be neglected in single-loop control design, but is considered in our technique. ε rad ε foc Fig.1. Schematic view of the optical data storage mechanism. E G(s) Controller i rad i foc P(s) Plant Fig.. The control system for an optical data storage system. Y IV. UNCERTAINTY AND PERFORMANCE SPECIFICATIONS On the basis of experience and physical reasoning the nominal plant model was assigned two types of uncertainties. The first type, parametric, consists of ±.5% variations about nominal values in each of the undamped natural frequencies of the three major vibration modes at.,.5 and 1.4 khz (Fig. 3). The second type, non-parametric, is related to the off-diagonal responses, and is defined as:

3 Asian Journal of Control, Vol., No. 3, September 6 Phase (degrees) Phase (degrees) P P 1 1e 1e3 1e4 1e 1e3 1e e 1e3 1e4-1e 1e3 1e4 Phase (degrees) 1 5 P P -5 1e 1e3 1e4-1e 1e3 1e e 1e3 1e4-4 1e 1e3 1e4 Phase (degrees) Fig. 3. Frequency response magnitudes of the nominal and measured plant. Table 1. Physical specifications. 4X CD 4X DVD vertical radial vertical radial Maximum deviation (µm) Allowable error (µm) Disc rotating speed (rpm) Maximum acceleration (m/s ) Controller bandwidth (Hz) Track pitch (µm) Minimum pit length (µm).8.4 P = p 11 ε +p 1 εp 11 +p 1, ε.1,.1 Note that the p ij terms above include parametric uncertainties. The two types of uncertainty result in a plant family denoted by. Our performance specifications are stated in terms of the frequency response of the sensitivity function, S = (I + PG) 1 = {s ij }, s ij (jω) η ij (ω), i, j = 1,, for each P and are derived from the standard physical specifications (Table 1). However, the QFT framework requires that specifications are stated in the frequency domain. Therefore, Table 1 must be translated into appropriate frequency domain specifications as follows. In this translation, there are three frequency ranges (low, mid and high frequency ranges) on the basis of experience. The maximum deviation, allowable error and maximum disc rotating speed are used to translate into the frequency domain specification in the low frequency range as the following: S Low = allowable error Maximum deviation, < ω maximum disc rotating frequency

4 7 M.S. Park et al.: Application of Multivariable Control Design to Dual-Mode Digital Versatile Disc Drive The maximum acceleration and controller bandwidth are used to translate into frequency domain specification in the mid frequency range as the following: S Mid = 1, 1+ Maximum acceleration (jω) maximum disc rotating frequency < ω controller bandwidth In addition, we use the constraint, s ii (jω), ω, to generate stability robustness by using the generalized Nyquist criterion. This is done as follows. p 1 p 1 1+ = 1 *1 1+ p 1 p 1 = 1 *1 1+p 1 11 p p, 1+p 1 p p 11 where * denotes a complex coefficient. Each loop will have to satisfy 1+p ii g i.5, ω, for each P. Note that 1 + p ii g i are the denominators of the single-loop s ii, where p 11 = p + det [P]1, p 1+ = p p 1 1 and where det[p] represents determinant of P. The final requirements are that the nominal open loop bandwidth in each loop should be kept sufficiently low to avoid amplifying high frequency noises and generating audible responses from the actuators. Naturally, the controller order should be kept to a minimum. These specifications are translated into the frequency domain by the DQFT design tool interactively (Fig. 4), and its results are shown in Fig. 5. Max. Spindle speed in rpm Max. Allowable vertical deviation in micro meter Max. Allowable vertical error in micro meter DQFT DESIGN TOOL Acceleration Amherst Applied Control SPECIFICATIONS ON FOCUS DIRECTION Margins (1/) Controller Bandwidth INTRODUCTION CONTINUE REDO QUIT Fig. 4. A program to translate specifications in the DQFT design tool. for the following reasons: 1. Undamped three natural frequencies (134, 33 and 965 rad/sec for both case). Controller bandwidth frequency (4691 and 1466 rad/ sec for DVD and CD, respectively) 3. Disc rotating frequency (67 and 1 rad/sec for DVD and CD, respectively) and its half value frequency as a starting frequency (335 and 15 rad/sec for DVD and CD, respectively) 4. Two high frequencies to guarantee robust stability (4398 and 683 rad/sec for both case) In this control design process, a controller for DVD is designed first and the designed controller is checked to CD for applicability. To compute QFT stability bounds, we use the following inequality [4]: 1+ p + det [P]1 + 1, ω, for each P Because in the previous equation is yet to be designed, we consider its extreme values [], namely, V. CONTROL DESIGN The first design step involves the vertical controller to satisfy robust stability and the robust sensitivity performance specifications. In QFT closed-loop specifications are converted in QFT bounds at several frequencies. These bounds indicate allowable frequency responses for the nominal loop such that robust performance is achieved. In our design we chose the following frequencies ω _dvd = [335, 67, 134, 33, 4691, 965, 4398 and 683 rad/sec] for 4X DVD ω _cd = [15,1, 134, 1466, 33, 965, 4398 and 683 rad/sec] for 4X CD 1 ω, for each P ( ) 1+ det [P] 1 ω, for each P ( ) To compute the sensitivity bounds, we use this following inequalities [4]: s 11 (jω) = 1+ p 1 s 1 1+ det [P] 1+ p 1 η 1 1+ det [P] η 11 (ω),

5 Asian Journal of Control, Vol., No. 3, September Vertical direction (4X CD) Vertical direction (4X DVD) Radial direction (4X CD) Radial direction (4X DVD) Fig. 5. Desired specifications η ij (ω), i, j = 1,,..., n. s 1 (jω) = p 1 + p 1 s p 1 + p 1 η η 1 (ω) 1+ det [P] 1+ det [P] where ω [,5 or,1] for each P. Robust stability bounds and robust sensitivity bounds were computed by using the DQFT GUI tools. These bounds and the synthesized nominal loop are shown on the Nichols chart in Fig. 6. The designed controller is given by (rounded off) = s s s s s The second design step is to design to satisfy the robust stability and robust performance specification while taking into account the known. The plant used in the second design step, p, is defined by p = p p 1 1 [4]. Robust stability bounds are computed from 1+ p + det [P] 1, ω, for each P, 1 1+ p + det [P]1 + 1, ω, for each P, Fig. 6. QFT bounds and nominal design p 11 in the first design step.

6 9 M.S. Park et al.: Application of Multivariable Control Design to Dual-Mode Digital Versatile Disc Drive Robust sensitivity bounds are computed from the following equations [4] s 1 (jω) = p 1 1+ p + det [P]g η 1(ω), 1 s 1 (jω) = 1 1+ p + det [P]g η 1(ω) 1 where ω [,4 or,18] for each P. The robust stability bounds, robust sensitivity bounds, and the syn-thesized nominal loop are shown on the Nichols chart in Fig. 7. The designed controller is given by (rounded off) = s s s s s Our multivariable control design resulted in a diagonal controller, G(s) = diag(, ). It is important to note that while this simple, diagonal structure has the same implemented following single-loop design, it meets the multivaribale robust performance specifications. Moreover, the time it took to complete our design-implement-tune process has been cut by a factor of one hundred compared with past experience with single-loop design. The simulated maximum sensitivity magnitude (over the 375 plants) and robust stability margin are shown in Fig. 8. Note that the lines with * and in Fig. 8 and Fig. 9 represent the specifications for 4X CD and 4X DVD, respectively. VI. IMPLEMENTAION RESULTS The experimental setup consisted of a Digital Versatile Disc Drive with an interface to a Digital Signal Processor (DSP) system. The actual implementation of the controller on the 4X CD in the DSP has been carried out with a proprietary program at Samsung Electronics Company, Ltd., Korea. Most problems occurring when implementing controllers involve problems such as scaling inputs and outputs to obtain the appropriate signal levels and to ensure that the resolution of the DSP is optimally used. The DSP system used is a Samsun6-bit processor with fixed-point arithmetic. The Analog Digital Converters (ADC) are 8-bit and have a conversion time of.1 µs. The maximum input voltage is -5 V. The Digital Analog Converters (DAC) are 1-bit, have a conversion time of.1 µs and of -5 V range. On the basis of the closed-loop relevant dynamics in the vertical and radial loops, the controller discretization was done at a sampling rate of khz. The measured closed-loop sensitivity magnitudes are shown in Fig. 1 and Fig. 11 for CD and DVD operating modes, respectively. For propriatary reasons, only simulation results are shown for the 4X DVD mode. VII. CONCLUSIONS The direct multivariable QFT technique has been successfully applied to the given robust performance and robust stability specifications in a dual-mode DVD drive. Our experience indicates that when combined with newly developed GUI program, this approach significantly reduces the time it takes to complete an industrial modelingdesign-implementation-iteration. With this technique it was possible to design a single controller for both CD and DVD playing modes which have different rotation speeds. REFERENCES Fig. 7. QFT bounds and nominal design p in the second step. 1. Compact-Disc Digital Audio System Description, Philips Electronics N.V. and Sony Corp (1981).. Compact Disc Digital Audio System, IEC 98, First

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