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Estimator-Based Sliding Mode Control of an Optical Disc Drive Under Shock and Vibration

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Estimator-Based Sliding Mode Control of an Optical Disc Drive Under Shock and Vibration Estimator-Based Sliding Mode Control of an Optical Disc Drive under Shock and Vibration Yu Zhou,1 Maarten Steinbuch,2 Senior Member, IEEE, and Dragan Kostić,3 Student Member, IEEE 1Electrical Development Department, Philips Optical Storage, 620A Lorong 1 Toa Payoh, Singapore 319762 2,3Dynamics and Control Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology (TU/e), P.O.Box 513, 5600 MB Eindhoven, The Netherlands Email: [email protected], [email protected], and [email protected] Abstract acceleration feed forward to both focus and radial servo loop to counteract the external disturbances. In combination with a A more robust servo control system using Sliding Mode number of modifications on the mechanism like pre-loading the Control to handle shock and vibration disturbances for upper porous bearing of the spindle motor these ideas were implemented and the mute level could be increased by a factor of optical disc drive systems is presented in the paper. An two. However, pre-loading the spindle motor will shorten the estimator-based SMC controller is used in the radial servo- motor lifetime, especially with the increase of the disc speed. loop instead of the traditional PID controller. Simulation Another way to increase the drive’s insensitivity to external and experimental results show a significant improvement of shocks and vibration disturbances is to develop a more robust the drive’s anti-shock performance in the radial direction. stable servo control system so that the laser spot stays on track at The same algorithm can be applied to the focus servo-loop. all times. Keywords: First appeared in the early sixties [4], the sliding mode control has been widely studied recently and has been successfully applied to robot manipulators, high-performance electric motors, automotive Servo, Anti-Shock, Sliding Mode Control, DVD engines and power systems [5,6], etc., due to its notable advantage of insensitivity to the disturbance and system uncertainties. This paper applies the SMC technique to the two-stage servo tracking 1. Introduction system of optical disc drive to improve the product shock and vibration performance. An observer based discrete-time sliding With the introduction and development of high density and high mode controller has been developed to control the fine actuator capacity optical discs (like digital versatile disc DVD), and with with improved tracking shock and vibration performance. increasing demands on higher data transfer rate, it becomes more challenging to provide the system margins which are necessary for reliable data playback. From a servo point of view, one of the major obstacles for reliability of read-out data is given by the 2. Problem Formulation internal and external disturbances. The most important disturbances present in optical disc mechanism are rotation of the Figure 1 illustrates the simplified block diagram of the spot disc, eccentricity and track irregularities, mechanical vibration and position control system during tracking for both focus and radial. shocks, and positioning sensing noise. The relative laser spot position error signal e(s) is detected by the optical pick up G1(s). The commonly used controller K(s) and the Control systems subject to periodic disturbances may well benefit actuator driver G2(s) feed the system with the currents. H(s) from the use of repetitive [1] and learning feedforward control. presents the transfer function from the control current to the radial But, maintaining the laser spot within acceptable limits of track or focus spot position. d(s) represents dynamic disturbances center under shock condition, especially when the shock or generated within the drive or from the external environment. This vibration lasts for a few milliseconds, is still a significant technical mainly includes radial and vertical track positions deviations challenge. As one of the importance quality ratings for the coming from disc unbalance, eccentricity, unroundness, etc., and compact disc system, a lot of effort has been put to improve the external disturbances from mechanical shocks and vibrations. The system shock immunity, especially, for optical data drives, reference signal r(s) predefines the reference situation at the disc. portable, Car CD/DVD players, etc. Some earlier research work It is given by the disc reflective laser in case of the focus control showed that, in order to obtain sufficient shock immunity, the loop, and by the center of the read-out track in case of the radial damping of the suspension should be higher and the servo gain at loop. Due to the spiral shaped track of the optical disc itself, the low frequencies should be sufficiently higher. Other research [2,3] laser spot along radial direction is controlled by the sledge- on the anti-shock system design for the Car CD system employed actuator radial loop with this PID-based controller to control the actuator fine displacements and the sledge positioning system to move the actuator outward at a slower space during tracking. According to the theory of Variable Structure Systems [4,5,9], the These two control systems form the two-stage servo tracking variations in the plant parameters and modeling uncertainties are system in the optical disc drive. matched only on the control channels. This means that by proper 0 selection of the control law, a total invariance to disturbances and Switch Control Electronics on PCB Tracking + parameter variations can be achieved on the sliding surface. For Xa - Sledge Sledge the discrete-time SISO system described by Eq. (1), the objective Seeking Track Controller Driver is to get the state x(k) of the actuator to track a desired time- counter varying state r(k) in the present of model uncertainty and disturbances. Consider a smooth sliding surface defined by: e(s) PID Controller Actuator Driver u(s) r(s) + K(s) G2(s) S(k) = ge(k) - = d(s) e(k) r(k) - x(k) (2) Xs + Position Detector Xa Radial Actuator = G1(s) H(s) where g is the constant row vector selected such that S(k) 0 + defines a stable sliding surface or sliding mode in the state space, the actuator desired tracking position invariant to disturbances or Sledge OPU Motor dynamic uncertainties. The convenient reaching condition for the discrete system to Figure 1. Simplified block diagram of the radial control guarantee the existence of the ideal sliding mode is given by [10]: Disturbances caused by the deviation from the nominal position, S(k +1) = (1- η)S(k) - εsgn(S(k)); ε > 0, η > 0 (3) rotation of the disk, eccentricity and track irregularities, etc., can be well regulated or controlled by the present PID controller and where ε is the control gain of SMC, and η is a positive constant some learning control algorithm [1,7,8] during tracking. However, affecting the response in the reaching phase. The system states the conventional PID controllers and the learning algorithms are will move monotonically toward the sliding surface from any no more effective to overcome the non-linear movement of the initial state when the reaching condition is met. The sliding track on the disc relative to the laser spot in the present of external manifold is attractive under the given reaching condition, which shock and mechanical vibration disturbances. Robustness to the can be proven using the Lyapunov Stability Theory [5]. modeling errors is also not guaranteed in the entire operating range. All these uncertainties of the system lead to the application Substituting equations (2) and (1) into (3), the equivalent control of SMC techniques to the servo system design. An observer based law to steer the errors from any finite value to the sliding surface SMC controller is developed here to replace the traditional linear and keep the state on the surface in the face of unknown PID controller for the optical disc drive servo system. Here, the disturbances can be then given by: radial direction, which has been proved to be the most critical, is investigated. The same algorithm is applicable to the focus loop. − u(k) = (gb ) 1{g[((1−η)I − A )x(k) d d (4) +ηr(k) + ∆r(k) − d(k)]+ ε sgn(S(k))} 3. Design of SMC for Radial Servo System where ∆r(k) = r(k +1) − r(k) . As can be seen in the equation The discrete-time state equations of the radial actuator for a general optical drive can be described as: (4), the control switching across the surface S(k) = 0 is necessarily imperfect in implementation. This would lead to + = + + x(k 1) A d x(k) b d u(k) d(k) control chattering, which is highly undesirable in practice since it (1) y(k) = c x(k) involves high control activity and may excite unmodeled high- d frequency dynamics. Smoothing out the control discontinuity in a thin boundary layer neighboring the switching surface is generally Where x(k) = [x(k) V (k)]T is the state vector consisting of the used to eliminate the control chattering. The equivalent control law can be then expressed as: radial actuator position x [m] and the radial actuator velocity V [m/s] at discrete time kT . Notice that this second order model = −1 −η − +η describes the rigid body dynamics of the actuator only. u(k) (gb d ) {g[((1 )I A d )x(k) r(k) Measurements show that in the frequency range of interest this is a S(k) (5) + ∆r(k) − d(k)]+ εsat( )} valid assumption (see also Figure 2). u is the scalar input. d Φ represents disturbances coming from mechanical shock and vibration, and is bounded according to the commercial where Φ is the boundary layer thickness, and sat(.) is the specification. y is a scalar output. A d , b d , and c d are saturation function.
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