1. Schematic of Hard Disk Drive with PZT-actuator 

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... chapter demonstrates the use of anti-windup compensation in the control loop of a micro-actuator which is nominally controlled by a linear, discrete robust controller. The micro-actuator is part of a hard disk drive dual-stage servo-control system for positioning of the read/write head. The actuator inputs are constrained to retain the micro-actuator’s displacement range of less than 0.4 μ m for mechanical protection. In the first part of the chapter, the anti-windup compensation scheme exemplifies an approach suggested by Weston & Postlethwaite [22]. Here, the scheme is posed as a discrete full-order compensator and the closed loop analysis uses a generalized circle citerion approach. The design of the compensator is posed in LMI-form. In the second part of the chapter, it is shown how the linear micro-actuator control loop with anti-windup compensation is incorporated into the non-linear servo-control scheme for positioning of the read/write head in a hard disk drive. Micro-actuators have been gaining of importance in practical systems during recent years. For instance, it is nowadays the target to integrate actuator, sensor and elec- tronics for powerful computations in one device of micro or nano-scale. These tech- nologies can be useful in optical communication systems, in electromechanical signal processing systems or in healthcare systems, such as BIO-MEMS for microchip- lab diagnostics or micro-devices for therapeutic targeting and delivery. Mechanical micro-actuators for nano-positioning have been of interest for the University of Leicester due to its importance in the servo-controller for the positioning of the read- write head in hard disk data-storage systems [5, 8, 11]. A micro-actuator is being used in a dual-stage control system to achieve high-banwidth positioning control. Significant research effort on hard-disk drive (HDD)-servo techniques has been in- vested in the area of dual-stage servo control [17, 18, 14]. The reason for this is the continuous increase in the track density and in storage capacity of HDDs. Recently, a track density of above 420 kTPI (TPI- track per inch) has been demonstrated (see [23, 2]) in a laboratory environment and about 149 kTPI density HDDs are nowadays available in the consumer market. In addition to the significant increase in data density, the increased demand for higher data rates requires the improved performance of the head-positioning servo system in a hard disk drive. A promising way to meet these demands is to augment the conventional voice coil motor (VCM) actuator with a second-stage, high bandwidth micro-actuator. Dual-stage servo systems in HDDs are now a feasible alternative to the single stage VCM-servo system. PZT-based micro-actuators using PZT-elements embedded in the head suspension are popular, e.g. the ‘FUMA’-actuator in [19] (Figure 1.1). However, the displacement range of secondary actuators is very limited, typically less than 1-2 μ m, and the input signal for the actuator is limited to prevent damage. In dual-stage servo-systems, the two actuators have to deal with the following servo-tasks: seek/settling and track following. Seek/settling control has to ensure a fast movement of the read/write head from one track to another. For track following, high bandwidth controllers are necessary to ensure good error rejection capabilities while counteracting disturbances. Therefore, the primary VCM-actuator is required for larger displacement and the secondary actuator provides large bandwidth. For servo-control of such a dual-stage actuator system, the method of [11, 12] is employed. It is based on a well known decoupled dual-stage controller structure of [13], where design and stability for the primary VCM-control loop and the secondary PZT-control loop are guaranteed independently. It will be shown [11, 12] that the primary and secondary loop remain stable independently regardless of the seek/settling/track-following control method used for the VCM-loop, providing the secondary control loop is stable in the presence of saturation limits. Hence, it seems logical to use for the secondary loop an AW compensator to guarantee overall large and small signal stability despite actuator saturation limits. AW compensators are most suitable, as they have been developed to retain the nominal performance of the original control system [9, 7, 20], e.g. high-bandwidth tracking in the servo-control of hard disk drives. This example study on AW-compensation will consider the following issues: 1. controller design for the micro-actuator loop and wind-up problems due actuator limits, 2. discrete anti-windup compensator design, anti-windup compensation for the micro-actuator control loop 3. the micro-actuator control loop as part of the overall seek-settling scheme for the hard disk ...

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... application of this computed AW-compensator to the control system of Section 1.2 with saturation limit improves the closed loop ( Figure 1.13). The oscillations ob- served without AW-compensation are minimized and the lag seems to be eradicated (Figure 1.13 and 1.10) for the sine sweep with 1 μ m amplitude. Thus, AW-compensation can achieve a significantly improved tracking performance considering the fact that the micro-actuator has a displacement limit of about ± 0 . 5 μ m . The micro-controller is to be incorporated into the control scheme for the servo- control of a hard disk drive actuator. The micro-actuator is directly embedded in the suspension of the voice-coil motor (VCM) actuator (Figure 1.1). A linear model of the actuator is given by the superposition of the two models of the PZT-actuator, P , and the VCM-actuator, P : The VCM actuator can be modeled as a double integrator which is affected by high frequency resonances and the dynamics of friction in low frequency. The VCM- actuator is usually controlled by a (proximate)-time-optimal control scheme [3, 6, 11] which achieves fast seeking for fast positioning of the read/write head, while a smooth transfer to a linear track-following scheme needs to be achieved for track- following (see [3, 6, 11] for a more detailed explanation). To achieve a higher track- following controller bandwidth, the secondary PZT-actuator is used. The constraints on both actuators (in particular for the PZT-actuator) need to be incorporated into the servo-control scheme. The approach is to use a decoupled control scheme as from [13], which incorporates the traditional time-optimal seek-settling scheme for the VCM-actuator [6, 11] and it allows an independent controller design for the PZT- micro-actuator so that the controller design of Sections 1.2-1.3 can be reused. The control scheme works on the assumption that the absolute position of the PZT-micro- actuator is measurable (see Figure 1.14). Employing the superposition principle, it is easily seen that the control scheme of Figure 1.14 is equivalent to the controller configuration of Figure 1.15, where the control loops for the PZT and the VCM-actuator are decoupled. Hence, both controllers can be designed independently in terms of stability. For the implementation of the scheme, it is necessary to use an observer which obtains the absolute position of the PZT-actuator (see Figure 1.16). It is easily verified that observer and controller separate due to the linearity of the plant. Using now a non-linear seek-settle control scheme for the VCM-actuator as pre- sented in [6, 11] and the linear control loop from Sections 1.2-1.3 with and without anti-windup compensation for the controller of the PZT-actuator, it is easily verified that the AW-compensation scheme significantly improves on seeking performance (see Figures 1.17 and 1.18). The controller with AW-compensation prevents for a 2 μ m -seek step a very large overshoot and allows fast settling to assume track following of the read/write head as quickly as possible. The control system of a PZT-micro-actuator has been investigated for its feasible range, i.e. the available displacement range of the micro-actuator. It has been shown that anti-windup compensation can improve tracking of demands which are not feasible. It limits controller lags and suppresses high frequency resonances for a practically valid hard disk drive micro-actuator. In connection with the recently established dual-stage track-seek/following scheme [6, 11], it has been shown that the AW-compensator suppresses large overshoots and enhances settling ...