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At bit densities now approaching 1 terabit per square inch, positioning the read-write head in a hard disk drive over data bits will require novel servo configurations and controllers. This paper presents a MEMS microactuator for installation in a dual-stage servo system for a hard disk drive and controller designs that utilize the microactuator to...
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... storage densities in hard disk drives increase, it becomes ever more difficult to position the read-write head over shrinking magnetic bits. Conventional disk drives position the read-write head using a single large voice-coil motor (VCM) that swings the read-write head across the disk on an arm and pivot consisting of a suspension and E-block (see figure 1). Unfortu- nately, airflow-induced vibration of suspension and E- block resonant modes disturbs this servo arm. ...
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... system performance can also benefit from dedi- cated vibration sensing, in the form of an instrumented suspension. Such a suspension incorporates strain sen- sors on the suspension (see Figure 1b). These can de- tect vibration at higher sampling rates than may be ob- tained from a drive's position error signal. ...
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... The first part of the PQ method directly addresses the issue of actuator interference as a function of frequency, and the second part allows the use of traditional loop shaping tech- niques to achieve the desired system performance. The reader is referred to (Schroeck and Messner, 1999) for more details of this method. Simulation results in Fig. 10 show the closed-loop sen- sitivity of the dual-stage system based on the identi- fied model when both RPES and instrumented suspen- sion are available. The closed-loop servo bandwidth is about 2.1 kHz, with enough low-frequency error rejection and a mild peak of 7.2 dB. The projected rms tracking error of such a system is 4.8 ...
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... the previous section. Without inner loop damping control of the suspension and MA, the PQ method can still be applied to design a track-following controller, but the servo bandwidth is only 650 Hz. Nevertheless, experimental measure- ments of the closed loop system verify operation of the current dual-stage setup and accuracy of the system model. Fig. 11 shows agreement between the pre- dicted and experimental sensitivity function, except near the flex cable vibration mode. Fig. 12 shows the significant closed-loop improvement of the PES power spectrum at low frequencies. Total rms tracking error of the system is reduced from 764 nm in the open-loop system to 10.8 nm in the closed-loop ...
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... track-following controller, but the servo bandwidth is only 650 Hz. Nevertheless, experimental measure- ments of the closed loop system verify operation of the current dual-stage setup and accuracy of the system model. Fig. 11 shows agreement between the pre- dicted and experimental sensitivity function, except near the flex cable vibration mode. Fig. 12 shows the significant closed-loop improvement of the PES power spectrum at low frequencies. Total rms tracking error of the system is reduced from 764 nm in the open-loop system to 10.8 nm in the closed-loop system. A robust, high force microactuator has been fabricated and used to suppress vibration in a dual-stage control scheme for ...
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Citations
... Coupled systems reported in the literature are in diverse areas including structural systems with active control [e.g., Haftka et al. (1986); Rao and Pan (1990)], micro-electrical mechanical systems, or MEMS [e.g., Carley et al. (2001); Oldham et al. (2005)], and robotics and mechatronics [e.g., Ravichandran et al. (2006); Zhu et al. (2001)]. In robotic applications, typical objectives for the artifact design are minimizing weight or minimizing deflection. ...
Optimization of a ‘smart’ product requires optimizing the design of both the physical system, or artifact, and its controller. If the artifact and control optimization are coupled, then a combined approach is typically used in order to produce optimal solutions. The combined approach presents certain disadvantages, however. This combined approach obviates a natural decomposition of the problem into smaller design and control sub-problems that can be a disadvantage from a modeling and solution practicality viewpoint. In this paper, it is shown that a modified sequential approach utilizing a Control Proxy Function (CPF) can be used to produce optimal, or near-optimal, solutions while allowing this decomposition. Two physical bases for CPFs are presented, natural frequency and the controllability Grammian matrix, and their range of applicability is discussed. These concepts are demonstrated, for a positioning gantry example and on an active/passive automotive suspension, to be quite effective.
... These include structural systems with active control (e.g., Refs.123), micro-electrical mechanical systems (MEMS, e.g., Refs. [4, 5]), and robotics and mechatronics (e.g., Refs.678). The experimental and analytical studies have shown that coupling must be considered and addressed and that doing so can present significant challenges (e.g., Refs.9101112). ...
Optimal system design of smart products requires optimization of both the artifact and its controller. When the artifact and the controller designs are independent, the system solution is straightforward through sequential optimization. When the designs are coupled, combined simultaneous optimization can produce system-optimal results, but presents significant computational and organizational complexity. This paper presents a method that produces results comparable with those found with a simultaneous solution strategy, but with the simplicity of the sequential strategy. The artifact objective function is augmented by a control proxy function (CPF), representing the artifact's ease of control. The key to successful use of this method is the selection of an appropriate CPF. Four theorems that govern the choice and evaluation of a CPF are given. Each theorem is illustrated using a simple mathematical example. Specific CPFs are then presented for particular problem formulations, and the method is applied to the optimal design and control of a micro-electrical mechanical system actuator.
... The development of 'smart' products will solve a wide range of problems in diverse fields. Some applications are structures with active control [1], [2], [3], mechatronics [4], [5], mechanisms [6], [7], and microelectrical mechanical systems (MEMS) [8], [9], [10]. Smart products consist of both a physical system, or artifact, and a controller. ...
Optimization of smart products requires optimizing the design of both the artifact and its controller. The existence of coupling between these problems currently cannot be established until they are solved. If coupling is expected to be present, then the problem is often solved as a simultaneous optimization. In this paper, it is shown that in several classical control problem formulations the presence of coupling can be established a priori by evaluating derivatives of the controllability Grammian. The concepts developed are demonstrated on a simple positioning gantry example.
... To overcome this challenge, a class of dual-stage actuators for HDDs has been proposed [3]–[8] . A microactuator (MA) is placed at the end of the suspension and moves the slider/head relative to the suspension tip, increasing servo bandwidth [9]. A dual-stage servo system using enhanced active-passive piezoelectric actuators was proposed in [7]. ...
This paper presents a novel technique for designing robust track-following output-feedback controllers in hard disk drives (HDDs). In this paper, the manufacturing variations of HDDs are modeled as polytopic parametric uncertainties in linear time-invariant discrete-time systems. For this model, the robust track-following control problem is formulated as the worst-case H<sub>2</sub> performance optimization. The optimization problem reduces to the one with bilinear matrix inequalities (BMIs), using the parameter dependent Lyapunov functions and the extended LMI condition introduced by de Oliveira. Although the formulated problem is nonconvex, and thus it is difficult to ensure global optimality, a numerical technique called ??G- K iteration?? is applied for optimization to guarantee monotonic non-increase of the worst-case performance during iterations. The proposed design technique will be useful in improving the track-following performance, and thus increasing the storage capacity of HDDs.
... To help achieve the desired level of performance, the use of a secondary actuator has been proposed to give increased precision in read/write head positioning . In this paper, we use a microactuator (MA) which directly actuates the head/slider assembly with respect to the suspension tip and generates measurements of the head MA displacement [8]. We will refer to these measurements as the relative position error signal (RPES). ...
This paper considers the problem of finding a controller for a discrete time linear periodically time-varying system with structured parametric uncertainty which achieves robust ℓ2 semi-norm performance (the equivalent of robust H2 norm performance for time-varying systems). This problem is shown to be a generalization of a guaranteed cost control problem when the structure of the uncertainty is neglected. To reduce the conservatism when the uncertainty structure is considered, static uncertainty scalings such as those used in the D-K iteration heuristic for μ-synthesis are introduced. Although the problem of simultaneously optimizing the controller and uncertainty scalings in non-convex, it is shown that it lends itself to a solution methodology conceptually similar to D-K iteration in which each step is a convex optimization. To demonstrate the effectiveness of the developed methodology, the control of a set of hard disk drives with multirate sampling characteristics and uncertain parameters is considered and a controller is designed which minimizes the worst-case ℓ2 semi-norm performance of the system. It is then shown that the resulting robust controller achieves worst-case ℓ2 semi-norm performance which is comparable to the best achievable ℓ2 semi-norm performance for the nominal system.
... Differential parallel-plate arrays are interlaced using deep-trench isolation. This feature along with high-aspect ratio trenches produced by deep reactive-ion etching (DRIE) result in excellent force generation, as has been described in previous publications [11] [12]. The differential configuration results in an actuation force that is linear to within 5% over a 1 µm stroke length. ...
Dual-stage servo systems have been proposed as a method for attaining increased bit densities from computer hard disk drives. To aid in controller operation, the second-stage microactuator used in a dual-stage system should operate at low voltages, feature relative position sensing, and have dynamics that interact well with the dynamics of the original drive servo. This paper describes a high-aspect ratio electrostatic microactuator modified to improve dynamic interactions, relative position sensor performance, and device yield. A multi-rate, multivariable control design technique was used to evaluate the closed- loop performance of a disk drive system with a microactuator and relative position sensing. Closed-loop simulations reveal that the proposed configuration can reduce off-track position error. Addressing both hardware design and control design, this paper demonstrates the success of an integrated mechatronic approach to hard disk drive servo control.
... In this paper we use a microactuator (MA) which directly actuates the head/slider assembly with respect to the suspension tip and generates MA displacement (RPES) measurements [6]. With this in mind, we would like to find controllers which minimize the PES variance subject to keeping the variance of each control input smaller than prescribed bounds. ...
... To help achieve this goal, the use of a secondary actuator has been proposed to give increased precision in read/write head positioning. In this paper we use a microactuator (MA) which directly actuates the head/slider assembly with respect to the suspension tip and generates MA displacement (RPES) measurements [6]. With this in mind, we ...
In this paper, we present a new algorithm for solving the LQG control problem with variance constraints which utilizes derivative information about the relevant H 2 costs to achieve quasi-Newton convergence. Using a lifting procedure, this algo-rithm is then generalized to work with linear periodically time-varying systems. This algorithm is then applied to the design of controllers for hard disk drives in order to assess the limits of performance of a particular setup. It is demonstrated that just by utilizing multirate sampling and actuation characteristics (i.e. without changing the hardware), the performance of this partic-ular setup can improved by more than 39%. 1 INTRODUCTION In the field of optimal control, control design problems are typically formulated as the minimization of a scalar cost func-tion involving the closed loop system. However, in real-world applications, it is often difficult to capture the tradeoffs inherent in controller design with a scalar cost function; the controller de-sign process is inherently multiobjective in nature. One example of such a control design problem is the minimization of the vari-ance of one closed loop signal subject to variance constraints on several other closed loop signals. This problem is known as the LQG control problem with variance constraints. In addition to being a useful tool for practical controller design, it is also use-ful as a mechatronic design tool to determine the limitations of performance of a given system. This can be used, for example, to compare several different hardware setups by determining the best possible closed loop performance that can be achieved for each one [1].
... The actuated slider approach results in a truly collocated system without exciting the structural resonance modes of the suspension and gimbal. Besides, the microactuator usually has very clean dynamic responses: it has a single spring-mass mode in the frequency range of 1-3 kHz, and there are no other significant modes up to 40 kHz [5][4][6]. With MEMS fabrication and integration techniques, the MEMS MA can be batch-fabricated and micro-assembled with the head and the gimbal on the suspension. ...
... There are two types of MEMS MAs: rotational [3] and translational [4][6]. In the rotational MA case, the actuation of the VCM and MA can be viewed as being decoupled with each other, i.e., each actuator contributes to the head motion independently, resulting in a truly parallel structure. ...
This paper presents the design and analysis of a dual-stage servo system with an instrumented suspension for use in hard disk drives. The dual-stage system is equipped with a microelectromechanical system microactuator (MA), either rotational or translational, as a secondary actuator. In both cases, the MA has a resonance mode at 2.2 kHz and has virtually no other modes up to 40 kHz. Two design approaches, the sensitivity decoupling design and the multiobjective optimization, are applied to the design of the servo system. With either approach, the translational dual-stage actuator achieves better tracking performance than the rotational one by about 13%, which is achieved mainly by attenuating airflow-excited suspension vibrations. This improvement is significant when the servo system's track misregistration (TMR) budget approaches the level of 5-10 nm. The airflow-excited suspension vibrations then become a significant contribution to the TMR
... where A m , ζ m and ω m are respectively the constant gain, the damping ratio and the natural frequency of the MA plant. Experimental results have verified that the transfer function in (4) accurately describes the dynamics of the MA [11]. However, because of fabrication variations, the parameters in (4) may vary from one MA to another. ...
... The sequence {Γ(k)} k≥0 captures the multi-rateness of our problem; at even times, we sample all the measurements, while at odd times, we cannot measurê y pes because of its slow sampling rate. Similarly, we can express the hold H as (11) where we take Ω(k) = I 2 for all k. This means that we send both control signals at the fast sampling rate of 50kHz, in order to achieve high track-following performance of the closed-loop system. ...
This paper proposes a multirate design method for robust track-following controllers in hard disk drives (HDDs). The HDDs to be considered are dual-stage multi-sensing systems. A track-following problem, which takes into account robust stability, is formulated as a periodic time-varying version of the standard mixed H 2 /H ∞ control problem. This problem is solved via the solution of linear matrix inequalities. Simulation results show that multirate controllers can achieve much better track-following performance than single-rate controllers, while achieving the same guaranteed robust stability margin.
