Ryozo Nagamune

Robust dynamic modeling and control of dual-stage actuators

In a hard disk drive with a dual-stage actuator the standard rotary actuation of the voice coil motor (VCM) is combined with an additional micro- or milli-actuation to accomplish high-bandwidth and highly accurate track following. For extremely high density recording, the servo control algorithm designed for a specific dual-stage actuator needs to maintain high performance track following in lieu of external disturbances and uncertainties in the dynamic response induced by product manufacturing tolerances. Essential in the robust design of a servo control algorithm is to bound these uncertainties and design a robust track following servos accordingly. In this paper, we present an experiment based methodology to characterize and bound the uncertainties in the dynamic response of a dual-stage actuator in the form of an uncertainty model. Subsequently, the uncertainty model is used for the analysis and synthesis of a robust dual-stage servo controller that is able to optimize position error variance in the presence of uncertainty information.

A comparison of multirate robust track-following control synthesis techniques for dual-stage and multisensing servo systems in hard disk drives

This paper presents the design and analysis of multirate robust track-following controllers for a dual-stage servo system with a MEMS microactuator (MA) and an instrumented suspension. Two major categories of controller design methodologies are considered. The first is based on sequential single-input single-output (SISO) design techniques, and includes the sensitivity decoupling (SD) method and the PQ method. High rate inner loop damping control is implemented followed by a low rate outer loop controller. The second category is based on multirate, multi-input multi-output (MIMO) design techniques, including mixed H2/Hinfin, mixed H2/mu and robust H2 synthesis. In this case, a set of controllers are designed all at once by explicitly considering plant uncertainty and hence robust stability. Comparisons are made between these design techniques in terms of nominal H2 performance, robust stability, and robust performance. The advantages and disadvantages of each of these methods are discussed, as well as the guidelines for practical implementation

Multirate track-following control with robust stability for a dual-stage multi-sensing servo system in HDDs

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 H2/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.

Closed-loop shaping based on Nevanlinna-Pick interpolation with a degree bound

This note presents a novel method for shaping the frequency response of a single-input-single-output closed-loop system, based on the theory of Nevanlinna-Pick interpolation with degree constraint. The method imposes a degree bound on the closed-loop transfer function and searches for a function with a desired frequency response. Numerical examples illustrate the potential of the method in designing controllers with lower degrees than the ones obtained by conventional H/sup /spl infin// controller design methods with weighting functions.

Sensitivity shaping with degree constraint by nonlinear least-squares optimization

This paper presents a new approach to shaping of the frequency response of the sensitivity function. A sensitivity shaping problem is formulated as an approximation problem relative to a desired frequency response and with respect to a function in a class of sensitivity functions with a degree bound. It is reduced to a finite dimensional constrained nonlinear least-squares optimization problem. A numerical example illustrates that the proposed method generates controllers of relatively low degrees.

Computation of bounded degree Nevanlinna-Pick interpolants by solving nonlinear equations

This paper provides a procedure for computing scalar real rational Nevanlinna-Pick interpolants of a bounded degree. It applies to a wider class of interpolation problems and seems numerically more reliable than previous, optimization-based, procedures. It is based on the existence and the uniqueness of the solution guaranteed by Georgious proof of bijectivity of a map between a class of nonnegative trigonometric polynomials and a class of numerator/denominator polynomial pairs of interpolants. Further analysis of this map suggests a numerical continuation method for determining the interpolant from a system of nonlinear equations. A numerical example illustrates the reliability of the proposed procedure.

Robust H2 Synthesis for Dual-stage Multi-sensing Track-following Servo Systems in HDDs

This paper presents a robust H2 synthesis technique for designing a track-following servo system for a hard disk drive (HDD) product line. The goal is to design a single robust controller that minimizes the worst case H2 performance of an entire disk drive product line, assuming that dynamic variations in the product line (i.e. variations from one unit to another) are accurately characterized by affine variations in several of the actuators model parameters, such as variations in the resonance frequency or damping ratio of a resonance mode. The advantages and disadvantages of the proposed method are discussed and an illustrative realistic example is presented

An extension of a Nevanlinna-Pick interpolation solver to cases including derivative constraints

This paper extends a previously proposed solver for scalar Nevanlinna-Pick interpolation problems with degree constraint to the ones including derivative constraints. The solver computes any real rational interpolant with a degree bound by solving an optimization problem of the same type as encountered in the problem without derivative constraint. A robust homotopy continuation method, previously devised by the second author for the problem without derivative constraint, can be applied to solve the new optimization problem.

A shaping limitation of rational sensitivity functions with a degree constraint

This note concerns a certain shaping limitation of sensitivity functions. The focus is on a frequency-wise infimum of gains of rational sensitivity functions with a degree constraint. An explicit infimum is derived for a special case. The result is useful for determining the inability of sensitivity functions of low degrees to achieve a specification in the frequency domain, and thus for motivating the use of higher degree sensitivity functions to fulfill the specification.

Optimization-based computation of analytic interpolants of bounded complexity

This paper provides a unifying algorithm for computing any analytic interpolant of bounded complexity. Such computation can be performed by solving an optimization problem, due to a theorem by Georgiou and Lindquist. This optimization problem is numerically solvable by a continuation method. The proposed numerical algorithm is useful, among other cases, for designing a low-degree controller for a benchmark problem in robust control. The algorithm unifies previously developed algorithms for the Caratheodory extension and the Nevanlinna–Pick interpolation to one for more general interpolation problems.