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Numerically Efficient Estimator Structures for Dasd Digital Servo

IP.com Disclosure Number: IPCOM000036092D
Original Publication Date: 1989-Sep-01
Included in the Prior Art Database: 2005-Jan-28
Document File: 4 page(s) / 120K

Publishing Venue

IBM

Related People

Ottesen, H: AUTHOR [+3]

Abstract

The digital servos used in magnetic disk drives employ a state variable-based estimator/controller to achieve seek/tracking performance. The standard structure of a servo algorithm does not take advantage of the control law structure in order to reduce computation time and numerical round-off errors. A compressed form of the estimator/controller structure that reduces the number of multiplications by a factor of (1/n+3) and summations by (1+(1/n))/(n+2) is disclosed herein (where n is the model order of the combined estimator/ (Image Omitted) controller). The compression reduces the computation time as well as noise contribution due to multiplication-based round-off errors. The algorithm is valid only when the controller is linear, which is in fact the case in the track-following mode.

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Numerically Efficient Estimator Structures for Dasd Digital Servo

The digital servos used in magnetic disk drives employ a state variable- based estimator/controller to achieve seek/tracking performance. The standard structure of a servo algorithm does not take advantage of the control law structure in order to reduce computation time and numerical round-off errors. A compressed form of the estimator/controller structure that reduces the number of multiplications by a factor of (1/n+3) and summations by (1+(1/n))/(n+2) is disclosed herein (where n is the model order of the combined estimator/

(Image Omitted)

controller). The compression reduces the computation time as well as noise contribution due to multiplication-based round-off errors. The algorithm is valid only when the controller is linear, which is in fact the case in the track-following mode. Further, the problem of taking the difference between two large numbers,
i.e., residue computation, using a finite word-length microprocessor is avoided by this algorithm. Two modified structures are also presented that either allow control law saturation, or avoid residue computation.

Using conventional notations the standard estimator/controller structure is shown in Fig. 1, and is referred to as structure-1. The number of arithmetic operations are shown next to each operational block in all the figures used. The computation involved in structure-1 is summarized below: State Update: x(+) = x(-) + L(Zn-Hx(-)) State Extrapolation: x(-) = Dx(+) + Tun-1 Controller Output: un = -Kx(+)

Note that in the state update the residue computation is explicitly carried out. The control law is assumed to be linear, but the estimator in structure-1 can in fact accommodate any input value, Un-1, including that with saturation. In a disk drive environment with

(Image Omitted)

digital sector servo, the position error signal (PES) is directly latched into the processor and utilized in the estimator without gain adjustment. Also, PES is the only output measurement that is used for state update. Therefore, only a single subtraction and no multiplication operation is assumed in the residue computation. (However, the results can be extended to a multi-input, multi- output system without any restriction where H may be a full matrix.) With this assumption, the state update requires n multiplications and n+1 summations, state extrapolation requires (n*n+n) multiplications and n*(n-1) + n summations, and control law requires n multiplications and (n-1) summations.

Assuming a linear control law, and by regrouping the state update term with a substitution for the extrapolated state x(-), structure-2 shown in Fig. 2 is obtained. The computations involved in structure-2 are: State Update: x(+) = Xn + Lzn State Extrapolation: xn = (l - LH)D - (l - LH)TK xn-1(+) Controller Output: un = - Kx(+)

1

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From Fig....