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Optimal controllers and adaptive controllers for multichannel feedforward control of stochastic disturbances

Optimal controllers and adaptive controllers for multichannel feedforward control of stochastic disturbances
Optimal controllers and adaptive controllers for multichannel feedforward control of stochastic disturbances
A time domain formulation for the multichannel feedforward control problem is used to derive an optimally condition for the least squares controller. It is also used to motivate an instantaneous steepest descent algorithm for the adaptation of the controller, which is known as the filtered error LMS algorithm. The convergence rate of this algorithm is limited by the correlation properties of each reference signal, their cross-correlation properties and the dynamics and coupling within the plant response. An expression is then derived for the transfer function of the optimum least squares controller. This suggests a new architecture for the adaptive controller whose convergence rate is not limited by the factors mentioned above. A set of white and uncorrelated reference signals are generated to drive a modified matrix of control filters, whose outputs are multiplied by the inverse of the minimum phase part of the plant response matrix before being fed to the physical plant. The error signals from the plant are then used to update this controller after being fed through the time-reverse transpose of the all-pass part of the plant matrix. The relationship is also discussed between this architecture and that using a singular value decomposition of the plant response, which is used to control tonal disturbances.
1053-587X
1053-60
Elliott, S.J.
4d1787f2-dcac-4ede-bc41-82ed658a9fac
Elliott, S.J.
4d1787f2-dcac-4ede-bc41-82ed658a9fac

Elliott, S.J. (2000) Optimal controllers and adaptive controllers for multichannel feedforward control of stochastic disturbances. IEEE Transactions on Signal Processing, 48 (4), 1053-60. (doi:10.1109/78.827539).

Record type: Article

Abstract

A time domain formulation for the multichannel feedforward control problem is used to derive an optimally condition for the least squares controller. It is also used to motivate an instantaneous steepest descent algorithm for the adaptation of the controller, which is known as the filtered error LMS algorithm. The convergence rate of this algorithm is limited by the correlation properties of each reference signal, their cross-correlation properties and the dynamics and coupling within the plant response. An expression is then derived for the transfer function of the optimum least squares controller. This suggests a new architecture for the adaptive controller whose convergence rate is not limited by the factors mentioned above. A set of white and uncorrelated reference signals are generated to drive a modified matrix of control filters, whose outputs are multiplied by the inverse of the minimum phase part of the plant response matrix before being fed to the physical plant. The error signals from the plant are then used to update this controller after being fed through the time-reverse transpose of the all-pass part of the plant matrix. The relationship is also discussed between this architecture and that using a singular value decomposition of the plant response, which is used to control tonal disturbances.

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Published date: 2000

Identifiers

Local EPrints ID: 10783
URI: https://eprints.soton.ac.uk/id/eprint/10783
ISSN: 1053-587X
PURE UUID: b3608ce5-b86e-4e5a-b88d-311857976298

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Date deposited: 29 Apr 2005
Last modified: 17 Jul 2017 17:05

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Author: S.J. Elliott

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