H 2 -optimal rejection with preview: geometric constraints and dynamic feedforward solutions via spectral factorization

Elena Zattoni

Kybernetika (2008)

  • Volume: 44, Issue: 1, page 3-16
  • ISSN: 0023-5954

Abstract

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In this work, a feedforward dynamic controller is devised in order to achieve H2-optimal rejection of signals known with finite preview, in discrete-time systems. The feedforward approach requires plant stability and, more generally, robustness with respect to parameter uncertainties. On standard assumptions, those properties can be guaranteed by output dynamic feedback, while dynamic feedforward is specifically aimed at taking advantage of the available preview of the signals to be rejected, in compliance with a two- degree-of-freedom control structure. The geometric constraints which prevent achievement of perfect rejection are first discussed. Then, the procedure for the design of the feedforward dynamic compensator is presented. Since the approach proposed in this work is based on spectral factorization via Riccati equation of a real rational matrix function directly related to the original to-be-controlled system, the delays introduced to model the preview of the signals to be rejected do not affect the computational burden intrinsic in the solution of the appropriate algebraic Riccati equation. A numerical example helps to illustrate the geometric constraints and the procedure for the design of the feedforward dynamic unit.

How to cite

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Zattoni, Elena. "$H_2$-optimal rejection with preview: geometric constraints and dynamic feedforward solutions via spectral factorization." Kybernetika 44.1 (2008): 3-16. <http://eudml.org/doc/33908>.

@article{Zattoni2008,
abstract = {In this work, a feedforward dynamic controller is devised in order to achieve H2-optimal rejection of signals known with finite preview, in discrete-time systems. The feedforward approach requires plant stability and, more generally, robustness with respect to parameter uncertainties. On standard assumptions, those properties can be guaranteed by output dynamic feedback, while dynamic feedforward is specifically aimed at taking advantage of the available preview of the signals to be rejected, in compliance with a two- degree-of-freedom control structure. The geometric constraints which prevent achievement of perfect rejection are first discussed. Then, the procedure for the design of the feedforward dynamic compensator is presented. Since the approach proposed in this work is based on spectral factorization via Riccati equation of a real rational matrix function directly related to the original to-be-controlled system, the delays introduced to model the preview of the signals to be rejected do not affect the computational burden intrinsic in the solution of the appropriate algebraic Riccati equation. A numerical example helps to illustrate the geometric constraints and the procedure for the design of the feedforward dynamic unit.},
author = {Zattoni, Elena},
journal = {Kybernetika},
keywords = {optimal design; geometric approach; linear systems; discrete- time systems; optimal design; geometric approach; linear systems; discrete-time systems},
language = {eng},
number = {1},
pages = {3-16},
publisher = {Institute of Information Theory and Automation AS CR},
title = {$H_2$-optimal rejection with preview: geometric constraints and dynamic feedforward solutions via spectral factorization},
url = {http://eudml.org/doc/33908},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Zattoni, Elena
TI - $H_2$-optimal rejection with preview: geometric constraints and dynamic feedforward solutions via spectral factorization
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 1
SP - 3
EP - 16
AB - In this work, a feedforward dynamic controller is devised in order to achieve H2-optimal rejection of signals known with finite preview, in discrete-time systems. The feedforward approach requires plant stability and, more generally, robustness with respect to parameter uncertainties. On standard assumptions, those properties can be guaranteed by output dynamic feedback, while dynamic feedforward is specifically aimed at taking advantage of the available preview of the signals to be rejected, in compliance with a two- degree-of-freedom control structure. The geometric constraints which prevent achievement of perfect rejection are first discussed. Then, the procedure for the design of the feedforward dynamic compensator is presented. Since the approach proposed in this work is based on spectral factorization via Riccati equation of a real rational matrix function directly related to the original to-be-controlled system, the delays introduced to model the preview of the signals to be rejected do not affect the computational burden intrinsic in the solution of the appropriate algebraic Riccati equation. A numerical example helps to illustrate the geometric constraints and the procedure for the design of the feedforward dynamic unit.
LA - eng
KW - optimal design; geometric approach; linear systems; discrete- time systems; optimal design; geometric approach; linear systems; discrete-time systems
UR - http://eudml.org/doc/33908
ER -

References

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