Robust fractional adaptive control based on the strictly Positive Realness Condition

Samir Ladaci; Abdelfatah Charef; Jean Jacques Loiseau

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 1, page 69-76
  • ISSN: 1641-876X

Abstract

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This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.

How to cite

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Samir Ladaci, Abdelfatah Charef, and Jean Jacques Loiseau. "Robust fractional adaptive control based on the strictly Positive Realness Condition." International Journal of Applied Mathematics and Computer Science 19.1 (2009): 69-76. <http://eudml.org/doc/207923>.

@article{SamirLadaci2009,
abstract = {This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.},
author = {Samir Ladaci, Abdelfatah Charef, Jean Jacques Loiseau},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {positive realness; robust adaptive control; fractional adaptive control; model reference adaptive control; feedforward; fractional calculus},
language = {eng},
number = {1},
pages = {69-76},
title = {Robust fractional adaptive control based on the strictly Positive Realness Condition},
url = {http://eudml.org/doc/207923},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Samir Ladaci
AU - Abdelfatah Charef
AU - Jean Jacques Loiseau
TI - Robust fractional adaptive control based on the strictly Positive Realness Condition
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 1
SP - 69
EP - 76
AB - This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.
LA - eng
KW - positive realness; robust adaptive control; fractional adaptive control; model reference adaptive control; feedforward; fractional calculus
UR - http://eudml.org/doc/207923
ER -

References

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