Robust Fractional Adaptive Control Based on the Strictly Positive Realness Condition

Samir Ladaci 1 , Abdelfatah Charef 2  and Jean Loiseau 3
  • 1 Department of Electrical Engineering, University of the 20th August 1955 of Skikda, BP 26, Skikda 21000, Algeria
  • 2 Department of Electronics, University of Mentouri of Constantine, Route de Ain El-bey, Constantine 25000, Algeria
  • 3 IRCCyN—Ecole Centrale de Nantes, 1, rue de la Noé, BP 92101 Nantes, 44321, France

Robust Fractional Adaptive Control Based on the Strictly Positive Realness Condition

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.

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