Abstract
A new fractional order model reference adaptive controller is proposed for fractional order plant in this paper. Different from the traditional fractional order model reference adaptive controller, the fractional order model reference adaptive controller is designed based on a new Lyapunov stability theory. The new Lyapunov function is constructed by introducing the fractional inequality. With the new Lyapunov function, the expression of the fractional order adaptive control law can be obtained. Furthermore, a fractional order Taylor expansion is introduced to the simulation process, which makes it possible for adaptive control law be used in the simulation of the model reference adaptive controller directly without solving the fractional order integral. The simulation results verify the effectiveness of fractional order model reference adaptive control (FOMRAC).
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