Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

Abstract

Abstract:In this paper, a Fractional Adaptive Fuzzy Logic Control (FAFLC) strategy based on active fractional sliding mode (FSM) theory is considered to synchronize chaotic fractional-order systems. Takagi-Sugeno fuzzy systems are used to estimate the plant dynamics represented by unknown fractional order functions. One of the main contributions in this work is to combine an adaptive fractional order PI λ control law with the fractional-order adaptive sliding mode controller in order to eliminate the chattering action in the control signal. Based on Lyapunov theory, the stability analysis of the proposed control strategy is performed for an acceptable synchronization error level. Numerical simulations illustrate the efficiency of the proposed fractional fuzzy adaptive control scheme through the synchronization of two different fractional order chaotic Duffing systems. We show that the introduction of the additional fractional adaptive PI λ control action is able to eliminate the chattering phenomena in the control signal.

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

“…The number of applications where fractional calculus has been used grows rapidly mainly for the reason that these mathematical phenomena allow to describe a real object more accurately than the classical methods. Approximation methods of fractional derivative and integral to rational functions permitted to use very easily fractional order systems in wide areas of applications such as control theory [5,8,12], economical systems [20], renewable energy, fractional chaotic systems [21], ... etc.…”

“…Two important and widely applied definitions are Grunwald-Letnikov definition is perhaps the best known due to its most suitability for the realization of discrete control algorithms [1,12]. The Grunwald-Letnikov definition is expresses as [21,[24][25][26][27]:…”

Sliding Mode Control Using SVM for Power Quality Enhancement in StandAlone System Based on Four-Leg Voltage

“…Sliding-mode control techniques even they are suited for power industrial applications due to their robustness under critical working conditions (disturbances and perturbations), their use in four leg with LC filter with an output LC filter is on date rarely reported in the literature. In the found research works [13,14], this technique seem to be well adapted for four leg inverter with an output LC filter. Several control approaches to minimize the Chattering in Induction-Motors, 6 DOF Octorotor, Doubly-Fed Induction Motor and Wind Energy Conversion have been reported in the literature [7][8][9][10][11][12][13][14].…”

Sliding Mode Control for 2 Degrees of Freedom Upper Limb Rehabilitation Robotic System under Uncertainties

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