The problem of stabilization of nonlinear fractional systems in spite of system uncertainties is investigated in this paper. First, a proper fractional derivative type sliding manifold with desired stability and convergence properties is designed. Then, the fractional stability theory is adopted to derive a robust sliding control law to force the system trajectories to attain the proposed sliding manifold and remain on it evermore. The existence of the sliding motion is mathematically proven. Furthermore, the sign function in the control input, which is responsible to the being of harmful chattering, is transferred into the fractional derivative of the control input. Therefore, the resulted control input becomes smooth and free of the chattering. Some numerical simulations are presented to illustrate the efficient performance of the proposed chattering-free fractional variable structure controller.
Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 10, 2013; final manuscript received August 22, 2013; published online February 13, 2014. Assoc. Editor: J. A. Tenreiro Machado.
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Pourmahmood Aghababa, M. (February 13, 2014). "Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach." ASME. J. Comput. Nonlinear Dynam. July 2014; 9(3): 031003. https://doi.org/10.1115/1.4025771
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