A non-integer sliding mode controller to stabilize fractional-order nonlinear systems

Advances in Difference Equations

Roveida Ziaratban¹  Ahmadreza Haghighi² 

[1] Department of Mathematics, Payame Noor University of Tehran, Tehran, Iran;Department of Mathematics, Technical and Vocational University, Tehran, Iran;

关键词: Fractional-order system;    Uncertainty;    Chattering;    Lyapunov theory;    Sliding mode control;    Frequency distributed model;   

DOI  :  10.1186/s13662-020-02954-w

来源: Springer

【 摘 要 】

In this study, we examine the stabilization of fractional-order chaotic nonlinear dynamical systems with model uncertainties and external disturbances. We used the sliding mode controller by a new approach for controlling and stabilization of these systems. In this research, we replaced a continuous function with the sign function in the controller design and the sliding surface to suppress chattering and undesirable vibration effects. The advantages of the proposed control method are rapid convergence to the equilibrium point, the absence of chattering and unwanted oscillations, high resistance to uncertainties, and the possibility of applying this method to most fractional order chaotic systems. We applied the direct method of Lyapunov stability theory and the frequency distributed model to prove the stability of the slip surface and closed loop system. Finally, we simulated this method on two commonly used and practical chaotic systems and presented the results.

【 授权许可】

CC BY