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

Ahmadreza Haghighi,Roveida Ziaratban

doi:10.1186/s13662-020-02954-w

Abstract

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.

Highlights

Fractional-order calculations play an important role in various scientific fields
The problem of fractional-order equations was first raised by Leibniz in a letter in September 1695 on the fractional-order derivative, and has become an issue for research that is still under investigation [2]
Scientists have recently shown that fractional order equations are capable of modeling different phenomena more accurately than the integer-order equations and are a powerful tool for describing the structures of a system with complex dynamics

Summary

Introduction

Fractional-order calculations play an important role in various scientific fields. Recently the application of fractional-order is known as an important topic in engineering [1]. One of the most commonly used methods for smoothing unwanted oscillations is to apply a fuzzy algorithm to determine the amplitude of a narrow boundary layer around the slip surface, but slowing control is a problem of this method [54] Another way is to exert high-order sliding mode control. Fractional integral sliding mode control (FISMC) is applied to the control of nonlinear chaotic fractional order dynamical systems. 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. In the rest of the paper, Dα is the Caputo fractional derivative

System description

Conclusion