A Fractional-Order Nonlinear Backstepping Controller Design for Current-Controlled Maglev System

The magnetic levitation system (Maglev) is a nonlinear system by which an object is suspended with no support other than magnetic fields. The main control perspective of the Maglev system is to levitate a steel ball in air by the electromagnetic force. However, the Maglev system has highly nonlinear dynamics which is inconvenient in the sense of sensitive control/regulation of its nonlinear dynamics. In this paper, the nonlinear backstepping controller based on the fractional-order derivative is proposed for the control of the nonlinear current-controlled Maglev system. After, the system dynamics and fractional-order backstepping controller design are given, the asymptotic stability of the closed-loop system is proved by employing the Lyapunov theory. Some computer-based numerical experiments are carried out to show the effectiveness of the proposed controller for the control of Maglev system.

💡 Research Summary

The paper addresses the challenging problem of controlling a current‑controlled magnetic levitation (Maglev) system, which exhibits highly nonlinear and unstable dynamics. The authors propose a novel nonlinear backstepping controller that incorporates fractional‑order calculus, specifically the Caputo definition of a fractional derivative, into each step of the backstepping design.

First, the physical model of the Maglev system is derived. The vertical position (y) of the steel ball, its velocity (v), and the coil current (i) are related through the electrical dynamics (coil resistance (R) and inductance (L)) and the mechanical dynamics governed by gravity and the electromagnetic force (F_e = Q/(y+Y_\infty)^2). By defining the state vector (