Chaos and Adaptive Control of the Fractional-Order Magnetic-Field Electromechanical Transducer

In this paper, we investigate chaos and adaptive control of the magnetic-field electromechanical transducer wherein the electric characteristics of the capacitor contain the fractional-order derivative. The phase diagrams for different values of the fractional-order exhibit chaotic characteristics of the magnetic-field electromechanical transducer. In the process of controller design, a continuous frequency distributed model is utilized to construct the indirect Lyapunov stability criterion and a Chebyshev neural network with weight, and fractional-order adaptive law is introduced to approximate the complicated unknown function. To suppress chaotic oscillation, an adaptive control scheme by fusing Chebyshev neural network and backstepping is presented to guarantee that the closed-loop system is globally asymptotically stable. To illustrate the feasibility of the proposed approach, simulation studies are done in the end.