Intelligent fractional-order backstepping control for an ironless linear synchronous motor with uncertain nonlinear dynamics

This study aims to develop an intelligent fractional-order backstepping controller to control the mover position of an ironless permanent magnet linear synchronous motor. First, we investigated the operating principle and dynamic modeling of the linear synchronous motor based on the field-oriented control method. Next, to improve the convergence speed and control accuracy of the conventional backstepping controller, we designed a fractional-order backstepping controller that has more degrees of freedom in the control parameters. However, designing the switching control gain is difficult owing to the unknown degree of uncertainty. To address this problem, we proposed an intelligent fractional-order backstepping controller to further enhance the adaptiveness and robustness of the fractional-order backstepping controller. In this intelligent controller, we proposed a Hermite-polynomial-based functional-link fuzzy neural network as an uncertainty estimator that can directly estimate system uncertainty, thereby improving the disturbance rejection ability and requiring no uncertainty bound information. Additionally, to compensate for the estimation error introduced by the estimator, we designed an exponential compensator that employs a smooth exponential self-regulation mechanism. We utilized the Lyapunov theorem to derive estimation laws for the online tuning of the control parameters. Experimental results demonstrate the effectiveness and high positioning performance of the proposed intelligent fractional-order backstepping controller in comparison with the backstepping controller and fractional-order backstepping controller in the linear synchronous motor control system.