Adaptive fuzzy fractional-order sliding mode controller for a class of dynamical systems with uncertainty

Abstract

A sliding mode control (SMC) strategy is proposed for a second-order non-linear system using fractional calculus and adaptive fuzzy compensator, named fuzzy fractional-order SMC (FFOSMC). The major contribution of this research includes the formulation of a robust fractional-order controller based on a novel non-integer sliding manifold. The proposed controller utilizes reduced discontinuous switching gain using a fuzzy logic system. A fractional-order adaptation law is derived to update the fuzzy logic system, which has more degrees of freedom to achieve the desired performance. The stability of the closed-loop system is guaranteed using fractional-order Lyapunov theory. The parameters of the proposed control method are optimized using Simulink response optimization. Finally, the performance of the FFOSMC is fully investigated and compared with a conventional SMC controller and an integral SMC controller. From simulation results, it is concluded that the proposed algorithm is effective and more robust.

Static Var Compensator with Fractional Order Dynamics for Enhanced Stability and Control

“…While minimizing the cost function, the parameters of the control system are adjusted online. The toolbox is associated with different optimization methods such as pattern search, simplex search, and gradient descent methods [39,40].…”

Control deslizante fraccionario de la trayectoria y orientación de un quadrotor con cargas suspendidas desconocidas

“…Además, en (Muñoz-Vázquez et al, 2014) los autores presentaron algunos resultados en donde aplican el control en modo deslizante de orden fraccionario. El control robusto de orden fraccionario se ha utilizado anteriormente para resolver el problema de control en sistemas no lineales con incertidumbre (Ullah et al, 2015), (Ullah et al, 2016), (Asghar et al, 2017), (Ullah et al, 2017), (Aghababa et al, 2014), (Efe, 2008), (Ebrahimkhani, 2016), (Kang et al, 2017) así como para resolver el problema de control de la orientación del quadrotor (Izaguirre-Espinosa et al, 2016). No obstante, los métodos de control introducidos para el caso de cargas suspendidas tan sólo ofrecen una solución parcial del problema, puesto que o bien se basan en la dinámica lineal del sistema, o bien se formulan para una aplicación más simple como únicamente el despegue o el aterrizaje de los quadrotores o bien no resuelven simultáneamente el problema de seguimiento de la posición y orientación del quadrotor.…”

Adaptive type‐2 fuzzy system for synchronisation and stabilisation of chaotic non‐linear fractional order systems

“…Efe [54] has proposed a fractional fuzzy adaptive sliding mode to control a 2-degrees of freedom direct drive robot arm with integer order equations. Ullah et al [55,56] have introduced a fractional order adaptive fuzzy sliding mode controller with a fractional order adaptation law to control the uncertain dynamical integer order systems. Although the results of [55,56] are noticeable, there is no guarantee that the error will successfully converge to zero.…”