Adaptive type‐II fuzzy nonsingular fast terminal sliding mode controller using fractional‐order manifold for second‐order chaotic systems

Abstract

A novel fuzzy adaptive finite‐time controller is designed for synchronization and control of the Duffing–Holmes and the gyroscope systems in the presence of uncertainty and external disturbance. The fractional‐order fast nonsingular terminal sliding mode manifold is used to ensure the finite‐time control, speed up the convergence rate, and address the singularity problem of the conventional terminal sliding mode controller. Also, the novel control law successfully reduces the chattering phenomenon. Adaptive biased type‐II fuzzy inference system is used to determine the optimal values of the switching control term. The adaptation rules of the novel fuzzy inference system are achieved based on Lyapunov stability theorem. Finally, by using numerical simulations, the effectiveness and superiority of the proposed control scheme are verified against some other methods.

Variable-Order interval Type-II Fuzzy Fractional PID Controller for Load Frequency Control Optimized via Hybrid Optimization

“…A FIS which uses interval type-II fuzzy sets is called interval type-II FIS. MF grade of type-I Fuzzy sets is crisp, whereas in interval type-II fuzzy sets grade of MFs is fuzzy and defined as an interval (Labbaf Khaniki, Manthouri and Ahmadieh Khanesar, 2023). This feature causes interval type-II fuzzy controllers to control systems without a precise mathematical model and in the presence of uncertainty better than type-I fuzzy controllers (Safari and Imani, 2022).…”

“…Additionally, these types of controllers can control systems without knowing the information about underlying dynamics. The combination of classical and intelligent controllers due to the advantages of the both methods can perform better (Labbaf Khaniki and Tavakoli-Kakhki, 2022), (Khaniki, Hadi and Manthouri, 2021). Some evolutionary optimization algorithms, like gases Brownian motion optimization (Zhang et al, 2023), imperialist competitive algorithm (Taher and Zeraati, 2021), biogeography-based optimization, particle swarm optimization (Singh and Ramesh, 2024) have been used to optimize the controllers.…”

Direct adaptive fractional-order non-singular terminal sliding mode control strategy using extreme learning machine for position control of 5-DOF upper-limb exoskeleton robot systems

“…However, the conventional TSMC suffers from singularity drawback. To cope with this problem in TSMC, non-singular terminal sliding mode controller (NTSMC) is introduced (Labbaf Khaniki et al, 2023). Zhang et al (2020) introduce an indirect adaptive SMC based on a radial basis function method for active rehabilitation exoskeleton robot.…”

Fractional‐order sliding mode control for a novel magneto‐electro‐elastic microtube robot

“…There is a range of FOSMCs, the most popular of which is based on non-integer PD α sliding manifolds that have been studied for different applications [27,28]. Zhang et al [29] applied a PD α -based controller to a synchronous motor, Tang et al [30] developed a fuzzy adaptive SMC based on the PD α manifold for a first-order antilock braking system, and Chen [31] synthesized the very control approach for precise position control of a class of linear motors.…”