Design of a Non-Singular Adaptive Integral-Type Finite Time Tracking Control for Nonlinear Systems With External Disturbances

Abstract

This paper proposes an adaptive non-singular fast terminal sliding mode control (FTSMC) with integral surface for the finite time tracking control of nonlinear systems with external disturbances. An appropriate parameter-tuning adaptation law is derived to tackle the disturbances. A new fast terminal sliding scheme with self-tuning algorithm is proposed to synthesize the adaptive non-singular fast integral terminal sliding approach. The proposed approach has the following features: 1) It does not require the derivative of the fractional power terms with respect to time, thereby eschewing the singularity problem typically associated with TSMC; 2) It guarantees the existence of the switching phase under exogenous disturbances with unknown bounds; 3) Because of the integral terms in the sliding surface, the power functions are hidden behind the integrator; 4) It ensures chattering-free dynamics. The effectiveness of the proposed approach is assessed using both a simulation and an experimental study. The obtained results showed that the FTSM control technique guarantees that when the switching surface is reached, tracking errors converge to zero at a fast convergence rate. Additionally, the integral term offers one extra degree-of-freedom and since the time-derivative of fractional power terms is not needed in the controller, the proposed switching surface provides a comprehensive framework for singularity avoidance.

Adaptive Integral Sliding Mode Based Course Keeping Control of Unmanned Surface Vehicle

“…In order to make control robust to disturbances and uncertainties, several approaches has been proposed in the SMC literature, see [22][23][24][25][26][27][28][29][30][31][32]. Some proposals of advanced sliding manifolds include recursive nonlinear sliding manifolds [33][34][35], adaptive integral sliding mode approach [36][37][38], non linear full order dynamics [39,40], sliding surfaces with adaptive damping parameters [41][42][43] and, in the last years, a vast collection of homogeneity based works, see [44] for instance. Applications of the properties of homogeneous systems is an important field of study in the current development of analysis and design of nonlinear controllers and observers.…”

Depth Control of an Oil Bladder Type Deep-Sea AUV Based on Fuzzy Adaptive Linear Active Disturbance Rejection Control

“…An SMC controller, with excellent anti-ability to disturbances, is widely used in the motion control of underwater vehicles. Some novel works related to SMC theory, such as the dynamic SMC method, the robust sliding mode method, multiple sliding mode methods, etc., have also been developed in [40][41][42][43], which all show superior control performance to underwater vehicles. However, most AUVs are non-linear with high-order systems whose accurate models are difficult to obtain.…”

Development of Sliding Mode Controller Based on Internal Model Controller for Higher Precision Electro-Optical Tracking System

“…Goel and Mobayen [21] created an adaptive control law that eliminates the necessity for a priori knowledge of the system uncertainties' upper bounds. For nonlinear systems with external disturbances, Alattas et al [22] suggested an adaptive non-singular fast terminal SMC with integral surface and a novel adaptive rate to relieve the chattering problem. Karami et al [23] proposed an adaptive integral terminal SMC approach for uncertain nonlinear systems subject to input saturation and external disturbance by integrating adaptive integral SMC with nonlinear extended-state observer.…”