Robust Nonsingular Fast Terminal Sliding Mode Control in Trajectory Tracking for a Rigid Robotic Arm

Abstract : In this paper, a novel concept of robust Nonsingular Fast Terminal Sliding Mode controller (NFTSMC) is adopted for the trajectory tracking problem of a non-linear system. The developed controller is based on NFTSM controller and approach. The use of the NFTSM controller offers a fast convergence rate, avoids singularities, but still suffers from chattering. In order to overcome this limitation, a new term in the control law is inspired by the technique of it interferes by managing uncertainties and external disturbances without knowing their upper bound. Stability analysis of the closed-loop system is accomplished using the Lyapunov criterion. Several simulation results are given to show the effectiveness of the proposed approach. 1. INTRODUCTION Among the existing control methodologies, sliding mode control (SMC) has found wide acceptance and continues to draw particular attention from the research community due to its strong robustness with respect to both modeling uncertainties and external disturbances [1-3]. The tracking of the desired tra-jectory is achieved through two steps. In the first one, the system is forced to attain a predefined sliding manifold and in the second step, the system must slide along this manifold to converge to the equilibrium point. To ensure the transition from the first step to the second one, we use the so-called switching control signal composed of a high gain and signum function [4]; this leads to chattering which can excite high-frequency dynamics and can, therefore, damage actuators, degrade the control performance and sometimes make the system unstable. The most common way to reduce chattering is the use of a boundary layer around the sliding surface with fixed thickness [4] or a variable on [5, 6], but this entails a larger response time; in this case, it is necessary to find a trade-off between the thickness of the boundary layer and the time response. Moreover, to design the switching signal assuring the approaching phase, the upper bounds of both the external disturbances and the structural uncertainties must be well known. Some authors have proposed an approximation of the sliding gain by an adaptive fuzzy system to eliminate the chattering phenomenon without requiring any particular knowledge about the upper bounds of both approximation errors and external disturbances [7-9]. However, the global stability of the closed-loop system in these approaches is guaranteed only for a good approximation level or for a particular choice of the initial values of the adjustable parameters. In [10], authors propose to use a modified sliding surface such that the system will be on at which allows removing the approaching phase, and hence overcoming the knowledge of the upper bound of disturbances required to guarantee the sliding condition and to eliminate effectively the chattering phenomenon. Furthermore, classical SMC cannot guarantee a defined finite time convergence. To obtain a defined finite time convergence, Terminal Sliding Mode (TSMC) has been studied [11-13]. Unlike the conventional SMC, which is designed based on a linear sliding surface, the TSMC uses a non-linear sliding surface, and thus it can guarantee a defined finite time convergence. Nevertheless, TSMC provides slow convergence when the system states are far away from the equilibrium point and singularity phenomenon problem when the system reaches the sliding mode. To tackle these drawbacks, Fast TSMC
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Submitted on : Tuesday, January 7, 2020 - 10:43:36 AM
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A Jouila, Najib Essounbouli, K Nouri, A. Hamzaoui. Robust Nonsingular Fast Terminal Sliding Mode Control in Trajectory Tracking for a Rigid Robotic Arm. Automatic control and computer sciences, 2019, 53, pp.511 - 521. ⟨10.3103/S0146411619060063⟩. ⟨hal-02420746⟩

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