Practical Variable Exponent Fixed-Time Nonsingular Sliding Mode Control for Nonlinear Systems and Its Applications

For a class of nonlinear systems with disturbances, a new fixed time nonsingular sliding mode control (SMC) method is proposed in this paper. A new fixed time stability lemma is proposed firstly. Compared with traditional fixed time stability, the exponent of the proposed lemma can switch to a positive constant greater than or less than 1 when the system states are far from or near the equilibrium point. On the basis of the proposed lemma, a practical fixed time stability lemma is proposed, which ensures that the system states converge to a domain within a fixed time. Based on the proposed lemma, this paper proposes a novel terminal SMC (TSMC), which can be adjusted adaptively in different stages to make the system converge fastly. In addition, this article uses a saturation function to solve the singular problem and a hyperbolic tangent function to reduce chattering. And the proposed method ensures that the system states are fixed time stable. Finally, the proposed control method is verified through simulation and experiments to have advantages such as fast convergence. Note to Practitioners—The motivation of this paper is to study the trajectory tracking problem of aircraft, but it is also applicable to the trajectory tracking problem of other nonlinear systems, such as robotic arms. The exponents of existing fixed time control methods are positive constants greater than 1 and less than 1, which cannot transition when the system states are far away from or close to the equilibrium point. This article proposes a new method that enables the exponent to switch to a positive constant greater than 1 or less than 1 when the system states are far away from or close to the equilibrium point. This paper combines sliding mode control with fixed time control to address the trajectory tracking problem of aircraft, taking into account the issues of chattering and singularity, and designing a suitable controller. Finally, the feasibility of the proposed method was verified through simulation and experiments.