Abstract
This paper proposes a nonsingular terminal sliding mode control scheme with fast fixed-time convergence for a class of second-order nonlinear systems in the presence of matched uncertainties and perturbations. First, based on fixed-time stability theory, a novel stable system is proposed. Then, using the fixed-time stable system, a fast fixed-time nonsingular terminal sliding surface is derived. The settling time is independent of the initial system state and can be set in advance with the design parameters; the upper-bound of convergence time is derived from the Lyapunov theory. Moreover, the proposed control scheme has an advantage in convergence rate over existing results and achieves better control performance with low control energy cost. The simulation results for a tracking system with a single inverted pendulum are presented to validate the effectiveness and superiority of the proposed control method.
Highlights
Sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a system by using a discontinuous control signal and forces the system to slide along a prescribed switching manifold [1]
Motivated by the above discussion, a novel fast fixedtime nonsingular terminal sliding mode (FFNTSM) control scheme is proposed in this paper, which is for second-order nonlinear systems with matched uncertainties and external disturbances, and the preset settling time is independent of initial conditions
The main contributions of this paper are as follows: (1) Based on fixed-time stability theory, a novel fixed-time stable system is presented; (2) The fixed-time stability is guaranteed with the proposed FFNTSM; (3) By using the saturation function method, the FFNTSM structure is nonsingular; and (4) The convergence time is independent of the initial state and can be preset by the design parameters
Summary
Sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a system by using a discontinuous control signal and forces the system to slide along a prescribed switching manifold [1]. Y. Tian et al.: Fast Nonsingular TSMC Method for Nonlinear Systems With Fixed-Time Stability Guarantees manifold was proposed to ensure fast dynamical response and overcome the singularity problem. Zuo and Tie [30] proposed a fixed-time TSMC surface, which suffers from a singularity problem, and the control input cannot be guaranteed to be bounded during the reaching phase.
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