Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

Abstract

An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.

Trajectory planning and low-chattering fixed-time nonsingular terminal sliding mode control for a dual-arm free-floating space robot

“…The simulation is mainly about the fixed-time reachability and chattering performance. Some current SMC methods [41,45] for robot are selected as comparison control methods, the SMC scheme in ref. [41] used the saturation function to reduce chattering of controller, but the fixed-time SMC cannot guarantee fixed-time stability in unknown initial error.…”

“…Some current SMC methods [41,45] for robot are selected as comparison control methods, the SMC scheme in ref. [41] used the saturation function to reduce chattering of controller, but the fixed-time SMC cannot guarantee fixed-time stability in unknown initial error. The novel super-twisting SMC method in ref.…”

“…8, the comparison controllers and the proposed controller have a similar actual control accuracy. Line a denotes the proposed controller, line b denotes the super-twisting SMC [45], and line c denotes the saturation-function-based SMC [41].…”

Reinforcement Learning-Based Fixed-Time Trajectory Tracking Control for Uncertain Robotic Manipulators With Input Saturation

“…In order to get rid of the constraints of the initial state and further improve the convergence performance of the closed loop system within the finite time, the fixed-time stability extended from the finite-time stability [9] was developed in recent years, and many theoretical results [11] [10] and practical applications [12] [13] have been made. On the basis of previous studies [6], the finite-time convergence is further improved to the fixed time convergence in [14], with effectively reducing the convergence time of tracking errors. In [15], a new cascade control structure, based on a fixed-time distributed observer, was developed to achieve the fixed-time consensus tracking control.…”

Time-Dependent Global Nonsingular Fixed-Time Terminal Sliding Mode Control-Based Speed Tracking of Permanent Magnet Synchronous Motor

“…Polyakov has also provided a fixed-time secondorder SMC for a linear system in [28]. A fixed-time adaptive SMC for uncertain mechanical systems has been proposed in [29]. Zuo [30] and Corradini et al [31] have proposed their own nonsingular fixed-time terminal sliding mode controls (NFTSMCs) for nonlinear systems, respectively.…”