Adaptive non‐singular fast terminal sliding mode based on prescribed performance for robot manipulators

Abstract

A fast convergent non-singular terminal sliding mode adaptive control law based on prescribed performance is formulated to solve the uncertainties and external disturbances of robot manipulators. First, the tracking error of robot manipulators is transformed by using the prescribed performance function, which improves the transient behaviors and steady-state accuracy of robot manipulators. Then, a novel fast convergent non-singular terminal sliding mode surface is brought up according to the transformed error, and the control law is derived to meet the stability requirements of robot manipulators. In practice, the upper boundary of the lumped disturbances cannot be accurately obtained. Therefore, an adaptive prescribed performance control (PPC) controller to lumped disturbances is brought up to ensure the stability and finite-time convergence of robot manipulators. Finally, the system stability of robot manipulators is proved by the Lyapunov theorem. Simulation results and comparative analysis demonstrate the superiority and robustness of the raised strategy.

Research on speed sensorless control strategy of permanent magnet synchronous motor based on fuzzy super-twisting sliding mode observer

“…The verification is carried out from two aspects of the constant speed variable load and variable speed variable load. Simulation conditions: fixed step size obe3, simulation time 0.7 s. References 49 , 50 shows that the parameters of the PMSM used in the simulation are shown in Table 2 .…”

Tracking control for robotic manipulators with prescribed performance and adaptive sliding mode disturbance observer

“…However, the robotic manipulators are a nonlinear system; meanwhile, the coupling joints, model perturbation, and external disturbance will affect the tracking accuracy of the motion trajectory. Aiming to achieve the excellent tracking performance, various control strategies are formulated, such as adaptive control (Moreno-Valenzuela et al, 2024; Zhang et al, 2023b), sliding mode control (SMC) (Xie et al, 2021; Zhang and Yang, 2022), time-delay estimation (TDE) control (Park et al, 2023), and robust control (Ferrara and Incremona, 2015; Wang et al, 2023). Therefore, the control strategies with fast convergence speed, high steady-state accuracy, good transient performance, and strong robustness are still the focus of current research.…”

“…However, linear sliding mode control (LSMC) can only satisfy the system to achieve asymptotic convergence. Terminal sliding mode control (TSMC) can guarantee the system convergence in a finite time; however, the singularity problem (Mien et al, 2019; Zhang et al, 2023b; Zhang and Yang, 2022) caused by sign function in sliding mode variable and chattering phenomenon (Edwards and Shtessel, 2016; Ferrara and Incremona, 2015; Han et al, 2016; Zhao and Zhu, 2014) generated by excessive control gain need to be settled. A nonsingular terminal sliding variable was constructed to eliminate the singularity problem (Zhang et al, 2023b; Zhang and Yang, 2022).…”

“…Terminal sliding mode control (TSMC) can guarantee the system convergence in a finite time; however, the singularity problem (Mien et al, 2019; Zhang et al, 2023b; Zhang and Yang, 2022) caused by sign function in sliding mode variable and chattering phenomenon (Edwards and Shtessel, 2016; Ferrara and Incremona, 2015; Han et al, 2016; Zhao and Zhu, 2014) generated by excessive control gain need to be settled. A nonsingular terminal sliding variable was constructed to eliminate the singularity problem (Zhang et al, 2023b; Zhang and Yang, 2022). Mien et al (2019) developed a backstepping nonsingular terminal sliding mode strategy, which cannot guarantee the finite-time convergence of robotic manipulators.…”

Symmetric Time-Variant IBLF-Based Tracking Control with Prescribed Performance for a Robot

“…However, determining how to design tracking control to ensure the performance requirements of the robotic system is still a challenge. The error in performance requirements of the robotic system is transformed via the performance envelope function to improve the transient response speed as well as the final stable error [30]. In [31], by constructing two smooth monotonic functions to complete the error transformation, a control scheme of a logarithmic BLF embedding the transformed error is presented to guarantee the performance requirements of the robot manipulators.…”