Adaptive finite‐time super‐twisting sliding mode control for robotic manipulators with control backlash

Abstract

This article aims at the problem of trajectory tracking for industrial robotic manipulators with control backlash. An arctangent terminal sliding mode surface is developed to deal with the lumped disturbance and enhance the robustness of the system. A novel adaptive super-twisting sliding mode control method is developed to achieve fast convergence and continuous control. The chattering in control law is surmounted by using super-twisting method. The lumped disturbance with unknown upper bound is compensated with the help of the adaptive technique. Based on the Lyapunov stability theory, the sliding mode surface will be arrived in a finite time and the trajectory tracking error will converge to zero in a finite time. The feasibility of the proposed control scheme is validated through an example of a two-link robotic manipulator.

Super‐twisting sliding mode trajectory tracking adaptive control of wheeled mobile robots with disturbance observer

“…10,11 Among them, SMC attracted lots of attention for its fast transient response and robustness against disturbance. 12,13 The design of traditional sliding mode surface (SMS) could only make the tracking error converge asymptotically. In order to accelerate the convergence speed, high gain was necessary.…”

Time‐varying nonsingular terminal sliding mode control for uncertain second‐order nonlinear systems with prespecified time

“…[1][2][3][4][5][6][7] In several control approaches, a linear sliding surface is employed to design a controller and this can only ensure asymptotic convergence. [8][9][10][11][12][13] To achieve finite-time convergence, terminal sliding mode (TSM) control techniques have been designed using nonlinear sliding surfaces and have been widely investigated for various nonlinear systems like power filters, 14,15 MEMS gyroscope, stochastic and strict-feedback nonlinear systems, 16,17 robotic manipulators, [18][19][20][21][22][23][24][25] and so forth. For example, the authors in References 18,19 propose a TSM control for the trajectory tracking problem of robotic manipulators with a super-twisting method.…”

“…1. Different from TSM [14][15][16][17][18][19][20][21][22][23][24][25] and fixed-time sliding mode [1][2][3][4][5][6][7][8][9][10][11][12][13][14]26,27 tracking controls, the state trajectories are constrained to the sliding surface from the very beginning of system response and thus the reaching phase is totally eliminated and the global robustness is ensured;…”

“…To achieve finite‐time convergence, terminal sliding mode (TSM) control techniques have been designed using nonlinear sliding surfaces and have been widely investigated for various nonlinear systems like power filters, 14,15 MEMS gyroscope, stochastic and strict‐feedback nonlinear systems, 16,17 robotic manipulators, 18–25 and so forth. For example, the authors in References 18,19 propose a TSM control for the trajectory tracking problem of robotic manipulators with a super‐twisting method. The proposed algorithms ensure fast convergence, chattering avoidance, and strong robustness against disturbances and uncertainties.…”

“…Motivated by the aforementioned discussions, in this work, the problem of global time‐varying nonsingular terminal sliding mode (GTV‐NTSM) control with predefined convergence time is first designed for uncertain second‐order nonlinear systems and then extended to control n ‐links rigid robotic manipulators. The major contributions of this article are stated as follows: Different from TSM 14–25 and fixed‐time sliding mode 1‐14,26,27 tracking controls, the state trajectories are constrained to the sliding surface from the very beginning of system response and thus the reaching phase is totally eliminated and the global robustness is ensured; Compared with the TV‐TSM, 5–7,28–31 the convergence time can be user‐defined through the adjustment of some system parameters, which is very meaningful for many practice engineering cases. Furthermore, the singularity problem is avoided and the control inputs are guaranteed to be smooth. Compared with Reference 36, we remove the requirement of prior knowledge of the upper bound of the lumped uncertainties by using adaptive tuning laws. By means of the general formulation for second‐order nonlinear systems, the proposed approach can be easily adapted to control many robotic systems. The remainder of this article is organized as follows: Section 2 present the problem statement.…”