A Non-Singular Fast Terminal Sliding Mode Control Based on Third-Order Sliding Mode Observer for a Class of Second-Order Uncertain Nonlinear Systems and its Application to Robot Manipulators

Abstract

This paper proposes a controller-observer strategy for a class of second-order uncertain nonlinear systems with only available position measurement. The third-order sliding mode observer is first introduced to estimate both velocities and the lumped uncertain terms of system with high accuracy, less chattering, and finite time convergency of estimation errors. Then, the proposed controller-observer strategy is designed based on non-singular fast terminal sliding mode sliding control and proposed observer. Thanks to this combination, the proposed strategy has some superior properties such as high tracking accuracy, chattering phenomenon reduction, robustness against the effects of the lumped uncertain terms, velocity measurement elimination, finite time convergence, and faster reaching sliding motion. Especially, two period times, before and after the convergence of the velocity estimation takes place, are considered. The finite time stability of proposed controller-observer method is proved by using the Lyapunov stability theory. Final, the proposed strategy is applied to robot manipulator system and its effectiveness is verified by simulation results, in which a PUMA560 robot manipulator is employed. INDEX TERMS Uncertain nonlinear systems, non-singular fast terminal sliding mode control, third-order sliding mode observer, controller-observer strategy, uncertainty compensation, robot manipulators.

A Sliding Mode Control Strategy for an ElectroHydrostatic Actuator with Damping Variable Sliding Surface

“…The integration of related algorithms, such the New Adaptive Reaching Law (NARL) [19] against chattering and the extended state observer (ESO) [22] for working condition estimation, is verified. State observers are commonly applied to control systems for the tasks of system uncertainties estimation and compensation [23][24][25]. In addition, Gao et al constructed a two-stage sliding mode control to retain its rapidity and employed an improved Lyapunov function to reduce system chattering [26].…”

Terminal Traction Control of Teleoperation Manipulator With Random Jitter Disturbance Based on Active Disturbance Rejection Sliding Mode Control

“…. Therefore, (28) can be written as follows: (29) is the sum of the observation errors of each state of the extended observer,q id −ẍ i1d is the difference between the desired acceleration before and after filtering, and its absolute value is bounded. Therefore, let (29) can be changed into the following inequality:…”

“…[22] investigated a novel digital fast terminal sliding mode control (FTSMC) approach for DC-DC buck converters with mismatched disturbances. To address the singular problem of terminal sliding mode control, a nonsingular terminal sliding mode was proposed [25]- [29]. [29] proposed a nonsingular fast terminal sliding mode control for a class of second-order uncertain nonlinear manipulator systems with only available position measurement.…”

“…To address the singular problem of terminal sliding mode control, a nonsingular terminal sliding mode was proposed [25]- [29]. [29] proposed a nonsingular fast terminal sliding mode control for a class of second-order uncertain nonlinear manipulator systems with only available position measurement. The mentioned control algorithms require the upper bound of the uncertainties in the robot system.…”

Adaptive Practical Fast Finite-Time Consensus Protocols for High-Order Nonlinear Multi-Agent Systems With Full State Constraints

“…Yu and Man proposed a novel fast terminal sliding mode (FTSM) control method, which combines terminal sliding mode control, finite-time control and conventional sliding-mode control together which can guarantee fast finite-time transient convergence whether at a distance from or at a close range of the equilibrium [13]. Furthermore, FTSM control method has been applied to various practical systems, and a large number of research results have investigated [14]- [17]. More recently, some novel fast FTC consensus protocols for first and second-order systems have been investigated [18], [19].…”