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.
Highlights
In the past decades, controlling uncertain nonlinear systems have been a topic that attracts attention from many researchers theoretically [1]–[3]
DESIGN OF OBSERVER-BASED NFTSMC ALGORITHM In this part, a NFTSMC algorithm is proposed for the class of second-order uncertain nonlinear systems (1) to handle the effect of the lumped uncertainties with low chattering and minimum tracking errors
The results show that when the switching gain, = 1, the proposed controller-observer method and the NFTSMC-TOSMO can provide almost the same position tracking performance
Summary
In the past decades, controlling uncertain nonlinear systems have been a topic that attracts attention from many researchers theoretically [1]–[3] This topic is crucial in practical because almost real-world systems have nonlinear dynamic characteristics. The dynamic model of the system is not clearly known because of the unknown uncertainties and/or external disturbances - in this paper, for more convenience and avoiding duplication, we will treat it as the lumped uncertainties. They affect directly to the control signal reduce the accuracy of the system.
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