Adaptive high-order sliding mode control based on quasi-time delay estimation for uncertain robot manipulator
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Control Theory and Technology http://link.springer.com/journal/11768
Adaptive high-order sliding mode control based on quasi-time delay estimation for uncertain robot manipulator Brahim BRAHMI 1† , Mark DRISCOLL 1 , Mohamed Hamza LARAKI 2 , Abdelkrim BRAHMI 2 1.Department of Mechanical Engineering, Musculoskeletal Biomechanics Research Lab, McGill University, Montreal, Canada; 2.Department of Electrical Engineering, University of Quebec, Montreal, Canada Received 10 April 2019; revised 23 November 2019; accepted 29 November 2019
Abstract This paper presents the design, and validation of a new adaptive control system based on quasi-time delay estimation (QTDE) augmented with new integral second-order terminal sliding mode control (ISOTSMC) for a manipulator robot with unknown dynamic uncertainty and disturbances. Contrary to the conventional TDE, the proposed Q-TDE becomes sufficient to invoke a fixed artificial time delay and utilize the past data only of the control input to approximate the unknown system’s dynamic uncertainties. The incorporating of new adaptive reaching law with ISOTSMC augmented with Q-TDE policy ensures the continuous performance tracking of the robot manipulator’s trajectories using output feedback. This combination may achieve high performance with a significant chattering reducing procedure. By utilizing the Lyapunov function theory, it can be demonstrated that the robot system is stable and all signals in closed-loop are converging in finite time. Consequently, Simulation and comparative studies with two degrees of freedom robot manipulator were carried out to validate the effectiveness of the designed control scheme. Keywords: Second-order sliding mode, quasi-time delay estimation (Q-TDE), adaptive reaching law DOI https://doi.org/10.1007/s11768-020-9061-1
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Introduction
A practical control system should be developed to ensure the stability of the a complex nonlinear system. Besides that, it must be robust against the perturbations produced by the internal dynamic parameters of the system including unmodeled dynamics, and external
disturbances. Control of uncertaint dynamics is one of the challenging matters facing nonlinear control engineering [1]. Numerous control schemes have discussed previously [2–5] to manage the dynamics uncertainty effect that impacts negatively the system’s performance. Sliding mode control (SMC) is a robust approach that
† Corresponding
author. E-mail: [email protected].
© 2020 South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature
B. Brahmi et al. / Control Theory Tech, Vol.
has vastly employed into robotics systems [6–9], and accomplishes the robust performance requirement. In SMC, a switching surface is selected so that the trajectory can start form anywhere and is forced to reach the switching surface in reasonable finite time. Once on the switching surface, the dynamics of the system is reduced to a stable linear time-invariant system whic
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