1. A novel robust discrete-time integral sliding mode tracking control design for time-varying delay MIMO systems with unknown uncertainties.
- Author
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Ghrab, Sonia, Ali, Sofiane Ahmed, Benamor, Anouar, Langlois, Nicolas, and Messaoud, Hassani
- Subjects
SLIDING mode control ,MIMO systems ,ADAPTIVE control systems ,AUTONOMOUS underwater vehicles ,LINEAR matrix inequalities ,CLOSED loop systems - Abstract
This paper proposes a novel robust tracking control scheme for discrete time linear uncertain Multiple-Input Multiple-Output (MIMO) systems subject to time-varying delay on the states. The considered system is affected by unknown but norm bounded uncertainties on parameters as well as matched disturbances on the states. The designed controller is based upon a proposed novel integral sliding surface and a new switching type of reaching law. Sufficient conditions based on Linear Matrix Inequalities (LMIs) and a suitable Lyapunov–Krasovskii Functional (LKF) are derived in order to guarantee the asymptotic stability of such system. The proposed controller ensures a good tracking performance despite the presence of the time varying delay and the matched/unmatched disturbances. Moreover and thanks to the proposed integral surface, the time reaching phase is eliminated and the chattering phenomenon is significantly reduced. The proposed controller is applied on an Autonomous Underwater Vehicle (AUV) to follow a prescribed desired trajectory. The simulation results illustrate the effectiveness of such controller. • The problem of the design of a robust discrete time integral sliding mode controllers for the tracking of an uncertain MIMO systems subject to time-varying delay on the states, and under the presence of matched and unmatched uncertainties has never been investigated before anyway. • Robustness against uncertainties is tackled in the present paper by considering the case of matched disturbances and unmatched Unknown But Norm Bounded (UBB) uncertainties. • In the current study we propose a novel discrete switching type reaching law, which is an extension of the one presented in Bartoszewicz and Latosinski (2014) to the MIMO case in the presence of delays, matched disturbances and unmatched uncertainties as well. • Based on a Lyapunov–Krasovskii Functional, the present work provides a sufficient condition guaranteeing the asymptotic stability of the closed-loop systems. With regard to that condition a new Integral Sliding Surface (ISS) has been proposed, which by canceling the reaching phase, it improves the performances of the designed controllers. • Discrete sliding mode controllers have been designed to ensure the occurrence of the sliding mode in finite time. One of these controllers lessens the chattering phenomenon. • The effectiveness of the proposed control algorithms are tested on an Autonomous Underwater Vehicle (AUV). The simulation results are promising. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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