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Uniform sliding mode controllers and uniform sliding surfaces (2012)

Cruz-Zavala, E., Moreno, J. A., Fridman, L.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2012-12-11

Beschreibung: In this note, we propose two uniform sliding mode controllers (SMCs) for a second-order uncertain system. They provide convergence to an arbitrarily small vicinity centred at the origin in finite time, which can be bounded by some constant independent of the initial conditions and uncertainties. Towards this aim, a non-linear sliding surface is designed ensuring convergence, during the sliding motion, of every trajectory to an arbitrarily small vicinity of the origin in a finite time bounded by some constant, independent of the initial condition on the surface. A first-order SMC is designed providing convergence of every trajectory to the sliding surface in a finite time, bounded by another constant independent of the initial conditions and uncertainties/disturbances of a special class. In order to adjust chattering, a super twisting-based controller is suggested providing convergence of the trajectories to the sliding surface in a finite time bounded by some constant independent of any initial condition and uncertainties/disturbances of another class.

Print ISSN: 0265-0754

Digitale ISSN: 1471-6887

Thema: Mathematik

Publiziert von Oxford University Press

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A Lyapunov approach to output feedback control using second-order sliding modes (2012)

Moreno, J. A.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publikationsdatum: 2012-09-06

Beschreibung: The objective of this paper is to provide for the second-order sliding modes (SOSM) output feedback (OF) a Lyapunov-based approach, in the same spirit as it is done for the observer-based output feedback control in conventional non-linear control. To reach this objective, we consider first the Lyapunov design of a state feedback (SF) control based on the twisting algorithm. We propose a (new) Lipschitz continuous strict Lyapunov function for the twisting controller, which assures its finite-time convergence and its robustness under bounded perturbations. In a second step, a Lyapunov design of a finite-time convergent and robust observer estimating the state of the plant is considered. It generalizes the super-twisting differentiator. In a final step, the properties of the interconnection of the observer and the controller in the OF controller are established by Lyapunov arguments, much in the same form as in the conventional non-linear control literature. It is shown that the SOSM-based OF controller (almost) satisfies a separation principle, a result similar to the linear case. Here, however, in order to guarantee the robustness of the OF, the observer has to be designed taking into account the SF controller.

Print ISSN: 0265-0754

Digitale ISSN: 1471-6887

Thema: Mathematik