New Robust and Adaptive Higher Order Sliding mode controllers

Mohamed Harmouche (1) , Salah Laghrouche (1) , Yacine Chitour (2)

1 SET - Laboratoire Systèmes et Transports
2 L2S - Laboratoire des signaux et systèmes

In this paper, we have presented a Lyapunov-based design for higher order sliding mode robust and adaptive controllers for nonlinear SISO systems with bounded uncertainties. In the robust control problem, the uncertainty bounds are known, whereas these bounds are unknown in the adaptive control problem. These problems have been formulated as the finite time stabilization of a chain of integrators with bounded uncertainties. The controllers have been developed from a class of nonlinear controllers which guarantee finite time stabilization of pure integrator chains. In the adaptive case, the controller design uses saturation functions. For the first controller, we prove finite time convergence to zero as for the controller in the adaptive case, we show finite time convergence to an arbitrary small neighborhood of the origin. The proposed controllers can be designed for any arbitrary order sliding mode. The simulation results demonstrate the effectiveness of the proposed techniques.

Mots clés: Higher order sliding mode; adaptive control; robust control; homogeneity

Domaines: Automatique

Mohamed Harmouche, Salah Laghrouche, Yacine Chitour. New Robust and Adaptive Higher Order Sliding mode controllers. 2012. ⟨hal-00703669v1⟩