In the present paper, preliminary results towards the generalization to the infinite-dimensional setting of some finite-dimensional second-order sliding mode control algorithms are illustrated. The main focus of the present paper is on the rejection of non-vanishing external disturbances. The "Twisting" and "SuperTwisting" second-order sliding-mode control algorithms (see (Levant (1993))) are properly generalized to address the state tracking problem for the wave and heat equations. Constructive proofs of stability are developed via Lyapunov functional technique, which leads to simple tuning rules for the controller parameters. Simulation results are discussed to verify the effectiveness of the proposed schemes.
Distributed-parameter second-order sliding-mode control techniques for the uncertain heat and wave equations
PISANO, ALESSANDRO;USAI, ELIO
2011-01-01
Abstract
In the present paper, preliminary results towards the generalization to the infinite-dimensional setting of some finite-dimensional second-order sliding mode control algorithms are illustrated. The main focus of the present paper is on the rejection of non-vanishing external disturbances. The "Twisting" and "SuperTwisting" second-order sliding-mode control algorithms (see (Levant (1993))) are properly generalized to address the state tracking problem for the wave and heat equations. Constructive proofs of stability are developed via Lyapunov functional technique, which leads to simple tuning rules for the controller parameters. Simulation results are discussed to verify the effectiveness of the proposed schemes.
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