Abstract To achieve good robustness against disturbances for a class of uncertain underactuated systems, a second-order adaptive sliding mode control method is proposed based on quadratic Lyapunov function to reduce the inherent chattering of conventional sliding mode control (SMC). Firstly, a second-order super-twisting algorithm is used by the discontinuous part of controller, which acts on the second-order derivative of sliding mode variables. Secondly, as for the effects of unknown disturbances on sliding mode surface, an adaptive law is designed to adjust the parameters. This method eliminates the restriction of the first derivative of disturbances boundary being known in the traditional second-order sliding mode control, which not only keeps convergence of sliding mode surface but also reduces chattering. Finally, a two-wheeled self-balancing cart is used to test the proposed approach. The simulation results show that compared with conventional SMC and ordinary second-order SMC, the proposed method outperforms the above methods on effectiveness and reducing chattering.
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2014, Vol. 27 
