Abstract
A method for the design of second-order sliding mode controllers is developed for a class of nonlinear systems. The key idea is the necessity of nullifying both the auxiliary output as well as its time derivative when the system is sliding. It is found that if the auxiliary output has a strong vector relative degree one, it is possible to design a continuous control input. This allows the application of the sliding mode control to systems that do not allow discontinuous control signals generated by the classical variable structure control. Robustness of the controllers is analyzed and dynamic bounds for the uncertainty are found for a class of nonlinear systems. The design technique could be extended to nth-order sliding controllers, though the complexity of the calculations increases and the robustness bounds become more restrictive. The application of the technique to a drum-type steam generating unit to solve a robust tracking problem is presented.
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