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This paper investigates a framework for the application of robust and smooth second order sliding mode control to a class of underactuated mechanical systems for the realization of high performance control applications. First, using input and state transformations, the dynamics of the class are transformed into a normal form which consists of a set of reduced order nonlinear subsystems and a set of reduced order linear subsystems. Then we present nonlinear sliding manifold and sliding mode control for the reduced order nonlinear subsystem known as the Lagrangian zero dynamics such that stability of the overall system is guaranteed. The control design procedure is illustrated for the Furuta Pendulum, the Overhead Crane, and the Beam-and-Ball system. Numerical simulations verify the effectiveness of the proposed framework. Additionally, we design swingup control law for the Furuta Pendulum to overcome the limitation of the sliding mode control law and achieve global stabilization in the presence of external disturbance.
Shah et al. (Mon,) studied this question.