Sliding Mode Control of Underactuated Mechanical Systems by Means of Nonlinear Sliding Surfaces

Sliding mode control design is a powerful method for robust control of nonlinear dynamical systems. We analyze the control of multivariable mechanical systems with less inputs than degrees of freedom. An existing method is based on a separation of the actuated configuration variables from the unactuated variables. It relies on a sliding surface constituted by a linear combination of the control errors and the corresponding derivatives. Limitations of this approach are outlined using the example of a nonlinear coupling crane control scheme. The existing method is generalized by proposing a more general structure of the sliding surface and a new design methodology. Experimental results are provided which validate the new control scheme.