Dynamic Sliding Mode Control Design based on an Integral Manifold for Nonlinear Uncertain Systems

An output feedback sliding mode control law design relying on an integral manifold is proposed in this work. The considered class of nonlinear systems is assumed to be affected by both matched and unmatched uncertainties. The use of the integral sliding manifold allows one to subdivide the control design procedure into two steps. First a linear control component is designed by pole placement and then a discontinuous control component is added so as to cope with the uncertainty presence. In conventional sliding mode the control variable suffers from high frequency oscillations due to the discontinuous control component. However, in the present proposal, the designed control law is applied to the actual system after passing through a chain of integrators. As a consequence, the control input actually fed into the system is continuous, which is a positive feature in terms of chattering attenuation. By applying the proposed controller, the system output is regulated to zero even in the presence of the uncertainties. In the paper, the proposed control law is theoretically analyzed and its performances are demonstrated in simulation.