Nonlinear filters for the generation of smooth trajectories (Q1975579)

A two-dimensional control system, composed by the cascade of two integrators, is considered. The problem of constructing a nonlinear feedback control law such that the output tracks ``at best'' the reference signal while the output derivatives remain bounded is studied. First, a controller is proposed for the case of an ``ideal sliding mode''. To avoid the chattering in the output by the actual implementations of this controller, a boundary layer around the sliding surface is introduced and the sliding mode variable is properly modified. Since the direct discretization of the controller does not ensure that the system trajectories remain within the boundary layer during the transient, and overshoot may also arise, a ``modified'' discrete-time version of the continuous-time scheme is studied and a suitable controller is designed. Simulation results are also presented.