Trajectory tracking control of an input delayed monocycle

This article describes the design of an observer-based robust linear output feedback controller for the output reference trajectory tracking tasks in an under-actuated, nonlinear, input-delayed system known as the monocycle, or the rolling penny. The unknown, possibly state-dependent, nonlinearities of the input-output description are modeled as absolutely bounded additive perturbation input signals simplifying the system description to a multivariable chain of integrators controlled by delayed inputs through a nonlinear gain matrix. The total perturbation input vector components can be locally approximated by arbitrary elements of, sufficiently high, fixed-degree family of Taylor polynomials. Generalized Proportional Integral (GPI) observers, which are the dual counterpart of GPI controllers, are shown to naturally estimate, in a rather close manner, the perturbation input of the simplified system and a certain number of its time derivatives, thanks to its embedded, internal time-polynomial model of the unknown, state dependent, perturbation input. This particular feature allows for a natural perturbation input prediction which completes the description of the simplified delay-free system (or advanced system) playing a central role in the direct application of the Smith Predictor controller design methodology. The results are applied to the dynamic model of a monocycle system in a trajectory tracking problem.