Feedforward control design for the wave equation with nonlinear boundary conditions modelling a torsional rod

This paper presents a flatness-based approach for the feedforward control design of the wave equation with nonlinear boundary conditions modelling a torsional rod with a tip load. It uses a subdivision of the relevant time-space region based on the characteristic curves of the system as well as the property of formal power series parameterizability of the underlying partial differential equation on the subregions to derive an expression for the nominal input to achieve perfect tracking performance of a prescribed desired output trajectory. Therefore, this contribution proves the applicability of the formal power series approach to second order hyperbolic partial differential equations.