Flatness-based motion planning for coupled elastic beams

A systematic method for flatness-based motion planning and feedforward control for a coupled flexible beam structure with embedded piezoelectric actuators is presented. By exploiting the spectral system representation an analytic construction of the flat output is obtained, which enables a differential parametration of the system variables. The convergence analysis of the parametrization makes use of properties of entire functions and asymptotic eigenvalue distributions. This results in a problem of trajectory assignment for the flat output. The proposed design approach directly yields an efficient semi-analytical realization by taking into account suitable approximation schemes for the equations of motion. Both techniques are analyzed, evaluated and illustrated in simulations and at the experimental set-up.