Numerically efficient motion planning for the Euler-Bernoulli beam

An inversion-based approach for the Euler-Bernoulli beam modeled in terms of a boundary controlled port-Hamiltonian system is presented. The goal is to achieve an open-loop finite-time transition between steady states. Exchanging the systems input by a new (fictitious) boundary condition in terms of a so-called basic output located at the boundary or inside the spatial domain, the port-Hamiltonian system is reformulated as a boundary value problem in the spatial domain. Input solution samples are numerically calculated with an inverse Laplace transformation or Fast Fourier Transformation algorithm by assigning a suitable desired trajectory for the basic output. The presented solution approach is evaluated by numerical calculations and simulations.