#7071. On the Calculation of Differential Parametrizations for the Feedforward Control of an Euler–Bernoulli Beam

December 2026publication date
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Journal’s subject area:
Mechanical Engineering;
Mechanics of Materials;
Materials Science (all);
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Abstract:
We are concerned with the motion planning for underactuated Euler–Bernoulli beams. The design of the feedforward control is based on a differential parametrization of the beam, where all system variables are expressed in terms of a free time function and its infinitely many derivatives. We derive an advantageous representation of the set of all formal differential parametrizations of the beam. Based on this representation, we identify a well-known parametrization, for the first time without the use of operational calculus. This parametrization is a flat one, as the corresponding series representations of the system variables converge. Furthermore, we discuss a formal differential parametrization where the free time function allows a physical interpretation as the bending moment at the unactuated boundary. Even though the corresponding series do not converge, a numerical simulation using the least term summation illustrates the usefulness of this formal differential parametrization for motion planning.
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