Semi-Discretization of a Euler-Bernoulli Beam and Its Application to Motion Planning
We consider a Euler-Bernoulli beam with sliding cantilever boundary conditions at both ends. The control input to the beam is the force acting on one of the cantilevers. We derive an <inline-formula> <tex-math notation="LaTeX">$n^{\mathrm {th}}$ </tex-math></inline-for...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10886930/ |
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| Summary: | We consider a Euler-Bernoulli beam with sliding cantilever boundary conditions at both ends. The control input to the beam is the force acting on one of the cantilevers. We derive an <inline-formula> <tex-math notation="LaTeX">$n^{\mathrm {th}}$ </tex-math></inline-formula>-order semi-discrete approximation of the beam PDE and prove that the solution to the <inline-formula> <tex-math notation="LaTeX">$n^{\mathrm {th}}$ </tex-math></inline-formula>-order semi-discrete system converges to the solution of the PDE as n tends to infinity. The motion planning problem addressed in this paper is to find a control input which will transfer the beam PDE from one steady state to another over a prescribed time interval. To address this problem, we design control inputs for transferring the semi-discrete systems from one steady state to another using the flatness technique. We show that a control input which solves the motion planning problem for the beam PDE can be obtained as a limit of a sequence of control inputs which solve certain motion planning problems for a sequence of semi-discrete systems of increasing order. We illustrate our theoretical results in simulations. |
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| ISSN: | 2169-3536 |