Boundary Control for A Flexible Inverted Pendulum System Based on A Pde Model |
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Authors: | Yawei Peng Jinkun Liu Wei He |
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Affiliation: | 1. School of Automation Science and Electrical Engineering, Beihang University, Beijing, People's Republic of China;2. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, People's Republic of China |
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Abstract: | A partial differential equation (PDE) model for a flexible inverted pendulum system (FIPS) is derived by the use of the Hamilton principle. To solve the coupling system model, a singular perturbation method was adopted. The PDE model was divided into a fast subsystem and a slow subsystem using the singular perturbation method. To stabilize the fast subsystem, a boundary control force was applied at the free end of the beam. It then was proven that the closed‐loop subsystem is appropriate and exponentially stable. For the slow subsystem, a sliding mode control method was employed to design a controller and the Linear Matrix Inequality (LMI) method was used to design the sliding surface. It then was shown that the slow subsystem is exponentially stable. |
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Keywords: | Flexible inverted pendulum sliding mode control boundary control LMI singular perturbation PDE |
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