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Boundary Control for a Flexible Inverted Pendulum System Based on a PDE Model with Input Saturation
Author(s) -
Peng Yawei,
Liu Jinkun
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1746
Subject(s) - inverted pendulum , control theory (sociology) , decoupling (probability) , singular perturbation , double inverted pendulum , perturbation (astronomy) , boundary (topology) , controller (irrigation) , sliding mode control , computer science , control engineering , engineering , nonlinear system , control (management) , mathematics , physics , mathematical analysis , agronomy , quantum mechanics , artificial intelligence , biology
This research considers the control problem of a flexible inverted pendulum system (FIPS) in the presence of input saturation. The model for a flexible inverted pendulum system (FIPS) is derived via the Hamilton principle. The FIPS model is divided into a fast subsystem and a slow subsystem via the singular perturbation method. We introduce an auxiliary system to deal with the input saturation of a fast subsystem. To stabilize the fast subsystem, a boundary anti‐windup control force is applied at the free end of the beam. It is proven that the closed‐loop subsystem is stable. For the slow subsystem, a sliding mode control method is employed to design a controller and a new decoupling method to design the sliding surface. Then it is shown that the slow subsystem is stable. Finally, simulation results are provided to confirm the efficacy of the proposed controller.