Boundary Control for A Flexible Inverted Pendulum System Based on A Pde Model. Issue 1 (15th July 2016)

• Record Type: Journal Article
• Authors: Peng, Yawei; Liu, Jinkun; He, Wei
• Is Part Of: Asian journal of control. Volume 20:Issue 1(2018)
• Page Start: 12
• Page End: 21
• Publication Date: 2016-07-15
• Subjects: Flexible inverted pendulum -- sliding mode control -- boundary control -- LMI -- singular perturbation -- PDE; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.1336
• Languages: English
• ISSNs: 1561-8625

Abstract

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.