Modeling and vibration control for a flexible pendulum inverted system based on a PDE observer. Issue 8 (3rd August 2017)

• Record Type: Journal Article
• Authors: Peng, Yawei; Liu, Jinkun
• Is Part Of: International journal of control. Volume 90:Issue 8(2017)
• Page Start: 1736
• Page End: 1751
• Publication Date: 2017-08-03
• Subjects: Flexible pendulum inverted system -- PDE observer -- vibration control -- sliding-mode control -- boundary control; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2016.1221136
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: This study addresses the problem of trajectory control of a flexible pendulum inverted system on the basis of the partial differential equation (PDE) and ordinary differential equation (ODE) dynamic model. One of the key contributions of this study is that a new model is proposed to simplify the complex system. In addition, this study proposed a nonlinear PDE observer to estimate distributed positions and velocities along flexible pendulum. Singular perturbation method is proposed to solve the coupling system of nonlinear PDE observer. The nonlinear PDE observer is divided into a fast subsystem and a slow subsystem by the use of the singular perturbation method. To stabilise this fast subsystem, a boundary controller is proposed at the free end of the beam. The sliding-mode control method is proposed to design controller for slow subsystems. The asymptotic stability of both the proposed nonlinear PDE observer and controller is validated by theoretical analysis. The results are illustrated by simulation.