Record Details

Stabilizing a Flexible Beam on a Cart: A Distributed Port-Hamiltonian Approach

DSpace at IIT Bombay

View Archive Info
 
 
Field Value
 
Title Stabilizing a Flexible Beam on a Cart: A Distributed Port-Hamiltonian Approach
 
Creator BANAVAR, R
DEY, B
 
Subject controlled lagrangians
systems
flow
stabilization of mixed systems
hamiltonian systems
energy-casimir technique
 
Description Motion planning and stabilization of the inverted pendulum on a cart is a much-studied problem in the control community. We focus our attention on asymptotically stabilizing a vertically upright flexible beam fixed on a moving cart. The flexibility of the beam is restricted only to the direction along the traverse of the cart. The control objective is to attenuate the effect of disturbances on the vertically upright profile of the beam. The control action available is the motion of the cart. By regulating this motion, we seek to regulate the shape of the beam. The problem presents a combination of a system described by a partial differential equation (PDE) and a cart modeled as an ordinary differential equation (ODE) as well as a controller which we restrict to an ODE. We set our problem in the port-controlled Hamiltonian framework. The interconnection of the flexible beam to the cart is viewed as a power-conserving interconnection of an infinite-dimensional system to a finite-dimensional system. The energy-Casimir method is employed to obtain the controller. In this method, we look for some constants of motion that are invariant of the choice of controller Hamiltonian. These Casimirs relate the controller states to the states of the system. We finally prove the stability of the equilibrium configuration of the closed-loop system.
 
Publisher SPRINGER
 
Date 2011-08-29T19:13:52Z
2011-12-26T12:58:43Z
2011-12-27T05:49:09Z
2011-08-29T19:13:52Z
2011-12-26T12:58:43Z
2011-12-27T05:49:09Z
2010
 
Type Article
 
Identifier JOURNAL OF NONLINEAR SCIENCE, 20(2), 131-151
0938-8974
http://dx.doi.org/10.1007/s00332-009-9054-1
http://dspace.library.iitb.ac.in/xmlui/handle/10054/12168
http://hdl.handle.net/10054/12168
 
Language en