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On the Dynamics and Multiple Equilibria of an Inverted Flexible Pendulum With Tip Mass on a Cart

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Title On the Dynamics and Multiple Equilibria of an Inverted Flexible Pendulum With Tip Mass on a Cart
 
Creator PATIL, O
GANDHI, P
 
Subject CHAOTIC NONPLANAR VIBRATIONS
THIN ELASTICA
BEAM
 
Description Flexible link systems are increasingly becoming popular for advantages like superior performance in micro/nanopositioning, less weight, compact design, lower power requirements, and so on. The dynamics of distributed and lumped parameter flexible link systems, especially those in vertical planes are difficult to capture with ordinary differential equations (ODEs) and pose a challenge to control. A representative case, an inverted flexible pendulum with tip mass on a cart system, is considered in this paper. A dynamic model for this system from a control perspective is developed using an Euler Lagrange formulation. The major difference between the proposed method and several previous attempts is the use of length constraint, large deformations, and tip mass considered together. The proposed dynamic equations are demonstrated to display an odd number of multiple equilibria based on nondimensional quantity dependent on tip mass. Furthermore, the equilibrium solutions thus obtained are shown to compare fairly with static solutions obtained using elastica theory. The system is demonstrated to exhibit chaotic behavior similar to that previously observed for vibrating elastic beam without tip mass. Finally, the dynamic model is validated with experimental data for a couple of cases of beam excitation.
 
Publisher ASME
 
Date 2014-12-28T12:58:59Z
2014-12-28T12:58:59Z
2014
 
Type Article
 
Identifier JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 136(4)
0022-0434
1528-9028
http://dx.doi.org/10.1115/1.4026831
http://dspace.library.iitb.ac.in/jspui/handle/100/16636
 
Language English