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

Flexible link systems are increasingly becoming popular for their superior performance in micro/nano positioning and several other advantages including less weight, compact design, lower power requirements and so on as compared to other precision micro-positioning systems. The dynamics and control of such systems is challenging, especially for cases where the system is in the vertical plane. A representative case, inverted flexible pendulum on cart system, is considered in this paper. A dynamic model for flexible pendulum with tip mass has been developed using the Euler Lagrange energy method with constraints for large deflection bending. The assumed modes method approach is used to represent significant contribution to dynamics by finite number of modes. For a lower tip mass, only one stable equilibrium in the center exists; however for higher mass this equilibrium becomes unstable and two stable equilibria on side emerge. An experimental setup of the system has also been developed and it is clear by measuring strain at the base of the pendulum that the nonlinear dynamics is captured well in the proposed model.