Mathematical modeling of flexible inverted pendulum on cart with tip mass

This paper presents a new mathematical model for the system of Flexible Inverted Pendulum on Cart with Tip Mass (FIPCTM). Springs are assumed in the system structure for accounting the flexibility of pendulum. The pendulum is assumed to be made up of chain of multiple sub-links one above the other. Each link is assumed to be connected horizontally (through a spring) to an imaginary surface rising from the cart. Practicality of system is taken care by assigning definite stiffness value to the springs, in decreasing order from bottom to top. Model is framed using energy approach. Proposed model is validated by comparing model simulation results with experimental data from actual plant behavior.