Modeling of Inverted Elastic Pendulum on Cart with Tip Mass (IEPCTM) system having multiple dynamic equilibria

A new mechanical approach is presented in this paper for modeling the system of Inverted Elastic Pendulum on Cart with Tip Mass (IEPCTM) exhibiting multiple dynamic equilibria. Torsional spring is assumed in the system structure to account the flexibility of pendulum. The condition of existence of multiple equilibria dynamically is also incorporated in this model. Mathematical model is framed using Euler-Lagrange analysis. Validation of proposed model is accomplished through comparison of simulation results with experimental data from actual plant behavior. Simple modeling idea & approach, ease in model reproducibility & simulation and simplicity from implementable control design perspective form the key features of the proposed IEPCTM system model in this work.