Modeling and output feedback control of Flexible Inverted Pendulum on Cart

A simplified mechanical model is presented in this paper for Flexible Inverted Pendulum with Tip Mass on Cart (FTPTMC) system. Also control input to be fed to the cart in order to stabilize the inverted flexible pendulum upright with reduced vibrations, is suggested along with. Flexibility of pendulum is accounted by the assumption of linear springs in system structure. Energy approach is used to frame the mathematical model using first principle method. Validation of proposed model is done by comparison of model simulation outputs with experimental results from actual plant. A simple Proportional Integral Derivative (PID) control is then applied to the system achieving output feedback control. In this process, only the cart motion information is fed back to the controller, while the angular displacement data of flexible inverted pendulum is not available. Yet, the pendulum oscillations are controlled and vibrations are reduced by assigning definite motion to the cart. Simulation outputs show that smooth PID controlled cart movement reduces the pendulum oscillations.