Reduced Order Observer Based Pole Placement Design for Inverted Pendulum on Cart

Abstract

The inverted pendulum is an under actuated system and unstable system without a controller. In this paper modelling of an inverted pendulum is done using the Euler-Lagrange equation for stabilization of it. The controller gain is evaluated through state feedback and reduced-order observer design techniques and the result for the different initial conditions is compared. The state feedback controller is designed by Pole- placement technique for different desired pole locations. The simulation of the inverted pendulum based on reduced order pole placement design has been done on MATLAB/SIMULINK. It has been observed from the simulation result that the angular velocity and cart speed tracks the system response for different initial conditions by varying the desired pole location for the left-hand plane of the s-plane. In general, if some of the systems are unknown and the other state is known we can design using a re-duced-order observer for any physical system.