Stabilization of Inverted Pendulum on Cart Based on LQG Optimal Control

An inverted pendulum on cart is an object which is a nonlinear, unstable system, is used as a standard for designing the control methods and finds most versatile application in the field of control theory. To achieve the stabilization of an inverted pendulum system state observer based linear quadratic Gaussian optimal control has been applied. As the separation principal of LQG states, first the control law has been obtained to design a state feedback controller and when the system's all states are not measurable as well as system is affected by process and measurement noise, Kalman Filter has been designed for the inverted pendulum system. The results shown that the new designed controller stabilizes the inverted pendulum system as well as eliminates process and measurement noise. Simulation has been carried out to show the approach.