Design of reduced-order observer and linear quadratic regulator for inverted pendulum on cart

This paper aims to design a reduced observer and optimal controller to stabilize an inverted pendulum on a cart. Pendulum moves with the cart in the direction of the circle tracking. We separately design a reduced-order observer and a linear quadratic regulator (LQR), then combine them to be observer-based controller. Simulation results will demonstrate the responses of pendulum angle and cart position and compare the design results of the reduced-order observer/LQR with the fullorder observer/LQR.