Comparative Study of Linear Quadratic Gaussian and Linear Quadratic Regulator Controllers for Rotary Double Inverted Pendulum in Parallel Type

In this article, two methods including Linear Quadratic Regulation (LQR) and Linear Quadratic Gaussian (LQG) are applied to the Rotary Double Inverted Pendulum in Parallel Type (PRDIP). PRDIP is a new, advanced system of single rotary inverted pendulum (RIP) which belongs to class of underactuated biped robots. Accordingly, responses of the output system with LQR and LQG are compared to demonstrate that the PRDIP with LQG control scheme has better quality and performance than LQR. Additionally, the two controllers are applied to the PRDIP system at the zero- $\boldsymbol{\pi}$ position which means one pendulum is in the upward position and the other is in the downward position for anti-oscillation with two test cases for demonstration purposes. Simulation results, together with explanations and discussions, are presented in this work to evaluate the focal points mentioned below.