Research of Parallel-Type Double Inverted Pendulum Model Based on Lagrange Equation and LQR Controller

Abstract

Car inverted pendulum system is often used as a benchmark for verifying the performance and effectiveness of a new control method. However, it's very unusual to use parallel-type double inverted pendulum. Based on Lagrange equation, this paper presents a novel state space model for the parallel-type double inverted pendulum system. In contrast to the modeling of traditional car inverted pendulum, the technical challenge in this system is that the analysis of the spring increases research complexity. Furthermore, this paper designs a LQR controller with the Lagrange modeling method. Simulation results are presented to demonstrate the feasibility and performance of the proposed model and controller.