Stability Analysis and Assessment of Double Inverted Pendulum with LQR and LQG Controllers


Dang Anh Duy, Le Hoai Phuong, Vo Duy Cong*


Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, VietNam.
Vietnam National University Ho Chi Minh City (VNU-HCM), Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam.

Corresponding Author Email: congvd@hcmut.edu.vn

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper presents the stability analysis and assessment of a double inverted pendulum on a cart with LQR and LQG control algorithms. First, the mathematical model of the system is presented. Then the LQR controller is designed to stabilize the inverted pendulum system without noise. The simulation results performed in the MATLAB environment show that the system has a good response. However, after adding noise, the system is no longer stable and oscillates around the equilibrium position. Therefore, the Kalman filter is applied in the LQG controller to filter out the noise. Simulations are performed and show the effectiveness of the Kalman filter in noise reduction. Finally, the LQG is applied to control the position of the cart.