Experimental LQR Control for a Double-Linked Inverted Pendulum on Cart

Abstract

This paper presents an experimental study on the stabilization of a double inverted pendulum on a cart using a Linear Quadratic Regulator controller. Building upon previous simulation-based research, the current work focuses on the practical implementation of the LQR control strategy on a real laboratory setup. The mathematical model of the system was first derived using Lagrangian dynamics and validated through simulations to ensure accuracy. An LQR controller was then designed and implemented on an experimental platform consisting of a DC motor, encoder sensors, and a real-time control unit. The experimental results clearly demonstrate the capability of the LQR controller to stabilize both pendulum links in the upright position while maintaining bounded cart motion and acceptable energy consumption. Furthermore, a systematic comparison between simulation and experimental results is provided, showing strong agreement and confirming the robustness of the proposed approach. This study highlights the feasibility of applying LQR control in real-world underactuated systems and provides a solid foundation for future research on advanced and intelligent control strategies, including nonlinear and adaptive methods.