Design, Simulation and Optimal Control of Two-Wheel Self-balancing Robot Using LQR and PID

Abstract

Two-Wheel Self-Balancing Robot (TWSBR), based on the principle of Inverted Pendulum on a cart, is designed to balance vertically. Without control, it has unstable, non-linear dynamics, falling forward or backward when disturbed. This type of robot, with its flexibility to turn in narrow paths, has applications in hospitals, catering, warehouse, surveillance and many more. The linearized TWSBR model's state-space representation was analyzed at equilibrium and a full-state feedback controller was designed and simulated. This was done using Linear Quadratic Regulator (LQR) and a hybrid controller (LQR+PID), focusing on the system states namely: cart position/velocity, pendulum tilt angle/angular velocity. An STM32 microcontroller was used for digital control, with an MPU6050 sensor for angle measurement. Comparing LQR and LQR+PID, the latter showed better tilt angle response, with faster response time, lower per-centage overshoot, and faster settling time while maintaining stability. Findings of this research highlight the potential of hybrid controllers in achieving better performance and robustness in controlling two-wheel self-balancing robots.