Discrete-Time Integral LQR and H∞ Control of a Two-Wheeled Self-Balancing Robot

Abstract

Inverted pendulum systems are widely used in both education and research within control theory. There are different types of inverted pendulums, such as the Furuta pendulum, cart-pole system, reaction wheel pendulum, etc. This study investigates the dynamics of a Two-Wheeled Self-Balancing Robot, a complex electromechanical system characterized by inherently
nonlinear dynamics, unstable equilibrium points, and underactuation (i.e., more degrees of freedom than control inputs), inspired by inverted pendulum systems. The primary objective pursued in this investigation is to guide the robot along a predefined trajectory while maintaining its vertical orientation. To achieve this, we designed and implemented two controllers with an integrator in the feedback loop for a Two-Wheeled Self-Balancing Robot prototype. One controller considers the Linear Quadratic Regulator (LQR) technique, and the second is based on the H∞ approach. Due to the use of a      microcontroller platform, we designed the controller in discrete time to implement it. Ramp-like and sinusoidal references were used to set the robot’s displacement targets, aiming to track these references while maintaining its vertical upright position. Simulations and practical tests were conducted using the Simulink® software within the Matlab® environment to evaluate the effectiveness of the proposed control strategies. The performances of the closed-loop system using each controller are compared. The results demonstrate the capability of the designed controllers to achieve the predefined objective, even in the presence.