A Study of Two-Wheel Self-Balancing Robot Dynamics for Control Systems Learning

The two-wheeled self-balancing robot (TWSBR), utilizing an inverted pendulum arrangement, exhibits dynamic stability while being statically unstable. Due to this behavior, the TWSBR system has been used to demonstrate fundamental principles of stability, nonlinear dynamics, and control theory. In this work, a computational study of the TWSBR was carried out to develop a mathematical model using Newtonian mechanics that serves as an educational tool in control education for demonstrating the impact of different control algorithms such as Proportional (P), ProportionalDerivative (PD), and Proportional-Integral-Derivative (PID) on system stability. The comparison of P, PD, and PID controllers was undertaken to demonstrate the practical advantages of each controller in improving the robot's stability and responsiveness. The PID controller was designed and optimized using the Root-locus techniques, with a damping ratio equal to 1 which exhibits a fast-settling time with minimum overshoots. When an impulse response was applied to the PID controller in the simulation environment it demonstrated system can reach a dynamic balance within 1.2 seconds demonstrating the effectiveness of the proposed PID controller. The optimal gain parameters K value and Kp, Ki, and Kd parameter values were determined using root-locus analysis, which allowed the system to operate with great stability and minimum settling time. These findings highlight the TWSBR's educational significance as a hands-on tool for teaching practical applications of control theory, as well as providing valuable insights into the design and optimization of control systems for dynamic balance tasks. This study emphasizes the relevance of control algorithms in achieving rapid and stable dynamic behaviors, making it a valuable learning resource for both students and instructors. Keywords: Two-wheeled self-balancing robot, Inverted pendulum, P, PD and PID controllers, Stability analysis, Control Education