Modeling and control of a two wheeled auto-balancing robot: A didactic platform for control engineering education

Abstract

This paper describes the modeling, instrumentation and control of a Two Wheeled Automatic Balancing Robot (TWABR). This mechatronic system has two independently driven wheels to balance in the gravity center above the axis of the wheels rotation. Its dynamic behavior has also served to illustrate fundamental concepts of stability, nonlinear dynamics, and modern control theory. The TWABR was designed using the ESP32 microcontroller as a digital control unit and the MPU6050 Inertial Measurement Unit as the main sensor. The dynamic model of the TWABR was analyzed through its representation in nonlinear differential equations and its linearized representation in the state space. With the linearized mathematical model around the equilibrium point, a classic PID controller and an optimal LQR controller were designed and simulated. The control objective was to balance the TWABR in the vertical equilibrium position, even when it is subjected to disturbances. The two control algorithms were simulated in the Matlab® / Simulink™ software platforms and implemented digitally on the physical TWABR system. As a result, the experimental comparison of the performance of the implemented controllers was performed, where its stabilization, control robustness and adequate dynamic response at the equilibrium point of the TWABR were evaluated.