Research and Evaluation Analysis of Sliding Mode Control based on Linear Matrix Inequality for Two-Wheeled Self-Balancing Robot

The dynamic model of a two-wheeled self-balancing robot (TWSBR) has the characteristics of multivariable, strong coupling, nonlinear, and unstable control performance. In this paper, the mathematical model of the motor is combined with the Lagrangian equation of motion, and the dynamic model of the TWSBR based on voltage as the control input is re-established. Based on this dynamic model, a novel sliding mode control method based on linear matrix inequality (LMI-SMC) optimization is designed. The stability of TWSBR is proved using Lyapunov’s theorem. Finally, the sliding mode control method and the stability of TWSBR are verified through simulation. A detailed comparison with other typical control methods is carried out. The simulation results show that the sliding mode controller reduces the steady-state error, suppresses the chatting, and is robust.