Control theory in practice : stabilization of a self-balancing robot using LQR and SMC

Control theory plays an important role in the design and stability of dynamic systems. It is necessary to understand how control strategies must be implemented and how they are tuned and modified to make them work in an actual system. This report presents result in a short study on the design, implementation, and analysis of two distinct control methods—Linear Quadratic Regulator (LQR) and Sliding Mode Control (SMC)—for controlling the Minseg$^{TM}$ robot, a type of self-balancing robot commerically available from minseg.com. The design process involved modelling of the physical system to obtain equations of motion and state space equations, followed by designing LQR and SMC controllers, which were then implemented on the actual system using an Arduino platform. The results showed that the designed LQR controller had an average difference between consecutive convergence times of 0.27 s and an average consecutive tracking error of 0.0353 rad, while the SMC controller achieved an average difference between consecutive convergence times of 0.08 s and an average consecutive tracking error of 0.0169 rad. Although, the SMC controller showed faster convergence times and lower tracking error, the LQR control showed better overall stability and was able to balance the robot for more time than SMC. Overall, the motivation behind this report was to gain understanding of control design and to demonstrate how some practical aspects of control theory can be applied.Mechanical Engineerin