LQI Control of a Self Balancing Robot: A Numerical Study of the Impact of the Integral Approximation

This work aims to explore the effects of the integral term in the discrete-time implementation of the LQI controller. To achieve this, a two-wheeled self-balancing robot system is used as a case study, and three types of numerical integration approximations are considered: Backward Euler, Forward Euler, and Tustin. Through simulations, the results obtained with each approximation are compared against the expected continuoustime design. The simulation results demonstrate that while there are no significant differences for small sampling times, the Tustin approximation exhibits notably better performance than the other alternatives as the sampling time increases.