Comparison of a Super-Twisting differentiator and a Luenberger observer for an Inertia Wheel Pendulum: An experimental approach

In this paper, the comparison between a Super-Twisting and a Luenberger observer for an Inertial Wheel Pendulum (IWP), linearized in its inverted position, is presented. Both are focused on the estimation of the arm and wheel velocity. To keep the pendulum at its operating point, a state feedback controller that requires the pendulum position and velocity is used. For the elimination of sensors needed to measure the pendulum position and velocity, the numerical derivative to obtain the IWP velocity through the measurement position is a method that has been applied, with the disadvantage of being sensitive to electrical noise in the system. To avoid this situation, the concept of state observer is introduced as a useful tool for velocity estimation. The Lineal Luenberger observer requires information of the mathematical model of the system while the Super-Twisting differentiator only requires the input and output measurement, besides it presents great robustness to disturbances. For those reasons, it is an excellent tool for velocity estimation in dynamical systems. The results are obtained numerically from experimental measurements.