Robust H∞ control with saturation of the control signal applied to a Ball on Plate system

Abstract

This paper presents an application of robust control in a Ball on Plate System, whose purpose is to equilibrate a sphere in a inclinable surface. To achieve it, the controller minimizes the H∞ norm while also guaranteeing stability under control input saturation. The approach used consists of utilizing LMIs for the controller synthesis, by the Bounded-Real Lemma with a stability condition for input saturation. A Kalman filter is used to estimate the non-measurable state of the system and filter the output in order to reduce the measurement noise from the sensor. The controller and filter are applied to a real plant utilizing an ESP32 microcontroller. For the construction of the plant, a resistive touchscreen is used in order to measure position and two servomotors are used to incline the plane in two directions. The results presented show the efficiency of robust controllers in stabilizing real plants even under disturbances and the filter’s capacity of improving the output measure while also estimating non-measurable states.