An Extremum Seeking Estimator Design and Its Application to Monitoring Unbalanced Mass Dynamics

When sensor information of a controlled-system output is not available, estimators can be used. Estimators are algorithms that take the available sensor data from the system and estimate the necessary data to be used by the feedback controller. Typically, estimation is done by running a model of the plant inside the controller and formulating an output error minimization mechanism to calculate the unknown dynamics and parameters. In this paper, a new estimation mechanism based on extremum seeking is presented. The method utilizes the idea of minimization of a non-linear error function of written in a specific structure, which may be suitable for systems with periodic dynamics such as systems with unbalanced masses. An estimation adjustment algorithm can be built based on the error between the model outputs and the actual sensor data. This adjustment algorithm drives the error between the model and the actual plant output to zero, while the feedback controller uses the information from the model. This proposed method is then applied to a mobile robotic system to improve its locomotion. Our initial results showed promising improvements up to five times more displacement with the same command on a testbed environment with challenges in eluding high-order dynamics and digital effects at high-frequency input.