Modeling and Control of a Ball-Balancing Robot

Blonk, J.W. van der (2014) Modeling and Control of a Ball-Balancing Robot.

Abstract:A Ball-Balancing Robot (BBR) is an omni-directional robot balancing on a single ball, which makes it inherently unstable. This project follows the goal of developing a model and a controller for this robot in order to make it balance and move around as a demonstrator on fairs. To achieve this goal, the three-dimensional dynamic behaviour of the robot is approximated by three independent two-dimensional models. Due to neglected dependencies between the twodimensional models and the conversions that had to made from the two-dimensional models to the three-dimensional system, a three-dimensional model is developed to describe the full dynamic behaviour of the BBR and it is linearized around the position the BBR stands upright. Based on the linearized three-dimensional model, a linear controller is designed. The controller calculates the appropriate motor torques based on the measured tilt angle, required to keep the BBR dynamically stable. First a simple, easily implementable controller is designed with LQR control theory to make the BBR `fair ready' as soon as possible. Later a more advanced controller is designed with SISO loopshaping. Simulations prove that the performance of the system with regard to balancing is signi�cantly higher with the controller, designed with SISO loopshaping. During the implementation of the �rst controller, it turns out that noisy sensor data forms a serious restriction on the performance of the BBR. In particular, noisy gyroscope data limits the magnitude of the controller gains. The noise is signi�cantly reduced by attenuating system vibrations, oversampling of the gyroscope and �ltering the motor inputs, which results in a robot that is able to balance. Furthermore, based on the developed three-dimensional model, research is done to investigate under what requirements the system remains stable with the developed controller. The aim of this research is to analyze the in uence of uncertainties in the developed model and to predict the in uence of future changes on the stability of the system.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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