Modeling, construction and control of a self-balancing unicycle. - Neves, Gabriel Pereira das (2017)
In this work, a unicycle system with reaction wheel is presented, considering the construction, the modeling, the design and test of the controllers. Firstly, a mechanical model considering a tridimensional computer aided design (3D CAD) is built in order to assist the construction and, after that, the modeling using the Lagrange method. In this work, linear controllers are designed and, therefore, the linearization of the system is done by the Jacobian, that is, assuming small variations around the equilibrium point. In this situation, there is no coupling between the pitch and the roll angles, thus resembling two inverted pendulums. The prototype is constructed by attaching the electronic components, the battery, the wheels and the motors to a body, to make it fully autonomous. The positioning of the parts has to balanced in order to maintain the position of the center of mass along the vertical and horizontal axis of symmetry. Then, a linear control project is done to stabilize the plant using two techniques that are validated considering simulations of the nonlinear coupled system. Then, the techniques were tested in the built prototype. The first one consists of the optimal LQR control that, although it worked, presented some problems due to parametric uncertainties. Therefore, the H2 control is used via LMI in such a way that the project becomes similar to the LQR, but in this way it is possible to insert parametric uncertainties and find a controller with some degree of robustness to them.