abstract: In the past decade, real-world applications of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAV) have increased significantly. There has been growing interest in one of these types of UAVs, called a tail-sitter UAV, due to its VTOL and cruise capabilities. This thesis presents the fabrication of a spherical tail-sitter UAV and derives a nonlinear mathematical model of its dynamics. The singularity in the attitude kinematics of the vehicle is avoided using Modified Rodrigues Parameters (MRP). The model parameters of the fabricated vehicle are calculated using the bifilar pendulum method, a motor stand, and ANSYS simulation software. Then the trim conditions at hover are calculated for the nonlinear model, and the rotational dynamics of the model are linearized around the equilibrium state with the calculated trim conditions. Robust controllers are designed to stabilize the UAV in hover using the H2 control and H-infinity control methodologies. For H2 control design, Linear Quadratic Gaussian (LQG) control is used. For the H infinity control design, Linear Matrix Inequalities (LMI) with frequency-dependent weights are derived and solved using the MATLAB toolbox YALMIP. In addition, a nonlinear controller is designed using the Sum-of-Squares (SOS) method to implement large-angle maneuvers for transitions between horizontal flight and vertical flight. Finally, the linear controllers are implemented in the fabricated spherical tail-sitter UAV for experimental validation. The performance trade-offs and the response of the UAV with the linear and nonlinear controllers are discussed in detail. / Dissertation/Thesis / Masters Thesis Aerospace Engineering 2018

The thesis contains a textbook for high school pupils. The aim of the textbook is to teach the reader how to solve problems concerning inequalities proposed at czech or international mathematical competitions for high school pupils. In the first part we present some basic ineqaulities (AG, Cauchy's inequality) and we show how to understand them and how to use them. In the second part we broaden reader's horizon by presenting rearrangement and Jensen's inequality. In the third part we present widely applicable methods such as "Abstract Concreteness Method" or "Sum of Squares Method". Some techniques concerning the Sum of Squares Method were written by Phan Kim Hung in 2006. We are trying to significantly involve the reader. We prefer just hints to many of the proposed problems rather than complete solutions and we give some harder problems to solve at the end of each part. 1