A mathematical model of a small fixed-wing aircraft was developed through application of parameter estimation techniques to simulated flight test data. Multiple controllers were devised based on this model for path following, including a self-scheduled linear parameter-varying (LPV) controller with path curvature as a scheduling parameter. The robustness and performance of these controllers were tested in a rigorous MATLAB simulation environment that included steady winds and gusts, measurement noise, delays, and model uncertainties. The linear controllers designed within were found to be robust to the disturbances and uncertainties in the simulation environment, and had similar or better performance in comparison to a nonlinear control law operating in an inner-outer loop structure. Steps are being taken to implement the resulting controllers on the unmanned aerial vehicle (UAV) testbed in the Nonlinear Systems Laboratory at Virginia Tech. / Master of Science

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第17889号 / 工博第3798号 / 新制||工||1581(附属図書館) / 30709 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 萩原 朋道, 教授 土居 伸二, 准教授 久門 尚史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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With the rapid growth of space activities and advancement of aerospace science and technology, many autonomous space missions have been proliferating in recent decades. Control of spacecraft in proximity operations is of great importance to accomplish these missions. The research in this dissertation aims to provide a precise, efficient, optimal, and robust controller to ensure successful spacecraft proximity operations. This is a challenging control task since the problem involves highly nonlinear dynamics including translational motion, rotational motion, and flexible structure deformation and vibration. In addition, uncertainties in the system modeling parameters and disturbances make the precise control more difficult. Four control design approaches are integrated to solve this challenging problem. The first approach is to consider the spacecraft rigid body translational and rotational dynamics together with the flexible motion in one unified optimal control framework so that the overall system performance and constraints can be addressed in one optimization process. The second approach is to formulate the robust control objectives into the optimal control cost function and prove the equivalency between the robust stabilization problem and the transformed optimal control problem. The third approach is to employ the è-D technique, a novel optimal control method that is based on a perturbation solution to the Hamilton-Jacobi-Bellman equation, to solve the nonlinear optimal control problem obtained from the indirect robust control formulation. The resultant optimal control law can be obtained in closedorm, and thus facilitates the onboard implementation. The integration of these three approaches is called the integrated indirect robust control scheme. The fourth approach is to use the inverse optimal adaptive control method combined with the indirect robust control scheme to alleviate the conservativeness of the indirect robust control scheme by using online parameter estimation such that adaptive, robust, and optimal properties can all be achieved. To show the effectiveness of the proposed control approaches, six degree-offreedom spacecraft proximity operation simulation is conducted and demonstrates satisfying performance under various uncertainties and disturbances.

Flutter is an aeroelastic instability phenomenon that can result either in serious damage or complete destruction of a gas turbine blade structure due to high cycle fatigue. Although 90% of potential high cycle fatigue occurrences are uncovered during engine development, the remaining 10% stand for one third of the total engine development costs. Field experience has shown that during the last decades as much as 46% of fighter aircrafts were not mission-capable in certain periods due to high cycle fatigue related mishaps. To assure a reliable and safe operation, potential for blade flutter must be eliminated from the turbomachinery stages. However, even the most computationally intensive higher order models of today are not able to predict flutter accurately. Moreover, there are uncertainties in the operational environment, and gas turbine parts degrade over time due to fouling, erosion and corrosion resulting in parametric uncertainties. Therefore, it is essential to design engines that are robust with respect to the possible uncertainties. In this thesis, the robustness of an axial compressor blade design is studied with respect to parametric uncertainties through the Mu analysis. The nominal flutter model is adopted from [9]. This model was derived by matching a two dimensional incompressible flow field across the flexible rotor and the rigid stator. The aerodynamic load on the blade is derived via the control volume analysis. For use in the Mu analysis, first the model originally described by a set of partial differential equations is reduced to ordinary differential equations by the Fourier series based collocation method. After that, the nominal model is obtained by linearizing the achieved non-linear ordinary differential equations. The uncertainties coming from the modeling assumptions and imperfectly known parameters and coefficients are all modeled as parametric uncertainties through the Monte Carlo simulation. As iv compared with other robustness analysis tools, such as Hinf, the Mu analysis is less conservative and can handle both structured and unstructured perturbations. Finally, Genetic Algorithm is used as an optimization tool to find ideal parameters that will ensure best performance in terms of damping out flutter. Simulation results show that the procedure described in this thesis can be effective in studying the flutter stability margin and can be used to guide the gas turbine blade design.

This dissertation addresses the problem of motion planning and control for nonholonomic mobile robots, particularly wheeled and tracked mobile robots, working in extreme environments, for example, desert, forest, and mine. In such environments, the mobile robots are highly subject to external disturbances (e.g., slippery terrain, dusty air, etc.), which essentially introduce uncertainties to the robot systems. The complexity of the motion planning problem is due to taking both nonholonomic and uncertainty constraints into account simultaneously. As a result, none of the conventional nonholonomic motion planning can be directly applied. The control problem is even more challenging since state constraints posed by obstacles in the environments must also be considered along with the nonholonomic and uncertainty constraints. In this research, we systematically develop a new type of motion planning technique that determines an optimal path for a mobile robot in a given environment. This motion planning technique is based on the idea of a maximum allowable uncertainty, which is a number assigned to each free configuration in the environment. The optimal path is a path connecting given initial and goal configurations through a series of configurations respecting the nonholonomic constraint and possessing the highest maximum allowable uncertainty. Both linear and quadratic approximations of the maximum allowable uncertainty, including their corresponding motion planners, have been studied. Additionally, we develop the first real-time robust control algorithm for the mobile robot under uncertainty to follow given paths safely and accurately in cluttered environments. The control algorithm also utilizes the concept of the maximum allowable uncertainty as well as the robust control theory. The simulation results have shown the effectiveness and robustness of the control algorithm in steering the mobile robot along a given path amidst obstacles without collisions even when the level of robot uncertainty is high. / Ph. D.

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Vertical Takeoff and Landing (VTOL) Unmanned Aerial Vehicles (UAVs) possess several beneficial attributes, including requiring minimal space to takeoff, hover, and land. The tailsitter is a type of VTOL airframe that combines the benefits of VTOL capability with the ability to achieve efficient horizontal flight. One type of tailsitter, the Quadrotor Biplane (QRBP), can transition the vehicle from hover as a quadrotor to horizontal flight as a biplane. The vehicle used in this thesis is a QRBP designed with special considerations for fully autonomous operation in an outdoor environment in the presence of model uncertainties. QRBPs undergo a rotation of 90° about its pitch axis during transition from vertical to horizontal flight that induces strong aerodynamic forces that are difficult to model, thus necessitating the use of a robust control method to overcome the resulting uncertainties in the model. A feedback-linearizing controller augmented with an H-Infinity robust control is developed to regulate the altitude and pitch angle of the vehicle for the whole flight regime, including the ascent, transition forward, and landing. The performance of the proposed control design is demonstrated through numerical simulations in MATLAB and outdoor flight tests. The H-Infinity controller successfully tracks the prescribed trajectory, demonstrating its value as a computationally inexpensive, robust control technique for QRBP tailsitter UAVs. / Master of Science / Vertical Takeoff and Landing (VTOL) Unmanned Aerial Vehicles (UAVs) are a special type of UAV that can takeoff, hover, and land vertically, which lends several benefits. VTOL aircraft have recently gained popularity due to their potential to serve as fast and efficient payload delivery vehicles for e-commerce. One type of VTOL aircraft, the Quadrotor Biplane (QRBP) combines the ability of a quadrotor aircraft to hover, with the efficient horizontal flight of a biplane. Such a vehicle is able to takeoff and land in confined spaces, and also travel large distances on a single battery. However, the takeoff maneuver of a QRBP involves pitching from vertical to horizontal flight, which causes the vehicle to experience strong aerodynamic effects that are difficult to accurately model. Thus, to autonomously perform this unique maneuver, a robust control technique is necessary. A robust UAV controller is one that functions even when there is a degree of uncertainty in the predicted behavior of the vehicle, such as differences between estimated and actual vehicle parameters, or the presence of external disturbances such as wind. Therefore, a robust controller known as H-Infinity is developed to regulate the altitude and pitch angle of the QRBP as it takes off, transitions to forward flight, flies as a biplane, transitions back to vertical flight, and lands. The performance of the proposed control design is validated using numerical simulations performed in MATLAB, and flight tests. The H-Infinity controller successfully tracks the prescribed trajectory, demonstrating its value as a reliable, computationally inexpensive, robust control technique for QRBP UAVs.

A method utilizing H2 control concepts and the numerical method of Polynomial Chaos was developed in order to create a novel robust probabilistically optimal control approach. This method was created for the practical reason that uncertainty in parameters tends to be inherent in system models. As such, the development of new methods utilizing probability density functions (PDFs) was desired. From a more theoretical viewpoint, the utilization of Polynomial Chaos for studying and designing control systems has not been very thoroughly investigated. The current work looks at expanding the H2 and related Linear Quadratic Regulator (LQR) control problems for systems with parametric uncertainty. This allows solving deterministic linear equations that represent probabilistic linear differential equations. The application of common LTI (Linear Time Invariant) tools to these expanded systems are theoretically justified and investigated. Examples demonstrating the utilized optimization process for minimizing the H2 norm and parallels to LQR design are presented. The dissertation begins with a thorough background section that reviews necessary probability theory. Also, the connection between Polynomial Chaos and dynamic systems is explained. Next, an overview of related control methods, as well as an in-depth review of current Polynomial Chaos literature is given. Following, formal analysis, related to the use of Polynomial Chaos, is provided. This lays the ground for the general method of control design using Polynomial Chaos and H2. Then an experimental section is included that demonstrates controller synthesis for a constructed probabilistic system. The experimental results lend support to the method. / Ph. D.