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.

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<p>In order to design robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low.</p><p>The approach used in the thesis is based on formulating the constraint on the maximum order of the plant as a polynomial equation. By using the fact that the polynomial is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex polynomial function is to be minimized over a convex set defined by linear matrix inequalities.</p><p>To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems.</p><p>The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.</p>

<p>Dynamiken för en starkt accelerande robot har modellerats. Modellen linjäriseras så att roboten beskrivs som ett linjärt tidsvariabelt system. Denna representation beskriver roboten väl då robotens anblåsningsvinkel, vilket är vinkeln mellan robotkroppen och robotens hastighet, är liten. Eftersom det ej är möjligt att mäta alla robotens tillstånd har en observatör tagits fram i form av ett Kalmanfilter. Problematik vid framtagandet av observatören diskuteras i rapporten. Den linjära tidsvariabla modellen har använts till att ta fram två regulatorer. En LQ-regulator och en H_∞-regulator. Hur dessa tas fram och vilka problem som finns diskuteras i rapporten. För att kunna se fördelar och nackdelar beträffande prestanda och robusthet har en mängd tester gjort. Testerna visar på olika fördelar hos de olika reglersystemen. Till exempel är det lättare att få bra prestanda med LQ-regulatorn än H_∞-regulatorn om systemet som styrs stämmer bra överens med systemet som använts vid reglerdesignen. H_∞-regulatorn har bättre förmåga att anpassa sig till modellförändringar givet att observatören gör bra skattningar. Det är dock svårt att utnämna en generell vinnare.</p>

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 135-140).

In order to design robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low. The approach used in the thesis is based on formulating the constraint on the maximum order of the plant as a polynomial equation. By using the fact that the polynomial is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex polynomial function is to be minimized over a convex set defined by linear matrix inequalities. To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems. The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.

This thesis is divided in to two different parts. The first part includes examination of the measurementsystem of an industrial robot using a resolver sensor. The main focus is on methods for suppressing noise in the angularvelocity signal without increasing timedelay. Five different methods are investigated. Three of these are based on oversampling: burstsamplingmethod, meanvaluemethod and correlationmethod. The meanvaluemethod and the correlationmethod have given good results. The two other methods are: extended kalmanfiltering and computation of the angular velocity without using numeric method to compute the angle. Extended kalmanfilter gives the overall best result. In part two the control structure design of an industrial robot has been studied and how different sampling times and motorinertias affect the disturbance rejection and stability of the control loop. Different control structure designs have also been studied with the aim to suppress disturbances. Mainly H-infinity and GIMC designs have been compared with an ordinary PID controller. Here it can be shown that both the H-infinity and the GIMC controller yields good disturbance rejection. But both the methods lack in the robustness of model uncertainty.

The objective of adaptive control is to design a controller that can adjust its behaviour to tolerate uncertain or time-varying parameters. An adaptive controller typically consists of a linear time-invariant (LTI) compensator together with a tuning mechanism which adjusts the compensator parameters and yields a nonlinear controller. Because of the nonlinearity, the transient closed-loop behaviour is often poor and the control signal may become unduly large. Although the initial objective of adaptive control was to deal with time-varying plant parameters, most classical adaptive controllers cannot handle rapidly changing parameters. Recently, the use of a linear periodic (LP) controller has been proposed as a new approach in the field of model reference adaptive control [1]. In this new approach, instead of estimating plant parameters, the “ideal control signal” (what the control signal would be if the plant parameters and states were measurable) is estimated. The resulting controller has a number of desirable features: (1) it handles rapid changes in the plant parameters, (2) it provides nice transient behaviour of the closed-loop system, (3) it guarantees that the effect of the initial conditions declines to zero exponentially, and (4) it generates control signals which are modest in size. Although the linear periodic controller (LPC) has the above advantages, it has some imperfections. In order to achieve the desirable features, a rapidly varying control signal and a small sampling period are used. The rapidly time-varying control signal requires fast actuators which may not be practical. The second weakness of the LPC [1] is poor noise rejection behaviour. The small sampling period results in large controller gains and correspondingly poor noise sensitivity, since there is a clear trade-off between tracking and noise tolerance. As the last drawback, this controller requires knowledge of the exact plant relative degree. Here we extend this work in several directions: (i) In [1], the infinity-norm is used to measure the signal size. Here we redesign the controller to yield a new version which provides comparable results when the more common 2-norm is used to measure signal size, (ii) A key drawback of the controller of [1] is that the control signal moves rapidly. Here we redesign the control law to significantly alleviate this problem, (iii) The redesigned controller can handle large parameter variation and in the case that the sign of high frequency gain is known, the closed-loop system is remarkably noise-tolerant, (iv) We prove that in an important special case, we can replace the requirement of knowledge of the exact relative degree with that of an upper bound on the relative degree, at least from the point of view of providing stability, and (v) A number of approaches to improve the noise behaviour of the controller are presented. Reference: [1] D. E. Miller, “A New Approach to Model Reference Adaptive Control”, IEEE Transaction on Automatic Control, Vol. 48, No. 5, pages 743-756, May 2003.

Dynamiken för en starkt accelerande robot har modellerats. Modellen linjäriseras så att roboten beskrivs som ett linjärt tidsvariabelt system. Denna representation beskriver roboten väl då robotens anblåsningsvinkel, vilket är vinkeln mellan robotkroppen och robotens hastighet, är liten. Eftersom det ej är möjligt att mäta alla robotens tillstånd har en observatör tagits fram i form av ett Kalmanfilter. Problematik vid framtagandet av observatören diskuteras i rapporten. Den linjära tidsvariabla modellen har använts till att ta fram två regulatorer. En LQ-regulator och en H∞-regulator. Hur dessa tas fram och vilka problem som finns diskuteras i rapporten. För att kunna se fördelar och nackdelar beträffande prestanda och robusthet har en mängd tester gjort. Testerna visar på olika fördelar hos de olika reglersystemen. Till exempel är det lättare att få bra prestanda med LQ-regulatorn än H∞-regulatorn om systemet som styrs stämmer bra överens med systemet som använts vid reglerdesignen. H∞-regulatorn har bättre förmåga att anpassa sig till modellförändringar givet att observatören gör bra skattningar. Det är dock svårt att utnämna en generell vinnare.