Orientador: Edvaldo Assunção / Resumo: A principal contribuição dessa tese é propor a representação H2/Hoo do regulador linear quadrático (LQR) para sistemas lineares invariantes no tempo e incertos. A motivação está em atender simultaneamente a minimização da função custo garantido e dos efeitos de entradas exógenas. De início, apresenta-se uma revisão da formulação do problema LQR usando-se a função de Lyapunov quadrática e, posteriormente, sua extensão aos modelos de incertezas. Neste ponto, a literatura volta-se exclusivamente ao uso de funções de Lyapunov com uma única matriz P para testar a estabilidade de todo o domínio de incerteza politópica, que naturalmente conduz a algum conservadorismo. Em vista de reduzir o pressuposto conservadorismo explorou-se técnicas de relaxação matricial através de lemas consolidados na literatura, i.e. Lema de Finsler e Lema da Projeção Recíproca. As novas formulações de síntese robusta permitem obter condições suficientes em desigualdades matriciais lineares (LMIs) por meio de funções de Lyapunov dependentes de parâmetros, embora não considere os efeitos da perturbação no processo de síntese de controle. Logo, o estudo da rejeição à perturbações permitiu obter condições LMIs inéditas envolvendo as normas H2/Hoo . Adicionalmente, é proposto o estudo da robustez da planta em malha fechada, via descrição combinada de incertezas nas matrizes de estados e de entradas, e do controlador, aplicando técnicas de fragilidade via incertezas limitadas por norma. Por fim, propõe-se um mét... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The main contribution of this thesis is to propose the H2/Hoo representation of the Linear Quadratic Regulator (LQR) for linear time-invariant uncertain systems. The motivation is to achieve the minimization of guaranteed cost and the effects of exogenous inputs, simultaneously. Initially, a review of the LQR problem formulation using the quadratic Lyapunov function is presented and after, its extension to the uncertain models. At this point, the literature turns to the use of Lyapunov functions with only one matrix P to test the stability of the whole polytopic domain, which naturally leads to some conservatism. The proposed to reduce the assumption conservatism allowed to explore techniques of matrix relaxation through classic lemmas in the literature, i.e. Finsler and Reciprocal Projection lemmas. The new robust synthesis formulations allow to obtain sufficient conditions in Linear Matrix Inequalities (LMIs) control by means of parameter-dependent Lyapunov functions; however, do not consider the perturbation effects on the control synthesis process. Thus, the study of disturbance rejection allowed to obtain new sufficient conditions via mixed H2/Hoo control. Furthermore, robustness studies of the closed-loop plant are proposed based on a mixed representation of uncertainties in the state and input matrices, and the controller robustness, by applying non-fragile theories via norm-bounded uncertainty. Finally, an LQR gain scheduling control method applied to linear time-vary... (Complete abstract click electronic access below) / Doutor

Cette thèse présente un nouveau cadre pour la conception de correcteurs à gain programmé. Une partie de ce cadre est une fusion novatrice de la théorie des systèmes et de la commande (la métrique ν-gap et sa variante fréquentiellle) et de l'analyse en grappes, technique commune en analyse de données statistiques, apprentissage automatique, fouille de données, etc. La combinaison des deux champs permet de subdiviser le domaine de fonctionnement d'un système non linéaire en secteurs afin de récupérer des informations sur le comportement en boucle fermée avant la conception de la commande. Chaque secteur représente une partie du domaine opérationnel ayant des propriétés de retour similaires, c'est-à-dire que les points de fonctionnement dans un secteur ont des comportements davantage similaires (mesurés par la mesure d'écart ponctuel) les uns des autres que les points de fonctionnement des autres secteurs. La solution de sectorisation est utilisée en vue de réaliser des correcteurs séquencés réglés à partir d'un modèle linéarisé. Par exemple, une distribution optimisée et parcimonieuse des points de synthèse pour les correcteurs LTI est sélectionnée et la distribution des secteurs est exploitée pour le mélange des correcteurs linéaires individuels en un correcteur non-linéaire couvrant l'ensemble du domaine de fonctionnement. L'avantage général de ce cadre est qu'il présente une procédure systématique qui réduit potentiellement le temps, les efforts et donc le coût global d'un projet de développement en réduisant les itérations inutiles au cours du cycle de conception. Le cadre proposé est évalué à partir d’un exemple générique de missile industriel. / This thesis presents a new framework for the design of gain-scheduled controllers. Part of this framework is a novel merging of system & control theory (the ν-gap and pointwise gap metric) and cluster analysis, a common technique in statistical data analysis, machine learning, data mining, etc. The combination of both fields allows for a subdivision of a nonlinear system's operating domain into sectors in order to retrieve information on the feedback behaviour before the actual control design. Each sector represents a part of the operating domain with similar feedback properties, i.e. operating points inside a sector are more similar (as measured by the pointwise gap metric) to each other than to operating points in other sectors. The sectoring solution is used in the proposed framework to support the design of a linearization-based gain-scheduled controller. For example, a reduced and optimized distribution of design points for the LTI controllers is selected and the sectors' distribution is exploited for the blending of the individual linear controllers into an operating domain wide nonlinear controller. The overall advantage of the framework is that it presents a systematic procedure that potentially reduces the overall time, effort, and therefore cost of a development project by preventing unnecessary iterations in the design cycle specifically associated with the control design. The proposed framework is verified at the example of a generic industrial missile benchmark.

<p>The goal of this Master thesis has on the one hand been to create a simulation environment for robots, where not only the simulations in this work can be performed, but also similar robot simulations, and on the other hand to study regulators that can increase the possibilities of rejecting disturbances on an industrial robot. The robot model used has three degrees of freedom, corresponding to the three main links on ABB:s IRB7600. </p><p>The simulation environment is created using Matlab, Simulink, and Robotics Toolbox. It is constructed in a general way and can be used for simulations of other robot objects created in Robotics Toolbox. </p><p>A gain scheduling is added to the LQ-regulator, where the feedback matrix is varied depending on the arm position in the workspace. The gain scheduling is implemented along a reference path in the workspace, around which the simulations and frequency analyses are performed. </p><p>The regulators that have been tested are a PID-regulator, a gain scheduled LQ-regulator, a gain scheduled LQ-regulator with reconstructed states, and finally a fix LQ-regulator with reconstructed states. Results from the tests show that the gain scheduling LQ-regulator is the one that yields the best rejection of disturbances, but the corresponding regulator with reconstructed states, which is more realistic, performs nearly as well. The model based regulators are, however, significantly better when it comes to rejecting disturbances than the PID-regulator.</p>

<p>The overall objective of the Wallenberg Laboratory for Information Technology and Autonomous Systems (WITAS) at Linköping University is the development of an intelligent command and control system, containing vision sensors, which supports the operation of a unmanned air vehicle (UAV) in both semi- and full-autonomy modes. One of the UAV platforms of choice is the APID-MK3 unmanned helicopter, by Scandicraft Systems AB. The intended operational environment is over widely varying geographical terrain with traffic networks and vehicle interaction of variable complexity, speed, and density.</p><p>The present version of APID-MK3 is capable of autonomous take-off, landing, and hovering as well as of autonomously executing pre-defined, point-to-point flight where the latter is executed at low-speed. This is enough for performing missions like site mapping and surveillance, and communications, but for the above mentioned operational environment higher speeds are desired. In this context, the goal of this thesis is to explore the possibilities for achieving stable ‘‘aggressive’’ manoeuvrability at high-speeds, and test a variety of control solutions in the APID-MK3 simulation environment.</p><p>The objective of achieving ‘‘aggressive’’ manoeuvrability concerns the design of attitude/velocity/position controllers which act on much larger ranges of the body attitude angles, by utilizing the full range of the rotor attitude angles. In this context, a flight controller should achieve tracking of curvilinear trajectories at relatively high speeds in a robust, w.r.t. external disturbances, manner. Take-off and landing are not considered here since APIDMK3 has already have dedicated control modules that realize these flight modes.</p><p>With this goal in mind, we present the design of two different types of flight controllers: a fuzzy controller and a gradient descent method based controller. Common to both are model based design, the use of nonlinear control approaches, and an inner- and outer-loop control scheme. The performance of these controllers is tested in simulation using the nonlinear model of APID-MK3.</p> / Report code: LiU-Tek-Lic-2002:11. The format of the electronic version of this thesis differs slightly from the printed one: this is due mainly to font compatibility. The figures and body of the thesis are remaining unchanged.

This research is concerned with the flight dynamic, pitch flight control and flying qualities assessment for the reference BWB aircraft. It aims to develop the longitudinal control laws which could satisfy the flying and handing qualities over the whole flight envelope with added consideration of centre of gravity (CG) variation. In order to achieve this goal, both the longitudinal stability augmentation system (SAS) and autopilot control laws are studied in this thesis. Using the pole placement method, two sets of local Linear-Time-Invariant (LTI) SAS controllers are designed from the viewpoints of flying and handing qualities assessment and wind disturbance checking. The global gain schedule is developed with the scheduling variable of dynamic pressure to transfer gains smoothly between these two trim points. In addition, the poles movement of short period mode with the varying CG position are analysed, and some approaches of control system design to address the problem of reduced stability induced by CG variation are discussed as well. To achieve the command control for the aircraft, outer loop autopilot both pitch attitude hold and altitude hold are implemented by using the root locus method. By the existing criteria in MIL-F-8785C specifications being employed to assess the augmented aircraft response, the SAS linear controller with automatic changing gains effectively improve the stability characteristic for the reference BWB aircraft over the whole envelope. Hence, the augmented aircraft equals to a good characteristic controlled object for the outer loop or command path design, which guarantee the satisfactory performance of command control for the BWB aircraft. The flight control law for the longitudinal was completed with the SAS controller and autopilot design. In particular, the SAS was achieved with Level 1 flying and handing qualities, meanwhile the autopilot system was applied to obtain a satisfactory pitch attitude and altitude tracking performance.

For research purposes Saab has developed a generic mathematical model denoted VEGAS of an aircraft with a configuration similar to JAS 39 Gripen. Today parts of Gripen backup control system are used also for VEGAS making the system subject to both corporate and defense secrecy. The main objective of this master thesis is to design, verify and implement public pitch axis flight control system for VEGAS. Furthermore, simplifications regarding the design process is to be examined. Design of pitch axis flight control system for the entire flight envelope has been carried out. Linearization of the dynamic model and programming design environment are used as development tools. The control system has been tested and verified in real-time simulator. Linear quadratic optimization (LQ) and gain-scheduling are often used when designing aircraft control system. This method tends to require extensive design effort. This thesis suggests an alternative method combining LQ and scaling of parameters.

Robust control design has become a major research area during the last twenty years and there are nowadays several robust design methods available. One example of such a method is the robust loop shaping method that was developed by K. Glover and D. C. MacFarlane in the late 1980s. The idea of this method is to use decentralized controller design to give the singular values of the loop gain a desired shape. This step is called Loop Shaping and it is followed by a Robust Stabilization procedure, which aims to give the closed loop system a maximum degree of stability margins. In this thesis, the robust loop shaping method is used to design a gain scheduled controller for a missile. The report consists of three parts, where the first part introduces the Robust Loop Shaping theory and a Gain Scheduling approach. The second part discusses the missile and its characteristics. In the third part a controller is designed and a short analysis of the closed loop system is performed. A scheduled controller is implemented in a nonlinear environment, in which performance and robustness are tested. Robust Loop Shaping is easy to use and simulations show that the resulting controller is able to cope with model perturbations without considerable loss in performance. The missile should be able to operate in a large speed interval. There, it is shown that a single controller does not stabilize the missile everywhere. The gain scheduled controller is however able to do so, which is shown by means of simulations.

The goal of this Master thesis has on the one hand been to create a simulation environment for robots, where not only the simulations in this work can be performed, but also similar robot simulations, and on the other hand to study regulators that can increase the possibilities of rejecting disturbances on an industrial robot. The robot model used has three degrees of freedom, corresponding to the three main links on ABB:s IRB7600. The simulation environment is created using Matlab, Simulink, and Robotics Toolbox. It is constructed in a general way and can be used for simulations of other robot objects created in Robotics Toolbox. A gain scheduling is added to the LQ-regulator, where the feedback matrix is varied depending on the arm position in the workspace. The gain scheduling is implemented along a reference path in the workspace, around which the simulations and frequency analyses are performed. The regulators that have been tested are a PID-regulator, a gain scheduled LQ-regulator, a gain scheduled LQ-regulator with reconstructed states, and finally a fix LQ-regulator with reconstructed states. Results from the tests show that the gain scheduling LQ-regulator is the one that yields the best rejection of disturbances, but the corresponding regulator with reconstructed states, which is more realistic, performs nearly as well. The model based regulators are, however, significantly better when it comes to rejecting disturbances than the PID-regulator.

<p>For research purposes Saab has developed a generic mathematical model denoted VEGAS of an aircraft with a configuration similar to JAS 39 Gripen. Today parts of Gripen backup control system are used also for VEGAS making the system subject to both corporate and defense secrecy. </p><p>The main objective of this master thesis is to design, verify and implement public pitch axis flight control system for VEGAS. Furthermore, simplifications regarding the design process is to be examined. </p><p>Design of pitch axis flight control system for the entire flight envelope has been carried out. Linearization of the dynamic model and programming design environment are used as development tools. The control system has been tested and verified in real-time simulator. </p><p>Linear quadratic optimization (LQ) and gain-scheduling are often used when designing aircraft control system. This method tends to require extensive design effort. This thesis suggests an alternative method combining LQ and scaling of parameters.</p>

<p>Robust control design has become a major research area during the last twenty years and there are nowadays several robust design methods available. One example of such a method is the robust loop shaping method that was developed by K. Glover and D. C. MacFarlane in the late 1980s. The idea of this method is to use decentralized controller design to give the singular values of the loop gain a desired shape. This step is called Loop Shaping and it is followed by a Robust Stabilization procedure, which aims to give the closed loop system a maximum degree of stability margins. In this thesis, the robust loop shaping method is used to design a gain scheduled controller for a missile. The report consists of three parts, where the first part introduces the Robust Loop Shaping theory and a Gain Scheduling approach. The second part discusses the missile and its characteristics. In the third part a controller is designed and a short analysis of the closed loop system is performed. A scheduled controller is implemented in a nonlinear environment, in which performance and robustness are tested. Robust Loop Shaping is easy to use and simulations show that the resulting controller is able to cope with model perturbations without considerable loss in performance. The missile should be able to operate in a large speed interval. There, it is shown that a single controller does not stabilize the missile everywhere. The gain scheduled controller is however able to do so, which is shown by means of simulations.</p>