Event-triggered control for rational and Lur’e type nonlinear systems

In the present work, the design of event-triggered controllers for two classes of nonlinear systems is addressed: rational systems and Lur’e type systems. Lyapunov theory techniques are used in both cases to derive asymptotic stability conditions in the form of linear matrix inequalities that are then used in convex optimization problems as means of computing the control system parameters aiming at a reduction of the number of events generated. In the context of rational systems, state-feedback control is considered and differentialalgebraic representations are used as means to obtain tractable stability conditions. An event-triggering strategy which uses weighting matrices to strive for less events is proposed and then it is proven that this strategy does not lead to Zeno behavior. In the case of Lur’e systems, observer-based state-feedback is addressed with event generators that have access only to the system output and observed state, but it imposes the need of a dwell-time, i.e. a time interval after each event where the trigger condition is not evaluated, to cope with Zeno behavior. Two distinct approaches, exact time-discretization and looped-functional techniques, are considered to ensure asymptotic stability in the presence of the dwell-time. For both system classes, emulation design and co-design are addressed. In the emulation design context, the control law (and the observer gains, when appropriate) are given and the task is to compute the event generator parameters. In the co-design context, the event generator and the control law or the observer can be simultaneously designed. Numerical examples are presented to illustrate the application of the proposed methods.Neste trabalho é abordado o projeto de controladores baseados em eventos para duas classes de sistemas não lineares: sistemas racionais e sistemas tipo Lur’e. Técnicas da teoria de Lyapunov são usadas em ambos os casos para derivar condições de estabilidade assintótica na forma de inequações matriciais lineares. Tais condições são então utilizadas em problemas de otimização convexa como meio de calcular os parâmetros do sistema de controle, visando uma redução no número de eventos gerados. No contexto de sistemas racionais, realimentação de estados é considerada e representações algébrico-diferenciais são usadas como meio de obter condições de estabilidade tratáveis computacionalmente. Uma estratégia de disparo de eventos que usa uma medida de erro ponderado através de matrizes definidas positivas é proposta e é demonstrado que tal estratégia não gera comportamento de Zenão. No caso de sistemas tipo Lur’e, considera-se o caso de controladores com restrições de informações, a saber, com acesso apenas às saídas do sistema. Um observador de estados é então utilizado para recuperar a informação faltante. Neste contexto, é necessária a introdução de um tempo de espera (dwell time, em inglês) para garantir a inexistência de comportamento de Zenão. Todavia, a introdução do tempo de espera apresenta um desafio adicional na garantia de estabilidade que é tratado neste trabalho considerando duas técnicas possíveis: a discretização exata do sistema e o uso de looped-functionals (funcionais em laço, em uma tradução livre). Para ambas classes de sistemas, são tratados os problemas de projeto por emulação e co-design (projeto simultâneo, em uma tradução livre). No projeto por emulação, a lei de controle (e os ganhos do observador, quando apropriado) são dados a priori e a tarefa é projetar os parâmetros do gerador de eventos. No caso do co-design, o gerador de eventos e a lei de controle ou o observador são projetados simultaneamente. Exemplos numéricos são usados para ilustrar a aplicação dos métodos propostos

A non-square sector condition and its application in deferred-action anti-windup compensator design

Abstract A sector condition for two connected deadzone nonlinearities is provided. By introducing an additional non-square operator which exploits their connectivity, a more general set of sector-like matrix inequalities is obtained. This "non-square" matrix inequality condition is applied to an anti-windup (AW) problem in which the AW compensator is not activated until the unconstrained control signal reaches a welldefined level beyond that of the physical actuator limits. The non-square sector condition allows such "deferred-action" AW synthesis to be performed in a manner much closer to traditional ("immediate") sector-based AW with either lowered conservatism or decreased computational effort in contrast to recent work. The non-square condition is applicable to other AW problems

A non-square sector condition and its application in deferred-action anti-windup compensator design

A sector condition for two connected deadzone nonlinearities is provided. By introducing an additional non-square operator which exploits their connectivity, a more general set of sector-like matrix inequalities is obtained. This “non-square” matrix inequality condition is applied to an anti-windup (AW) problem in which the AW compensator is not activated until the unconstrained control signal reaches a well-defined level beyond that of the physical actuator limits. The non-square sector condition allows such “deferred-action” AW synthesis to be performed in a manner much closer to traditional (“immediate”) sector-based AW with either lowered conservatism or decreased computational effort in contrast to recent work. The non-square condition is applicable to other AW problems

Single chip solution for stabilization control & monocular visual servoing of small-scale quadrotor helicopter

This thesis documents the research undertaken to develop a high-performing design of a small-scale quadrotor (four-rotor) helicopter capable of delivering the speed and robustness required for agile motion while also featuring an autonomous visual servoing capability within the size, weight, and power (SWaP) constraint package. The state of the art research was reviewed, and the areas in the existing design methodologies that can potentially be improved were identified, which included development of a comprehensive dynamics model of quadrotor, design and construction of a performance optimized prototype vehicle, high-performance actuator design, design of a robust attitude stabilization controller, and a single chip solution for autonomous vision based position control. The gaps in the current art of designing each component were addressed individually. The outcomes of the corresponding development activities include a high-fidelity dynamics and control model of the vehicle. The model was developed using multi-body bond graph modeling approach to incorporate the dynamic interactions between the frame body and propulsion system. Using an algorithmic size, payload capacity, and flight endurance optimization approach, a quadrotor prototype was designed and constructed. In order to conform to the optimized geometric and performance parameters, the frame of the prototype was constructed using printed circuit board (PCB) technology and processing power was integrated using a single chip field programmable gate array (FPGA) technology. Furthermore, to actuate the quadrotor at a high update rate while also improving the power efficiency of the actuation system, a ground up FPGA based brushless direct current (BLDC) motor driver was designed using a low-loss commutation scheme and hall effect sensors. A proportional-integral-derivative (PID) technology based closed loop motor speed controller was also implemented in the same FPGA hardware for precise speed control of the motors. In addition, a novel control law was formulated for robust attitude stabilization by adopting a cascaded architecture of active disturbance rejection control (ADRC) technology and PID control technology. Using the same single FPGA chip to drive an on-board downward looking camera, a monocular visual servoing solution was developed to integrate an autonomous position control feature with the quadrotor. Accordingly, a numerically simple relative position estimation technique was implemented in FPGA hardware that relies on a passive landmark/target for 3-D position estimation. The functionality and effectiveness of the synthesized design were evaluated by performance benchmarking experiments conducted on each individual component as well as on the complete system constructed from these components. It was observed that the proposed small-scale quadrotor, even though just 43 cm in diameter, can lift 434 gm of payload while operating for 18 min. Among the ground up designed components, the FPGA based motor driver demonstrated a maximum of 4% improvement in the power consumption and at the same time can handle a command update at a rate of 16 kHz. The cascaded attitude stabilization controller can asymptotically stabilize the vehicle within 426 ms of the command update. Robust control performance under stochastic wind gusts is also observed from the stabilization controller. Finally, the single chip FPGA based monocular visual servoing solution can estimate pose information at the camera rate of 37 fps and accordingly the quadrotor can autonomously climb/descend and/or hover over a passive target

A differential game theory approach to DC-DC buck converter control

Tribunal: Prof. Rafael Canetti, Prof. Eleonora Catsigeras (Universidad de la República), Prof. Martin Ordonez (University of British Columbia, Canadá).This thesis deals with the problem of controlling a generic synchronous buck converter against unpredictable, and possibly discontinuous, but bounded load disturbances. The problem is canonically framed as a dynamical conflict between the automatic controller in charge of the output voltage regulation and an hypothetical disturber. In particular, the conflict is regarded as a pursuit-evasion game in distance. Applying classical methods of differential game theory, the game is completely solved identifing three qualitative different cases that can take place depending on how a positive derived parameter value compares to unity. The game’s solution provides optimal strategies for the controller and the disturber which can be used, respectively, for worst-case-aware control and benchmark testing (of any control method). Furthermore, from the topography of the game’s value function, qualitative and quantitative information about the physical limits of buck converter control is gained, allowing for early design stage optimization of the converter’s LC filter towards regulation performance, regardless of the control method that might finally be selected.Esta tesis aborda el problema de controlar un convertidor sincrónico tipo buck genérico frente a perturbaciones impredecibles, y posiblemente discontinuas, pero acotadas de la corriente de carga. El problema se plantea en forma canónica como un conflicto dinámico entre el controlador automático encargado de la regulación del voltaje de salida y un perturbador hipotético. En particular, el conflicto es visto como un juego de persecusión-evasión en distancia. Aplicando métodos clásicos de la teoría de juegos diferenciales, el juego es completamente resuelto identificando tres casos cualitativamente distintos que pueden ocurrir dependiendo de si el valor de un parámetro derivado positivo es menor, igual, o mayor que uno. La solución del juego provee estrategias óptimas para el controlador y para el perturbador que pueden ser utilizadas, respectivamente, para implementar control ante el peor caso y para realizar pruebas de referencia (aplicables a cualquier método de control). Además, de la topografía de la función valor del juego, se obtiene información cualitativa y cuantitativa acerca de los límites físicos inherentes al control de convertidores tipo buck, permitiendo la optimización del filtro LC con respecto al desempeño de la regulación en las primeras etapas de diseño, aun antes de haber finalmente elegido un método de control

Wind Power

This book is the result of inspirations and contributions from many researchers of different fields. A wide verity of research results are merged together to make this book useful for students and researchers who will take contribution for further development of the existing technology. I hope you will enjoy the book, so that my effort to bringing it together for you will be successful. In my capacity, as the Editor of this book, I would like to thanks and appreciate the chapter authors, who ensured the quality of the material as well as submitting their best works. Most of the results presented in to the book have already been published on international journals and appreciated in many international conferences