Dinámica no lineal en un convertidor buck de tres celdas controlado por un PWM digital

Los convertidores multicelulares se han desarrollado con el fin de mejorar las deficiencias existentes en los dispositivos de conmutación que son usados normalmente. El control en sistemasmulti-celulares tiene dos propósitos principales: equilibrar las tensiones entre los switches y regular la corriente en la carga a un valor deseado. En este estudio, se utiliza un controlador digital con PWM para un convertidor buck de tres celdas. El análisis del circuito se hizo con modelado en tiempo discreto utilizando mapas de Poincaré. Se obtuvieron simulaciones numéricas usando el modelo matemático, estas muestran que el sistema puede presentar fenómenos no lineales en forma de bifurcaciones. Este hecho se confirmó con un software simulador de circuitos. Varios tipos de comportamientos se pueden detectar al variar algunos parámetros de diseño. Se encontraron puntos fijos y se hizo un análisis de estabilidad de las órbitas periódicas. Estos resultados validaron los diagramas de bifurcación al detectar la primera bifurcación. Diagramas de bifurcación de dos y tres dimensional fueron obtenidos. Se utilizó también un método en el cual hay una aproximación para el método de Poincaré, de este método se obtuvieron diagramas de una y dos dimensiones. Este método también se utilizó para hacer el análisis de estabilidad de los puntos fijos / Abstract: Multi-cell converters have been developed to overcome shortcomings in usual switching devices. The control systems in multi-cell converters have two main purposes: balance the voltages between the switches and regulate the load current to a desired value. In this work, a PWM digital control is applied to a three-cell buck converter. The circuit analysis was carried out by using discrete time modeling in the form of Poincare map. Numerical simulations obtained from the mathematical model show that the system can undergo nonlinear phenomena in the form of bifurcations. This was confirmed with software to simulate circuits. Different kinds of behaviors are detected by varying some design parameters. Fixed points were found and orbital stability analysis was made. These results helped to validate bifurcation diagrams by recognizing the first bifurcation. Two and three dimensional bifurcation diagrams were also obtained. An approximation of the Poincare map method was used as well, one and two dimensional bifurcation diagrams were obtained using it. It was also applied in the stability analysis of the fixed points.Maestrí

Optimal, Multi-Modal Control with Applications in Robotics

The objective of this dissertation is to incorporate the concept of optimality to multi-modal control and apply the theoretical results to obtain successful navigation strategies for autonomous mobile robots. The main idea in multi-modal control is to breakup a complex control task into simpler tasks. In particular, number of control modes are constructed, each with respect to a particular task, and these modes are combined according to some supervisory control logic in order to complete the overall control task. This way of modularizing the control task lends itself particularly well to the control of autonomous mobile robot, as evidenced by the success of behavior-based robotics. Many challenging and interesting research issues arise when employing multi-modal control. This thesis aims to address these issues within an optimal control framework. In particular, the contributions of this dissertation are as follows: We first addressed the problem of inferring global behaviors from a collection of local rules (i.e., feedback control laws). Next, we addressed the issue of adaptively varying the multi-modal control system to further improve performance. Inspired by adaptive multi-modal control, we presented a constructivist framework for the learning from example problem. This framework was applied to the DARPA sponsored Learning Applied to Ground Robots (LAGR) project. Next, we addressed the optimal control of multi-modal systems with infinite dimensional constraints. These constraints are formulated as multi-modal, multi-dimensional (M3D) systems, where the dimensions of the state and control spaces change between modes to account for the constraints, to ease the computational burdens associated with traditional methods. Finally, we used multi-modal control strategies to develop effective navigation strategies for autonomous mobile robots. The theoretical results presented in this thesis are verified by conducting simulated experiments using Matlab and actual experiments using the Magellan Pro robot platform and the LAGR robot. In closing, the main strength of multi-modal control lies in breaking up complex control task into simpler tasks. This divide-and-conquer approach helps modularize the control system. This has the same effect on complex control systems that object-oriented programming has for large-scale computer programs, namely it allows greater simplicity, flexibility, and adaptability.Ph.D.Committee Chair: Egerstedt, Magnus; Committee Member: Ferri, Bonnie; Committee Member: Lee, Chin-Hui; Committee Member: Reveliotis, Spyros; Committee Member: Yezzi, Anthon