Controle multivariável aplicado ao conversor back-to-back

Abstract

This thesis presents a study on back-to-back converter based on the multivariable system perspective. Multivariable systems have some unique characteristics. Thus, before studying the converter as a MIMO system, the work reviews the main concepts of MIMO systems and presents guidelines for analyzing and controlling multivariable power electronic converters. The main difference between the SISO and MIMO systems is the presence of directions. As the SISO system is one-dimensional, the output/input gain is a function only of the frequency value. MIMO systems deal with vectors and, as a consequence, the output/input gain not only depends on the frequency value but is also affected by the input vector direction. In this sense, the concept of maximum and minimum singular values are addressed as a fundamental part of analysis and control of multivariable plants. With the singular values decomposition, it is possible to find the directions in which a non-square system cannot be controlled. Based on other MIMO tools, it is possible to define, for plants that have more outputs than inputs, which outputs cannot be controlled. In this work the centralized control approach is adopted because it allows the overall control law optimization, which is not possible when the decentralized technique is used. In this context, the linear quadratic regulator becomes an interesting alternative due to its robustness and performance properties as well as easy implementation. The BTB topology is studied as a multivariable system in two different applications: i) interfacing two AC grids and ii) feeding local loads. For each system a comprehensive state-space model is developed and its main characteristics analyzed from a multivariable point of view. A systematic design is proposed to guide the choices of LQR weighting matrices. The criterion is based on the analysis of the singular values of the sensitivity, complementary sensitivity and disturbance sensitivity matrices and on the minimization of their infinity norms. Experimental results are presented to validate the theoretical approach and to show the effectiveness of the proposed multivariable control.