Fixed-structure Control of LTI Systems with Polytopic-type Uncertainty:Application to Inverter-interfaced Microgrids

This thesis focuses on the development of robust control solutions for linear time-invariant interconnected systems affected by polytopic-type uncertainty. The main issues involved in the control of such systems, e.g. sensor and actuator placement, control configuration selection, and robust fixed-structure control design are included. The problem of fixed-structure control is intrinsically nonconvex and hence computationally intractable. Nevertheless, the problem has attracted considerable attention due to the great importance of fixed-structure controllers in practice. In this thesis, necessary and sufficient conditions for fixed-structure H_inf control of polytopic systems with a single uncertain parameter in terms of a finite number of bilinear matrix inequalities (BMIs) are developed. Increasing the number of uncertain parameters leads to sufficient BMI conditions, where the number of decision variables grows polynomially. Convex approximations of robust fixed-order and fixed-structure controller design which rely on the concept of strictly positive realness (SPRness) of transfer functions in state space setting are presented. Such approximations are based on the use of slack matrices whose duty is to decouple the product of unknown matrices. Several algorithms for determination and update of the slack matrices are given. It is shown that the problem of sensor and actuator placement in the polytopic interconnected systems can be formulated as an optimization problem by minimizing cardinality of some pattern matrices, while satisfying a guaranteed level of H_inf performance. The control configuration design is achieved by solving a convex optimization problem whose solution delivers a trade-off curve that starts with a centralized controller and ends with a decentralized or a distributed controller. The proposed approaches are applied to inverter-interfaced microgrids which consist of distributed generation (DG) units. To this end, two important control problems associated with the microgrids are considered: (i) Current control of grid-connected voltage-source converters with L/LCL filters and (ii) Voltage control of islanded microgrids. The proposed control strategies are able to independently regulate the direct and quadrature (dq) components of the converter currents and voltages at the point of common couplings (PCC) in a fully decoupled manner and provide satisfactory dynamic responses. The important problem of plug-and-play (PnP) capability of DGs in the microgrids is also studied. It is shown that an inverter-interfaced microgrid consisting of multi DGs under PnP functionality can be cast as a system with polytopic-type uncertainty. By virtue of this novel description and use of the results from theory of robust control, the stability of the microgrid system under PnP operation of DGs is preserved. Extensive case studies, based on time-domain simulations in MATLAB/SimPowerSystems Toolbox, are carried out to evaluate the performance of the proposed controllers under various test scenarios, e.g., load change, voltage and current tracking. Real-time hardware-in-the-loop case studies, using RT-LAB real-time platform of OPAL-RT Technologies, are also conducted to validate the performance of the designed controllers and demonstrate their insensitivity to hardware implementation issues, e.g., noise and PWM non-idealities. The simulation and experimental results demonstrate satisfactory performance of the designed controllers

Contribuições à teoria de controle de sistemas afins com comutação com aplicações em eletrônica de potência

Orientador: Grace Silva DeaectoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Esta tese é dedicada ao estudo da teoria de controle de sistemas afins com comutação e algumas de suas aplicações no contexto de eletrônica de potência. Após discussões preliminares, as contribuições principais são apresentadas. O objetivo comum ao longo deste trabalho é desenvolver, sob a perspectiva de otimização convexa, estratégias capazes de governar eventos de chaveamento em sistemas dinâmicos afins de maneira a levar a trajetória do estado a um ponto de referência desejado ou a rastrear uma trajetória variante no tempo. Metodologias de projeto, baseadas em uma função de Lyapunov quadrática generalizada, para função de comutação dependente do estado ou da saída são fornecidas para sistemas afins com comutação a tempo discreto para os quais apenas estabilidade prática é possível de ser assegurada. Subsequentemente, novas condições para estabilidade prática são introduzidas baseadas em desigualdades de Lyapunov-Metzler e levando em conta uma função de Lyapunov do tipo mínimo, que permite reduzir o conservadorismo referente à garantia de estabilidade. Uma metodologia para projetar ciclos limites e assegurar a estabilidade assintótica global foi também apresentada, que leva em conta uma função de Lyapunov variante no tempo e permite tratar otimização de desempenho H2 e Hinf. Ademais, novas discussões sobre a estabilidade de uma classe de sistemas com comutação não-lineares a tempo contínuo são introduzidas, nas quais o problema de rastreamento de trajetória é tratado. O estudo desta classe é de interesse visto que ela modela o comportamento dinâmico de conversores de potência CA-CC e de máquinas síncronas de ímã permanente alimentadas por inversores de tensão. Esta nova abordagem permite o controle de forma mais simples quando comparada a estratégias clássicas de controle vetorial. Finalmente, alguns resultados experimentais são apresentados, validando as estratégias de controle desenvolvidas. As condições de estabilidade e projeto são majoritariamente escritas em termos de desigualdades matriciais lineares e, logo, podem ser resolvidas de forma eficiente por resolvedores de programação semi-definida prontamente disponíveisAbstract: This dissertation is devoted to the study of switched affine systems control theory and some of its applications in power electronics context. After some preliminary discussions, the main contributions are presented. The common goal throughout this work is to develop, from a convex optimization viewpoint, strategies capable of governing switching events in dynamical affine systems in order to bring the state variable to a desired reference value or to track a time-varying trajectory profile. Design methodologies for state or output dependent switching function based on a generalized Lyapunov function are provided for discrete-time switched affine systems, where only practical stability is possible to be assured. Subsequently, novel practical stability conditions are proposed, based on Lyapunov-Metzler inequalities and taking into account a min-type Lyapunov function, which allows us to reduce conservativeness regarding stability guarantee. A methodology for designing limit cycles and assuring their global asymptotic stability is also presented, which takes into account a time-varying Lyapunov function and permits to cope with H2 and Hinf performance optimization. Afterward, novel discussions on the stability of a continuous-time nonlinear switched systems class are introduced, where the trajectory-tracking problem is addressed. The study about this class is of interest as it models the dynamic behavior of AC-DC power converters and permanent magnet synchronous machines fed by voltage source inverters. This new approach allows their control in a simpler manner when compared to classical field-oriented control strategies. Finally, some experimental results are presented, validating the developed control strategies. Stability and design conditions are mostly written as linear matrix inequalities and, thus, can be efficiently solved by readily available semi-definite programming solversDoutoradoMecatrônicaDoutor em Engenharia MecânicaPDSE 88881.187487/2018-01CAPESCNPQFAPES