Observability and observer design for switched linear systems

Hybrid vehicles, HVAC systems in new/old buildings, power networks, and the like require safe, robust control that includes switching the mode of operation to meet environmental and performance objectives. Such switched systems consist of a set of continuous-time dynamical behaviors whose sequence of operational modes is driven by an underlying decision process. This thesis investigates feasibility conditions and a methodology for state and mode reconstruction given input-output measurements (not including mode sequence). An application herein considers insulation failures in permanent magnet synchronous machines (PMSMs) used in heavy hybrid vehicles. Leveraging the feasibility literature for switched linear time-invariant systems, this thesis introduces two additional feasibility results: 1) detecting switches from safe modes into failure modes and 2) state and mode estimation for switched linear time-varying systems. This thesis also addresses the robust observability problem of computing the smallest structured perturbations to system matrices that causes observer infeasibility (with respect to the Frobenius norm). This robustness framework is sufficiently general to solve related robustness problems including controllability, stabilizability, and detectability. Having established feasibility, real-time observer reconstruction of the state and mode sequence becomes possible. We propose the embedded moving horizon observer (EMHO), which re-poses the reconstruction as an optimization using an embedded state model which relaxes the range of the mode sequence estimates into a continuous space. Optimal state and mode estimates minimize an L2-norm between the measured output and estimated output of the associated embedded state model. Necessary conditions for observer convergence are developed. The EMHO is adapted to solve the surface PMSM fault detection problem

Robust Full-Order and Reduced- Order Observers for a Class of Uncertain Switched Systems

This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMI) constraint, a robust sliding-mode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reduced-order switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reduced-order switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a full-order switched observer exists also guarantee the existence of a reduced-order switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified three-tank system

Time-triggered and event-triggered control of switched affine systems via a hybrid dynamical approach

This paper focuses on the design of both periodic time- and event-triggered control laws of switched affine systems using a hybrid dynamical system approach. The novelties of this paper rely on the hybrid dynamical representation of this class of systems and on a free-matrix min-projection control, which relaxes the structure of the usual Lyapunov matrix-based min-projection control. This contribution also presents an extension of the usual periodic time-triggered implementation to the event-triggered one, where the control input updates are permitted only when a particular event is detected. Together with the definition of an appropriate optimization problem, a stabilization result is formulated to ensure the uniform global asymptotic stability of an attractor for both types of controllers, which is a neighborhood of the desired operating point. Finally, the proposed method is evaluated through a numerical example.Agence Nationale de la Recherche (ANR)France Grant ANR-18-CE40-0022-01Agencia Estatal de Investigación (AEI)-Spain Grant PID2019-105890RJ-10

Estimation and stability of nonlinear control systems under intermittent information with applications to multi-agent robotics

This dissertation investigates the role of intermittent information in estimation and control problems and applies the obtained results to multi-agent tasks in robotics. First, we develop a stochastic hybrid model of mobile networks able to capture a large variety of heterogeneous multi-agent problems and phenomena. This model is applied to a case study where a heterogeneous mobile sensor network cooperatively detects and tracks mobile targets based on intermittent observations. When these observations form a satisfactory target trajectory, a mobile sensor is switched to the pursuit mode and deployed to capture the target. The cost of operating the sensors is determined from the geometric properties of the network, environment and probability of target detection. The above case study is motivated by the Marco Polo game played by children in swimming pools. Second, we develop adaptive sampling of targets positions in order to minimize energy consumption, while satisfying performance guarantees such as increased probability of detection over time, and no-escape conditions. A parsimonious predictor-corrector tracking filter, that uses geometrical properties of targets\u27 tracks to estimate their positions using imperfect and intermittent measurements, is presented. It is shown that this filter requires substantially less information and processing power than the Unscented Kalman Filter and Sampling Importance Resampling Particle Filter, while providing comparable estimation performance in the presence of intermittent information. Third, we investigate stability of nonlinear control systems under intermittent information. We replace the traditional periodic paradigm, where the up-to-date information is transmitted and control laws are executed in a periodic fashion, with the event-triggered paradigm. Building on the small gain theorem, we develop input-output triggered control algorithms yielding stable closed-loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise environment, the developed algorithm yields stable, asymptotically stable, and Lp-stable (with bias) closed-loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on Lp-stability are presented. Prediction of a triggering event is achieved by employing Lp-gains over a finite horizon in the small gain theorem. By resorting to convex programming, a method to compute Lp-gains over a finite horizon is devised. Next, we investigate optimal intermittent feedback for nonlinear control systems. Using the currently available measurements from a plant, we develop a methodology that outputs when to update the control law with new measurements such that a given cost function is minimized. Our cost function captures trade-offs between the performance and energy consumption of the control system. The optimization problem is formulated as a Dynamic Programming problem, and Approximate Dynamic Programming is employed to solve it. Instead of advocating a particular approximation architecture for Approximate Dynamic Programming, we formulate properties that successful approximation architectures satisfy. In addition, we consider problems with partially observable states, and propose Particle Filtering to deal with partially observable states and intermittent feedback. Finally, we investigate a decentralized output synchronization problem of heterogeneous linear systems. We develop a self-triggered output broadcasting policy for the interconnected systems. Broadcasting time instants adapt to the current communication topology. For a fixed topology, our broadcasting policy yields global exponential output synchronization, and Lp-stable output synchronization in the presence of disturbances. Employing a converse Lyapunov theorem for impulsive systems, we provide an average dwell time condition that yields disturbance-to-state stable output synchronization in case of switching topology. Our approach is applicable to directed and unbalanced communication topologies.\u2

Almost sure H∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays

This paperinvestigatesthealmostsure H1 sliding mode control (SMC) problem for non linear stochastic systems with Markovian switching and time-delays. An integral sliding surface is first constructed for the addressed system. Then, by employing the topping time method combined with martingale in equalities, sufficient conditions are established to ensure the almost surely exponential stability and the H 1 performance of the system dynamics in the specified sliding surface. ASMC law is designed to guarantee the reach ability of the specified sliding surface almost surely. Furthermore, the obtained results are applied to a class of special nonlinear stochastic systems with Markovian switching and time-delays, where the desired SMC law is obtained in terms of the solutions to a set of matrix in equalities. Finally, a numerical example is given to show the effectiveness of the proposed SMC scheme

Design of switching strategies with applications in photovoltaic energy generation

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2014.Abstract : This work presents control strategies and stability analysis for switched systemswith a proposed application to photovoltaic energy generation systems.The conditions are based on Linear Matrix Inequalities (LMIs).Initially, a general description of the photovoltaic systems is presented coveringthe following aspects: the modeling of a photovoltaic array, some commonconnection topologies, the main objectives, techniques for maximizingthe generated power, among other informations. This content is necessary forthe control design method proposed in this work.Next, a design technique for the stabilization of affine switched systems isshown. The methodology used is based on the Lyapunov?s theory for stabilityof systems, describing sufficient conditions for the proposed switchingrule design in the form of LMIs and solving them using existing softwarepackages. In the sequel, the switching strategy is extended for a class ofnonlinear systems of great interest, especially for the control of photovoltaicsystems. This class is composed of systems containing sector-bounded nonlinearities.Furthermore, a method for stability analysis of switched systemsis proposed, extending the class of switched systems analyzed by the currentliterature. Numerical examples illustrate all the approaches developed.At the end, the application of the nonlinear control techniques to photovoltaicgeneration systems is presented. The main objectives considered are thetracking of the maximum power generation, with robustness to variations ofthe input parameters of the photovoltaic array, and the delivery of only activepower to the grid. Finally, simulation results demonstrate the applicabilityof the methodology for the control of this type of system, evidencing thecompliance of the stated objectives.Resumo expandido : Durante a última década, a tecnologia de sistemas fotovoltaicos tem mostrado potencial para se tornar uma das principais fontes de energia para o mundo, com crescimento contínuo e robusto, mesmo em tempos de crise econômica e financeira. Visando ampliar o aproveitamento da energia gerada e até mesmo reduzir os custos do sistema, o projeto de técnicas de controle eficientes apresenta grande importância para este tipo de sistema. Em sistemas fotovoltaicos o controle é realizado através de conversores de potência, que são sistemas chaveados. Por este motivo, o foco principal deste trabalho é a apresentação de estratégias de controle e análise de estabilidade para sistemas chaveados com uma proposta de aplicação para sistemas de geração de energia fotovoltaica. As condições de projeto e análise são todas baseadas em desigualdades matriciais lineares (LMIs). Inicialmente, uma descrição geral dos sistemas fotovoltaicos é apresentada, contendo a modelagem de um arranjo fotovoltaico, algumas topologias comuns de conexão, os principais objetivos, técnicas para a maximização da potência gerada, dentre outras informações necessárias para o projeto da técnica de controle proposta para este sistema. Na sequência é mostrada uma técnica de projeto de estratégias de chaveamento, cujo objetivo principal é garantir estabilidade e desempenho de sistemas comutados. A metodologia usada é baseada na teoria de estabilidade de Lyapunov, de modo a descrever condições suficientes para o projeto da lei de chaveamento em forma de LMIs e resolvê-las usando pacotes computacionais existentes. O método se aplica à classe de sistemas chaveados onde cada subsistema tem um campo vetorial afim e considera-se uma lei de chaveamento baseada no máximo entre funções auxiliares. A estabilidade do sistema em malha fechada é garantida mesmo se modos deslizantes ocorram em qualquer superfície de chaveamento resultante do projeto. Os resultados são apresentados para os casos de realimentação completa e realimentação parcial dos estados do sistema. Em seguida, uma das principais contribuições da tese, a proposta de uma extensão da lei de chaveamento para uma classe de sistemas chaveados não lineares é apresentada. O sistema pode conter não linearidades dependentes do estado limitadas em setor, como é o caso da não linearidade existente no modelo de painéis fotovoltaicos. As funções não lineares podem conter também parâmetros incertos, contanto que a função permaneça dentro dos limites do setor dado para toda a faixa de valores de interesse do parâmetro. Além disso, condições de projeto de leis de chaveamento independentes do equilíbrio são fornecidas e, portanto, neste caso a técnica se torna robusta a mudanças no ponto de operação desejado. Por fim, considerações sobre limitar a frequência de chaveamento são discutidas. A aplicação das técnicas descritas anteriormente para topologias comuns de conexão de sistemas fotovoltaicos é apresentada em seguida. Alguns dos desafios superados são a presença de referências variáveis, não linearidades limitadas em setor e medição parcial de estados no mesmo sistema. A aplicabilidade da metodologia para controlar o sistema fotovoltaico é ilustrada através de simulações baseadas em um exemplo numérico usando parâmetros de um sistema real. Como resultado requisitos importantes são satisfeitos, como o rastreamento do ponto de máxima potência e robustez com relação aos parâmetros incertos do painel fotovoltaico. Para a obtenção da robustez foram derivadas equações para determinar um setor que contem a não linearidade para quaisquer valores dos parâmetros. As dificuldades e perspectivas para o caso mais complexo (conexão com a rede elétrica) também são apresentadas. Motivado pela falta de técnicas de análise de estabilidade de sistemas seccionalmente afins contendo modos deslizantes na literatura atual, condições LMI suficientes para resolver este problema são propostas, resultando em outra importante contribuição da tese. As condições são baseadas em uma função de Lyapunov composta pela combinação convexa de funções quadráticas diferentes para cada região do sistema. As condições propostas incluem o importante caso onde o ponto de equilíbrio está localizado na fronteira entre subsistemas afim. Adicionalmente, condições suficientes para análise independentemente da parametrização das superfícies de chaveamento são derivadas, isto é, a superfície de chaveamento pode ser desconhecida neste caso. A nova técnica leva a uma metodologia unificada para a análise de estabilidade de sistemas seccionalmente afins e de sistemas chaveados afins com uma superfície de chaveamento previamente projetada. Esta tese é organizada em sete capítulos, quatro apêndices e referências. O Capítulo 1 tem o objetivo de contextualizar e motivar de forma breve o assunto da tese. O conhecimento básico sobre sistemas fotovoltaicos necessário para a aplicação proposta no documento é concentrado no Capítulo 2. O Capítulo 3 apresenta uma técnica de projeto de uma lei de chaveamento para o controle de sistemas chaveados com campos vetoriais afim. Esta técnica serve de base para as principais contribuições teóricas desta tese, apresentadas nos Capítulos 4, 5 e 6. No Capítulo 4, é apresentado o projeto de leis de chaveamento para sistemas chaveados contendo não linearidades limitadas em um setor, enquanto o Capítulo 5 apresenta a aplicação desta técnica para o controle de sistemas fotovoltaicos. No Capítulo 6, um método para análise de estabilidade de sistemas seccionalmente afins é introduzida. Exemplos numéricos são utilizados para ilustrar todas as contribuições da tese em seus respectivos capítulos. Algumas conclusões são discutidas no Capítulo 7, incluindo uma lista de sugestões para trabalhos futuros. Por fim, três apêndices demonstram o equacionamento de ferramentas de circuitos elétricos trifásicos utilizadas na tese e um apêndice apresenta resumos das publicações geradas pelo autor durante o período de doutorado

Hybrid control of power converters

Cette thèse propose la conception de lois de commandes hybrides pour les convertisseurs électroniques de puissance. Ce nouveau type de lois de commande est basé sur l'utilisation de modèles hybrides qui capturent les comportements dynamiques macroscopiques de ces dispositifs électroniques, essentiellement leur nature hybride. Dans le contexte de la régulation des convertisseurs DC-DC ou AC-DC, en appliquant la théorie des systèmes hybrides, il est ainsi prouvé que les lois de commandes proposées assurent la stabilité de la boucle fermée ainsi que certaines performances de type LQ. Pour un onduleur en demi-pont (convertisseur DC-AC), une loi de commande hybride est proposée afin que la tension de sortie suive une référence sinusoïdale souhaitée. Dans le cas d'une charge inconnue, une loi de commande adaptative est alors couplée à la commande hybride permettant l'estimation de la charge et donc une régulation ou un suivi de trajectoire plus précis. Notons que pour obtenir une régulation ou un suivi parfait, une fréquence infinie est souvent obligatoire pour les lois de contrôle proposées, ce qui est inappropriée en pratique. Pour résoudre ce problème, une régularisation de l'espace d'état ou du temps est ajoutée à la boucle fermée assurant un temps de maintien entre deux sauts consécutifs et réduisant ainsi considérablement la fréquence de commutation.This thesis proposes the design of hybrid control laws for power electronics converters. These new type of control laws are based on some hybrid models which capture the macroscopic dynamical behaviors of such electronic devices, essentially its hybrid nature. In the context of the regulation of DC-DC or AC-DC converters, applying the hybrid dynamical theory, the proposed control laws are proved to ensure the stability of the closed loop as well as some LQ performances. For a half-bridge inverter (DC-AC converter), a hybrid control law is proposed in order that the output voltage tracks a desired sinusoidal reference. In the case of unknown load, an adaptive control law is coupled to the hybrid control allowing the estimation of the load and therefore leading to a more precise regulation or tracking. Notice that in order to achieve a perfect regulation or tracking, an infinite frequency is often mandatory for the proposed control laws, which is inappropriate in practice. To tackle this problem, a space- or time-regularization are added to the hybrid closed-loop ensuring a dwell time between two consecutive jumps and reducing thus drastically the switching frequency

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

Multiple Objective Co-Optimization of Switched Reluctance Machine Design and Control

This dissertation includes a review of various motor types, a motivation for selecting the switched reluctance motor (SRM) as a focus of this work, a review of SRM design and control optimization methods in literature, a proposed co-optimization approach, and empirical evaluations to validate the models and proposed co-optimization methods. The switched reluctance motor (SRM) was chosen as a focus of research based on its low cost, easy manufacturability, moderate performance and efficiency, and its potential for improvement through advanced design and control optimization. After a review of SRM design and control optimization methods in the literature, it was found that co-optimization of both SRM design and controls is not common, and key areas for improvement in methods for optimizing SRM design and control were identified. Among many things, this includes the need for computationally efficient transient models with the accuracy of FEA simulations and the need for co-optimization of both machine geometry and control methods throughout the entire operation range with multiple objectives such as torque ripple, efficiency, etc. A modeling and optimization framework with multiple stages is proposed that includes robust transient simulators that use mappings from FEA in order to optimize SRM geometry, windings, and control conditions throughout the entire operation region with multiple objectives. These unique methods include the use of particle swarm optimization to determine current profiles for low to moderate speeds and other optimization methods to determine optimal control conditions throughout the entire operation range with consideration of various characteristics and boundary conditions such as voltage and current constraints. This multi-stage optimization process includes down-selections in two previous stages based on performance and operational characteristics at zero and maximum speed. Co-optimization of SRM design and control conditions is demonstrated as a final design is selected based on a fitness function evaluating various operational characteristics including torque ripple and efficiency throughout the torque-speed operation range. The final design was scaled, fabricated, and tested to demonstrate the viability of the proposed framework and co-optimization method. Accuracy of the models was confirmed by comparing simulated and empirical results. Test results from operation at various torques and speeds demonstrates the effectiveness of the optimization approach throughout the entire operating range. Furthermore, test results confirm the feasibility of the proposed torque ripple minimization and efficiency maximization control schemes. A key benefit of the overall proposed approach is that a wide range of machine design parameters and control conditions can be swept, and based on the needs of an application, the designer can select the appropriate geometry, winding, and control approach based on various performance functions that consider torque ripple, efficiency, and other metrics