Multi-converter electronic systems are becoming widely used in many industrial applications; therefore, the stability of the whole system is a big concern to the real-world power supplies applications. A multi-converter system comprised of cascaded converters has a basic configuration that consists of two or more converters in series connection, where the first is a source converter that maintains a regulated dc voltage on the intermediate bus while remaining are load converters that convert the intermediate bus voltage to the tightly regulated outputs for the next system stage or load. Instability in cascaded systems may occur due to the constant power load (CPL), which is a behavior of the tightly regulated converters. CPLs exhibit incremental negative resistance behavior causing a high risk of instability in interconnected converters. In addition, there are other problems apart from the CPL, e.g., non-linearities due to the inductive element and uncertainties due to the imprecision of a mathematical model of dc-dc converters. Aiming to effectively mitigate oscillations effects in the output of source converter loaded with a CPL, in this paper, an interval robust controller, by linear programming based on Kharitonov rectangle, is proposed to regulate the output of source converter. Several tests were developed by using an experimental plant and simulation models when the multi-converter buck-buck system is subjected to a variation of power reference. Both simulation and experimental results show the effectiveness of the proposed controller. Furthermore, the performance indices computed from the experimental data show that the proposed controller outperforms a classical control technique. INDEX TERMS Constant power load (CPL), multi-converter buck-buck system, parametric uncertainties, robust control based on Kharitonov rectangle, mitigation oscillations in multi-converter buck-buck system.

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Resumo -Este artigo propõe uma estratégia de controle preditivo baseado em modelo aplicado a um conversor boost com célula de comutação de três estados que confere mais simplicidade e sistematização nas fases de projeto e análise do controlador, cujo ganho integral ajustável dispensa o reprojeto nas matrizes de ponderação. Para simplificar a análise de estabilidade do controlador, utiliza-se o conceito de elipsoides de estabilidade, um assunto ainda pouco explorado neste contexto. O controle preditivo proposto parte da modelagem da planta no espaço de estados médio linear e variante no tempo, cujas variações paramétricas são tratadas como incertezas politópicas expressas por meio de desigualdades matriciais lineares (LMIs) com relaxações.Aspectos teórico-experimentais são aplicados e analisados em um conversor de 1 kW com incertezas na tensão de entrada e na carga. Além disso, para estabelecer uma base de desempenho, o MPC proposto é comparado com o controlador LQR clássico conhecido na literatura. A estratégia de controle proposta apresenta vantagens considerando as variações do modelo decorrente dos testes de cargas em aplicações de conversores estáticos CC-CC. Palavras-chave -Conversor ROBUST MPC-LMI CONTROLLER APPLIED TO THREE STATE SWITCHING CELL BOOST CONVERTERAbstract -This paper proposes a Model Predictive Control (MPC) strategy applied to Three State Switching Cell boost converter which leads more simplicity to the design steps and analysis to the controller, whose adjustable integral gain does not need the redesign of weighting matrices. To simplify the controller analysis, the ellipsoid stability concepts are used, a field few explored in this context. The proposed MPC starts from of Linear Time Varying(LTV) state space plant modeling whose parametric variables are modeled as politopic uncertainties via linear matrix inequalities (LMIs) approach with relaxations.Theoretical and experimental aspects are applied to 1 kW boost converter with voltage input and load uncertainties. Morevover, to lead the performance testing, the proposed MPC is compared with the classical LQR known in the literature.The proposed control strategy presents advantages considering the model variations due to load testing in DC-DC converters applications. Keywords -