This article presents a dead-time compensation strategy for grid-tied inverters with large output current ripple. A current prediction over the switching sequence is proposed to obtain the current polarity at each switching transition. As a result, the effect of the dead time on the inverter output voltages can be determined and the duty cycles are compensated to maintain the original switching transitions instants. In addition, a disturbance observer is used to mitigate the current prediction error, caused by the nonidealities of the grid-tied inverter system. The constraints obtained from the dead-time compensation method are included in the optimization problem of the model predictive control algorithm to ensure operation in the feasible region of the space-vector diagram. Hardware-in-the-loop and experimental results are obtained to compare the proposed method with a classical compensation strategy without current prediction over the switching period, as well as to demonstrate the good performance and effectiveness of the proposed strategy.

This paper proposes a Repetitive Dynamic Matrix Control (RDMC) for systems with periodic specifications. The new algorithm is able to track periodic references and reject repetitive disturbances with a known period based on a modified prediction error. A repetitive version of the Generalized DMC (GDMC) is also proposed such that it can be applied to control open -loop unstable systems. Only the step -response coefficients are required to describe the dynamical system such that the RDMC preserves the modeling simplicity of the Dynamic Matrix Control (DMC). The proposed solution can be interpreted as an extension of the DMC for repetitive control applications. A data -driven filter design is proposed in order to ensure null prediction steady-state error in the presence of periodic disturbances even for unstable open -loop systems. Two case studies are presented to show the usefulness of the proposed strategy for control systems with periodic specification and to illustrate the typical advantages and drawbacks of the proposed repetitive control extension of the DMC algorithm.

The growing use of distributed energy resources is driving several improvements in power electronics and their control strategies, especially regarding voltage-source converters, which are crucial to integrate these resources into the electric grid. Control strategies such as classical linear proportional-integral, proportional-resonant, state feedback and deadbeat are generally employed for these applications. However, these strategies usually do not take into account nonlinearities such as control action saturation and current limitations. To solve these issues, Model Predictive Control (MPC) has become a very powerful alternative for controlling grid-connected converters (GCCs), allowing to encompass in the control design different linear and nonlinear constraints. Among the MPC controllers, the Finite Control Set MPC (FCS-MPC) is an attractive solution for controlling GCCs. In FCS-MPC, an optimization problem is formulated with a cost function that expresses the control objectives, such as current reference tracking, capacitor voltage regulation, minimization of losses and common-mode voltages. Besides, FCS-MPC can be implemented with one voltage vector per sampling period, or with a switching sequence, characterizing the Modulated MPC. In this context, this chapter will present different MPC strategies for GCCs and how they can be implemented, tested and validated using the Typhoon HIL platform and the Test-Driven Design (TDD) approach. In power electronics, the TDD can be used to address the performance of GCCs, and also provides a tool to benchmark different implementations of current controllers in a fair way. In this chapter, TDD will be used in order to test, validate and compare the performance of MPC controllers for three-phase GCCs with LCL filters. TDD was carried out using Python scripts and the Typhoon HIL platform, testing the current controllers under different steady-state and transient conditions.

Este trabalho apresenta o uso do Filtro de Kalman Estendido (EKF) para compensação de atraso de transporte em processos não-lineares. O atraso é um desafio para o controle de processos, e o estudo propõe um preditor baseado na estrutura Observador-Preditor, utilizando o EKF como estimador. Esse preditor utiliza o EKF para estimar os estados do sistema e, em conjunto com o modelo do processo, realiza a predição dos estados ou saídas após o atraso. O preditor possui vantagens, como a estimação de diferentes tipos de perturbação e a aplicação em sistemas com diversas dinâmicas (estável ou não). Além disso, sua sintonia permite ajustar de forma simples as características de rejeição de perturbações e a robustez do sistema em malha fechada. O estudo de caso apresenta as vantagens da abordagem no contexto de um reator continuamente agitado. Um estudo de caso baseado num reator continuamente agitado é utilizado para apresentar as vantagens da proposta.

This article introduces a method called geometrical modulated model predictive control (GM2PC) for three-phase power converters. Its objective is to guarantee voltage synthesis, current limiting, fixed switching frequency, no need for weighting factors or cascaded control structure, and fast dynamic response, while also addressing overmodulation issues and distributing PWM signals in cascaded H-bridge (CHB) multilevel converters in a simple and efficient manner. A convex optimization problem is formulated using a discrete-time model to minimize the output tracking error in a three-phase converter connected to an LC output filter. This formulation includes two quadratic constraints and takes into account external disturbances. To solve this problem, the constraints are treated as circular areas within the space vector diagram for current limitation and voltage synthesis. The Karush–Kuhn–Tucker (KKT) conditions are applied to obtain an unconstrained solution that identifies the mode of operation, which is used to geometrically find an optimal solution. Unlike conventional quadratic minimization algorithms, the proposed method does not require recursive solutions nor the analysis of all vectors or sectors in the space vector diagram, reducing significantly the computational burden. The method is validated for a five-level CHB, and the results demonstrate its efficiency and fast control algorithm.

O crescimento na utilização de inversores vem sendo impulsionado pela geração distribuída de energia elétrica e pela eletrificação dos meios de transporte. Desta forma, muitos grupos de pesquisa estão desenvolvendo estratégias de controle para estes dispositivos. Porém, em muitos casos, a validação experimental não é feita por conta da dificuldade de se projetar e construir um inversor. E, quando um inversor experimental é utilizado, raramente são disponibilizadas as informações do projeto para que o inversor em si possa ser replicado. Assim, este trabalho busca disponibilizar um inversor full-bridge em projeto aberto de modo a propiciar que grupos de pesquisa tenham a possibilidade de aplicar suas estratégias desenvolvidas e obter resultados experimentais sem a necessidade de conceber um projeto do inversor.

Dead-time is a phenomena that is present in many industrial processes and it presents a challenge for feedback control, especially for multivariable processes. To attenuate the dead-time effects, a common method is the use of predictor structures, which use input/output information of the process to predict the output (or states) of the system after the dead-time. In this paper, the Modified Kalman Predictor (MKP) is proposed, which is a novel predictor for linear multivariable square systems with multiple dead-time (or delays) based on the Kalman Filter that has disturbance estimation and can cope with systems of any order or dynamics, including unstable ones. It uses a specific state-space representation of the process which makes its implementation more straight-forward when compared to other methods. The MKP affects the disturbance rejection but not the closed-loop stability in the nominal case, and it can help to improve closed-loop robustness in the uncertain case. The impacts of the MKP tuning in the closed-loop response considering disturbance rejection and robustness are analyzed using standard frequency domain tools. To illustrate the benefits of the MKP, two examples are used that highlight the tuning guidelines for disturbance rejection and robustness improvements.

This article proposes a space vector modulated model predictive control (SVM $^{2}$ PC) for voltage source converters. It overcomes limitations of standard finite control set model predictive controller, ensuring fast dynamic response, fixed switching frequency, and low computational burden. It combines control and modulation in a convex optimization problem with affine inequality constraints to minimize the tracking errors of the output variables. First, the sector of the space vector diagram where the unconstrained solution lies is identified. Then, using the Karush–Kuhn–Tucker conditions, feasible duty cycles are computed for both linear and overmodulation regions. The proposed SVM $^{2}$ PC is extended to multilevel converters. Hardware in the loop results are presented for three different case studies: 1) Grid-forming inverter with LC filter; 2) two-level grid-following inverter with LCL filter; and 3) grid-following neutral point clamped inverter with LCL filter. Experimental results demonstrate that the proposed SVM $^{2}$ PC provides good performance, fast response, and low computational burden when compared with previously reported alternatives.

This paper presents a dead-time compensation method for grid-tied inverters controlled by Space Vector Modulated Model Predictive Control. This method is general and can be applied to grid-tied inverters with an LCL filter and large high-frequency ripple in the inverter-side currents, which can result in multiple zero crossings in the currents during each switching period. A current prediction over the switching sequence is proposed to obtain the current polarity information at each switching transition, allowing to determine the effect of the dead time in the inverter output voltages and compensate the duty-cycles to maintain the original instants of the switching transitions. The constraints obtained from the dead-time compensation method are included in the optimization problem of the control algorithm to ensure operation in the feasible region of the space-vector diagram. In addition, hardware-in-the-loop results are obtained to demonstrate the good performance and effectiveness of the proposed dead-time compensation method.

This work presents the development of an advanced control strategy using Model Predictive Control (MPC) for controlling the gas compression system of an offshore platform. It includes details about the complete phenomenological model of the system and of the software infrastructure developed to support the system implementation in real conditions. The proposed control structure has two main goals: (i) avoid unwanted regions of operation; and (ii) increase stability margins and availability. These goals are achieved by using a zone-control MPC and by adequately interacting with the regulatory control level. Although the proposed structure is general, this work exemplifies its application in a particular compression unit of a real offshore platform. Simulation results are presented in two different scenarios, one to test how the controller rejects a gas-load varying disturbance and another to analyze how the controller copes with an abnormal situation, losing real-time data of process variables or manipulated variables during operation. The good performance obtained in these two cases confirm the benefits provided by the proposed MPC strategy to the operation of the gas compression unit.

This paper investigates the impact of the dead-time compensation on fixed frequency space vector modulated model predictive control for grid-tied inverters. Since grid-tied inverters with LCL filters may have inverter-side currents with large high-frequency current ripple, multiple zero crossings should be properly considered for dead-time compensation. Therefore, this paper proposes a method to predict the current at the switching instants within the sampling period. It is demonstrated that there is a significant improvement in terms of low-frequency harmonics and tracking error of the grid-side currents with the proposed method. In addition, the constraints imposed by the dead-time compensation are included in the optimization problem of the Space Vector Modulated Model Predictive Control algorithm. Finally, Hardware-in-the-loop results are presented to demonstrate the good performance of the proposed dead-time compensation technique.

Este trabajo propone una técnica de control predictivo para ser aplicada en procesos rápidos utilizando optimización en línea. Actualmente, en el sector industrial, los controladores avanzados son cada vez más necesarios en los bajos niveles de automatización, que están asociados con tiempos de muestreo del orden de milisegundos o microsegundos. La programación cuadrática resultante del problema de control de un algoritmo de control predictivo con restricciones, como por ejemplo el control por matriz dinámica (en inglés Dynamic Matrix Control - DMC), que es uno de los más usados en la industria, se puede considerar computacionalmente costosa y se convierte en una limitación para empotrar y usar el DMC en plantas con tasas de muestreo rápidas. Este artículo propone una solución a este problema basada en el método de proyección de gradiente acelerada dual, que tiene tiempos de convergencia menores que otras soluciones de la literatura basadas en estrategias de control predictivo con optimización en línea. Además, el control propuesto se implementó en una matriz de puertos programables (en inglés field-programmable gate array – FPGA) y el problema de programación cuadrática resultante se calculó en microsegundos, lo que permite el uso del DMC en procesos muy rápidos.

This paper proposes a Geometrical Modulated Model Predictive Control (GM 2 PC), for grid-connected converters, ensuring voltage synthesis and current limiting with fast dynamic response, low computational burden and fixed switching frequency, also addressing the overmodulation issue. A discrete-time model for a converter with LC output filter and external disturbances is derived. Then, a convex optimization problem with two quadratic inequality constraints is formulated for minimizing the output tracking error. To solve this problem, each constraint is considered to be a circular area over the space vector diagram for voltage synthesis and current limitation. Using the Karush–Kuhn–Tucker conditions, an unconstrained solution is obtained in order to identify in which mode the proposed method should operate. Finally, a Hardware-in-the-Loop validation for a three-phase two-level inverter is presented. The results demonstrate that the proposed method is capable of providing good performances with a fast and efficient control algorithm.

This paper proposes a modulated model predictive strategy suitable for current control of grid-connected converters with LCL filters, allowing fast dynamic responses with a fixed switching frequency, for both strong and weak grid conditions. The duty cycles are optimized within each switching period based on the minimization of a quadratic cost function with linear constraints from the space vector modulation. Full and reduced-order models are considered for the control design, and closed-form analytical solutions for the optimization problem are derived based on the Karush-Kuhn-Tucker conditions. The closed-form expressions for the optimal solution make it possible to implement the algorithm in real time using off-the-shelf microcontrollers. Extensive evaluation illustrates good transient and steady state performances for different grid conditions. In addition, the proposed MPC takes into account the voltage synthesis capability of the inverter and copes with overmodulation in an orderly fashion even in large transients.

This paper proposes fast algorithms for constrained generalised predictive control based on two first-order methods, namely accelerated dual gradient projection method and fast alternating minimisation algorithm. Theoretical bounds on the number of iterations, which play an important role in the context of real-time model predictive controllers, are provided for both algorithms. Also, some implementation issues in parallel architectures are discussed. The methods are firstly validated by simulation and their results are compared with the ones presented by commercial solvers. A three-phase grid-connected LCL-filtered inverter was used as a case study. The algorithms were evaluated in an FPGA with the quadratic program computed in microseconds.

Dead-time processes are common in industry and represent a challenge for feedback control. The use of predictor structures with the controllers can attenuate this. A predictor is proposed here based on the Kalman filter, the Kalman Predictor (KP), that has only one tuning parameter for SISO systems and can be used with non-minimum phase, open-loop unstable and integrative systems of any order, and is also capable of estimating many types of disturbances. It is shown that the KP implicitly defines a Filtered Smith Predictor (FSP), hence, all tools used to analyze the closed-loop properties of the FSP can be used, including robustness and disturbance rejection. Tuning guidelines are provided and simulation examples with comparisons with other predictor structures are used to illustrate the advantages of the proposed KF. (C) 2021 Elsevier Ltd. All rights reserved.

Constrained model predictive control (MPC) usually requires the computation of a quadratic programming problem (QP) at each sampling instant. This is computationally expensive and becomes a limitation to embed and use MPC in plants with fast sampling rates. Several special solvers for MPC problems have been proposed in the last years, but most of them focus on state-space formulations, which are very popular in academia. This paper proposes a solution based on alternated direction method of multipliers, tailored for embedded systems and applied to generalized predictive control (GPC), which is a very popular formulation in industry. Implementations issues of parallel computation are discussed in order to accelerate the time required for the operations. The implementation in an FPGA proved to be quite fast, with the observed worst case execution time of 11,54 µs for the presented example. These results contribute to embed GPC applications in processes that are typically controlled by classical controllers because of their fast dynamics.

Este artigo apresenta uma alternativa para a implementação de um controle preditivo baseado em modelo com conjunto de controle finito aplicada a inversores conectados à rede elétrica. Em comparação a algoritmos da literatura, a principal modificação consiste em incluir na função custo a predição de um vetor de estados contendo a integral do erro de rastreamento de corrente em coordenadas síncronas. Dessa forma, o controlador proposto permite garantir erro nulo de rastreamento em regime permanente na presença de erros de modelagem sem comprometer o desempenho dinâmico do controlador. Ainda, o controlador proposto permite rejeitar o distúrbio proveniente das tensões da rede sem a necessidade de considerar a realimentação destas tensões na predição das correntes, o que é uma importante vantagem em relação a outras alternativas. Para validar a proposta, resultados de simulação são apresentados para um inversor trifásico conectado à rede por meio de um filtro L, confirmando o bom desempenho transitório e em regime permanente do controlador proposto e a superioridade dos resultados obtidos em comparação com uma solução baseada na literatura, nas mesmas condições.

Historicamente, o controle preditivo generalizado (GPC) vem sendo mais utilizado em plantas com dinâmicas lentas, devido ao alto custo computacional requerido para o cômputo da ação de controle. Mais recentemente, soluções de cômputo rápido do sinal de controle do GPC vêm sendo apresentadas. Nesse sentido, o presente trabalho visa contribuir com a proposta de dois algoritmos baseados no método de ponto interior (IP) e no método de programação quadrática paralela (PFQP). É também apresentado um estudo comparativo com dois algoritmos de GPC da literatura que utilizam os métodos GPAD e ADMM. Para servir de referência, foi utilizado o otimizador comercial Gurobi. A partir do estudo comparativo, pôde-se verificar um melhor desempenho do algoritmo GPAD e a sensibilidade dos algoritmos ADMM e PFQP em cenários com tolerâncias menores e diferentes tipos de restrição. Ressaltou-se também que, apesar de mais lento, o algoritmo com IP apresentou baixa variação no tempo de cômputo com os cenários propostos.

Este artigo propõe uma adaptação à técnica de controle preditivo robusto baseado em tubo (TRMPC) para rastrear referências do tipo degrau. O controlador TRMPC proposto na literatura garante a satisfação robusta das restrições, a estabilidade, e a convergência para o estado estacionário desejado supondo que os estados do sistema estão disponíveis para medição, o que não acontece na prática. A adaptação proposta visa permitir a aplicação da técnica em sistemas baseados em dados de entrada e saída, dispensando o uso de observadores. Um exemplo ilustrativo é simulado para comparar a abordagem proposta com o estado da arte atual.