Optimal fuzzy PID control tuned with genetic algorithms

Fuzzy logic controllers (FLC) are intelligent systems, based on heuristic knowledge, that have been largely applied in numerous areas of everyday life. They can be used to describe a linear or nonlinear system and are suitable when a real system is not known or too difficult to find their model. FLC provide a formal methodology for representing, manipulating and implementing a human heuristic knowledge on how to control a system. These controllers can be seen as artificial decision makers that operate in a closed-loop system, in real time. The main aim of this work was to develop a single optimal fuzzy controller, easily adaptable to a wide range of systems – simple to complex, linear to nonlinear – and able to control all these systems. Due to their efficiency in searching and finding optimal solution for high complexity problems, GAs were used to perform the FLC tuning by finding the best parameters to obtain the best responses. The work was performed using the MATLAB/SIMULINK software. This is a very useful tool that provides an easy way to test and analyse the FLC, the PID and the GAs in the same environment. Therefore, it was proposed a Fuzzy PID controller (FL-PID) type namely, the Fuzzy PD+I. For that, the controller was compared with the classical PID controller tuned with, the heuristic Ziegler-Nichols tuning method, the optimal Zhuang-Atherton tuning method and the GA method itself. The IAE, ISE, ITAE and ITSE criteria, used as the GA fitness functions, were applied to compare the controllers performance used in this work. Overall, and for most systems, the FL-PID results tuned with GAs were very satisfactory. Moreover, in some cases the results were substantially better than for the other PID controllers. The best system responses were obtained with the IAE and ITAE criteria used to tune the FL-PID and PID controllers.

A New Approach in the Design of Air Stripping Columns for the Treatment of Groundwater Contaminated With Volatile Organic Compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for column design for any type of packing and contaminant which avoids the necessity of an arbitrary chosen diameter. It also avoids the employment of the usual graphical Eckert correlations for pressure drop. The hydraulic features are previously chosen as a project criterion. The design procedure was translated into a convenient algorithm in C++ language. A column was built in order to test the design, the theoretical steady-state and dynamic behaviour. The experiments were conducted using a solution of chloroform in distilled water. The results allowed for a correction in the theoretical global mass transfer coefficient previously estimated by the Onda correlations, which depend on several parameters that are not easy to control in experiments. For best describe the column behaviour in stationary and dynamic conditions, an original mathematical model was developed. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting ODE can be solved by analytical methods, and in dynamic state the discretization of the PDE by finite differences allows for the overcoming of this difficulty. To estimate the contaminant concentrations in both phases in the column, a numerical algorithm was used. The high number of resulting algebraic equations and the impossibility of generating a recursive procedure did not allow the construction of a generalized programme. But an iterative procedure developed in an electronic worksheet allowed for the simulation. The solution is stable only for similar discretizations values. If different values for time/space discretization parameters are used, the solution easily becomes unstable. The system dynamic behaviour was simulated for the common liquid phase perturbations: step, impulse, rectangular pulse and sinusoidal. The final results do not configure strange or non-predictable behaviours.

Modified Discrete PSO to Increase the Delivered Energy Probability in Distribution energy Systems

This paper proposes a PSO based approach to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The statistical failure and repair data of distribution components is the main basis of the proposed methodology that uses a fuzzyprobabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A Modified Discrete PSO optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

Reinforcement Learning Based on the Bayesian Theorem for Electricity Markets Decision Support

This paper presents the applicability of a reinforcement learning algorithm based on the application of the Bayesian theorem of probability. The proposed reinforcement learning algorithm is an advantageous and indispensable tool for ALBidS (Adaptive Learning strategic Bidding System), a multi-agent system that has the purpose of providing decision support to electricity market negotiating players. ALBidS uses a set of different strategies for providing decision support to market players. These strategies are used accordingly to their probability of success for each different context. The approach proposed in this paper uses a Bayesian network for deciding the most probably successful action at each time, depending on past events. The performance of the proposed methodology is tested using electricity market simulations in MASCEM (Multi-Agent Simulator of Competitive Electricity Markets). MASCEM provides the means for simulating a real electricity market environment, based on real data from real electricity market operators.

Study of Load Curves Concerning the Influence of Socioeconomic and Cultural Issues

The increase of electricity demand in Brazil, the lack of the next major hydroelectric reservoirs implementation, and the growth of environmental concerns lead utilities to seek an improved system planning to meet these energy needs. The great diversity of economic, social, climatic, and cultural conditions in the country have been causing a more difficult planning of the power system. The work presented in this paper concerns the development of an algorithm that aims studying the influence of the issues mentioned in load curves. Focus is given to residential consumers. The consumption device with highest influence in the load curve is also identified. The methodology developed gains increasing importance in the system planning and operation, namely in the smart grids context.

Voltage Analysis and Load Curtailment Minimization in Sub-transmission Networks with Distributed Generation

Most of distributed generation and smart grid research works are dedicated to network operation parameters studies, reliability, etc. However, many of these works normally uses traditional test systems, for instance, IEEE test systems. This paper proposes voltage magnitude and reliability studies in presence of fault conditions, considering realistic conditions found in countries like Brazil. The methodology considers a hybrid method of fuzzy set and Monte Carlo simulation based on the fuzzy-probabilistic models and a remedial action algorithm which is based on optimal power flow. To illustrate the application of the proposed method, the paper includes a case study that considers a real 12-bus sub-transmission network.

Novel optical PVC probes for on-site detection/determination of fluoroquinolones in a solid/liquid interface: Application to the determination of Norfloxacin in aquaculture water

A novel optical disposable probe for screening fluoroquinolones in fish farming waters is presented, having Norfloxacin (NFX) as target compound. The colorimetric reaction takes place in the solid/liquid interface consisting of a plasticized PVC layer carrying the colorimetric reagent and the sample solution. NFX solutions dropped on top of this solid-sensory surface provided a colour change from light yellow to dark orange. Several metals were tested as colorimetric reagents and Fe(III) was selected. The main parameters affecting the obtained colour were assessed and optimised in both liquid and solid phases. The corresponding studies were conducted by visible spectrophotometry and digital image acquisition. The three coordinates of the HSL model system of the collected image (Hue, Saturation and Lightness) were obtained by simple image management (enabled in any computer). The analytical response of the optimised solid-state optical probe against concentration was tested for several mathematical transformations of the colour coordinates. Linear behaviour was observed for logarithm NFX concentration against Hue+Lightness. Under this condition, the sensor exhibited a limit of detection below 50 μM (corresponding to about 16 mg/mL). Visual inspection also enabled semi-quantitative information. The selectivity was ensured against drugs from other chemical groups than fluoroquinolones. Finally, similar procedure was used to prepare an array of sensors for NFX, consisting on different metal species. Cu(II), Mn(II) and aluminon were selected for this purpose. The sensor array was used to detect NFX in aquaculture water, without any prior sample manipulation.

Definition of MV Load Diagrams via Weighted Evidence Accumulation Clustering using Subsampling

A definition of medium voltage (MV) load diagrams was made, based on the data base knowledge discovery process. Clustering techniques were used as support for the agents of the electric power retail markets to obtain specific knowledge of their customers’ consumption habits. Each customer class resulting from the clustering operation is represented by its load diagram. The Two-step clustering algorithm and the WEACS approach based on evidence accumulation (EAC) were applied to an electricity consumption data from a utility client’s database in order to form the customer’s classes and to find a set of representative consumption patterns. The WEACS approach is a clustering ensemble combination approach that uses subsampling and that weights differently the partitions in the co-association matrix. As a complementary step to the WEACS approach, all the final data partitions produced by the different variations of the method are combined and the Ward Link algorithm is used to obtain the final data partition. Experiment results showed that WEACS approach led to better accuracy than many other clustering approaches. In this paper the WEACS approach separates better the customer’s population than Two-step clustering algorithm.

Determination of electricity consumers’ load profiles via weighted evidence accumulation clustering using subsampling

With the electricity market liberalization, the distribution and retail companies are looking for better market strategies based on adequate information upon the consumption patterns of its electricity consumers. A fair insight on the consumers’ behavior will permit the definition of specific contract aspects based on the different consumption patterns. In order to form the different consumers’ classes, and find a set of representative consumption patterns we use electricity consumption data from a utility client’s database and two approaches: Two-step clustering algorithm and the WEACS approach based on evidence accumulation (EAC) for combining partitions in a clustering ensemble. While EAC uses a voting mechanism to produce a co-association matrix based on the pairwise associations obtained from N partitions and where each partition has equal weight in the combination process, the WEACS approach uses subsampling and weights differently the partitions. As a complementary step to the WEACS approach, we combine the partitions obtained in the WEACS approach with the ALL clustering ensemble construction method and we use the Ward Link algorithm to obtain the final data partition. The characterization of the obtained consumers’ clusters was performed using the C5.0 classification algorithm. Experiment results showed that the WEACS approach leads to better results than many other clustering approaches.

Optimal methodology for distribution systems reconfiguration based on OPF and solved by decomposition technique

This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, balancing load among feeders and subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages and radial optimal operation of networks. The Generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages; the first one is the Master problem and is formulated as a mixed integer non-linear programming problem. This stage determines the radial topology of the distribution network. The second stage is the Slave problem and is formulated as a non-linear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in GAMS. The effectiveness of the proposal is demonstrated through two examples extracted from the literature.

Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Modelo de previsão meteorológica baseado em sistemas de inferência difusa

Mestrado em Engenharia Electrotécnica e de Computadores

Sistema de modelização tridimensional de galerias subterrâneas

A presente dissertação apresenta uma solução para o problema de modelização tridimensional de galerias subterrâneas. O trabalho desenvolvido emprega técnicas provenientes da área da robótica móvel para obtenção um sistema autónomo móvel de modelização, capaz de operar em ambientes não estruturados sem acesso a sistemas de posicionamento global, designadamente GPS. Um sistema de modelização móvel e autónomo pode ser bastante vantajoso, pois constitui um método rápido e simples de monitorização das estruturas e criação de representações virtuais das galerias com um elevado nível de detalhe. O sistema de modelização desloca-se no interior dos túneis para recolher informações sensoriais sobre a geometria da estrutura. A tarefa de organização destes dados com vista _a construção de um modelo coerente, exige um conhecimento exacto do percurso praticado pelo sistema, logo o problema de localização da plataforma sensorial tem que ser resolvido. A formulação de um sistema de localização autónoma tem que superar obstáculos que se manifestam vincadamente nos ambientes underground, tais como a monotonia estrutural e a já referida ausência de sistemas de posicionamento global. Neste contexto, foi abordado o conceito de SLAM (Simultaneous Loacalization and Mapping) para determinação da localização da plataforma sensorial em seis graus de liberdade. Seguindo a abordagem tradicional, o núcleo do algoritmo de SLAM consiste no filtro de Kalman estendido (EKF { Extended Kalman Filter ). O sistema proposto incorpora métodos avançados do estado da arte, designadamente a parametrização em profundidade inversa (Inverse Depth Parametrization) e o método de rejeição de outliers 1-Point RANSAC. A contribuição mais importante do método por nós proposto para o avanço do estado da arte foi a fusão da informação visual com a informação inercial. O algoritmo de localização foi testado com base em dados reais, adquiridos no interior de um túnel rodoviário. Os resultados obtidos permitem concluir que, ao fundir medidas inerciais com informações visuais, conseguimos evitar o fenómeno de degeneração do factor de escala, comum nas aplicações de localização através de sistemas puramente monoculares. Provámos simultaneamente que a correcção de um sistema de localização inercial através da consideração de informações visuais é eficaz, pois permite suprimir os desvios de trajectória que caracterizam os sistemas de dead reckoning. O algoritmo de modelização, com base na localização estimada, organiza no espaço tridimensional os dados geométricos adquiridos, resultando deste processo um modelo em nuvem de pontos, que posteriormente _e convertido numa malha triangular, atingindo-se assim uma representação mais realista do cenário original.

Controlo difuso de um AGV

Neste trabalho pretende-se introduzir os conceitos associados à lógica difusa no controlo de sistemas, neste caso na área da robótica autónoma, onde é feito um enquadramento da utilização de controladores difusos na mesma. Foi desenvolvido de raiz um AGV (Autonomous Guided Vehicle) de modo a se implementar o controlador difuso, e testar o desempenho do mesmo. Uma vez que se pretende de futuro realizar melhorias e/ou evoluções optou-se por um sistema modular em que cada módulo é responsável por uma determinada tarefa. Neste trabalho existem três módulos que são responsáveis pelo controlo de velocidade, pela aquisição dos dados dos sensores e, por último, pelo controlador difuso do sistema. Após a implementação do controlador difuso, procedeu-se a testes para validar o sistema onde foram recolhidos e registados os dados provenientes dos sensores durante o funcionamento normal do robô. Este dados permitiram uma melhor análise do desempenho do robô. Verifica-se que a lógica difusa permite obter uma maior suavidade na transição de decisões, e que com o aumento do número de regras é possível tornar o sistema ainda mais suave. Deste modo, verifica-se que a lógica difusa é uma ferramenta útil e funcional para o controlo de aplicações. Como desvantagem surge a quantidade de dados associados à implementação, tais como, os universos de discurso, as funções de pertença e as regras. Ao se aumentar o número de regras de controlo do sistema existe também um aumento das funções de pertença consideradas para cada variável linguística; este facto leva a um aumento da memória necessária e da complexidade na implementação pela quantidade de dados que têm de ser tratados. A maior dificuldade no projecto de um controlador difuso encontra-se na definição das variáveis linguísticas através dos seus universos de discurso e das suas funções de pertença, pois a definição destes pode não ser a mais adequada ao contexto de controlo e torna-se necessário efectuar testes e, consequentemente, modificações à definição das funções de pertença para melhorar o desempenho do sistema. Todos os aspectos referidos são endereçados no desenvolvimento do AGV e os respectivos resultados são apresentados e analisados.

Sintonia de controladores baseada em Sistemas de Inferência Difusa

Este trabalho de pesquisa e desenvolvimento tem como fundamento principal o Conceito de Controlo por Lógica Difusa. Utilizando as ferramentas do software Matlab, foi possível desenvolver um controlador com base na inferência difusa que permitisse controlar qualquer tipo de sistema físico real, independentemente das suas características. O Controlo Lógico Difuso, do inglês “Fuzzy Control”, é um tipo de controlo muito particular, pois permite o uso simultâneo de dados numéricos com variáveis linguísticas que tem por base o conhecimento heurístico dos sistemas a controlar. Desta forma, consegue-se quantificar, por exemplo, se um copo está “meio cheio” ou “meio vazio”, se uma pessoa é “alta” ou “baixa”, se está “frio” ou “muito frio”. O controlo PID é, sem dúvida alguma, o controlador mais amplamente utilizado no controlo de sistemas. Devido à sua simplicidade de construção, aos reduzidos custos de aplicação e manutenção e aos resultados que se obtêm, este controlador torna-se a primeira opção quando se pretende implementar uma malha de controlo num determinado sistema. Caracterizado por três parâmetros de ajuste, a saber componente proporcional, integral e derivativa, as três em conjunto permitem uma sintonia eficaz de qualquer tipo de sistema. De forma a automatizar o processo de sintonia de controladores e, aproveitando o que melhor oferece o Controlo Difuso e o Controlo PID, agrupou-se os dois controladores, onde em conjunto, como poderemos constatar mais adiante, foram obtidos resultados que vão de encontro com os objectivos traçados. Com o auxílio do simulink do Matlab, foi desenvolvido o diagrama de blocos do sistema de controlo, onde o controlador difuso tem a tarefa de supervisionar a resposta do controlador PID, corrigindo-a ao longo do tempo de simulação. O controlador desenvolvido é denominado por Controlador FuzzyPID. Durante o desenvolvimento prático do trabalho, foi simulada a resposta de diversos sistemas à entrada em degrau unitário. Os sistemas estudados são na sua maioria sistemas físicos reais, que representam sistemas mecânicos, térmicos, pneumáticos, eléctricos, etc., e que podem ser facilmente descritos por funções de transferência de primeira, segunda e de ordem superior, com e sem atraso.