A new fractional-order chaotic system with its analysis, synchronization, and circuit realization for secure communication applications

YesThis article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the sug-gested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications

DESIGN AND IMPLEMENTATION OF FRACTIONAL-ORDER CONTROLLER IN DELTA DOMAIN

In this work, a fractional-order controller (FOC) is designed in a discrete domain using delta operator parameterization. FOC gets rationally approximated using continued fraction expansion (CFE) in the delta domain. Whenever discretization of any continuous-time system takes place, the choice of sampling time becomes the most critical parameter to get most accurate results. Obtaining a higher sampling rate using conventional shift operator parameterization is not possible and delta operator parameterized discretize time system takes the advantages to circumvent the problem associated with the shift operator parameterization at a high sampling limit. In this work, a first-order plant with delay is considered to be controlled with FOC, and is implemented in discrete delta domain. The plant model is designed using MATLAB as well as in hardware. The fractional-order controller is tuned in the continuous domain and discretized in delta domain to make the discrete delta FOC. Continuous time fractional order operator (s±α) is directly discretized in delta domain to get the overall FOC in discrete domain. The designed controller in implemented using MATLABSimulink and dSPACE board such that dSPACEboard acts as the hardware implemented FOC. The step response characteristics of the closed-loop system using delta domain FOC resembles to that of the results obtained by continuous time controller. It proves that at a high sampling rate, the continuous-time result and discrete-time result are obtained hand to hand rather than the two individual cases. Therefore, the analysis and design of FOC parameterized with delta operator opens up a new area in the design and implementation of discrete FOC, which unifies both continuous and discrete-time results. The discrete model performance characteristics are evaluated in software simulation using MATLAB, and results are validated through the hardware implementation using dSPACE

Metodologia baseada em algoritmos evolutivos para otimização de controladores de ordem fracionária

Orientador: Gustavo Henrique da Costa OliveiraCoorientador: Gideon Villar LeandroTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Engenharia Elétrica. Defesa : Curitiba, 06/12/2022Inclui referências: p. 159-171Área de concentração: Engenharia ElétricaResumo: Nos últimos anos, o cálculo de ordem fracionária ganhou muita atenção, especialmente no campo da teoria de sistemas dinâmicos e do projeto de sistemas de controle. Algoritmos de controle com ordem fracionária permitem expandir a quantidade de parâmetros de projeto visando melhorar o desempenho do sistema em malha fechada. No entanto, os graus de liberdade são acompanhados com uma complexidade na síntese. Dentro dessa perspectiva, encontra-se o controlador PID de ordem fracionária (FOPID), que possui as ordens integral e diferencial ajustáveis, criando a possibilidade de fornecer melhor desempenho de controle, desde que corretamente sintonizado. Da mesma forma, a sintonia do controlador CRONE e suas gerações também é um desafio, onde a escolha incorreta dos parâmetros pode comprometer o desempenho do controlador. Em vista disso, este trabalho apresenta três objetivos principais, sendo o primeiro uma nova estratégia híbrida de controle, chamada AFOPID. Nesta estratégia, os cinco parâmetros do FOPID são sintonizados online de forma que, na ocorrência de alguma perturbação, a Lógica Fuzzy atualiza os coeficientes kp, ki e kd do FOPID para adaptar a malha fechada à nova condição de operação. Em seguida, os coeficientes fracionários (lambda) e µ, que são as ordens integral e diferencial do controlador, são atualizados usando um algoritmo de Evolução Diferencial (DE). Para fins de validação da metodologia proposta, uma planta de uma usina hidrelétrica baseada em um sistema real é utilizada. Através dos resultados, percebeu-se que o sistema híbrido melhorou a solução geral, fornecendo melhor desempenho em malha fechada do que soluções semelhantes, o que pôde ser comprovado através da análise dos índices de desempenho ISE, ITAE e ITSE. O segundo objetivo desta tese consiste na proposta de um algoritmo de otimização multiobjetivo para os controladores CRONE gerações 1 e 2. Para tanto, utiliza-se o algoritmo NSGA-II Multiobjetivo baseado em dois objetivos principais: (i) Minimizar o sinal de controle; (ii) Reduzir o erro em regime permanente. Os resultados mostraram que além de facilitar o processo de escolha dos parâmetros, não dependendo tanto do conhecimento do projetista, o controlador otimizado conseguiu fornecer bons níveis de desempenho, ou seja, minimizou o sinal de controle e reduziu o erro em regime permanente. Por fim, como terceiro objetivo deste trabalho, tem-se o desenvolvimento de uma plataforma computacional chamada UFPR-FracControl. A plataforma contém os controladores CRONE 1 e 2, convencional e otimizado, FOPID, PID convencional e, visa a utilização desses controladores por usuários não especialistas. Os resultados demonstraram que esta nova plataforma facilitará o uso de sistemas de controle de ordem fracionária pelo fato de ser leve, não depender de instalação, não depender de licenças e pelo fato de ser de fácil implementação. Por fim, conclui-se que os três objetivos aqui propostos obtiveram sucesso em melhorar o desempenho e facilitar o uso dos controladores de ordem fracionária.Abstract: In recent years, fractional order calculus has gained a lot of attention, especially in the field of dynamical system theory and control system design. Control algorithms with fractional order allow expanding the number of design parameters to improve the performance of the closed-loop system. However, the degrees of freedom are accompanied by complexity in the synthesis. Within this perspective, there is the fractional order PID controller (FOPID), which has adjustable integral and differential orders, creating the possibility of providing better control performance, as long as it is correctly tuned. Likewise, the tuning of the CRONE controller and its generations is also a challenge, where the incorrect choice of parameters can compromise the performance of the controller. Given this, this work presents three main objectives, the first being a new hybrid control strategy, called AFOPID. In this strategy, the five parameters of the FOPID are tuned online so that, in the event of any disturbance, the Logic Fuzzy updates the coefficients kp, ki and kd of the FOPID to adapt the closed loop to the new operating condition. Next, the fractional coefficients (lambda) and µ, which are the integral and differential orders of the controller, are updated using a Differential Evolution (DE) algorithm. To validate the proposed methodology, a plant of a hydroelectric plant based on a real system is used. Through the results, it was noticed that the hybrid system improved the overall solution, providing better closed-loop performance than similar solutions, which could be proven through the analysis of the ISE, ITAE, and ITSE performance indexes. The second objective of this thesis consists in proposing a multiobjective optimization algorithm for CRONE controllers generations 1 and 2. For this purpose, the NSGA-II Multiobjective algorithm is used based on two main objectives: (i) Minimize the control signal; (ii) Reduce the steady-state error. The results showed that in addition to facilitating the process of choosing the parameters, not depending so much on the designer's knowledge, the optimized controller was able to provide good levels of performance, that is, it minimized the control signal and reduced the steady-state error. Finally, as the third objective of this work, there is the development of a computational platform called UFPR-FracControl. The platform contains CRONE 1 and 2 controllers, conventional and optimized, FOPID, and conventional PID, and aims to use these controllers by non-specialist users. The results showed that this new platform will facilitate the use of fractional order control systems because it is lightweight, does not depend on installation, does not depend on licenses, and because it is easy to implement. Finally, it is concluded that the three objectives proposed here were successful in improving performance and facilitating the use of fractional order controllers

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks