Controle Usando a Resposta em Frequência from Coursera

Neste curso você aprenderá a obter a resposta em frequência de um sistema Linear e Invariante no Tempo (LIT) e a usá-la para projetar controladores que atinjam requisitos de reposta transitória e em regime estacionário. Você aprenderá a obter o diagrama de Bode a partir de dados de amplitude e fase de entradas e saídas senoidais. Também será capaz de esboçar o diagrama de Bode de um sistema dada a sua função de transferência. Outrossim, será capaz de representar a resposta em frequência na carta de Nichols-Black.

A fim de se determinar a estabilidade do sistema, você aprenderá a aplicar o critério de Nyquist, que faz uso da resposta em frequência em malha aberta e permite determinar se um sistema será estável em malha fechada.

Ao fim do curso, você será capaz de projetar controladores com dinâmica, isto é, com polos e zeros, portanto mais complexos do que um simples ganho de realimentação. Essa flexibilidade permitirá que você projete controladores para satisfazer simultaneamente requisitos de sobressinal e tempo de resposta que seriam impossíveis de atender com um simples ganho. Também poderá com isso alterar as características da resposta em regime estacionário, aumentando as constantes de erro sem alterar (muito) a resposta transitória.

Por fim, você aprenderá a projetar controladores do tipo PD, PI e PID, que estão entre os mais disseminados em aplicações de engenharia de controle.

What's inside

Syllabus

Resposta em Frequência e Diagrama de Bode

Neste módulo você verá que a resposta de sistemas lineares e invariantes no tempo a uma uma entrada senoidal é também uma saída senoidal, com mesma frequência, decorrido certo tempo. Esse fato será usado para motivar a obtenção da resposta em frequência de um sistema, isto é, relacionar a amplitude e fase da senoide de saída com características do sistema linear e com a frequência das senoides. Em seguida, essa resposta será usada para projeto de sistemas de controle com um ganho proporcional de modo a atender requisitos de sobressinal.

Carta de Nichols-Black. Especificação de desempenho no domínio da frequência.

Você aprenderá a representar a resposta em frequência graficamente de outra maneira: a carta de Nichols-Black. Você será capaz de relacionar a amplitude do pico de ressonância da resposta em frequência de malha com o fator de amortecimento do sistema em malha fechada. Também será capaz de relacionar a frequência de cruzamento de 0 dB em malha aberta com a frequência natural em malha fechada. Assim, poderá projetar controladores proporcionais para atingir sobressinal desejado ou tempo de resposta requerido, apenas a partir da resposta em frequência de malha aberta do sistema.

Diagrama de Nyquist. Atraso.

Você aprenderá a representar a resposta em frequência na forma polar e a usar essa representação para avaliar a estabilidade do sistema em malha fechada. Para isso, usará o chamado critério de Nyquist, que permite que você determine quantos polos de malha fechada o sistema terá no semiplano direito. Você também aprenderá a computar o efeito do retardo de tempo na resposta em frequência do sistema e a estimar os efeitos que isso terá na resposta temporal.

Projeto de controladores no domínio da frequência.

Neste módulo você aprenderá a projetar controladores mais complexos, envolvendo zero e polo, de maneira a poder manipular tanto a margem de fase quanto a frequência de cruzamento de 0 dB, sendo capaz de atender requisitos de sobressinal e de tempo de resposta. Também será capaz de alterar o ganho em baixas frequências, mudando as constantes de erro do sistema, sendo capaz de atender requisitos em regime estacionário, sem comprometer a resposta transitória do sistema.

Controladores PD, PI e PID no domínio da frequência.

Após esse último módulo, você estará familiarizado com o projeto dos controladores mais comuns no dia-a-dia do engenheiro: PI, PD e PID. Será capaz de determinar qual deles é necessário para atender os requisitos de desempenho desejados e a projetá-los de acordo. Concluindo, ao término do curso você será capaz de projetar controladores dinâmicos para atender requisitos de sobressinal, tempo de resposta e erro em regime estacionário.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Ensina conceitos de controle que são fundamentais para os engenheiros de controle

Aborda técnicas de projeto e análise de sistemas de controle que são amplamente utilizadas na prática profissional

Oferece uma base sólida para alunos de graduação e pós-graduação em engenharia de controle, automação e áreas relacionadas

Fornece exemplos práticos e estudos de caso para ilustrar os conceitos e técnicas abordados

Requer conhecimento prévio em sistemas lineares e teoria do controle

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Controle Usando a Resposta em Frequência with these activities:

Organize course materials

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Helps you stay organized and prepared for the course by ensuring you have all the necessary materials readily accessible.

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Gather all course materials
Create a physical or digital folder
Organize materials by topic or module
Label each file with relevant information

Review basic control theory

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Solidifies your foundation in control theory, ensuring you have a strong base for the concepts covered in this course.

Browse courses on Control Theory

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Review concepts of feedback control
Refresh your understanding of transfer functions
Practice converting between different transfer function representations

Join a study group

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Provides an opportunity to engage with peers, exchange ideas, and deepen your understanding of course material through collaborative learning.

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Connect with other students enrolled in the course
Schedule regular meetings to discuss course topics
Share knowledge and insights with fellow students

Five other activities

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Practice bode and root locus plotting

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Enhance your understanding of system stability and frequency response by practicing plotting and analyzing Bode and Root Locus Diagrams.

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Use online tools or MATLAB to plot Bode plots
Plot Bode plots for various transfer functions
Analyze the Bode plots to determine system characteristics
Plot Root Locus plots and analyze them

Compile a toolbox of frequency response analysis tools

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Empowers you with a collection of resources to perform frequency response analysis efficiently, enhancing your problem-solving capabilities.

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Gather MATLAB scripts or Python libraries for frequency response analysis
Create a document or repository to organize the tools
Test and verify the functionality of each tool

Explore advanced topics in frequency response analysis

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Extends your learning beyond the course by exploring advanced topics in frequency response analysis, expanding your knowledge and enhancing your professional skills.

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Identify areas where you want to expand your knowledge
Search for online tutorials or courses covering these topics
Follow the tutorials and complete the exercises

Design a controller using frequency response methods

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Provides hands-on experience in applying frequency response methods to design and implement controllers, deepening your understanding of control system design.

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Select a system to control
Develop a mathematical model of the system
Obtain the frequency response of the system
Design a controller using frequency response methods
Implement the controller and evaluate its performance

Build a physical system and implement a controller

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Through a hands-on project, you will gain practical experience in the entire control system design process, from modeling to implementation and evaluation.

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Choose a physical system to control
Design and build the physical system
Model the physical system
Design and implement a controller
Test the controller and evaluate its performance

Career center

Learners who complete Controle Usando a Resposta em Frequência will develop knowledge and skills that may be useful to these careers:

Control Systems Engineer

Control Systems Engineers are responsible for designing and implementing control systems in a variety of industries, including manufacturing. The 'Controle Usando a Resposta em Frequência' course offered by the Instituto Tecnológico de Aeronáutica would be particularly beneficial to aspiring Control Systems Engineers as it would provide them with the skills and knowledge necessary to analyze and design control systems using frequency response methods. Engineers who work in this field should expect to use the concepts from this course in their day-to-day jobs.

See salaries and explore the career path for Control Systems Engineer

Robotics Engineer

Robotics Engineers design, build, and maintain robots for use in a variety of applications, including manufacturing, healthcare, and space exploration. Robotics Engineers who take the 'Controle Usando a Resposta em Frequência' course will gain a deeper understanding of the control systems that are used to control robots. This course will give them the skills and knowledge necessary to design and implement control systems that will enable robots to perform tasks with greater precision and accuracy.

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Electrical Engineer

Electrical Engineers design, develop, test, and maintain electrical systems and components. Those working in control systems may find the 'Controle Usando a Resposta em Frequência' course particularly useful as it provides a deep dive into the frequency-based analysis and design of control systems. The skills and knowledge gained from this course will allow Electrical Engineers to develop control systems with improved performance and stability.

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Mechanical Engineer

Mechanical Engineers design, develop, and test mechanical systems and components. This course could also be useful for Mechanical Engineers who work in the field of control systems. The course will introduce a range of frequency-based techniques for analyzing and designing control systems, which are essential for ensuring the stability and performance of mechanical systems.

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Aerospace Engineer

Aerospace Engineers design, develop, test, and maintain aircraft, spacecraft, and other aerospace systems. This course would be of particular interest to Aerospace Engineers who work in the field of flight control. The course will provide them with the skills and knowledge necessary to analyze and design flight control systems using frequency response methods.

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Automotive Engineer

Automotive Engineers design, develop, test, and maintain automobiles and other vehicles. This course could be useful for Automotive Engineers who specialize in the design of vehicle control systems. The course will provide them with the skills and knowledge necessary to analyze and design vehicle control systems using frequency response methods.

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Systems Engineer

Systems Engineers are responsible for designing, developing, and integrating complex systems. This course may be useful for Systems Engineers who work in the field of control systems. The course will provide them with the skills and knowledge necessary to analyze and design control systems using frequency response methods.

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Biomedical Engineer

Biomedical Engineers design, develop, and test medical devices and systems. This course may be useful for Biomedical Engineers who specialize in the design of medical control systems. The course will provide them with the skills and knowledge necessary to analyze and design medical control systems using frequency response methods.

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Software Engineer

Software Engineers design, develop, and maintain software systems. The course may be of interest to Software Engineers who work in the field of control systems software. The course will provide them with the skills and knowledge necessary to analyze and design control systems software using frequency response methods.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve problems in a variety of industries, including manufacturing and healthcare. This course may be useful for Operations Research Analysts who work in the field of control systems. The course will provide them with the skills and knowledge necessary to analyze and design control systems using frequency response methods.

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Data Scientist

Data Scientists use data to solve problems and make predictions in a variety of industries, including finance and healthcare. This course may be useful for Data Scientists who work in the field of control systems. The course will provide them with the skills and knowledge necessary to analyze and design control systems using frequency response methods.

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Quality Control Inspector

Quality Control Inspectors ensure that products meet quality standards. This course may be useful for Quality Control Inspectors who work in the field of manufacturing. The course will provide them with the skills and knowledge necessary to analyze and design control systems using frequency response methods.

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Technical Writer

Technical Writers create documentation for a variety of products and services. This course may be useful for Technical Writers who specialize in writing documentation for control systems. The course will provide them with the skills and knowledge necessary to understand and explain control systems using frequency response methods.

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Sales Engineer

Sales Engineers sell technical products and services. This course may be useful for Sales Engineers who specialize in selling control systems. The course will provide them with the skills and knowledge necessary to understand and explain control systems using frequency response methods.

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Product Manager

Product Managers are responsible for the development and marketing of products. This course may be useful for Product Managers who specialize in control systems. The course will provide them with the skills and knowledge necessary to understand and explain control systems using frequency response methods.

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