Controle a Tempo Discreto from Coursera

O objetivo deste curso é apresentar o assunto de Controle a Tempo Discreto para sistemas lineares e invariantes no tempo. São apresentadas técnicas para lidar com implementação de controladores por computador, requerendo a consideração da discretização do tempo inerente aos seu uso. A importância dos conhecimentos apresentados nesse curso se justifica pela onipresença de controladores digitais em aplicações atualmente.

O curso é dividido em 4 módulos, resumidamente:

1) Apresentação de modelos para sistemas operando a tempo discreto e critérios para avaliar sua estabilidade.

2) Formas de discretizar aproximadamente uma função de transferência a tempo contínuo e estimação do efeito da discretização na resposta do sistema.

3) Projeto do controlador diretamente em tempo discreto, usando duas abordagens: resposta em frequência e Lugar Geométrico das Raízes (LGR).

4) Projeto do controlador diretamente em tempo discreto, usando o espaço de estados.

Ao longo do curso, ferramentas computacionais de projeto de controladores auxiliado por computador são usadas para ilustrar a aplicação das técnicas através de exemplos. Apesar de ser possível concluir o curso prescindindo dessas ferramentas, seu uso é recomendado por dois motivos: facilidade de realizar as operações mais tediosas, liberando mais tempo para focar no conteúdo, e aproximação com o que é feito na prática de projetos no âmbito de atuação do(a) profissional.

Ao final desse curso, o(a) aluno(a) deve ser capaz de adaptar criteriosamente um projeto de controlador feito a tempo contínuo para aplicação em sistemas controlador por computador digital e projetar diretamente um controlador a tempo discreto para o mesmo uso.

What's inside

Syllabus

Sistemas a tempo discreto, equações a diferenças, Transformada Z de sinais a tempo discreto, função de transferência e estabilidade

Neste módulo você aprenderá a modelar sistemas dinâmicos a tempo discreto por meio de Equações a Diferenças. Em seguida, uma ferramenta para facilitar a análise de sistemas a tempo discreto, a chada transformada Z será apresentada, juntamente com suas propriedades. Com isso, você estará apto a determinar uma função de transferência para o sistema a tempo discreto, podendo analisá-lo de maneira mais simples do que por meio da solução direta da Equação a Diferenças para uma determinada entrada. Por fim, será definida a estabilidade de um sistema a tempo discreto e você aprenderá como ela pode ser verificada e usará três critérios para avaliá-la: os critérios de Nyquist, de Routh-Hurwitz com mapeamento bilinear e de Jury.

Amostragem de sistemas a tempo contínuo e equivalentes discretos

Neste módulo você aprenderá a determinar os efeitos de se amostrar um sinal a tempo discreto, em particular aprenderá que frequência de amostragem mínima se deve usar para poder reconstruir com fidelidade o sinal a tempo contínuo. Também aprenderá a determinar os efeitos de se amostrar um sinal na resposta temporal. Em seguida, você aprenderá a determinar funções de transferência a tempo discreto cuja resposta aproxime a resposta de funções de transferência a tempo contínuo nos instantes de amostragem de três maneiras diferentes: aproximação de integrais, casamento de zeros e polos, e Segurador de Ordem Zero.

Controle direto digital: domínio da frequência e plano Z

Neste módulo você aprenderá a determinar a resposta em frequência de um sistema amostrado. Com isso, serão traduzidos critérios de desempenho no domínio tempo em malha fechada para o domínio da frequência em malha aberta, permitindo o uso da resposta em frequência para projeto de leis de controle para atingir requisitos de tempo de resposta, sobressinal e erro em regime estacionário. Você aprenderá a projetar compensadores de avanço e atraso de fase usando a resposta em frequência. Além disso, você aprenderá a determinar que lugares do plano complexo as raízes de malha fechada podem ocupar quando se varia um ganho positivo em cascata com o sistema com realimentação negativa unitária. Usando esse conhecimento e as relacionando as posições dos polos de malha fechada com o desempenho associado no domínio do tempo, você aprenderá a projetar compensadores de avanço e atraso de fase usando a o Lugar Geométrico das Raízes da função de transferência em malha aberta.

Controle direto digital: espaço de estados

Neste módulo você aprenderá a obter realizações no espaço de estados à partir da função de transferência a tempo discreto do sistema, com particular enfoque na realização canônica controlável. Você aprenderá a projetar um controlador por realimentação de estado completo a fim de alocar os autovalores da matriz de estado de malha fechada nas posições desejadas e a determinar um ganho de pré-filtro para que a saída do sistema em malha fechada siga um comando degrau sem erro em regime estacionário. Também aprenderá a projetar um observador para estimar os estados à partir apenas da saída e da entrada, permitindo usar a lei de controle de realimentação de estado completo mesmo quando não se tem acesso a medidas dos estados.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Ensina aos alunos métodos e ferramentas importantes para a área de controle, que são muito utilizados na prática profissional

Os instrutores são reconhecidos por seu trabalho na área de controle

O curso oferece uma mistura de mídia, incluindo vídeos, leituras e discussões, o que o torna mais envolvente e eficaz

O curso requer que os alunos tenham algum conhecimento prévio em sistemas lineares e invariantes no tempo

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 a Tempo Discreto with these activities:

Revise formulas

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Strengthen your foundation in formulas used in discrete-time control systems for better understanding during the course.

Browse courses on Transfer Functions

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Review the formulas for discrete-time systems, such as the difference equation and the Z-transform.
Practice using the formulas to solve problems related to discrete-time systems.

Explore control theory software

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Gain practical experience using software tools commonly used in control theory and engineering.

Browse courses on Control Systems

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Choose a control theory software package, such as MATLAB, Simulink, or Scilab.
Follow tutorials or online courses to learn the basics of the software.
Use the software to simulate and analyze control systems.

Solve control problems

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Reinforce your understanding of control theory concepts by solving practice problems.

Browse courses on Control Systems

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Find practice problems from textbooks, online resources, or your instructor.
Solve the problems using the concepts and techniques learned in the course.
Check your solutions against the provided answers or discuss them with your instructor or peers.

Ten other activities

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Review Laplace transforms

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Laplace transforms are crucial for analyzing and solving problems in time-invariant linear systems.

Browse courses on Laplace Transforms

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Review the basics of Laplace transforms, including the definition and properties.
Practice solving problems involving the Laplace transform of simple functions.
Apply Laplace transforms to analyze the stability of linear systems.

Compile resources on discrete-time control

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Having a curated collection of resources can enhance understanding and aid in future reference.

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Gather online resources, such as articles, videos, and tutorials, on topics related to discrete-time control.
Organize the resources into a logical structure, such as by topic or difficulty level.
Create a document or website to share the compilation with others.

Discuss stability criteria

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Engage with peers to discuss and clarify concepts related to stability criteria for discrete-time systems.

Browse courses on Stability analysis

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Form a study group with other students.
Choose a stability criterion to focus on.
Discuss the strengths and weaknesses of the criterion.
Apply the criterion to analyze the stability of discrete-time systems.

Discuss control system design strategies with peers

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Discussing with peers can provide diverse perspectives and enhance understanding.

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Find a study partner or group with similar interests.
Schedule regular meetings to discuss course material, share ideas, and work on problems together.
Actively participate in discussions, ask questions, and share your own insights.

Solve difference equations

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Solving difference equations is essential for understanding the behavior of discrete-time systems.

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Review the methods for solving linear difference equations with constant coefficients.
Practice solving difference equations with time-varying coefficients.
Apply difference equations to model and analyze real-world systems.

Design a block diagram for a discrete-time control system

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Creating block diagrams helps visualize and understand the flow of signals in a control system.

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Identify the components of the control system, including the plant, controller, and sensor.
Draw the block diagram using standard symbols and conventions.
Label the signals flowing between the blocks.
Analyze the block diagram to determine the overall system behavior.

Use MATLAB or Python for discrete-time control system design

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MATLAB and Python are widely used tools for control system design and analysis.

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Learn the basics of MATLAB or Python programming.
Install and configure the necessary toolboxes or libraries for control system design.
Follow tutorials on how to use MATLAB or Python for specific control system design tasks.
Practice using MATLAB or Python to design and simulate discrete-time control systems.

Design a discrete-time controller

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Apply the concepts learned in the course to design and implement a discrete-time controller for a specific system.

Browse courses on Control Design

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Define the requirements for the controller.
Choose a controller design method.
Implement the controller using a programming language.
Test the controller on a simulated or real system.

Build a simple robot that uses discrete-time control

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Building a robot is a hands-on way to apply the concepts of discrete-time control.

Browse courses on Robotics

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Design the robot's mechanical structure and choose appropriate sensors and actuators.
Develop a mathematical model of the robot's dynamics.
Design and implement a discrete-time controller for the robot.
Build the robot and test its performance.
Refine the controller and mechanical design as needed.

Design a digital controller for a real-world system

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Designing a digital controller is the ultimate application of the concepts learned in this course.

Browse courses on Control Systems

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Identify a real-world system that requires control, such as a robotic arm or a temperature regulation system.
Develop a mathematical model of the system.
Design and simulate a digital controller using the techniques learned in the course.
Implement the controller on a microcontroller or embedded system.
Test and evaluate the performance of the controlled system.

Career center

Learners who complete Controle a Tempo Discreto will develop knowledge and skills that may be useful to these careers:

Controls Engineer

Controls engineers apply their understanding of mechanical, electrical, and mathematical principles to improve the performance of a wide variety of systems that interact with the physical world. These systems include everything from self-driving cars and aircraft flight control systems to chemical plants and manufacturing robots. The principles of discrete-time control are foundational to designing and implementing systems that use computers to interface with these mechanical and electrical components. This course offers a comprehensive introduction to the major principles and techniques in this field, and will equip you with the skills and knowledge necessary to enter or advance in this career.

See salaries and explore the career path for Controls Engineer

Control Systems Engineer

Control systems engineers research, design, and implement control systems that manage, command, direct, or regulate the behavior of other devices or systems. They use their understanding of system dynamics, control theory, and computer science to create systems that meet specific performance requirements. This course provides a foundation in the theory and practice of digital control systems, which are essential for many modern control systems. The course will help you to understand how to design and implement control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Control Systems Engineer

Systems Engineer

Systems engineers are responsible for designing, developing, and integrating complex systems. They work across disciplines to ensure that all aspects of a system are working together seamlessly. This course provides a strong foundation in the principles of discrete-time control, which is essential for understanding and designing systems that interact with the physical world. The course will help you to develop the skills and knowledge necessary to succeed in this challenging and rewarding career.

See salaries and explore the career path for Systems Engineer

Robotics Engineer

Robotics engineers design, build, and maintain robots. They use their knowledge of mechanical engineering, electrical engineering, and computer science to create robots that can perform a variety of tasks, from manufacturing and assembly to healthcare and space exploration. This course provides a foundation in the fundamentals of discrete-time control, which is essential for designing and implementing control systems for robots. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Robotics Engineer

Mechatronics Engineer

Mechatronics engineers combine their knowledge of mechanical engineering, electrical engineering, and computer science to design and build products that integrate physical systems with computer-based controls. This course provides a strong foundation in the principles of discrete-time control, which is essential for understanding and designing mechatronic systems. The course will help you to develop the skills and knowledge necessary to succeed in this rapidly growing field.

See salaries and explore the career path for Mechatronics Engineer

Aerospace Engineer

Aerospace engineers design, build, and test aircraft, spacecraft, and other related systems. They use their knowledge of aerodynamics, thermodynamics, and control theory to create vehicles that are safe, efficient, and reliable. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for aerospace vehicles. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Aerospace Engineer

Automotive Engineer

Automotive engineers design, build, and test automobiles. They use their knowledge of mechanical engineering, electrical engineering, and computer science to create vehicles that are safe, efficient, and reliable. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for automobiles. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Automotive Engineer

Chemical Engineer

Chemical engineers design, build, and operate chemical plants and other facilities that produce chemicals and other products. They use their knowledge of chemistry, thermodynamics, and control theory to create processes that are safe, efficient, and environmentally friendly. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for chemical plants. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Chemical Engineer

Electrical Engineer

Electrical engineers design, build, and test electrical systems. They use their knowledge of electricity, electronics, and control theory to create systems that are safe, efficient, and reliable. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for electrical systems. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Electrical Engineer

Industrial Engineer

Industrial engineers design, improve, and install integrated systems for managing industrial production and distribution. They use their knowledge of mathematics, science, and engineering to improve the efficiency and effectiveness of industrial processes. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for industrial processes. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Industrial Engineer

Manufacturing Engineer

Manufacturing engineers design, build, and operate manufacturing systems. They use their knowledge of mechanical engineering, electrical engineering, and industrial engineering to create systems that are efficient, reliable, and cost-effective. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for manufacturing systems. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Manufacturing Engineer

Materials Engineer

Materials engineers research, develop, and test new materials. They use their knowledge of chemistry, physics, and engineering to create materials that have the desired properties for a variety of applications. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for materials processing. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Materials Engineer

Nuclear Engineer

Nuclear engineers design, build, and operate nuclear power plants. They use their knowledge of nuclear physics, thermodynamics, and control theory to create systems that are safe, efficient, and reliable. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for nuclear power plants. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Nuclear Engineer

Petroleum Engineer

Petroleum engineers design, build, and operate systems for extracting and producing oil and gas. They use their knowledge of geology, thermodynamics, and control theory to create systems that are safe, efficient, and environmentally friendly. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for oil and gas production. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

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Software Engineer

Software engineers design, develop, and maintain software systems. They use their knowledge of computer science and engineering to create software that is reliable, efficient, and user-friendly. This course provides a foundation in the fundamentals of discrete-time control, which is essential for understanding and designing control systems for software systems. The course will help you to understand how to design control systems that are robust, reliable, and efficient.

See salaries and explore the career path for Software Engineer