Modeling of Feedback Systems from Coursera

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Syllabus

Introduction to Control Systems and Laplace Transforms

Welcome to Modeling Feedback Systems. This first week combines the essential concepts of control systems and differential equations. You will explore the foundations of control theory, understand the significance of feedback control, and master the application of Laplace transforms in solving ordinary differential equations. By the end of this week, you will possess a solid understanding of linearity, time-invariance, modeling approaches, and the practical uses of control systems.

Modeling of Physical Systems

During the second week of this course, you will delve into the foundational laws used in modeling feedback systems. You will explore how these laws are applied to model simple mechanical, electrical, and electromechanical systems by deriving differential equations from fundamental principles such as Newton's laws of motion, Kirchhoff's laws, and the Motor/Generator laws. Additionally, you will gain proficiency in representing these systems as transfer functions using Laplace and inverse Laplace transforms, which will enable you to analyze and understand their behavior in the frequency domain. By the end of this week, you will have acquired the essential knowledge and skills to effectively model and analyze a wide range of dynamic systems.

Block Diagram Analysis and Dynamic Response

In the third week of this course, you will dive deeper into the application of Laplace transforms. You will start by learning how to use the initial/final value theorems to calculate the values of time-domain signals using their Laplace-domain representation. Additionally, you will develop the skills to manipulate block diagram representations of interconnected systems, enabling you to analyze complex systems and understand their overall behavior. You will also explore the dynamic response of 1st- and 2nd-order systems, gaining insights into their transient and steady-state characteristics. Lastly, you will discover techniques to approximate higher-order systems reasonably well by utilizing the impulse and step responses of lower-order systems. By the end of this week, you will have acquired advanced tools and techniques to analyze and model a wide range of dynamic systems with precision and accuracy.

Transient Step Response Specifications

In the fourth week of this course, you will focus on system performance analysis using transient step response specifications. You will learn how to calculate and evaluate key performance metrics such as rise time, settling time, and overshoot using the step response of a system. By understanding the relationship between pole locations and step response performance specifications, you will gain insights into how system dynamics affect the overall performance. Furthermore, you will utilize transient step response data to estimate the 2nd-order transfer function approximation, enabling you to model and analyze complex systems accurately. Lastly, you will compare the impact of zeros and additional poles on the step responses of systems, deepening your understanding of how system components influence the overall behavior. By the end of this week, you will be equipped with the skills to assess and optimize system performance based on transient step response characteristics.

Modeling From Transient Response Data and Stability

Congratulations on making it to the 5th and final week of this course. This week you will delve into the concept of Bounded-Input Bounded-Output (BIBO) stability and its application in analyzing Linear Time-Invariant (LTI) systems. You will learn the necessary and sufficient conditions for BIBO stability and apply them to assess the stability of dynamic systems. Additionally, you will explore Routh's stability criterion, which allows you to determine system stability. Furthermore, you will discover how to design stable proportional-feedback systems using Routh's stability criterion, enabling you to create control systems that exhibit desirable behavior. By the end of this week, you will have acquired the knowledge and skills to analyze, assess, and design stable systems using BIBO stability and Routh's stability criterion.

Good to know

Know what's good

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Develops modeling and analysis skills for dynamic systems, which is a core topic in mechanical, electrical, and chemical engineering

Covers Laplace transforms, a mathematical tool widely used in modeling and control systems

Teaches Routh's stability criterion, which helps analysts assess and design stable systems

Instructed by Dr. Lucy Pao, an experienced researcher and educator in control systems

Examines Bounded-Input Bounded-Output (BIBO) stability, a fundamental concept for analyzing system stability

Prerequisites may be required as the course explicitly advises taking other courses first

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 Modeling of Feedback Systems with these activities:

Gather Course Materials

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Bring together notes, assignments, and old exams to provide scaffolding and organization for future work

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Print syllabi and class schedule
Get a notebook, binder, folder, or digital note collection system ready for materials
Look for or create digital copies of presentations and supplemental materials

Review Laplace Transform Techniques

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Refresh your knowledge of Laplace transform techniques, essential for analyzing dynamic systems.

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Review the definition of Laplace transform.
Practice finding Laplace transforms of common functions.
Practice using Laplace transforms to solve differential equations.

Review Matrix Algebra

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Matrix algebra is critical for understanding control theory concepts

Browse courses on Matrix Algebra

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Review notes and textbooks from previous linear algebra courses
Solve practice problems

Eight other activities

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Review Calculus I & II

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Brings foundational calculus concepts into recent memory for more efficient learning

Browse courses on Differential Calculus

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Review notes from Calculus I
Review notes from Calculus II
Solve practice problems

Establish Study Group

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Encourages collaboration, promotes knowledge sharing, and enhances problem-solving

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Form a study group with peers in the course
Meet regularly to review course material, discuss concepts, and solve problems together

Practice Modeling Dynamic Systems

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Reinforce your understanding of modeling dynamic systems using fundamental principles.

Browse courses on Newton's Laws

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Identify the forces acting on a system.
Apply Newton's laws to derive differential equations.

Follow Electronics Tutorials

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Provides a structured and guided practice setting for students

Browse courses on Control Theory

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Search for relevant tutorials on platforms like Coursera, MIT OpenCourseWare, or YouTube
Follow the tutorials and take notes using your own real-world examples

Attempt Practice Problems

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Provide a hands-on approach to reinforcement and mastery

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Solve practice problems from the textbook or online resources
Compare answers with solutions to identify areas for improvement
Repeat the process until comfortable with the material

Design a Feedback Control System

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Offers an opportunity to apply acquired knowledge, and promotes higher-order thinking and problem-solving

Browse courses on Feedback Control

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Identify a real-world problem that can be addressed using feedback control
Design a feedback control system using the principles learned in the course
Simulate and analyze the performance of the designed system

Mentor Junior Students

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By helping to teach concepts to others, students deepen their own understanding and improve their communication skills

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Volunteer to mentor students who are struggling with the course material
Review course concepts and prepare materials
Meet with mentees regularly to provide guidance and support

Contribute to Open-Source Control Projects

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Provides exposure to real-world applications and fosters collaboration and teamwork

Browse courses on Control Theory

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Identify open-source control projects on platforms like GitHub or SourceForge
Review the project documentation and identify areas where contributions can be made
Make code contributions, report bugs, or improve documentation

Career center

Learners who complete Modeling of Feedback Systems will develop knowledge and skills that may be useful to these careers:

Control Systems Engineer

As a Control Systems Engineer, you will analyze, design, and implement control systems for various applications. This course, Modeling of Feedback Systems, will provide you with a solid foundation in control theory, modeling of dynamic systems, and Laplace Transforms. You will learn how to derive differential equations from physical principles and convert them into transfer functions. The hands-on approach you will gain in this course is essential for success in this field. You will also become familiar with the tools and techniques used in the analysis and design of control systems.

See salaries and explore the career path for Control Systems Engineer

Control Systems Analyst

As a Control Systems Analyst, you will analyze and evaluate the performance of control systems. This course, Modeling of Feedback Systems, will provide you with a thorough understanding of control theory, modeling of dynamic systems, and Laplace Transforms. You will learn how to derive differential equations from physical principles and convert them into transfer functions. Additionally, you will become proficient in using block diagram representations and analyzing system performance using transient step response specifications. These skills are essential for success in this role and will give you the confidence to excel.

See salaries and explore the career path for Control Systems Analyst

Dynamic Modeler

As a Dynamic Modeler, you will develop and analyze mathematical models of dynamic systems to predict their behavior. This course, Modeling of Feedback Systems, will help you build a foundation in dynamic modeling and Laplace Transforms. You will learn how to derive differential equations from fundamental principles and convert them into transfer functions. Additionally, you will become proficient in using block diagram representations and analyzing system performance using transient step response specifications. These skills are crucial for success in this field.

See salaries and explore the career path for Dynamic Modeler

Mechatronics Engineer

As a Mechatronics Engineer, you will design and develop systems that combine mechanical, electrical, and computer engineering. This course, Modeling of Feedback Systems, will help you build a strong foundation in modeling and analyzing dynamic systems, which is crucial for the successful design of mechatronic systems. You will learn how to derive differential equations from physical principles and convert them into transfer functions. Additionally, you will become proficient in using block diagram representations and analyzing system performance using transient step response specifications. These skills are highly sought after in this field and will give you a competitive edge.

See salaries and explore the career path for Mechatronics Engineer

Robotics Engineer

As a Robotics Engineer, you will design, build, and test robots for various applications. This course, Modeling of Feedback Systems, will help you build a strong foundation in modeling and analyzing dynamic systems, which is essential for the successful design and control of robots. You will learn how to derive differential equations from physical principles and convert them into transfer functions. Additionally, you will become proficient in using block diagram representations and analyzing system performance using transient step response specifications. These skills are highly sought after in this field and will give you a competitive edge.

See salaries and explore the career path for Robotics Engineer

Electronics Engineer

As an Electronics Engineer, you will design and develop electronic circuits and systems. This course, Modeling of Feedback Systems, will help you build a strong foundation in modeling and analyzing dynamic systems, which is crucial for the successful design of electronic circuits and systems. You will learn how to derive differential equations from physical principles and convert them into transfer functions. Additionally, you will become proficient in using block diagram representations and analyzing system performance using transient step response specifications. These skills are highly sought after in this field and will give you a competitive edge.

See salaries and explore the career path for Electronics Engineer

Systems Engineer

As a Systems Engineer, you will design, develop, and integrate complex systems. This course, Modeling of Feedback Systems, will help you build a solid foundation in modeling and analyzing dynamic systems, which is essential for the successful design and integration of complex systems. You will learn how to derive differential equations from physical principles and convert them into transfer functions. Additionally, you will become proficient in using block diagram representations and analyzing system performance using transient step response specifications. These skills are crucial for success in this role and will give you the confidence to excel.

See salaries and explore the career path for Systems Engineer

Software Engineer

As a Software Engineer, you will design, develop, and maintain software systems. This course, Modeling of Feedback Systems, may be useful for you if you are interested in developing software for control systems or other applications that require dynamic modeling. The course will provide you with a basic understanding of control theory, modeling of dynamic systems, and Laplace Transforms.

See salaries and explore the career path for Software Engineer

Electrical Engineer

As an Electrical Engineer, you will design and develop electrical systems and components. This course, Modeling of Feedback Systems, may be useful for you if you are interested in designing electrical systems that require dynamic modeling and control. The course will provide you with a basic understanding of control theory, modeling of dynamic systems, and Laplace Transforms.

See salaries and explore the career path for Electrical Engineer

Mechanical Engineer

As a Mechanical Engineer, you will design and develop mechanical systems and components. This course, Modeling of Feedback Systems, may be useful for you if you are interested in designing mechanical systems that require dynamic modeling and control. The course will provide you with a basic understanding of control theory, modeling of dynamic systems, and Laplace Transforms.

See salaries and explore the career path for Mechanical Engineer

Aerospace Engineer

As an Aerospace Engineer, you will design and develop aerospace systems and components. This course, Modeling of Feedback Systems, may be useful for you if you are interested in designing aerospace systems that require dynamic modeling and control. The course will provide you with a basic understanding of control theory, modeling of dynamic systems, and Laplace Transforms.

See salaries and explore the career path for Aerospace Engineer

Nuclear Engineer

As a Nuclear Engineer, you will design and develop nuclear power plants and systems. This course, Modeling of Feedback Systems, may be useful for you if you are interested in designing nuclear power plants and systems that require dynamic modeling and control. The course will provide you with a basic understanding of control theory, modeling of dynamic systems, and Laplace Transforms.

See salaries and explore the career path for Nuclear Engineer

Civil Engineer

As a Civil Engineer, you will design and develop civil infrastructure systems. This course, Modeling of Feedback Systems, may be useful for you if you are interested in designing civil infrastructure systems that require dynamic modeling and control. The course will provide you with a basic understanding of control theory, modeling of dynamic systems, and Laplace Transforms.

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Biomedical Engineer

As a Biomedical Engineer, you will design and develop medical devices and systems. This course, Modeling of Feedback Systems, may be useful for you if you are interested in designing medical devices and systems that require dynamic modeling and control. The course will provide you with a basic understanding of control theory, modeling of dynamic systems, and Laplace Transforms.

See salaries and explore the career path for Biomedical Engineer

Chemical Engineer

As a Chemical Engineer, you will design and develop chemical processes and systems. This course, Modeling of Feedback Systems, may be useful for you if you are interested in designing chemical processes that require dynamic modeling and control. The course will provide you with a basic understanding of control theory, modeling of dynamic systems, and Laplace Transforms.

See salaries and explore the career path for Chemical Engineer