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Dr. Lucy Pao
In this course, you'll explore modeling of dynamic systems and feedback control. The course begins with an introduction of control theory and the application of Laplace transforms in solving differential equations, providing a strong foundation in linearity, time-invariance, and dynamic system modeling. The following week will delve into the laws governing the modeling of dynamic systems, with a focus on deriving differential equations from fundamental principles like Newton's laws and Kirchhoff's laws, as well as mastering the representation of systems as transfer functions in the Laplace domain. The third week delves deeper into Laplace transforms, emphasizing initial/final value theorems, block diagram manipulation, and dynamic response analysis. Moving into the fourth week, you'll learn to analyze system performance using transient step response specifications, enabling you to assess and optimize system behavior effectively. Finally, in the fifth week, you'll explore Bounded-Input Bounded-Output (BIBO) stability and Routh's stability criterion, gaining the skills to assess, analyze, and design stable systems. By the course's end, you'll be well-equipped to navigate the intricacies of control systems and dynamic modeling.
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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.
Read more
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.
Read more
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
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
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
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Activities
Be better prepared
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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
Show steps
-
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
Show steps
Refresh your knowledge of Laplace transform techniques, essential for analyzing dynamic systems.
Show steps
-
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
Expand to see all activities and additional details
Show all 11 activities
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
Show steps
Encourages collaboration, promotes knowledge sharing, and enhances problem-solving
Show steps
-
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
Show steps
Reinforce your understanding of modeling dynamic systems using fundamental principles.
Browse courses on
Newton's Laws
Show steps
-
Identify the forces acting on a system.
-
Apply Newton's laws to derive differential equations.
Follow Electronics Tutorials
Show steps
Provides a structured and guided practice setting for students
Browse courses on
Control Theory
Show steps
-
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
Show steps
Provide a hands-on approach to reinforcement and mastery
Show steps
-
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
Show steps
Offers an opportunity to apply acquired knowledge, and promotes higher-order thinking and problem-solving
Browse courses on
Feedback Control
Show steps
-
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
Show steps
By helping to teach concepts to others, students deepen their own understanding and improve their communication skills
Show steps
-
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
Show steps
Provides exposure to real-world applications and fosters collaboration and teamwork
Browse courses on
Control Theory
Show steps
-
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
Gather Course Materials
Show steps
Bring together notes, assignments, and old exams to provide scaffolding and organization for future work
Show steps
Show steps
Show steps
- 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
Show steps
Refresh your knowledge of Laplace transform techniques, essential for analyzing dynamic systems.
Show steps
Show steps
Show steps
- Review the definition of Laplace transform.
- Practice finding Laplace transforms of common functions.
- Practice using Laplace transforms to solve differential equations.
Review Matrix Algebra
Show steps
Matrix algebra is critical for understanding control theory concepts
Browse courses on
Matrix Algebra
Show steps
Show steps
Show steps
- Review notes and textbooks from previous linear algebra courses
- Solve practice problems
Eight other activities
Expand to see all activities and additional details
Show all 11 activities
Review Calculus I & II
Show steps
Brings foundational calculus concepts into recent memory for more efficient learning
Browse courses on
Differential Calculus
Show steps
Show steps
Show steps
- Review notes from Calculus I
- Review notes from Calculus II
- Solve practice problems
Establish Study Group
Show steps
Encourages collaboration, promotes knowledge sharing, and enhances problem-solving
Show steps
Show steps
Show steps
- 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
Show steps
Reinforce your understanding of modeling dynamic systems using fundamental principles.
Browse courses on
Newton's Laws
Show steps
Show steps
Show steps
- Identify the forces acting on a system.
- Apply Newton's laws to derive differential equations.
Follow Electronics Tutorials
Show steps
Provides a structured and guided practice setting for students
Browse courses on
Control Theory
Show steps
Show steps
Show steps
- 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
Show steps
Provide a hands-on approach to reinforcement and mastery
Show steps
Show steps
Show steps
- 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
Show steps
Offers an opportunity to apply acquired knowledge, and promotes higher-order thinking and problem-solving
Browse courses on
Feedback Control
Show steps
Show steps
Show steps
- 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
Show steps
By helping to teach concepts to others, students deepen their own understanding and improve their communication skills
Show steps
Show steps
Show steps
- 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
Show steps
Provides exposure to real-world applications and fosters collaboration and teamwork
Browse courses on
Control Theory
Show steps
Show steps
Show steps
- 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
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.
Control Systems Analyst
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.
Dynamic Modeler
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.
Mechatronics Engineer
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.
Robotics 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.
Electronics 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.
Systems 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.
Software 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.
Electrical 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.
Mechanical 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.
Aerospace 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.
Nuclear 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.
Civil 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.
Biomedical Engineer
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.
Chemical 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.
For more career information including salaries, visit:
OpenCourser.com/course/cp26yc/modeling
Reading list
We've selected 11 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Modeling of Feedback Systems.
This classic textbook provides a comprehensive overview of feedback control systems, with a focus on stability, performance, and design. It covers a wide range of topics, from basic concepts to advanced techniques, and is suitable for both undergraduate and graduate students.
This textbook widely used introduction to modern control engineering. It covers a wide range of topics, including state-space models, frequency response, and optimal control. It is suitable for both undergraduate and graduate students.
This textbook provides a comprehensive overview of control systems engineering, with a focus on practical applications. It covers a wide range of topics, including system modeling, analysis, and design. It is suitable for both undergraduate and graduate students.
Save
This textbook provides a comprehensive overview of nonlinear systems, with a focus on stability and control. It covers a wide range of topics, including Lyapunov stability, nonlinear feedback control, and chaos. It is suitable for both graduate students and researchers.
This textbook provides a comprehensive overview of robust control, with a focus on both theory and applications. It covers a wide range of topics, including robustness analysis, robust controller design, and uncertainty modeling. It is suitable for both graduate students and researchers.
This textbook provides a comprehensive overview of linear control systems, with a focus on both theory and applications. It covers a wide range of topics, including state-space models, frequency response, and optimal control. It is suitable for both undergraduate and graduate students.
This textbook provides a comprehensive overview of control systems design, with a focus on practical applications. It covers a wide range of topics, including system modeling, analysis, and design. It is suitable for both undergraduate and graduate students.
This textbook provides a comprehensive overview of modern control technology, with a focus on both theory and applications. It covers a wide range of topics, including nonlinear systems, optimal control, and robust control. It is suitable for both graduate students and researchers.
This textbook provides a comprehensive overview of system dynamics, with a focus on both theory and applications. It covers a wide range of topics, including system modeling, analysis, and design. It is suitable for both undergraduate and graduate students.
This textbook provides a comprehensive overview of modeling, analysis and control of dynamic systems, with a focus on both theory and applications. It covers a wide range of topics, including system modeling, analysis, and design. It is suitable for both undergraduate and graduate students.
This textbook provides a comprehensive overview of control systems, with a focus on both theory and applications. It covers a wide range of topics, including system modeling, analysis, and design. It is suitable for both undergraduate and graduate students.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/cp26yc/modeling
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Effort
About 5 Weeks
Level
Intermediate
Via
Coursera
Institution
University of Colorado Boulder
Instructor
Dr. Lucy Pao
Language
English
Good to know
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
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