University of Colorado Boulder

Modeling of Feedback Systems

Taught in English

1,604 already enrolled


Gain insight into a topic and learn the fundamentals

Dr. Lucy Pao

Instructor: Dr. Lucy Pao


(12 reviews)

Intermediate level

Recommended experience

14 hours to complete
3 weeks at 4 hours a week
Flexible schedule
Learn at your own pace

What you'll learn

  • Derive differential equations and transfer functions for simple mechanical, electrical, and electromechanical systems.

  • Analyze the dynamic response of 1st and 2nd order systems.

  • Explain the relationship between pole locations of 2nd-order systems and common step response performance specifications.

  • Characterize Bounded-Input Bounded-Output (BIBO) stability and determine the number of unstable roots using Routh’s stability criterion.

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6 quizzes, 5 assignments

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There are 5 modules in this course

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.

What's included

9 videos2 quizzes1 assignment

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.

What's included

10 videos1 assignment

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.

What's included

9 videos1 quiz1 assignment

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.

What's included

12 videos1 quiz1 assignment

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.

What's included

10 videos2 quizzes1 assignment


Instructor ratings
4.8 (7 ratings)
Dr. Lucy Pao
University of Colorado Boulder
1 Course1,604 learners

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