2016 Modeling and Control Theory

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Academic unit or major
Undergraduate major in Mechanical Engineering
Omata Toru  Sato Kaiji  Tadano Kotaro 
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Course description and aims

This course focuses on modeling of a variety of electric circuits and vibration systems, and analysis techniques of linear time-invariant systems. It covers the fundamentals of linear control theory. The topics include transfer function derivation of dynamic models and analytical techniques of system characteristics using the transfer functions, definition of system stability, some stability criterions, design methods of feedback control systems.

Student learning outcomes

At the end of this course, students will be able to:
1) Derive transfer functions of linear time-invariant systems from their dynamic model.
2) Have an understanding of analytical techniques using block diagram, vector locus and bode diagram, and based on them, examine system characteristics expressed as transfer functions.
3) Explain the definition of stability and confirm system stability.
4) Have an understanding of basic control system design methods and deign control systems which satisfy the design specifications


Laplace transforms,Transfer function, Block digram, Bode diagram, stability, PID control

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Lectures for two classes are carried out in a day. At the beginning of each lecture, solutions to exercise problems that were assigned during the previous lecture are reviewed. Towards the end of the lecture, students are given exercise problems related to the lecture given that day to solve. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction to control Understand the concept of feedback control
Class 2 The Laplace transform Understand the Laplace transform
Class 3 Dynamic model and transfer function of physical systems Understand how to model physical systems, for example, electric circuits and vibration systems and how to derive their motion equations and transfer functions
Class 4 Block diagram Understand block diagrams and how to transform their structures
Class 5 Inverse Laplace transform - Time response Understand the relationship between transfer functions and time responses
Class 6 System stability and the Routh-Hurwitz stability criterion Understand system stability in control theroy and the Routh-Hurwitz stability criterion
Class 7 Frequency response and vector locus Understand the relationship between transfer functions and characteristics in the frequency domain
Class 8 Review of the first half of the course (classes 1–7) and midterm exam. Revise what was taught during classes 1-7 to prepare for the exam.
Class 9 Bode diagram Understand bode diagram expression and how to utilize asymptotic curves
Class 10 The Nyquist criterion Understand stability of feedback control systems and the Nyquist criterion
Class 11 Phase margin and gain margin Understand the definition and the usage of phase margin and gain margin
Class 12 Feedback control system characteristics - Sensitivity charactersitic and steady state charactersitic Understand the definition and the usage of sensitivity charactersitic and steady state charactersitic
Class 13 PID control Understand the charactersitics of a PID controller and its design method
Class 14 Phase lag compensation and phase lead compensation Understand the structure of a phase lag compensation and a phase lead compensation and their design methods
Class 15 Two degree-of-freedom control system Understand the structure and the characteristics of a two degree-of-freedom control system


Sugie, Toshiharu. Fujita, Masayuki. Introduction to Feedback Control. Corona Publishing, ISBN 978-4339033038. (Japanese)

Reference books, course materials, etc.


Assessment criteria and methods

Students’ course scores are based on midterm and final exams (80%) and exercise problems (20%).

Related courses

  • Robot Kinematics
  • Fundamentals of Instrumentation Engineering

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Engineering Mechanics, Complex Function Theory and Ordinary Differential Equations or have equivalent knowledge.

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