2020 Modeling and Control Theory B

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

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

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 models.
2) Have an understanding of analytical techniques using block diagram, vector locus and bode diagram, and on the basis of them, examine system characteristics expressed as transfer functions.
3) Explain the definition of stability and confirm system stability.
4) Have an understanding of feedback control systems and their design methods based on classical control systems and deign control systems that satisfy design specifications


System and Modeling, Laplace transforms, Transfer function, Block diagram, Transient response, Frequency characteristics, Nyquist diagram, Bode diagram, stability, stability criterion, PID control,Dynamic compensator

Competencies that will be developed

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

Class flow

Two lectures take place in one day. In the second half of the lecture, students are asked to work on exercises on the content for the day. Read the objectives of each lesson carefully and prepare and review. To deepen the understanding through examples, MATLAB assignments are given.

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 motor systems 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 Frequency response and vector locus Understand the relationship between transfer functions and characteristics in the frequency domain
Class 7 Bode diagram Understand bode diagram expression and how to utilize asymptotic curves
Class 8 Small exam. System stability and the Routh-Hurwitz stability criterion Check the understanding of what was taught during classes 1-7. Understand system stability in control theory and the Routh-Hurwitz stability criterion
Class 9 The Nyquist criterion Understand stability of feedback control systems and the Nyquist criterion
Class 10 Phase margin and gain margin Understand the definition and the usage of phase margin and gain margin
Class 11 Feedback control system characteristics - Sensitivity charactersitic and steady state charactersitic Understand the definition and the usage of sensitivity characteristic and steady state characteristic.
Class 12 Performance evaluation of control systems, PID control Understand the performance evaluation of control systems, the characteristics of a PID controller
Class 13 Phase lag compensation Understand the structure of a phase lag controller and its design method
Class 14 Phase lead compensation Understand the structure of a phase lead controller and its design method


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 little exams and final exam (80%) and exercise problems (20%).

Related courses

  • Robot Kinematics
  • Fundamentals of Instrumentation Engineering
  • MEC.I332 : Exercise in Mechatronics

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. It is desirable to take this course for taking MEC.I332:Exercise in Mechatronics.

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