### 2019　Dynamical Systems

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Instructor(s)
Miyake Yoshihiro  Ogawa Kenichirou
Course component(s)
Lecture
Day/Period(Room No.)
Tue1-2(W242)  Fri1-2(W242)
Group
-
Course number
CSC.T373
Credits
2
2019
Offered quarter
3Q
Syllabus updated
2019/4/1
Lecture notes updated
-
Language used
Japanese
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### Course description and aims

Cyber physical systems (CPSs) have received great attention as technologies of Internet of Things (IoT) advance. Therefore, to learn information engineering, you need to deeply understand not only computers (cyber) but also real world (physical) modeling. In this course, you will learn the foundation of expression and analysis of real world as a dynamical system. In particular, you will obtain basic knowledge on state equations, system expression of transfer functions, and some analysis methods.

### Student learning outcomes

The purpose is to:
1) understand the whole picture of dynamical systems;
2) learn the foundation of representation and analysis of dynamical systems;
3) learn a method for modeling dynamical systems using state space and transfer functions;
4) learn a method for analyzing dynamical systems using state space and transfer functions; and
5) visualize behaviors of dynamical systems by numerical analysis.

### Keywords

Dynamical systems, System representation, System analysis, State space, State equations, Modeling, Isomorphism, Primary system, Secondary system, Stability, Transfer function, Block diagram, Transient response, Frequency response, Numerical analysis, Nonlinear system, Cyber physical system

### Competencies that will be developed

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

### Class flow

This course is mainly composed of lectures. In addition, you will do a little exercise or test to deeply understand the content of the lectures.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction: Why do you learn dynamical systems? Why are dynamical systems needed in information engineering? What is system? What is modeling?
Class 2 State space representation and analysis: state space representation (part 1) State equations on spate space Review of linear algebra
Class 3 State space representation and analysis: state space representation (part 2) State space and state equations thereon Review of linear algebra
Class 4 State space representation and analysis: modeling and isomorphism Modeling of mechanical systems, electric systems, biological systems Isomorphism
Class 5 State space representation and analysis: state space and trajectory (part 1) Analysis of primary system and secondary system Stability
Class 6 State space representation and analysis: state space and trajectory (part 2) Analysis of primary system and secondary system Stability
Class 7 State space representation and analysis: exercise Exercise and test
Class 8 Transfer function representation and analysis: transfer function representation (part1) Transfer functions and block diagrams Review of Laplace transformation
Class 9 Transfer function representation and analysis: transfer function representation (part2) Transfer functions and block diagrams Review of Laplace transformation
Class 10 Transfer function representation and analysis: transient response and stability Impulse response and step response Stability
Class 11 Transfer function representation and analysis: frequency response Frequency response Bode diagram and Nyquist diagram
Class 12 Transfer functions and analysis: exercise Exercise and test
Class 13 Numerical analysis using computer: visualization of dynamical systems Numerical analysis and MATLAB Review of numerical calculation method
Class 14 Numerical analysis using computer: Expansion into nonlinear systems Expansion into nonlinear systems Attractors
Class 15 Conclusion: Information engineering and dynamical systems Importance of dynamical systems in technologies of IoT Cyber physical systems

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### Reference books, course materials, etc.

Lecture materials will be handed out each time.

### Assessment criteria and methods

Your grade for the course will be based on the following components: reports (50%) and tests (50%).

### Related courses

• CSC.T362 ： Numerical Analysis
• CSC.T351 ： System Analysis
• CSC.T374 ： Control Systems
• CSC.T342 ： Problem Solving and Decision Making
• ART.T456 ： Non-linear Dynamical Systems
• ART.T452 ： Modeling of Continuous Systems
• ART.T452 ： Modeling of Continuous Systems

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### Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Yoshihiro Miyake　email: miyake[at]c.titech.ac.jp, ext.: 5656
Ken-ichiro Ogawa　email: ogawa[at]c.titech.ac.jp, ext.: 5656

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