Fundamentals of Control Theory

Course title

33023600

Middle-level Diploma Policy (mDP)

Program / Major	mDP	Goals
Mathematical Sciences Course	DP-4・2	キャリアを見据えた高度な専門知識現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。

Purpose of class

Lecture of classic control based on transfer function approach. Cover Laplace transform, transfer function, various system response, stability criteria, steady state by feedback, PID control, bode diagram, etc.

Course description

Control engineering plays an important role in real systems involving mechanical and electrical systems. There are two types of control, the first one is classic control based on transfer functions, and the second one is modern control based on state-space representation. This course is focused on the first one, studying the fundamentals in classic control theory. It will cover Laplace transform, transfer function, various system response, stability criteria, steady state by feedback, PID control, bode diagram, etc. The course will be delivered through lectures together with some MATLAB/Simulink simulations.

Goals and objectives

Students can describe system modeling and compute state response of systems.
Students can compute poles of systems, and judge stability with stability criteria of systems.
Students can perform system analysis and design based on frequency transfer functions

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Middle exam	Final exam	Quizzes in class	Total.
1.	15%	10%	5%	30%
2.	15%	15%	10%	40%
3.		25%	5%	30%
Total.	30%	50%	20%	-

Evaluation method and criteria

Evaluate by middle exam (30%), final exam (50%), and quizzes in class (20%).

Pass when reaching 60% in the whole evaluation, or in other words, reaching the level of deriving the transfer function of simple control systems, and then obtaining the solution of the system together with some stability analysis and frequency design.

Language

Japanese(English accepted)

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Introduction of the course. What is Control?	Investigate what control means in a practical control system	190minutes
2.	Mathematical modeling of systems	Physical and mathematical modeling of systems. Review the definition of derivative, integral and differential equations	190minutes
3.	Transfer functions and block diagrams	Review of Laplace transforms and ODEs	190minutes
4.	Transfer functions and block diagrams, responses of dynamical systems	Review of Laplace transforms, ODEs and block diagrams with signal flow (operation)	190minutes
5.	Response proterty of systems, response of 2nd order systems	Review of Laplace transforms, inverse Laplace transforms, and basic calculus for maximum value, etc. Try to understand properties of second-order systems with different parameters in real applications.	190minutes
6.	Pole and stability	Review of polynomials with real coefficients and the zeros of polynomials.	190minutes
7.	Routh stability condition, Matlab Simulation	Review of polynomials, and try to use MATLAB/Simulink to plot system states.	190minutes
8.	Review and middle exam	Review of the content and problems in the first 7 weeks.	190minutes
9.	Design of control systems and its stability	Check the definition and the meaning of stability in feedback control systems with inputs and disturbances.	190minutes
10.	PID control	Investigate the history and prepare the structure of PID control.	190minutes
11.	Steady state property of feedback control systems, Bode diagrams (1)	Check the definition and the meaning of steady state errors in feedback control systems, Investigate the definition and meaning of Bode diagrams.	190minutes
12.	Bode diagrams (2), etc	Check the definition and the meaning of steady state errors in feedback control systems, Investigate the definition and meaning of Bode diagrams.	190minutes
13.	Matlab/Simulink Simulation	Try to use various Matlab commands for responses, stability, trajectory plot, and bode diagrams.	190minutes
14.	Review and exercise, final exam	review of the entire course with examples and exercises	190minutes
Total.	-	-	2660minutes