Advanced Control Theory

Course title

3302700A

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

Provide fundamental knowledge about modern control theory. More precisely, it covers state space representation (modeling), transfer function, state transition matrix, state solution (various response), system stability, controllability, state feedback, pole assignment, optimal control, etc. Aim at understanding various analysis and design tools in control engineering, and using MATLAB/Simulink for numerical simulation.

Course description

It is known that control engineering plays a very important role in real-world applications involving mechanical and electrical systems, and it includes classic control theory which is based on transfer function representations and modern control theory which is based on state space representations. This course is focused on the latter, deals with basic knowledge in modern control. We will learn system representation (modeling), transfer function, state solution (various response), frequency based analysis and design, system stability, controllability and observability, state feedback, optimal control, etc. The course will be delivered through lectures in English, together with some exercises and MATLAB/Simulink simulations.

Goals and objectives

Can understand state space representation, and obtain various system responses.
Can understand stability, controllability and observability of control systems.
Can understand state feedback and optimal control.

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

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

Evaluation method and criteria

Quiz during class: 20%
Middle exam: 30%
Final exam: 50%
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Pass when reaching 60% of the whole evaluation, or in other words, reaching the level of writing state space representation of simple control systems, and then obtaining the system’s solution, analyzing system stability, and designing proper state feedback for the control system.

Language

English

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Course introduction and preliminary English words in mathematics and control	Review simple English words in mathematics and control area	190minutes
2.	Classic control and modern control, transfer function, state space representation	Review calculus, matrix basics and Laplace transform	190minutes
3.	Various state space representations in control systems	Review of simple mechanical systems, RLC circuit and Newton’s Law	190minutes
4.	State variable diagram State transformation	Review of ordinary differential equations (ODEs) and their solutions	190minutes
5.	Zero-input system response State transition matrix	Review of matrix operation and Laplace transform	190minutes
6.	Response of linear systems with inputs	Review of matrix operation and Laplace transform together with state transition matrix	190minutes
7.	Stability of systems	Review of matrix eigenvalues and Routh condition in classic control	190minutes
8.	Review and middle exam	Review of No. 1 through No. 7, focusing on state space representation and state transition matrix	190minutes
9.	State feedback	Review stability of control systems	190minutes
10.	Pole assignment	Review stability of control systems and characteristic polynomial of a matrix	190minutes
11.	Controllability and observability	Review definition and computation of matrix rank	190minutes
12.	State feedback, pole assignment and optimal control	Review of stability, controllability of control systems	190minutes
13.	Optimal control	Review state feedback, and preview cost function	190minutes
14.	Review/exercise and final exam	Review all from No.1 through No. 14	190minutes
Total.	-	-	2660minutes

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
Feedback in/outside the class.

Textbooks and reference materials

Mainly handouts (No textbook)

Reference Books:
(1) Sato, Shimomoto, Kumasawa: Modern Control Theory for Beginners (Koudansya, Japanese)
(2) K. Ogata, Modern Control Engineering (Prentice Hall)

Prerequisites

Office hours and How to contact professors for questions