Course Syllabus: LMI in Control Engineering
Division: Master and PhD Degrees of Control Engineering
Course Number: 110140385
Course Title: LMI in Control Engineering
Academic Semester: Fall
Academic Year: 2022-2023
Semester Start Date: 18 September 2022
Semester End Date: 4 January 2023
Class Schedule: Saturdays (16-18) and Sundays (9-11)
Instructor Name: Dr. Hadi Azmi
Email: h_azmi@sut.ac.ir
Course Information
Comprehensive Course Description
The important role that linear matrix inequalities (LMI) have attained in the last years makes it compulsory to include them in the education of a control engineer. As the development of efficient semidefinite programming algorithms date from the early nineties, there is a lack of teaching experience in this field (at least when it is compared with other well established aspects of control theory). This course proposes a simple way to introduce linear matrix inequalities in a control systems. The main objective of the course is to show that in the formulation of (robust) control problems as linear matrix inequalities a very reduced number of elementary technical results are required. It is illustrated how to introduce, in a progressive way, these technical results along with motivating examples. All of this is done in such a way that it facilitates the assimilation of this important subject.
Goals and Objectives At the end of this course, students should:
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Contains four well-structured parts: Preliminaries, Control Systems Analysis, Control Systems Design, and Applications, as well as an introduction chapter and two appendices
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Summarizes most of the technical lemmas used in the book in one preliminary chapter, and classifies them systematically into different groups
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Includes many examples, exercises, and practical application backgrounds
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Summarizes most of the important results in the last section of each chapter, in a clear table format
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Contains an application part composed of two chapters that respectively deal with missile and satellite attitude control using LMI techniques
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Provides a brief and clear introduction to the use of the LMI Lab in the MATLAB® Robust Control Toolbox
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Supplies detailed proofs for all main results, with lengthy ones clearly divided into different subsections or steps—using elementary mathematics whenever possible
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Uses a pole assignment Benchmark problem, in support of the numerical reliability of LMI techniques, where numerical unreliability could result in a solution to a problem that is far from the true one
References:
* Linear Matrix Inequalities in System and Control Theory, Stephen Boyd, Laurent El Ghaoui, Eric Feron, and Venkataramanan Balakrishnan
* Linear Matrix Inequalities in Control, Carsten Scherer, SiepWeiland
* LMI Methods in Optimal and Robust Control, Matthew M. Peet
Method of evaluation:
(10 / 25) - Final exam
(6 / 25) - Midterm exam (4 December 2022 - 13 Azar 1401 - Monaday 9 - 11)
(4 / 25) - Homework /Assignments
(5 / 25) - Matlab Project