ELL 333, I semester 2022-23
This is the the webpage for ELL 333, I semester 2022-23
Multivariable Control
Instructor
Shaunak Sen
E-mail: shaunak.sen@ee.iitd.ac.in
Lectures: MTh 8:00-9:20am
Room: LH 316
Teaching Assistants
Sidhanta Mohanty
Rudra Prakash
Gunjan Chorasiya
Announcements
25.11.2022: Solutions (draft) to the Major Exam.
14.11.2022: Major Exam scheduled for 2-4pm on Wednesday 23.11.2022 in LH 526.
29.09.2022: Solutions (draft) to the Minor Exam held on 28.09.2022. The document also contains the analysis related to the project discussed in class.
15.09.2022: Some Problems. Kindly also solve Examples and Problems listed in the Readings below.
04.08.2022: Project Guidelines. Due date: Sep 19 (in class) — > Oct 13 (in class).
02.08.2022: Webpage online.
Lectures
+ Introduction
Bicycle, Multivariable, Model, State
Lecture 1
Aug 4, 8
Reading: AM Ch 1, Ch 2, Ch 3, Ch 4; F Ch 1, Ch 2
K. J. Astrom, R. E. Klein, A. Lennartsson, “Bicycle dynamics and control”, IEEE Control Systems Magazine, 25(4), 26-47, 2005.
A. L. Schwab & J. P. Meijaard, “A review on bicycle dynamics and rider control”, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, 51(7), 1059-1090, 2013.
TEDx Talk: A. Schwab, “Why bicycles do not fall”, youtube, accessed 13.10.2020.
+ Dynamics
State Space Model, Matrix Exponential, Diagonalization, Jordan Canonical Form, Stability
Lecture 2
Aug 8, 18, 22
Reading: AM Ch 5, Ch 6; F Ch 3
“Yellow Bicycle” Demos accessed 13.10.2020.
+ Control
Why Control?, Kalman's Example, Controllability, State Solution, Rank Test, Controllable Subspace, Design of Control, State Feedback
Lecture 3
Aug 25, 29, Sep 1, 5, 8
Reading: AM Ch 6, 7.1, 7.2, 7.3, F Ch 5, Ch 6
+ Observe
Why Observe?, Kalman's Example, Observability, Output Solution, Rank Test, Duality (Observable Subspace), Design of Observers (Duality with Control Design)
Lecture 4
Sep 12, 15, 19, 22
Reading: AM Ch 6, 8.1, 8.2, 8.3, F Ch 5, Ch 7
+ Design
Separation Principle, Choice of Observer and Controller Eigenvalues
Lecture 5
Calculation of the response of a 1D system for different controller and observer eigenvalues.
Oct 6, 10
Reading: AM 8.3, F 8.1, 8.2
+ Frequency
Transfer Function, Poles = Eigenvalues, Pole-Zero Cancellation, Gain (Norms, Induced Norms, Quadratic Forms)
Lecture 6
Exploration of a Quadratic Form.
Demonstration of an Induced Norm.
Oct 10, 13, 17
Reading: AM 10-22, 23
+ Discrete Time
Models, Stability, Controllability, Observability
Lecture 7
Illustrations from a Discrete Time System.
Oct 17, 20
Reading: AM 3-14, 3-15
+ Optimize
+ Network
+ Summary
Inverted Pendulum on a Cart.
The aim of this computation is to summarize main concepts of the course, both the basic ones and the advanced ones.
Nov 14
References to AM examples are in the linked file.
Reference Textbooks
(AM) K. J. Astrom and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Second Edition, Princeton University Press, 2008.
(Kindly see FBSwiki)
(F) B. Friedland, Control System Design, An Introduction to State-Space Methods, Dover Books on Electrical Engineering, 2005.
K. Ogata, Modern Control Engineering, Pearson, 5th edition, 2010. (Chapters 9 and 10 may be useful at a basic level relative to Lectures)
G. E. Dullerud and F. Paganini, A Course in Robust Control Theory: A Convex Approach, Springer (Texts in Applied Mathematics), 2000. (Sections 1.1, 1.3, 2.1, 2.2, 2.3, 2.4 may be useful at an advanced level relative to Lectures)
(AnMo) B. D. O. Anderson and J. B. Moore, Optimal Filtering, Prentice-Hall Information and Systems Sciences Series, 1979.
Lecture slides 7 and 8 from Prof. S. Boyd's course page may be useful.
(S) S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994.
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