ELL 333, I semester 2019-20
This is the the webpage for ELL 333, I semester 2019-20
Multivariable Control
Instructor
Shaunak Sen
E-mail: shaunak.sen@ee.iitd.ac.in
Lectures: TThF 11:00-11:50am
Room: LH 615
Teaching Assistants
Krishan Kumar Gola
Abhilash Patel
Announcements
26.11.2019: Solutions to Major Test.
15.11.2019: REMINOR TEST.
12.11.2019: Solutions to Minor Test 2.
08.11.2019: MAJOR TEST scheduled from 1-3PM on Tue, 19.11.2019 in LH108. Please check Exam Schedule for up-to-date information.
24.09.2019: MINOR TEST 2 scheduled from 4-5PM on Wed, 25.09.2019 in LH108. Please check Exam Schedule for up-to-date information.
20.09.2019: Solutions to Minor Test 1.
06.09.2019: Following problems from AM may be practised for controller design. 7.3, 7.5, 7.7, 7.9, 7.10, 7.14. Additionally, examples in the Advised Reading of the Table below are also advised to be practised.
22.08.2019: MINOR TEST 1 scheduled from 4-5PM on Sun, 25.08.2019 in LH108. Please check Exam Schedule for up-to-date information.
10.08.2019: Webpage online.
Lectures
| S. No. | Date | Topic | Advised Reading | Lectures |
| 1 | Week 1
(Jul 23, 25, 26) | Course Plan & Objectives, Bicycle
Models, Examples - Pendulum & Bicycle, (Linearization)
Dynamics & Stability, State, Standard Equations, Homogeneous Solution | F 1, AM 1, 2
F 2, AM 3, 4, 6.4
F 3.1, 3.2, AM 5.1, 6.1, 5.3 | Jul 23
Jul 25
Jul 26 |
| 2 | Week 2
(Jul 30, Aug 1, 2) | Matrix Exponential, Diagonalization
Eigenvalue test, Jordan Canonical Form Example, Quiz 1
Kalman Decomposition Example | F 3.3, 3.6, AM 6.2
F 4.4
F 5.1, 5.2 | Jul 30
Aug 1
Aug 2 |
| 3 | Week 3
(Aug 6, 8, 9, 10) | Input can shape steady-state, dynamics
Particular Solution, Quiz 2
Controllability, iff Grammian is non-singular |
F5.3, AM 6.3
AM 7.1 | Aug 6
Aug 8
Aug 9
Aug 10 |
| 4 | Week 4
(Aug 16) | iff rank{[B AB … A^{n-1}B]} = n | F5.4 | Aug 16 |
| 5 | Week 5
(Aug 20, 22) | Eigenvalue Assignment, Companion Form, Quiz 3
Single Input Case | F 6.1, 6.2, 6.4, AM 7.2, 7.3 | Aug 20
Aug 22 |
| 6 | Week 6
(Aug 29, 30) | Controller Design
Multiple Input Example, Quiz 4 | F 6.3 | Aug 29
Aug 30 |
| 7 | Week 7
(Sep 3, 5, 6, 7) | Bicycle Controller, Controllable Subspace
Observability
Output Solution, Ker{C exp(At)}, = Ker{[C; CA;…; CA^{n-1}]}
Observability Grammian, Quiz 5 |
F 5.3, 5.4, AM8.1 | Code, Sep 3
Sep 5
Sep 6
Sep 7 |
| 8 | Week 8
(Sep 12) | iff Grammian is non-singular, iff (A’, C’) controllable | | Sep 12 |
| 9 | Week 9
(Sep 17, 19, 20) | Observer Design
Eigenvalue Assignment, Duality with State Feedback Quiz 6
Example, Quiz 7 | F 7.1, 7.2, 7.3, AM 8.2 | Sep 17
Sep 19
Sep 20 |
| 10 | Week 10
(Sep 24) | Separation Principle | F 8.1, 8.2, AM 8.3 | Sep 24 |
| 11 | Week 11
(Oct 1) | Bicycle Observer, Quiz 8 | | Oct 1, Code |
| 12 | Week 12
(Oct 10, 11) | Optimal Gains, Quiz 9
Kalman Filter |
AM 8.4 | Oct 10
Oct 11 |
| 13 | Week 13
(Oct 15, 17, 18) | Noise, Discrete-time Kalman Filter
Error Covariance Minimization
Positive Definiteness, Quiz 10 |
AM 8.4, 5-22 | Oct 15
Oct 17
Oct 18 |
| 14 | Week 14
(Oct 22, 24, 25) | Conditional Probability, Minimum Mean Square Estimate (MMSE), = Conditional Mean
X given Y when X, Y are jointly Gaussian
MMSE in Static Linear Measurement | AnMo Ch 2 | Oct 22
Oct 24
Oct 25 |
| 15 | Week 15
(Oct 29, 31, Nov 1) | MMSE in Dynamic Linear Discrete-time System
Measurement Update + Time Update = Kalman Filter, An Optimal Observer, Quiz 11
Example: Filter Converges?, Ricatti Equation | AnMo Ch 3, 4 | Oct 29
Oct 31
Nov 1 |
| 16 | Week 16
(Nov 5, 7, 8) | Discrete Maps
Some Problems
Cobwebs = Global Convergence in 1D Maps, Local Stability, Quiz 12 | S Ch 10 | Nov 5
Nov 7
Nov 8 |
| 17 | Week 17
(Nov 13, 14) | Problems: Canonical Forms, Lyapunov Function idea
Problems: Controllable Subspace | | Nov 13
Nov 14
|
Reference Textbooks
(F) B. Friedland, Control System Design, An Introduction to State-Space Methods, Dover Books on Electrical Engineering, 2005.
(AM) K. J. Astrom and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. (Please see FBSwiki)
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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