EEL 829, I semester 2012-13
This is the the webpage for EEL 829, I semester 2012-13
Selected Topics in Advanced Control & Systems Theory - 1
Instructor
Shaunak Sen
E-mail: shaunak.sen@ee.iitd.ac.in
Lectures: TuWF 8:00-8:50am
Room: Block VI - 429
[Poster]
Course Description
EEL829 covers topics aimed at providing an introduction to dynamics. It is useful for students who wish to pursue work in control theory and/ or mathematical modeling with differential equations. In addition, this course will be beneficial to studies of electrical & biomolecular circuits, mechanics & physics (especially planetary dynamics) and the biological & chemical sciences.
The course will focus on basics of ordinary differential equations oriented towards applications in control and dynamical systems. Topics include: Equilibrium points & Stability, Oscillators & Limit cycles, Bifurcations, Perturbation & Averaging. Overview of Chaos, Non-normal growth and Control.
Announcements
Course project presentations on Tue, 06.11.2012 and Fri, 09.11.2012 in Control Lab, BlockII-214 from 2-4PM.
Lecture Plan
Linear systems, Classification of equilibria
Existence & uniqueness, Linearization
Stable, unstable & center manifolds, Lyapunov functions
Limit cycles & Oscillations, van der Pol oscillator
Poincare-Bendixson Theorem, Index theory
Bifurcations: Saddle-node, Pitchfork, Transcritical, Hopf
Perturbation & Averaging
Regular perturbation
Averaging theory
Singular perturbations
Overview of Chaos, Non-normal growth and Control
Lectures
| S. No. | Date | Topic | Suggested Reading | Homework |
| 1 | Week 1
(Jul 24, 25, 27) | Linear systems,
Classification of equilibria | Strogatz 5.1-5.2 | HW1
Solutions |
| 2 | Week 2
(Jul 31, Aug 1, 3) | Linearization,
Existence & Uniqueness | Strogatz 6.1-6.3 | HW2
Solutions |
| 3 | Week 3
(Aug 7, 8) | Stable, unstable & center manifolds | Strogatz 6.4 | |
| 4 | Week 4
(Aug 14, 17) | Lyapunov functions,
Limit Cycles & Oscillations,
van der Pol oscillator | Strogatz 7.0-7.1 | HW3
Solutions |
| 5 | Week 5
(Aug 22, 24) | Poincare-Bendixson Theorem | Strogatz 7.3 | HW4
Solutions |
| 6 | Week 6
(Aug 28, 29, 31) | Bifurcations: Saddle-node, Pitchfork,
Transcritical, Hopf | Strogatz 8.0-8.2 | |
| 7 | Week 7
(Sep 3 - MINOR TEST 1
Sep 5, 7) | MINOR TEST 1 Solutions | | |
| 8 | Week 8
(Sep 11, 12, 14) | Regular Perturbations | Strogatz 7.6 (Pg 215-8)
Approximate solutions to van der Pol oscillator (.m file)
Variation of Parameters
Optional: Verhulst 9.1, Khalil 10.1-10.3
Example of resonance in bridges | |
| 9 | Week 9
(Sep 18, 19) | Poincare-Lindstedt Method,
Singular Perturbations | Strogatz Ex 7.6.19,21
Optional: Verhulst 10.1, Khalil 11.1 | HW5
Solutions |
| 10 | Week 10
(Sep 25, 26, 28) | Singular Perturbations,
Averaging | Strogatz Ex 7.6.25
Verhulst 11.1 | HW6
Solutions |
| 11 | Week 11
(Oct 3, 5) | Averaging | Verhulst 11.2-11.3 | |
| 12 | Week 12
(Oct 8 - MINOR TEST 2
Oct 10, 12 | MINOR TEST 2 Solutions | | |
| 13 | Week 13
(Oct 15, 16, 18) | Non-normal/ Transient Growth | | |
| 14 | Week 14
(Mid-Semester Break) | | | |
| 15 | Week 15
(Oct 30, 31, Nov 2) | Chaos
Lorenz and Rossler systems | Strogatz 9.3, 9.5, 12.3 |
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Reference Textbooks
S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978 — 0738204536
H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978 — 0130673893
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer; 2ed Edition, 1996. ISBN: 978 — 354060934
Older Announcements
10.10.2012: MINOR TEST 2 answer books returned. Please note solutions.
05.10.2012: MINOR TEST 2 scheduled for 11:00am-12:00pm on 08.10.2012. Room assignment is II-LT3. Please check Exam Schedule for up-to-date information.
05.10.2012: HW6 solutions posted.
26.09.2012: HW6 issued, due 03.10.2012. HW5 solutions. posted.
18.09.2012: HW5 issued, due 25.09.2012.
12.09.2012: Please note instructions from Associate Dean Academics (Curriculum) regarding the mid-semester feedback. Kindly complete the feedback online on the WBAMS (Wipro) system by 18.09.2012.
05.09.2012: MINOR TEST 1 answer books returned. Please note solutions.
31.08.2012: MINOR TEST 1 scheduled for 11:00am-12:00pm on 03.09.2012. Room assignment is II-LT3. Please check Exam Schedule for up-to-date information.
31.08.2012: HW4 Solutions posted.
28.08.2012: Lecture scheduled for 8:00-8:50am on 29.08.2012 will be held in the Control Lab (Block II - 214).
27.08.2012: HW3 Solutions posted.
24.08.2012: HW4 issued, due 31.08.2012.
17.08.2012: HW3 issued, due 24.08.2012.
15.08.2012: Note update to HW1 Solutions.
05.08.2012: HW1 Solutions posted.
03.08.2012: HW2 issued, due 14.08.2012 (note updated due date).
27.07.2012: HW1 issued, due 03.08.2012.
19.07.2012: Lectures in Block VI, Room 429.
18.07.2012: Webpage online.
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