History; examples; future directions.
Feedback systems
Often we are interested in finding and characterizing the evolution of patterns over time. This course introduces formal tools to design, model, and analyze evolving interconnected systems in which information, data sensing, and decision-making mechanisms strongly couple two or more subsystems. Formal techniques include frequency-domain and time-domain methods.
The alternative to deterministic predictability, when it comes unachievable, comes from feedback…Jeff G. Bohn
Overview
Instructors: Jorge Finke / Juan Manuel Nogales
Level: undergraduate
Schedule
| Date (week starting on…) | Recitation (Mon) | Lecture (Wed.) | Labs (Fri) | |||
|---|---|---|---|---|---|---|
| July 26 (week 1) | Lec 1.1 (intro) | Lec 1.2 (modeling) | ||||
| Aug. 2 (week 2) | Lec 2.1 (equilibria) | Lec 2.2 (stability) | ||||
| Aug. 9 (week 3) | Lec 3.1 (Lyapunov) | Lec 3.2 (Lyapunov proof) - HW1 due | Lab 1 | |||
| Aug. 16 (week 4) | - | Lec 4.1 (Lyapunov functions) - HW2 due | ||||
| Aug. 23 (week 5) | Project | Lec 4.2 (Lasalle) - HW3 due | Lab 2 | |||
| Aug. 30 (week 6) | Project | Lec 5.1 (linearization) - HW4 due | ||||
| Sept. 6 (week 7) | Lec 5.2 (stability LS) | Lec 6.1 (reachability) - HW5 due | Lab 3 | |||
| Sept. 13 (week 8) | Project | Lec 6.2 (feedback controller) | ||||
| Sept. 20 (week 9) | Midterm I | Lec 7.1 (observability) - HW6 due | ||||
| Sept. 27 (week 10) | Project | Lec 7.2 (the observer) - HW7 due | ||||
| Oct. 4 (week 11) | Lec 8.1 (TF func.) | Lec 9.1 (Bode) - HW8 due | Lab 4 | |||
| Oct. 11 (week 12) | Project | Lec 10.1 (Nyquist) - HW9 due | ||||
| Oct. 18 (week 13) | - | Lec 11.1 (PID) | ||||
| Oct. 25 (week 14) | Project | Lec 12.1 (PID) | Lab 5 | |||
| Nov. 1 (week 15) | - | Lec 13.1 (PID) HW10 due | ||||
| Nov. 8 (week 16) | Final review | Q&A |
Assignments
To access the problem sets and lab assignments please use the password provided in class.
Homework sets
HW1 - Introduction to feedback (submit)
HW2 - Modeling dynamical systems (submit)
HW3 - State-space representations, equilibria and stability (submit)
HW4 - Lyapunov analysis (submit)
HW5 - Krasovskii-Lasalle’s Theorem (submit)
HW9 - Transfer function, block algebra, root locus and Hurwitz stability criterion (submit)
HW10 - Nyquist and PID controller (submit)
Lessons
Dynamics and modeling
What a is a dynamic model? What does a model say about a system? Define concepts of state, dynamics, inputs and outputs. Non-linear vs. linear systems; overview modeling techniques.
Stability and performance
Lyapunov stability for time-invariant systems.
Lyapunov stability theory
Lyapunov stability for time-invariant systems.
Lasalle theorem
Krasovskii-Lassale Invariance Principle; Lyapunov functions for linear systems.
Linearization
Compute linearization of a nonlinear system around an equilibrium point; Lyapunov Indirect Method; Examples.
State feedback
Define reachability of a system; test for reachability of linear systems; state feedback for linear systems
Output feedback
Define observability; conditions for linear systems; state estimation; examples.
Transfer functions
Content: Transfer function; Routh-Hurwitz criterion; Canonical form realizations
Frequency domain design
Bode plot; Sketching Bode Plots; Block algebra.
Nyquist plots
Loop transfer function; Nyquist plots; Stability margins.
PID (part 1)
PreviewPID (proportional–integral–derivative controller); basic properties; PID implementation.
PID (part 2)
PID implementation; Empirical tuning methods.
PID (part 3)
Identification of linear time invariant systems
Course review
PreviewValidation of linear time-invariant models using barrier certificates