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.
Overview
Instructor: Jorge Finke
Office hours: Mondays 2:00pm – 4:00pm
Level: undergraduate
TA: Kevin Diaz
Labs: Fridays, 9:00-11:00am
Schedule
Date (week staring…) | Lectures (Mondays) | Recitations (Wednesdays) | Labs (Fridays) |
---|---|---|---|
Jan 20 (week 1) | Lec 1 - Intro to feedback systems | ||
Jan 27 (week 2) | Lec 2 - Dynamics and modeling | ||
Feb 3 (week 3) | Lec 3 - Stability and performance | ||
Feb 10 (week 4) | Lec 4 - Lyapunov stability theory | Quiz 1 | |
Feb 17 (week 5) | Lec 5 - Lasalle theorem | Lab 1 | |
Feb 24 (week 6) | Lec 6 - Linearization | Quiz 2 | |
Mar 2 (week 7) | Lec 7 - State feedback | Lab 2 | |
Mar 9 (week 8) | Lec 8 - Output feedback | Quiz 3 | |
Mar 16 (week 9) | —— | Midterm review | |
Mar 23 (week 10) | —— | spring break | —— |
Mar 30 (week 11) | Lec 9 - Transfer functions | Lab 3 | |
Apr 6 (week 12) | Lec 10 - Frequency domain design | ||
Apr 13 (week 13) | Lec 11 - Nyquist plots | Quiz 4 | Lab 4 |
Apr 20 (week 14) | Lec 12 - PID controlers | ||
Apr 27 (week 15) | Lec 13 - PID controlers | Lab 5 | |
May 4 (week 16) | Lec 14 - System identification | Final course review |
Assignments
To access the problem sets and lab assignments please use the password provided in class.
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