Feedback systems

Often we are interested in finding and characterizing luginattern which appear over time. This lecture introduces formal tools to design, model, and analyze evolving socio-technological systems in which information, data sensing, and decision-making mechanisms strongly couple two or more systems. Formal techniques include frequency-domain and time-domain methods.

The alternative to deterministic predictability,  when it comes unachievable,  comes from feedback…Jeff G. Bohn


Instructor: Jorge Finke

Office hours: Fridays 11:00am – 1:00pm

Level: undergraduate

TA: Javier Alejandro Velasco



Week starting on… Lectures (Mondays) Recitations (Wednesdays) Labs (Fridays)
July 24 Lec 1 (intro)
July 31 Lec 2 (modeling)
Aug. 7 - Lec 3 (stability) Lab 1
Aug. 14 Lec 4 (Lyapunov) Quiz 1
Aug. 21 Lec 5 (Lasalle) -
Aug. 28 Lec 6 (linearization) Project Lab 2
Sept. 4 Lec 7 (reachability) Quiz 2
Sept. 11 Lec 8 (observability) Quiz 3
Sept. 18 Lec 9 (transfer functions) Midterm review Lab 3
Sept. 25 Lec 10 (transfer functions) Midterm I
Oct. 2 Lec 11 (Nyquist) First report
Oct. 9 Lec 12 (PID) Quiz 4 Lab 4
Oct. 16 - Lec 13 (PID)
Oct. 23 Lec 14 Project
Oct. 30 Last class - Lab 5
Nov. 6 Final review -


 If you taking this course for credit, please fill out this form. After registering,  login and click on “enroll for this course.” You should  now be able to submit homework solutions online. Quizzes will be based on homework problems.



To access the problem sets and lab assignments please use the password provided in class. 


Homework sets

HW1 – due August 18th (submit)

HW2 – due August 25th (submit)

HW3 – due September 1st (submit)

HW4 – due September 8th (submit)

HW5 – due September 15th (submit)

HW6 – due September 22nd (submit)

HW7 – due September 29th (submit)

HW8 – due October 6th (submit)

HW9 – due October 13th (submit)

HW10 – due October 27th (submit)



Data generator

Data generator version 2

City boundaries

Street hierarchy

Road network

Neighbors network

Heat maps

Lab assignments

Lab1 – due September 1st

Lab2 – due September 22nd

Lab3 – due October 13th

Lab4 – due November  3rd

Lab5 – due November 17th

Past midterm and final exams

midterm 2013-2

midterm 2013-2 solution

midterm 2014-1

final 2013-2

final 2014-1

Midterm solutions

midterm solutions 2014-2

final exam solutions 2014-2

final solutions 2015-2



List of lectures

2. 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.

5. Lasalle theorem

Krasovskii-Lassale Invariance Principle; Lyapunov functions for linear systems.

6. Linearization

Compute linearization of a nonlinear system around an equilibrium point; Lyapunov Indirect Method; Examples.

7. State feedback

Define reachability of a system; test for reachability of linear systems; state feedback for linear systems

8. Output feedback

Define observability; conditions for linear systems; state estimation; examples.

12. PID

PID (proportional–integral–derivative controller); basic properties; PID implementation.

13. PID

PID implementation; Empirical tuning methods.