Feedback systems

Often we are interested in finding and characterizing pattern 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: Tu 11:00am – 1:00pm

Level: undergraduate

TA: Danny Cartagena



Week Lectures Recitations Labs
Jan 23 Lec 1 - Intro to feedback systems
Jan 30 Lec 2 - Dynamics and modeling Lec 3 - Stability and performance / HW 1
Feb 6 Lec 4 - Lyapunov stability theory Quiz 1 / HW 2
Feb 13 Lec 5 - Lasalle theorem HW 3 / Project
Feb 20 Lec 6 - Linearization HW 4 Lab 1
Feb 27 Lec 7 - State feedback HW 5
Mar 6 Lec 8 - Output feedback HW 6
Mar 13 Review Quiz 2 / HW 7 Lab 2
Mar 20 Midterm / HW 8
Mar 27 spring break
Apr 3 Lec 9 - Transfer functions Project
Apr 10 Lec 10 - Frequency domain design HW 9 Lab 3
Apr 17 Lec 11 - Nyquist plots Quiz 3
Apr 24 Lec 12 - PID controlers Lab 4
May 1 Lec 13 - PID controlers Quiz 4
May 8 Lec 14 - Model validation HW 10 Lab 5
May 15 Project presentations 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 Feb 1st (submit)

HW2 – due Feb 8th (submit)

HW3 – due Feb 15th (submit)

HW4 – due Feb 22nd (submit)

HW5 – due March 1st (submit)

HW6 – due March 22nd (submit)

HW7 – due March 29th (submit)

HW8 – due April 7th (submit)

HW9 – due April 19th (submit)

HW10 – due May 17th (submit)



Data generator

Data generator version 2

City boundaries

Street hierarchy

Road network

Neighbors network

Heat maps

Lab assignments

Lab1 – due March 3rd

Lab2 – due September 4th

Lab3 – due September 18th

Lab4 – due October 30th

Lab5 – due November 18th

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.