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: Mondays and Fridays 11:00am – 12:00pm

Level: undergraduate

TA: Luis Felipe Guevara Gómez

Labs: Mondays, 2:00-4:00pm



Week Lectures Recitations Labs
Jan 22 Lec 1 - Intro to feedback systems
Jan 29 Lec 2 - Dynamics and modeling
Feb 5 Lec 3 - Stability and performance
Feb 12 Lec 4 - Lyapunov stability theory Quiz 1
Feb 19 Lec 5 - Lasalle theorem Lab 1
Feb 26 Lec 6 - Linearization Quiz 2
Mar 5 Lec 7 - State feedback Lab 2
Mar 12 Lec 8 - Output feedback Quiz 3
Mar 19 —— Midterm review
Mar 26 —— spring break ——
Apr 2 Lec 9 - Transfer functions Lab 3
Apr 9 Lec 10 - Frequency domain design
Apr 16 Lec 11 - Nyquist plots Quiz 4 Lab 4
Apr 24 Lec 12 - PID controlers
Apr 30 Lec 13 - PID controlers Quiz 5 Lab 5
May 7 Lec 14 - System identification
May 14 Lec 15 - Model validation Final course 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. 

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Homework sets

HW1 – due February 19th (submit)

HW2 – due February 26th (submit)

HW3 – due March 5th (submit)

HW4 – due March 12th (submit)

HW5 – due March 9th (submit)

HW6 – due March 26th (submit)

HW7 – due April 2th (submit)

HW8 – due April 9th (submit)

HW9 – due April 16th (submit)

HW10 – due April 23th (submit)

Lab assignments

Lab1 – due March 5th

Lab2 – due March 19th

Lab3 – due April 16th

Lab4 – due April  3oth

Lab5 – due May 14th

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


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Notebooks (how to..)

Create state space representations and phase diagrams

Simulate an inverted pendulum

Find Lyapunov functions for linear modes

Linearize models

Test reachability and observability

Create transfer function representations and root locus diagrams

Create Bode and Nyquist diagrams

Design PID controllers [/column] 


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.

Lasalle theorem

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


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


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


PID implementation; Empirical tuning methods.