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

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 theoryQuiz 1
Feb 17 (week 5)Lec 5 - Lasalle theoremLab 1
Feb 24 (week 6)Lec 6 - LinearizationQuiz 2
Mar 2 (week 7)Lec 7 - State feedbackLab 2
Mar 9 (week 8)Lec 8 - Output feedbackQuiz 3
Mar 16 (week 9)——Midterm review
Mar 23 (week 10)——spring break——
Mar 30 (week 11)Lec 9 - Transfer functionsLab 3
Apr 6 (week 12)Lec 10 - Frequency domain design
Apr 13 (week 13)Lec 11 - Nyquist plotsQuiz 4Lab 4
Apr 20 (week 14)Lec 12 - PID controlers
Apr 27 (week 15)Lec 13 - PID controlersLab 5
May 4 (week 16)Lec 14 - System identificationFinal 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.

Assignments

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

 

Homework sets

HW1 – due Feb 5th (submit)

HW2 – due Feb 5th (submit)

HW3 – due Feb 12th (submit)

HW4 – due Feb 19th (submit)

HW5 – due Feb 26th (submit)

HW6 – due March 4th (submit)

HW7 – due March 11th (submit)

HW8 – due March 18th (submit)

HW9 – due March 25th (submit)

HW10 – due April 1st (submit)

Lab assignments

Lab1 – TBD

Lab2 – TBD

Lab3 – TBD

Lab4 – TBD

Lab5 – TBD

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

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 

 

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.

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

PID (part 1)

Preview

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

Course review

Preview

Validation of linear time-invariant models using barrier certificates