Studies basic continuous control theory as well as representation of functions in the complex frequency domain. Covers generalized functions, unit impulse response, and convolution; and Laplace transform, system (or transfer) function, and the pole diagram. Includes examples from mechanical and electrical engineering.

Haynes Miller hrm@math.mit.edu
Jerry Orloff jorloff@mit.edu

Dates: Tuesday, January 19 -- Friday, January 29, 2016
Classes: Daily, 1:00 -- 3:00, 4-261
Syllabus and calendar
Information and policies
Exam: 1:00, Friday, Jan 29, 2016, 4-261.

Office Hours
Haynes Miller: Thursday Jan. 21 4:30-6 in 2-478; Monday Jan. 25 3-4:30 in 4-261; Thursday Jan. 28 3-4:30 in 4-261.
Jerry Orloff: Thursday Jan 21 3-4:30 in 4-261; Wednesday Jan. 27 3-4:30 in 4-261.

Class stellar page

Class 1: review of LTI systems: constant coefficient ODEs, stability, gain.
Class 2:
(i) frequency response, transfer functions, block diagrams.
(ii) pole diagrams (read sections 1-7)
Classes 3,4: Laplace transform. (read sections 1-14)
Class 5: Step and delta functions.
Class 6: Laplace transform: t-translation rule.
Class 7: Convolution.

Note on poles and zeros from 2.14

Laplace table
PSet 1 • solutions
PSet 2 • solutions

Complex numbers and exponentials
Stability: including the Routh-Hurwitz criteria
Partial fractions decompositions (includes the coverup method)

Answer to last board question from Friday 1/22
Notes on PID controllers

The MIT Mathlets are a set of small applets that dynamically illustrate various mathematical concepts. They can all be found at mathlets.org/mathlets

Here are direct links to some of the applets --MIT mathlets and others-- referenced in 18.031.
Amplitude Phase Second Order I
Amplitude Phase Second Order II
Bode and Nyquist Plots
Amplitude Response: Pole Diagram
Series RLC Circuit
LRC Filters

Here is a description of the Course Mascot, pictured above.
And here is a mathematical account of this kind of feedback mechanism.