Course description
This is the IAP 2017 website for course 18.031. This course was previously taught by H. Miller and J. Orloff and is heavily based on their materials, lecture notes etc.
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.
Goals
The course will cover linear time invariant systems (LTI). By the end we will have learned about frequency response, impulses and impulse response, the transfer (or system) function, the Laplace transform and systems with feedback. By the end you should be able to do the following things.
- Define the notions of stability, gain, phase lag, frequency response and system function for LTI systems.
- Analyze LTI systems in the frequency domain:
- Compute the transfer function for an 18.03 style constant coefficient linear differential equation.
- Compute the transfer function for a general LTI system from a block; including for diagrams with feedback loops.
- Use the transfer function to determine stability of the system.
- Use the transfer function to find the periodic response to sinusoidal input to the system.
- Interpret the pole diagram of a system in terms of stablity, gain and resonance/
- Define the Laplace transform of a function and compute it for our standard set of functions.
- Use the inverse Laplace transform to compute the unit impulse response of a system modeled by a differential equation.
- Use block diagrams to describe an LTI system.
- Compute the transfer function from an LTI system.
Lecture notes & reading (by H. Miller & J. Orloff)
- 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.
Other material
- Note on poles and zeros from 2.14
- Complex numbers and exponentials
- Stability: including the Routh-Hurwitz criteria
- Partial fractions decompositions (includes the coverup method)
Slides
Problem sets
There will be two problem sets, which will be posted on Stellar
