University of Notre Dame
Aerospace and Mechanical Engineering

AME 437: Control Systems Engineering
Homework 5

B. Goodwine
Spring, 2003		 Issued: February 12, 2003
Due: February 19, 2003

Unless otherwise indicated, the problems are from the course text, John Dorsey, Continuous and Discrete Control Systems, McGraw Hill, 2002.

  1. 5.8.1: 1, 5, 9
  2. 5.8.2: 1
  3. 5.8.3: 1
  4. 5.8.6: 1
  5. The following are the famous Lorenz equations:

    \begin{eqnarray*} \dot x &=& \sigma(y - x) \\ \dot y &=& \rho x - y - xz \\ \dot z &=& -\beta z + xy. \end{eqnarray*}

    Modify the Runge-Kutta program you wrote for homework 3 to numerically solve these equations for
    \begin{eqnarray*} x(0) &=& 0 \\ y(0) &=& 0.05 \\ z(0) &=& 0.05 \\ \sigma &=& 10.0 \\ \beta &=& 8.0/3.0 \\ \rho &=& 28.0. \end{eqnarray*}

    Submit your code as well as a three dimensional plot of $x, y$ and $z$ for $t = 0$ to $50$ seconds.
  6. (Optional -- 5 points extra credit). In 100 words or less, describe who Lorenz was, where he was, what these equations were nominally modeling and why one might describe them as famous.

Last updated: February 12, 2003.
B. Goodwine (goodwine@controls.ame.nd.edu)