1. Find a system of at least six coupled ordinary differential equations from any of the following references:
• Textbook other than the course text
• Technical paper
2. Submit for approval a one page word document with the equations and a description of the reference and one output (call it y(t)) that exemplifies the system performance.
3. Perform several simulations for enough system parameters to identify one key parameter (call it KP) that gives a significant difference in the output.
4. Calculate the maximum response of y(t) for five values of this key parameter over a suitable range. Apply linear regression to the results of max(y) vs. KP. Provide a plot of the five data points and the linear estimate. Repeat for nonlinear regression.
5. Set up an optimization objective for the design variable x=KP using the integral of the absolute value of y(t) from 0 to some suitable time T. Thus .
6. Apply an optimization method to determine the x value that minimizes F(x).
7. Submit a professional word report providing all equations, Matlab programs & commands, plots, a descriptions of the problem, a descriptions of the approach, and a description of the results.