### University of Notre Dame

Aerospace and Mechanical Engineering

### AME 437: Control Systems Engineering

Homework 3

B. Goodwine
Spring, 2003 |
Issued: January 31, 2003
Due: February 5, 2003 |

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

- 3.8.1: 1,3,5,7
- Assuming a transfer function of the form G(s) = K/((s+p
_{1})(s+p_{2})) and further assuming that p_{1} and p_{2} are such that p_{2}/p_{1} > 3, find values for K, p_{1} and p_{2} such that G(s) that closely matches the data in
- file 1 and
- file 2.

The data in each file are evenly spaced in time from 0 to 10 seconds. In each case, after determining the values, use the step()

command in Matlab to compare your answer with a plot of the data. Submit this comparison on one plot which clearly distinguishes which curve or data points are from the data and which are from your G(s).
- 3.8.8: 5
- For any two of the four differential equations you solved last week in 2.9.5, also verify your answer by plotting your solution and a solution obtained by numerically solving the equation using a fourth order Runge Kutta routine written in C, C++, FORTRAN or the Shakespeare Programming Language.

*Last updated: January 31, 2003.*

B. Goodwine (*goodwine@controls.ame.nd.edu*)