project4

# project4 - ECE 220 Signals and Systems I Fall 2007 MATLAB...

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ECE 220 Signals and Systems I Fall 2007 MATLAB Project #4: Analysis of a second order system Report due: Nov 3 In this project, you will analyze a second order system. You will investigate what happens if the roots of the characteristic equation are real and what if they are complex. Further, you will look at the effect of the size of the roots and, in the complex case, the size of their real and imaginary part. You will also study certain properties of the transient response, such as the rise-time and the settling time. 1. System description Recall that in class we described a second order system by the differential equation y(t) + α 1 (dy(t)/dt) + α 2 (d 2 y(t)/dt 2 ) = x(t) (1) We obtained this form from the analysis of a second order circuit. In system analysis, it is more general to write the differential equation as (d 2 y(t)/dt 2 ) + a 1 (dy(t)/dt) + a 0 y(t) = b 0 x(t) (2) The main difference between the two forms is not the order (sequence) of the terms but the fact that while in form (1), the y(t) term has unit coefficient, in form (2) it is the (d 2 y(t)/dt 2 ) term that has unit coefficient. It is easy to convert from one form to the other.

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## This note was uploaded on 02/03/2011 for the course ECE 220 taught by Professor Janos during the Fall '08 term at George Mason.

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project4 - ECE 220 Signals and Systems I Fall 2007 MATLAB...

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