# Ps1 - EE 428 PROBLEM SET 2 DUE 10 SEP 2007 Reading assignment Ch 1 Ch 2 and Ch 3 sections 3.1 and 3.2 The goals of the first problem set are to 1

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EE 428 PROBLEM SET 2 DUE: 10 SEP 2007 Reading assignment: Ch 1, Ch 2, and Ch 3 sections 3.1 and 3.2. The goals of the Frst problem set are to: 1. Review basic concepts and mathematical tools from EE 350. 2. Obtain an ODE model of a physical system from Frst principles. 3. Convert from one method of representing a dynamic system to another method of representation. ±or example, given an ODE representation, Fnd a corresponding state-space representation. Problem 1: (30 points) A SISO system with input u ( t ) and output y ( t ) has the ODE representation ˙ y + y u + 100 u. 1. (5 points) Determine the transfer function representation of the system. Express your answer in the standard form Y ( s ) U ( s ) = b m s m + b m 1 s m 1 + ··· + b 1 s + b 0 s n + a n 1 s n 1 + + a 1 s + a 0 , and specify the poles and zeros of the transfer function, as well as the DC gain of the system. 2. (5 points) Express the frequency response function in a form suitable for sketching a Bode magnitude and phase plot, that is, Y ( ) U ( ) = K jω/ω 1 +1 jω/ω 2 , and specify the numeric value of the parameters K , ω 1 ,and ω 2 . What is the signiFcance of the parameter

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## This note was uploaded on 07/23/2008 for the course EE 428 taught by Professor Schiano during the Fall '07 term at Pennsylvania State University, University Park.

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Ps1 - EE 428 PROBLEM SET 2 DUE 10 SEP 2007 Reading assignment Ch 1 Ch 2 and Ch 3 sections 3.1 and 3.2 The goals of the first problem set are to 1

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