che446_10_hw2 - Homework#2 ChE 446 Fall 2010 Problem 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework #2 ChE 446 Fall 2010 Problem 1. Consider the following set of differential equations, dy 1 dt = - 2 y 1 - y 2 + u ( t - 2) dy 2 dt = 3 y 1 + y 2 - u ( t - 2) where: y 1 (0) = y 2 (0) = 0. 1. Derive the following transfer function: Y 2 ( s ) U ( s ) = G ( s ) = - s + 1 s 2 + s + 1 e - 2 s Find the pole(s) and zero(s) of the transfer function and plot them in the complex plane. 2. Considering the following input change: u ( t ) = e + t . Derive the time domain solution y 2 ( t ) and determine: lim t →∞ y 2 ( t ). Explain why the output converges to a constant even though the input is an exponentially increasing function of time. Problem 2. Consider a process described by a first-order transfer function with a steady- state gain of 1 3 and a time constant of 1 3 . 1. Use partial fractions to derive the open-loop response y 0 ( t ) for the following input change: u 0 ( t ) = 4 te - 2 t . 2. Use the y 0 ( t ) relation to determine lim t →∞ y 0 ( t ). Verify the result by applying the final value theorem. Problem 3. Consider a catalyst delivery system for a polymerization reactor. The catalyst
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 02/06/2011.

Page1 / 2

che446_10_hw2 - Homework#2 ChE 446 Fall 2010 Problem 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online