me304_hw8_sol

# me304_hw8_sol - MIDDLE EAST TECHNICAL UNIVERSITY MECHANICAL...

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ME304/Spring 2007/Sections 03+04/HW8 Page 1 / 5 SOLUTIONS TO HOMEWORK 8 for Sections 03 & 04 Prepared by Kartal ÇA Ğ ATAY, Günay ORBAY (B-175) Problem 1 a) The given input can be expressed as a combination of 3 ramp inputs with different slopes and different starting time as given in the following figure: And the expression of the forcing as a function of time will be: ) 10 ( ) 10 ( 4 . 0 ) 5 ( ) 5 ( 8 . 0 ) ( 4 . 0 ) ( + = t h t t h t t h t t r ω where h(t) is unit step function. ω r (t) 5 0 10 Slope of 0.4 time Slope of -0.8 Slope of 0.4 2 MIDDLE EAST TECHNICAL UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT ME 304 CONTROL SYSTEMS SPRING 2007

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ME304/Spring 2007/Sections 03+04/HW8 Page 2 / 5 b) The response expression of the system to a unit ramp input is written in Laplace domain as: 2 2 1 ) ( 1 ) ( ) ( s K B Js K s s G s r + + = = ΩΩ Using Heaviside Partial Fraction Expansion the response can be written as: 2 2 2 1 1 ) ( 1 ) ( ) ( s K B K s
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## This note was uploaded on 05/16/2011 for the course ME 304 taught by Professor Samim during the Spring '11 term at Middle East Technical University.

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me304_hw8_sol - MIDDLE EAST TECHNICAL UNIVERSITY MECHANICAL...

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