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Unformatted text preview: ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F09 Homework 2 Due Friday, October 9, 2009 Explain all answers! Problem 1 For the transfer functions below, give a graphical explanation for your answers to the following questions: i. What is the magnitude and phase for s = 0? ii. What is the magnitude and phase for s = ω where ω → ∞ . iii. What are all of the values of s in the complex plane for which the phase angle is equivalent to 180 degrees. (Note that any number 180 + ‘ · 360, where ‘ is a positive or negative integer, is equivalent to 180 degrees.) a ) 64 ( s- 4) 4 , b ) 50 ( s + 10) 3 , c ) 16 ( s + 4) 2- 25 , d ) 6 s ( s + 6) , e ) 28 ( s + 1)( s + 4)( s + 7) . For question iii for the transfer function in e), you only need to be precise about which part of the real axis gives a phase angle equal to 180 degrees, and then try to estimate other values where the phase is 180 degrees. For this transfer function, will there be any points with positive real part that give phase 180 degrees?real part that give phase 180 degrees?...
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- Spring '10
- 180 degrees, θ