hw4sol - ME 475 PROBLEM 1: Given: R(s) + Homework #4...

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ME 475 Homework #4 Solution Spring 2011 PROBLEM 1 : Given : where Find : (a) Use Routh-Hurwitz to determine how many roots of the characteristic equation are in the left half plane, in the right half plane, and on the imaginary axis. Explain your answer. (b) Use MATLAB to find the closed loop root locations and confirm your results from part (a). Solution : (a) Form CLTF: Char. eqn.: Form R-H Table: s 5 1 7 8 s 4 4 4 0 s 3 b 1 b 2 s 2 c 1 c 2 s 1 s 0 where , , This is a row of zeros. G(s) R(s) C(s) +
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2 form auxiliary polynomial from row above: form s 2 row from coefficients of derivative of auxiliary polynomial: 24s 2 8 RH Table: s 5 1 7 8 s 4 4 4 0 s 3 8 8 ……. ……………. ..……………………… s 2 24 8 s 1 0 s 0 There are 3 roots symmetric about the origin (since auxiliary polynomial is third order). There are no sign changes in 1 st column before row of zeros 2 remaining roots are in LHP. There is one sign change in 1
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hw4sol - ME 475 PROBLEM 1: Given: R(s) + Homework #4...

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