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HWCE_2_Solution

# HWCE_2_Solution - HW/CE#2 Solution EE 362K Spring 2010 I...

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HW/CE#2 Solution EE 362K Spring 2010 I. Except where noted otherwise, do parts a through g below using MATLAB: Given the following closed loop transfer function: Y(s) = T(s) = 1.335(S2 + 90s + 2000) R(s) S3 + 40s 2 + 389s + 2670 a. Find the poles and zeroes for and identify the dominant poles »num=1.335*[1 902000]; » den=[l 403892670]; » roots(den) ans = -30.0000 -5.0000 + 8.0000i -5.0000 - 8.0000i » roots(num) ans= -50 -40 '", b. Determine, by hand, the values of S and W n for the dominant poles. ( ~ +-30 )(('\$-;-:;- )~f- 3 ~ ) -=: (>r't»( f l- + /.Js;'i- 1(1 ) t.J-It.u·~ diTJfYJl 'n ~ /" It' ~;~ - r t::. i ~ Z- S~~ :; ~z. -I- / (){, i- f' J -= ~ z- + ;;;r~ t.J~ ~ i~~ tJ lot

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c. Determine, by hand, rise time I r , settling time Is , and overshoot M p , based on the approximate relationships for dominant second order poles. -t - I. ~ - -t-~ = -4,~ I' - -;J~- - - '~W." d. Find the step response for the system. Include your plot in your tum-in. Estimate. from the plot. rise time I r settling time t.f • and overshoot M" and compare these values to what you determined in part c. above. » T=tf(num.den) Transfer function: 1.335 s A 2 + 120.1 s + 2670 » step(T) S1e~ Res~onse 1.4 -- System: T Peak Bm~lilude: 1.14 Overshoot (%): 13.9 1.2. .
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HWCE_2_Solution - HW/CE#2 Solution EE 362K Spring 2010 I...

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