A#21_Solutions - Assignment #21 -— Solutions — p.1...

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Unformatted text preview: Assignment #21 -— Solutions — p.1 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 04/17/09 1(30). Use the Routh array to determine the number of roots in the right half of the s-plane, if any. Use the roots command in Matlab to check your answers. (a) s4+s3+252+53+8 3% 1 1 5 W .i \ 53» ; 5 ‘ IL 9m? W my a A x a 37’ 26' 8 j 5‘ " {.53 I 32-} New VWHCJA o 0 $5 » 352.311 0* 5 \ C> ’ (b) s5+s4+2s3+s+5 r 543546. 69% pmsgm: :7 722+? war/{4‘3 55 i 2; I 37* } o S SS “2:; ,flkizv :7. PHP Vet/“ti g 2 5 r 53,.0198331'58 ""“7 Ji -5 Wkwlgi/mo‘é‘slj ; 4,2, g” 5 (c) s5+2s4+2s3+4s2+11s+10 5.5 1 1 {1 $41 [1/1 fl/Z 40: 3 y—s :4, r Ore—é“ filo, cjw‘r/LL, 3 23% /// 7Mé‘70 W6 7 e Mfg) m”? / -(o ' 5 S2“ W2: / 6:} 99.525, “*7 //V®¢ 6”®”"/€:.z"”“7(/ {My ,. / fl 51 (yam—5e / 3 e 2 a? m Assignment #21 —- Solutions -— p.2 ECSE—2410 Signals & Systems — Spring 2009 Due Fri 04/17/09 2(10). For the polynomial. 19(5) = s4 + S3 + 352 + 23 + K , use the Routh array to determine the range of K > 0 such that all roots have negative real parts. Use Matlab to verify your bounding (between right and left half planes) value of K i.e., substitute your bounding K into Matlab roots and show that the resulting roots of 19(3) contain a pair of j a) — axis roots and two real roots that have negative real parts. gall 3 K ’ Wm l (432, Mg War Z M6363 4V §Ll+§>+ $522!" “fl/~30 «fine, 3"” mm!" New 42+ .3: fiasco. T7344 gl+wzno C} ((W‘lé:?/ 1 aw g4”) 3++35+Ssa+29+§2~ .. airs/.2; ,2” wag; fi> _ $33» alts: gala «la La .‘”‘“*W”‘W“"“”f/fl\ ngEéls awe Qéifz. 1 x 7 z 7?? Mat CM. €3+$+ (5%): 31+3i—l=(§+® +5; :— ”“ ”“ ” "MT—MM W53? Wfimmw mutt; Assignment #21 - Solutions -- p.3 ECSE—2410 Signals & Systems - Spring 2009 Due Fri 04/17/09 3(30). Sketch the root locus plots. Also find the properties requested. X(S) 1 (a)(10) G(s)= . Find PZE, AA, AL, and the BAP. ss 2 i REE: Z.( + ) bewa AA»:- Lgi-a: ‘iofi; -— fio" AL 7.: €3"‘2.“'(,03 ==—=—i 2a- ieKés): H K 23 20: $329K (b)(5) G(s)= s(s + 2) I ' I S“fla“e‘ 14,54. W? -Z "t éfl‘ao’fi 3S2;bé3+220 m (Mme) n aka/1“ V Assignment #21 — Solutions — p.4 ECSE—2410 Signals & Systems — Spring 2009 Due Fri 04/17/09 4(30) Text. 1 1 .52. Hint. The approximation starts breaking down when the frequency of the signal to be integrated is at the 3dB point of the Bode plot representing the approximate integrator transfer function determined in class (which is Fig P11.500 in problem 11.50). E t“... Mil—«o U/LML matzLél-a M ’22. E39” 51+ @1132, K Lat ..‘. ,. £-§CQ«Z§-E i—«K m .2 “new .7... .. K M JEN mag-‘54:? W+l>$€+i “MT—~— / a y Mate .3)“ .._ ZME... __ __ {ac i / ideal Assignment #21 — Solutions — p.5 ECSE—2410 Signals & Systems - Spring 2009 Due Fri 04/17/09 W 4(30) Continued. ...
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This note was uploaded on 05/03/2009 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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A#21_Solutions - Assignment #21 -— Solutions — p.1...

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