# matlab5_sol - BB 301 Matlab Project 5 EE 301-04-05 jgh This...

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Unformatted text preview: BB 301 Matlab Project 5 EE 301-04,-05 jgh 11/18/02 This project is the ﬁnal team effort in Matlab, and as such, its goal is to provide an opportunity to investigate the relationship between the time and the frequency domain representations for a linear time invariant system. We will study the response to a ﬁrst and second order system. Below is an uncommented m-ﬁle. Enter the m-ﬁle script ﬁle, provide comments, and print the code and ﬁgures. Then, for each system, respond to the following: A. For the ﬁrst order system 1. From the frequency response, estimate the bandwidth. 2. From the impulse response, estimate the time constant. 3. Compare the two estimates and relate to the value of the pole, and discuss the results in terms of the pole-zero plot. B. For the second order system 1.From the frequency response, estimate the resonant frequency, the bandwidth, and the damping factor. 2. From the impulse response, estimate the frequency and the damping factor of the damped sinusoid. 3. Compare the estimates for resonant frequency and damping factor, and relate to the values of the poles in terms of the pole-zero plot. Each team is to provide their Matlab m-ﬁle code with their cements following good practices, annotated ﬁgures, pole-zero plots, and the responses to the questions above. The report should conclude with the individual paragraphs from each of the team members discussing what they have learned from the experience. The report is due Fmdav Dpnpmlﬁpr 6 2n“? LIHUVLLLU Arm w—logspace(l 6, 200); Hw — (10 4). /(j*w+lO 4); Hm = 20*log10(abs(Hw)); Hp = l80/pi)*angle(Hw); subplot(2,l,l) semilogx(w,Hm) title 'magnitude of H(w), first OIG er ) Xlabe;('f:equency(rad/s)') ylabei('magnitude(dB>’) subplot(2,l,2) semilogx(w,Hp) title 'phase of H(w), first order') xlabel('ftequency(raj/s") ylabe;(‘phase{deg)' ) %time domain b=[l] a=[l ;OA4] [r,p,k]=residue(b,a) m=abs p) theta=angle(p) t=O:lOA-6:5* h=lOA4*exp(— figure plot(t,h) title('imp" xlabel(' ylabel( w=logspace(l, Hw = ((10 6)* Hm = 20*logl Hp = (lSO/pi figure subplot(2,l, Lplieldl" 100-3; 1004*t); 6, 200); (100+j*w 0(abs( (Hw) )*angle(H SVV 1) semilogx(w,Hm) title('magnit xlabel(‘frequency'rad/s) ylabel('magni subplot(2,l, ude of H(w) - ~ a!) (D x) ) B)') 2) semilogx(w,Hp) of H{ w), second order') xlabel(' frequencyi rad/s) ') title('f chase ylabel(’ phase %tév b=[l 100] a=[l 4000 10A 'due(b,a) [r,p,k]=re5l m=abs(p) domain ('deg) ) 8] theta=angle(p) t=O:lOA-6:5* h=2000*exp( figure plot(t, h) title(' 100-3; . response h(t), first order') .5. A ,‘\ /§5‘4+40003+1 )./(1008+j*w*4OOO-w.*w); —2000*t).*cos(9798*t-l.7722); econd order') ’\ A r: U r: ) 3 Student License —— for use in conjunction with courses offered at a A? degree—granting institution. Professional and commercial use prohibited. To get started, type one of these: helpwin, helpdesk, or demo. For product information, visit . EDU» matlab5 b = l a = 1 10000 r : l p = —10000 k = m = 10000 theta = 3:1416 b = l 100 a = l 4000 100000000 r = 0.5000 + 0.0970i 0.5000 — 0.0970i l.Oe+003 * -2.0000 + 9.7980i —2.0000 - 9.7980i k: m: 10000 10000 theta = 1.7722 —1.7722 EDU» I ()3 magnitude(dB) % phase(deg) “9%: My} ; 553*“ A» , in 1b.; 0 0‘0 c'p o 1o1 102 103 1o4 4. 1o5 10 frequency(rad/s) . a) 34% = ‘0 . moi/5 phase of H(w), first order _1OOL1—I_L._I_J|_L_I'I L L_llJ_|L_IJ I ll 10 1o2 103 1o4 105 1o6 frequency(rad/s) Student Version of MA TLAB impluse response h(t), first order 10000 9000 8000 7000 6000 4000 33:10:! 3000 2000 1000 0 ' . . 0 0.5 1 1.5 2 2.5 3 3.5 4 45 5 4 3M H CS3 : S + we => 901g 05. - so 6% , 13 ~——- 0‘ \ - s a ‘ afoé \ é f .../ l” ' ‘ 1 1 ~ 1:.) PSCXQ) 7‘ I}. \V\ K?“ *dfg ) W {YMCA \, S M i h V‘aY-SQ V‘Z,1£}T§-Qv\\ 5L 1‘? TM. \chx “=1 , 11a \ov‘gar +10. demﬂix Md HQ Syn-Akr- “EL; *HM Cahs'ngJé‘ , Student Version of MA TLAB sh} - , 'F- r“ N _ ‘ A“ M} Mr» W” PUZ - —- was; 4 q .299; ~ C“ ﬂ. A A 040% 9/3 ‘ 1 w 1" :z 504 “sf/5 V‘QEGV‘O’V‘CQ 7Q ‘3 Coo, ’ G- + A it ) 3%”ch MAM-9‘1 T Hmoﬂas : 4am ‘ , i ”—- 1 ' 1 4 (Ag 2‘) I '20” V .. HWW’) ”Sm “Q“ __. ”,4. m 2 QGQMWM was A , :3 W9. ’ 0 4 z .. \ZoaOLVOd/T) X i g- :3ng g wcwo‘rq: ’0' +000“ : r~-;<2f_(§:~333___.__ :3 Rb»: : ww L912 1‘ W”). 3:33;) 1 4:13;? Lmég) HQ)- 51+40903+ 30% 9;,(9 magnitude(dB) 10 10 10 10 _ 4 10 10 frequency(rad/s) “’9 ‘ ’0 phase of H(w), second order ﬂ Q phase(deg) 1o1 102 1o3 10“ 1o5 106 frequency(rad/s) ‘ L430 \ a £533 Shh» wa‘fmwcgoﬁr (ckfséemaj Q : “ME ~— 2 ”g -» "9;?va _ if?“ i ‘ f i . W .. m» 6» mm:- ~: *Wr‘r : "r w w M , an 5% ~ i?» :2 ~=~ mg "" m 3%.»: 3*" ‘* s g ‘ ”3’ Student Version of MA TLAB \ 3443 ’ 1000 500 -500 {Jobs 08* Hm = ~20mt 3017019, 1500 . - 1" m «335...... "MW?" 1:." 9 1 g 4 5:5 W'- P‘Mﬁ “ ”W“ Maven” 3’” k ’ ,morft «1546074) kw) = 20006. CMPVMQ’ I 6‘11. Una/Ex 1:, 1‘ 0 “ﬁrms _ ow, O‘K'hi—‘fﬂ @433; . k e - ~ - e .. 5:.) = Li's-a ~— 8 = 5755 ”‘95. i .. , g...“ (Lgm3/(a‘ggé a gigﬁgj jam) .7 [L557 3 ma\$hs+wj§cﬁgi£ﬂ~t {10¢ _6‘~_9:- «355.. W. 4.0 s-ﬁo’ua' W-o.\ga4 Awfég‘w‘“ impluse response h(t), second order \/ :5 0.5 5 1 1.5 2 2.5 3 3.5 4 4.5 5 f -. time (3) x10'3 \ \ Apr ‘mgk a ( m} 08* w 55W”? Seer-Law é (4 i) \ 5-. WOWW/s‘), w z 104 (We) 2 We , ‘5 = 0‘20 .SJ’Y‘Q Ci ELM CLT‘ ( w = 155'» (“Pm/s}, Lad : 51954 “:5ng 2 {.50 *S: 049 *W ) Student Version of MA TLAB ...
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