Question

need to solve number 20

- HI-POLYMER ERASER Pentue 2 Name: 20. An LTIC system is given by the ABCD matrices A = (1 -] B = {. q} c = {11} D = bb a The input and initial conditions are x(t) = {41}} q(0) = {1} a) Find the ZIR for the system. b) Find the ZSR for the system. 21. Draw the amplitude Bode plot for the transfer function 22. Draw the amplitude Bode plot for the transfer function H(s) =$+10 5+1 H() = (s + 10) (s + 1)(s + 100)

Answer 1

do) Given ABCD matrices of liic is ALLE: Ber:] cotin? and se [..] and input and initial conditions are +1+1=2 {main} qto)-( :] X = AX + BU The solation to state equation is in at xCe) = T C CL-Aj' ]260) + ' [ 81-'s.com] m " ZIR ZSR -17 The Beratit 53-0 = [5:1-6-] 23:1-E--] *[**] Sj * S+1 Lt -1 St (51-A) - Adj IsJ-A] I SI-AI Tsui') -1 S+ ((sti) There is contain St. با به ریه راهی

ten260] t. 49- ez? som z ' [ 449 40) St1 00) 910) - (St . 141 <+1 SAI ST ) 271 t (+1)+ (+) 1 -1 + (S+1) (5+1)+1 J 2x2 S+2 Sa+2S + 2 rist1) + 1 ST1+1 (6) ~ (8+1+1 { 46 2001 - pieton) + (6+vi) 7 i n-3 (caste) (cost & sint ) (cost - Sint)

-) zelo ZSR i [ 4c9) B Rus)] elp X (5)=2&act)} = iş ult)} = 5 L &LER 5+1) + s+ it 069) BX39]- i $+1+1 * tus 7 t"}] S+ Sti1 G+ 1 (6+27 - - F 6+2 + 2 SOC+1)*) Gogo) + -1 S16+141) 5+1 (+ ) Given to +507)

e 25t 's (+131) 3² +5-) slikti?+1) 1 i ett test + cs 3+25+2 st25+2 ونهاي 22 AS + LAS + 2A + BS + cs? Ac) ser (248) St LA 4+0=0, 2A+ B 2, 2A=1 - A=/ CE-12 B- 1 lly DU FSC + 2D +Es+ 2D z2S + S- D+F=1,2D+E=1,2D = -1 F = 312 ,E=2, 25 (5+) 2 (5+1)+ Ľ test the per te drive ei test stinet, 2017 ( Seth 5+1) + (sajt 2S Sti+ siĪ L ult) + e sinta-zé ( cost-Siny J ult) + dē*sint + et (cost-Sint? a

= [ ule) + é* ( cost +3sintuloy 7 loucester (grast + sint) uces F +11+ ē clost+isint) ult) 7 į (-stēt (scost +siðt) uley 25Raseda H(s) = · Stros ( +) Shake where Kalo 5+1 (5+1) amplitude Bode or magnitude i Bode plot de rology = no logro = 20 dB stalling point | Hos) les A code t - Rodbida Bide odsto -14.06.20€ O - - weo ( 1957 4 (4(s)] 1002 alw210 TOT OD = -148 solog (HCS) ! 1*

3) Given to = (sting? S+) S+100) = , *=!. 190 CS+) 2 19 (t) Clot) Stašting point , зоворк в овоо. = о в is suteren (MCB) o ws/0 Frant. que = 20809 [rectantes - Do song (Towa).- 20 800 for more [ 20 10g (ve).- 20 Jog Jon -20 10g (570.01) - 3 le 20.04dB - D043 dB 2 -17.08dB [24cs) | at ww- 100 = 2000g tit 2002 - 20log rito? -ro 100({ i+ 100%) =rolog Sioi - zalog 17100²-rologie = 20-04 dB -40 dB-3 dB = -22- 3 dB (ves) at wal = -20.40g sit too lolog J2-2010 Vitae = 0.04.dB - 3 dB - ON OD) - 296 dB

Bodeplot يا رب. 10 مد Odl f= 464و - ہج ۔۔ -37-04dB - - لا - - - - + ملا۔ : ومه .