Question

1 3. i) Write state variable equations to realize 915): 0545 +5+1 5+45 735+4 liiWaite state variable equation for : во, гряг? Г = interna - Lot @ Seemmer Sunner C

Answer 1

I (387s+s+l). us) o Gos)= 3s?'ist! 53425'+35+4 Balle let con= ys) ss18! U 2+25+35+4 Tetus splitt the giren transfer function into tiso parts jie xls) = 633?ts'f'sti). I - 3+25+35+4) bat yang - 38++$75+) let yes) - 3357st) and to 23 +28+35+4 =) yes)=(35+5+5+1)x15) 1653425+ 3s +4)*15)= uc) -> 445)= 38x<5) tšX+5xs)txes) = $xcs) +25x65)+35x45) - Apply inverse laplace p. tuxus) sued . Transforms I Apply inverse laplace I'[Yes"]='31'[53x59)+7'[xxes] Transformans +t sx:55)+(xa) (c[x)+ ( xs)Hz (xo) -) y(t)= 3 ü ct) ä'ct)+ict)+264 +46'[xcs)) = Illucs)) - 0 =) ¿CĐ)+22"(t)+3 x (t) letus Choose the state variables as tuxlt) cult let 2C4)= X,16) 9 rict) = CH= xsct) 6 - ü (t) = x2Ct) = x2(t) J place @ in ② - zz(t)+22364)+382 (4) +421147-ult) a iz(t)= -4014) -3126) -273(+) tult) to - ☺

in AB,C place = y(t) = 3¢¢¢4)+ x34)+226) +2164) - place ® in above equation » yct)= 36-422,64) -3X24) -2X364)+uct))+%3Ct)+2264) - tailt) y(t)= -1271(k) –9x2ct) – 673(t)+3464) +23(+422[t)+8464) » Y.Ct) = -11464) -82,64) - 513C4) +3uct) - © State variable Cuationale -". The state Cuations are for reby aj Ct)= x2(t) x264) = x316) zg(t) = -42144)-8X244) -22344)+ auct) y a output equation and yet)= -112, (t)- 822t)-523(t)+3ult state space form is průlt) ? co i ofr2ct) con ritt) o o L sizct)] L-4 -3 22 luct) a2ct) I fruct) / +(3] ult) act)= -1 - 8 -/ a2ct) I L x3(t) ]

from Summing point 6, iz = 272+2,+ura froms Summing point , ☺ L = 3x,+22 — .. and output equation y=x, - state variable equations are xi = 32, +32 ni =%0,+2x2+4 and output equation y=x (31-1 : 1) 12*2004 y = (1 094) +Cobu