Question

10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26 59495t/35ES b Ple)

Answer 1

10 From tugiven Muhomi caysten Aintions M auTe forM1 forMgg | + B¥ Arly opla trarm Srom 2 5 2 = F) ŠSCx)+ 2-X) = 9 (S S 1s) 2 1 C3 - 2S

2. 7 Subtikut in 2+) -s( FO) - 2S 3 SS 51S +252S Ft +3s+ 5 FS) S F(S) Tramfer fntim Usna state spae det = Ai xutut input 1,2171,A4,S anu tale 3+ cs*4 S + 2) ipzoi,ds FO X5+ i 3 R5 y-6 -4 2 a F O C -2 -44 -6 -5 -3 output equatio tade space for

25t G0) Phay vania ble pyubi Y(3) s5t9 2 5t (s)X $59 25t s75+9 2 1 9v) ニ0 9 -11,-9%1 U 9-7 take egatiom 2 12

Frowgivn datu A o.62S tate ypa ce Comvust into Tramgfer fundtim c ST-A TF C1-5 0. 62 St 4 (1.5 6.625 1 s(st4)+ 2S S O.62S s244t6 Ix2 2X1 3St S 3St5 T.F s24t6

8sT10 RU) +SSPS sN+ss3+sS+ 1 ニス O 2 o O -1S-5-1 -5 ertion 0 8 hu outyut ニ72)

-8 -13 1 ale eadi 11 -tput euation