Question

3. A system is modeled with the following equations. * = y – 5x + d(t) y = 10f (t) – 30x The outputs are x(t) and y(t); the inputs are f(t) and d(t). a) b) c) From the two equations above, draw a complete block diagram for the model with X(s) at the rightmost position and F(s) at the leftmost position. All arrows must be shown clearly. Indicate the location of Y(s) in the block diagram. Using any of the two methods, find the transfer function X/F. Using any of the two methods, find the transfer function X/D. Determine the characteristic function. e)

For a Mechanical Engineering System Dynamics class

Answer 1

Selection Geven data 2- y -5x + d( t) y = (of 1 ) - 30 Now we are apply laplace transform to equation © ¢ @ O Laxf = [ {4} - 5 Lyx} +Lydity z Nole:- Lazb= 'SXCS) ③ L Lý}=2&lof(t) 6-2230x) LK - Sys) SY(S) = 10F (S) - 30x (5) Lo{atly =D(0) Y(S) = - 30x(S)+10F(s) La flt) }=F(S) SXCS) - YCS)-5X(S)+0() S Klow we are substitute O is ☺ SX (S) -308(5) +10F(S) -58 (5)+005) s**(s) = -30X (S) + (OF (S)-55X()75D(S) X(S) is '+587303 = 10F(S) +FD () X(S) = 10 F(S)+ DCS) 5455730 s 5455430 Y CS!= -30 X (S) + f (8) Q: - From the horo equahong above, draw a compleli diagraon for the model with XCS) at the right most position and FCJ) at the lebimost posihon. All arrows must be shown clearly

10 3 is y() F() 30 iti locahanol YOU! 10 Sv+55130 FCS) X() X (s) SV455 +30 pocsi known Important points during drawing the block diagram make sure the isput &cefpect of the System are Considering from equahon @ 865) is connected with Fos) & DCS) with the values of Co-efficient connect the FCS) & DCS) by multiplying the co-ebicient of FCS)&D(S) Ycs) és connected with XCS) & FCS I those make connection approparately C:- using any of the foo methods find the transfer functim wie Now find the transfer tenchon XCS) thens DOS)-O YCS)-0 from equation @ XCS) FCS) to $9455+30 FCS) 10 XCS) FCS) 59455630 di- To find the transfer funchon XCD XCS) DOSIF()=0, YCS)=0

From equation ③ S XCS) = 0+ DCS) 59455430 S XCS) D(S) S455+30 e Determine the characteriushc function the characteristic equahon can be obtained from the denominater of XCS) (ov) XCS) there fore FCS) D(S) Do Charadic equahan QCS) = 54+55+30 =0

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