Question

3. A system is modeled with the following equations. x = y-5x+d(t) j = 10f(t) – 30x The outputs are x(t) and y(t); the inputs are f(t) and d(t). a) b) c) d) e) 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.

Answer 1

Solution:

If you found this solution useful then please upvote

Thank you

Answer: * . 4- 5x+ d(0 --- ý - Loft) – 30 - Apply Laplace transform to eq 0) { @ 1984-1944-51$x4 + 1$d 1874 Note: + {x} Ť S XLS) iş 44 s yes) Lş dt)4- DCS [ { fcal4 - FC52 SX(S) = y 15 ) - 5X15) + DCS) - (4) {$44: 1$rofily - 2$ 30x syls): 107(5.) - 30X(S) yes) - 30X(S) +10 FCS) -- lii) S

substitute (il inlig - 30X45 ) +10 FCS) 5X(S) + DOS) SX(S) : S s’x15) -30X1S)+10F(S)- 55X65) + S DCS) 10 FCS) + SDCS) X151 15'+55 +30) S a) DCS) 5455+30 (50x 10 FCs) + s?+55 +30 - 30 x5 + is 10 FES) yis) Given that Xcs) should at the Left most position, FC82 Q! the lebt most positio Yasy Jo 10 S -30 - Location of YCS) FLS) S (5) (5) X 10 (51X $ 455+30 F(5) TUS s 59455+30 D(S)

are Note: While drawing the block draqram { outpur of the make sure the inputs system known. ". since from eq @ X(S) connected with of coefficien values Fos) & pes) with the FIS) & Des) by the connect Multipleyring the co-ebbierenu clo FCS& DC5) the 2 yes) connected with Xis) & Fcsi make connection appropriately IS

O To find the transfer function XLs) theo Its) DCS=0 yes): 0 from ea a o X(S) 10 FIS) + 555 +30 XCS) FLS) 10 5755730

TO bend XCS) FC89=0 Y(S) = 0 DCS) from cg @ XCS) S ot D(S) s2+55+30 XCS) S S455730 D(S) e The Characteristic equation can be obtained from the denominator of xes.com) FOS? X.CS) pes) characterisbee equation Qis); s458 +300