Question

A system is modeled with the following equations. x = y - 5x + d(t) y = 10f () - 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

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

S'x15) : -30X75) +10FCS) - 5SXCS) + S Des? substitute Coil in the - 30X() +10 705) 5 x(s) + DOS) SX05) S 10 FCS) + SDCS) xis1s+55 +30 ] @ 10 5 t (sat DCS) 8455+30 X(S) : s+55 +30 6 yos) -39 xos 1+ FCS) Given that x(s) should at the left most position, F(S) Q! the lebt most positio 1 → Y65) UL al 10 S J. Location of YCS) -30 S FLS) (5) X(S) Q1 (57% I(S) $+55+30 IS S $455+30 D(S) then (57% (9) to find the transfer function 015)-0 YCS): 0 from eq FOS) + 0 X(5) 8455 +30 a 10 XOSI FIS) 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