Control ENG HW_Part_49

# Control ENG HW_Part_49 - = X – Y(a(2 =(1(3(b(3 = G1(2...

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Soln. (a) Balances at each node (1) = GaX (2) = (1) – Y = GaX – Y (3) = Gb(2) = Gb(GaX – Y) (4) = (3) + X = Gb(GaX – Y) + X Y = Gc(4) = Gc (Gb(GaX – Y) + X) = GaGbGcX – GbGcY + GcX GbGc GaGb Gc X Y + + = 1 ) 1 ( (b) Balances at each node (1) = X – (4) (2) = Gb(1) = Gb( X – (4)) (5) = GcX/Ga (3) = Gc(2) = GbGc( X – (4)) (4) = (3) + (5) --------------------------- 5 = GbGc( X – (4)) + GcX/Ga Y = Ga(4) From the fifth equation (4) = GbGcX – GbGc(4) + GcX/Ga ----------- 6 Ga GbGc X Gc GaGbGc ) 1 ( ) ( ) 4 ( + + = From the sixth equation ) 1 ( ) 1 ( GbGc Gc GaGb X Y + + = Q – 12.2 Find the transfer function y(s)/X(s) of the system shown

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Soln: Balance at each node (1)
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Unformatted text preview: = X – Y ---------(a) (2) = (1) + (3) ----------(b) (3) = G1(2) where G1 = 1/(τ 1 s + 1) ----------(c) (4) Y = G2(3) where G2 = 0.5/(τ 1 s/2 + 1) ----------(d) From (d) and (c) Y = (2)G1G2 = G1G2 (X – Y + (3) ) ----------(e) Also from (b) and (c) (3) = G1((1) + (3)) (3)(1 – 1/(τ 1 s + 1)) = 1/(τ 1 s + 1) (3) τ 1 s = 1 (3) = 1/(τ 1 s ) = (X – Y) / (τ 1 s) Substitute this in (e) ( ) Y X s s s Y- + + + = 1 1 1 1 1 ) 1 2 )( 1 ( 5 . τ 1 2 1 1 2 2 1 + + = s s X Y Q – 12.3. For the control system shown determine the transfer function C(s)/R(s)...
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## This note was uploaded on 11/13/2011 for the course COP 4355 taught by Professor Koslov during the Spring '10 term at University of Florida.

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Control ENG HW_Part_49 - = X – Y(a(2 =(1(3(b(3 = G1(2...

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