Control ENG HW_Part_11

Control ENG HW_Part_11 - Y(s) = G(s).X(s) Y ( s) = 11 A BC...

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Unformatted text preview: Y(s) = G(s).X(s) Y ( s) = 11 A BC = + +2 2 1 + τs s 1 + τs s s A = τ 2 B = − τ C =1 τ2 τ1 Y ( s) = − +2 1 + τs s s Y ( t ) = τe − t / τ − τ + t (a) the difference between the indicated temperature and bath temperature at t = 0.1 min = X(0.1)_ Y(0.1) = 0.1 - (0.2e-0.1/0.2 - 0.2+0.1) since T = 0.2 given = 0.0787 deg C (b) t = 1.0 min X(1) - Y(1) = 1- (0.2e-1/0.2 - 0.2 +1) = 0.1986 (c) Deviation D = -Y(t) +X(t) = -τe-t/T+T =τ (-e-t/T+1) For maximum value dD/dT = τ (-e-t/T+(_-1/T) = 0 -e-t/ = 0 as t tend to infinitive D = τ (-e-t/T+(_-1/T) = τ =0.2 deg C 5.2 A mercury thermometer bulb in ½ in . long by 1/8 in diameter. The glass envelope is very thin. Calculate the time constant in water flowing at 10 ft / sec at a temperature of 100 deg F. In your solution , give a summary which includes (a) Assumptions used. (b) Source of data (c) Results T = mCp/hA = ( ρAL)C p h ( A + πDL) Calculation of NU d = Re d = Pr = hD = CRem (Pr) n K Dvρ µ Cpµ K = (1 / 8 * 2.54 * 10 −2 )(10 * 0.3048)103 = 9677.4 10 −3 = 4.2 KJ / KgK Source data: Recently, Z hukauskas has given c,m ,ξ,n values. For Re = 967704 C = 0.26 & m = 0.6 NuD = hD/K = 0.193 (9677.4)*(6.774X10-3) = 130 .h = 25380 5.3 Given a system with the transfer function Y(s)/X(s) = (T1s+1)/(T2s+1). Find Y(t) if X(t) is a unit step function. If T1/T2 = s. Sktech Y(t) Versus t/T2. Show the numerical values of minimum, maximum and ultimate values that may occur during the transient. Check these using the initial value and final value theorems of chapter 4. Y ( s) = T1s + 1 T2 s + 1 X(s) =unit step function = 1 X(s) = 1/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_11 - Y(s) = G(s).X(s) Y ( s) = 11 A BC...

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