Control ENG HW_Part_18 - denoted values at steady...

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Cb = heat capacity of glass bulb. .hi = convective co-efficient between the bulb and the surrounding fluid. .ho = convective co-efficient between bulb and surrounding fluid. T = temperature of mercury. Tb = temperature of glass bulb. Tf = temperature of surrounding fluid. Determine the transfer function between Tf and T. what is the effect of bulb resistance and capacitance on the thermometer response? Note that the inclusion of the bulb results in a pair of interacting systems, which give an overall transfer function different from that of Eq (7.24) Writing the energy balance for change in term of a bulb and mercury respectively Input - output = accumulation dt dT C m T T A h T T A h b b b b i i b f = - - - ) ( ) ( 0 0 dt dT C m T T A h b i i = - - 0 ) ( Writing the steady state equation 0 ) ( ) ( 0 0 = = - - - dt dT C m T T A h T T A h bs b b s bs i i bs fs 0 ) ( = - s bs i i T T A h
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Where subscript
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Unformatted text preview: denoted values at steady subtracting and writing these equations in terms of deviation variables. dt dT C m T T A h T T A h b b b m b i i b f =---) ( ) ( dt dT C m T T A h m m b i i =--) ( Here T F = T f - T fS T B = T b- T bS Tm = T - T S Taking laplace transforms ) ( ) ( )) ( ) ( ( s T C m T T A h s T s T A h B b b m B i i B F =-------(1) And ) ( )) ( ) ( ( s sT mC s T s T A h B m B i i =-------(2) = ) ( ) ( )) ( ) ( ( s sT C m s mCST s T s T A h B b b m B F =--From (2) we get ) 1 ( ) ( 1 ) ( ) ( + = + = s s T s A h mC s T s T i m i i m B τ Where i i i A h mC = Putting it into (1) ) 1 ))( 1 ( ) ( ) ( = + + +-s A h mC s s s T s T i m F...
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