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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec12-2

# KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec12-2

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1 Chapter 4 ( 29 ( 29 ( 29 ( 29 ( 29 0 (8) i V C sT s T t wC T s T s Q s ρ e - = = - - ( 29 ( 29 ( 29 1 (10) 1 1 i K T s Q s T s s s τ τ @ = + + + ( 29 1 and 11 V K wC w ρ τ @ @ G 1 and G 2 are transfer functions and independent of the inputs, Q′ and T i ′. Note G 1 (process) has gain K and time constant τ . G 2 (disturbance) has gain=1 and time constant τ . gain = G(s=0). Both are first order processes. If there is no change in inlet temperature (T i ′= 0), then T i ′(s) = 0. System can be forced by a change in either T i or Q (see Example 4.1). (s) T (s) G (s) Q (s) (s)=G T i + 2 1

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2 Chapter 4 Transfer Function Between and Q V T V Suppose is constant at the steady-state value. Then, Then we can substitute into (10) and rearrange to get the desired TF: i T ( 29 ( 29 ( 29 0 0. i i i i T t T T t T s V = = = ( 29 ( 29 (12) 1 T s K Q s s τ = +
3 Chapter 4 Thus, rearranging ( 29 ( 29 1 (13) 1 i T s T s s τ = + Transfer Function Between and T V : i T V Suppose that Q is constant at its steady-state value: ( 29 ( 29 ( 29 0 0 Q t Q Q t Q s V = = =

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4 Chapter 4 Answer : See (10). The same TFs are valid for simultaneous changes. Note that (10) shows that the effects of changes in both Q and are additive . This always occurs for linear, dynamic
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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec12-2

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