KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec13

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec13

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1 Chapter 4 Linearization of Nonlinear Models So far, we have emphasized linear models which can be transformed into TF models. But most physical processes and physical models are nonlinear. - But over a small range of operating conditions, the behavior may be approximately linear. - Conclude : Linear approximations can be useful, especially for purpose of analysis. Approximate linear models can be obtained analytically by a method called “linearization”. It is based on a Taylor Series Expansion of a nonlinear function about a specified operating point.
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2 Chapter 4 Consider a nonlinear, dynamic model relating two process variables, u and y : ( 29 , (4-60) dy f y u dt = Perform a Taylor Series Expansion about and and truncate after the first order terms, u u = y y = ( 29 ( 29 , , (4-61) y y f f f u y f u y u y u y o o = + + where and . Note that the partial derivative terms are actually constants because they have been evaluated at the nominal operating point, Substitute (4-61) into (4-60) gives: u u u o = - y y y o = - ( 29 , . u y
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3 Chapter 4 The steady-state version of (4-60) is: ( 29 0 , f u y = Substitute above and recall that , dy dy dt dt o = (4-62) y y dy f f u y dt u y o o o = + Linearized model ( 29 , y y dy f f f u y u y dt u y o o = + +
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4 Chapter 4 q 0 : control, q i : disturbance 0 i q q dt dh A - = Use L.T. 0
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