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Homework 08 - Second Order Dynamics

Homework 08 - Second Order Dynamics - Chemical Engineering...

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Chemical Engineering Department University of Florida ECH 4323 Process Control Theory HOMEWORK No. 8 — SECOND-ORDER DYNAMICS 1.0 A force-momentum balance on a mercury manometer results in the equation 4 d 2 x dt 2 + 0.8 dx dt + x = p(t) where x is the displacement of the mercury column from its equilibrium position, and p(t) is the time-varying pressure acting on the manometer. (a) Find the transfer function relating x to p , assuming that the system is initially in equilibrium. (b) Find the gain, time-constant, and damping coefficient for the system. Classify the system based on the value of the damping coefficient. (c) Calculate the response of the manometer to the pressure input p(t) = 2 e -4 t S(t). 2.0 Modified version of Exercise 5.12 in Seborg, Edgar and Mellichamp (3 rd . Edition) Consider the linear differential equation d 2 ! y dt 2 + " d ! y dt + 4 ! y (t) = ! u (t) with initial condition ! y (0) = 0 and ! u (0) = 0 , and where ! is a non-negative real number. The following questions regard the response of the system when input is the unit step function ! u (t) =
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  • Spring '10
  • Crissale
  • Chemical Engineering Department, Chemical Engineering Department University of Florida, appropriate mass balance

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