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 δξ δτ + ξ = π(τ29 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 ψ δτ 2 + α δ ′ ψ δτ + 4 ′ ψ(τ29 = υ (τ29 with initial condition ψ(029 = 0 and υ (029 = 0 , and where α is a non-negative real
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Homework 08 - Second Order Dynamics - Chemical Engineering...

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