Process Dynamics And Control, 4e
Process Dynamics And Control, 4e
16th Edition
ISBN: 9781119385561
Author: Seborg, Dale E.
Publisher: WILEY
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Chapter 3, Problem 3.13E
Interpretation Introduction

(a)

Interpretation:

The response of the given system is to be estimated to be oscillatory or not for an arbitrary change in u.

Concept introduction:

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt   ....... (1)

Here, F(s) represents the Laplace transform, s is a variable that is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

PFE is the partial fraction expansion is the method of expanding the denominator of a fraction into simpler terms.

Laplace transform of higher-order derivatives is given by:

L(dnfdtn)=snF(s)sn1f(0)sn2f(1)(0)sf(n2)(0)f(n1)(0)   ....... (2)

For the general form of the transfer function;

Y(s)X(s)=1τ2s2+2τζs+1

The response of the transfer will be underdamped or oscillatory if ζ<1, critically damped if ζ=1, and overdamped or nonoscillatory if ζ>1.

Interpretation Introduction

(b)

Interpretation:

The steady-state value of yis to be calculated when

u(t2)=1.

Concept introduction:

The value of Kp, steady-state value is calculated by s=0 in the transfer function for the unit step disturbance, that is,

lims0[sY(s)]=Kp

Interpretation Introduction

(c)

Interpretation:

The value of y(t) for a step-change in u is to be calculated.

Concept introduction:

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt   ....... (1)

Here, F(s) represents the Laplace transform, s is a variable that is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

PFE is the partial fraction expansion is the method of expanding the denominator of a fraction into simpler terms.

Laplace transform of higher-order derivatives is given by:

L(dnfdtn)=snF(s)sn1f(0)sn2f(1)(0)sf(n2)(0)f(n1)(0)   ....... (2)

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Homework 8 View Policies Show Attempt History Current Attempt in Progress Question 3 of 5 Entering Steam > > Check table lookups for correct values. Check significant figures. Check unit conversions. Calculate the required flow rate of the entering steam in m³/min. 0.00132 m³/min eTextbook and Media Hint 0/1 Assistance Used Determine the specific enthalpy change of each stream first. Then use the known flow rate of the methanol to calculate the steam flow rate. Save for Later Heat Transferred × Check units and significant figures. Calculate the rate of heat transfer from the water to the methanol (kW). i 44.5 kW Hint Don't forget to convert minutes to seconds. Save for Later Attempts: 3 of 5 used Submit Answer Assistance Used Attempts: 2 of 5 used Submit Answer
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