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 3.16E
Interpretation Introduction

(a)

Interpretation:

Time functions in the given dynamic model of the process are to be determined.

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 which 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)

Interpretation Introduction

(b)

Interpretation:

The value of y(t) for Y(s)=s+1s(s2+4s+8) is to be determined using PFE is required.

Concept introduction:

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

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which 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.

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