Process Dynamics and Control, 4e
Process Dynamics and Control, 4e
4th Edition
ISBN: 9781119285915
Author: Seborg
Publisher: WILEY
Question
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Chapter 3, Problem 3.4E
Interpretation Introduction

(a)

Interpretation:

Time functions in the given dynamic model of the process where u(t) is be2t 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 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)

Interpretation Introduction

(b)

Interpretation:

Time functions in the given dynamic model of the process where u(t) is ct 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 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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