PROCESS DYNAMIC+CONTROL-EBOOK>I<
PROCESS DYNAMIC+CONTROL-EBOOK>I<
4th Edition
ISBN: 2819480255712
Author: Seborg
Publisher: INTER WILE
Question
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Chapter 4, Problem 4.1E
Interpretation Introduction

(a)

Interpretation:

The steady-state gain of the equation Y(s)U(s)=dbs+c needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Expert Solution
Check Mark

Answer to Problem 4.1E

The steady-stategain of equations as: dc.

Explanation of Solution

Given:

The transfer equation is Y(s)U(s)=dbs+c.

Calculation:

The steady-state gain can be expressed as:

U(s)=1s

Substituting in the given equation,

Y(s)=dsbs+c×U(s)Y(s)=dsbs+c×1s

Steady-state value can be given as:

lims0=dbs+c×1slims0=dc

Hence, the steady-state gain of equations is dc.

Interpretation Introduction

(b)

Interpretation:

Whether the output will be bounded for all the values of b,c and d constants for the step change of magnitude M in the input or not needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Expert Solution
Check Mark

Answer to Problem 4.1E

The Mdc has bounded response for a finite value of d and c or finite ratio dc.

If the ratio of d and c will infinite then it will tend to unbounded.

Explanation of Solution

Given:

The transfer equation is Y(s)U(s)=dbs+c.

Calculation:

The steady-state gain can be expressed as:

U(t)=MU(s)=Ms

Substituting in the given equation,

Y(s)=dbs+c×MY(s)=dbs+c×Ms

Steady-state value can be given as:

lims0=dbs+c×Mslims0=Mdc

Hence, the steady-state gain of equations is Mdc.

This Mdc has bounded response for a finite value of d and c or finite ratio dc.

If ratio of d and c will infinite then it will tend to unbounded.

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