(a) Interpretation: For a change of unit rectangular pulse in the input of a heating process, the steady-state response is to be determined. Concept introduction: For a large value of time, the asymptotic value of y ( t ) can be calculated using Final Value theorem (FVM) as shown below: lim t → ∞ y ( t ) = lim s → 0 [ s Y ( s ) ] .......... (1) This theorem is applicable only if lim s → 0 [ s Y ( s ) ] exists for all values of Re ( s ) ≥ 0 .

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Answer 1

Question

Chapter 5, Problem 5.23E

Interpretation Introduction

(a)

Interpretation:

For a change of unit rectangular pulse in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(b)

Interpretation:

For a change of unit ramp in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(c)

Interpretation:

The answers in part (a) and part (b) are to be explained physically along with any physical limitation that might be present on the ramping of the heating rate.

Concept introduction:

An input change when the process is subjected to a sudden step-change in the input which gradually then returns to its original value is known as a rectangular pulse change.

This change can be approximated as:

uRP(t)={0 t<0h 0≤t<tw0 t≥tw

Here, h is the magnitude of the change and tw is the pulse width which can vary from very short to very long.

An input change when the process is subjected to a gradual upward or downward change in the input for some time period with a constant slope is known as ramp change.

This change can be approximated as:

uR(t)={0 t<0at t≥0

Here, a is the magnitude or slope of the change.

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Answer 2

Question

Chapter 5, Problem 5.23E

Interpretation Introduction

(a)

Interpretation:

For a change of unit rectangular pulse in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(b)

Interpretation:

For a change of unit ramp in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(c)

Interpretation:

The answers in part (a) and part (b) are to be explained physically along with any physical limitation that might be present on the ramping of the heating rate.

Concept introduction:

An input change when the process is subjected to a sudden step-change in the input which gradually then returns to its original value is known as a rectangular pulse change.

This change can be approximated as:

uRP(t)={0 t<0h 0≤t<tw0 t≥tw

Here, h is the magnitude of the change and tw is the pulse width which can vary from very short to very long.

An input change when the process is subjected to a gradual upward or downward change in the input for some time period with a constant slope is known as ramp change.

This change can be approximated as:

uR(t)={0 t<0at t≥0

Here, a is the magnitude or slope of the change.

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Answer 3

Question

Chapter 5, Problem 5.23E

Interpretation Introduction

(a)

Interpretation:

For a change of unit rectangular pulse in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(b)

Interpretation:

For a change of unit ramp in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(c)

Interpretation:

The answers in part (a) and part (b) are to be explained physically along with any physical limitation that might be present on the ramping of the heating rate.

Concept introduction:

An input change when the process is subjected to a sudden step-change in the input which gradually then returns to its original value is known as a rectangular pulse change.

This change can be approximated as:

uRP(t)={0 t<0h 0≤t<tw0 t≥tw

Here, h is the magnitude of the change and tw is the pulse width which can vary from very short to very long.

An input change when the process is subjected to a gradual upward or downward change in the input for some time period with a constant slope is known as ramp change.

This change can be approximated as:

uR(t)={0 t<0at t≥0

Here, a is the magnitude or slope of the change.

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Answer 4

Question

Chapter 5, Problem 5.23E

Interpretation Introduction

(a)

Interpretation:

For a change of unit rectangular pulse in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(b)

Interpretation:

For a change of unit ramp in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(c)

Interpretation:

The answers in part (a) and part (b) are to be explained physically along with any physical limitation that might be present on the ramping of the heating rate.

Concept introduction:

An input change when the process is subjected to a sudden step-change in the input which gradually then returns to its original value is known as a rectangular pulse change.

This change can be approximated as:

uRP(t)={0 t<0h 0≤t<tw0 t≥tw

Here, h is the magnitude of the change and tw is the pulse width which can vary from very short to very long.

An input change when the process is subjected to a gradual upward or downward change in the input for some time period with a constant slope is known as ramp change.

This change can be approximated as:

uR(t)={0 t<0at t≥0

Here, a is the magnitude or slope of the change.

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Answer 5

Chapter 5, Problem 5.23E

Interpretation Introduction

(a)

Interpretation:

For a change of unit rectangular pulse in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(b)

Interpretation:

For a change of unit ramp in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Interpretation Introduction

(c)

Interpretation:

The answers in part (a) and part (b) are to be explained physically along with any physical limitation that might be present on the ramping of the heating rate.

Concept introduction:

An input change when the process is subjected to a sudden step-change in the input which gradually then returns to its original value is known as a rectangular pulse change.

This change can be approximated as:

uRP(t)={0 t<0h 0≤t<tw0 t≥tw

Here, h is the magnitude of the change and tw is the pulse width which can vary from very short to very long.

An input change when the process is subjected to a gradual upward or downward change in the input for some time period with a constant slope is known as ramp change.

This change can be approximated as:

uR(t)={0 t<0at t≥0

Here, a is the magnitude or slope of the change.

Answer 6

Chapter 5, Problem 5.23E

Interpretation Introduction

(a)

Interpretation:

For a change of unit rectangular pulse in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Answer 7

Chapter 5, Problem 5.23E

Interpretation Introduction

(a)

Interpretation:

For a change of unit rectangular pulse in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Answer 8

Interpretation Introduction

(b)

Interpretation:

For a change of unit ramp in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Answer 9

Interpretation Introduction

(b)

Interpretation:

For a change of unit ramp in the input of a heating process, the steady-state response is to be determined.

Concept introduction:

For a large value of time, the asymptotic value of y(t) can be calculated using Final Value theorem (FVM) as shown below:

limt→∞y(t)=lims→0[sY(s)] .......... (1)

This theorem is applicable only if lims→0[sY(s)] exists for all values of Re(s)≥0.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The answers in part (a) and part (b) are to be explained physically along with any physical limitation that might be present on the ramping of the heating rate.

Concept introduction:

An input change when the process is subjected to a sudden step-change in the input which gradually then returns to its original value is known as a rectangular pulse change.

This change can be approximated as:

uRP(t)={0 t<0h 0≤t<tw0 t≥tw

Here, h is the magnitude of the change and tw is the pulse width which can vary from very short to very long.

An input change when the process is subjected to a gradual upward or downward change in the input for some time period with a constant slope is known as ramp change.

This change can be approximated as:

uR(t)={0 t<0at t≥0

Here, a is the magnitude or slope of the change.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The answers in part (a) and part (b) are to be explained physically along with any physical limitation that might be present on the ramping of the heating rate.

Concept introduction:

An input change when the process is subjected to a sudden step-change in the input which gradually then returns to its original value is known as a rectangular pulse change.

This change can be approximated as:

uRP(t)={0 t<0h 0≤t<tw0 t≥tw

Here, h is the magnitude of the change and tw is the pulse width which can vary from very short to very long.

An input change when the process is subjected to a gradual upward or downward change in the input for some time period with a constant slope is known as ramp change.

This change can be approximated as:

uR(t)={0 t<0at t≥0

Here, a is the magnitude or slope of the change.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 5 - Prob. 5.1E Ch. 5 - Prob. 5.2E Ch. 5 - Prob. 5.3E Ch. 5 - Prob. 5.4E Ch. 5 - Prob. 5.5E Ch. 5 - Prob. 5.6E Ch. 5 - Appelpolscher has just left a meeting with Stella...Ch. 5 - Prob. 5.8E Ch. 5 - Prob. 5.9E Ch. 5 - Prob. 5.10E

Solution Summary: The author explains that the steady-state response for a change of unit rectangular pulse in the input of the heating process is calculated to be 0.

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Chapter 5 Solutions