(a) Interpretation: The given transfer function should be written in a standard constant form of time or gain. 4 ( s+2 ) ( 0 .5s+1 ) ( 2s+1 ) e -5s . Concept introduction: A transfer function model characterizes the dynamic relationship of two process variables: A dependent variable (or output variable). An independent variable (or input variable). Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior, such as a process that can be modeled by a linear ODE. If the process is nonlinear, a transfer function can provide an approximate linear model.

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Chapter 6, Problem 6.2E

Interpretation Introduction

(a)

Interpretation:

The given transfer function should be written in a standard constant form of time or gain.

4(s+2)(0.5s+1)(2s+1)e-5s.

Concept introduction:

A transfer function model characterizes the dynamic relationship of two process variables:

A dependent variable (or output variable).

An independent variable (or input variable).

Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior, such as a process that can be modeled by a linear ODE. If the process is nonlinear, a transfer function can provide an approximate linear model.

Interpretation Introduction

(b)

Interpretation:

The value of gain, poles and zeroes of standard transfer function should be determined.

Concept introduction:

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Interpretation Introduction

(c)

Interpretation:

The values of gain, poles and zeroes if the time delay function is replaced by (11) should be determined.

Concept introduction:

The Pade approximation for a time delay is a ratio of two polynomials in (s) with coefficients selected to match the terms of a truncated Taylor series expansion of (e-θs).

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

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Answer 2

Question

Chapter 6, Problem 6.2E

Interpretation Introduction

(a)

Interpretation:

The given transfer function should be written in a standard constant form of time or gain.

4(s+2)(0.5s+1)(2s+1)e-5s.

Concept introduction:

A transfer function model characterizes the dynamic relationship of two process variables:

A dependent variable (or output variable).

An independent variable (or input variable).

Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior, such as a process that can be modeled by a linear ODE. If the process is nonlinear, a transfer function can provide an approximate linear model.

Interpretation Introduction

(b)

Interpretation:

The value of gain, poles and zeroes of standard transfer function should be determined.

Concept introduction:

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Interpretation Introduction

(c)

Interpretation:

The values of gain, poles and zeroes if the time delay function is replaced by (11) should be determined.

Concept introduction:

The Pade approximation for a time delay is a ratio of two polynomials in (s) with coefficients selected to match the terms of a truncated Taylor series expansion of (e-θs).

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

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Answer 3

Question

Chapter 6, Problem 6.2E

Interpretation Introduction

(a)

Interpretation:

The given transfer function should be written in a standard constant form of time or gain.

4(s+2)(0.5s+1)(2s+1)e-5s.

Concept introduction:

A transfer function model characterizes the dynamic relationship of two process variables:

A dependent variable (or output variable).

An independent variable (or input variable).

Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior, such as a process that can be modeled by a linear ODE. If the process is nonlinear, a transfer function can provide an approximate linear model.

Interpretation Introduction

(b)

Interpretation:

The value of gain, poles and zeroes of standard transfer function should be determined.

Concept introduction:

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Interpretation Introduction

(c)

Interpretation:

The values of gain, poles and zeroes if the time delay function is replaced by (11) should be determined.

Concept introduction:

The Pade approximation for a time delay is a ratio of two polynomials in (s) with coefficients selected to match the terms of a truncated Taylor series expansion of (e-θs).

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

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Answer 4

Question

Chapter 6, Problem 6.2E

Interpretation Introduction

(a)

Interpretation:

The given transfer function should be written in a standard constant form of time or gain.

4(s+2)(0.5s+1)(2s+1)e-5s.

Concept introduction:

A transfer function model characterizes the dynamic relationship of two process variables:

A dependent variable (or output variable).

An independent variable (or input variable).

Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior, such as a process that can be modeled by a linear ODE. If the process is nonlinear, a transfer function can provide an approximate linear model.

Interpretation Introduction

(b)

Interpretation:

The value of gain, poles and zeroes of standard transfer function should be determined.

Concept introduction:

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Interpretation Introduction

(c)

Interpretation:

The values of gain, poles and zeroes if the time delay function is replaced by (11) should be determined.

Concept introduction:

The Pade approximation for a time delay is a ratio of two polynomials in (s) with coefficients selected to match the terms of a truncated Taylor series expansion of (e-θs).

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

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Answer 5

Chapter 6, Problem 6.2E

Interpretation Introduction

(a)

Interpretation:

The given transfer function should be written in a standard constant form of time or gain.

4(s+2)(0.5s+1)(2s+1)e-5s.

Concept introduction:

A transfer function model characterizes the dynamic relationship of two process variables:

A dependent variable (or output variable).

An independent variable (or input variable).

Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior, such as a process that can be modeled by a linear ODE. If the process is nonlinear, a transfer function can provide an approximate linear model.

Interpretation Introduction

(b)

Interpretation:

The value of gain, poles and zeroes of standard transfer function should be determined.

Concept introduction:

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Interpretation Introduction

(c)

Interpretation:

The values of gain, poles and zeroes if the time delay function is replaced by (11) should be determined.

Concept introduction:

The Pade approximation for a time delay is a ratio of two polynomials in (s) with coefficients selected to match the terms of a truncated Taylor series expansion of (e-θs).

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Answer 6

Chapter 6, Problem 6.2E

Interpretation Introduction

(a)

Interpretation:

The given transfer function should be written in a standard constant form of time or gain.

4(s+2)(0.5s+1)(2s+1)e-5s.

Concept introduction:

A transfer function model characterizes the dynamic relationship of two process variables:

A dependent variable (or output variable).

An independent variable (or input variable).

Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior, such as a process that can be modeled by a linear ODE. If the process is nonlinear, a transfer function can provide an approximate linear model.

Answer 7

Chapter 6, Problem 6.2E

Interpretation Introduction

(a)

Interpretation:

The given transfer function should be written in a standard constant form of time or gain.

4(s+2)(0.5s+1)(2s+1)e-5s.

Concept introduction:

A transfer function model characterizes the dynamic relationship of two process variables:

A dependent variable (or output variable).

An independent variable (or input variable).

Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior, such as a process that can be modeled by a linear ODE. If the process is nonlinear, a transfer function can provide an approximate linear model.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The value of gain, poles and zeroes of standard transfer function should be determined.

Concept introduction:

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The value of gain, poles and zeroes of standard transfer function should be determined.

Concept introduction:

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The values of gain, poles and zeroes if the time delay function is replaced by (11) should be determined.

Concept introduction:

The Pade approximation for a time delay is a ratio of two polynomials in (s) with coefficients selected to match the terms of a truncated Taylor series expansion of (e-θs).

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The values of gain, poles and zeroes if the time delay function is replaced by (11) should be determined.

Concept introduction:

The Pade approximation for a time delay is a ratio of two polynomials in (s) with coefficients selected to match the terms of a truncated Taylor series expansion of (e-θs).

Gain: At steady state, the proportional value which shows the relationship between the magnitude of input and output signal, is known as Gain of the Transfer Function.

Poles: The values of (s) at which the denominator of the transfer function is equal to zero, is known as Poles of Transfer function.

Zeroes: The values of (s) at which the Numerator of the transfer function is equal to zero, is known as Zeroes of Transfer Function.

Answer 12

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Answer 15

Ch. 6 - Prob. 6.1E Ch. 6 - Prob. 6.2E Ch. 6 - Prob. 6.3E Ch. 6 - Prob. 6.4E Ch. 6 - Prob. 6.5E Ch. 6 - Prob. 6.6E Ch. 6 - Prob. 6.7E Ch. 6 - Prob. 6.8E Ch. 6 - Prob. 6.9E Ch. 6 - Prob. 6.10E

Solution Summary: The author explains that a transfer function model characterizes the dynamic relationship of two process variables. Transfer function models are only directly applicable to processes that exhibit linear dynamic behavior.

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Chapter 6 Solutions