(a) Interpretation: It is to be estimated and explained if the given process will exhibit an overshoot for a step change in u . Concept introduction: For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances. The process models generally include algebraic relationships which commence from thermodynamics , transport phenomena , chemical kinetics, and physical properties of the processes. For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus, Y ( s ) = Y 1 ( s ) Y 2 ( s ) … Y n ( s ) ...... (1) The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value. From the definition of the overshoot, it can be written as: OS = y max ( t ) − K M K M ...... (2) Overshoot (OS) can also be defined as: OS = exp ( − π ζ 1 − ζ 2 ) ...... (3) For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is: e − θ s = 1 e θ s = 1 1 + θ s Provided the value of θ is very small.

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Answer 1

Question

Chapter 6, Problem 6.23E

Interpretation Introduction

(a)

Interpretation:

It is to be estimated and explained if the given process will exhibit an overshoot for a step change in u.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(b)

Interpretation:

The approximated maximum value of y(t) for the given process at given conditions for a step change in u of magnitude 3 is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(c)

Interpretation:

The time at which the maximum value occurs is to be calculated.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(d)

Interpretation:

The response of the both the actual and the approximated model for the given process are to be simulated and plotted. Also, both the plots are to be generated for τ1=1 and τ1=5 and the results are to be compared graphically.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

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A pilot process is being planned to produce antibiotic P. Antibiotic P is a compound secreted by microorganism A during the stationary phase. To produce P, substrate S is required. The growth of microorganism A follows the Monod equation, with a maximum specific growth rate $\mu_m = 1 h^{-1}$ and a half-saturation constant $K_s = 700\ mg/L$.The pilot process uses a chemostat with a working volume of $1000\ L$. In this chemostat, the outflow is processed to separate microorganisms, which are then concentrated tenfold and recycled. A sterile medium containing $15\ g/L$ of substrate is supplied at a flow rate of $100\ L/h$, while the recycled flow (concentrated) contains $5\ g/L$ and is also fed into the chemostat.Microorganism A yields $0.5\ g$ of biomass per $1\ g$ of substrate consumed $(Y^M_{X/S} = 0.5\ g\ A/g\ S)$, and its death rate $(k_d)$ is negligible. Additionally, $1\ g$ of microorganism A produces $0.05\ g$ of antibiotic P per hour $(q_P = 0.05 g\ P/h\cdot g\ A)$, and $1\ g$…

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Answer 2

Question

Chapter 6, Problem 6.23E

Interpretation Introduction

(a)

Interpretation:

It is to be estimated and explained if the given process will exhibit an overshoot for a step change in u.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(b)

Interpretation:

The approximated maximum value of y(t) for the given process at given conditions for a step change in u of magnitude 3 is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(c)

Interpretation:

The time at which the maximum value occurs is to be calculated.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(d)

Interpretation:

The response of the both the actual and the approximated model for the given process are to be simulated and plotted. Also, both the plots are to be generated for τ1=1 and τ1=5 and the results are to be compared graphically.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

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Answer 3

Question

Chapter 6, Problem 6.23E

Interpretation Introduction

(a)

Interpretation:

It is to be estimated and explained if the given process will exhibit an overshoot for a step change in u.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(b)

Interpretation:

The approximated maximum value of y(t) for the given process at given conditions for a step change in u of magnitude 3 is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(c)

Interpretation:

The time at which the maximum value occurs is to be calculated.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(d)

Interpretation:

The response of the both the actual and the approximated model for the given process are to be simulated and plotted. Also, both the plots are to be generated for τ1=1 and τ1=5 and the results are to be compared graphically.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 6, Problem 6.23E

Interpretation Introduction

(a)

Interpretation:

It is to be estimated and explained if the given process will exhibit an overshoot for a step change in u.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(b)

Interpretation:

The approximated maximum value of y(t) for the given process at given conditions for a step change in u of magnitude 3 is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(c)

Interpretation:

The time at which the maximum value occurs is to be calculated.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(d)

Interpretation:

The response of the both the actual and the approximated model for the given process are to be simulated and plotted. Also, both the plots are to be generated for τ1=1 and τ1=5 and the results are to be compared graphically.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 6, Problem 6.23E

Interpretation Introduction

(a)

Interpretation:

It is to be estimated and explained if the given process will exhibit an overshoot for a step change in u.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(b)

Interpretation:

The approximated maximum value of y(t) for the given process at given conditions for a step change in u of magnitude 3 is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(c)

Interpretation:

The time at which the maximum value occurs is to be calculated.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Interpretation Introduction

(d)

Interpretation:

The response of the both the actual and the approximated model for the given process are to be simulated and plotted. Also, both the plots are to be generated for τ1=1 and τ1=5 and the results are to be compared graphically.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 6

Chapter 6, Problem 6.23E

Interpretation Introduction

(a)

Interpretation:

It is to be estimated and explained if the given process will exhibit an overshoot for a step change in u.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 7

Chapter 6, Problem 6.23E

Interpretation Introduction

(a)

Interpretation:

It is to be estimated and explained if the given process will exhibit an overshoot for a step change in u.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The approximated maximum value of y(t) for the given process at given conditions for a step change in u of magnitude 3 is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The approximated maximum value of y(t) for the given process at given conditions for a step change in u of magnitude 3 is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The time at which the maximum value occurs is to be calculated.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The time at which the maximum value occurs is to be calculated.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 12

Interpretation Introduction

(d)

Interpretation:

The response of the both the actual and the approximated model for the given process are to be simulated and plotted. Also, both the plots are to be generated for τ1=1 and τ1=5 and the results are to be compared graphically.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 13

Interpretation Introduction

(d)

Interpretation:

The response of the both the actual and the approximated model for the given process are to be simulated and plotted. Also, both the plots are to be generated for τ1=1 and τ1=5 and the results are to be compared graphically.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For n processes in series, the output of the entire process is the product of all the outputs of all the processes taking place internally of the system. Thus,

Y(s)=Y1(s)Y2(s)…Yn(s) ...... (1)

The maximum value of the response of a system to achieve its peak from the desired response of the given system is known as overshoot. It exceeds its final steady-state value.

From the definition of the overshoot, it can be written as:

OS=ymax(t)−KMKM ...... (2)

Overshoot (OS) can also be defined as:

OS=exp(−πζ1−ζ 2) ...... (3)

For higher order transfer function approximation, higher order models are approximated using the time delays into lower order models of approximate similar dynamics and steady-state characteristics. Formula used for this approximation is:

e−θs=1eθs=11+θs

Provided the value of θ is very small.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

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 the concept of an overshoot for a step change in u.

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