Chapter 5, Problem 5.19E

Interpretation Introduction

(a)

Interpretation:

The surge system that can handle the larger step disturbances in $q_i$ is to be identified and the answer is to be justified.

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 large value of time, the asymptotic value of $y\left(t\right)$ can be calculated using Final Value theorem (FVM) as shown below:

$\underset{t\to \infty }{\lim }y\left(t\right)=\underset{s\to 0}{\lim }\left[sY\left(s\right)\right]$

This theorem is applicable only if $\underset{s\to 0}{\lim }\left[sY\left(s\right)\right]$ exists for all values of $\mathrm{Re}\left(s\right)\ge 0$.

Interpretation Introduction

(b)

Interpretation:

The system that provides best damping for a step disturbance in $q_i$ is to be identified and the answer is to be justified.

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.

An influence on or within an oscillatory system which results in the reduction, restriction, or prevention of its oscillations is termed as damping. There are three types of damping in a control system, namely, underdamped system, critically damped system, and overdamped system.

Interpretation Introduction

(c)

Interpretation:

The results in part (a) and part (b) are to be verified using computer simulation.

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.

An influence on or within an oscillatory system which results in the reduction, restriction, or prevention of its oscillations is termed as damping. There are three types of damping in a control system, namely, underdamped system, critically damped system, and overdamped system.