Process Dynamics And Control, 4e
Process Dynamics And Control, 4e
16th Edition
ISBN: 9781119385561
Author: Seborg, Dale E.
Publisher: WILEY
Question
Book Icon
Chapter 5, Problem 5.16E
Interpretation Introduction

(a)

Interpretation:

The expression for the time to first peak of the underdamped second-order system is to be derived.

Concept introduction:

For the second order transfer function of the form,

G(s)=Y(s)U(s)=Kτ2s2+2ζτs+1   ..... (1)

Where, K,τ, and ζ are the system parameters.

Interpretation Introduction

(b)

Interpretation:

The expression for the fraction overshoot of the underdamped second-order system is to be derived.

Concept introduction:

For the second order transfer function of the form,

G(s)=Y(s)U(s)=Kτ2s2+2ζτs+1   ..... (1)

Where, K,τ, and ζ are the system parameters.

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.

Interpretation Introduction

(c)

Interpretation:

The expression for the decay ratio of the underdamped second-order system is to be derived.

Concept introduction:

For the second order transfer function of the form,

G(s)=Y(s)U(s)=Kτ2s2+2ζτs+1   ..... (1)

Where, K,τ, and ζ are the system parameters.

The ratio of the successive peaks sizes is termed as the decay ratio (DR).

Interpretation Introduction

(d)

Interpretation:

The expression for the settling time (ts) of the underdamped second-order system is to be derived. Also, it is to be stated if a single expression can be used for ts over the full range of ζ(0<ζ<1).

Concept introduction:

For the second order transfer function of the form,

G(s)=Y(s)U(s)=Kτ2s2+2ζτs+1   ..... (1)

Where, K,τ, and ζ are the system parameters.

Settling time is defined as the time which is required for the process output to reach and remain in a band with its width equal to ±5% of the total change occurring in y for 95% of the response time.

Trigonometric identity used is:

sin(A+B)=sinAcosB+cosAsinB

Blurred answer
Students have asked these similar questions
can you do specific control loop for dc including reboiler and condenser
The periodic array below denotes a hypothetical lattice in 2D. 1. Is this a Bravais lattice? Why or why not?  2. Draw 3 different versions of unit cells. Of those 3, make one a primitive unit cell. 3. There is a special type of primitive unit cell that is called a ’Wigner-Seitz’ cell (look it up on- line, or in text books). In words, describe how it is defined, and draw it for the lattice above.  4. Why would it be useful to draw the primitive unit cell of a lattice as a Wigner-Seitz cell, rather than another random choice? Hint : What geometric property of a lattice was described to be useful in guessing material properties
The schematic figure below shows a face-centered cubic (FCC) lattice with a lattice constant of a. Draw the lattice vectors of a primitive unit cell for the FCC lattice. Also write them in equation form and derive an expression for the reciprocal lattice vectors of an FCC lattice Using these sets of reciprocal lattice vectors, draw (or generate) the reciprocal lattice of FCC in re- ciprocal space. Show that this reciprocal lattice is equivalent to a body-centered cubic lattice with a lattice constant of 4pi/a
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Introduction to Chemical Engineering Thermodynami...
Chemical Engineering
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:McGraw-Hill Education
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemical Engineering
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY
Text book image
Elements of Chemical Reaction Engineering (5th Ed...
Chemical Engineering
ISBN:9780133887518
Author:H. Scott Fogler
Publisher:Prentice Hall
Text book image
Process Dynamics and Control, 4e
Chemical Engineering
ISBN:9781119285915
Author:Seborg
Publisher:WILEY
Text book image
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:9781285061238
Author:Lokensgard, Erik
Publisher:Delmar Cengage Learning
Text book image
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:9780072848236
Author:Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:McGraw-Hill Companies, The