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 5.1E
Interpretation Introduction

Interpretation:

The time needed for output to reach the steady state depend on the magnitude of input needs to be determined.

Concept introduction:

Fourth order plus time delay system is used for describing the dynamics of chemical process.

Just by selecting proper choice of τDT and τ it represents the dynamics of several industrial processes.

Expert Solution & Answer
Check Mark

Answer to Problem 5.1E

Magnitude of change increase with A increased with time and vice versa that is Y(s) is depend on the A.

Explanation of Solution

Given:

For given transformation,

G(S)=K(τ1s+1)(τ2s+1)(τ3s+1)(τ4s+1)eθs

Calculation:

  • To find the stead state value of Y(s):
  • Given transformation-

    G(S)=K(τ1s+1)(τ2s+1)(τ3s+1)(τ4s+1)e-θsG(S)=Y(s)U(s)

    Step input is applied in system input

    U(S)=1S

    As magnitude is 1

    So, Y(S)=1S×K(τ1s+1)(τ2s+1)(τ3s+1)(τ4s+1)e-θs

    At the steady state of output,

    limx¥

    f(t) to lims¥

    f(s),

  • For the steady state value of
  • Y(t)=lims0×S×1SK(τ1s+1)(τ2s+1)(τ3s+1)(τ4s+1)e-θsY(t)t0=K(1)(1)(1)(1)e(0)Y(t)t0=K

  • If step input magnitude A,
  • U(S)=AS

    When magnitude is A,

    Y(s)=ASK(τ1s+1)(τ2s+1)(τ3s+1)(τ4s+1)e-θsY(s)t0=lims¥×S×Y(s)Y(s)t0=A×K(1)(1)(1)(1)e(0)Y(s)t0=A×K 

Conclusion

Thus, steady state value of Y(s) is mainly depends on the magnitude of step input in A.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
2. A single-effect evaporator is concentrating a feed solution of organic colloids from 5 to 50 wt %. The solution has a negligible boiling point elevation. The heat capacity of the feed is cp . 4.06 kJ/kg K and the feed enters at 15.6 °C. Saturated steam at 101.32 kPa is available for heating, and the pressure in the vapor space of the evaporator is 15.3 kPa. A total of 4536 kg/h of water is to be evaporated. The overall heat-transfer coefficient is 1988 W/m². K. What is the required surface area in m² and the steam consumption?
A mixture with 4% n-pentane, 40% n-hexane, 50% n-heptane, and 6% n-octane is to be distilled at 14.7 lb/in² (1 atm.) with 98% of the hexane and 1% of the heptane recovered in the distillate. If the liquid feed is a saturated liquid (i.e., q = 1). Calculate i.) The product compositions, ii.) The top and bottom temperature iii.) Minimum reflux ratio (Rm), iv.) Minimum theoretical plates and v.) Actual plates when the reflux ratio is 2Rm. Table 1: Component boiling point and molar mass Component Boiling point n-C5 97°F n-C6 156.2°F n-C7 209.1°F n-C8 258.1°F Molar mass 72.2 86.2 100.2 114.2 Hint: Since 1% of heptane is specified to be recovered in the distillate, 99% of heptane is to be recovered in the bottom.
H.W 1. A plant wishes to dry a certain type of fiberboard. To determine drying characteristics, a sample of 0.3 × 0.3 m with edges sealed was suspended from a balance and exposed to a current of hot dry air. The initial moisture content was 75%. The sheet lost weight at the rate of 1 104 Kg/s unit the moisture content fell to 60%. It was established that the equilibrium moisture content was 10 %. The dry mass of the sample was 0.90 Kg. All moisture contents were on a wet basis. Determine the time for drying the sheets from 75% to 20% moisture under the same drying conditions?
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