1. UNIVERSITÀ DEGLI STUDI DI SALERNO
Bachelor Degree in Chemical Engineering
Course:
Process Instrumentation and Control
(Strumentazione e Controllo dei Processi Chimici)
REFERENCE LINEAR DYNAMIC SYSTEMS
DEAD TIME
Rev. 2.6 – May 4, 2019

2. GENERAL DEFINITION OF TIME CONSTANT
Process IN
OUT
A definition of time constant is given by the following general law :
Time constant = capacity rate [=] time
Chemical Engineering Dynamics: An Introduction to Modelling and Computer Simulation, Third Edition
Copyright © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
J. Ingham, I. J. Dunn, E. Heinzle, J. E. Prenosil, J. B. Snape
ISBN:
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Process Instrumentation and Control - Prof M. Miccio

3. GENERAL DEFINITION OF RESIDENCE TIME
OUT
“CAPACITY”
Unit Operation
→ see GLOSSARY
e.g.:
Tank
Chemical Reactor
Mixer
Flow tube
 Because the process unit operation has a "volume" we say that it has a "capacity“.
[=] s
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Process Instrumentation and Control - Prof M. Miccio

4. Process Instrumentation and Control - Prof M. Miccio
DEAD TIME or TRANSPORTATION LAG or PURE TIME DELAY or DISTANCE-VELOCITY LAG
Dynamic system
with delay of
transport
f(t)
y(t)
It is defined as the time elapsed between a variation of the input variable f(t) and the beginning of the observed effect on the output variable y(t)
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Process Instrumentation and Control - Prof M. Miccio

5. Process Instrumentation and Control - Prof M. Miccio
Pipe Flow Demo
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Process Instrumentation and Control - Prof M. Miccio

6. DEAD TIME: Example of pipe flow
f(t)
y(t) L
Whenever material or energy is “physically” transported in a process unit or plant component, there is a time delay associated with it.
The transportation time between points 1 and 2 in pipe flow is : td = L/v
Examples: 1) TL(t) = T0(t-td)
2) cL(t) = c0 (t-td)
In general:
from:
Romagnoli & Palazoglu (2005),
“Introduction to Process Control”
 This occurs in PLUG FLOW: (v≠f(r); Re>>2100):
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Process Instrumentation and Control - Prof M. Miccio

7. DEAD TIME: Example of a distant measuring point
The following are assumed:
The pipe between the tank and the measuring point is well insulated
The flow of the liquid through the pipe is ideal plug flow T
(t) i
measures TL(t)=T(t-td)
T(t) TI
DEAD TIME:
td = L/v L
from:
Romagnoli & Palazoglu (2005),
“Introduction to Process Control”
20/10/2019
Process Instrumentation and Control - Prof M. Miccio

8. DEAD TIME: Example of a distant measuring point of the weight
TRANSPORT AND WEIGHING OF A BASIC SORBENT TO NEUTRALIZE
SO2 IN COMBUSTION OFF-GAS
HOPPER
GRANULAR MATERIAL (LIMESTONE, DOLOMITE, etc.) L v
Load cell
The transportation time is:
td = L/v
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Process Instrumentation and Control - Prof M. Miccio

9. Process Instrumentation and Control - Prof M. Miccio
TRANSFER FUNCTION
Dynamic system
with delay of
transport
f(t)
y(t)
G(s)
y(t) = f(t-td)
 TF not rational
20/10/2019
Process Instrumentation and Control - Prof M. Miccio