McMaster University
DigitalCommons@McMaster Open Access Dissertations and Theses
Open Dissertations and Theses
9-1-1986
Application of Adaptive Control to a Reciprocating Plate Liquid-Liquid Solvent Extraction Column Mehmet Cihan Camurdan
Follow this and additional works at: http://digitalcommons.mcmaster.ca/opendissertations Part of the Chemical Engineering Commons Recommended Citation Camurdan, Mehmet Cihan, "Application of Adaptive Control to a Reciprocating Plate Liquid-Liquid Solvent Extraction Column" (1986). Open Access Dissertations and Theses. Paper 1068.
This Thesis is brought to you for free and open access by the Open Dissertations and Theses at DigitalCommons@McMaster. It has been accepted for inclusion in Open Access Dissertations and Theses by an authorized administrator of DigitalCommons@McMaster. For more information, please contact
[email protected].
,
APPLICATION OF' ADAPTIVE CONTROL TO A
RECIPROCATING PLATE LIQUID-LIQUID SOLVENT
EXTRACTION COLUMN
by
MEHMET CIHAN CAMURDAN. M. Sc.
,
A THESIS Submitted to the School of Graduate Studies o~
in Partial Fulfilment
the Requirements
for the Degree Doctor of Philosophy
McMaster Unfversity
SEPTEMJlER. 1986
'.
..
LIQUID-LIQUID EXTRACTION, \
ADAPTIVE CONTROL
o
•
•
DOCTOR OF PHILOSOPHY (1986) Engineering)
McMASTER UNIVERSITY Hamilton, Ontario Canada
(Chemi~al
TITLE:
Application
o( Adaptive Control to a Solvent-Extraction Column.
Reciprocating
Pla~e,
Liqu~Liquid
AUTHOR:
Mehmet Cihan Camurdan, B.Sc. (Istanbul Technical University) M.Sc. (Bradford University)
SUPERVISORS:
.'
Dr. M.H.I. Baird Dr. P.A. Taylor
NUMBER OF PAGES:
xvii, 145
\
--_.
-
11
-
. ABSTRACT /
An digital
experimental
control
(DOC)
investigation has
been
of
the
application
of
carried out with continuous
direct chemical
processing equipment, namely a liquid-liquid solvent extraction column. The type of extractor used was the Karr reciprocating plate column.
Steady st'ate sImulations of the column were carried out using both
a
semi-empirical
model
for
studying
the
hydrodynamics
of
the
column, and a mechanistic model for studying the mass transfer characteristic~ of
the column.
The results of these simulations were used to
interpret the closed loop response characteristics of the column. types
of
control schemes were studied;
(1)
an adaptive self
Two
tuning
regulator (STR), (ii) the Dahlin algorithm.
\
Though
the dispersed phase holdup is not
variabte',- its instability. holdup. dispersed
control
is
essential
The frequency of
to
the primary control
prevent
the
hydrodynaln1c
reciprocation was used to control the'
The relationship between the frequency of reciprocation and the phase
holdup
is
highly
nonlinear
therefore
an
,
adaptive '
controller (in this work, a self tuning regulator) has to be used to control this process.
Previous work on holdup control has been extended "
iii
to
include
a
wider, range
of
operating
conditions
and
prevention of
covariance windup by using an empirical discounting factor.
The
primary control objective was
concentration.
This
was
done
ca!,caded control to manipulate
in the
two
the control of
ways~
The first
frequency of
the inner loop was the holdup control.
the extract scheme wss
a
reciprocation whereby
An STR-STR ,cascade arrangement
was .compared with cascade a .PI-STR arrangement.
It was found that the
restrictions imposed on the outer loop meant that the PI-STR arrangement, was as effective as the STR-STR arrangement.
The second control
scheme manipulated the continuous phase. flow rate with (MIHO) and without (SISO)
the simult~neous control of
the frequency of reciprocation.
the holdup via manipulation of
A variable dead time Dahlin controller
was used
to control the extract concentration in this
scheme.
In the MlHO case, decoupling was not 'necessary since one loop
had
a
positive
gain while
the
o~her
had
a
second controi
negative gain and-so the
interactions were constructive. ---;---
,--
iv
"
-
• ACKNOWLEDGEMENTS (
I I would like to thank my supervisors Dr. M.H.l. Baird and Dr. P.A. Taylor for their guidance throughout my research.
I ·also would like to extend my thanks to: Slater,
Mr.
L
Suggett
and
Mr.
W.
Marriner
Mr. R.S. Hood, "Mr. G.M. for
their
technical
assistance; McMaster University for financial aid, and Mrs. Z.M. Unelli, .for the· wo""d processing of the manuscript.
v
.!..
TABLE OF CONTENTS
PAGE 1.
Int roduction 1• 1
General Introduction Brief Overview of the Liquid-Liquid Extraction
1
Proc~s
5
1.3 1.3.1 1.3.2 1.4
Mathematical Models of the Extraction Process Mechanistic Models ~ Empirical Models Literature Survey on the Control of Extraction Columns
1.2
2.
• 3.
4.
1
Apparatus, Control Objectives, and Step Tests 2.1 Reciprocating Plate Extraction Column 2.1.1 The Extraction System and the Experimental Apparatus. 2.1.1.1 Measurement Devices 2.1.1.2 Auxiliary Control Elements ---2.2 Distributed Computer System 2.3 Control Objectives 2.3.1 The Controlled and Manipulated Variables 2.4 Step Tests Steady State Behaviour of the Extraction Process 3.1 Hydrodynamics of ~he Column 3.1.1 Background Information on the Hydrodynamics of the,Karr Column Experimental Procedure 3.1.2 3.1.3 Results and Discussions Mass Transfer Characteristics of the Column 3.2 3.2.1 Simulation Results and Discussion 3.3 ConclusIOns Pertinent Control Theory 4.1 Stochastic Controllers 4.1.1 Prolegomenon to Control 4.1.2 Optimal Controllers 4.1.3 Self -Tuning Regulators 4.1.3.1 General Introduction 4.1.3.2 Clarke-Gawthrop Self-Tuner 4\1.3.3 Some Problems Associated With the Estimation 'Algorithmn . vi
•
7 II
12 13 III 'Ill 22
24 26 .27
29 30 31
35 35 35 40 41 44 49 51
53 53 53 57 61 61 b4 71
~
,
4.2 4.3
5.
Dahlin Controller 73 --Multivariable Systems and Interaction Measure--~ 77
Control Studies on Holdup Alone 5.1 Mod~ ling the Sys tem 5.2 ResuT"" and Di~cussions 5.2.1 Servo Control of the Holdup Under No Mass Transfer Conditions 5.2.2 Servo Control of the Holdup Under Mass Transfer Conditions 5.3 Conclusions
80 80 85 85 93 96
6. , Control of Extract Concentration by Manipulating the Frequency of Recipr~cation; Cascaded Control •The Control Scheme 6.1 6.2 Experimental Procedure 6.3 Results and Discussions 6.3.1 STR-STR Cascade Arrangement 6.3.2 Performance of a PI Outer and STR Inner Control Arrangement 6.4 Conclusions
1.
8.
Control of Extract Concentration by Manipulating Continuous Phase Flow Rate; SISO and MIMO Case 7.1 Experimental Identification of the System, Step Tests 7.2 Bristol Relative Gain Array for the Karr Column 7.3 Dahlin Controller 7.4 Results and Discussions 7.4.1 Control of Extract Concentration by Manipulating Continuous Phase Flow Rate; SISO case 7.4.1.1 Servo Control· 7.4.1.2 Regulatory Control 7.4.2 Control of Extract Concentration Along With Holdup Control; MIMO Case 7.4.2.1 Regulatory Control 7.4.2.2 Servo Control 7.5 Conclusions
97 99 100 100 101 108 III
113 114 116 117 119 120 120 125 125 129 132 135
Conclusions and Recommendations for Future" Work 8.1 Conclusions 8.2 Recommendations
137 137 140
References
142
G\;'
vii
L1ST OF FIGURES FIGURES
' TITLES
PAGE
1.1
Schematic diagram of
2.1
Holdup vs. frequency of reciprocstion.
2.2
Schemat~c
2.3
Holdup response to a step change in the frequency of reciprocation. (U d a .32 cm/s, Uc - 0.4 ern/s, f: 1.9+2.3 Hz.
32
Extract concentration response to a step change in the frequen~y. of reciprocation. (U d - 0.3 ern/s, Uc - 0.32 cm/s, f: 1.3+2.3 Hz.)
32
Holdup response to a step change in the continuous phase flow rate. (Ud a 0.32 cm/s, f - 2.0 Hz, Uc : 0.4-1().55 . cm/s).
34
Extract concentration response to a step change in the continuous phase flow rate. (U d - 0.32 cm/s, f - 2 Hz, U: 0.4+0.55 cm/s). c '
34
2.4
2.5
2.6
differe~tial
shell balance.
10
19
diagram of the experimental apparatus •.
3.1
ComparJ.son between observed and calculated holdup values. 42
3.2
Typical data compared with mod~l. (U d - 0.26 em/s, Uc - 0.33 cm/s, x data points without mass transfer, model p~ediction (~ - 0.233)).
42
Extract concentration vs. holdup. {Solid curve: U
