NAMP
PIECE
Tier III
Open-ended problem
Module 5 – Controllability Analysis
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NAMP
PIECE
Tier III Statement of intent
The goal of this tier is to solve few real-life applications of
Controllability Analysis, in which the student must interpret the
results obtained from a range of Controllability Analysis tools. At
the end of Tier III, the student should be able to identify the
following:
Benefits of the use of Controllability Analysis tools
Potential cost saving opportunities from the use of
Controllability Analysis tools
Environmental impact reduction resulting from the
application of Controllability Analysis tools
How the application of Controllability Analysis tools can be
used to obtain an operable process
Module 5 – Controllability Analysis
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NAMP
3.1
PIECE
Doukas and Luyben reported the transfer function model for the
distillation column with a side stream product. The feed contains
benzene (B), toluene (T) and xylene (X), with the benzene in the
side stream of much less importance than the other controlled
variables.
The linearized transfer function model is:
 -1.986e-0.7s
5.984e -2.24s 
5.24e -60s


14.3s+1
400s+1
66.7s+1


-0.42s
-0.7s
-0.6s

 0.002e
2.38e
-0.33e
 XDT (s )  
2  RR (s )
2
2
 1 
 XS (s )    7.14s+1
1.43s+1
2.4s+1







 B =
-1.9s  LSu(s) 
-0.5s
-0.5s
-11.7e
4.48e
 XD X (s )  -0.176
  QB(s) 
2
 



12.2s+1
11.1s+1

6.9s+1
)
s
(
XB


 T 


-1.6s
-3.8s
-7.75s
-9.81e
-11.3e

 0.374e
2
 22.2s+1
11.4s+1 
21.7s+1




The process is shown on the next slide.
Module 5 – Controllability Analysis
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NAMP
PIECE
Distillation column with a side stream product.
RR (Ratio)
Feed flow
rate
XDT (mole fraction)
XSB (mole fraction)
LS (lb mol/ hr)
XSX (mole fraction)
QB (BTU/ hr)
XBT
Determine the best loop pairing and calculate the Niederlinski Index
for each subsystem considered.
Module 5 – Controllability Analysis
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NAMP
3.2
PIECE
The transfer function model for a pilot scale binary distillation
column used to separate ethanol and water was given in TIER 2,
The process variables are (in terms of deviations from their
respective steady state values):
y1 = overhead mole fraction ethanol
u1 = overhead reflux flowrate
y 2 = side stream ethanol mole fraction
u2 = side stream draw-off rate
y3 = Temperature on Tray #19
u3 = reboiler steam pressure
 0.66e-2.6s

6.7s+1

y
 1
-6.5s
 y  =  1.11e
 2   3.5s+1
 y 3  
 -33.68e-9.2s

 8.15s+1
-0.61e-3.5s
8.64s+1
-2.3e-3s
5s+1
46.2e-9.4s
10.9s+1
Module 5 – Controllability Analysis

-0.0049e-s

9.06s+1
 u 
  1
-0.012e-1.2s
 u2 
7.09s+1
 u 
0.87 11.61s+1 e-s   3 

 3.89s+118.8s+  
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NAMP
PIECE
Distillation column used in separating ethanol and water
Overhead mole
fraction ethanol (y1)
Temperature on tray #19 (y3)
Feed flow rate (d)
Overhead reflux
flow rate (u1)
Mole fraction of ethanol in
the side stream (y2)
Reboiler steam
pressure (u2)
Design a steady state decoupler using the generalized approach,
with GR(0) chosen as Diag[G(0)].
Module 5 – Controllability Analysis
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NAMP
3.3
TH1
PIECE
S.G.Oliveira and F.S.Liporace [3] have obtained the Gain Array for the
HEN showed below, where the manipulated variables are f1, f4, f5 , f7
and f8 should be used to control the outlets temperature TC1,TH1,TH2.
C1A
C1
HE 1
Q1 A1 TD1
f1
300 K
C1B
TH2
T1
395 K
365 K
f4
C2
m1
HE 2
Q2 A2 TD2
T6
m5
C1A1
400 K
T5
C1B1
398 K
Module 5 – Controllability Analysis
T2
H1
HE 3
Q3 A3 TD3
f5
T3
575 K
m4
TC1
C3
358 K
m8
T4
f7
HE 4
Q4 A4 TD4
T7
m7
f8
718 K
H2
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NAMP
PIECE
The gain array obtained for the system is:
 17.483 4.733 6.267 11.652 8.088 

K=  45.778 5.133 6.867
0
0

 25.39
0
0 90.851 63.143 
f1
f4
f5
f7
TC1
TH1
TH2
f8
Choose the best pairing, using the RGA and SVD.
Module 5 – Controllability Analysis
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PIECE
References
[1] Wood, R,K. and M.W. Berry, “Terminal Composition
Control of a binary distillation column,” Chem. Eng. Sci.,
29, 1808 (1973).
[2] Ogunnaike, B. A., J.P. Lemaire, M. Morari, and W.H. Ray,
“Advanced multivariable control of a pilot plant distillation
column”, AICHE, 29, 632 (1983).
[3] Oliveira, S.G., Lopirace, F.S., Araujo, O.Q.F. et al. The
importance of control considerations for heat exchanger
network synthesis: a case study. Braz. J. Chem. Eng., June
2001, vol.18, no.2, p.195-210. ISSN 0104-6632.
[4] Ogunnaike, B. A. and Ray, W. H., Process Dynamics,
Modeling and Control, Oxford University Press, New York
(1994).
[5] Marlin, T. M., Process Control Designing Processes and
Control Systems for Dynamic performance, McGraw-Hill,
United States of America (1995).
Module 5 – Controllability Analysis
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