9th International Conference PROCESS CONTROL 2010
June 7 – 10, 2010, Kouty nad Desnou, Czech Republic
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CONTROL OF CHEMICAL PROCESSES USING COMPLEX
CONTROL STRUCTURES
KARŠAIOVÁ MÁRIA, BAKOŠOVÁ MONIKA, VASIČKANINOVÁ ANNA
Department of Information Engineering and Process Control, Faculty of Chemical and Food Technology,
Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia
tel. + 421 2 59 325 353, fax: + 421 2 52 496 469,
e-mail: ( maria.karsaiova,,monika.bakosova, anna.vasickaninova) @stuba.sk
Abstract: The paper compares two types of complex control structures and their using for control
of two types of chemical processes. The designed complex control structures are cascade control
and control with an auxiliary manipulated variable. A system of three serially connected tanks and
a distillation column are considered as controlled processes. These processes are influenced by
non-measurable disturbances. The distillation column represents also a process with slow
dynamics. The possibility to use both control structures for disturbance rejection is verified by
simulations. The advantages of using of complex control structures are compared with simple PID
control.
Key words: PID control, complex control structure, cascade control, auxiliary manipulated
variable, technological processes
1 INTRODUCTION
The performance of a control system is determined by the nature of the process, the
characteristics of the controller, and the location and magnitude of disturbances. When disturbances
are significant or dead time is very long, using conventional simple feedback control cannot be
effective. In these cases, more complex control schemes can be considered [Aström et all, 1994],
[Harriot, 1964], [Ogunaike, 1994].
2 CASCADE CONTROL
One of the best ways of using an additional controller to decrease upsets is to use the cascade control
(Fig. 1). Cascade control is one way to use several measured signals in a feedback loop with one
control variable. The system in Fig. 1 has two loops. The inner loop is called the secondary loop. The
outer loop is called the primary loop. The output of the primary controller is used to adjust the set
point w2 of a secondary controller, which in turn sends a signal to the controlled process. The process
output y1 is fed back to the primary controller, and a signal from an intermediate stage of the process
y2 is fed back to the secondary controller. The main advantage of cascade control is that the
performance is better for all types of load disturbances. For disturbances d2 that enters near the
beginning of the system, the secondary controller starts corrective action before output shows any
control error, and the error may be from 10 to 100-fold lower than with a single controller. For the
disturbances d1 that enters the last element of the process, the error integral may be reduced about 2 to
5-fold because the cascade system has a higher natural frequency [Harriot, 1964]. Figure 1 shows the
block scheme of cascade control of three serially connected tanks. Disturbances were represented by
pressure changes in the inlet pipe. The varying pressure involved flow rate fluctuations of the inlet
stream passing the regulatory valve. This pressure is 5 atm and it increases on 5.5 atm in time 50 min
and it decreases on 4.5 atm in time 100 min. Controlled variable is level h3 in the 3rd tank and
manipulated variable is opening of the regulatory valve ov. Steady state is represented by following
values of input and output variables: ovs = 40%, h3s = 0.64 m, valve constants k11= k22= k33 = 2.25 m2.5
min-1 and cross-sections of tanks F1 = F2 = F3 = 1 m2. Control accuracy δ was chosen 20% w, where w
is 1 m.
The first step in design of secondary and primary controllers was finding approximate models of the
three controlled tanks. The transfer functions describing the controlled process were identified from
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June 7 – 10, 2010, Kouty nad Desnou, Czech Republic
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the step response data by the Strejc method [Fikar et all, 1999] in the form:
G p (s ) =
q 0 (s )
h (s )
0.025 −0.82 s
1.1835
e
e −0.25 s
=
and G s (s ) = 3
=
3
ov(s ) (2s + 1)
q 0 (s ) (2.16 s + 1)3
where Gp represents the transfer function of the pipe and Gs is the transfer function of the system of
tanks. Than the standard procedure for cascade controller tuning was done. The secondary controller
was tuned at first to give a fast inner-loop response required for effective cascade control. Then the
primary controller was tuned with the inner loop in operation.
Figure 1 – Simulink scheme of cascade control system
Using various experimental methods and choosing the maximum gain, the secondary P controller was
tuned in the form GRP=230. Then the primary controllers were tuned as PI or PID controllers in the
1
1⎞
⎛
⎛
⎞
+ 0.69s ⎟ . The cascade control of tanks was
form G RH (s ) = 2.25⎜1 + ⎟ and G RH (s ) = 4.72⎜1 +
4
.
46
s
8
⎝
⎠
⎝
⎠
compared with control in a simple feedback control loops using PI controller
1 ⎞
⎛
G R (s ) = 15.62⎜1 +
⎟ . The criteria of quality was IAE and cascade control was better as simple
4.16s ⎠
⎝
feedback control loops. The comparison of two cascade control by IAE shows, that both cases are
convenient. Simulation results obtained using simple feedback control and cascade control are
presented in Fig. 2 and Fig. 3.
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June 7 – 10, 2010, Kouty nad Desnou, Czech Republic
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Figure 2 Control responses of a system of tanks using simple feedback (PI) and cascade (cascada)
control system with PI primary controller
Figure 3 Control responses of a system of tanks using simple feedback (PI) and cascade (cascada)
control system with PID primary controller
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3 CONTROL SYSTEM WITH AUXILIARY MANIPULATED VARIABLE
Figure 4 – Simulink scheme of control system with auxiliary manipulated variable
Control system with auxiliary manipulated variable can be used, when it is possible to split controlled
process onto two parts, the slow and the fast ones. Then, it is necessary to find two manipulated
variables, one influencing the slow part and the whole process and the second one influencing only the
fast part. Such control configuration allows speeding up the control response of systems with slow
dynamics or of time-delay systems. Disturbances will also be rejected faster then in a simple feedback
control loop. The additional auxiliary control signal is inserted between the actuator of the main
control loop and the controlled variable. Figure 4 shows the corresponding Simulink scheme. The
choice of the auxiliary variable must be done so that it avoids the slow part of the controlled process
and directly influences only the fast part of it. This control structure was used for control of the plate
distillation column, which serves for splitting the binary mixture benzene – toluene. The column has
25 plates, the feed plate is the 12th plate. The boiler efficiency is 100% and the plate efficiency is 60%.
The feed is supplied to column with molar flow rate nF = 22.5 kmol h-1, and the molar fraction of
toluene in the feed is xF = 0.23. The distillate composition represented by the molar fraction of toluene
xD is the controlled variable. The vapour flow rate nG represents the control input and can be
manipulated by the boiler heating. The reflux flow rate nL is auxiliary manipulated variable. The
steady state is represented by following values of variables: nGs = 30 kmol h-1, nLs = 22. 26 kmol h-1,
xDs = 0.667. The distillate composition is controlled with accuracy 3% from w and w is 0.85. The
appropriate models for controller tuning were obtained by identification from step response data. The
transfer functions describing the controlled process are in the following form:
x (s ) − 0.1056 −0.5 s
x (s ) 0.1132
GG (s ) = D =
e
=
and G L (s ) = D
nG (s ) (0.22s + 1)
n L (s ) (0.2 s + 1)
where GG is the transfer function of the slow part of the controlled process and GL is the transfer
function of the fast part of the controlled process. The controllers were tuned using various
1 ⎞
⎛
experimental methods and the PI controller with transfer function G R (s ) = −2.778⎜1 +
⎟ was
⎝ 0.22s ⎠
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9th International Conference PROCESS CONTROL 2010
June 7 – 10, 2010, Kouty nad Desnou, Czech Republic
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chosen for the simple feedback control scheme. In the control system with the auxiliary manipulated
variable, there were selected three combinations of controllers; the first one, where the main controller
1 ⎞
⎛
is PI controller with the transfer function G R H (s ) = −2.778⎜1 +
⎟ and the auxiliary controller is
⎝ 0.22s ⎠
P controller GR = 176.678. The second combination includes the main PID controller
1
⎞
⎛
G RH (s ) = −4.53⎜1 +
+ 0.145s ⎟ and the auxiliary P controller GR = 111.344. Simulation results
⎠
⎝ 0.476
obtained using simple feedback control and using control system with auxiliary manipulated variable
are presented in Fig. 5 and Fig. 6. The third case, the main controller was PI controller
1 ⎞
⎛
G R H (s ) = −2.083⎜1 +
and the auxiliary controller was also PI controller
⎟
⎝ 0.22s ⎠
1 ⎞
⎛
G R (s ) = 117.785⎜1 +
⎟ . Figure 7 shows the simulation results obtained for the third combination
⎝ 0.2s ⎠
of controllers. For control of a distillation column using simple feedback (PI) and complex control
system with auxiliary manipulated variable (CC) with PI-PI controllers
Figure 5 Control responses of a distillation column using simple feedback (PI) and complex control
system with auxiliary manipulated variable (CC) with PI-P controllers
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June 7 – 10, 2010, Kouty nad Desnou, Czech Republic
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Figure 6 Control responses of a distillation column using simple feedback (PI) and complex control
system with auxiliary manipulated variable (CC) with with PID-P controllers
Figure 7 Control responses of a distillation column
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4 CONSLUSIONS
It is clear from simulation results, that it is possible to improve control responses of controlled
processes significantly using more complex control structures especially in the presence of
disturbances. In such cases, the quality of control using simple feedback control systems is usually not
adequate. The cascade control is really often used in practice to improve control responses and to
reject load disturbances. The reason is that the controlled system has to have only one control input
and more measured variables. The control system with auxiliary manipulated variable is used rarely.
The reason is that it is not so easy to split the process onto the slow and fast parts and to find two
manipulated variables, one of them influencing the whole process and the second one influencing only
the fast part of the process. The presented methods and used simulation examples are involved in the
courses oriented on process control taught in the bachelor study at the DIEPC FCHT STU in
Bratislava.
References
ASTRÖM, K. J. ; HÄGGLUND, T. 1994. PID Controllers. Triangle Park : Instrument Society of
America, 343. ISBN 1-55617-516-7.
FIKAR, M.; MIKLEŠ, J. 1999. Identifikácia systémov. Bratislava : STU, 114. ISBN 80-227-1177-2.
HARRIOT, P. Process control. 1964. New York : McGraw-Hill, 374. ISBN 07-062785-5.
OGUNAIKE, B. A. 1994. Process dynamics, modeling, and control. New York : Oxford University
Press, 1259. ISBN 0-19-509119-1.
Acknowledgement
The authors gratefully acknowledge the contribution of the Scientific Grant Agency of the Slovak
Republic under the grants 1/0071/09, 1/0537/10 and the Slovak Research and Development Agency
under the project APVV-0029-07.
The authors gratefully acknowledge also the support by a grant No. NIL-I-007-d from Iceland,
Liechtenstein and Norway through the EEA Financial Mechanism and the Norwegian Financial
Mechanism. This project is also co-financed from the state budget of the Slovak Republic.
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June 7 – 10, 2010, Kouty nad Desnou, Czech Republic
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