3160
Ind. Eng. Chem. Res. 1994,33,3160-3167
PROCESS DESIGN AND CONTROL Nonlinear Model-Based Startup and Operation Control of a Distillation Column: An Experimental Study Massimiliano Barolo,*G. Berto Guarise, Sergio A. Rienzi, and Antonio Trotta Istituto di Impianti Chimici, Universith di Padova, via Marzolo, 9,I-35131 Padova PD, Italy
A nonlinear model-based control law has been derived within the globally linearizing control structure in a differential geometric setting, and it has been applied for the startup and operation control of a pilot plant distillation column. The control algorithm is computationally inexpensive and has been implemented by using a personal computer via the RS232C standard interface. Experimental results confirm that the proposed algorithm allows fast column startup as well as effective disturbance rejection and servo operation without the need of further controller tuning when switching from startup control to operation control. The superior performance of the proposed control algorithm over a conventional linear controller has been experimentally shown to result from the presence of the model term i n the control law.
Introduction The startup of a continuous process is known to represent a very challenging control problem, because the wide range of operating conditions encountered during startup often makes the use of linear controllers inadequate. During startup there is no appropriate point for local linearization, and to ensure stability over the whole range of operating conditions linear controllers must be significantly detuned, so that the control system performance may be severely degraded. Because of these features, nonlinear control proves to be an attractive tool in order to provide effective control of such a batch process. The highly nonlinear behavior of a distillation column during startup has been investigated by Ruiz et al. (1988) by simulation studies. These authors showed that the most critical phase during startup is the socalled “semicontinuous phase”, in which operation is switched from total reflux to specified reflux; in order to reduce instability problems, the switching may be carried out in steps and at the end of the phase the control system designed to maintain the column around the specific steady state is switched on. Experimental studies on automatic column startup can be traced back to the pioneering works of Stainthorp and West (1974) and Salrninen and Halmu (1977). More recently, Bertucco et al. (1984) used a conventional startup procedure t o show that the settling time can be significantly decreased by filling the reflux drum with feed mixture before starting up the column; the optimal switching time is found by the use of rules of thumb. Yasuoka et al. (1987) proposed a semiempirical characteristic function for determining the optimal switching time from total reflux to steady state operation; the optimal switching time is given fairly accurately by the time corresponding to the minimum in the characteristic function; however, the experimental results presented by the authors are very limited. Fieg et al. (1993) proposed t o continuously feed the column during the
* To whom correspondence should be addressed. E-mail:
[email protected]. 0888-5885/94/2633-3160$04.50/0
total reflux phase in order to reduce the startup time; unfortunately, for this mode of operation no minimum is observed in the characteristic function of Yasuoka et al. (1987), so that the switching time needs to be chosen heuristically. Barolo et al. (1993) developed a computational inexpensive model-based control law by using the generic model control (GMC;Lee and Sullivan, 1988) framework, which was able to track the column composition profile to the desired setpoint. Very recently, Ganguly and Saraf (1993) applied an improved nonlinear model predictive control (Eaton and Rawlings, 1990) to control a distillation column startup; due to the need of solving an on-line optimization problem, the computational demand of the control procedure proposed by Ganguly and Saraf (1993) is very high. None of the above works addressed the problem of developing a control algorithm that proves to be efficient for both column startup and column operation, without the need of further tuning when switching from startup control to operation control. This paper presents a nonlinear model-based control algorithm that allows fast column startup as well as effective disturbance rejection and servo operation. The control law is developed according to the globally linearizing control (GLC) framework of Kravaris and Chung (1987) in a differential geometry setting, and it is tested on a pilot plant facility.
Experimental Apparatus Pilot Plant Column (Figure 1). The distillation column consists of 30 sieve trays and has a diameter of 300 mm; tray spacing is 200 mm. A vertical shell-andtube thermosiphon reboiler (total exchange area 4.65 m2) is heated by the steam produced from an oil-fired steam boiler. A water-cooled total condenser of the shell-and-tube type (total exchange area 7.65 m2) is placed at the top of the column and provides subcooled liquid to the reflux accumulator drum (open to the atmosphere; total capacity 0.05 m3). The column may be run under a wide range of operating conditions. Typically, 150 L/h of a subcooled liquid ethanovwater feed ( ~ 2 8 % by weight EtOH) enters the column above 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 12,1994 3161
X Figure 1. Schematic of the pilot plant distillation column.
the eighth stage (numbering from the bottom) to give 90% by weight EtOH in the distillate and almost pure water in the bottoms, with a reflux ratio of around 3 (steady state). Temperature is measured along the column by means of eight resistance thermometer detectors (RTD’s)placed on trays 4, 8, 12, 16, 18, 22, 26, and 30; RTD probes also allow the measure of bottom, feed, reflux, and steam temperatures as well as temperature difference of cooling water across the condenser. Differential pressure cells are used to measure top and bottom levels. Pressure transducers provide the measure of steam pressure and pressure drop in the column. Feed, reflux, distillate, bottom, cooling water, and steam volumetric rates are measured by means of turbine meters. Electropneumatic valves control feed, reflux, distillate, bottom and steam flows. No facility is provided for feed and reflux preheating. Thus feed enters the column a t room temperature and reflux temperature is determined by the subcooling obtained in the condenser. Since the experimental runs have been performed over a wide period of time (spring through winter), marked differences were observed in both feed and cooling water temperatures. Moreover, due to the large amount of feed required to run a startup plus operation control test, it was impossible t o both ensure the same feed composition between tests and provide different feed compositions during the same test. For this reason, feed composition was allowed to vary in the range 25-30 wt % EtOH during the whole experimentation, so as to take a reasonable feed composition disturbance into account. Data Sampling and Control. The set of 23 analogue signals is sampled every 6 s by means of an IBM PS/2 80286 PC (with mathematical coprocessor) via the standard RS232C port. Data are digitally filtered and
processed by the control routine, and finally control signals are sent to the control valves through the same interface. Filtering of distillate rate, pressure drop, and bottom level is provided by the modified first-order filter of Rhinehart (1991), whose tuning can be very easily obtained off-line as described by Barolo (1994);standard noise-spike filters are used for all of the other signals. DDC control algorithms are employed in all of the control loops. The whole routine for data sampling and process control has been written in MicrosoR QuickBasic 4.5 programming language. Tray 18 was chosen as the reference control tray because upper tray temperatures are not sensitive enough to composition and manipulated variable (reflux rate) changes.
Control Strategy Controller Model. The behavior of a distillation column during startup is somewhat similar to the one exhibited during normal operation by a column in which a sharp separation takes place. In fact, during startup the temperature profile moves up and down the column due to the large amount of disturbances that enter the column (feed and reflux inflows, reflux temperature and composition changes, product outflows). In order to cope with the large gain of conventional temperature control loop, it is necessary to reduce the feedback gain, so that the resulting control action may be sluggish (Barolo et al., 1993). Luyben (1972)pioneered a profile composition control strategy that allowed to greatly reduce the process gain, thus increasing the controller performance. The key idea of Luyben (1972) was to control the temperature profile position by scanning a number of thermocouples up and down the column. This idea was drawn on by
3162 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 the control affine system
30 28
26
y = h(x)
24 x
(3)
is exactly inpulioutput linearized. In eq 2, L@x) is the ith order Lie derivative of the scalar function q(x) with respect to the vector functionp(x), r is the relative order of the process, Pi’s are tuning parameters, and u is an “external” linear controller. According to the above model (11, the control law (2) is easily found to become
22
20 18
16 78
82
86 90 temperature [“C]
94
98
Figure 2. Dynamic temperature profiles for a -15% step disturbance given at t = 0 on feed volumetric rate (open loop).
Barolo et al. (1993),who obtained a very simple controller model by grouping a number of component dynamic balance equations into one dynamic equation. In this work, we use the same simplified dynamic process model, that is, when an external PI controller of the form
where NP is the control tray, NT is the top tray, D stands for distillate, V is the vapor mole rate, L is the liquid mole rate, Lo is the reflux mole rate, M is the liquid holdup, x is the liquid composition, and y is the vapor composition. In the above model, Cz\p(Mx)i is the controlled variable and Lo is the manipulated variable. The knowledge of zE\p(Mx), allows an easy evaluation of the temperature front position along the column. Figure 2 refers to a run in which a step change (-15%) has been assigned t o the feed volumetric rate in an open loop fashion starting from time t = 0 (steady state); as the heavy component front is moving toward the top of the column, the Zz;p(Mx), value decreases according to the igcrease of the area contained between the curves a t t = t and t = 0. The location of plate NP has been chosen according to the requirement of controller sensitivity, and keeping in mind that the closer one gets to the feed stage the better the controller speed of response is, since feed is a primary source of disturbances entering the process. The value of z,rJlfp(Mx),is related to the overhead composition in the same way the control tray temperature is related to the overhead composition in conventional temperature control. The simplified lumped model (1)has the advantage of being written in a control affine form, and of being of relative order 1with respect to the manipulated input. Moreover, the model is relatively accurate and flexible enough to account for the nonlinear behavior of the process (as will be shown experimentally), and is computationally very fast. Note that in model 1both feed and steam act like unmeasured disturbances. Control Law Formulation. Kravaris and Chung (1987) showed that under the static state feedback 11
is employed. In eqs 4 and 5 subscript “d” refers to the desired value. The superior range of performance of the GLC algorithm over the GMC one has been discussed by Barolo (1994a,b). The desired value of CETm(Mx)i can be easily found from steady state data or through numerical simulation in such a way as to correspond to the desired product composition, as is usually done in conventional temperature control. Startup Procedure. The main features of the startup sequence are the same as described by Ruiz et al. (1988) and by Ganguly and Saraf (1993). After the reboiler is filled with feed mixture, the reboiler is heated up and vapor boilup is held constant throughout. When a sufficient amount of liquid has accumulated in the reflux drum, reflux and feed are introduced into the column and bottom level control is set on. Operation proceeds in a total reflux mode until all of the plates have been filled with liquid; this can be easily detected by checking total pressure drop in the column. When all of the plates have been filled with liquid, the computation of reflux rate according to eq 4 is started, but the GLC controller is not switched on if the calculated value of Lo,d hits the upper constraint to which reflux is subject. When this constraint is fulfilled, the GLC controller is set on, a reflux flow controller is cascaded to the GLC controller, and distillate is withdrawn by the top level controller. The setpoint of the reflux flow controller is updated by eq 4 once every seven sampling intervals. Once the steady state is attained, the same controller is used for operation control. On-Line Estimation of Unmeasurable Variables. The on-line estimation of unmeasurable variables is performed by using the same models described by Barolo et al. (1993), with the only exception of distillate composition which is set equal to ~ N during T the whole operation in order to avoid numerical instability problems.
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3163 110
110
1
l a )
bottom ----
-
100
_x--
Y
2 90 3
s 80
c .
n
E
c.
30 70
I 70
60 5 10 15 20 25 30 35 40 45 50 55
0 0.30 0.27 Y
5.- 0.24 b
> m
1 Ill/ 10
0
20
r
30
40
50
60
70
80
time [min]
time [min]
0.30
1b)
= I 0.27
Y
0.238
m
0.238
Z f
p 0.21
E
g
c.
0.18 0.15
0.15 0
5 10 15 20 25 30 35 40 45 50 55 time [min]
250
= 200 2
5
150
g -f
100
>
50
E .-0 0
t"
i;
reflux
I
1
I
"---distillate
0 0
5 10 15 20 25 30 35 40 45 50 55 time [min]
Figure 3. GLC-controlled column startup. (a) Temperature profiles (the numbers on the curves indicate tray number); (b) controlled variable; ( c ) manipulated variable and distillate rates.
Results and Discussion Preliminary tuning of the GLC controller was performed by using a detailed mathematical model of the column according to the guidelines outlined by Soroush and Kravaris (1992) and by Barolo (1994b). The values of the tuning parameters were subsequently adjusted on the plant for fully satisfactory performance, getting PO = 1,PI = t~= 10.5 min, and& = 8.37. These values have been used throughout all the experimental runs presented here. Startup Control. Figure 3a shows typical trends of the temperature profiles in the column during startup. The controlled variable is plotted in Figure 3b. Zero time corresponds to the instant in which steam is supplied to the reboiler. Temperatures move fast and
1 0
10
20
30
40
50
60
70
80
time [min]
Figure 4. PI-controlled column startup. (a)Temperature profiles (the numbers on the curves indicate tray number); (b) controlled variable.
smoothly to their steady state values. The GLC controller acts quite aggressively on the reflux rate (Figure 3c): immediately after plates are sealed (total reflux operation), the reflux rate is dramatically decreased by the GLC controller in order to allow the light component move toward the top of the column; this causes a small temperature overshoot on plate NP, which is in fact promptly damped by the controller. It has been verified that the temperature overshoot can be eliminated by slightly modifying the startup procedure, that is by introducing the feed only after the sealing of the plates, but in this case the settling time is increased (Barolo, 1994b). The contribution of the control law model term on the performance of the GLC controller is shown when the column is started up by using a PI algorithm to control C ~ ~ p ( M x By ) i .neglecting the model terms in eq 4, one gets a PI controller whose tuning parameters are &,PI = KJPl and q p =~ TI. Field test runs confirmed that, by using these parameter settings, the PI controller was able to compensate satisfactorily for step disturbances on the feed rate. Figure 4a shows that the cloumn is indeed driven t o the desired steady state, but the temperature overshoot during the startup is more marked than in Figure 3b, and the settling time is also increased (Figure 4b). On the other hand, due to process/model mismatch and measurement errors, the model term in the control law (4) was proved to be unable to remove the offset when the integral term was not used (Barolo, 199413). Disturbance Rejection. The ability of the GLC controller in rejecting a step disturbance assigned to the
3164 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 110
I
1
I
-I a)
bottom
100
A==-
- 4
.-
I
0.27
I
= 0.26
I
Y
11'
I
65 105
E
-
0.26
100
1
70
75
80
85 90 time [min]
1b)
95
100
bottom
105
I
I
I
25.0.25
0
10 20 30 40 50 60 70 80 90 100 110 time [min]
Fz
2 200
1
al 0
L
170
-E
.- 150 L
1 100 0 >
c
2 50
140 E
1 E
0
110 c
I
E
I I ' , '
0
l
"
'
l
'
~
al c
I
x
-s Y
I
L
-Y----
75
1
u)
80
10 20 30 40 50 60 70 80 90 100 110 time [min]
Figure 5. GLC controller performance on the rejection of a +lo% step disturbance on steam mass rate. (a) Temperature profiles (the numbers on the curves indicate tray number); (b) controlled variable; (c) manipulated variable and steam rates.
steam rate is evidenced in Figure 5 . After the column was started up, a 10% increase was imposed to the steam mass rate starting from minute 79 (Figure 5c): the reflux rate is immediately increased by the controller, and the controlled variable is promptly set back to the desired value. Again, the model term contribution in the control law (4)can be evidenced when a PI algorithm is used to control Cfj_TNP(Mx),.For the same disturbance as in the previous figure, the controlled variable response is very poor (Figure 6a) and the temperature profiles hardly seem to settle down (Figure 6b). Figure 7 shows the controller and column response to two step changes in the feed volumetric rate. Despite the severeness of the disturbance, the controller performance is very good.
-
22 26
65
- 200
250
1
80
l
70
75
l
l
80
l
l
l
85 90 time [min]
30 "
'
95
1
'
100
1 105
Figure 6. PI controller performance on the rejection of a +lo% step disturbance on steam mass rate (minute 70.2).(a) Controlled variable; (b) temperature profiles (the numbers on the curves indicate tray number).
Servo Behavior. A change in the desired product specification is usually specified by changing the control tray temperature setpoint. According to the process model (11, this can be alternatively done by changing the target setpoint cfJ_TNp(MX)z,d. With reference to Figure Ba, after the column was started up, the target setpoint was changed (minute 70.2) from 0.238 to 0.244 kmol: the light component content in the top plates of the column is increased by the controller, and the new steady state is rapidly attained. Then (minute 90.3) the cETT,(MX)c,dvalued was suddenly decreased to 0.232 kmol: the controller promptly pushes the heavy component up to the column, and temperatures quickly settle to their steady state value (Figure 8b). When a PI controller is used to force the column to a different steady state, the settling time significantly increases (Figure 9), thus confirming that the model term in the control law allows the controller to better cope with process nonlinearities. On the other hand, the effects of process/model mismatch, as well as of measurement errors, are clear when two "symmetrical" step changes in the Zz%p(MX),,d values are considered (Figure 10). Even if the choice of TI = ,&/PO should be able to guarantee an "overall" closed loop first-order response (Barolo, 1994a1, this is not observed experimentally. Nevertheless, a certain degree of "linearity" is still preserved in the overall closed loop response, as is evidenced by the fact that the CzNp(Mx),responses are "almost~'symmetrical. Effect of Increasing the Control Interval. The linearizing state feedback (2) is continuous in nature,
Ind. Eng. Chem. Res., Vol. 33,No. 12,1994 3165 105
0.27 bottom
100
-E
a)
95
-ssn 90 i
n m L m
.-
-
0.24
a,
f 85
ec
w
c)
0.22
0
80
0.21
75
0.20 55
60 65
70
E
I
1
60
a 0.26
v
1
75 80 85 90 95 100 105 time [min]
0.27
n
4
= 0.26 i
a)
105
I
100
c
1 65
70
75
80 85 90 time [min]
95
100 105
I
bottom
0.25
Q
:.
m >
'p
-
0.24 0.23
8c 0.22 Q
0 0
0.21
i
0.20
I
'
80 I
'
I
'
I
'
I
'
I
'
I
'
I
'
I
'
I
75
'
~
'
60
250
-f 220
reflux
~
1
65
'
1
70
1
1
75
~
1 .' ',261
80 85 90 time [min]
'
1
95
22 30 '
1
'
1
'
100 105
Figure 8. GLC controller servo behavior for two step changes of the controlled variable setpoint. (a) Controlled variable; (b) temperature proiiles (the numbers on the curves indicate tray number).
I
2,
0.27
;190
= 0.26
E
E-
.-0
2 160 a,
n
0.25
I I
-s
:.
m >
130
'p
-
I
0.238
a,
0.24
0.232
0.23
P)
100
55 60 65 70 75 80 .E5 90 95 100 105 time [min]
Figure 7. GLC controller performance on the rejection two step diskrbances on feed volum&c rate. (a)Temperature profiles (the numbers on the curves indicate tray number); (b) controlled variable; (cj manipulated variable and feed rates.
so that it is interesting to show the effect on controller performance of an increase in the control interval. The results obtained for the startup control when the L o , d value is updated once every 14 sampling intervals are shown in Figure l l a . Repeated oscillations are observed in the central section of the column, as a result of the reduced contribution given by the model term in the control law. Controller performance is partially degraded also in servo problems (Figure l l b ) .
Conclusions A nonlinear model-based control law has been derived within the GLC control structure and has been applied for the startup and operation control of a pilot plant
g c
0.22
0
0.21 0.20
n~ 68
71
74
77
80 83 86 89 92 95 time [rnin] Figure 9. PI controller servo behavior for a step change in the controlled variable setpoint.
distillation column. The control algorithm is computationally inexpensive and can be easily implemented on a cheap personal computer. Controller tuning can be preliminarily performed by using a detailed mathematical model of the process, but the values of the tuning parameters need t o be subsequently adjusted on the plant for fully satisfactory performance. Column startup is fast and smooth and disturbance rejection is very good. The control algorithm can also easily handle servo problems. The superior performance of the proposed control algorithm over a conventional linear controller has been experimentally shown to result from the presence of the model term in the control law,
3166 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994
7
0.26
=
g
-I 0.25 -
I
0.244
I
Y
the desired specification, further research needs to be addressed on studying the effect of processlmodel mismatch and measurement errors on the possibility of decoupling the control actions. On the other hand, for multicomponent mixtures temperature is not uniquely related to composition and the proposed model is no longer valid.
Acknowledgment -
I
0.21
I
0
5
I
I
10
15
'
25
20
30
time interval [min] Figure 10. Impact of modeling inaccuracies and measurement errors on the GLC response to two step changes in the controlled variable setpoint. Dark curves correspond to the theoretic responses of a first order system with gain 1 and time constant
Pi&.
110 100
70 60 0
10
20
30 40
50
60
70
80
90
time [min]
0.27
4
0.25 a
-
E
1
ib)
= 0.26 0
'
0.238
-
gc 0 0
0.22
1-
0.21
I
0.20 1 100 !
~
l
l
105
'
l
110
'
l
115
Financial support granted to this work by the Italian National Research Council (CNR, Progetto Finalizzato Chimica Fine) is gratefully acknowledged.
1
'
1
120 125 130 135 140
time [min] Figure 11. Impact of an increase of the control interval on the GLC controller performance. (a) Temperature profiles during column startup (the numbers on the curves indicate tray number); (b) controlled variable response to a step change in the desired setpoint.
Since no further tuning of the control algorithm is necessary when switching from startup control to operation control, the proposed approach is believed to significantly reduce the time expense connected with controller tuning. This study is limited to single composition control in a binary distillation column. Though the proposed approach is still valid when implementing a second control loop in order to maintain bottom composition to
Nomenclature D = distillate flow rate, kmoYs Kc = proportional gain of the external PI controller in the GLC control law = proportional gain of the PI controller LLq = ith order Lie derivative of the scalar function q with respect to the vector function p Lo = reflux flow rate, kmoVs M = tray liquid holdup, kmol t = time, s u = process input V = vapor flow rate, kmoYs u = input of the linearized process 3c = liquid mole fraction of the light component y = vapor mole fraction of the light component
Greek Symbols pi = GLC design parameters, eq 2 E = error, eq 5 TI = reset time of the external PI controller in the GLC control law, s TI,PI = reset time of the PI controller, s 1 ~ '= transformation, eq 5 Subscripts and Superscripts d = desired value D = overhead product i = tray number NP = control tray NT = top tray r = relative order of the output with respect to manipulated input Acronyms GLC = globally linearizing control GMC = generic model control PI = proportional-integral
Literature Cited Barolo, M. On the Equivalence Between the GMC and the GLC Controllers. Comput. Chem. Eng. 1994a, 18, 769-772. Barolo, M. Model Based Startup and Operation Control of a Distillation Column. Ph.D. Dissertation, Istituto di Impianti Chimici, Universita di Padova, Italy, 1994b (in Italian). Barolo, M.; Guarise, G. B.; Rienzi, S.; Trotta, A. On-line Startup of a Distillation Column Using Generic Model Control. Comput. Chem. Eng. 1993,17 (S), 349-354. Bertucco, A.; Guarise, G. B.; Rienzi, S.; Trotta, A. Computer Controlled Distillation Column Start-up. Proc. Italian-YugoslawAustrian Chem. Eng. Conf. 1984, 4th. Eaton, J. W.; Rawlings, J. B. Feedback Control of Chemical Processes Using On-Line Optimization Techniques. Comput. Chem. Eng. 1990,14,469-479. Fieg, G.; Wozny, G.; Kruse, C. Experimental and Theoretical Studies of the Dynamics of Startup and Product Switchover
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1429-1448. Stainthorp, F.P.; West, B. Computer Controlled Plant Start-up. Chem. Eng. 1974,Sept, 526-530. Yasuoka, H.; Nakanishi, E.; Kunigita, E. Design of an On-Line Startup System for a Distillation Column Based on a Simple Algorithm. Znt. Chem. Eng. 1987,27,466-472.
Luyben, W. L. Profile Position Control of Distillation Columns with Sharp Temperature Profiles. AlChE J. 1972,18,238-240. Rhinehart, R. R. Method for Automatic Adaptation of the Time Constant for a First-Order Filter. Znd. Eng. Chem. Res. 1991,
Received for review March 21,1994 Revised manuscript received August 4, 1994 Accepted August 15,1994@
30,275-277. Ruiz C. A.; Cameron, I. T.; Gani,R. A Generalized Dynamic Model for Distillation Column-111. Study of Startup Operations. Com-
put. Chem. Eng. 1988,12,1-14.
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Salminen, K K.; Halmu, A. Computer Controlled Start-up of a Distillation Column. Kemia-Kemi 1977,4,465-469. Soroush, M.; Kravaris, C. Nonlinear Control of a Batch Polymerization Reactor: An Experimental Study. AZChE J. 1992,38,
@
Abstract published in Advance ACS Abstracts, October 15,
1994.
