REV.CHIM.(Bucharest)♦ 69♦ No. 9 ♦ 2018 http://www.revistadechimie.ro 2585

Distillation Column Hierarchical Control

MARIAN POPESCU*Petroleum Gas University of Ploiesti, Automatic Control, Computers and Electronics Department, 39 Bucuresti Blvd., 100680,Ploiesti, Romania

This paper treats the problem of hierarchical control of a butylene-butane distillation column (BBDC). Ahierarchical control system with three levels is proposed for BBDC. First hierarchical level, which is representedby the column with its conventional automation, is simulated and the results led to the idea of using adecoupler for the process crossed channels. Thus, it is proposed a nonlinear decoupler which determinesautomatically its parameters and type. At the second hierarchical level are implemented two internal modelcontrollers for the top and bottom concentrations. Finally, the third hierarchical level consists of an optimalcontrol system for the butylene-butane separation process.

Keywords: distillation column, nonlinear model, hierarchical control, decoupling, internal model control,optimal control

Distillation is one of the most important processes forseparating large multicomponent streams into high purityproducts. These processes are large consumers of energywith about 3% of the total energy consumption in the world[1]. This amount of energy is introduced in the bottom ofthe column and approximately the same amount isremoved in the top, but at significantly lower temperature,which makes this process one of the most effective forthe separation of mixtures [2].

Operation methods of distillation columns directly affectthe product quality, production rates and utility usage.Hence suitable control of the distillation tower is veryimportant from an economic viewpoint [3]. One of themost important objective for a distillation column is toimprove performance by minimizing costs to obtain aproduct at a specified quality [4], which is an optimizationproblem that usually refers to the activation of the purityconstraint for the most valuable product. This means thatas much as possible of the valuable product should beproduced, or in other words, the selling of this product atlow prices should be avoided [5].

Distillation processes complexity given by theirdimensions, the multiple objectives which they have tosatisfy, nonlinearity, restrictions etc., implies difficulties inmodeling and controlling these processes. In most casesa hierarchical approach can be the solution for this problem.Hierarchical control permits a decomposition of thecomplex systems control problem into a series ofsubproblems with lower complexity, which are easier tosolve and can be organized as a hierarchical structure [6].

The distillation process analyzed in this paper is thebutylene-butane separation process whose purpose is toseparate a mixture composed of isobutane, isobutylene,n-butane, cis- and trans-butylene in two productsconsisting mainly of isobutane and isobutylene at the topand mainly of the other three components at the bottom ofthe column in which the process takes place.

The paper proposes for the butylene-butane distillationcolumn a hierarchical control system with three levels:first level is associated with conventional automation,second level is the advanced control level, and the thirdlevel is dedicated to optimal control. In the following willbe presented the characteristics of each hierarchical level.

First hierarchical levelAccording to [7], the most suitable control configuration

for the butylene-butane distillation column is LB structure* email: mpopescu@upg-ploiesti.ro

(presented in fig. 1) which represents the first level of thehierarchical control system. This structure assumes thatthe top pressure and levels in the reflux drum and in thecolumn bottom are controlled. What remains is acomposition control problem with two variables, namelythe concentrations xD (at the top) and xB (at the bottom)for whose control are used the reflux flowrate (L) andbottom product flowrate (B) respectively.

Fig. 1. LB control structure

The column was simulated in SIMULINK®, themathematical model for the column incorporated in thesimulator being a nonlinear one [8, 9] based on equationsof liquid-vapor equilibrium and total and componentmaterial balance, similar to the ones described in thefollowing.

For the tray K of the column, the material balance canbe written

(1)

A component material balance for tray K is given byrelation

(2)

The liquid-vapor equilibrium is given by Fenske’sequation for binary mixtures with constant relative volatility

(3)

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Using the relation

(4)

and taking into account relations (1) and (2) the followingequation is obtained

Relation (5) is the most used differential equationassociated to mass transfer and is used to calculate theconcentration xK.

In order to utilize the above mentioned model, thecolumn was considered a pseudo-binary one with xD theconcentration of the mixture isobutane + isobutylene inthe top light product and xB the concentration of the samemixture in the bottom heavy product. The simulator wasconfigured and validated based on industrial data(flowrates, levels, compositions, design data of the columnetc.) obtained from a refinery. The initial data used for thesimulation of this column is presented in table 1.

The most important aspect of the results from figures 2and 3 is that the process presents interactions on thecrossed channels, namely the concentration xB isinfluenced by control agent L and also control agent B hasan effect on concentration xD. Consequently, before theimplementation of the second hierarchical level, adecoupler is designed in order to reduce or eliminate theseinteractions.

Control loops decoupling for BBDCAfter closing pressure and levels control loops (fig. 1)

the butylene-butane distillation column becomes a 2x2multivariable system (with two control agents-L and B -available for control of the two concentrations - xD and xB).As stated above, a decoupler must be designed to diminishthe influence of L on xB and the influence of B on xD.

The system consisting of the column and the decoupleris presented in figure 4 where it is considered that controlsignal c1 has an effect only on xD and control signal c2influences only xB.

(5)

Table 1INITIAL DATA FOR BBDC

SIMULATOR

The simulation of this column consisted in most part inchanges of the control agents L and B and recordings ofthe top and bottom concentrations (xD and xB) timeevolutions. Figure 2 shows the evolution of xB to a changein reflux flowrate and figure 3 presents the evolution of xDto a change in bottom product flowrate.

Fig. 2. Time evolution of concentration xB to a 3% change of L

Fig. 3. Time evolution of concentration xD to a -3% change of B

Fig. 4. Decoupling schemeThe proposed method of decoupling is based on a

decoupler with standard structure implementable in fourversions depending on process dynamic characteristics.The decoupler has two inputs and two outputs with unitgains on direct channels and at least two static channelsout of four.

The general form of the decoupler [10] is

(6)

Depending on the input-output channels dynamics thereare four types of the decoupler [11] obtained from thegeneral form (6) by analyzing the dynamic of the directchannels in relation to the crossed channels.

The decoupler gains (Kd) are obtained from the steady-state decoupling condition as ratios of correspondingprocess gains, and the decoupler time constants (Td) arecalculated as differences between process time constantson the appropriate channels for each of the four decouplertypes.

A first step in the design of the decoupler for the butylene-butane distillation column was the identification of theprocess gains (Kp) and transient times (Ttr) at stepvariations of the control agents L and B. Using relation Tp =Ttr / 4 are obtained the process time constants (Tp)necessary for the decoupler time constants calculation.

A selection of the variations of the process gains Kp andtime constants Tp on different channels according to controlagents (L and B) variations is shown in figures 5-6.

This phase of the decoupler design consisted inapproximation of the process gains and time constantsdependencies on control agents’ variation by determiningthe degrees of polynomial regression functions so that thebest possible approximation is achieved, as it can be seenin figures 5-6. Using these regression functions, processgains and time constants can be calculated for variationsof L and B other than the considered ones [12].

Using a function developed in MATLAB® by the author,the values of Kp and Tp are calculated automatically

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depending on control signals variations, by interpolation(when c1 and c-2 are within the initial considered ranges)or using the regression functions (when c1 and c-2 areoutside the initial considered ranges). Also, this functionautomatically determines the decoupler gains (Kd) and timeconstants (Td) and its type according to process input-output channels dynamics. Depending on the decouplertype, four decoupling schemes are implemented. Each ofthis scheme is chosen automatically and uses thecorresponding values of the parameters Kd and Td [12].

The system composed of the decoupler and thebutylene-butane distillation column was simulated inSIMULINK® to verify the effects of the decoupling oncrossed channels L- xB and B -xD.

Figures 7 and 8 show the time evolution of concentrationxD to changes of the second control signal and timeevolution of concentration xB to changes of the first controlsignal, with and without decoupler, where can be observedthe important effect of the decoupler on process crossedchannels. The decoupling offers the possibility of treatingthe concentration multivariable control system as twoindependent monovariable control systems, implementedat the second level of the hierarchical system.

Second hierarchical levelThe hierarchical control system with two levels

associated to BBDC is illustrated in figure 9.At the second hierarchical level (ACS – Advanced Control

System) are implemented two feedback internal modelcontrollers having as inputs the current values of the twoconcentrations and their set-points, and as outputs the set-points for the reflux flowrate and bottom product flowratecontrol systems. In this representation the decouplerproposed in section 3 is included in ACS.

Fig. 6. Variation of Tp depending on B variation on B - xD channel

Fig. 5. Variation of Kp depending on L variation on L - xD channel

Fig. 7. xB time evolution to a -6% change of c1

Fig. 8. xD time evolution to a -1% change of c2

Fig. 9. Hierarchical control system with 2 levelsThe block diagram of the hierarchical control system

with two levels is shown in figure 10.

Fig. 10. Block diagram of the concentration control system

As stated before the two controllers from figure 10 arebased on internal model control (IMC) method which willbe presented briefly in the following.

The main motivation of internal model control is basedon the principle that good control involves the inclusion inthe control system of a representation (implicit or explicit)of the process to be controlled [13].

The standard internal model control method used in thisresearch has as main characteristic the fact that at stepset-point the control signal has also a step form [14]. Forthe system to be tunable, in the controller structure wasincluded a proportional element with gain KC whosestandard value is 1.

A stable and overdamped process, characterized by gainKp, transient time Ttr and dead time Tm, can have associatedthe model [14]

(7)

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In practical applications model gain KM can beconsidered equal to process gain Kp, and the model timeconstant TM H≈Ttr/6 [14].

The standard internal model controller has four mainparameters, namely: three process parameters (Kp, Ttr, andTm) and a tuning parameter (KC).

The above described method can be used for processeswith overdamped response. As it can be seen from figure11 the process response on the direct channel c1 - xD isunderdamped with overshoot.

Fig. 11. Time evolution of xD to c1 change

In order to obtain an overdamped response on thischannel in series with the process a filter will be used [14]

(8)

The filter time constant Tf is determined so that theprocess response to be overdamped (without overshoot).

As a result of identification of the compensated process(filter + process) on channel c1 – xD the following valuesfor the model parameters were obtained: KM1 = 0.3, TM1 =43 min and Tm = 10 min. These values will be used asstarting parameters in the tuning of the controllerassociated to top concentration.

Fig. 12. Time evolution of xD to parameter KM1 changes

Fig. 13. Time evolution of xD to parameter TM1 changes

Taking into account the time responses of concentrationxD obtained at step changes of set-point, illustrated infigures 12 and 13, the best tuning parameters for topconcentration controller are: KC = 1, KM1 = 0.4, TM1 = 30min.

On c2 -xB channel the process response is suitable forthe application of the standard internal model controlmethod. The process parameters identified for this channeland used as starting parameters in the tuning of the bottomconcentration controller are: KM2 = 1.83, TM2 = 75 min, andTm = 10 min.

Fig. 14. Time evolution of xB to parameter KM2 changes

Fig. 15. Time evolution of xB to parameter TM2 changesHaving as purpose to obtain a response without

overshoot and a proper transient time, as it can be seen infigures 14 and 15, the best tuning parameters obtained forthe bottom concentration controller are: KC = 1, KM2 = 1.8,TM2 = 70 min.

In the following figures are presented the evolutions ofthe two concentrations at disturbances (F and xF) changes.

Analyzing figures 16 and 17 it can be observed that thetwo internal model controllers associated to theconcentrations xD and xB eliminate the errors caused bydisturbances modifications.

Fig. 16. Time evolution of xD to a 3% change in F

Fig. 17. Time evolution of xB to a 3% change in xF

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The results from this section lead to the conclusion thatthe used internal model control method is robust for bothset-point and disturbance changes. The obtained resultsare also confirmed by [15-17].

Third hierarchical levelThe hierarchical control system with three levels for the

butylene-butane distillation column is presented in figure18.

The control system from the third hierarchical level isan optimal control system for the butylene-butaneseparation process. The quality specification for the topproduct refers to the concentration of the isobutane +isobutylene mixture in the overhead product and is stiffwith value xD

i = 0.96 mole fr., and the specification for thebottom product which refers to the concentration of theisobutane + isobutylene mixture in the bottom product isflexible, xB

i ∈ [0.01…0.09] mole fr.The objective function at this level aims the optimal

recovery of the isobutane + isobutylene mixture in theconditions of an energy effort as low as possible:

(9)where: pricesteam - price of the steam [euro/kg]; ∆p –difference between the price of isobutane + isobutylenemixture and the price of n-butane + (cis- + trans)-butylene

Fig. 18. Hierarchical control system with 3 levels

mixture [euro/kg]; B – bottom product flowrate [kmole/min]; MMB – molar mass of n-butane + (cis- + trans)-butylene mixture [kg/kmole].

The term r·(F+L-B) represents (practically) the steamflowrate. Parameter r [kg/kmole] is the ratio between thelatent heat of vaporization of the mixture from the bottomof the column and the latent heat of condensation of thesteam.

The first term from relation (9) is associated to therecovery of the valuable product and represents thefinancial loss generated by the non-recovery of the valuablecomponent from the bottom product. The second termdefines the operating effort which refers to the steam usedin the reboiler. The optimal value of the set-point xB

i isobtained by minimizing the objective function.

At this level, the controller contains a controlmathematical model of the process, the objective function(9) and an algorithm to calculate the optimal value of xB

i.The representation of the objective function is shown in

figure 19.By solving the optimization problem it was obtained

= 0.0721 mole fr., value which is sent as set-pointfor the control system from level 2 (ACS), and to be moreprecise for the internal model controller associated toconcentration xB.

The block diagram of the hierarchical control system ispresented in figure 20.

The control system with three hierarchical levels wassimulated in SIMULINK® the results being presented infigure 21.

Figure 21 shows that when the set-point xBi is modified

the concentration xD practically is not influenced (due tothe presence of the decoupler), and the control systemassociated to the bottom concentration manages to bringxB to the optimal set-point value received from the thirdhierarchical level (represented by the optimal controller).

Fig. 20. Block diagram of the hierarchical controlsystem

Fig. 19. Objective function representation

Fig. 21. Time evolutions of concentrationsxD and xB to xB

i change

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ConclusionsThe purpose of this paper was to present the design of

the hierarchical control system for the butylene-butanedistillation column. The proposed hierarchical system hasthree levels: first level represented by the column with itsconventional automation, second level is the advancedcontrol level and the third level has implemented an optimalcontrol system.

The column with the conventional automation wassimulated and the results confirmed the fact that there arecrossed interactions between process channels. In orderto diminish these interactions a nonlinear decoupler wasdesigned. This offers the possibility of treating theconcentration multivariable control system as twoindependent monovariable control systems.

At the second hierarchical level two internal modelcontrollers were proposed for control of the top and bottomconcentrations (xD and xB). The internal model controllersproved their robustness to set-point and also todisturbances modifications.

The third hierarchical level was dedicated to optimalcontrol. At this level was proposed an objective functionwhich aims the optimal recovery of the isobutane +isobutylene mixture in the conditions of an energy effort aslow as possible. The controller from this hierarchical levelcontains a control mathematical model of the process,the objective function and an algorithm to calculate theoptimal value of xB

i.Future work could include the design of a hierarchical

control system for the whole plant from which the butylene-butane distillation column takes place.

NotationsMK - tray K liquid holdupLFK, VFK - external liquid and vapor feed flowrates of tray KLK, VK -flowrates of liquid and vapor which leave tray KxF_K -concentration of the light component in the external liquid feedof tray KyF_K -concentration of the light component in the external vapor feedof tray KxK - concentration of the light component in the liquid phaseon tray KyK - concentration of the light component in the vapor phase on trayKα - relative volatilityNT - number of theoretical traysNF-feed tray

F, xF – feed flowrate and compositionL, V – reflux and boilup flowratesqF – feed liquid fractionK – theoretical tray number (1 – bottom, NF - feed, NT - total condenser)

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Manuscript received: 8.09.2017