Eindhoven University of Technology

MASTER

Model Predictive Control of a binary high-purity distillation column

Oonincx, M.M.E.M.

Award date:1996

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7361

Eindverslag van de eerste fase opleidingINFORMATIETECHNIEK

Final report of the graduate projectINFORMATIONTECHNICS

Model Predictive Control ofa binary high-purity distillation colum

M.M.E.M. Oonincx

Industrial supervisor: Ir. J.H.J.M. BazelmansDSM-Servïces, Geleen (NL)

University supervisors: Dr. Ir. A.J.W. van den BoomProf. Dr. Ir. P.P.J. van de Boschfaculty ofelectrical engineering and information technicsTechnical university, Eindhoven

September 1995

Abstract

Model predictive control is a control method that uses a model to predict the futureconsequences of control actions. At every time step, this prediction is used to compute theoptimal control action, with respect to a certain criterion. Contrary to most conventionalcontrol methods, model predictive control is able to handle constraints on the processvariables. This report is the result ofan investigation about the applicability of modelpredictive control on a high purity, binary distillation column.

It appeared that the high purity, binary distillation process, is strongly interactive, badlyscaled and highly nonlinear. The statie behaviour of an extensive dynamic simulator based ona real column is significantly different from the statie behaviour of that real column. Thedynamie responses of the outputs to combined actions of the inputs can be intens.Conventional advanced process control is applied to the simulator in the fonn of a doublequality controller. This decoupling ofthe process works well in practice, but on the simulatorit is not able to control all the outputs at the same time.

A linear model predictive controller is applied to a simpIer computer model and appearedto be succesful. Tuning the controller parameters is very time consuming. Even more successwas obtained when a nonlinear model predictive controller was implemented. Such acontroller uses a nonlinear model to predict the effect of past and future control actions.Finding the optimal control actions is still a linear optimization problem, where the linearmodel is apdated. These adjustments are based on so called error through linearization.

From experiences with this application and reading many articles one can conclude thatmodel predictive control is a powerfull, general method. lts advantages, compared toconventional control, lie in controlling multi-input-multi-output processes with constraints onthe inputs and outputs. When there is a model-plant mismatch, the process is ill-conditionedor the process contains nonminimum phase behaviour, some precautions are to be taken,otherwise the model predictive controller will try to invert the process, which could lead toinstability. When the process is highly nonlinear, some nonlinear model predictive controllershould be considered.

2

Contents

1 Introduction , 5

2 Model predictive control 62.1 History and idea of MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62.2 Description of MPC 6

2.2.1 Modelling the plant and the observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82.2.2 The predictor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82.2.3 The optimizer 9

2.3 MIMü processes 102.3.1 Some remarks , 102.3.2 An example 11

2.4 Nonlinear MPC 142.4.1 Non-linear optimal control 142.4.2 Linearized optimal control 152.4.3 Iterative QDMC 16

2.5 An overview 18

3 Binary, high purity distillation 193.1 What is binary, high-purity distillation? 193.2 The processes 193.3 The equipment 223.4 The environment 253.5 The simulator 25

4 Modeling a binary, high purity distillation column 274.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 274.2 Statie models in Aspen 284.3 Statie behaviour ofthe C2-splitter and the simulator , 334.4 Dynamie modeling 364.5 Dynamie behaviour of the simulator and the Matlab-model . . . . . . . . . . . . . . . . . . .. 40

5 Controlling a binary, high-purity distillation column , 425.1 Tuning basic controlloops 425.2 Double quality control 445.3 Linear Model Predictive control 515.4 Nonlinear Model Predictive control 52

6 Applicabilty of MPC in chemical industry 546.1 In general . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 546.2 MIMü and nonlinear processes 54

7 Conclusions, discussion and further investigation 56

3

Bibliography 0 •••••• 0 •••••••••••••••••••••••••••••••••••••••••••••••••• 0 • • • •• 57

A An investigation to literature 0 •••••••••••••••••••••••••••••••••••••• 0 61

B Stepresponses ..... 0 •••••••••••••••••••• 0 •••••••••••• 0 • 0 • • • • • • • • • • • • • • • • • •• 69

C DQC results on the simulator 0 •• 0 • • • • • • • • •• 78

D MPC results on Matlab-model 0 • • • • • •• 87

4

I Introduction

This report is the result ofthe author's final project as a graduate student in technicalphysics and infonnation technies at the Eindhoven University of Technology. The project wascarried out at DSM in Geleen, from November 1994 until September 1995. It was part of aninvestigation about the applicability of Model Predictive Control at DSM, which was carriedout at the department CPC-APC (Centre for Process Control- Advanced Process Control).

Model Predictive Control (MPC) is widely used in oil industry, but not yet in chemicalindustry. Within CPC-APC, there was a need to know more about the applicability of MPCfor chemical plants. Some theoretical knowledge was present already, and the next step was toapply MPC at a plant, in order to learn more about the practical advantages and difficulties ofMPC. A high purity distillation column separating ethane and ethylene was chosen as anexample. This had several reasons. First, it seems to be a good example for MPC. Importantfeatures of MPC, such as constraint handling, play a role. Another advantage was that there isa rigorous simulator of the column available. The MPC controller could be tested on thissimulator first, before it would be applied to the real column. Another motivation to use thiscolumn is that there is a need for improvement ofthe control strategy. Especially in the casewhen the working area changes, the current control method is not able to keep the distillationproduets at their specifications.

The aim of this project was to implement an MPC controller at the simulator of thedistillation column, and to compare its perfonnance to the current controller. In a firstapproach in coorporation with Adersa, a French engineering company specialized in MPC, alinear model predictive controller named Hiecon was implemented. Hiecon controls theprocess, but the results are not satisfactory. During experiments it was found that thedistillation process was highly nonlinear. Statie and dynamic models were obtained to capturethe nonlinearities. In this report the statie and dynamie behaviour of the distillation process asweIl as some advanced controllers are designed. The results of the controllers are presentedand some general conclusions about the applicability ofMPC at DSM were to be drawn.

The remaining of this report is organized as follows. First, some theoretical backgroundsabout MPC and its nonlinear variants are given in chapter 2. Then, in chapter 3, distillation isoutlined. What are the processes and in what ofan environment does distillation occur ? Inchapter 4 the process is modelled statically and dynamically. The behaviour of a high-purity,binary distillation column is studied. In chapter 5 a double quality controller, a linear and anonlinear model predictive controller are applied to the column. Their results are presentedand finally in chapters 6 and 7 some general conclusions are drawn about the applicability ofMPC in chemical industry and the behaviour of the high purtiy distillation column.

5

Model predictive control

2.1 History and idea of MPC

The current interest in MPC can be tracked back to a set of papers that appeared in the late1970s. In 1978 Richalet et al. [20] described successful applications of 'Model PredictiveHeuristic Control' and in 1979 engineers from Shell outlined 'Dynamic Matrix Control'(DMC) [5]. Both algorithms use an explicit dynamic model ofthe plant to predict the effect ofpast and future actions of the manipulated variables on the output (Thus the name ModelPredictive Control). The future moves ofthe manipulated variables are found by optimizationwith the objective of minimizing the predicted error subjected to operating constraints. Theoptimization is repeated at each sampling time based on updated information (measurements)from the plant.

2.2 Description of MPC

People who want a more detailed description are advised to read the report of Van der Burg[24]. The theory ofmpc and some single-input-single-output (SISO) examples are outlinedthere in detail. In this chapter only basic ideas and important equations are viewed.

Consider a process with one or more inputs, one or more outputs, and zero or moremeasured disturbances. In MPC, a discrete time model of the process is used to predict theoutputs over a certain time horizon, for different sequences of control actions on the inputs.

Desired outputs (reference trajectory) are given, and the sequence of control actions thatgives the 'best' results is chosen. To decide what the 'best' control sequence is a criterion isgiven. From this control sequence the first control action of each input is applied to theprocess. Then, at the next time step, new measurements are available, and the same thing isdone again. Every time, only the first contoI action of the computed sequence is used. This isillustrated in Figure 2.1 on the next page: at time k, a control sequence u(k), u(k+1), ...,u(k+m-l) is determined such that the output over a horizon p tends to its setpoint (the dashedline) in a desired way. The input u(k) is applied to the process. At the next time point (thesecond graph), the output is measured, and it is different from what was predicted. A newcontrol sequence is determined, using the new information such that the new predicted output(indicated with *, the old one is indicated with 0) tends to its setpoint in a desired way.

Actually, it seems a very natural thing to do: one looks at the consequences of each controlaction, and determines an action based on these predicted consequences. However, thisrequires a lot of computation time at every time step. Due to this, MPC has become moreinteresting with the development of faster computers.

6

MPC is especially useful for processes with constraints on the inputs or outputs. MPC cantake these constraints directly into account. One should be careful in putting constraints on thevariables, especially on the outputs, since it may make the problem infeasible, and it alsotakes more computation time.

time=k

u(k+i)

k k+m

time=k+l

k+p

- - - - -~;s-'-'-lII! lil! lIIl )IE y(k+i+l)* ~ ~ ~* 0o

u(k+i+1)

k+l k+m+l k+p+l

Figure 2.1: Illustration ofModel Predictive Contra/.

In MPC three horizons have to be chosen: the model horizon n, the prediction horizon pand the control horizon m. The model horizon is the number of samples needed for a responseof a stabie output to reach a steady value on a step action on an input. The prediction horizonis the number of samples for which the prediction is computed. This horizon should be chosenlarge enough to incorporate all important effects. The control horizon is the number ofsamples over which the inputs may vary. After this period, the inputs are assumed to beconstant.

A model predictive controller can be constructed of the following parts:

*A model of the process* An observer to correct and update the state of the model*A predictor to predict the effect of past control moves and disturbances* An optimizer for finding the best control sequence.

7

All of these parts will be outlined. The MPC algorithm will be fonnulated in state-spacefonn. Later on it will be shown that an extension of linear MPC to nonlinear MPC is thereplacement of some of these parts by their nonlinear versions. Note that the theory ofMPCcontrollers is not limited to single-input-single-output (SISO) processes, but is especiallyattractive for MIMO processes. In the describtion of MPC the assumption of applicabilityonly to SISO processes is never made and if the text may suggests it one should bear in mindthat the intention is controlling MIMO processes.

2.2.1 Modelling the plant and the observer

Suppose that predictions of the output i Yi(k), Yi(k+1), ..., Yj(k+n-l) are available at time k.In these predictions the inputs, disturbances and measurements up to time k are taken intoaccount. Let's name this set ofoutputs together with similar sets for the other outputs the stateY(k). After the optimizer has calculated the best control sequence the first control move àu(k)of each input has to be applied and the state has to be updated, taking the control actions intoaccount. At the same time the prediction Y(k) has to be shifted, by multiplying with 'shift'matrix M, to get the prediction Y(k+1) containing the outputs at time k+1, k+2, ..., k+n.

In most of the original MPC fonnulations a stepresponse model of the plant is used topredict the future behaviour ofthe controlled variables. Stepresponse models give goodinsight in the process, although the number ofparameters can be plentiful. For a MIMOsystem with nu inputs and ny outputs we get a stepresponse matrix S with dimensions ny x nu inwhich the element Sjj is the response of output i caused by a unit step at input j.

State estimation is achieved by adding the difference between current measurements ymek)and the current predicted states y(k) multiplied by a filter F. In this report F contains thearbitrarily tuned 'filtergains' but it could also be a calculated Kalman filter. The currentpredicted state y(k) is just the first state of each output in Y(k). The matrix N selects thesestates.

The model can be represented in the following state space fonn

Y(k+l) = MY(k) + Sàu(k) + F[Ym(k) - y(k)]y(k) = NY(k)

2.2.2 The predictor

(2.1)(2.2)

The objective ofthe predictor is to generate a vector Yp(k+llk) ofpredicted open-loopoutputs over a horizon of p future time steps, the prediction horizon. This prediction vector isthen used as an input to the optimizer. The predictor is described by the following equation:

(2.3)

where Mp is also a shift matrix, which selects just the first Pi states of output Yi (Pi 5: nj).

8

2.2.3 Tbe optimizer

The optimizer finds a control sequence that optimizes an objective function. As objectivefunction

J = min { Ilry [Ym(k+llk) - R(k+llk)]f + IlrdU dU(klk)1I 2} (2.4)

dU(klk)

is used where dU(klk) is the optimal control sequence computed at time k for m future inputmoves (mi is the input horizon for input i and mi s: min(p). Ym(k+11k) is a vector of outputspredicted at time k, over a horizon of p future time steps, including the effect of the m futureinput moves. R(k+11k) is a vector describing the desired output trajectory (setpoints). Finallyr y and r 4U are weighting matrices.

To this objective function several terms can be added. If the process allows it one can addlimits or setpoints to the inputs as weIl. Even economic or environmental objectives can beadded. The weigth matrices determine the 'value' of the different objectives.

When there are no constraints neither on the output nor on the input, the least squaressolution to this problem can be analytically calculated. Only the first move of each input isimplemented, and the resulting optimizer is a constant gain matrix Kmpc, which can becalculated off-line. The first control move of each input becomes

du(k) = K [ R(k + 11 k) - Y (k + 1Ik) ]mpc p

The algorithm is illustrated in Figure 2.2 on the next page.

In reallife processes however constraints are always present. Their importance hasincreased, because supervisory optimizing control schemes frequently push the operatingpoint towards the intersection of constraints. The main attraction of MPC is that theengineer/operator can enter the constraints directly and the algorithm will find the bestsolution satisfying all of them.

(2.5)

One can distinguish two kinds of constraints, i.e. soft and hard constraints. A 'solution' ofan optimizing problem with soft constraints is always found but the solution technique issensitive to local minima. An optimizing problem with hard constraints can be solved. Hardconstraints however might make the problem infeasible.

9

. Model :1,-- ~---------------- -t~_JOlII(--1

,-- ---~~---- 1 Y (k)

,~_u(k) ~ - ~~~ Plant ~---~-r~I :

! I I~.---.-----~ i

--I

iI

·i -

!

Optimizer Predictor Observer

Figure 2.2: The MPC algorithm based on stepresponses pictured in state space form.

2.3 MIMO processes

2.3.1 Some remarks

An advantage of MPC is that it can handle multi-input-multi-output (MIMO) processes.One needs a model that describes all relations between inputs and outputs and MPC willcontrol the process in an optimal way, making sure the constraints are respected.

Gelormino et al [13] report about a successful MIMO MPC application to achieve aneconomic and technical objective. A quotation: 'We describe the application ofMPC to alarge-scale, constraint-dominated problem: the minimization of combined-sewer overflows(CSOs) in the Seattle metropolitan area. The key decision variables are flowrates at 23locations throughout the sewer network. There are approximately 40 output variables thatmust he kept between lower and upperbounds. MPC reduces CSOs by 26%'.

Theoreticaly one can think of a MPC controller for a whole plant that predicts and controls.The outputs of certain processes are the disturbances of other processes. If one could design aMPC controller that controls both processes, it could predict the disturbances of someprocesses simply by predicting the outputs of other processes. What used to be an unknowndisturbance now becomes a known variabie, which value is predicted over a time horizon. SoMPC can take the necessary precautions knowing the major future disturbances. This is oneadvantage ofthe 'predictive' part of MPC.

10

There are cases with model-plant mismatch when a MPC controller does not perform weIl.There always is a certain mismatch between a real process and a model. The mismatch canhave various sources: uncertainties in the model parameters and the model structure,inaccuries of the actuators and measurement devices, etc.

Multi-variable systems introduce a special problem here, because the 'gain' of a multi­variabie process varies not only with frequency, but also with 'direction'. It is shown that if aplant is ill-conditioned irrespective of scaling, that the control performance is stronglyaffected by input uncertainty, in particular, when the controller is trying to invert the plant.The MPC controller is such a controller, especially, ifthe penalty weight on the input movesis low. Since there is always some input uncertainty, it should be clear that a MPC controlleris potentially bad when used for an ill-conditioned plant. The binary, high-purity column willappear to be such an ill-conditioned plant.

2.3.2 An example

Now let's look at a MIMü two by two process. The model and the process are bothdescribed with the same four stepresponses shown in Figure 2.3. For this process two MPCcontrollers are designed. In experiment 1 there are no constraints and there is almost noweight on the control moves. In experiment 2 the weight on the control moves is increasedand the outputs and inputs are limited. The constraints are

o ~ y, ~ 2-0.I~Y2~0

I~ud ~ 0.2 for i = 1,2.

The filter F is not of much use here, since both the model and the measurements are 'perfect'.

11

Steprespol'L'ie ofyl on input uI Steprespol'L'ie ofyl on input u2

403010 20sample

Steprespol'L'ie ofy2 on input u2

403010 20sample

Steprespol'L'ie ofy2 on input uI

-8

or--<"---~--~---------'

-2

-4

-10

-12L--_~__~__~_-----'

o

>. -6

0.8

0.6S!.

0.4

0.2

-0.5S!.

-1

403010 20sample

o403020sample

10ol---"-~__~__~_-----'

o

Figure 2.3: The stepresponses used in the MIMO example.

First the setpoint is changed at timesample 2 from R = [0 0]' to R = [1 -0.1]'. The outputresponses, reference trajectories and the input manipulations are shown in the Figures 2.4 and2.5. The reference trajectories are plotted with dashed lines, the outputs and inputs ofexperiment 1 with dotted lines and the inputs and outputs of experiment 2 with normallines.The setpoint changes are assumed not to be known in advance otherwise the MPC controllerscould have given an even better result. At timesample 31 the setpoint changes to R = [2 0]'.

12

Response output variabie yl2.5

.... ---2 r---·----------"--------":.~

I, 1

1 ,", /1.5

; I ">. ,\ I

, ,\ ,"0.5

10 20 30 40 50 60 70 80 90 100t(samples)

Response output variabie y20.1

I\

0.05 """

0I, ;'_r---'-ï-- - -- -- - ïL ------- _:--

~ " ,, , ,-0.05 ' , ,,

\ ," , \ ,

-0.1, \ I

-0.150 10 20 30 40 50 60 70 80 90 100

t (samples)

Figure 2.4: The responses ofthe outputs in experiments 1(:) and 2(-).

Action manipulated variabie ui

0,

-I,I- ,

:::J ,-2 I -, --

"," "

-3 " --

-40 10 20 30 40 50 60 70 80 90 100

t (samples)

Action manipulated variabie u2

""

"0 " ,,'-I,

SI-I,,~r I

I ---- ... _-------2 - 1- ,,- ~ ,.

-30 10 20 30 40 50 60 70 80 90 100

t (samples)

Figure 2.5: The inputs in experiments 1(.) and 2(-).

13

The setpoints are reached and the controller 2 even satisfies the constraints. The outputsand the inputs are much smoother applying controller 2. This is due to the constraints and theweighing of the change in inputs. It is easy to implement constraints and weights in MPC andthey are straightforward. A sharp reader might notice by looking at thestepresponses that theycould describe a high-purity distillation column. The interactions between the inputs andoutputs are significant. This is seen by the large control actions needed to reach the finalsetpoint. Interaction will also be a topic in chapter 4.

2.4 Nonlinear MPC

A question that arises is how to handle nonlinear systems. While we can deal with mildnonlinearities just by detuning linear controllers, it is likely that in the presence of strongnonlinearities nonlinear controllers offer distinct advantages. Though there are manyimportant unresolved details, the conceptual extension ofthe MPC structure to nonlinearsystems is straightforward. For nonlinear systems the assumption of an unmeasured additivedisturbance acting at the process output is usually artificia1. Indeed, for nonlinear systems theissues ofmodel error (robustness) and unmeasured disturbances become indistinguishable.

All blocks in an MPC controller can be nonlinear. The process model is a simulationprogram where the nonlinear differential equations are solved on-line in parallel with theprocess. A general technique for the design of the nonlinear controller is not available to date.Three attempts reported in the literature will be discussed next.

2.4.1 Non-linear optimal control

In analogy one can define the general nonlinear objective function

ti

min G[x(if)] + JF[x(t),u(t)]dtu

subjected to

x = f[x(t),u(t)]dt • x(to) = Xoh(x,u) = 0g(x,u) ~ O.

(2.6)

(2.7)(2.8)(2.9)

The solution to this problem when (2.8) is not present and g(x,u) varies only with u can befound in all classical references on optimal contro1. The variational methods becomeextremely complex when inequalities involving the states are present. Because of thecomputational complexity, these methods are not suitable for on-line use.

It is more promising to discretisize the control vector with respect to time and to convert(2.6)-(2.9) into a nonlinear programming problem (NLP). It is also possible to use a 'blackbox' simulation model instead of (2.7) and to compute the gradients necessary for themathematical program numerically.

14

A powerful method for solving NLP problems is successive quadratic programming (SQP).SQP approximates the objective function of an NLP problem by a locally quadratic function,and the constraints by locally linear functions. By solving this approximate problem using·quadratic programming, a search direction is obtained. The objective function is minimized inthis search direction, and the process is repeated at the new location until the optimum to theNLP problem is determined. Thus, SQP is an infeasible path optimization method. It does notrequire that the constraints be satisfied (the model equations be solved) at each iteration, butfinds the optimum and satisfies the constraints simultaneously.

Rhiel et al. [19] implemented a nonlinear modelbased inferential control scheme on a 42tray, column with a binary system.

2.4.2 Linearized optimal control

Garcia [7] linearized a problem similar to (2.6)-(2.9) and solved the linear problem by theDMC/QDMC approach. As the state changes new stepresponse coefficients are obtained toupdate the linear model. The nonlinear model is used to perform the model prediction. That is,the nonlinear differential equations are integrated on-line, in parallel with the process, whilethe controller is a linear QDMC controller.

This method is a logical extension ofthe general description oflinear MPC. It starts withthe description of a process by some nonlinear differential equations. The nonlinear modelpredicts the states by integration. Integration of the linearized equations at every scan time fora unit step change will produce the coefficients of S. Having both the predicted states and Sthe MPC problem can be solved and the optimal control moves can be calculated. This is stilla QP problem !!. Figure 2.6 illustrates the algorithm.

In this Figure the usual MPC structure can be recognised. The dashed lines indicateupdates ofthe block Kmpc and F. With an update ofKmpc we mean the update ofthe linearmodel (the stepresponse S) in the optimizer algorithm. The major disadvantage ofthenonlinear QDMC algorithm by Garcia (from now on NLQDMC) is that it may not performwell in controlling integrating processes and may lead to instabilities when applied to open­loop unstable processes. Stability, better disturbance rejection and better performance areobserved when Gw:cia's nonlinear version ofQDMC to open-loop unstable nonlinearprocesses is extended with state estimation. The state estimation could be a Kalman filter (F)designed from the linearization of the nonlinear process. If the linearization changes everysample time the filter has to be updated.

Note that several approximations have been made to simplify the nonlinear problem. First, "the superposition of past and future effects is not rigorously valid for nonlinear systems.Secondly, the coefficients ofS are actually different for each ofthe future moves. The majoradvantage of the proposed algorithm compared to the nonlinear programming approache isthat only a single quadratic program is solved on-line at each sampling time using the sametechniques as for linear systems, which makes the proposed algorithm an attractive option forindustrial implementation.

15

u(k) 1--------1~ -~~ Plant r--

I I, .••...•_. __... . ----'I

.....• -I-

Model

y. (k)m

-~--I

-j F f-.(- -- .

1_-----------J

lil I I I

I i-~-~=li~-~a~1 Y (k) . I-i Y(k) i II--------'-~ model r-----T~·~lN r----~-'

,_~I-----1 l------r-.--~.-i

I IK mpc !"'<-'------- Observer

R(k+llk)

Optimizer

.•• t o.

I

Y(k+ llk);-- I

.- .-- - Mp ~-

Predictor

Figure 2.6: An imbedded non-linear model. The QDMC approach.

2.4.3 Iterative QDMC

Simminger et al. [22] go even further. They extend the linear Kmpc 'algorithm' into anonlinear one. If a linear model is used for the future control moves the nonlinearcontributions are not included. Let's model those contributions as good as possible. If anonlinear model is available the errors made by linearization can be modeled as disturbance(Figure 2.7)

nonlinear 1-1y :/~

.---,------ I I"~ mear

/1 y

---~~---

1-------

k k+l

.-f-

Errors due to nonlinearities dn1

-' ... ------- ---r- T-----~

k+P

Figure 2. 7: Errors due 10 nonlinearities

16

This is globally what Simminger proposed, but we slightly changed the procedure. Themodified version will be explained from Figure 2.8. Since the effect of one control movecannot be calculated for reasons that will be explained in chapter 4, the effect of past controlmoves is obtained with a linear stepresponse model (switch A = 0). The same model is used ina QDMC algorithm finding the first 'optimal' control sequence.

yr----

----,-__J~----.: Plant: i

L_

R

Linearmodel

, I

~------------------------------------------------

Figure 2.8: Block algorithm ofthe algorithm.

This control sequence and the current disturbances are implemented and the predictednonlinear output Ymnl is calculated (switch B = 1). Simminger then subtracts the linearprediction which results in a 'disturbance' due to nonlinearities. Note however that he has theeffect of past control moves calculated with a nonlinear model, so a more accurate state tostart the optimization with. Since such a state is not available the errors due to 'past' and'future' nonlinearities cannot be distinguised. To correct for both ofthem the linear effect ofthe control moves is subtracted from the predicted nonlinear output Ymnl, resulting in ypnl. ypnl isthe effect of past control moves, current and past disturbances and even a first correction ofthe stepresponse model.

This predicted output is used for a second QDMC run (switch A = 1) resulting in a new'optimal' control sequence. With this sequence a new Ymnl and a new ypnl are calculated. Thisprocedure should be repeated until a certain stop criterium is satisfied. The procedure is verytime consuming and if one wants to use it on-line the stop criterium should be loose. The final'optimal' control sequence is then applied to the plant (switch B = 0).

Examples of Simmingers theory only handle CSTR-processes. The modified theory justtreated is applied to a model of a binary, high purity distillation column. The results are foundin chapter 5.

17

2.5 An overview

Attention has been given to five different MPC algorithms i.e.linear MPC, nonlinearoptimal control, NLQDMC, iterative QDMC and modified iterative QDMC in order ofappearance. In table 2.1 an overview is given of the way the different aspects of MPC aretreated.

Table 2.1: An overview ofsome MPC controllers.

name past stepresponses optimizer time (s)

linear MPC linear once linear <20

modified iterative linear, nonlinear once linear, <600QDMC corrected iterative

NLQDMC non-linear at every sample linear

iterative QDMC non-linear at every sample linear,or once iterative

Non-linear non-linear of no interest non-linearoptimal control for this method

The first column contains the name of the algorithm. Then the way the effect of pastcontrol moves and disturbances is calculated is described. The third column denotes the timesthe stepresponses are indentified. Then the optimizer algorithm is classified. Finallysomething is said about the time needed for a mpc-controller action if it is implemented inMATLAB and tries to control a high-purity distillation column.

Only the first two controllers are implemented. The controllers are ordered on the assumedtime-consumption of controller steps, i.e. a linear MPC step takes about 20 seconds and anonlinear optimal control step is dependent on the accuracy of the answer, but will take greattime. It is not clear if the most time-consuming is also the best performing algorithm, althoughnonlinear optimal control probably is.

18

Binary, high purity distillation

What is to be controlled is a binary, high purity distillation column. In this chapter theprocess of distillation, some of the needed equipment and an environment are outlined. In thisway one gets more acqainted with the nomenclature and the processes. This will come in handwhen in chapter 4 the process is to be modeled.

3.1 What is binary, high-purity distillation?

Distillation is widely used in chemical and petroleum industries to separate mixtures ofcomponents into purer product streams. This separation is based on differences in 'volatilities'(tendencies to vaporize) among various chemical components.

One speaks of distillation if the vapour phase is created by adding heat to and evaporizingofthe liquid phase. By absorption or rectification of a component out of a vapourphase theabsortionmedium is fed back as liquid phase (reflux). If a component out of the liquid phase isremoved by means of adding vapour phase (vapour generated by reboiling), one speaks ofstripping.

The separation is based on the difference in composition between vapour and liquid atequilibrium. There is an enrichment ofthe most volatile component in the vapour phase.Through condensating the vapourflow a liquid is obtained that is richer in the most volatilecomponent than the original mixture. If a part of the gained distillate is vaporized again thevapour would become richer again. This principle is the essence ofwhat is called rectifyingdistillation.

In binary distillation two components are involved. High purity distillation means that themixture has to be separated into very pure components. So binary, high purity distillationhandles the highly separation through distillation of a mixture containing two components.

3.2 The processes

One ofthe basic laws of nature is that there must be a driving force to achieve motion.Water flows downhill because of the force ofgravity, just as electricity flows from highpotential to low potential. Similarly, the driving force within a distillation system allows theseparation of one component from another. This driving force for separation is the differencein vapour pressure between components in a system.

Consider a pure liquid at a temperature and pressure at which it is in equilibrium with itsvapour. If equilibrium is defined as a state in which there is no driving force for change, thenequilibrium can be used to define vapour pressure. This equilibrium pressure is called thevapour pressure of the liquid at the given temperature.

19

Vapour pressure and boiling point are closely related (Figure 3.1). The vapour pressure isthe system pressure at which a pure component will boil at a given temperature. For purewater at 1DODe, the vapour pressure is 1 atmosphere. Distillation occurs because of differencesin component vapour pressures, for, at a fixed temperature, one component in a mixture has ahigher vapour pressure and is more volatile.

Vapour pressure

,Benzene (more volatiIe /

//

//

//"

____ -- -- Toluene (lm volatile)o -------;-~-"'--'--,------,-,---~~,-'-T---

O.S

Vapour pressure(alm)

/Vapour pressure of water

J

O.S

Vapour pressure(alm)

o SO 100TemperaturerC)

o SO 100TemperaturerCl

Figure 3.1: Vapour pressure-temperature curveslor water, benzene and toluene.

The volatility of a component in a mixture is defined as

*Y j

K. -I

(3.1)x.

I

in which yt is the mole part of component i in the vapour phase in equilibrium with the liquidphase with molepart Xi' The relative volatility of component i with respect to j can be writtenas

(X, .. ­IJ K.

J

(3.2)

In case of binary systems the indices can be omitted and x and y are referred to the mostvolatile component. The relative volativity then becomes

ex = Y *(1 - x).

x(1 - Y *)(3.3)

20

In principle IX is a function of temperature, pressure and composition, but often IX remainsconstant in a certain temperature range. For ideal systems we can apply Raoult's law

" 0 "PI = XPI =Y P t (3.4)

in which PI" is the partial pressure ofthe most volatile component, PlO is the vapourpressure ofthe pure component by the actual temperature and PI is the total pressure. For a binary systemwe can write for the total pressure

• "0 0P t = PI + P2 = xPI + (1 - x)P2 (3.5)

After some calculations one can derive for the relative volality of an ideal binary system

ex = (3.6)

The relative volatility is an indicator for the ease of separation. The higher IX the easier wecan separate the components from eachother. When IX = 1 separation ofthe two componentsby simple distillation is impossible. In Figure 3.2 the temperature-composition, pressure­composition and composition-compositiondiagram are plotted.

Vapour

PreS9ure constant

Liquid

o X

Male fratlian 1in liquid

..""~>.5

-------/'i/ /

/1/ /

/ /

/ /" / /

~ >': ///ö /I i / /

oL _

Temperature constant

Liquid

~-_._--,._._-------_.__._-----o X3 I

Mole fraction I

y-J,BUbblc.points x v~P~~1 pi

I I •-, I -- -- ----/ -

J.i! /fr- ------- --/-- I

~ .p2 I I

: I Dew.pointl Y VI pressurei

Vapour

bplBubble-pointl x VI temp

"- - --_._-------_ .._.._-- ----~o x,y 1

Mole fraction I

bp2; I Dcw.points y vs tcmp:~_M

"h-/\,\ I K -

~, ':

J: '~..::-,ol D

Figure 3.2: T-x, P-x andy-x diagram/or a non-ideal normal system.

We can see that we are not dealing with an ideal system, because the line pressure versus xisn't a straight line, which it would be ifwe would apply Raoult's law. Suppose we heat up aliquid-mixture with a composition G at a given constant pressure (in a cylinder closed with aplunger). The Figure shows that the liquid boils at a temperature H (bubble point). Thecomposition ofthe first vapour that is created is J. Further heating will drag x from H to N andy in equilibrium with x from J to M. As long as the boiling point stays between H en M themixture-state is in a boiling cycles and we have a liquid-vapour equilibrium. As soon as thelast liquid with composition N evaporates, only vapour is left with a composition G. The other

21

way around: if we have a vapour-mixture 0 and we cool this down, then shall the first liquid­drop occur by a temperature M (dew point).

To give an impression how non-ideal (and thus how big the deviation from Raoult's law)the system can be the same diagrams as in Figure 3.2 are plotted, but now for an azeotropicmixture ofCSz-acetone (Figure 3.3). This isjust an impression. Such systems will not beconsidered in this report.

Pressure constant

I Vapour

i !bp2.~.iDDoowW"IPoinll Y VI lompi

~I\~~ ~i: \:- \1"'-_/:bPI

.- ~Bubble·points x VII tem~

Liquid

'---------_...._------------,o x,y I

Mole fraction 1

p2

Temperature constant

iLiquid i

Bubble.points x: VI pressu+I!

/! --

!Dew.points)' VI prcSlurej

VapourL . ... •••. i

o x,y 1Male fraction I

pi

-I

J ,I

.sI

.~ J~ I /

~ ! /i i

I :rQ iL__~ ,

o X

Mole fraction I in liquid

Figure 3.3: T-x, P-x andy-x diagramfor a non-ideal azeotropic system.

3.3 The equipment

In this paragraph the equipment needed for distillation will be viewed. We will start withtrays, those are the places where the true separation is achieved and end in the next paragraphwith the description of a plant that refines raw oil.

downcomer

Two stages in a distil/ation column

outlet _weir

Iiquid

active trayarea --"'+----~

Figure 3.4:

Figure 3.4 shows a section of adistillation column. Vapour generatedbelow this section is transcending throughthe 'holes' in the active trayareas and theliquid holdups on the trays. Liquid formedabove this section is flowing downstairsthrough the downcomers, over the traysand over the outlet weirs if the holdup isbig enough. In the liquid holdup above theactive tray area energy is exchanged andseparation is achieved. The vapour thatarises from the hold up contains more ofthe most volatile component than thevapour that enters this holdup.Analogously the liquid that leaves thisholdup by passing the outlet weir is richer of least volatile component than the liquid that

22

enters the holdup through the downcomer. So on each tray the separation of the components iscarried out a bit further.

The change in concentration at a stage is dependent on the concentrations in the stream thatenter the stage. The difference in concentration is the source ofthe change (diffusion) as weshall see in chapter 4. The higher these differences in concentration are, the more effective achange in streams will be.

The vapour stream toot transcends and the liquid stream that flows down and theirconcentrations determine the performance of a tray. The higher the streams, also called flows,the higher the total separation will be. That is of course if the trays operate in the normalworking area. Ifthe flows take on extreme values different effects take place (see [14]).

The way the fluid and the vapour are mixed on a tray also depends on the magnitudes ofthe flows. One can read about it in the literature [12]. It may be clear that when the processleaves the normal working area the tray-efficiency will be reduced and the separation will beless. It is therefore important to stay in the normal working area.

---~--_._-

Overhead vapour

~\ Reflux---- 1 \-<---,- 2 !

Now let's consider the whole distillationunit including a column, a reflux vessel, acondenser and a reboiler. These are themajor parts to do distillation and theconfiguration is drawn in Figure 3.5. Thetrays inside the column are numbered fromthe top downward starting with 1 andending with the total number of trays n.

iCondenser-(ç;;--- Qc

i,~ Refluxvessel

I, ~V,kliiii;;r. Distillate~.-~ ---------.

Lt DColumn xd

___ nrtI

_ n! Vb,..----,~ 9_R~;ileri

B ! Bottomsxb,

c

Feed •--~

FAt tray nf a mixture of components

called feed enters the column. The amountof feedflow is denoted as F and thecomposition as c. Since we will discuss onlybinary distillation all compositions will bereproduced as the concentration of the mostvolatile component.

At the top ofthe column the vapour Figure 3.5: A distillation unit.stream leaving tray 1, which is calledoverhead vapour, is condensed in the condenser. Heat is transferred out ofthe condenser at arate Qc' The fluid created is gathered in a reflux vessel. From this vessel flow a product flowD and a refluxflow Lt. The product flow D with composition Xd' called distillate, flows tosome destination elsewhere. The refluxflow Lt is pumped back into the column on tray 1. Theliquid flow inside the column largely depends on this reflux.

At the bottom of the column below tray n there is a liquid holdup. From this holdup a flowis tapped. A part of this flow is the product flow B with concentration xb, called bottoms. Theremaining part is evaporated by transferring heat at a rate Qr into the reboiler. The resulting

23

vapour flow is led back into the columnjust beneath tray n and largely prescribes the vapourflow inside the column.

What is outlined is a standard distillation unit that can separate a (binary) mixture into itscomponents. The column that is to be controled is the c451 distillationcolumn at the NAK4 ofDSM (Figure 3.6). The c451 distillation column also called the C2-splitter is a 96-metre highdistillation column containing 156 trays and is used for separating ethylene (C2H4) and ethane(C2H6)·

Ethylene, the most volatile componentis the main product. Most of it leaves thecolumn at the top. A small part of theoverhead vapour is the productstream Dv­

The remaining part is condensed and ledinto the refluxvesse1. A distillate flow DIand a reflux flow L t leave the refluxvesse1.

Ethane leaves the column at the bottomas a flow B. Not at the bottom but from abig 'tray' just above, a liquid flow istapped, evaporated in two reboilers intovapour and fed back into the column justbeneath tray 156. Because the capacity ofthe reboilers at the bottoms is not enough,an intermediate reboiler is added at tray139.

Dl

The feed can enter the column at tray126 and at tray 114. In practice thefeedvalve at tray 114 is closed, so weassume a feedentrence only at tray 126.

Several quantities are measured andcontrolled in this unit. The most importantmeasurements are:

* the compositions x t and Xb,

* pressuredrop over the column,* the feed flow F and concentration c,* levels in the reflux vessel and the

bottom,* five temperatures in the column* the temperatures of the flows that

leave and enter the column.

Qr

B

Figure 3.6: The 'C2splitter' ofthe NAK4

24

Note that Xl is not analysed in the distillate but in the overhead vapour and that Xb is notanalysed in the bottoms but in the liquid at tray 156. The analysis takes 12 minutes for Xb andIS minutes for Xl. The main manipulated values are the flows Lt, Dl, Dv, Ir, Qr and B.

3.4 The environment

At the NAK4 crude oil, also called NAFTA is cracked and then refined into more valuablecomponents. Some ofthe components are hydrogen, methane, ethane, ethylene, ethyne,acetylene, etc. The plant consists offurnaces, columns, reboilers, condensers, vessels, etc. Theplant can be divided in three parts, i.e. a 'front-factory', a 'middle-factory' and an 'end-factory'.In the front-factory are the furnaces in which the NAFTA is cracked. Then some majorseparations take place, like the separation of hydrogen, C2-groups, C3-groups, etc. In themiddle-factory and end-factory the separation of components is carried out further. The c451column is in the endfactory.

The feed ofthe distillation column c451 is the topproduct of the distillation column c431that separates ethane and ethylene from heavier components. The bottoms ofthe c2-splittercontains the less valuable ethane. This is fed back to the fumaces and cracked again intomore valuable components. The reboilers and condensers subtract and add energy to apropylene (C3) flow that acts as the heat system. A part ofthe vapourtopproduct is sent to the'IS ato' net (also called 'logistic'). The remaining part is complemented with evaporated fluiddistillate to maintain a '5 ato' net. The remaining fluid distillate is cooled down further andsent to the fluid ethylene storage.

3.5 The simulator

To train personnel and to develop new control strategies an extensive dynamicalmathematical model has been made. The model is available on a mainframe computer. Themodel is so complex that it takes the same time to do a simulation as it does to do a realexperiment. The reliability of the model was checked by process operators who normallyoperate the real situation. It appeared to be a 'hifi' model.

The simulator gives thus a good representation of the real situation. Though there are somedifferences. The simulator only represents a part ofthe end-factory. i.e. from the column c451to the distributions to the 5 ato net, the IS ato net and the liquid storage. The c2-splitter in thesimulator contains only 105 trays (with an efficiency of 100%) instead of 156 as in the rea!column. The assumption was that the efficiency ofthe trays in the rea! column isapproximately 80%.

In the simulator it is possible to manipulate and measure the feedflow andfeedconcentration. In the real column feedflow and concentration are disturbances, whichmeans that they are given and cannot be influenced.

25

VAX

Agnes

model,---_.~-- -----~-

DEC stations

• place for something new,

e.g. a new mpc version

VMS

Figure 3. 7: The way the simulator is build up and Us communication possibilities.

One can interact with the simulator via GIDS. GIDS is the userinterface between user andmodel (Figure 3.7). Via GIDS it is possible to operate all valves, setpoints, etc. There are alsowritten some userprograms in FORTRAN that communicate with GIDS. In Figure 3.7 asection Hiecon is drawn which is the linear model predictive controller implemented by theFrench firm Adersa that is specialised in MPC. Furthermore one can see the interactiveprograms this controller needs to communicate with GIDS.

It is also possible via GIDS to change or look at variables, such as sizes of vessels,concentrations and temperatures. A program that saves simulation-results makes it possible toplot and study simulation runs off-line.

26

Modeling a binary, high purity distillation column

In controlling the simulator one has to know its statie and dynamie behaviour. Distillationprocess can have large time constants resulting in long settling times. This means thatexperiments can last for days (even weeks). The simulator, which simulates more than onlythe column, needs the same time as the real process. In order to study the behaviour of theprocess and to design and test model predictive controllers some models were derived.

4.1 Introduction

This chapter describes the modeling ofthe binary, high purity distillation column. Severalmodels and simulators will be treated so it is useful to name the different processes. It allstarted with the real distillation column C451 at the DSM business unit NAK4. This columnwill be called the 'C2-splitter'. A high order dynamie model of the C2-splitter is available andwill be called the 'simulator'. From both processes statie models are obtained. Those modelsare set up in the software package 'Aspen 9.0'. The model describing the C2-splitter will becalled 'Aspen-C2-splitter'. The model describing the simulator will be called the 'Aspen­simulator'. Finally a nonlinear dynamie model of the simulator is programmed in the softwarepackage Matlab/Simulink. This model will be called the 'Matlab-model'.

An overview ofthe models is given in Figure 4.1. In this Figure the models (and theprocess) are ordered. The arrows in the Figure indicate the relations the models have. If anarrow is pointing from model A to model B, model B is a simplified description of model A.

_____ I~ simulator ~ MaUab-model F I

_J -~--. : dynamie- i I

~--~-------i-------------I-------

:1 Y I---- ------ ,--------, I statie: Aapen-C2-lIplitter: - -~ Aspen-.lmulator: I~--- -----._-- -- ----------- - I

real proce..

Figure 4.1: An overview of(he used modeIs.

Though the Aspen-simulator is not a simplified descpription of the aspsen-C2-splitter, theyare c10sely related. A model of the Aspen-C2-splitter was already at hand and with somemodification and some tuning a duplicate model was fitted on the simulator. That is why thearrow from the Aspen-C2-splitter to the Aspen-simulator is dashed.

27

4.2 Statie models in Aspen

To ohtain good insight in the static hehaviour of a process, without excessive hurdening theprocess, a static computer model can he used. In such a simplified model modifications caneasily he made and the static hehaviour can he studied.

For distillation processes static models rely on the principles ofconserving mass andenergy. Distillation is a process where no mass or energy is created, nor a process where massand energy are transformed into eachother. One can look at the principles of conservationseparately to form a static model.

Taking the principle of conservation of mass alone into account will he a first approach. Aschematic plot of the distillation unit is drawn in Figure 4.2. Since only static resuits areconsidered holdups on trays are no longer important neither are the levels in the reflux vesseland the hottom. The refluxvessel and the hottom can actually he modelled as a tray.

In Figure 4.2 a dashed line separating the distillation unit from the environment is drawn.Mass conservation can he translated in 'what enters the unit also has to leave the unit'. Somerelations hetween the flows entering and leaving the unit can he derived. The conservation lawalso applies to all the stages. So from all the stages relations can he derived. Finally there willhe a complete set of equations.

------../--- "

/ \/ \

; .... -~ ~/v" QI

.~.~ D, xdi

I--r Ii ; /

\ "...t., /\ I~. Q

I '~--,...J _/

-1--I

YB, xb

_ _._~_._._'.._q----_._',.------_. ".",,'' ------ i (xd,yd), II I I

---.-- I :

~7 ' :./<~ / :

/ / / I

I / I (c,c) I

i / ' I,----/ I I

I I! / I I! ,I! I I i

, i ! j' I I 1

1: I I I 'I ,/ I I

'i/(xb,yb): : i, I I I i_.__. ,~__~ ....LJ

F, C I'"

I

I!

I --- I~ ~'~Qf-'C--~ : f

1

y

oo x 1

Figure 4.2: A dis/illa/ion unit. Figure 4.3: A McCabe-Thiele diagram.

The solution of this set of equations will give the static mass hehaviour inside the unit. Theconcentrations at the trays can now he calculated. Strikingly is the importance of the ratiohetween the liquid flow and the vapour flow inside the column. These flows determine theconcentrations on the stages. A McCahe-Thiele diagram visualizes the relations.

28

In Figure 4.3 such a McCabe-Thiele diagram for a unit without an intermediate reboiler isdrawn. In this diagram the concentration in the liquid phase (x) in relation to the concentrationin the vapour phase (y) is sketched. The curved line describes the relation between x and yinequilibrium. The x = y line is drawn as a reference to indicate the ease of separation. Astaircase line gives the concentrations in the liquid and vapour holdups at the stages. Thestraight line starting in (Xb,yb) is called the bottomworkline. lts slope is determined by the ratiobetween the liquid flow and the vapour flow at the bottom. The straight line starting in (Xd,Yd)is called the topworkline and represents a similar relation but then for the top. The straight linestarting at (c,c), with c the concentration in the feed, is called the q-line.

A detailed explanation of the terms and the construction of a McCabe-Thiele diagram canbe found in [12]. The set of equations is solved iteratively. What one actually does is trying tofit a staircase line, like in Figure 4.3, into the space between the worklines and the equilibriumcurve. The intersections of the staircase line with the worklines give the concentrations in theliquid phase at the stages. The intersections with the equilibrium curve give the concentrationsin the vapour phase at the stages.

It may be c1ear that solving the equations is sensitive to errors and time consuming if theease ofseparation (a) is low. Furthermore adding an intermediate reboiler will give an extraworkline and the problem gets more complex. The worklines, which are until now assumed tobe straight lines, become curved by adding energetic relations. To account for al thesemodifications a license for a professional software package'Aspen' was obtained. Aspensolves a much more complex set of equations than outlined before. Nonlinearities in theequilibrium relations are also taken into account. Another advantage was that a fitted model ofthe C2-splitter was available. This model has been duplicated. The duplicate is altered andfitted on the simulator. A drawing ofthe worksheet in Aspen containing the Aspen-simulatoris given in Figure 4.4.

29

File ~dit Farms Run ~nalysis F!owsheet fFO View HOs! ~ettings !::!elp

r Resuns Present Section: GLOBAL ...I I .J PFO~ Nextl

'" f'.111-lclel

CloseI

C4~1 ~~ . .....-J\.,.,...... ~ ~ ~&TRE80ll

Type........." ~ eedIProd

~ ~

~"/Splitlash/llX

colUllll

-IE[]- ......J:!E :ii:il

R.eactor........." UIlp/COllp

~ipe

TREllSH Model

..fTiffii1l..

Icon

ASPEH PLUS Graphics - Use 1eft button to select. Use rlght button for popup .enu

Figure 4.4: Aspen worksheet containing the Aspen-simulator.

Fitting a model is done by tuning two parameters in the Aspen model. One starts with atemperature profile of the process one wants to model. A temperature profile is a table or plotofthe temperature against the stage number. With the parameters in Aspen one can fit thetemperature profile generated by Aspen to the temperature profile ofthe process. In Figure 4.5two temperature 'profiles' are plotted. One for Aspen-C2-splitter that is fitted on C2-splitter ofwhich only 5 temperatures in the bottom are available. For the Aspen model ofthe simulatorthe temperatures at all stages were available. These profiles are plotted in Figure 4.6.

30

Temperature profiles ofC2-splitter and aspen-C2-splitter265r----...,----r------.-------,-----,-------,---,--------,

260

:2' 255'-'

~! 250

245

rx><0x

xo

x

x

xxx~

x

o C2-splitter

I ~~~~~~:::::::::~----;!;c__-_____..,:-!:-::-----:-±:x~as:pe:n-:C2:-:Sp:li:tte:rJ240~o W ~ ~ W \00 lW \~ \~

stage number (-)

Figure 4.5: Temperature profiles ofthe C2-splitter and the Aspen-C2-splitter.

Temperature in relation to stage nwnber265r--------,-------,-----...,-----,--------r-----------,

260

255

+ aspen-simulatoro simulator

235 !:------='=-----f=-------f;c__-----=-=---------:--=----~o 20 40 60 80 100 120stage nwnber (•)

Figure 4.6: Temperature profiles ofthe simulator and the Aspen-simulator.

31

One can see that the last fit is excellent. In Figure 4.7 the difference between the profiles ofthe Aspen-simulator and the simulator is drawn which underscribes the quality ofthe fit.Notice the difference in shape ofthe profiles ofthe Aspen-simulator in Figure 4.6 and theprofile ofthe Aspen-C2-splitter in Figure 4.5. This difference in temperature profile indicatesalready a significant difference in static behaviour.

Difference in temperature in relation to stage number0.2,-------------,------.-----.---------,------.------,

o\I)

~ -0.2...\I)

~~ -0.4

-0.6L-----___,,1_----~---______:~---___,,1_-----~---___,_Jo 20 40 60 80 100 120

stage nwnber (-)

Figure 4. 7: Difference between temperature projiles ofAspen-simulator and simulator.

The tuning parameters also vary. Some parameters and the tuning parameters for theAspen-C2-splitter and the Aspen-simulator are given in tabel 4.1.

Tabel 4.1: Differences in parameters for the Aspen-C2-splitter and the Aspen-simulator.

parameters Aspen-C2-splitter Aspen-simulator

number of stages

interrnediate reboiler overheating

157

25 K

107

OK

tuning parameters

efficiency of rectifyingstages 1.50 0.90

efficiency of strippingstages 1.50 0.95

'componentsinteractionparameter' 0.0188 -0.002

The efficiency of the stages in the Aspen-C2-splitter are extremely high. The cause of thisis the high throughput. In the next paragraph the static models wiIl be used to study the staticbehaviour. For the simulator some extra experiments are done. In this way a certain workingarea could be focus on.

32

4.3 Statie behaviour of the C2-splitter and the simulator

With the models derived in the previous paragraph the statie behaviour is studied.The formthat is chosen to represent this behaviour is arelation between bottomquality and topquality atconstant reflux. The intermediate reboiler, feedflow, feedconcentration, etc are assumed to beconstant and the reboiler heat (or the generated vapour flow at the reboiler) is altered. Somerelations for the simulator are given in Figure 4.8.

Top- and bottornquality at constant refltlX118.7

Reflux

180 t/h

200 t/h

220 t/h

bottomquality (%)

Figure 4.8: Top- and bottomqualitylor the Aspen-simulator.

At the right of the lines of constant reflux the value of the reflux is given. Above the linesthere are numbers that indicate the value ofthe vapour flow, which is evaporated in thereboiler in tons/h. The difference in reflux between the lines is 20 tons/h. On a line the vapourflow generated by the reboiler changes also 20 tons/h. However ifthe reflux is constant say200 tons/h and the vapour flow is increased from 123.4 to 124.8 tons/h the bottomqualitychanges from about 2% to 0.9 % and the topquality changes from 2 ppm to 3000 ppm. So thebottom gets purer and the top impurer. Ifone wants to change the topquality from 2 ppm to3000 ppm and the bottomquality from 0.9 % to 2%, i.e. both impurer, one has to change thereflux from 215 to 185 tons/h and the vapour flow from 142 to 110 tons/h.

33

~, yl

, yO-------

'Strong' Directions

As has been noted by Alsop [1] and foundhere: high purity distillation columns are ill­conditioned systems. Alsop defined 'weak'and 'strong' directions in a plot like Figure4.8. The strong direction in Figure 4.8 is thedirection were one products gets purer andthe other impurer. A weak direction is whereboth get purer or both get impurer (yO ... yI).Movements in a weak direction require largechanges in the flows with much of thechange in one flow being used to cancelmovement in undisered directions (seeFigure 4.9).

~v

~R

{' 'Weak' Directions

~

Figure 4.9: Graphical description ofmovement in 'strong' and 'weak' directions.

The same graph but now for Aspen-C2­splitter is drawn in Figure 4.10. Here thelines of constant reflux are almost horizontal.The weak direction for Aspen-C2-splitter is a change in topimpurity and the strong directionis a change in bottomimpurity.

Top- and bottornquality at constant reflux

104.4 104.4 104.8 104.7 Reflux104 Jl(-1l'---*)I:-~JI(f--*~(__"JI(II(--___*JI(-~JI(f--*JI(__"JI(II(--___*JI(-~JI(~_lIE)l:e---lI(-)l:-~ll(f___lJl(IE--~'"

113.7 113.7 114.2 114.1 ~ 180t/hJI(-~JI('----,*----lIE--)I(--lIE--____lIEf--JI(--)I(-----lIE----JlE----JlE--lIE-_4)I: JI( ~( JI( ~( )I: JI( lK JI( )I( lil J1(~2.1

\ 190t/h

200 t/h

121.8

133.2 133.3 133.8)I: )I: lK JI( JI( )I: JI( JI(

_-)I(-12_3_l1E.2ó-l1E-l-23-.2_J1(__----l~_JI(__*1-23-. 7--JIE-----i1l(--~~123.6

10' 133.7

JI( JI( ll( ~.~31.9

143.3 143.4 143.9 143.8 ~ 210 t/h10° J1(lf<------JlEJI(-~*f--**__.,*II(--___**---lI*f___lIEJI('-JI()l(_____lIEJI(f___lJl(~_lIEll(~ll( _ __""~ 142

'~ 220t/h

10" 10°bottornquality (%)

_.J-__ ----I.- __~.......l_--*------.f-___.L..LL __ , ......1 _ _I•. ----L __....L.....l-LL.J....1 .------l..._m_----I.----L..~_._L______.L_.!

10,2, , , . ti

10'

Figure 4.10: Top- and bottomquality at constant rejluxfor the Aspen-C2-splitter.

34

The behaviour ofthe simulator doesn't describe the real C2-splitter ofNAK4 very well inthis perspective, but the behaviour of other C2-splitters and other binary columns often issimilar to the simulator.

As was mentioned earlier for the simulator aspecific working area was focussed on. Agraph of the working area is plotted in Figure 4.11. Next to the lines the reflux (tons/h) isgiven. On one line the vapour flow changes Iess than 0.14 tons/h. The strong direction for thesimulator is a change in topquality the weak direction is a change in bottomquality. Althoughthe C2-splitter is operating in the same working area as the simulator, the directions arecompletely twisted.

Top- and bottomquality at constant reflux700

600

rfl90rfl9Srf200rf20Srf2IS rf210100

200

500

1400

iè:.:: 300gj

!

o __--L--_.. J~ ._ ..L .J~ ~_._~ --,.'--'-

I 1.2 1.4 1.6 1.8 2 2.2 2.4Bottomquality (% ethylene)

2.6 2.8

Figure 4.11: Top- and bottomquality at constant rejlux for the Aspen-simulator.

The behaviour ofthe column is not only dependent ofreflux and reboiler. The feed flow,feed concentration and the intermediate reboiler also have an effect on the bottom- andtopquality. To study these interactions many Aspen runs were done and the results weresaved. These experiments were done for the design of a double quality controller (chapter 5).The results are more or less the same as in Figure 4.11. It is just that the lines are shifted or alittle bit more curved.

35

4.4 Dynamic modeling

After some experiments with the simulator it appeared that the simulator acts 'highlynonlinear'. Not only static results but also dynamic results indicate this nonlinearity. To studythis phenomenon, without doing excessive time-consuming runs, a simplified dynamiccomputer model is developed. This model is programmed in Matlab.

In order to characterize a distillation process one needs a set of fundamental dependentquantities whose values describe the natural state. Next to these quantities a set of equations isneeded which describe how the natural state changes with time. The fundamental quantitiescan be characterized by variables such as density, concentration, temperature, etc. Thesecharacterizing variables are called state variables and their values define the state.

The equations that relate the state variables (dependent variables) to the variousindependent variables are derived from application of the conservation principles. These stateequations yield a set of differential equations with the fundamental quantities as the dependentvariables and time as the independent variabie. The solution of the differential equations willdetermine the dynamic behaviour of the process.

One can never model the reality perfect. Important when modeling a process is the purposeof the model. Since observing the global nonlinearities is the main goal the model does nothave to be very accurate. An accurate set of equations is given in the literature [3 and 4]. Themodel programmed in Matlab is based on the principle of conserving mass only. For a binarycolumn at all stages total mass has to be conserved as well as the mass of the most volatilecomponent. So still two states per stage are needed.

When modeling a distillation column the processes at every stage are modelled. Therefluxvessel and the bottom (or the reboiler vessels) are modelled as the uppermost and loweststage respectively. Counting stages from the top downward to the bottom, the reflux vesselbecomes tray 1 and the bottom tray n+2 if there are n normal stages in the column.

i-I

A simple model ofa stage.

L·1

_'iLo1 I I 1-1, -+ i II , ,I

Sj I M j '''i I Vi +.-----------)-------- . --+-!, 1 i-.-

i -+ I:: I '

" I Vj+l

Figure 4.12:

In modelling the column the approach ofStephanopoulos [23] is followed. Severalassumptions are made in simplifying thereality. Lets look at a model of a stage(Figure 4.12). In this Figure we see twostages i.e stage i-I and stage i. Considerstage i. On this stage some flows interact. Aliquid flow is comming from stage i-I, L i_h

and a liquid flow is leaving stage i, L i .

There also is a vapor flow comming fromstage i+ 1, V i+1, and a vapor flow leavingstage i, Vi. For the states at every stage themassholdup Mi and the concentration ofmost volatile component Xi are taken. Options for a stage are the feedflow Fi withconcentration Ci and the tap Sj.

36

Several assumptions are made

- the vapourholdup, the amount ofvapour at a stage, is negligible,- the molar heats of both components are equal,- there are no heat losses to surroundings (perfect isolation),- the equilibrium relations are ideal and- the tray efficiency is 100%.

Some results from the assumptions

- only the liquid holdup at a tray has to be considered,- unless a feed enters as a vapour the vapourstream is constant (VI = VI+t ),

- no heat balances have to be considered and- relative volatility a is constant.

The two states on every stage follow from the principles ofconservation. First there is theprinciple of conservation of total mass at one tray (Equation 4.1). Secondly the most volatilecomponent (also called the concentration in binary distillation) has to be conserved (Equation4.2). In this equation (4.1) can be substituted. The result is Equation 4.3 describing themovement ofthe concentration at stage i in time. Notice that the movement is based on thedifferences between the concentration in the streams leaving or entering the stage and theconcentration in the liquid holdup (diffusion !). Next some extra relations are needed to relatethe states 'liquid holdup' Mi and the 'concentration in liquid' Xi to the variables in the model.One of them is an equilibrium relation between the concentration in the liquid and theconcentration in the vapour (Equation 4.4). A hydrodynamic relation between the leavingliquid flow and the liquid holdup completes the model of a tray (Equation 4.5).

(4.1)

(4.2)

=

Y; =1 + (ex - 1 )x

j

(4.4)

Lj = f(MJ =hydro*M j (linear ).

37

(4.5)

The simulator has some additional entries and taps. The vapor distillate flow is modelled asa (vapour) tap at stage 2, S2 [kglh]. The intermediate reboiler is modeled as a liquid tap Snir+1[kglh] and a vapor feed one tray below Fnir+2 [kglh]. nir is the traynumber where theintermediate reboiler taps the fluid and the term + I is added to correct for the refluxvesselwhich is modeled as stage I. The dynamic behaviour of the intermediate reboiler is not takeninto account, just the flow that flows through and changes of phase.

Resuming:

the statesM·1x·1

the liquid massholdup at stage ithe concentration of most volatile component

in the liquid fase at stage i

[kg],

[kg/kg],

the inputs (manipulated values)L 1 the refluxFnir+2 and Snir+1 the intermediate reboilerVn+2 the reboilerSI the liquid distillate flowS2 the vapor distillate flowSn+2 the bottoms

[kg/h],[kglh],[kglh],[kg/h],[kglh],[kg/h],

the disturbaneesFnf+1

Cnf+1

the outputsle6(l-Y2)

the feedflowthe feedconcentration

the concentration of the least volatile componentin the vapour fase in the overhead vapour in ppm

the concentration of the most volatile componentin the liquid fase at tray n in %

the liquid holdup in the reflux vesselthe liquid holdup in the bottom/reboilers

[kg],[kg/kg],

[kg/kg],

[kg/kg],[kg] and[kg].

There is an advantage in modelling the column tray by tray in Matlab. Matlab isspecialized in matrixcalculation. The refluxvessel as tray I, the column (n trays) and thebottom (reboilers) as tray n+2 can be seen as a vector oflength n+2. The states Mi can be putin vector M and the states Xi in a vector x. The same thing can be done with the other variablesat a stage. Instead of obtaining the variables stage for stage they are calculated for the wholedistillation unit at once.

The relative volatility a is set to 1.5 which is a representive number for an ethane-ethylenemixture.There was no idea. what number to take for hydro. This constant determines thesettling time of the holdups at the trays. The value was fitted on the response of the bottom onstep actions ofthe reflux and the reboiler, both +1 ton/h. (Figure 4.13).

38

Response bottomlevel (kg)O....,.--------,------r------r------,....-----,....----------,

~ -100'-'

Ö[; -200Ëg -300o

.D

.5 -400~] -500(J

-600 L- ----.,.L- .L.- ------:.L.- .L.- .L- ------,J

o 10 20 30 40 50 60time (min)

Figure 4.13: Response bottomlevel (Mn+JJ.

The positive step on the reboiler is immediately felt on all stages, because the vapourholdup is neglected. The positive step of the reflux implicates a first order response at all thestages. So it takes more time for the fluid to arrive at the bottom. With the parameter hydrothe settling time ofthis response can be influenced. With a hydro of200 h- I the settling timebecomes about 35 minutes which seems to be appropriate.

Actually there are two sets of equations that are being solved separately. First the liquidholdup at the trays is calculated. If one substitutes (4.5) in (4.1) a linear set of equations willfollow, which can be solved ifthe inputs (flows) are given. The response ofthe bottom on achange in reflux has the largest setling time. The settling time of the responses of the liquidholdups is therefore less than 1 hour.

The dynamic liquid holdup responses are then used for the calculation of the responses ofthe concentrations. This set of equations is nonlinear. Another problem is that the settling timeofthe concentrations is much bigger than 1 hour. What happens is that a set of equations hasto be solved with parameters varying with a small timeconstant «< 1 hour) and a largetimeconstant (» 1 hour). These so called stiff systems need special care. In Matlab's odesuitetooibox algorithms are found which are especially designed for stiff systems.

Earlier was mentioned that some MPC algorithms were not suited. This is because withthis model the effect of past control moves and past and current disturbance can not bepredicted. These actions can force the mass holdups to pass zero and become negative, whichmeans that mass is generated. This is of course nonsense and the calculation of theconcentrations becomes impossible. One notices this through the error message Matlab willgenerate when a liquid holdup becomes zero. When this happens Equation (4.3) can not beevaluated.

39

4.5 Dynamic behaviour of the simulator and the Matlab-model

First the dynamic behaviour of the Matlab-model will be discussed. Since the liquidholdups obey a linear model these responses are linear. The stepresponses of theconcentrations are nonlinear. Not only do the differ for various stepamplitudes, they alsodiffer in stepdirection. This means that the response on a positive step of 1000 kg/h on forinstance the reflux significantly differs from the response on a negative step of 1000 kg/h.

The settling time of the liquid holdups is in the order of an hour. The settling time of theconcentrations can be several weeks. The response to a change in feedconcentration is themost nonlinear. The nonlinear effects ofthe flows are less and similar to eachoter.Stepresponses from all inputs and disturbances to the outputs refluxlevel and bottomlevel asweIl as some stepresponses of the concentrations on different input changes are found inappendix B.

The idea of defining a new set of inputs came to mind. Combinations of the original inputscould effect the weak and strong directions seperately. Changes in these directions are stillnonlinear, but the problem of finding the optimal control move would be better conditioned.An input uI was defined as a positive step on the reflux together with a negitive step on thereboiler (strong direction) and an input u2 as a positive step on the reflux and a positive stepon the reboiler (weak direction). The results are plotted in Figure 4.14. The stepsize on uI was+10 kg/h and on u2 was 1000 kg/h. For the simulator similar results were obtained which canbe found in appendix B.

Although the changes in uI (l0 kg/h) are much smaller compared to the changes in u2 (lton/h) the amplitude ofthe steady state responses are ofthe same order. This indicates againthat the process is badly scaled and strongly interactive. In Figure 4.14 some close ups aremade displaying the first 45 hours of the response. Both responses act violentlyon the inputactions. The response ofthe top on input U2 shows an inverse response!

Since a change in the original inputs do not result in violent responses, these inputs aremaintained in the MPC algorithms.

40

Response topimpurity on step uI (-) and step u2(--)100r------,-----,-----r----,------,-----.----.----,.----,-----,

i-l~~~.~------------------------------ ------'s...9

-200

-------------------1-300 ~-~c::__-~_=__-~::__-_=':_:,_______..,c_::'_::_,_____=-::7:,_______:_-f=-~~-__='-:-::----::-::'o 200 400 600 800 1000 1200 1400 1600 1800 2000

time (hours)

Response topimpurity on step uI (-) and step u2(--)20r----.-------,------,------,---,---,--------,-------.-----,

---- ------ -------à -20'5

-40~'ë..

-60.9

-80

-1000 5 10 IS 20 25

time (hours)30 35 40 45

Response bottomimpurity on step uI (-) and step u2(--)0.05 r------,-----,------r---.-----,-----.----.----,.----,-----,

0"'----à'1-0.05

'ëg -0.1

.8-0.15

-0.2 !:----=-:!c::__---:-:!-_=__--:-!-::__--::-!-:,_______..,:-::'=c,_____=~,_______:_~-~='=-=--____:_::'=-::----='o 200 400 600 800 1000 1200 1400 1600 1800 2000time (hours)

Response bottomimpurityon step uI (-) and step u2(--)0.05 r----,.-----.--------,-----,----,----.-----r--------.-----,

àt-~:.: I /----------------- - - - - - - - - - - - - - - - -

= J.8 -0.15 \I

-0.2 ~---!~-____:l~-____:l_=__-____:!~-____:!;:__-____;;;~-____!;;___-____;;;__-_____1o 5 10 IS 20 25 30 35 40 45time (hours)

Figure 4.14: Responses on the new defined inputs.

41

Controlling a binary, high-purity distillation column

During experiments the simulator often crashed. This partly due to the improper tuning ofthe basic loops. If one wants to implement a higher order controller, the basic loop need totuned correctly. Another cause of crashes is the way the experiments were setup. If onereduces the feed flow, one has to know that that implies a smaller distillate and bottoms. Thesimulator however simules more than only the column. These other processes are set on aspecific distillate and bottoms of the simulated column. If they change the settings need to bealtered.

A good example is the control of the reflux vessel. First this control is not tight enough.Secondly, the flow that controls the higher part ofthe refluxlevel has in steady state amagnitude ofabout 4 tons/h. If the feed flow changes in such a way that the change indistillate becomes more than 4 tons the higher part ofthe reflux vessel will give an alarmbecause it cannot be controlled anymore. Some other flow will be used to control the lowerpart ofthe reflux vessel. Ifthis flow decreases significantly the processes depending on thisflow will get unstable. So one has to setup his experiments and his controller correctly.

5.1 Tuning basic control loops

Feedback control is the most important technique used in process control and is used alonein the majority of controlloops. It involves measuring a variabie, comparing it to a targetvalue and adjusting some final control element to try to make the measured variabie (output)equal to the target (setpoint). The technique thus uses measurements ofthe process variabie tobe controlled, rather than exact knowledge ofthe process to work effectively.

The PID controller has been used in conventional analog instrumentation for decades, andit is still flourishing in today's control applications. The PID controller has a theoretical basisfor first order process transfer functions but works effectively for the higher order processtransfer functions of the process industry.

The series algorithm, one of the PID algorithms, is by far the most commonly appliedcontroller algorithm for analog as weIl as digital controllers. It's Laplace domain equation is

(5.1)

This kind of controller is used to maintain flows, levels, temperatures, etc. If a level has tostay at aspecific value (setpoint), a valve is manipulated. These manipulations are mostlydone by PID controllers. They respond on the difference between the measurement of thelevel and its setpoint. Figure 5.1 shows such a Level Indicator .controller. The total ofmeasurement, valve and controller is called a basic loop. The setpoint ofthe level can be setby a higher level controller, such as a double quality controller or a model predictivecontroller.

42

These higher level controllers only perform well ifthe basic loops are tuned correctly, i.e.ifthe setpoints set by the higher level controller are reached in a specified way. In theapplication ofthe simulator some basic loops had to be tuned.

inletflow

outletflow

Level contro!.

-~I

6I ~ __'-------~

---~,

. ,

There were two PI controllers, which controlled thelevels in the ref1uxvessel and in the bottom. Incontrolling a level, a choice has to be made betweentight and averaging control. Averaging control tries tokeep the outletf1ow ofthe vessel as smooth aspossible, preventing the level from reaching its high orlow alarm limits. In this way variations are smoothedout.

Tight control tries to manipulate the outletf1ow insuch a way that the setpoint is reached as soon as

Figure 5.1:possible. The levels in the ref1uxvessel and the bottomdetermine the dynamic behaviour ofthe concentrations. When a higher order controller wantsto inf1uence the concentrations and/or wants to smooth the outlet f10w of a level, the basicloop, containing the PI controller, should be tightly tuned. Ifthe PI controllers cannot controlthe basic loop in the desired way, the higher level controller will stimulate larger controlactions resulting in an unstable process operation.

Before applying the double quality controller, the control ofthe ref1uxlevel and the bottomwas set to tight control. This because these controllers caused the crashes. The tuning wasdone by increasing the proportional gain and decreasing the intregrative gain. An integrativegain is not really needed, because a level in a vessel is an integrative process. The increase inproportional gain was somewhat arbitrairely. Values between 0 and 100 are often used. Thechange in proportional and integral parameters are given in Table 5.1. The values gavesufficient results (see appendix C).

Table 5.1: Changed basic controlloops.

name proportional Kc Integral 'ti Setpoint

old new ola new old new

level ref1uxvessel 2.5 30 25 90 20 40LIC4505s

level bottom 5 30 50 90 40 50LIC4501s

level condensor 5 20 60 90 20 35LIC4514s

Note: The condensor with level controller LIC4514s often got instabie resulting in a crash ofthe simulator. The control structure ofthis condensor was changed and the resultinglevel controller LIC4514s was tuned tightly.

43

5.2 Double quality control

Double quality control is a conventional advanced control strategy. It is applied to thesimulator to compare its results with a model predictive controller. In this paragraph the basicideas are outlined and some results are given.

For the C2-splitter the top stream, ethylene, is the mean product. lts impurity, ethane, hasto be below a certain level otherwise the product will be sent to the flare. There are twoincentives to have the maximum ethane in the top. First it reduces the energy consumption,and second the distillate will increase and ethane is sold as ethylene, which is more valuable.The bottoms, mainly ethane, is recycled via a furnace where it is cracked. The amount of .impurity indicates the loss ofvaluable ethylene which is cracked into less valuable products.

For double quality control the reflux and the reboiler are used as inputs and the top- andbottomquality are the outputs. There exists astrong interaction between the inputs and theoutputs and this often leads to instability for the traditional control scheme (bottom qualitycontrolled by the reboiler heat input and top quality controlled by the amount of reflux). Evenifthe loops are properly tuned, they tend to fight each other. The purer the product streams,the higher the interaction and the more severe the effects.

In fact the separation of a column depends on the ratio between the down-going liquidstream and the up-going vapor stream. Rectification or separation in the top section isimproved by a higher LN ratio (more reflux), whereas stripping or separation in the bottomsection is improved by a lower LN (more heat input). Both internal flows act on both flowsleaving the column: the heat and mass balance are coupled. Thus increasing the amount ofreflux to increase the top purity must also be followed by an increase in heat input tocompensate for the higher amount of liquid to the bottom. From the material balance one canconclude that an imbalance between these streams causes a unnecessarily high impurity in oneofthe two ends, as seen in Figure 5.2.

200 tonlh

100 tonlh

80% light2()O.!o heavy

80 ton/h--r- --~

II

~IIiI

iI ! 180 tonlh

l_T)fC--.-I

20ton/h

100 ton/h

80% light20% heavy

76tonlh

(-----'----,\

~-J

300ton/h

iI

·1!

: i 276 ton/h

LJ-ll__ ~

24ton/h

Figure 5.2: An improperly balanced reflux and bottom heat causes a high bottom impurity.

44

Figure 5.2 shows two situations for a binary distillation column. In both cases the feed,which is at dew point and thus just vaporized, contains 80 ton/h light component and 20 ton/hheavy component. On the left the reflux-feed ratio is RIF = 2; on the right RIF = 3. In the righthand case there is an imbalance between the amount of reflux and the heat input: the amountof flow out ofthe bottom is even more than the heavy component in the feed. The surplus of4ton/h must be light component, causing an impurity ofat least 20%.

In the case of normal operation the magnitudes of the product streams mainly consists ofthe amount of heavy component in the feed for the bottom stream and the amount of lightcomponent for the top stream. Therefor the heat input and the amount of reflux need to be inbalanee. In fact for a given feed the net heat input needs to be constant:

Qnet = R AHR + Freb Ahreb (5.2)

where R = reflux (ton/h)AHR = difference ofheat contents between overhead flow and reflux (kj/ton)Freb = reboiler flow (ton/h)Ahreb = difference of heat contents between reboiler flow inlet and oudet (kj/ton).

To compensate for feed flow variations the Qnet is normalized by the feed flow: Qnet / F.

An operator gave the fol1owing metaphor. Increasing R / F while holding Qnet / F constantpresses the concentration profile like the bellows of an accordion. Increasing Qnet / F whileholding R / F constant is moving the concentration profile upward like moving the accordionas a whole without changing the form ofthe bellow. See Figure 5.3.

To understand separation and Qnet better, two separation factors are introduced. Thephilosophy behind the control scheme was derived from the inverse Nyquist array method:combinations of measured variables give new variables; the same is true for manipulatedvariables.

The separation performance indicator (SPI) indicates the degree of total separation of thecolumn: the lower this number is, the lower is the 'tota!' impurity and the better is theseparation:

(5.3)

For the simulator the changes in separation performance indicator is similar to a transition inthe weak direction and is related to the amount of energy put into the column.

45

Bellows are squeezed together by

increasing R / F

Bellows are moved vertically by

increasing Q net / F

Tray number

~I

II

i

Xlight

I!

Ii

iII

) ,....

HR/F>R/F

Qnet constant

Tray number

~

II

Xlight

LR = constant

Qnet / F < Qnet / F

'Weak direction' 'Strong direction'

Figure 5.3: Metaphor ofthe bellows ofan acordion to explain the influences on theconcentration profiles.

The separation accent indicator (SAI) indicates where the accent of the separation isplaced: bottom, top, or divided equally. The higher this number is, the more the concentrationprofile is pushed to the lower end (the bottom) ofthe column. This means that the top is morein favor than the bottom, regarding the impurities. The separation accent indicator can becompared with the cutpoint:

(5.4)

For the simulator a change in the separation accent indicator is similar to a transition in thestrong direction and is related to Qnet / F. The constant c accounts for different scales of topand bottom measurements and the design ofthe collumn, especially the location ofthe feedtray in relation to the feed composition.

In applying the ideas ofthe double quality controller to the simulator, some difficultiesoccured. The Aspen results were obtained to determine the relations for a double qualitycontroller. A major difficulty arrised in the determination ofthe coefficients decribing Qnet.First there is the inaccuracy ofthe Aspen results. The reboiler heat is ofthe order of 107 W.The differences in reboiler heat at a line ofconstant reflux are small compared to the actualvalues. The values of reboiler heat are not on a straight line, they form a broad band. Secondlythere is Equation (5.2), which suggests a linear relation between Qnet' the reflux and thereboiler. In satisfying this linear relation some coefficients are obtained. A good relationbetween Qnet' the reflux and the reboiler for the simulator, is far from linear. The deviations

46

which occur through linearization are much bigger than the differences in reboiler heat. Thismeans that the relation for Qnet' are only valid for a narrow working area, i.e. some part on aline of constant ref1ux.

At constant feedf10w and constant ref1ux the seperation performance index is constant. Theseparation performance indices describe the lines of constant ref1ux. From the Aspen results aconstant c in the order of 10-6 is found, with the topquality measured in ppm, thebottomquality measured in percent. Such a small number is due to the steep lines of constantref1ux. There is almost no change in bottomquality at a line of constant ref1ux. The problemthat arises is that the separation indicator and the separation accent are almost the same. Thedifference between them, due to changes in the topquality, is completely negligeble.

The double quality controller designed was implemented with the found coefficients, butdid not stabilize the system. A global approach, keeping the double quality idea in mind, usesthe singular value decomposition. In this method the system gain matrix K is decomposed intoU~VT. U and V are orthogonormal matrices and ~ is a diagonal matrix of singular values (oJwhere al > O2 > ... > On . Given that

K=U~VT,

then by rearrangement:

~=U~V.

(5.5)

(5.6)

By using the rotationallinear transformations u = Vu" and Y"=UTy we can make the systemdiagonal at steady state. The resulting decoupled system requires the design of two SISOlinear controllers rather than a 2 x 2 MIMO linear controller. Figure 5.4 shows a blockdiagram for the controlled system. With Sp the setpoints, e the error between setpoints andoutputs

y = ( topqua/ity ) y" = ( spi ) u' = ( reflux) and u = ( reflux )bottomqua/ity' sai' Q"et reboiler

the idea ofthe double quality controller is integrated.

Sp

___ J

Figure 5.4: SVD-based structurally compensated control system.

47

Using logarithms ofthe qualities, the error in topquality, which used to he in ppm,hecomes ofthe same order as the error in hottomquality, which used to he in percent(Equations 5.7).

(In (topquality) ) (rejlUx)

In (bottomquality) = K reboiler (5.7)

The gains in the matrix K are found from the Matlah-simulator. The matrices K, U, ~, V andthe values of the PI controller parameters are given in appendix C. This variant is called thelog-variant. The response on a change feedflow of 5 tons/h is given in Figure 5.5. The linesare the responses and the dashed lines are the setpoints.

Response output variabIe topimpurity in del

]_1...----.1......--:~_~.I......--~_:c::.L..-~_Jo 5 10 15 20 25

time (hours)Response output variabIe bottomimpurity in de I

.:t-----------'----.l...--:~----1..----~______I...____~~_Jo 5 10 15 20 25

time (hours)Response output variabie liquid holdup in ref1uxvessel in de I

]_I...----l.....---;:;;;:;:.l...---.L----Jo 5 10 15 20 25

time (hours)Response output variabIe liquid holdup in bottom in de I

:in----------l.----.l:_s:zs:zs~~_lo 5 10 15 20 25

time (hours)

Figure 5.5: Responses ofthe outputs in double quality experiment 1.

The response is very sluggish, hut seems stahilizing. It takes however much to long andthe rohustness is expected to he very low. 80 let's return to the process without the logarithmstaken of the impurities.

48

With the Matlab-model the static gains are determined like in Equation (5.8). The desireddecoupling has a form like in Equation (5.9). Substituting (5.8) in (5.9) and taking the inverseof gain-matrix K will also give two decoupled systems, one for the topquality and one for thebottomquality. Equation (5.10) gives the required inputs. In this way one gets a clearer viewofwhich outputresponse is effected by tuning a PI controller.

( topquality ) = K ( reflux )bottomquality reboi/er

( topquality) = (

PI error topquality )bottomquality PI error bottomquality

( reflux ) = K- 1 ( PI error topquality )reboi/er PI error bottomquality

(5.8)

(5.9)

(5.10)

This variant is called the inv-variant and results of some experiment are plotted in appendixC. One ofthem is given in Figure 5.6. In this experiment the initial state was not stabie andthe system had to reach the given setpoint first. Then at 23 hours after startup a feedflowchange of 5 tons/h was given.

Response output variabie IOpimpurity in de2

:~tr=-~ :Vf'c;- : Jo 10 20 30 40 50 60 70

time (hours)

Response output variabie botlOmimpurity in de2

l~~~ Jo 10 20 30 40 50 60 70

time (hours)

Response output variabie liquid holdup in refluxvessel in de2

10 60 70

:ii~_"'<?"~:------Y..-i2----'--------------l.-~_lo 10 20 30 40 50 60 70

time (hours)

Figure 5.6: Responses ofthe outputs in double quality experiment 2.

49

The response is still sluggish with much overshoot, but much better then in double qualityexperiment 1. The controller does not control the bottomquality weIl. A large deviation fromthe setpoint is not responded t~. The topquality however reaches its setpoint.

What is still missing is a correction for the feedflow like the factor 1IF. As is mentionedbefore, the liquid vapour ratios detennine the separation. When the feed concentration doesnot change, these ratios have to be maintained. 80 ifthe feedflow changes, which enters thecolumn as a vapour, the other flows have to manipulated keeping the ratios constant. Theseratios are:

between top and feedref/ux

Cl = ---------'''----------feedf/ow + intermediate reboiler + reboiler

(5.11)

between feed and intennediate reboilerref/ux

c2

= --------='--------intermediate reboiler + reboiler

(5.12)

between intennediate reboiler and reboiler c3

= ref/ux - intermediate reboiler

reboiler(5.13)

Applying this correction with the same PI gains as in the double quality experiment de2makes the system unstable. The bottomloop is detuned and the responses of the then stabIesystem are plotted in Figure 5.7. This variant is called 'inv + c's'.

Response output variabIe topimpurity in de8

':Irc-?:,-;;: : J-50 ----'--__-'-- __'___~_-----L.____'___~_----L____'___

o 2 4 6 8 10 12 14 16 18 20time (OOurs)

Response output variabIe bottomimpurity in de8

J

J20

20

18

18

16

16

14

14

12

128

; ;10

time (OOurs)Response output variabIe liquid OOldup in refluxvessel in de8

_:~:z.o 2 4 6 8 10

time (OOurs)Response output variabIe liquid OOldup in bottom in de8

-~~; ;-.o 2 4 6

8 10time (OOurs)

12 14 16 18 20

Figure 5. 7: Responses ofthe outputs in double quality experiment 8.

50

Although the overshoot is less, the response is still sluggish. Although the topquality iscontrolled tighter, the bottomquality deviates even more. Part of it is due to keeping the ratiosof liquid and vapour constant. The major part however is due to detuning the bottomloop. Itseems impossible to control both topquality and bottomquality tightly.

Double quality control is based on decoupling the system. Weischedel et al. [25] concludedthat the decoupling of a high purity column in not feasible. They show that in one case theaddition ofdecouplers leads to a deterioration in control system performance. In that case therelative gain ofthe process was 18.4. Weischedel states that the higher the relative gain theless effective the decoupling. The relative gain for the simulator is dependent of the directionofthe action steps. lts average is 22 which means that the decoupling probably is also notfeasible.

5.3 Linear Model Predictive control

The Matlab-model was controlled by model predictive controllers. In Matlab it is easy toimplement a model predictive controller. In this paragraph the linear model predictivecontroller is outlined.

Let's define the control problem again. The system is sketched in Figure 5.8. In this Figurethe input, disturbances and the outputs are given. This model ofthe MIMO process holds forthe C2-splitter, the simulator and the Matlab-model. Since there are constraints on both theinputs as on the outputs a linear model predictive controller is applied to the Matlab-model.

feedflow

Jfeedconcentration

r 1,I '

reflux -----+-! \/.l ~ topqualityintermediate reboiler -----+-t ~ I •

reboiler -----..; - ~ bottomquahty

liquid distillate~ g L..level refluxvesselvapour distillate~ ~ i

bottoms ----, ~ i level bottom

Definition ofthe control problem.Figure 5.8:

Two different approaches usingdifferent sampling times arestudied. The first idea wascontrolling the process with amodelhorizon describing only thefull responses of the liquidholdups. The approach uses asampling time of 1 minute. Thelinear stepresponses that areindentified, are assumed to beintegrative, and are sampled foronly one hour. The results can befound in appendix D. The bottomquality is not controlled well, probably because in the shortstepresponse of 1 hour no separation can be made between a strong and a weak direction. Thecontrol thus only react in the strong direction.

In the other application the sampling time is set to 5 minutes and the responses are sampledfor far more than 1 hour. The prediction horizon was set to 4 hours. The change in the inputshas to be weighted severe, otherwise the system becomes unstable. Severe weighing the inputsimplies a nonagressive controller. To make the controller more agressive the control sequenceis expanded to a length of 8 control moves for each input. The results of an experiment aregiven in Figure 5.9.

51

In this experiment at 1 hour and 24 hours the reference is changed. At 48 hours thefeedflow is decreased 5 tons/h and at 72 hours the feedconentrations is increased with 5 %.The responses ofthe other variables are given in appendix D. In this example the topquality asweIl as the bottomquality are controlled. Although the bottomquality varies intens thecontroller is able to control in the weak. direction.

Response output variabIe topimpurity in mpc_exp3

400 \

j350 ~Ë300 ~];'f250

~~ ~.~ f\.9 200IJ

\500 \0 20 30 40 50 60 70 80 90 \00

time (hours)

Response output variabIe botlomimpurity in mpc_exp31.25

1.2

ïl.1S~:!< 1.1~

'f 1.05

·î \.8

0.95

0.90 \0 20 30 40 50 60 70 80 90 \00

time (hours)

Figure 5.9: The responses ofthe top- and bottomquality in mpc experiment 3

5.4 Nonlinear Model Predictive control

The nonlinear model predictive controller, based on iterative QDMC (paragraph 2.4.3),was also applied on the Matlab-model. The stopcriterion was replaced by a 5 time loop. Thusinstead of repeating a loop until a certain criterion was satisfied, the loop was repeated only 5times. The resuIts of this controller are plotted in Figure 5.10. In the experiments the samechanges were applied as in the experiments with the linear controller. The weighing oftheinputchanges and the outputs, as weIl as the horizons and constraints are the same as in mpcexperiment 3.

52

Response output variabie topimpurity in mpc_exp4400

""'"]350

Cl>

~300 I'-'è !\'~2S0

f\ ~ï5..200 vg

ISO0 10 20 30 40 SO 60 70 80 90

time (OOurs)

Response output variabie bottomimpurity in mpc_exp41.3

""'"~i 1.2Ü

<Je~l.l

l I'.;:l

.80.9

0 10 20 30 40 SO 60 70 80 90time (OOurs)

Figure 5.10: The responses ofthe top- and bottomquality in mpc experiment 4.

Tbe result is better than with linear model predictive controller. What is significantly betteris the reaction on the disturbances in feed flow (t = 48 h) and feed concentration (t = 72 h).Especially the latter is highly nonlinear, so it was expected that the error through linearizationwas big. Tbe nonlinear variant of MPC reacts therefor better on this disturbance.

53

I- -------------------

Applicabilty of MPC in chemical industry

6.1 In general

Model Predictive Control can control most processes adequately, although sometimesmodifications are necessary. One should put as much knowledge in the controller as isavailable. For example, ifthere is some knowledge about the future disturbances, one shoulduse this knowledge for the prediction.

IfModel Predictive Control is compared to conventional control, the advantage ofMPC isthat it is a general method. It can be applied to almost all cases, and there is for example noswitching between different types of control. For processes with dead time or inverseresponse, MPC can perform equally weIl as a compensated PID controller. A great advantageofMPC compared to conventional controllers is that MPC can handle constraints on theprocess variables.

The application of a Model Predictive Controller requires the presence ofa model of theprocess that should be controlled. Obtaining this model is often the most time consuming partof the application of an MPC controller. After the model has been obtained, severalparameters, such as horizons and weights have to be chosen. This is an iterative process. Bylooking at the results of previous experiments, new parameters are implemented. Althoughthere are guidelines for these parameters, tuning an MPC controller is not as easy as issometimes suggested.

There are some cases with model-plant mismatch when a MPC controller does not performweIl. There always is a certain mismatch between a real process and a model. When there is asevere mismatch the MPC controller forces the process to follow the predicted values. Thesevalues can vary intensly, while the true future outputs are smooth. When this happens themanipulations of the MPC controller can make the process unstable. The conventionalcontrollers (PID) controllers don't have an intemal model, so they don't have this problem.They respond only to the difference between output value and setpoint.

6.2 MIMO and nonlinear processes

MPC has an even larger advantage compared to conventional control in the case of multi­input-multi-output processes. With a good model ofthe process MPC calculates the optimalcontrol sequence. In conventional control relative gain arrays suggest a decoupling based onstatie gains. One could imagine an example were the dynamie behaviour suggests a differentdecoupling. MPC does not decouple the system. It will optimize the control sequence over acertain prediction horizon. If on that horizon one input is preffered to control an output it willbe used even when opposing the decoupling suggested by the relative gain array.

Multi-variable nonlinear systems introduce a special problem in model-plant mismatch,because the 'gain' of a multi-variable process varies not only with frequency, but also with'direction'. It is shown that if a plant is ill-conditioned irrespective of sealing, the control

54

performance is strongly affected by input uncertainty, in particular, when the controller istrying to invert the plant. The MPC controller is such a controller, especially, ifthe penaltyweight on the input moves is low. It should be dear that a MPC controller is potentially badwhen used for an ill-conditioned plant.

The processes do not always have to show their non-minimum phase behaviour in stepresponses. When a MPC controller is designed and the input moves are not sufficientlyweighed, the controller will try to invert the process. Inverted non-minimum phase processesare unstable processes.

Ifthe process we are dealing with is nonlinear and the model predictive controller is linear,the controller has to be detuned to deal with the nonlinearities. Detuning a MPC controllergives the same problems as tuning a MPC controller. For highly nonlinear processes, oneshould use some nonlinear MPC controller or suitable transformations.

Summarizing, one could say that the most interesting processes for applying MPC areprocesses with constraints on the process variables or measured disturbances. The processesshould not be too nonlinear in the operating range, and multi-input-multi-output processes areprobably more interesting for applying MPC than single-input-single-output processes. Iftheprocess is ill-conditioned one should be careful.

55

Conclusions, discussion and further investigation

Model predictive control can control most processes adequately. Although sometimesmodifications are necessary. Especially multi-input-multi-output processes offer advantagescompared to conventional control. It is a general method that can handle constraints on theinputs and the outputs. During the optimalisation ofthe control moves a model predictivecontroller can take technological as weIl as economic objectives into account.

Binary, high purity distillation handles the highly separation ofa mixture containing twocomponents. The separation is based on the differences in volalities (tendencies to vaporize).The process is carried out on trays in a distillation column. On each tray the separation iscarried out a bit further. The distillation process is part ofthe rifining process of cracked crudeoil.

An extensive dynamical simulator simulates the real binary, high purity distillation columnC451 and some adjacent processes. From the simulator and the process some static and adynamic model are derived. These models are used to describe the static and the dynamicbehaviour of the process. The static behaviour of simulator doesn't describe the staticbehaviour ofthe column C451. In the same working area the defined weak and strongdirections are completely twisted. Nevertheless the behaviour of other binary columns is oftensimilar to the behaviour ofthe simulator. The dynamic model is a simplified model andincreasing the model complexity could be the subject for further investigation.

Binary, high purity distillation is a highly-nonlinear, badly scaled, ill-conditioned process.Controlling such a process demands the use of advanced control. Before applying such ahigher order controller some basic loops are tuned differently. A double quality controller isapplied to the simulator. This controller decouples the multi-input-multi-output interactiveprocess and controlles the resulting single-input-single-output systems. The applied controlleris not able to control all the outputs tightly at the same time. Although the literaturecontradicts the feasibility of decoupling a high purity distillation column, the method isapplied in practice and the good results and experiences are there for many years. Furtherinvestigation could be finding a more accurate decoupling and better tuned controllers.

A linear model predictive controller was applied to a simplified modelofthe simulator.Tuning this controller was time consuming. The controller is able to control all the outputs atthe same time. A nonlinear model predictive controller was also applied and performed evenbetter. Further investigation in nonlinear model predictive controllers and their applicability tothe high purity distillation processes should lead to a better controlled simulator.

Obtaining the model for the model predictive controller is a very time consuming part. Incase of a model-plant mismatch the mpc controller will perform less. The controller will forcethe process to follow the model. Model-plant mismatch occurs for instance when the processis highly nonlinear and a linear model is identified. In such a case a nonlinear modelpredictive controller should be considered. When the process is ill-conditioned or showsnonminimum-phase behaviour an mpc controller potentially bad, because it will try to invertthe process. In such a case some precautions have to be taken.

56

Bibliography

[1] Alsop, A. W. and T.F. EdgarNonlinear control ofa high-purity distillation column

by the use ofpartia/ly linearized control variablesComputers chem. Engng, vol. 14, 1990, no. 6, 665-678

[2] Bosley, J.R. and T.F. Edgar, A.A. Patwardhan, G.T. WrightModel-Based control: A surveyIn: Proc. Advanced Control of Chemical Processes (ADCHEM '91)Toulouse, France, 14-16 Oct. 1991.Oxford, UK: Pergamon 1991Selected Papers from the IFAC Symposium, pp. 127-136

[3] Cloodt, H and J. LaurensLIG-evenwichten C2-splilters (in dutch)DSM Services, Dept. Engineering-Stamicarbon, Technology, ModellingUrmond (The Netherlands), 1994Intemal DSM note number 94444 or CRO ME 82 456 WPB-l

[4] Cloodt, H and M. VesterOntwikkeling dynamisch model ter verbetering regeling propaankolom (C651)

Nak 4 (in dutch).DSM Research, Dept. PT-WPGeleen (The Netherlands), 1991Intemal DSM report number RC 919341

[5] Cutler, C.R. and B.L. RamakerDynamic matrix contro/: A computer control algorithmHouston: AIChE 86th National Mtg, 1979

[6] Ganguly, S and D.N. SarafA semi-rigorous dynamic distillation modelfor on-line optimization and nonlinear

contro/.Joumal ofProcess Control, vol. 3, 1993, iss. 3, 153-161.

[7] Garcia, C.E.Quadratic/dynamic matrix control ofnonlinear processes: An application to a

batch reaction process.San Francisco, 1984, AiChe Annual Meeting

[8] Garcia, C.E. and D.M. Prett, M. MorariModel predictive control: Theory and practice, a surveyAutomatica, vol. 25, 1989, no. 3, 335-348.

57

[9] Gelormino, M.S. and N.L. RikerModel-predictive control ofa combined sewer systemInternational Journal of Control, vol. 59, 1994, iss. 3, 793-816.

[10] Jong, P. de and J. Bazelmans, P. DjavdanModel predictive control.Lecture notes internal DSM session, 1995

[11] Jorgi, H.P. and T. Kirnbauer, A. Wiener, F. KluwikNonlinear modelling and linear predictive control ofa distillation plantAdvanced Control ofChemical Processes (ADCHEM '91).Toulouse, France, 14-16 Oct. 1991Oxford, UK: Pergamon 1991Selected Papers from the IFAC Symposium, 53-58

[12] Kerkhof, P.J.A.M.Stofoverdrachtsprocessen (course in duteh, 3 volumes)Department of chemical technology, Technical UniversityEindhoven, 1994Numbers 6760 + 6766 + 6774

[13] Leegwater, H.Industrial experience with double quality multivariable distillation control based on

two separation indicators and net heat inputLuyben, W.L.Practical distillation controlNew Vork, Van Nostrand Reinhold 1992Chapter 16 page 331

[14] Leegwater, H. and P. de Jong, 1. Bazelmans, P. Djavdan, R. EverinkDistillation controlLecture notes internal DSM session, 1995

[15] Lundström, P. and J.H. Lee, M. Morari, S. SkogestadLimitations ofDynamic Matrix ControlCom. chem. Engng., vol 19, 1995, no 4, pp. 409-421

[16] Nisenfeld, A. E. and R.C. SeemanDistillation ColumnsUSA, The Instrument Society of America, 1981

58

[17] Papon, J. and O. GerbiHiecon application to the C2-simulatorAdersa, Paris, France 1994Final research project report, agreement n° 175023

[18] Patwardhan, A.A. and 1.8. Rawlings, T.F. EdgarModel predictive control ofnonlinear processes in the presence ofconstraintsIn: Nonlinear Control Systems Design.Capri, Italy, 14-16 June 1989.UK: Oxford: Pergamon 1990.Selected Papers from the IFAC Symposium, 345-349

[19] Rhiel, F. F. and F. KrahlA model-based control system for a distillation column.Chem. Eng. Technol. 11 (1988) 188-194.

[20] Richalet,1. and A. Rault, J.L. Testud, 1. PaponModel predictive heuristic control: Applications to industrial processes.Automatica, vol. 14, 1978,413-423.

[21] Shinnskey, F.GDistillation ControlUSA, McGraw-Hill Book Company, 1977.

[22] Simminger, 1. and E. Hemandez, Y. Arkun, F.J. SchorkA constrained multivariable nonlinear model predictive controller based on iterative

QDMC.Advanced Control of Chemical Processes (ADCHEM '91).Toulouse, France, 14-16 Oct. 1991.UK: Pergamon 1992.Selected Papers from the IFAC Symposium, 149-154.

[23] Stephanopoulos, G.Chemical Process Control, an introduction to theory andpracticeNew Jersey: Prentice Hall, 1984

[24] Van der Burg, M.W.Applications ofmodel predictive control in chemical industryInstitute for cotinuing education, Eindhoven univerity of Technology, 1994.Final report ofthe postgraduate programme Mathmatics for Industry.

[25] Weischedel, K. and TJ. McAvoyFeasibility ofdecoupling in conventionally controlled distillation columnsInd. Eng. Chem. Fundam., Vol. 19, 1980, No. 4, 379-384.

59

[26] Wilkinson, D.l and M.T. Tham, A.l. Morris (Shell)High performance distillation-case studies in constrainedpredictive control.Advanced Control ofChemical Processes (ADCHEM '91)Toulouse, France, 14-16 Oct. 1991.Oxford, UK: Pergamon 1991.Selected Papers from the IFAC Symposium, 121-126.

60

I An investigation to literature

An investigation to literature

for the Masters Thesis

Model Predictive Control ofa binary high-purity distillation colurn

61

auteurdateid-nr.SubgroupSupervisors:

M.M.E.M. Oonincxapril 1995356834ER, Measurernent and ControlIr. J.H.J.M. Bazelmans (DSM)Dr. ir. A. van de Boom (ER)

1. What was the assignment for the flnal graduation project ?

Study Model Predictive Control (MPC). Use MPC 10 control a hillh-purity distillationcolumn. Such a column is higWy-nonlinear so focus on nonlinear MPC. Good controlperfonnance is due to a good understanding of the process. Therefore we model the plant.

2. What was the related assignment for literature research?

Find literature which deals with the area mentioned in 1. Some books covering the areawould he appreciated. Articles will do also, but keep the subject restricted to applications ofMPC to multivariabie nonlinear processes whereas distillation has the highest interest. Sincethere wiIl probably be plenty articles search recent articles in english or dutch.

3. Concept contents flnal report

AbstractContents1. Introduction2. Model predictive control

2.1. Linear model predictive control2.2. Nonlinear model predictive control

3. Binary high-purity distillation4. Modelling a binary high-purity distillation column5. Controlling a binary high-purity distillation column6. Applicahility ofmodel predictive control on industrial processes7. Conclusions. discussion and further investigationBibliographyAppendix A: An investigation in literatureAppendix B: More about distillation

4. List of terms used for searching

The following tenns were used in search of literature.

#1: Predictive#2: Control#3: Nonlinear#4: Fuzzy#5: Neural

Note: First I started searching in Vubis with the keyword "Optimale regelsystemen", hut thiswas not sufficient. A combination of the ahove tenns #1..#5 in the title word index was muchmore appropriate.

62

5. List of sourees use

When the final project started there was aIready literature available through earlierresearch. During my research some literature was contributed by people who were aIsointerested and involved in some ofthe developments. So two categories can be formed:

Literature already available andLiterature through relevant contributions.

Further literature was searched using the foIIowing sources:

Vubis,INSPEC (CD-ROM 1989 - sept 1994),Dissertations Abstracts (CD-ROM 1988 - march 1995) andScience Citation Index (Cit. Anal. since 1978).

6. Number of seleeted referenees per souree

Literature aIready available:

Literature through relevant contributions:

Vubis#1 and #2 6selected on titie or discription 0

INSPEC 1994 Oan - sept)#1 and #2 and #3 55#1 and #2 and #3 andnot #4 51selected on titie or abstract 2

INSPEC 1993#1 and #2 and #3 62#1 and #2 and #3 andnot #4 45#1 and #2 and #3 andnot #4 andnot #5 43selected on titIe,abstract or article 6

INSPEC 1992#land#2and#3andnot#4 54#1 and #2 and #3 andnot #4 andnot #5 38selected on titie or abstract 2

INSPEC 1991#1 and #2 and #3 andnot #4 andnot #5 27selected on titie or abstract 0

63

INSPEC 1990#1 and #2 and #3 andnot #4 andnot #5 19selected on title or abstract 1

INSPEC 1989#1 and #2 and #3 andnot #4 andnot #5 26selected on title or abstract I

Dissertations Abstracts 1993 - march 1995#1 and #2 and #3 andnot #4 andnot #5 14selected on title or abstract 1

Dissertations Abstracts 1988 - 1993#1 and #2 and #3 andnot #4 andnot #5 22selected on title or abstract 0

Scîence Citation Index 1978 - 0

Note: Scïence citation index was interesting. but did not have new infonnation. The articlesfound in the science citation index were already found in the previous sources.

7. Selection criteria

A major selecting criteria was that the publications are written in dutch or englich. Furtherit is preferred that the literature deals with distillation (high purity, binary) and nonlinearpredictive contro!. Only the interesting publications were being severely evaluated becausethere are plenty.

64

8. Diagram of 'snowbalmethod'

1995 15

1993 6

1992 22

1991 2 11 25

1990 1 18

1989 8

1988 19

1984 7

1979 5

1978 20

9. Diagram of 'citationmethod'

1995 15

1993 6

1992 22

1991 2 11 25

1990 1 18

1989 8

1988 19

1984 7

1979 5

1978 20

65

10. Relations between literature and report contents

no. \ report contents --> no. \ report contents -->2.1 2.2 3 4 5 6 2.1 2.2 3 4 5 6

I x x x 14 x x x x x2 x x x x 15 x x3 x x 16 x4 x x· 17 x x x5 x x x 18 x6 x x x x x 19 x x x7 x x x 20 x x8 x x x 21 x9 x 22 x x x x

10 x x x 23 x x11 x x x 24 x x x12 x 25 x x13 x x x

11. Conclusions

Many publications on nonlinear model predictive control describe a simulated application.There are few industrial (read: rea!) applications. This is problably hecause the technique isrelatively new and not proven yet. The theory is still in a research state and that is probablythe reason why we don't see many books about this subject.

One can see an explosion ofarticles about model predictive control and all kinds ofapplications. If the applications are simulated and the models used are nonlinear we rarely seea model ofa distillation column. Probably hecause the dynamic hehaviour is not captured in afew equations, which makes the model complicated.

The literature that is found should he sufficient to start a graduation project on (nonlinear)model predictive control on binary high-purity distillation processes.

12. Final bibliography

< see bibliography earlier in report >

66

Stepresponses

In this appendix the different stepresponses for the Matlab-model from the inputs to theoutputs are given. The responses oftop- and bottomquality are frrst plotted as a response of960 hours (40 days)~ Then the responses ofthe reflux vessel and the bottomlevel are given for1 hour. These responses are integrative. The slope at 1 hour remains constant. Th.en there is aclose up from the top- and bottomquality (time scale 5 hours).

The liquid distillate and the vapour distillate have only effect on the reflux vessel. Th.ebottoms has only effect on the bottom level. The responses ofthe liquid distillate and thevapour distillate are the same as the response of the reflux on the reflux vessel. Th.e responseofthe bottoms is the same as the response ofthe reboiler on the bottom level. The repsonsesof the liquid an d vapour distillate and the responses of the bottoms are not plotted in thisparagraph.

At the end of this paragraph the responses to a step in a strong and weak direction areplotted. These are responses to a step change in combined original inputs ofthe simulator.First the reflux and the reboiler are both decreased 4 tonslh. This is a step in the weakdirection ofthe simulator. Then the reflux is decreased 0.02 tonslh and the reboiler increasedwith 0.02 tonslh. The latter is a step in the strong direction.

67

Response topimpll'ity (ppm ethanc) on step of+ I kWh refllD(.l;- 0

l:C:::=: : : : : : : : j.9 0 100 200 300 400 500 600 700 800 900 1000

time (oours)-3 Response bottomimpll'ity (% e1hyIcnc) on step of+1 kWh refllD(.

~ 1xl0

I~~ : : : : : : : : 1.8 0 100 200 300 400 500 600 700 800 900 1000

tim: (oours)Response reftlJl(Vcssel (kg) on step of+1 kgIh reftlD(.

- 0

: : : : : : ; : 1J~~tu .1.. 0 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 I

tim: (murs)Response bottomlevel (kg) on step of+1kgIh refllD(.

r~1 : : : : : : : : : ].8 -O.S

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Itim: (hours)

Response topimpurity (ppm ethane) on step of+I kWh refllD(.

I.S 2 2.S 3 3.5 4time(ll>ln)

Response bottornimpll'ity (% elhylenc) on step of+1kWh reftux

5

54.5

4.S43.S2 2.5 3tim: (oours)

1.5

0

-0.1

.~

i-o.21S•.9

-0.3

-0.40 O.S

~

SX 10

4

.~ 3

12Ë!j 1

0

-I0 O.S

68

Response topimpurity (ppm ethane) on step of+I kWh internx:diate reboiler

i~C;::: : : : : : : : 1.9 0 100 200 300 400 soo 600 700 800 900 1000

time (hoIB'S)·3 Response bottomimpll"ity (% ethylene) on step of+I kWh il'f.el1llediate reboiler

.~ I x 10

lOb : : : : : : : : : 1g ·1oB 0 100 200 300 400 SOO 600 700 800 900 1000

time (hoIB'S)Response reftuxvesscl (kg) on step of+I kWh internx:diate reboiler

- I

: : ; : : : : : : j1o~f.. 0 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 I

time (hoIB'S)Response bottomlevel (kg) on step of+1 kWh intermediate reboiler

- I

: : : : : : : :1.:1 j0 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 1

time (holl"s)

Response topimpurity (ppm ethane) on step of+I kWh internx:diale reboiler0.4r---......,--_._---.---...,.....--~--r_-......,--_._--__r--_,

0.3l;-'S~0.2

]-0.1

O=-==---="~-__!_--:_'_:_-----,~--+:___-_±_-___:::L:_-......J:___-......,...,:___-_:!.o I.S 2 2.S 3 3.5 4 4.5 5time (hoIB'S)

I x IO~ Response bottomimpll"ity (% ethylene) on step of+I kWh imermediate reboiler

ob'§ ·1

~ -2'ëi -3oB

-4

-S~-_;'_;;---_!_-___:l~-_+----;_h_-_:--*--7_-~p_-~o 0.5 1.5 2 2.5 3 3.5 4 4.5 Stime (hoIB'S)

69

Response topimpurity (ppm ethare) on sll:p of+I kgIh reboiler

:r:~: : : : : : : : js 0 100 200 300 400 Soo 600 700 800 900 1000

time (oours).J Response bottomill1plrity (% ethylene) on sll:p of+l kgIh reboiler

.~ OxlO

f~+;; : : : : : : : : ~8 .1.8 0 100 200 300 400 SOO 600 700 800 900 1000

time (oours)Response refluxvessel (kg) on sll:p of+I kgIh reboiler

B : : : : : ; : : : ~.. 0 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 I

time (00111'5)

Response bottomlevel (kg) on sll:p of+I kgIh reboiler- 0

: : : : : : : : jj 'I~.B ·2

0 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9 Itime (oours)

Response topimplrity (ppm ethare) on sll:p of+I kgIh reboiler0.4'--~--"""T"""--""""-- __'-------'---"""""'--"'------'--"""""'--'"

0.3l:-

·t°.2's.s

0.1

o0~=--='"::----!-----:JI.~S----2!---""2:L:.S:----=3---=3.~S--4":---4~.s::-----!.S

time (00urs)

Response bottomimplrity (% ethylene) on step of+1 kgIh reboiler

.So~--:=l::---+--.........,.JI.:-----!------:~-~-----=l.:--~--i-~-~SO.S l.S 2 2S 3 3.S 4 4.S

time (murs)

70

Response topimpurity (ppm ethane) on step of+I lcgIh feed flow

ot

.~ I XIO

f.:E~:~·:~:~:~: r;:=:;:~:~:1.8 0 100 200 300 400 500 600 700 SOO 900 1000

. time (holl'S)

Response reftuxvessel (kg) on step of+11cgIh feed tlow

H;?: : : : : : : : 1SS 0 100 2±00;;--~3dO~0-~40b:0-"""""":'5OO~--;600h---;7~00~-S::d00b:--~9OO~--:-::1000

time (holl'S)

Response bottomimpurity (% e1hylene) on step of+I lcgIh feed flow

]0.:[=:::::;;:~:=:::=:~::::=:j.. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 O.S 0.9 I

time (holl'S)

Response bottomlevel (kg) on step of+I lcgIh feed flow

t~ol~:----::,:=:=:==:=:=:==: =:0.1 0.2 0.3 0.4 0.5 0.6 0.7 O.S 0.9time (holl'S)

Response topimpurity (ppm ethane) on step of+I lcgIh feed flow0.2....----.........---r---.........---,,..-----r---r---..-------r---r-------,

·S2.5 x 10

0.15b1;~ 0.1'6-SS

0.05

0~---='"=__-_7_--~----:~-~=__-_=_---:::":_-~:__-__:'_::--~o 1.5 2 2.5 3 3.5 4 4.5 5time (holl'S)

Response bottomimpurity (% e1hy\ene) on step of+I lcgIh feed tlow

2b.~ 1.5

'Ë!B I.8

0.5

O~~~~-_+_--:_L:_-----!~-_+::_-~----::":_---':__-__:'_::---_!.o 1.5 2 2.5 3 3.5 4 4.5 5time(oo...s)

71

Response topimplD'ity (ppm ethare) on sll:p of+0.01 feed concenlrationb 0

l:[ : : : : : : : : : Js 0 ----:-�oo~--::2:±00."...--"="30~0,...--4,-!,00."...--':":Soo!:-:---::6OO~-~7=!OO~--::8±00=---90~0-......,.,1000

time (holD'S)

.';Ë~ lOSU Re_S_po_nse~bo_tto_nu_.mp_W-_i_ty_("_o_e_thyI_enc_)_o_n_ste_p_O_f_+O_._OI_feed__co_nce_nlrati__·on___ ]

CL: : : : : : : : : ]j 00 100 200 300 400 soa 600 700 800 900 1000time (holD'S)

Response retluxvessel (kg) on step of+0.0 I feed concenrration-I,----,-----r---.----,---,---"'T"""--.--.......--......-----,Uc--:-:-:-:-:-:-:-:-:-... 0 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.8 0.9

time (holD'S)

Response bottomlevel (kg) on step of+0.01 feed concentration

1.:01=:=:=:==:=:=:=:=:=QI U ~ U U U ~ U Utime (holD'S)

Response topimplD'ity (ppm ethare) on step of+0.01 feed concenrration

I.S 2 2.S 3 3.S 4 4.S Stime (holD'S)

Response bottomimpw-ity (% e1hyIene) on step of+0.01 feed co11CenlratÏon

0

-50b.~

~-Ioo

'aS

-ISO

-2000 O.S

0.4

b O.3

10.2i.B 0.1

00 I.S 2 2.S 3

time (holD'S)

72

3.S 4 4.S

Response output variabIc topimpurity

-400 S 10 IS 20 2S 30 3S 40 4S SO

time (oours)

Response output variabic bouomimpurityO.S

0.4

0.3

0.2

0.1

00 S 10 IS 20 2S 30 3S 40 4S SO

time (oours)

Action manipulated variabIc ret1Ul(0

-I

-2

-3

-4

-S0 S 10 IS 20 2S 30 3S 40 4S SO

time (oours)

Action manipuIated variabIc reboilcr0 .

-I

-2

-3

-4

-S I

0 S 10 IS 20 2S 30 3S 40 4S SOtime (oours)

73

Action manipulated variabIe refluxO,...---___,.--~--___r__--r__-___,.--__._--_r_--._-___._--....,

-0.005

-0.01

5 10 15 20 2S 30 35 40 45 50time (hours)

Action manipulared variabIe reboilcr0.03 .

0.025.1

0.02 . r T0.015

0.01

0.005

00 5 10 15 20 2S 30 35 40 45 50

time (hours)

74

I DQC results on the simulator

In this appendix the double quality controllers' types and parameters are given. Thedifferent types are explained in chapter 5. For the log variant the gains are

(-0.0418108 0.0415118 )

K = 0.00105215 -0.00109510

and with K =USV· this implies

u =( -0.999668 0.0257596)

0.0257596 0.999668

s = ( 0.058

0

9379 0 )

0.0000358057

v = ( 0.709628 -0.704576)

-0.704576 -0.709628

For the inv variant the gains are

(-0.0142295 0.0141469 ]

K = 0.00737134 -0.00783966

with inverse

K -J = 103 ( -1.07788 -1.94506]

-1.01349 -1.95643

(C.I)

(C.2)

(C.3)

(C.4)

(C.S)

(C.6)

The different parameters are given in Table C.l. TOPPIDP and TOPPIDI refer to theproportional and integrative action, respectively, ofthe series PI controller applied to thetopsection. BODPIDP and BODPIDI refer to the proportional and integrative action,respectively, ofthe series PI controller applied to the bottomsection. In same oftheexperiments the system became instabIe and sometimes it even crashed. When this happenedthe controller was marked unstable.

7S

Table Cl: Double kwality controllers' types andparameters.

naam type TOPPIDP TOPPIDI BODPIDP BODPIDI stabie ?

del log 10 0.02 5 0.01 yes

de2 mv 100 0.2 1 0.002 yes

deS mv 100 0.02 2 0.004 no

de6 mv SO 0.2 1 0.002 yes

de7 inv + c's 100 0.2 1 0.002 no

deS inv + c's 100 0.2 0.1 0.0002 yes

In the latter of this appendix the results of the controllers just described in Table C.I areplotted.

76

Response output variabIe topimpurity in del

]_L.....---L..--::;;_~L..--.......-::;:;;'_'0.1-.---~_~o 5 10 15 20 25

time (hours)Response output variabIe bottomimpurity in de I

1---,--~:=_""'=7--'---~-L...--:i'C_~o 5 10 15 20 25

time (hours)Response output variabIe Iiquid holdup in refluxvessel in de I

]---L-~_;::;;;;;;-~~~o 5 10 15 20 25

time (hours)Response output variabIe Iiquid holdup in bottom in del

:~~------L.....---1---:~S:ZS:ZS;---'----'---~o 5 10 15 20 25

time (hours)

Action disturbance variabIe feedflow in de I

time (hours)Action manipulared variabIe ethylencflow to Iiquid storage in de I

time (hours)Action manipulared variabIe reflux. in de I

252015105

]--:~~o

time (hours)Action manipulared variabIe reboiler in del

l--:~~o 5 10 15 20 25

time (hours)

77

Response output variabie topirnplrity in de2

~~-; ~;-; Jo 10 20 30 40 SO 60 70

time (lxnl'5)Response oUlput variabie bottomimplrity in de2

_~~= :-~:~ ~ Jo 10 20 30 40 SO 60 70

time (oours)Response output variabie Iiquid ooldup in refllro'essel in de2

7060:F-----J--.-....L---:~ ---->----?---'---'--'--:--L.---J

o 10 20 30 40 SOtime (oours)

Response oUlput variabie Iiquid ooldup in bottom in de2

10 20 30 40time (oours)

SO 60 70

Action disturbance variabie feedflow in de2

-~~: I ~-4 .

-60 10 20 30 40 SO 60 70

time (bours)Action manipulated variabie e~lell:flow to liquid storage in de2

j~ j0 10 20 30 40 sa 60 70

time (bours)

Action manipulated variabie refllDC in de2

_~F- : :~ J0 10 20 30 40 sa 60 70

time (bours)Action manipulated variabie reboiler in de22:F: __ : v;- i-20

0 10 20 30 40 SO 60 70time (oours)

78

Response output variabIe topimpuri1)' in deS

]==~~==-===-==-==-===-Jo 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8time (hours)

Response output variabIe bottomimplI"i1)' in deS

.:I==::e=~:· ====:=!.----lL Jo 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8

time (hours)Response output variabIe liquid holdup in reftUltVessel in deS

0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8time (hours)

Response output variabIe Iiquid holdup in bottom in deS

0.2 0.4 0.6 0.8 Itime (hours)

1.2 1.4 1.6 1.8

Action disturbance variabIe feedflow in deS

t : ~·60 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8

time (hours)Action manipulalCd variabIe ethylencflow to Iiquid storage in deS

t; : : : :d\: : 7= ~0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8

time (hours)Action manipulalCd variabIe reft\ll( in deS

] ~ L J0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8

time (hours)

]Action manipulated variabIe reboiler in deS

:'\ J

0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8time (hours)

79

40

40

Response oUlput variabie topimpurity in de6

]~r--=~:~;ç_A..~:::~c====---=-:-=--=-_jo 5 10 15 20 25 30 35

time (oours)Response oUlput variabie bottomimpurity in de6

_~t===:~?'=7~:~;;--L.-~=--L..===-jo 5 10 15 20 2S 30 35 40

time (oours)Response output variabie liquid ooldup in refluxvessel in de6

J==~:~==-S:Z:~--L.-:=-----'-------'---~o 5 10 15 20 25 30 35

time (001.l"s)Response output variabie liquid ooldup in bottom in de6

:~~--'---~:V:-l-..----'------'----.L.-~o 5 10 15 20 25 30 35 40

time (oours)

Action disturbance variabie feedflow in de6

~~ : I : ~·60 5 10 15 20 25 30 35 40

time (oours)Action manipulated variabie ethyleneflow to liquid storage in de6

t~ -~..: C;; :;::::;: j-2

-40 5 10 15 20 25 30 3S 40

time (oours)Action manipulated variabie reflUl( in de6

~I : ~: j·20

0 5 10 15 20 2S 30 35 40time (oours)

Action manipulated variabie reboiler in de6

2:,: ;:;-;; : j

-200 5 10 15 20 25 30 35 40

time (oours)

80

1.6 1.8

Response oUlpUt variabie topimpurity in de7

]_'..1....-:......r....-:-L..--:~:.--L..--...L._:L.-.-rJ

o 0.2 0.4 0.6 0.8 I 1.2 1.4time (0011'5)

Response oUlpUt variabie bottomimp....ity in de7

0.2 0.4 0.6 0.8 I 1.2 1.4time (0011'5)

Response oUlpUt variabie Iiquid ooldup in refluxvessel in de7

0.2 0.4 0.6 0.8 I 1.2 1.4time (0011'5)

Response oUlput variabie Iiquid ooldup in bottom in de7

1.6 1.8

1.6 1.8

0.2 0.4 0.6 0.8 Itime (oours)

1.2 1.4 1.6 1.8

Action disturbance variabie feedflow in de7

~l : : ~·60 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8

time (hoII'S)

Action manipulated variabie ethyteneftow to liquid storage in de7

~rs:: : A : ;J\ : ~-s0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8

time (0011'5)Action manipulated variabie reflux in de?

:~ :\

: ~ \: r~

0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 tBtime (hoII'S)

Action manipulated variabie reboiler in de?

3 I

: :; : ;r : \: : ,J0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8

time (0011'5)

81

time (oours)Respome output variabie bottomimplI'ity in de8

:f5; :--- : : ; : 1-I0 2 4 6 8 10 12 14 16 18 20

time (hours)Response oUlput variabie liquid holdup in reflUKVessel in de8

.:G5:::Z : : : 10 2 4 6 8 10 12 14 16 18 20

time (OOll's)Response oiÇut variabie liquid holdup in bottom in de8

:d~::??: ~0 2 4 6 8 10 12 14 16 18 20

time (hours)

Action disturbance variabte feedflow in de8

~t ~0 2 4 6 8 10 12 14 16 18 20

time (hours)Action manipulated variabie ethyleneflow to liquid storage in de8

~b: : -: : : j0 2 4 6 8 10 12 14 16 18 20

time (hours)Aetion manipulalcd variabie reflUK in deS

'I:~ : : l-200 2 4 6 8 10 12 14 16 18 20

time (hours)Aetion manipulated variabie reboiler in deS

.::k2 :- : : : l0 2 4 6 8 10 12 14 16 18 20

time (hours)

82

I MPC results on Matlab-model

In this appendix the mpc results on the simulator are plotted. The reference traject is thesame for all the experiments. So are also the disturbances. The reference and the disturbanceschanges as follows:

t = 0 the reference for the topquality is 400for the bottomquality is Ifor the reflux vessel is 5000for the bottom is 3500

t = I the reference changes for the topquality to 200changes for the reflux vessel to 4000

t = 24 the reference changes for the bottomquality to 1.2changes for the bottom to 3000

t =48 the f~ed flow changes from 80 to 75 tonslht = 72 the feed concentration changes from 0.80 to 0.85.

The experiments are ordered as follows:

expo I:exp.2:exp.3:exp.4:

Linear mpc with sample time I minLinear mpc with sample time 5 minLinear mpc with sample time 5 min and more severe bottomquality weightsNonlinear mpc with sample time 5 minutes.

In the experiments 3 and 4 only the control strategy is altered. Not the weigths or the horizons.

83

Response 0UIpUI wriable IlIp8npuri1y .. mpc_upI400

_350!!~300E

.5250

:1200\

î \50 ~100

0 10 20 30 40 50 60 70 10 90 100tine{hotn)

Response 0UIpUI wriable bollomnpgiIy .. mpc_ClIpI1.8

1.6

I~1.411

i1.:

:80.8

0.60 10 20 30 40 50 60 70 10 90 100

tme{hotn)

Response 0UIpUI wriable \iquid hold~ .. rdkaxvesscI" mpc_ClIpI5200

~5000

]4800

~4600...044009-~4200=I ~,E4000

~ ,3800

0 10 20 30 40 50 60 70 10 90 100tine(holn)

Response OlIIpUI-mbie Iiquid hoId~ iI boaom iI mpc_ClIpI3800

..3600l!!.

J3400'032009-

:la,83000

12800

26000 10 20 30 40 50 60 70 10 90 100

tine(holn)

84

is x \0'.;:!.

~7.16151--L_--'-_---L.-_.....L...-_..L..-----I_----L_---'-_.....L-----J

.~ 0 \0 20 30 40 50 60 70 BO 90 \00.mc(holn)

rEo \0

: : : ;: :Î: : j~ 30 40 50 60 ~ BO 90 ~

.mc(holn)

x \0'

i.;:!.4121-------------------IO~----'-_......L..__.L._____L_ ___L..__..L.......___L_ ___L..._ _'______'

o 10

ioe!. k,V'- ..J--------""'\§\.5 f"'V"

j

85

x 10· Açtion dislurbanc:e variable icdIIow it mpc_CII'I8.1

8

7.9~o!!. 7.8

ju.7.6

7.S -7.4

0. I

10 20 30 40 SO 60 70 80 90 100line(boln)

Adion cIisIurbancc variabIc feeck:oI_lIIa1ÏOü it JDPC_CII' I. .0.8S i-

SO.84

1°·83

u 0.82

i O.81

0.8

0.79° 10 20 30 40 SO 60 70 80 90 100

line(boln)

lS..------,-----.......-----r------r-------r------,SlO

·1 S •.~.:- "-'. .l::.. ····.···· .. : ,........ . ~., ..-- -_-.-:.,.,;......:.................~~

.

°0~---~1000~----:2000-:'-:-----:3-:'000-:-----4....ooo~----5000~:-----~6000

-..0.08...-----,-----...,.------r------r-------r------.0.06-·······- '-'---"_."-'- ----- .-----.-.•. ---...-.-----.-.---•• ••• _. ••__••_ - • __ 0 __.- ..._ ••

~ 0.04

·1 0.02

01----------------------------o.020L..-----1000~----2000.J-----3000....L-----4OOO..J-----.-:'-----~6000

anpIe

lSr-----,-----,...----..-----...,....-----r-----,10

-;;-iSo,....-----~------:.----------:.--o-- .....--

·5L..- ~ ...L_ ....L... ..J_ ._:'_ ~

o 1000 2000 3000 4000 5000 6000-..

86

SSOO.____--.____-~.____--.____-___,r__-_,r__-___,--___,--___,--____r--___,

~

I:o

I IA A

.lil 4OOOj-lHII\.Jc,.-------v-------..,...,------t/-"-\-,....--.....=-I V W u V

10 20 30 40 SO 60.... (hoIn)

70 10 90 UlO

4OOO.____----,--~-- ....--.,...--...,....--...--r_-.......,r-----r--__,

lSOOO~--I':-O---:'20i:-----:30i:-----J40L-----JSOL-----J6OL-----l,0'-------:lIOi:------:l90i:--~UIO

.... (hoIn)

87

,2.1 x 10

i 2.Î'------'- ~ ...,

i 1.9

10 20 30 40 SO 60tine(hocn)

70 80 90 IClO

• Action manipuIated wriable iltenncdiate reboiler in DlpC_cxp2i 7

XI0

f"t : : : : ~ : :ZJ16

.11 s.so 10 20 30 40 SC) ~ 70 80 90 100tine(hocn)

1.3 x 10' Action manipulared wriabIe reboiler in DlpC_cxp2

i 12~

,ij.81.1I!

10 10 20 30 40 sa 60 70 80 90 100

tine(hocn)

10' Action manipuIatcd variabIe iquid disb1aIe in DlpC_cxp24.2 x

~ 4Ol

i 3.8...].3.6

3.40 10 20 30 40 sa ~ 70 80 90 100

tine(hocn)

X10' AClion manipuIatcd wriable Y8pOIW cIistiaIe in DlpC_exp2

i~4

!!

t2

Jo . .,

0 10 20 30 40 sa ~ 70 80 90 100tine(hocn)

U xtO'AI:tion~ vftbIe boIloms .mpc_ap2

i 1.6o!!-JU

1.2

I0 10 20 30 40 sa ~ 70 80 90 100

tine(hocn)

88

II \0' Action di!lulblncc wriIble bd1Iowmmpc:_ClIp28.1

8

7.9~~7.8

IJ]7.17.6

7.'

7..(

° 10 20 30 40 ~ 60 70 80 90 UlObne(holn)

Action di!lulblncc \'U'iab\e feedtoIll:CIlluilion mmpc:_exp2

0.8'

_0.84..:..{O.SJ

0.82:2,0.8\

0.8

0.79

° \0 20 30 40 '0 60 70 80 90 UlObne(holn)

Modelcalculalion bne iJ mpc:_exp230.------...,.._----....,.------,.------...,..-----....,.----~

200 400 800 \000 \200

0.08.------..,...----~-----r_----...,.._----~----__,

O.Q16 •• --••_--••••••-_._••••••_._--- ••••••• ----. ----••_- ....----.- __ a --.-.

$ 0.04

·1 0.02

°-o.020!------:200~----4OO:-L:-----6OO~----IOO-L.:-----~1000L----~I200...U,-----.....,----......,.------r----~----.,...----ï

\0$.1 ' ... C\ """"-------

o.,L- ....L.. --1 .L.- ..L. --1 --J

o 200 400 600 800 \000 \200...89

400n----,r---__,~-__,~-___r--....--_,_--_,_--_,_--..,..--__,

ISO20 30 SO 60 70 800 10 40 90 100

tme(boln)

Raponsc~ variable lJoltonWuplfty ÎI mpc_cxp31.25

1.2

just~ 1.1e;..

.;- 1.0S

.t Ij0.9S

0.90 20 30 40 SO 60 70 80 90 100

tme(boln)

Response~ variable Iiquid holdup ÎI rellux\asel ÎI nJPC_cxp35S00 r

'Ol!

1::f\I!

AOS9"4000

'V VVI} 3500

30000 10 20 30 40 SO 60 70 80 90 100

tine(boln)

Raponsc~ variable Iiquil~ ÎI boaDm ÎI nJPC_cxp3

l3500)3000OS

12500

120001500

0 10 20 30 40 50 60 70 80 90 100tme(boln)

90

lt \0' Action~ wriable rdult .. mpc:_cxp32.\

i 2V'- -...~

.II! 1.9

1.80 10 20 30 40 50 60 70 10 90 100

tine(holn)

i lt\O' Action~wriabIe iItcnncdiab: rdloiler .. mpc:_ap37.5

~

~ 7.8I! 6..5.11 6.11 5.50 10 20 30 40 50 60 70 10 90 \00

1Re(holn)

lt \0' Action manipulaled wriable reboiler iI mpc:_cxp31.3 ....r-

i 1.2 -~

.11.1i I -

0.90 \0 20 30 40 50 60 70 10 90 \00

tine(holn)

10' AcIion manipuIatcd wriobIe iquid cIisIiIate iI mpc:_ap3

IJl~ : : : : 1: :r' : I:r·6

3.40 \0 20 30 40 50 60 70 10 90 \00

tine (\lOIn)

lt \0' Action manipuIatcd wrilble vapour dÎSdl* is mpc_ap3

î4

12JO .

0 10 20 30 40 50 60 70 10 90 \00bne(\lOln)

• AcIion~ wriabIe boaoms iImpc_ap31.B x 10

i 1.6~~

§1.4.11.2

I •0 \0 20 30 40 50 60 70 10 90 \00

bne(\lOln)

91

.

x 10' AcIion disturbancc wriablc '=cdlIow • mpc_ClIp38.1

8

7.9~è!- 7.8

ju7.6

7.S

7.4

° 10 20 30 40 50 60 70 80 90 100-(boln)

AcIion cIislurbance wriablc~ il mpc.ClIP3

0.8S

_0.84..:..lo.n" 0.82

10.81

0.8

0.79

° 10 20 30 40 50 60 70 80 90 100linc(holn)

-a:~: : : (i ; ~ ~ jI" _~~\ . ". : \"'~".= .:_.), i.;."------__ :.~'-""'_ :__ ~- _o 200 400 600 800 1000 1200

sample

0.08.-------,.-----...,.-----...,...----....,....----.....,..-------,0.06 _- •• - ••• - ••••• _•• " ••••••••••••••••••••••••••_.- •••• _ ••••••••••_.

g 0.04

.I 0.02

01--------------------·--------­.-o·020L-----200.L-----4OO.........----6OO........-----800........----1000.J.-----I....200

sample

3r-----,-----,----....,..-----r-----"ï-----,

oL- ......l. ...J.... ..L.- --lL- ~:__----::

o 200 400 600 800 1000 1200sample

92

"

Respome outputvariabIe topimpurity in mpc_exp4

9070 80

400...----r----r----r---..........--"""T'"----r----.---r-------.

j350Ü

[300Q,......

'~250 \ ~·[2001-l1----:~_----'-...c.::::::.._-----I-~-----rl----=::::::.-- -lS V

150L..---"----..........---'---.........---.L.----'------'---L..----'o 10 20 30 40 SO 60

time (tours)

Respome ol1put variabIe bottomimplrity in mpc_cxp4

Ir- ( V-I

I~IV

1.3

î]-1.2Ür/.bl.1.~

.~ 1oB

0.9o 10 20 30 40 SOtime (tours)

60 70 80 90

Respome output variabie liquid ooldup in retllro'essel in mpc_exp4i5S00r-----,---..,..---,-----,.--.....,----r----.,,.-----r-~......

15000u

~4sooe'ö4oool-+il\~-------------++_:,,_-----"""T'"P_"'----_1: V V]3Soo"0'S •·2'3oooL..!..__...L-__....a....__-L__--L.__--'-__--I L-__.l..-_--J

- 0 10 20 30 40 SO 60 70 80 90time (tours)

Respome output variabIe Iiquid toldup in bottom in mpc_cxp438oor----r---r--..,..----r---r----r---r--..,..------,

~3600e H----:=---~j3400...;3200

~3000..e"0]-2800

26oo0~---JIOL.....----120---3..J..0---4O.L.---SOL----'6OL.....----170----J.80--.....J90

time (b>urs)

93

,::f: ::_~:v~~\re'~i.:_~ :c: j1.8 --L....._"""'--_~----L_-.L.._--'--_....I..--..::= __

o la 20 30 40 SO 60 70 80 90time (m...s)

~ 104 Action manipulated variabie intermediate reboilcr in n1pC_cxp4~6.4 x ~-""""""-----'---""""----'---'------r--"""'---

i~:f: :~: : \ : :cl~s.s

.~_ 0 la 20 30 40 SO 60 70 80 90time (murs)

1.3 x 105 ----.-_--r-_Aet_ion""""Tmarn_·_pul_ate""T""dv_aria_ble_re.---bo_ilcr_in.......mpc cxp4~_----r-_

I:::L: :'-: : ~ : :;: jo la 20 30 40 SO 60 70 SO 90

time (murs)

i 4 X 104 Action manipulated variabic liquid distilate in mpc_cxp4

!:~[---'----'--:: --.--:~:~~:: [----r--j.2"3.4- 0 W ~ ~ 40 ~ 60 ~ 80 90

time (murs)

i x~IO~4---.-__AT"""Ctl_·on_marn--,·p_u1ate_d_var...,....ia_blc_vapo---,--... _disti_late--,i_nmpc__cxp4~_-r--_

I:ot : : : : : : : : J:.> la 20 30 40 so 60 70 80 90

time (murs)

2 x 104----._~-ACti-·o-nmaN.-·puI_ate.......d v_ari_abl_cbo-r-ttD_ms_in-Tmpc cxp4~_--,.-_

I'o:E: : ~: : : : :L : 1o la 20 30 40 SO 60 70 80 90

time (murs)

94

, ,

Action disturbance variabie feedflow in ntpC_exp4

81-----------------,

~7.9

~78~ .~7.71102 7.6

9080706040 SOtime (oours)

Action disturbance variabie feedconcenlration in ntpC_exp4

7.S I-

7.4L..---........--........--"----"----"----"'----"'----...L---'o 10 20 30

0.8S

90

.

80706040 SOtime (oours)

302010

:Z0.a4

]0.83~-.;0.82

8.0.81

0.81-------------------------

0.790

Modelcalculation time in ntpC_exp4

200 400 600sample

800 1000 1200

o.~! : ~_~~M_ln_..~ : I006 •... - - ••....•. _... .•.••..••... - ••...••. _.•••• _ .•--.- •h~ _ ;.._ '" -.'_'.o"'" _ •••~ ••

-0.02o 200 400 600 800 1000 1200

sampleMPC optimi2lllion time in mpc_exp4

300r-----....,..----~---.....,...----~----,.---__,

,.,.,. t ~ ••e.. .,-... 200 ri. .\ .....;-... r' .~

iIOO_·~·~;~~:·?~"t~~;:~l:..~~·- -. ~~:.. '. :'...Ol....- -'-- --L .l.-- --L.. --I'-__-!o 200 400 600 800 1000 1200

sample

9S