Nov. Applying Model Predictive Controllers on ... · Abstract- Implementation ofModelPredictive...

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The 33rd Annual Conference of the IEEE Industrial Electronics Society (IECON) Nov. 5-8, 2007, Taipei, Taiwan Two Case Studies for Applying Model Predictive Controllers on Chemical Processes N. Danesh Pour, A. Montazeri, J. Poshtan, M.R. Jahed Motlahgh Iran University of Science and Technology E-mail: n daneshpour@iust. ac. ir, amontazeri@iust. ac.ir, jposhtangius. ac.ir, j [email protected]. ir Abstract- Implementation of Model Predictive Control as the most famous advanced process control method, in real processes has some practical issues that are ignored in many simulation studies and needs more attention especially in implementing the controller. For this purpose, in this paper two chemical processes are simulated in HYSYS software as a more realistic environment that exhibits many properties of real plants. The control and identification is performed by connecting HYSYS and MATLAB softwares in a real-time manner. Some of the main practical issues that are considered here are: pre-test of the plant, test design and identification requirements, dealing with low-level control loops and controller tuning to attain the best performance. Simulation results show that without having enough knowledge on such important points, practical implementation of this very useful advanced process control method will be very challenging. I. INTRODUCTION Model Predictive Control (MPC) is widely adopted in the process industry as an effective means to deal with large multivariable constrained control problems. The main idea of MPC is to choose the control action by online repeated solving of an optimal control problem. This aims at minimizing a performance criterion over a future horizon, possibly subject to constraints on the manipulated inputs and outputs, where the future behavior is computed according to a model of the plant. MPC has been used in industry for more than 30 years, and has become an industry standard (mainly in the chemical and petrochemical industry) due to its intrinsic capability for dealing with constraints and with multivariable systems. Most commercially available MPC technologies are based on a linear model of the process [1]. In spite of this amount of practical implementations of MPC in process control in the last decades, a very few percents of thousands of papers published in this area are dedicated to study practical issues of applying model predictive control [2, 3]. In this work two different chemical processes are simulated in HYSYS software and a complete procedure for applying MPC control is done for each one including pre tests, design of test signal, system identification, controller design, pre tuning, final tuning and dealing with low-level control loops. The paper is organized in five sections. After this introduction, section 2 gives a review to MPC method and its corresponding system identification procedure used in this work. Section 3 is a brief overview on how to apply model predictive control on low-level PID loops and their relative considerations. In section 4, two chemical processes are introduced and simulation results are shown. Final section gives some concluding remarks. II. MODEL PREDICTIVE CONTROL In this section a brief introduction to model predictive control and system identification methods used in this work is given. A. MPC Algorithm Various MPC techniques such as Dynamic Matrix Control (DMC) [4], Model Algorithmic Control (MAC) [5], and Internal Model Control (IMC) [6] have demonstrated their effectiveness in industrial applications during the last two decades [1, 6, 7]. However, generalization of the 'traditional' MPC techniques to more complex cases has been with some difficulties. For example, most of the traditional techniques incorporate feedback into the algorithm in an ad hoc way, such as by adding a constant bias term in the prediction of the future outputs. In addition, the traditional techniques are not applicable to integrating systems (which are common in chemical process industries), when using step or impulse response models. Recently, there have been efforts to interpret MPC in state-space framework [8, 9, 10]. This not only permits the use of well-known state-space theorems, but also allows straightforward generalization to more complex cases such as systems with general stochastic disturbances and measurement noise. In this work, MPC formulation presented in [11] is adopted for controller design based on state-space model. B. System Identification Procedure The most important, time consuming and costly part in implementation of model predictive control is process identification [12]. This includes gathering priori information about the system, pre-tests, identification test design, data treatment and applying identification algorithm on collected data. Operator information and historical data can be very useful to prevent doing pre-tests and even some final tests. But when there is not any information available a priori (like the one in this work) pre-tests are necessary. The simplest way to do the pre-test is to apply step change to each manipulated input and measurable disturbance separately. This is required for determining proper sample time based on the fastest response of the process and also getting some idea about ranges of the semi-linear operation of the process. The proper sampling time will influence the quality of the identified model 1-4244-0783-4/07/$20.00 C 2007 IEEE 580

Transcript of Nov. Applying Model Predictive Controllers on ... · Abstract- Implementation ofModelPredictive...

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The 33rd Annual Conference of the IEEE Industrial Electronics Society (IECON)Nov. 5-8, 2007, Taipei, Taiwan

Two Case Studies for Applying Model PredictiveControllers on Chemical Processes

N. Danesh Pour, A. Montazeri, J. Poshtan, M.R. Jahed MotlahghIran University of Science and Technology

E-mail: n daneshpour@iust. ac. ir, amontazeri@iust. ac.ir, jposhtangius. ac.ir, [email protected]. ir

Abstract- Implementation of Model Predictive Control as themost famous advanced process control method, in real processeshas some practical issues that are ignored in many simulationstudies and needs more attention especially in implementing thecontroller. For this purpose, in this paper two chemical processesare simulated in HYSYS software as a more realistic environmentthat exhibits many properties of real plants. The control andidentification is performed by connecting HYSYS and MATLABsoftwares in a real-time manner. Some of the main practical issuesthat are considered here are: pre-test of the plant, test design andidentification requirements, dealing with low-level control loopsand controller tuning to attain the best performance. Simulationresults show that without having enough knowledge on suchimportant points, practical implementation of this very usefuladvanced process control method will be very challenging.

I. INTRODUCTION

Model Predictive Control (MPC) is widely adopted in theprocess industry as an effective means to deal with largemultivariable constrained control problems. The main idea ofMPC is to choose the control action by online repeated solvingof an optimal control problem. This aims at minimizing aperformance criterion over a future horizon, possibly subject toconstraints on the manipulated inputs and outputs, where thefuture behavior is computed according to a model of the plant.MPC has been used in industry for more than 30 years, and

has become an industry standard (mainly in the chemical andpetrochemical industry) due to its intrinsic capability fordealing with constraints and with multivariable systems. Mostcommercially available MPC technologies are based on alinear model of the process [1].

In spite of this amount of practical implementations ofMPCin process control in the last decades, a very few percents ofthousands of papers published in this area are dedicated tostudy practical issues of applying model predictive control [2,3]. In this work two different chemical processes are simulatedin HYSYS software and a complete procedure for applyingMPC control is done for each one including pre tests, design oftest signal, system identification, controller design, pre tuning,final tuning and dealing with low-level control loops.The paper is organized in five sections. After this

introduction, section 2 gives a review to MPC method and itscorresponding system identification procedure used in thiswork. Section 3 is a brief overview on how to apply modelpredictive control on low-level PID loops and their relative

considerations. In section 4, two chemical processes areintroduced and simulation results are shown. Final sectiongives some concluding remarks.

II. MODEL PREDICTIVE CONTROL

In this section a brief introduction to model predictivecontrol and system identification methods used in this work isgiven.A. MPC Algorithm

Various MPC techniques such as Dynamic Matrix Control(DMC) [4], Model Algorithmic Control (MAC) [5], andInternal Model Control (IMC) [6] have demonstrated theireffectiveness in industrial applications during the last twodecades [1, 6, 7]. However, generalization of the 'traditional'MPC techniques to more complex cases has been with somedifficulties. For example, most of the traditional techniquesincorporate feedback into the algorithm in an ad hoc way, suchas by adding a constant bias term in the prediction of the futureoutputs. In addition, the traditional techniques are notapplicable to integrating systems (which are common inchemical process industries), when using step or impulseresponse models. Recently, there have been efforts to interpretMPC in state-space framework [8, 9, 10]. This not only permitsthe use of well-known state-space theorems, but also allowsstraightforward generalization to more complex cases such assystems with general stochastic disturbances and measurementnoise. In this work, MPC formulation presented in [11] isadopted for controller design based on state-space model.B. System Identification ProcedureThe most important, time consuming and costly part in

implementation of model predictive control is processidentification [12]. This includes gathering priori informationabout the system, pre-tests, identification test design, datatreatment and applying identification algorithm on collecteddata. Operator information and historical data can be veryuseful to prevent doing pre-tests and even some final tests. Butwhen there is not any information available a priori (like theone in this work) pre-tests are necessary. The simplest way todo the pre-test is to apply step change to each manipulatedinput and measurable disturbance separately. This is requiredfor determining proper sample time based on the fastestresponse of the process and also getting some idea aboutranges of the semi-linear operation of the process. The propersampling time will influence the quality of the identified model

1-4244-0783-4/07/$20.00 C 2007 IEEE 580

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and transient response of controlled process. Also, linearoperation ranges of the process give an approximate magnitudeof the final test signals. There are some useful test signalswhich are used in industrial MPC products such as multi-inputstep tests and PRBS signals. Here, a quasi-PRBS signal withmodified spectrum, named Generalized Binary Noise (GBN)[12] is used, which is especially fitted to MPC application andused more frequently in real applications. Low-pass filteringon collected data is needed, if there is measurement noise.After data preparation, a subspace identification algorithm,named SMI [13], is used to identify a state space model of theprocess.

III. APPLYING MPC ON Low-LEVEL CONTROL LooPs

Traditionally industrial processes have relied strictly onregulatory loops that are designed to stabilize operation of theprocess. These loops are generally based on PID regulatorycontrol. When implementing an advanced control system, suchas Model Predictive Control, on a process with regulatory PIDloops, one is faced with the following two options [14]:

Direct Control: Break the loops and have the model basedcontroller to manipulate the control valves directly.

Cascade Control: Leave the loops and have the model basedcontroller to manipulate the setpoints of these loops.

In the following a brief overview on how to interfacingmodel predictive control and low-level control loops ispresented which is mainly based on [14].

A. Direct ControlA general scheme of direct control is represented in Fig. 1.

In this appraoch, the following procedure must be followed:1- Break the low-level loops.2- Identify a process model. Inputs are the valve positions

and outputs are process variables.3-Design a conventional model predictive control.Since the inputs of the model are the valve positions, valve

limits can be entered directly into the algorithm as the inputconstraints. Therefore, handling of the actuator constraints canbe done straightforwardly. However, because the low-levelloops are taken out, one may lose the efficiency in disturbancerejection. Note that disturbance dl must propagate through theprocess to affect y before any control action can take place.

dil d2lsP y

NWC ~~~~Plant

-.

Fig. 1. Direct MPC implementation

Furthermore, identification can be unsafe, costly and time-consuming with these loops taken out, especially when theprocess contains unstable or excessively slow dynamics.

B. Casecadet ControlCascade control is depicted in Fig. 2. The following

procedure applies to this approach:1. Identify a process model in which the inputs are setpoints

to the low-level loop controllers and the outputs are processvariables.

2. Design a model predictive controller.The resulting cascade control structure helps to eliminate the

disturbances that may occur inside the loops more efficientlyand quickly. In addition, identification can be made easiersince unstable or excessively slow dynamics are stabilized ormade faster by regulatory loops. On the other hand, since thevalves are not directly manipulated, handling of valveconstraints becomes more complicated and also performanceof the MPC controller is affected by the inner-loop controllers.

sP

2*I_

Fig.I.. Cascade MPC implementation

Fig. 2. Cascade MPC implementation

IV. SIMULATIONS

In this section, at first two chemical processes and thereasons for selecting them as the benchmark for this study areintroduced. Also, results of identification and control gained byconnecting HYSYS and MATLAB softwares in a real-timeenvironment will be presented. The models of these processesare selected from [15].

A. Plug-flow reactorThe first process is a plug-flow reactor (PFR) which is useful

in many industrial processes particularly those in which a solidcatalyst is required. This reactor has a vessel that is packedwith solid catalyst. Unlike CSTR reactors, in tubular reactorstemperature and composition vary down the length of thereactor, and they also vary with time. This makes models anddynamics more complicated. A diagram of this process isshown in Fig. 3 in a HYSYS folwsheet. Outlet pressure iscontrolled by valve V6 and reactor temperature is controlled bycoolant water flow rate. Feed flowrate is considered as adisturbance variable.

PFR3 PC3F3 VS 5="""<; *5 ..R3utv5out ~~~~~~~~~~~v6out

Q3 ~~~~~~~V6

FC3TC3 lags3

Fig. 3. Plug-flow reactor flowsheet

581

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In order to obtain an idea on how to manage control loops toget the performance simulations are performed in four differentcontrol structures: Only PID control, direct MPC, cascadeMPC and PID control and finally one loop controlled by PIDand another one by direct MPC.

In the first, second and fourth structures, PID control is runby embedded PID controllers in HYSYS software and in allcases, MPC is run in MATLAB environment. For eachstructure, both disturbance rejection and setpoint trackingcapabilities of the controllers are examined. In each case, bestcontroller tunings are obtained for regulatory response, becausethe most common task defined for a real process is to work ona predefined operating point and the most important task of thecontroller is rejecting the effects of arriving disturbances.A complete system identification procedure is done

individually for each of the mentioned MPC implementationapproaches and three different state space models areidentified. The step test results depicted in Fig. 4 are used todetermine the sampling time (Ts), magnitude of the GBNsignals and duration of test signal to excite the plant around itsnominal operating point. Based on the shortest settling time ofdifferent channels with and without PID loops, sampling timeto collect data is chosen to be 30 seconds for all identificationexperiments. Besides, the magnitude of the GBN test signalhas been set to 5 percents of nominal value for each input. Theduration of the test by the measure proposed in [12] is chosen1800 minutes. The first half of data is selected foridentification and the second half is used for validationpurpose.

temperature pressure177.5

¶ //I2 \

177

176.50 50 100 150 200

the system are plotted in log-scale in Fig. 7. Based on thisinitial result and some trial and errors, the order ofthe model isselected n=12. The identified state-space matrices are validatedusing second half of data as shown in Fig. 8. The VAF criteriafor this data are 88.3070 for output 1 and 99.9261 for output 2.Besides, the step responses of the real plant and identifiedmodel for two outputs are plotted in Fig. 9. This step responseexhibits a better validation for MPC framework. Theidentification for two other structures is accomplished in thesame way and due to lack of space their results are notincluded here. These models are used for predicting thebehavior ofthe process in model predictive controller.

The control results for applying four different structures areshown in Figs. 10 to 13. PID controllers are tuned based onrelay-feedback method [16]. These controllers have fairly gooddisturbance rejection, but poor setpoint tracking. However, ascan be seen in Fig. 10, the response of temperature controllerto input flow change assumed as a disturbance, is slow. DirectMPC and Cascade MPC-PID implementations show quitedifferent responses, especially in the tracking problem.

TC setpoint300.

280hlIIl

260

2400 200 400 600 800 1000 1200 1400 1600 1800

PC setpoint190

170~1

160 1.0 200 400 600 800 1000 1200 1400 1600 1800

Feed rate0.42,

0.3610 200 400 600 800 1000 1200 1400 1600 1800

time (min)

Fig. 5. GNB test signalstemperature

290

280

270k

260-

2500 200 400 600 800 1000 1200 1400 1600 1800

pressure

Pnn,~~~~~~~~~~~~~~~~~~~~

Fig. 4. Step pre-test results

By these settings, the GBN test signals which excite theplant around the nominal inputs are shown in Fig 5. Since theaim is to obtain a single multivariable state-space model, theseinputs are applied simultaneously and the resulting outputs are

shown in Fig. 6. Before identification, in order to obtain a

measure of the order of the system, Hankel singular values of

190

180

170 I u ~~II~ IiI1

160

0 200 400 600 800 1000 1200 1400 1600 1800time (min)

Fig. 6. GNB test signals

582

C0

U. 1+1_1

0.4

0.38

0

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singular value plot

a) 10

'in 1 0

100

io-1100 5 10 15 20 25

number

Fig. 7. singular values ofthe plant using collected data

20 X real output L- - - - validation output

10-

-0

performance. As can be seen in Figs. 11 and 12 regulatoryresponses are different but both are better than PID case.However, pressure regulation is better handled by the PIDcontrol. This is because of the interaction effects betweeninputs in a multivariable structure. Direct MPC shows fastertracking with overshoots and no offset error in comparisonwith cascade MPC-PID control which presents a slow trackingwith offset error and no overshoots. Properties of the latterapproach mainly come from PID control system behaviour. Incomparison with PID control it can be said that an overallbetter performance is obtained, but referring to pressurechanges and its corresponding control actions, these twostructures are not completely suitable for use in thisapplication.

30 Another control structure is obtained by breakingtemperature PID control loop and using MPC to do this jobwhile keeping PID control for pressure regulation. Thisapproach gives the best results in comparison with threeprevious methods. Fast tracking, better pressure andtemperature regulations and completely acceptable controlactions are obtained in this way.

-20 -6 6.5 7 7.5 8 8.5 9 9.5 10 10.5

xl

11

104

20 F

C\M

0

6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11t(sec) x 104

300

Fig. 8. Plant and model outputs for validation data

Step response of identified low order model vs. real plant

Direct MPC

2550 100 200 300

time (min)

lYU:'0,

185

180

1750 2000 4000 6000 8000 10000 120

t(sec)Fig. 9. Step responses of plant and identified model

)OO

Identified linear models were used for the initial parametertuning ofMPC controllers in each case and some corrections inthe tuned parameter is required for obtaining the best possible

400 500 600

Fig. 10. Temperature control (tracking response)

B. Azeotropic Distillation ColumnDistillation is the most frequently used separation technique

in the chemical and petroleum industries. The design andcontrol of this important unit operation is vital for the safe andprofitable operation of many plants. The column used here forsimulations is a heterogeneous azeotropic distillation column.

In theoretical columns ideal VLE behaviour is assumed, butin this column components have such positive deviations fromideality (large repulsion) that two liquid phases can occur. Thecolumn operates at 124.1 kPa at the top and 152 kPa at thebottom. The decanter temperature is 40 degree C andcondenser duty is designed to be 16 GJ/hr.

583

TT 1 T T~~

104

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274.5

274

Cascade MPC-PID273.5

273I I -~~~~~~~

Q3 utility flow rate46

44

42

40 _

380 100 200 300

time (min)400 500 600

20 40 60 80 100 120 140time (min)

Fig. 11. Temperature control (regulatory respor

181

180

l Casca

Direct MPC/

176

PID- - - Direct

CascaMPC&

100 200 300 400time (min)

Fig. 12. Pressure control (regulatory response

160 180 Fig. 13. Control actions

nse) Column pressure is controlled by valve V6 in the overheadvapour line using PCI. Decanter temperature is controlled bymanipulating decanter heat removal (TC3) and a traytemperature (tray 5) is controlled by manipulating reboiler heat

de MPC-PID input (TC1). In addition to these controlled variables, there arethree associated variables which must be maintained in a

'ID specific range: column base level, aqueous and organic levels.Column feed rate and refluxed organic phase flow rate are

- considered as measurable disturbances. The nominal value ofthese two DVs are 275 and 350 kmol/hr, respectively.

Since the task of keeping the mentioned levels in requiredlimits can be done well by PID controllers, the best approachhere is to maintain these loops unchanged and cascade \PCcontrol with PID low-level loops in column pressure and

MPC temperature and decanter temperature control.PID The main control problem is to maintain controlled variables

in their setpoints against incoming disturbances. For evaluation500 600 of setpoint tracking ability of the controller, a step change in

decanter temperature is also considered to be followed bycontroller. Simulation is carried out for 6 hours. After one

FC2

r

RCYt-1

I vI wk3wkUsU-Ufl I

cUt LG I

W1k I

p 1 pl V22out ,C_tX'

Fig. 14. Azeotropic distillation column flowsheet

584

Vale V6 action

MPC&PIDPID

272.51~~~-

272

271.5

271

Direct MPC

270.5

270

- PID- - - Direct MPC

Cascade MPC-PIDMPC&PID

175

174 _

173o

Amm-L

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hour, column feed rate has been changed to 335 kmol/hr andminute 150, a step reduction in refluxed organic flow rate hbeen applied. After 4 hours, decanter temperature setpoint hbeen changed to 35 degree oC. Figs. 15 and 16 shows tlresults of simulations for comparing PID control performanwith cascade MPC-PID structure in both disturbance rejectiand setpoint tracking.

V. CONCLUSION

In this paper, the task of applying model predictive contron two chemical processes was considered. HYSYS arM\ATLAB were connected in the same computer to providereal-time environment for simulations. HYSYS software w(used for simulating dynamic behavior of the processes aiM\ATLAB software was connected to it in order to run contralgorithms. Different control strategies were examined on ea(process and simulation results showed that in these two casethe best approach for improving control performance is to ke(some control loops under PID control and replace the others tor cascade them with model predictive control systerHowever, selection of a suitable structure is not necessarieasy. In [14], it is suggested that cascade control might b(

Column temperature (tray 5)121

atasas,heice

on

rolnd

,asndrolch

epbym.ily

Decanter temperature1,

step changeto feed rate

step change torefluxed organic flow rate

--- PID

l,0 50 100 150 200 250 300 350

time (min)

Fig. 15. Column and decanter temperatures

Column pressure126

MPC125- -----

PID

I0A _--- 1/- VI

I I% I'I

I

II

selected for fast control loops while direct MPC is suitable forslower loops. Anyway, our results show that part of controltask should be performed by previous PID structure withoutany change.The most difficult part of MPC implementation is model

identification. In cases that historical data or operatorsexperience is not available, a very risky and time consumingprocedure is also needed to be done for gathering informationof the plant linear operating range, suitable sampling time andduration of the test signal. Here multivariable state-spacemodels were identified for all cases studied and the resultswere validated using step response data and validation outputsof the real plant. Validation is one of the important parts inidentification procedure, because if the identified model givespoor predictions, plant retesting will be required that is verycostly and undesirable for plant owners. The results obtainedfrom this study show why the use of dynamic simulators forevaluating the performance of advanced controllers beforepractical implementations is so popular today.

REFERENCES

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[2] D. Morrison. "Is it time to replace PID?," InTech Letters, March 2005.[3] Morari, M. and JH Lee "Model Predictive Control: Past, Present and

Future,"Computer and Chemical Engineering," vol. 23, pp. 667-682,1999.

[4] C.R. Cutler, and B.L. Remaker, "Dynamic matrix control a computercontrol algorithm," in Proc Automatic Control Conf, Paper WP5-B, SanFrancisco, CA, 1980.

[5] R. Rouhani, and R.K. Mehra, "Model algorithmic control (MAC): basictheoretical properties," Automaitca, 18, 401-406, 1982.

[6] C.E. Garcia, D.M. Prett, and M. Morari, "Model predictive control theoryand practice-a survey," Automatica, 25, 335-348, 1989.

[7] J. Richalet, A. Rault, J.L. Testud, and J. Papon, "Model predictiveheuristic control application to industrial processes," Automatica, Vol.14, pp. 413-420, 1978.

[8] K.Y. Lim, and D.G. Fisher, "A state space formulation for modelpredictive control," AIChE Journal, Vol. 35, pp. 241-249, 1989.

[9] J.P. Navratil, K.Y. Lira, and D.G. Fisher, "Disturbance feedback inmodel predictive control systems," Proc IFAC Workshop on Model-Based Process Control, pp. 63-68, Atlanta, GA, 1988.

[10] J.H. Lee, M. Morari, and C.E. Garcia, "State-space Interpretation ofModel Predictive Control," Automatica, Vol. 30, No. 4, pp. 707-717,1994.

[11] M. Maciejowski, Predictive Control With Constraints. Prentice-Hall,London, 2002.

[12] Y. Zhou, Multivariable System Identification For Process Control.Elsevier, 2001.

[13] M. Verhaegen, P. Dewilde "Subspace model identification: part 1: Theoutput-error state-space model identification class of algorithms" Int. J.Control, Vol. 56, No.1, pp.1187-1210, 1992.

[14] Y. Lee, J.H. Lee and S. Park, "On interfacing model predictivecontrollers with low-level loops," Industrial and Engineering ChemistryResearch, Oct. 1999.

[15] W.L. Luyben, Plantwide Dynamic Simulators In Chemical Processingand control. M.Dekker, 2002.

[16] K Astrom, and T. Haggland, PID Controllers: Theory, Design andTuning. Second ed., ISA, 1995.

1210 50 100 150 200 250 300 350

Fig. 16. Column pressure

585

40 -

38

36

123 _

122 H

12,~--