Soft Constrained based MPC for RobustControl of a Cement Grinding Circuit

Guru Prasath ∗ Bodil Recke ∗∗ M. Chidambaram ∗∗∗,2

John Bagterp Jørgensen ∗∗∗∗,1

∗ FLSmidth Private Limited, FLSMIDTH HOUSE, 34, Egatoor,Chennai - 6030103 (e-mail: mgp-in@flsmidth.com)

∗∗ FLSmidth A/S, Valby, Denmark (e-mail: bre@flsmidth.com)∗∗∗National Institute of Technology, Tiruchirappalli, India

∗∗∗∗DTU Compute, Technical University of Denmark, Kgs. Lyngby,Denmark, (e-mail: jbjo@dtu.dk)

Abstract: In this paper, we develop a novel Model Predictive Controller (MPC) based onsoft output constraints for regulation of a cement mill circuit. The MPC is first tested usingcement mill simulation software and then on a real plant. The model for the MPC is obtainedfrom step response experiments in the real plant. Based on the experimental step responsesan approximate transfer function model for the system is identified. The performance of theMPC in the real plant compares favorably to the existing control system based on fuzzy logic.Compared to the other controllers, soft MPC handles the real time uncertainties effectively. Italso regulates the cement mill circuits better and in a plant friendly way by using less variationin the manipulated variables (MVs).

Keywords: Model Predictive Control; Cement Mill; Industrial Process Control

1. INTRODUCTION

The annual world consumption of cement is around 1.7billion tons and is increasing at about 1% a year. Theelectrical energy consumed in the cement production is ap-proximately 110 kWh/ton. Global cement production useapproximately 2% of the worlds primary energy consump-tion and 5% of the total industrial energy consumption(Concil, 1995; Austin et al., 1984). 30% of the electricalenergy is used for raw material crushing and grinding whilearound 40% of this energy is consumed for grinding clinkerto cement powder (Fujimoto, 1993; Jankovic et al., 2004).

Clinker grinding can be done either using a ball mill ora vertical roller mill. It is the final stage in cement pro-duction where the clinker is ground with other materialsto form fine cement powder. The ball mill is the mostcommon process for cement grinding. The reasons are ithigh reliability, its possibility of gypsum dehydration andthe easy maintenance of ball mills.

The ball mill, is designed for grinding of clinker, gypsumand dry or moist additives to produce any type of cementand for separate dry grinding of similar materials withmoderate moisture content. All mill types may operatein either open or closed circuit and with or without pre-grinder, to achieve maximum overall grinding efficiencyand high flexibility in terms of product quality. Fig. 1shows a typical layout of the mill. Usually ball millsare divided into two chambers depending on the size ofthe input material used and the availability of a clinker

1 Corresponding author.2 present address: Department of Chemical Engineering, IndianInstitute of Technology, Chennai, India (e-mail: chidam@iitm.ac.in)

Mill inlet

Mill discharge

Ball filling 2. compartment

Ball filling 1. compartment

Drive

Intermediate diaphragm

Discharge diaphragm

Fig. 1. Ball mill layout

pre-grinding circuit. Up to 5% gypsum and/or naturalanhydrite is added to regulate the setting time of thecement. Other chemicals, such as those which regulateflow or air entrainment, may also be added. Fine grindingusing ball mills is in general extremely energy inefficient.Many plants use a roll crusher to achieve a preliminarysize reduction of the clinker and gypsum. Just 4% of theenergy available is efficiently used for grinding.

Efficient control is required in order to reduce the specificproduction costs while maintaining the product qualityat an acceptable level. The control philosophy for cementmill thus remains challenging as low production resultsin huge power consumption and high production maycause inefficient grinding. The cement grinding controllermust provide economically efficient production which is

Preprints of the 10th IFAC International Symposium on Dynamics and Control of Process SystemsThe International Federation of Automatic ControlDecember 18-20, 2013. Mumbai, India

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equivalent to delivery of a consistent on target productquality with minimal power consumption.

Conventionally, the grinding circuits are controlled bymulti-loop PID controllers and linear predictive controllers(Chen et al., 2008). The uncertainties in the linear pre-dictive model of the cement mill circuit stems from largevariations and heterogeneities in the feed material as wellas operational variations. These sources of variations giverise to nonlinear behavior and variations in the dead-times of the cement mill circuit. The models are obtainedfrom step response experiments conducted on the cementmill circuit. The uncertainties may be characterized bythe gains, time constants, and time delays in a transferfunction model. To control such circuits, we propose aMPC that uses soft constraints (soft MPC) to robustlyaddress the large uncertainties present in models thatcan be identified for cement mill circuits (Prasath andJørgensen, 2009; Prasath et al., 2010).

The developed soft MPC is compared to a normal MPCon the ECS/Cemulator (Prasath et al., 2010). In thispaper, we provide the details on the implementation ofsoft constrained MPC on a real cement grinding circuitand compare its performance to the existing fuzzy logicbased control system.

This paper is organized as follows. The principle of predic-tive controller consisting of a regulator and an estimatorwith soft output constraints is described in section 2.Section 3 gives the details of model identification and thecomparison of soft MPC with fuzzy logic controller in areal cement milling process and the results are discussedfrom the plots. Conclusions are given in Section 4.

2. SOFT MPC ALGORITHM

The principle of soft MPC algorithm used to control thecement mill circuit is discussed in Prasath and Jørgensen(2009). The cost function is formulated as a regularized`2 output tracking problem with input and soft outputconstraints as given in (1a).

min{z,u,η}

φ =1

2

N−1∑k=0

‖zk+1 − rk+1‖2Qz + ‖∆uk‖2S

+

N∑k=1

1

2‖ηk‖2Sη + s′ηηk (1a)

subject to the constraints

zk = bk +

n∑i=1

Hiuk−i k = 1, . . . N (1b)

umin ≤ uk ≤ umax k = 0, . . . N − 1 (1c)

∆umin ≤ ∆uk ≤ ∆umax k = 0, . . . N − 1 (1d)

zk ≤ zmax,k + ηk k = 1, . . . N (1e)

zk ≥ zmin,k − ηk k = 1, . . . N (1f)

ηk ≥ 0 k = 1, . . . N (1g)

in which ∆uk = uk − uk−1.

The output predictions used by the regulator are generatedbased on the finite impulse response coefficients extractedfrom the model. To have offset free steady state controlwhen unknown step disturbances occur, we include a

Fig. 2. Penalty function for soft MPC (red) and normalMPC (blue).

integrator feedback loop to the controller (Prasath andJørgensen, 2009).

The objective function with input and soft output con-straints is converted into a dense quadratic program whichcan be solved efficiently. The cost function and the solutionof the quadratic program are discussed by Prasath andJørgensen (2008, 2009). The feedback loop to the givencontroller is a simple integrator based on the FIR modelsobtained to add as a simple bias to the estimator. Herewe make an assumption that the disturbances enter thecontroller as constant output disturbances. The valuesof zmin,k − ηk and zmax,k + ηk are determined based onvariance of the noise in each measurements. Figure 2illustrates the basic principle of soft constrained basedMPC (soft MPC). The soft MPC provides one way to de-tune the controller such that it can handle the significantuncertainties in the process. The main difference betweenthe normal MPC and the soft MPC is that the penaltyfunction of the normal MPC is quadratic whereas thepenalty function of the soft MPC is constructed such thatit is zero or almost zero within the dead-zone betweenthe soft limits and grows quadratically when the set-pointerror exceeds the soft limits. The small penalty within thesoft limits ensures that the controller produces a steadystate offset free response. Also the small penalty withinthe limits makes the controller react only a little to smallvariations in the measurements.

3. SYSTEM IMPLEMENTATION

The developed soft MPC is initially implemented forthe ECS/CEMulator. The ECS/Cemulator is a rigorouscement plant simulator that is normally used for operatortraining and can also used as a realistic surrogate for areal cement mill for comparing different controllers bycreating similar operating conditions. Prasath et al. (2010)provides a comparison of the soft MPC and the normalMPC using the ECS/Simulator. In this paper, the softMPC is tested in a real cement mill and compared withthat of the existing high level controller based on thefuzzy logic principle. The main difference in controllingthe cement mill in the CEMulator and the real plant isthat the CEMulator has uncertainty and noise defined by

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Fig. 3. Typical operator station of a cement mill controller

the user and operates the same way all the time. TheCEMulator is based on a first principle models of theprocess and mechanical conditions. The real plant has anumber of significant uncertainties to be handled becauseof raw material variations, wear and tear of mechanicaldevices etc.

The plant where we implement the controllers is an in-dependent grinding unit. The major raw material clinkeris obtained from plants from different parts of India andtransported through railway wagons. The cement millpresent in the plant is a closed circuit ball mill with twochambers. The cement ball mill has a design capacity of150 tonnes/hour with a sepax separator. The separatorcan be varied around 70% to have better efficiency. Therecirculation ratio of the circuit is 1.5%. The final producttypes are Ordinary Portland Cement (OPC) and Puzza-lona Portland cement (PPC). The difference between OPCand PPC is that in PPC, fly-ash is added as one of the rawmaterial to improve the fineness of the cement. Thus theproduction level and the operating range is different forOPC and PPC. A typical operator station for the cementmill circuit is shown in Figure 3.

All the signals coming from the sensors of the grindingprocess are collected in an ECS SCADA (SupervisoryControl And Data Acquisition of FLSmidth) system. Themeasurement data is obtained from a PLC and loggedevery 10 seconds in the system. The quality measurementdata (fineness/blaine) is entered every hour as an off-linemeasurement using the samples collected through an auto-sampling system.

The real time implementation of the soft MPC applicationis done using a high level expert system tool developed byFLSmidth. The execution interval of MPC will be 1 minand the data update in the expert tool will be 30 seconds.

The normal running range of the elevator load is from20 kW to 35 kW for obtaining blaine of 300 cm2/g. Thefuzzy calculation engine executes every 30 seconds. Thecontroller actions can be shifted from Fuzzy to MPC andvice-versa using a software switch. The measurement dataobtained from the PLC through input/output modulesin the field is filtered, scaled and validated before usedin the controller. The output from the controller is alsoscaled and configured for bump less transfer when it ismade online. This is important in order to have smoothertransition of set points when the controller is shifted frommanual to auto control loop. Interlocks are included in caseof emergency shut down during abnormal conditions likepower failure, feed starvation etc.

3.1 Model Identification

The models of the system are identified in open-loop by do-ing step response tests. The general principle in the modelconstruction phase is to stabilize the system around itsdesired operating point and then perturb the system witha step change of each of the process inputs. The responsesof the output (measurement) variables are recorded. Theprocess inputs must be perturbed individually. By thedata obtained using this procedure, a model describingthe influence of the process inputs on the process outputscan be constructed. The controller uses this model forcomputation of the control actions. From Figure 4, it isevident that the model obtained using step response testsare quite uncertain. Thus when these models are used fordesigning the controller, the performance of the controllerdegrades because of uncertainties in the model (Prasathand Jørgensen, 2008).

The feed and separator speed are perturbed individuallyand the possible output values are measured and logged.

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Fig. 4. Model identification using plant data from step response tests. The model identified is indicated by a solid blackline. The other lines indicate plant data obtained from step response tests.

The lab measurement (fineness) is modeled by increasingthe frequency of sample collection i.e., collecting samplesfor every 15 min and then generating a model based onthe data.

We consider 2 × 2 MPC controllers based on the modelsY (s) = G(s)U(s) with Y (s) = [Elevator Load; Fineness]and U(s) = [Feed; Separator Speed]. Based on the plotsfrom the step experiments as shown in Fig. 4, we identifythe system transfer function

G(s) =

(0.47)(2s+ 1)

(17s+ 1)(15s+ 1)e−4s

1

12s+ 1e−3s

(−0.9)

(10s+ 1)(12s+ 1)e−5s

2.5

(4s+ 1)

(2)

3.2 Controller Performance Comparison

Since the source of raw material for grinding is obtainedfrom different regions, the physical and chemical propertiesof the clinker are different for each batch of the clinkerused. This varies the grinding pattern for each of theclinker types and impacts the grinding efficiency of thecement mill. Hence the operating region of the parameters

in the mill shifts continuously. To compensate for thequality variations in the feed material, we include targetadaptation using a real time optimizer over the controllers.This helps in deciding the optimum operating range of themill for improving the grinding efficiency. The elevator loadis the parameter for control and so the target of elevatorload is changed periodically depending on the quality ofthe final product. This helps to achieve optimum produc-tion while achieving the desired fineness.The controllervaries the feed and separator speed to maintain elevatorload and fineness.

The frequent power restrictions in the plant do not allowto run the cement mill more than 16 hours in a day.Normally the plant runs during the night, when theexternal electricity demand is low, and is stopped duringthe day. Mostly, the cement mill produces PPC as the mainproduct. Also based on the demand, the cement plant maydecide to run with OPC product for 3 − 4 hours. Hence,we normally get only 12 − 15 hours of continuous millrun to test our controllers. Depending on the dispatchrequirements, sometimes the plant will be deciding onthe type of cement to be produced for the particular dayresulting in frequent shifting of operating points for thecontroller.

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0 2 4 6 8 10

25

30

35

Soft MPC

Ele

vato

r

0 2 4 6 8 10

340

345

350

Fin

enes

s

0 2 4 6 8 1065

70

75

Sep

Spe

ed(%

)

0 2 4 6 8 10140

145

150

155

160

time (hours)

Fee

d(t/

h)

0 5 10 15

25

30

35

Fuzzy Controller

0 5 10 15

340

345

350

0 5 10 1565

70

75

0 5 10 15140

145

150

155

160

time (hours)

Fig. 5. Comparison of soft MPC with the fuzzy logic controller for a cement grinding circuit. The controlled variablesare elevator (denotes the elevator load in kW) and fineness (cm2/g) and the manipulated variables are feed (tph)and separator speed (%). The red line indicates the reference targets in measurements and blue line indicates theactual values. The dotted lines denote limits for both actuators and measurements

To have a common platform for comparison of the fuzzylogic controller and the soft MPC, both controllers aremade online in similar operating conditions by runningthe controllers with the same source of clinker. This helpsus to have a fair comparison of the controllers with similarmaterial properties and it is quite easy to evaluate theperformance based only on the process variations. Thetarget adaptation based on operating range shift is alsomade available for both controllers.

First, the fuzzy controller is taken online for 15 hoursand then the controller is switched to soft MPC forthe next 12 hours. Both controllers are tested with thecement mill running continuously in a single recipe andproducing Puzzalona Portland Cement(PPC). In PPC,

gypsum, clinker and fly ash are the feed materials. Thisis to make sure that the controllers are compared in afair basis with same operating conditions. It is confirmedthat the fuzzy controller is perfectly tuned such that thesoft MPC is tested against the best controller availablein the plant. This is justified as the plant runs the fuzzycontroller continuously whenever the mill is started andthe plant personnel is quite satisfied with the performanceof the fuzzy controller.

The following tuning and weighting factors are used whileapplying the soft MPC scheme to control the grindingcircuit: Prediction- and control horizon N = 300, numberof impulse response parameters n = 100. The tuningweights on the errors are Qz = [5 × 10−2 0; 0 2.5 ×

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0 0.5 1 1.5 2 2.5 358

60

62

64

Sep

Spee

d(%

)

0 0.5 1 1.5 2 2.5 3135

140

145

time (hours)

Feed

(t/h

)

0 0.5 1 1.5 2 2.5 3

20

25

30

Ele

vato

r

0 0.5 1 1.5 2 2.5 3270

280

290

300

time (hours)

Fine

ness

Fig. 6. Control variables (CVs) and actuator variations (MVs) with soft MPC running the controller online with OPCproduct. The pink line in the plot indicates the recipe change over and also the time when the controller is takenonline

10−5]; the tuning weights on the manipulated variablesare S = [5 × 102 0; 0 2.5 × 105]; and the quadratic softconstraint tuning weights are Sη = [9× 103 0; 0 5× 102].The sampling time Ts = 1 min. The linear soft constrainttuning weight is set to zero.

The tuning weight on the fineness is small compared tothe tuning weight on elevator load; the fineness is anhourly sampled measurement and less accurate comparedto elevator load. Also the weight on the separator speedis set to a large value because it is not permitted to moveaggressively. This ensures a relatively stable operation.

From Fig. 5, we see that the soft MPC has the ability tocontrol and stabilize the cement mill. The manipulatedvariables are smooth with the controlled variables arereasonably controlled. However it can be seen that thecontroller runs at its high limits and hence the actuatormovements are restricted to move on the higher side. Theseconditions occur because of the conditions in the plantwhere there is inconsistency in quality variations of theraw material fed into the mill. Nevertheless, because ofthe limited variations in the separator speed, we observethat the standard deviation of the fineness has improvedsignificantly for the soft MPC compared with the fuzzylogic controller.

Fig. 6 illustrates the performance of the soft MPC fora case where there is a large margin for the controllerto adjust its actuator to maintain the desired target ofcontrolled variables. The MPC algorithm uses soft con-straints to create a piecewise quadratic penalty functionin such a way that the closed loop system is less sensitiveto model uncertainties. Thus the soft MPC moves theactuator very little within the soft constraints and takesaggressive actions outside the soft limit band resulting insmooth and stable operation of the cement mill circuit.

During the tests, it has been observed that the softMPC handles operating point transitions better than theFuzzy controller. In addition soft MPC reduces the qualityvariations (variations in fineness).

4. CONCLUSION

A controller with soft output constraints for handlingthe uncertainties of the cement mill circuit has beendeveloped and implemented in a real cement grindingcircuit plant. We implemented the controller in a realtime cement plant to compare the performance of thecontroller with the existing Fuzzy controller running onthe plant. The results indicate that the soft MPC handlesthe significant uncertainties efficiently and provides verygood performance compared to other controllers.

REFERENCES

Austin, L.G., Klimpel, R.R., and Luckie, P.T. (1984).Process Engineering of Size Reduction: Ball Milling.Society of Mining Engineers, New York.

Chen, X.S., Li, Q., and Fei, S.M. (2008). Constrainedmodel predictive control in ball mill grinding process.Powder Technology, 186, 31–39.

Concil, W.E. (1995). Efficient Use of Energy UtilizingHigh Technology: An Assessment of Energy Use inIndustry and Buildings. World Energy Council, London,United Kingdom.

Fujimoto, S. (1993). Reducing specific power usage incement plants. World Cement, 7, 25–35.

Jankovic, A., Valery, W., and Davis, E. (2004). Cementgrinding optimisation. Minerals Engineering, 17, 1075–1081.

Prasath, G. and Jørgensen, J.B. (2008). Model predictivecontrol based on finite impulse response models. In ACC2008, 441–446. American Control Conference 2008, Sea-tle, Washington.

Prasath, G. and Jørgensen, J.B. (2009). Soft constraintsfor robust MPC of uncertain systems. In ADCHEM2009. IFAC, Koc University, Istanbul, Turkey.

Prasath, G., Recke, B., Chidambaram, M., and Jørgensen,J.B. (2010). Application of soft constrained mpc to acement mill circuit. In 9th International Symposium onDynamics and Control of Process Systems, DYCOPS2010, 288–293. IFAC, Leuven, Belgium.

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