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KColumn otation

Process control

2009 Elsevier Ltd. All rights reserved.

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* Corresponding author. Tel.: +1 418 656 7487; fax: +1 418 656 5343.E-mail addresses: jbouchard@xstrataprocesssupport.ca (J. Bouchard), desbiens@gel.ulaval.ca (A. Desbiens), rene.delvillar@gmn.ulaval.ca (R. del Villar).

1 Partially supported by NSERC (Canada).2 Partially supported by FQRNT (Qubec).

Minerals Engineering 22 (2009) 519529

Contents lists available at ScienceDirect

Minerals Engineering

journal homepage: www.elsevier .com/locate /mineng3 Tel.: +705 693 2761x3427; fax: +705 699 3431.4.1. Intermediate level control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5244.2. Control strategies based on metallurgical objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

5. Current practice, research trends & future applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5245.1. Current practice and challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5245.2. Steady-state simulation: metallurgical performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5245.3. Sensor development and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5255.4. Dynamic modelling and simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5255.5. Process control myths and reality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527Contents

1. Introduction . . . . . . . . . . . . . . . . .2. Process description. . . . . . . . . . . .3. Modelling . . . . . . . . . . . . . . . . . . .

3.1. Prediction of recovery . . . .3.2. Dynamic behaviour . . . . . .3.3. Soft sensors . . . . . . . . . . . .

4. Process control . . . . . . . . . . . . . . .0892-6875/$ - see front matter 2009 Elsevier Ltd. Adoi:10.1016/j.mineng.2009.02.004. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523ModellingSimulationccepted 3 February 2009

eywords:

important contributing factor is certainly the under usage of available control capabilities. Researchers andpractitioners have been interested in column otation simulation and control for more than two decades.This paper provides an overview of the literature focused on these specic elds of research. It also dis-cusses some future investigative issues and how the current industrymay benet frompast developments.history:d 9 August 2008

Even after having been used for several years in mineral processing plants, the full potential of the columnotation process is still not fully exploited. There is obviouslymore than one reason explaining this, but oner t i c l e i n f o a b s t r a c tpartement de gnie des mines, de la mtallurgie et des matriaux, Qubec, Qubec, Canada G1V 0A6a Process Support, 6, Edison Road, Falconbridge, Ontario, Canada P0M 1S0(Laboratoire dobservation et doptimisation des, procds Process Observation and Optimisation Laboratory), Universit Laval, Pavillon Adrien-Pouliot,ment de gnie lectrique et de gnie informatique, Qubec, Qubec, Canada G1V 0A6(Laboratoire dobservation et doptimisation des procds Process Observation and Optimisation Laboratory), Universit Laval, Pavillon Adrien-Pouliot,olumn otation simulation and control: An overview

celyn Bouchard a,1,2,3, Andr Desbiens b,1, Ren del Villar c,*,1, Eduardo Nunez a,3Cll rights reserved.

1. Introduction

The introduction of otation columns in mineral processingplants caught the attention of many researchers in the last twodecades of the twentieth century. Column otation simulationand control progressively became prevailing elds of investigation.Almost twenty-ve years after the installation of the rst commer-cial otation column in the Western world (Finch and Dobby, 1990),it is worth examining where these studies have led, what are thecurrent research interests, and how the current mining industryand practitioners may benet from past developments. This paperaims at complementing the last published review (Bergh andYianatos, 2003). It provides an overview of the literature dealingwith column otation simulation and control, and discusses re-search trends and industrial application issues.

Emphasizing the operating variables, Section 2 gives adescription of the process. A summary of relevant with respectto simulation and control publications dealing with modellingconsiderations are presented in Section 3. The discussion is orga-nized according to three research areas: the prediction of therecovery, the analysis of the process dynamic behaviour and thedevelopment of soft sensors. Section 4 focuses on process controlaspects and reviews most of the published applications. Finally,Section 5 discusses industrial practice, research interests and fu-ture developments required to meet the present industrial needs.

520 J. Bouchard et al. /Minerals Engi2. Process description

A schematic representation of a otation column is given inFig. 1. A typical unit has three input streams (conditioned mineralpulp feed, air, and wash water), and two output streams (the con-centrate and tailings). Under normal operating conditions, the col-umn volume is split into two distinct regions according to their aircontent (volume fraction): a collection or pulp zone (less than 20%of air) and a cleaning or froth zone (more than 70% of air).

To perform a otation separation, several reagents are gener-ally required: collectors, frothers, and regulators (activators,Fig. 1. Flotation column.depressants and pH modiers). These chemicals are added in apreliminary stage, i.e. the pulp conditioning, and/or directly tothe otation cell, and have obviously an important impact onthe metallurgical performance. However, as the type and concen-tration of most of the reagents may be determined off-line in lab-oratory and strongly depend on the duty, they are not consideredin this paper.

Specic variables characterize a otation column operation,namely: the froth depth also called froth layer height and corre-sponding to the complement of the pulp level (or pulpfroth inter-face position) , bias, gas hold-up, and bubble surface area ux.They are explained hereafter.

Froth depth. The froth depth (H) denes the relative heightof the cleaning and collection zones. Consequently, it determinesthe mean solids residence time in the column, partially affectingthe recovery in both the pulp and the froth.

Bias. Dened as the the net downward ow of water throughthe froth (Finch and Dobby, 1990), the bias may be qualitativelyinterpreted as the fraction of the wash water ow used for frothcleaning. It is worth noting that the on-line dynamic measurementof the bias (Jb, expressed as a supercial velocity) still presents adifculty (see Section 3.3).

Air hold-up. It represents the gas volume fraction within the col-lection zone. The air is often considered as a otationreagent andpractitioners have been interested in monitoring the gas dispersionwithin the column using the air hold-up (g).

Bubble surface area ux. The collection of mineral particles bybubbles greatly depends on the amount of bubble surface avail-able. Therefore, a more adequate way of tracking the inuenceof gas to the otation process is to use the amount of bubble sur-face per unit time and unit of column cross sectional area insteadof the gas hold-up. This becomes obvious when comparing theotation performance of similar volumes of air in the form of aswarms of small bubbles (large specic area) or a swarm of fewerlarger bubbles (smaller specic area). The resulting bubble sur-face area ux, or Sb, may be evaluated from the bubble ow rate(nb), the bubble surface, and the cross-sectional area of the col-umn (Ac). Assuming a suitable mean bubble diameter (db), itcan be estimated with

Sb nbd2bp

Ac 6Jg

db1

where Jg is the gas supercial velocity. Fig. 2 illustrates the bubblesurface area ux concept. However, industrial bubblers usually pro-duce a broad bubble size distribution, making the use of a singlemean value rather inacurate, since this same value could be ob-tained from quite different size distributions.

Finch et al. (2000) presented a discussion on gas dispersioncharacterization. Using data from literature, they suggested a qua-si-linear relationship restricted to the range of calibration be-tween g and Sb. Heiskanen (2000) criticized the work of Gorainet al. (1995a,b, 1996, 1997, 1999) on the gas dispersion in otationmachines, with respect to measuring methods for gas velocity andbubble size. According to him, further studies on the linear rela-tionship between the otation rate constant (k) and the bubblesurface area ux proposed by Gorain et al. (1997) are also required.Deglon et al. (1999) were also critical about the linear kSb rela-tionship. Based on the results of a simulation study, they claimedthat the near linear region corresponds to a transition from the pre-dominance of the sub-process of particlebubble attachment to that ofparticlebubble detachment in mechanical otation cells (Deglonet al., 1999).

neering 22 (2009) 519529General instrumentation issues for on-line monitoring of col-umn otation operation are discussed by Bergh and Yianatos(2003) and Bouchard et al. (2005b).

Engi3. Modelling

For process control purposes, research work dealing with col-umn otation modelling can be organized in three categoriesaccording to their aim: prediction of the recovery, analysis of dy-namic behaviour and development of soft sensors.

3.1. Prediction of recovery

Besides works for scale-up purposes (e.g. Finch and Dobby(1990), Rubinstein (1995), Alford (1992) and OConnor et al.(1995)), other studies aimed at predicting the recovery of columnotation operations were presented but considering control andoptimisation applications.

Pioneering efforts started in the eighties. Luttrell et al. (1987),proposed a static simulator based on a population mass balance(air bubbles, unattached solid particles, and bubbleparticle aggre-gates). Mass transport was considered in the model using uidows and particle buoyancy, while the bubbleparticle rate attach-ment was evaluated using rst principles. Some processes, such asthe bubble loading and mixing properties, were explained underpre-specied operating conditions, using a semi-fundamental ap-proach requiring the calibration of two empirical coefcients. Thesimulator attempted to predict the recovery of a specic columnotation operation for design, control, optimisation and scale-up

Fig. 2. Sb concept.

J. Bouchard et al. /Mineralspurposes.At the same time, Sastry and Lofftus (1988) also developed a

simulator using a similar approach, but considering the dynamicmass balance equations. The resulting tool opened the door totime-dependent investigations, which are very useful to study pro-cess control strategies. The assumption of constant air and waterhold-up, along with the impossibility to analytically solve the gen-eral model, represented the greatest limitations of their work.

The addition of air and water mass balance equations to a vewell-mixed zone approximation instead of the three zones modelof Sastry and Lofftus (1988) made the simulator proposed by Pateand Herbst (1989) a more exible tool. Their approach also re-placed the axially dispersed plug ow model with a distributedvolume mixers-in-series approximation to increase computationalefciency. The air mass balance was however considered on a sta-tic basis according to the assumption that air hold-up is subject tovery fast changes compared to water volume. Particles could be ofany size and were divided in three classes: free valuable mineral,free gangue and locked. Similarly to above-mentioned simulators,the proposed model exhibited certain empirical features regardingthe calibration of rate constants and the description of some phe-nomena using correlations (water entrainment, water drainage,etc.). Later on, the same research team used this dynamic simulatorto design a methodology for selecting a control strategy for a col-umn otation unit (Lee et al., 1991).

Cruz (1997) made a further step and proposed a fully dynamicsimulator of column otation metallurgical performance. Herwork, notably based on fundamental considerations, included acomprehensive description of complex phenomena, such as bubblecoalescence in the froth and bubble loading, and considered parti-cle and bubble size distributions as well as a particle compositiondistribution. The design was based on the application of a popula-tion balance to a vertically distributed volume mixers-in-seriesframework: a perfectly mixed aeration zone, a perfect-mixers-in-series lower collection zone, a single perfectly mixed feed zone, aperfect-mixers-in-series upper collection zone, the interface, andthree plug ow volumes for the froth (stabilized froth, wash wateraddition zone, and draining froth). Notwithstanding improvementsin column otation simulation, being impossible to carry out dy-namic ow rate variations signicantly narrowed the extent of po-tential control applications. In fact, operating conditions were xedoff-line and stayed constant throughout the simulation. The pro-cess was then driven from an initial to a nal state as dened bythe simulated operating conditions. Gas hold-up and solids owrate changes were computed, but the dynamic variations of frothdepth were not considered. Despite this limitation, Cruz neverthe-less achieved a major breakthrough, even though it seems that thiswork remained unnoticed by the mineral processing community.

Recently, Bouchard et al. (2006) made a new attempt to developa dynamic fundamentally-based column otation simulationframework, but only preliminary results were presented.

Using a more global approach, Kho and Sohn (1989) obtained apredictive model for talc recovery based on empirically estimatedrate constants and residence time distributions for the liquid andsolids.

Luttrell and Yoon (1991), noticeably inspired by research worksupervised by Finch (Finch and Dobby, 1990), developed a staticsimulator based on hydrodynamic principles, aiming at predictingthe recovery of a column otation operation. In 1993, they pro-posed a scale-up procedure (Luttrell et al., 1993). Besides vesselgeometrical characteristics considerations, their discussionemphasized on air spargers and wash water distribution systems.The column diameter was determined from the maximum frothcarrying capacity, while the rate constant and mean particle reten-tion time were used to obtain its height. The effect of axial mixing,air hold-up, and gas and liquid ow rates were also considered inthe procedure.

Following similar ideas, Alford (1992), from the JKMRC in Aus-tralia, gathered the results of many researchers to develop a col-umn otation static simulator. The model was global (exhibitingonly a single zone) and was considered a useful tool to study owsheet congurations and scale-up of industrial units, assuming anappropriate calibration.

Tuteja et al. (1994) published a review of the most relevantmodels for the prediction of recovery under a clear classication:kinetic models and non-kinetic models, i.e. completely empiricalregression models.

teyaka and Soto (1995) were interested in the modelling of therecovery of negative bias column otation operation. Neglectingthe effect of the turbulence within the vessel, the model was basedon the probability of recovering a given particle to the concentrate.Gupta et al. (1999) also worked on this topic, focusing on phos-phate otation. In order to nd some relationships between rateconstants and operating variables, they suggested a hybrid modelcombining rst principles and neural networks. Once calibrated,

neering 22 (2009) 519529 521the prediction of the effect of frother concentration, particle size,air ow rate, and bubble diameter on phosphate recovery wasmade possible.

ngiIt must be emphasized that for industrial applications, calibrat-ing any model is a tedious process, and the difculty increases withthe number of parameters. The more the model relies on empiricaldata the more its validity is compromised as process conditionsexit the range of calibration. However, requiring a calibrationshould not preclude the use of a given model since many sensorscommonly utilized rely on calibration (e.g. on-stream analyzer,density-meter, etc.).

Other researchers approached the issue of modelling of therecovery from a more particular point of view. For instance, Yiana-tos et al. (1998) developed a semi-empirical model to predict thefroth recovery in an industrial otation column, as a function ofthe main operating variables (air and water supercial velocitiesand froth depth). Neethling and Cilliers (2001) suggested a com-prehensive fundamental model to study the effect of wash wateron froth performance. Many complex phenomena were incorpo-rated in their description: bubble coalescence, liquid drainage, par-ticle settling and particle dispersion.

New developments and studies dealing with characterizinghydrodynamic properties will help improving current models andsimulators. A revision of underlying assumptions commonly usedpreviously is to be expected as macroscopic behaviours are betterunderstood.

3.2. Dynamic behaviour

Despite the validity of the approach initiated by Sastry and Loff-tus (1988) and pursued by Pate and Herbst (1989) and Cruz (1997),the dynamic modelling of column otation based on rst principleshas not yet been successful to stand out as a solution to practicalproblems. These attempts were eventually dropped to focus onempirical techniques (transfer functions, state-space or fuzzy mod-els) to model the behaviour of process variables such as frothdepth, air hold-up, and concentrate grade. Noteworthy resultswere obtained with linear models for restricted ranges of operation(Pal and Masliyah, 1990; Pu et al., 1991; Bergh and Yianatos, 1994;Bergh et al., 1995; del Villar et al., 1999; Bouchard et al., 2005b).However, some limitations were identied when consideringwider operating regions (Carvalho et al., 1999) as the linear behav-iour assumption does not hold anymore. Desbiens et al. (1998) andMilot et al. (2000) tested gain-scheduling and multi-modelschemes to overcome these problems and cope with nonlinearitiesin a straightforward manner.

More recently, Vieira et al. (2005) proposed a fuzzy modellingstrategy to obtain a MIMO (multiple inputs/multiple outputs) rep-resentation of the behaviour of froth layer height, bias and air hold-up. Despite a good agreement between the model and process,their work illustrates fairly well the main difculty associated withempirical-based representations attempting to stand as fully gen-eral tools: the empirical cost. In fact, the accuracy of black-boxmodels relies almost exclusively on the information containedwithin the experimental data. The more complex is the behaviourto be modeled as a result of the number of independent variables,interactions and nonlinearities the more data are required forcalibration purposes. In practice, following the example presentedin their paper, empirical nonlinear models must be restricted torelatively narrow range of operations. Other researchers followeda hybrid path to overcome such a problem. For instance, Dumontet al. (2001) used two models of the froth depth behaviour essen-tially based on rst principles to demonstrate how mixing theempirical approach with the fundamental one, using basic physicallaws (Newtons second law, ideal-gas law, Archimedes principle,etc.), leads to more general tools which require less experimental

522 J. Bouchard et al. /Minerals Edata for calibration.The development of dynamic relationships linking operating

variables (froth depth, bias, air hold-up, and bubble surface areaux) to the metallurgical performance of otation columns (gradeand recovery) is another interesting issue. Empirical graphical rela-tionships were presented by Nesset et al. (2005), Hernandez-Agu-ilar et al. (2006) and Bartolacci et al. (2008). Work by Alexanderet al. (2005) and Schwarz et al. (2008) showed the use of Sb; g ,froth recovery (Rf ), entrainment and drainage parameters (n andd), and the ore oatability parameter Pi to predict otation perfor-mance from simulations.

3.3. Soft sensors

Modelling efforts also targeted improving the instrumentationfor otation columns. The pulp level has attracted considerableattention through experimental work to improve pressure- andconductivity-based techniques (Finch and Dobby, 1990; Berghand Yianatos, 1993; del Villar et al., 1995a,b, 1999; Maldonadoet al., 2008a).

In the past few years, noteworthy prototypes have also beenpresented for the air hold-up, even though no commercial applica-tions seem to be reported in the literature. As for the froth depth,sensors using pressure gauges were rst suggested (Finch and Dob-by, 1990), but the more accurate conductivity probes constitutethe current research trend (Gomez et al., 1995; Tavera et al.,1998; Prez-Garibay and del Villar, 1999; Tavera and Escudero,2002; Nez et al., 2006a). In fact, as shown by Nez et al.(2006a), the assumption of a constant slurry density may introducesome inaccuracy problems with pressure-based sensors. A uniquesolution to the gas holdup monitoring problem is also offered byCiDRA Corporation with the SONARtrac

TM. OKeefe et al. (2007,

2008) reported successful applications of this multivariable uidvelocity/gas hold-up sensor, based on a passive sonar technology,in a variety of mineral processing facilities. Despite a great dealof work, on-line estimation techniques for the bubble surface areaux and the bias have not reached the same degree of maturity,although work is ongoing at Universit Laval and McGillUniversity.

Bubble surface area ux monitoring issues are related to bubblesize estimation. Off-line devices for bubble size estimation havebeen developed by Randall et al. (1989), at McGill University (Finchet al., 1999; Chen et al., 2001; Hernandez-Aguilar et al., 2002; Go-mez and Finch, 2002, 2007), by Grau and Heiskanen (2002, 2003),Schwarz and Alexander (2006a) and also by Rodrigues and Rubio(2003). For fully on-line applications, only an indirect methodbased on the so-called drift ux theory (Dobby et al., 1988; Yianatoset al., 1988; Xu and Finch, 1990; Zhou et al., 1993; Banisi and Finch,1994; Ityokumbul et al., 1995; Li, 2003) seems conceivable at themoment. However, recent advances in bubble size distributionestimation and modelling are promising for accurate on-line com-putation of mean bubble diameter (Maldonado et al., 2008b).

Soft sensors developed for bias estimation have always beenbased either on conductivity or mass balance calculations, director indirect (i.e. through calibrated empirical relationships such asneural networks or regression models), and assumed a steady-stateoperation (Uribe-Salas et al., 1991; Bergh et al., 1995; Prez et al.,1996; Carvalho et al., 1999; Bouchard et al., 2005b). It is only re-cently that Maldonado et al. (2008c) proposed a way to monitorthe transient state of this variable at least in a two-phase (waterand air) laboratory application. The innovation comes from an esti-mation of the dynamics through a change of conductivity belowthe interface. It is worth mentioning that this is the rst attemptever showing some potential for industrial applications. However,the method is yet not adapted for slurries and the required calibra-tion is likely to put a curb on sustainable use in a plant unless it

neering 22 (2009) 519529could be performed in a laboratory-scale column.Persechini et al. (2000) also developed and tested three soft sen-

sors to monitor froth depth, bias and air hold-up for a simplied

Engitwo-phase system. The latter process variables were inferred usingonly two ow-meters (air and wash water) and two pressuregauges mounted on the column side. The proposed approach is cer-tainly interesting but would require further developments. A fewreservations that are worth mentioning are:

simplistic models were used to make up for the absence of pulpowmeters (ow rate proportional to the voltage at the pumpterminals),

the instrumentation would need to be adapted for a slurry appli-cation, which represents the ultimate objective, and

reliability and validity of the bias and gas hold-up measure-ments were not assessed, even for the steady-state operation.

In a previous study, Hyma and Salama (1993) suggested a sim-ilar approach, but only preliminary results were presented.

4. Process control

Column otation process control objectives may be structuredaccording to a three-level hierarchy.

(1) This is the basic regulatory control layer. Above all, it aims ata steady operation for the column inputs (slurry feed ifupstream uctuations are damped in the pump box, air,wash water and reagents), but refers in general to all controlelements (valves and pumps, including that of the tailings).From a process/design standpoint, the rst level alsoincludes damping feed ow-rate disturbances as much aspossible using the surge capacity of a pump box.

(2) The intermediate level aims at maintaining process variableshaving a strong inuence on metallurgical results (grade andrecovery), namely froth depth, bias, froth parameters, airhold-up or bubble surface area ux, in a bounded region,i.e. an acceptable operating zone where it is possible to han-dle the process and reach production objectives. This level isoften called stabilizing control (Finch and Dobby, 1990;Kosick et al., 1991; Hyma and Salama, 1993; Bergh andYianatos, 1993; Bergh and Yianatos, 1995; Rubinstein,1995; Bergh et al., 1998; Bergh and Yianatos, 1999). Processand security constraints should normally be included at thislevel. This could include handling a circulating load in acleaning circuit for instance. A model-based predictive con-troller (MPC) can manage such constraints very easily. Thealternative when only PID controllers are available is touse either an override or a pseudo-cascade scheme (Lestageet al., 1999).

(3) The third layer involves the determination of metallurgicaltargets according to an economic criterion. From these tar-gets, operating set-points for the subordinate level arefound to drive the process or the circuit from its currentstate to a new one in order to achieve the economic objec-tive. Finch and Dobby (1990), Kosick et al. (1991), Hymaand Salama (1993) and Rubinstein (1995), among others,refer to this upper level as optimizing control. The termsupervisory control is also commonly used when other taskssuch as data validation, fault detection, security or limitingconditions are also carried out (Bergh and Yianatos, 1993;Bergh et al., 1998; Bergh and Yianatos, 1999). However,when based on the rigorous resolution of a quantitativeoptimisation problem, the control community rather refersto real-time optimisation (RTO). Supervisory control structureare often based on fuzzy rules, trying to emulate the best

J. Bouchard et al. /Mineralspossible operator. The main difference between the twoschemes is one aims at optimising, and the other, at improv-ing. An optimisation refers to the objective search for thebest solution, based on a process model, between all possi-ble cases in a given range and considering input and outputconstraints. An improvement consist in nding a better sit-uation than the base case.

For industrial applications, advanced control strategies gener-ally require data validationestimation stages, such as massbal-ance reconciliation (e.g. Bilmat Real-Time

TM), observers (e.g.

Kalman-like lters), and fault detection and diagnosis (Bertonand Hodouin, 2003), for more robustness and accuracy. It must alsobe emphasized that the success of any advanced control strategystrongly relies on the regulatory control layer. Upgrading from alower to a higher level should be considered only if the lower levelis fully and sustainably implemented. Robustness, reliability andsimplicity should be the primary focus regarding any choice ofinstrumentation and control algorithm.

Finch and Dobby (1990), Bergh and Yianatos (1993) and Rubin-stein (1995) have presented general discussions about column o-tation control. Process and instrumentation issues are covered, butconclusions drawn about the controllability of the process and theability of conventional feedback control algorithms to handle it(Bergh and Yianatos, 1993) are not in line with multivariable con-trol practice, nor with other results found in the literature as ex-plained below.

A physical analysis of the system shows that there are multi-ple interactions between the input (independent) and output(dependent) variables. The computation of the RGA (relative gainarray) matrix allows to quantify this level of interaction for thesteady-state. Persechini et al. (2004) have thus shown that forthe froth depth bias gas hold-up system, respectively con-trolled using the wash water, tailings, and air ow rates, theRGA matrix is almost an identity matrix. The process would thusexhibit low interactions and therefore, be a good candidate fordecentralized control strategies. Similar observations were alsomade by Maldonado et al. (2007a). Even if this result is obtainedfor a simplied two-phase system, it is difcult to imagine thatthe result for a slurry operation would be substantially different.It should be emphasized that tuning decentralized PIDs is trickierthan tuning PIDs for completely independent processes. Good re-sults are difcult to achieve without an understanding of multi-variable feedback control theory (see Skogestad andPostlethwaite, 2005). For TITO (two-inputtwo-output) decentral-ized control schemes, Desbiens et al. (1996) presented a PID tun-ing technique.

The critics of the control performance of standard feedback con-trol techniques are difcult to understand since useful results wereobtained by some researchers at least for restricted ranges of oper-ation using PI controllers alone (del Villar et al., 1999; Persechiniet al., 2004; Bouchard et al., 2005b, linear predictive controllersPu et al., 1991; Chuk et al., 2001; Maldonado et al., 2007b), andmulti-model schemes (Milot et al., 2000; Bouchard et al., 2005b).It must be emphasized that the controllability of any process re-mains unaffected by uctuating operating conditions as long asmanipulated variables are unsaturated and the dynamic behaviourdoes not vary signicantly (compared to the model used for thecontroller design). However, uctuating operating conditions adda challenge that cannot be neglected. This can even lead to the fail-ure of a given control strategy if the limitations are not clearlyunderstood and properly dealt with, no matter what control algo-rithm is being used. In fact, the vast majority of industrial controlissues come from instrumentation problems (type, design, locationand/or condition), control strategy (pairing, objective, etc.) and

neering 22 (2009) 519529 523controller tuning. Very seldom they are inherent to the controltechnique per se.

for periodic cleaning.

ngi4.1. Intermediate level control

SISO control strategies have been suggested for secondary con-trol objectives. The most widely used in the industry is froth depthcontrol using the tailings ow rate. Mauro and Grundy (1984) al-ready reported the early application of such a strategy at LornexMining Corporation. A few years later, Nicol et al. (1988) tested itwith a pilot-scale unit, and Moys and Finch (1988b), using a labo-ratory-scale unit. Desbiens et al. (1998) proposed a gain-scheduledtechnique to cope with nonlinearities. Barrire et al. (2001) testedtwo nonlinear controllers based on semi-physical models devel-oped by Dumont et al. (2001). Another version of pulp level controlis based on the wash water ow rate (Moys and Finch, 1988a;Finch and Dobby, 1990). An application at Les Mines Gasp was re-ported by Cienski and Cofn (1981).

TITO strategies have also been tested to achieve intermediate le-vel control objectives. They all involve the froth depth and anothervariable, the bias or gas hold-up. Ameluxen et al. (1988) intended afroth depth and bias control, using thewashwater ow rate and thetailings ow rate respectively, at Southern Peru Copper Corporation(Cuajone Division). Using a two-phase laboratory-scale column, delVillar et al. (1999) tested a decentralized control structure, butusing the wash water ow rate to control the bias, and the tailingsow rate for the froth depth. Slurry operation pilot-scale resultswere presented by Bouchard et al. (2005b) for the same TITO sys-tem. Milot et al. (2000) used a two-phase application to test a mul-tivariable nonlinear predictive controller (GlobPC GlobalPredictive Control) also to control froth depth and bias.

Pu et al. (1991) proposed a predictive controller (DMC Dy-namic Matrix Control) for a slurry laboratory application involvingthe froth depth and gas hold-up. Process variables were estimatedusing three pressure-transducers. Using a similar approach, Chuket al. (2001) and Nez et al. (2006b) tested a GPC (GeneralizedPredictive Controller) and a GlobPC (Global Predictive Control),respectively.

Persechini et al. (2004) and Maldonado et al. (2007a) testeddecentralized strategies for bias, froth depth, and gas hold-up (sim-plied two-phase water-air system). Another strategy, combining aPI controller for the froth depth and a predictive controller for thebias and gas hold-up was also proposed for the same system byMaldonado et al. (2007b).

Other researchers and practitioners have tried more qualitativetechniques. Kosick et al. (1991) reported the implementation of anexpert system at Doe Run Viburnum (Misouri, USA) and at NercoCon Mine (Yellowknife, Canada). Carvalho and Duro (2002) testeda fuzzy logic controller for the froth depth, bias, and gas hold-up ona two-phase laboratory-scale unit.

4.2. Control strategies based on metallurgical objectives

Examples of column otation control based on metallurgicalobjectives are scarce in the technical literature. Generally, the pro-posed schemes try to improve the performance in terms of themetallurgical efciency of an individual unit or a circuit and copewith irregular or undesirable situations.

Expert systems were implemented by McKay and Ynchausti(1996) to supervise column operation by manipulating froth depth,air ow rate, and wash water ow rate set-points. Other applica-tions have been presented by Bergh and Yianatos (1996) (El Te-niente, Codelco-Chile), and Bergh and Yianatos (1999) (Salvador,Codelco-Chile). Besides illustrating the benets of improving con-trol strategies, the latter papers show the overall work associatedwith industrial implementations, including a pre-diagnosis step

524 J. Bouchard et al. /Minerals Eto detect and correct operation and maintenance problems. Ven-dors like Metso Minerals and SGS Minerals Services also proposeexpert systems to handle column otation operations.Pinch valves are commonly used for tailings ow control. Eventhough they provide a satisfactory performance, they remain rela-tively high maintenance control elements. Recent experiences (e.g.at Xstrata Nickel Raglan) show that ceramic ball valves can nowa-days be considered for long term and low maintenance operation.

In large column circuits, splitting a feed evenly into severalgravity fed parallel units in order to fully utilize the processingcapacity is challenging. Unfortunately, designing suitable pulpdistributors does not seem to be straightforward and has to bedealt with on a case-by-case basis.

5.2. Steady-state simulation: metallurgical performance sensor development and applications, and process control.

5.1. Current practice and challenges

Performance of industrial column is still often limited by designand maintenance issues. Air sparger or nozzles require recurrentcleaning to cope with water accumulation in air lines (if the airsupply is not pre-dried) and plugging with slurry (from the col-umn). Such problems must be diagnosed by monitoring the pres-sure at every air injection point and dealt with rapidly becausethey prevent a steady gas ow-rate and proper aerodynamics con-ditions in the column.

Another common issue with column otation operation is theuneven wash water distribution. Wrong design and fouling of thewash water tray are the main causes. Correcting the design is gen-erally relatively easy, by adding bafes and/or feeding the water tothe tray at more than one point for instance. Fouling issues aremore difcult to cope with because they require a lot of diligenceConcentrate grade control in a zinc cleaning column using fuzzylogic was reported by Hirajima et al. (1991). The control rules wereobtained by interviewing skilled operators. The strategy wasmainly based on manipulating the air ow rate to reach concen-trate grade objectives.

Karr (1996) discussed the possibility of using a column otationneural network model within an adaptive control architecture.

Simulation studies have also been conducted. Bergh et al.(1998) presented a hybrid system combining expert and fuzzy lo-gic for the supervision of a decentralized PID control strategy (frothdepth, wash water, and air ow rates). Chuk et al. (2005) suggesteda supervising expert system to prevent froth collapse.

5. Current practice, research trends & future applications

Previous sections have shown that considerable effort has al-ready gone into developing column otation models and designingsuitable process control strategies. That being said, one can nowask:

How the current industry could, from a practical point of view,benet from these developments?

What are the needs for further investigations?

This section examines these issues according to four topics,namely

steady-state simulation of metallurgical performance of columnotation,

dynamic modelling,

neering 22 (2009) 519529Based on recent experimental developments, a new Windows-based version of JKSimFloat, a otation simulator commercialized

Engiby JKTech, is available. Harris et al. (2002) described how the soft-ware incorporates new ideas and models, and discussed practicaland specic issues related to design and optimisation studies.JKSimFloat V6.1 is the tangible result of a collaborative researchproject involving the Julius Kruttschnitt Mineral Research Centre(JKMRC) at the University of Queensland (Australia), the MineralProcessing Research Unit at the University of Cape Town (SouthAfrica), and the Mineral Processing Group at McGill University(Canada). Previous outcomes of this project were the developmentof measuring devices and procedures for the diagnostic performanceevaluation of otation cells and circuits, a methodology for modelingthe performance of otation circuits for optimisation studies, and amethodology for modeling the performance of otation pilot-plantsfor design studies (Harris et al., 2002). Application case studieswere presented by Schwarz and Alexander (2006b).

The software could become a powerful tool for process engi-neers to choose operating points for secondary-objective variables(e.g. froth depth, gas hold-up, etc.) in order to reach metallurgicalobjectives. As part of an off-line or real-time optimisation strategy,the determination of column operating conditions could then bemade on a quantitative basis. However, establishing explicit rela-tionships linking the metallurgical performance to the pulp level,bias, gas hold-up and/or bubble surface area ux is still an inexactscience. The software raises high expectations: applications inindustrial optimisation studies will show if they can be fullled.

As a part of a comprehensive design methodology, the softwarealso aspires to become a key scale-up tool for otation units andcircuits.

5.3. Sensor development and applications

Over the past two decades, new measuring devices have beenproposed although industrial applications remain scarce. Indus-trial-academic partnerships could be of great benet for better pro-cess supervision. In fact, equipment and service suppliers have thetechnical and practical expertise to design robust and reliableproducts, whereas the universities have the facilities and mandateto develop theoretical concepts and explore new avenues. The jointwork of JKMRC and its commercial branch JKTech is one exampleof a successful combination of fundamental and industrial andR&D. By taking advantage of the best of both worlds, nearly maturetechnologies like conductivity-based probes for froth depth andgas hold-up could then rapidly become standard devices.

Froth depth determination based on conductivity exhibits avery good accuracy in laboratory- and pilot-scale units. Unlikeoat- and pressure-based techniques, it is unaffected by any uc-tuations in the pulp density or by air hold-up. The evaluation ofthe conductivity prole across the froth could also allow an on-linemonitoring of the bias. However, a comprehensive trial in a plantenvironment is yet to be performed. It is only then that a validcomparison with commonly used methods (i.e. oat- and pres-sure-based) will become possible.

The standard addition method developed by Prez-Garibay anddel Villar (1999) for gas hold-up monitoring has also been testedby Arizmendi-Morquecho et al. (2002) for solids hold-up measure-ment. Such a technique could become a low-cost and safe substi-tute for nuclear densimeters.

Current industrial use of bubble surface area ux (local refer-ence) is nowadays for operation diagnosis, but opportunities forprocess control to achieve a target metallurgical performance could originate from the development of accurate and robuston-line estimation method. Unfortunately, important informationrelated to the shape of the bubble size distribution, such as mul-

J. Bouchard et al. /Mineralsti-modal, narrowness and tail behaviour is completely lost whenusing a mean bubble diameter as with Sb. Therefore, formal controlstrategies should take into account the Sb value in conjunction withthe shape of the bubble size distribution, which must be estimatedon-line from sequential bubble size data points (Maldonado et al.,2008b).

Supervision methods based on multivariate image analysis(MIA) are promising options for froth characteristic monitoring.For certain applications, MIA could complement on-stream analyz-ers (OSA) and help to overcome their limitations (e.g. time delays,need of sampling systems, maintenance, calibration, etc.). For in-stance, Duchesne et al. (2003) proposed an application of MIA forconcentrate grade prediction. In this case, the grade predictionscould either be used to ll in gaps between OSA analyses or tomonitor extra concentrates without upgrading the sampling andmultiplexing systems. Liu et al. (2005) presented a novel methodto extract textural and color information related to the bubble sizedistribution, and the presence and amount of clear windows (orblack holes) on otation froth bubbles. Liu and MacGregor (2008)presented how the scores of the MR-MIA (multiresolutional multi-variate image analysis) features could be directly used in froth con-trol. Froth image analysis based on MIA could become thealternative to some instrumentation problems of otation col-umns, for instance, to monitor water entrainment. If froth colorand/or texture is related to water content, it is possible to build aregression model linking froth image characteristics to the waterhold-up of the concentrate. As in any image analysis application,conclusions would be drawn using only surface features. Therefore,even if the technique may provide a valuable information, the localnature of the results should never be forgotten (the state of thebubbles even one layer below the surface remains unknown). Amore detailed discussion on numerical image analysis potentialfor the monitoring of froth characteristics was presented by Bartol-acci et al. (2006).

Commercial froth imaging systems are available to monitor dif-ferent froth parameters such as velocity, bubble size, stability andcolour intensity (e.g. Metso Minerals and SGS). They are widelyused in otation plants and there is a growing demand both fornew and existing column installations.

Another challenging area for future developments is the on-lineevaluation/modelling of the bubble size distribution (BSD). The useof the BSD for control purposes could lead to great metallurgicalbenets, particularly if it can be matched to the prevailing particlesize distribution feeding the otation unit. Work is presentlyunderway regarding this matter at Universit Laval.

5.4. Dynamic modelling and simulation

Above all, dynamic models are required for process control pur-poses. Laboratory- and pilot-scale studies have shown a high po-tential for the use of linear empirical models (transfer functionsand state-space models). However, such a black-box approachhas a limitation: it is restricted to conditions found in the data usedfor calibration (operating points, ore characteristics, conditioning,etc.) and, therefore, may require frequent recalibration. To over-come this drawback, to better understand the interacting processinvolved and to obtain more versatile controllers, phenomenolog-ical model development should be the focus of researchers. Afterthe rst attempts in the late eighties (Sastry and Lofftus, 1988,1989), Cruz (1997) made signicant progress in column otationdynamic simulation. Combining the latest work on froth modelling(Neethling and Cilliers, 2001; Neethling and Cilliers, 2002a; Neeth-ling and Cilliers, 2002b; Neethling, 2008; Stevenson et al., 2003;Stevenson, 2007; Nguyen et al., 2003) with the approaches pro-posed by Cruz (1997) and Bouchard et al. (2006) will probably pro-vide the next generation of column otation dynamic simulators.

neering 22 (2009) 519529 525Fundamental dynamic models may be used to build robust sim-ulators. For process control engineers, dynamic simulators are use-ful tools since:

ating window. Moreover, mass-balancing technique using mean or

ngi(1) they allow the development and study of control strategieswithout upsetting production,

(2) they allow pre-tuning before the actual implementationhence reducing the commissioning period, and

(3) they can be used directly as a process model in predictivecontrollers as suggested by Henson (1998).

Desbiens and Bouchard (2004) and Bouchard et al. (2005a) pre-sented novel predictive control formulations to make use of thislatter concept.

It must be emphasized that simulator calibration and recali-bration requirements can become overwhelming and therefore,the number of empirical parameters should remain reasonable.The range of validity and robustness can be extended typicallyby including fundamental knowledge (i.e. physical laws, conserva-tion principles, etc.) into the models, hence minimizing the depen-dence over empirical parameters and the data used forcalibration to explain the behaviour. Moreover, general trendsare more important than the actual accuracy for advanced processcontrol applications, particularly when the aim is to control lowfrequencies or steady-states (e.g. grade and recovery).

5.5. Process control myths and reality

Column otation control is often seen as a problem that cannotbe handled by standard feedback control techniques. Such a visioncertainly put a curb on a major breakthrough in column control.

Most of column otation control issues are instrumentationmatters, related to the lack of commercial sensors to monitor keyprocess variables. Obviously, any linear control law is restrictedto a certain range of operation, but it does not automatically pre-clude their use for processes exhibiting some nonlinear behaviour.In fact, column otation should be classied under the category ofquasi-linear systems with different operating points. Therefore, itis not different from any other industrial process where standardfeedback control techniques have been successfully implemented.Moreover, if a wide operating region must be considered, usinggain-scheduling and multi-model schemes may enlarge the rangeof applicability of the controllers (Bouchard et al., 2005b).

To solve many column otation control problems, simple andeffective control techniques are already available as discussed byBouchard et al. (2005b). At the very least, pulp level control shouldalways be implemented. PID controllers are well suited for such anoperation and inexpensive commercial on-line pulp level measur-ing devices are already available (pressure gauges or oat coupledwith ultrasounds). Even though there is still room for improve-ment, plant practice shows that this is actually no longer a criticalissue since most of industrial applications involves froth depthcontrol. If, in addition, air ow-meters are used, the effect of theair ow rate can easily be implemented to ensure a wider rangeof operation (Desbiens et al., 1998). A tight froth depth control pro-vides several possibilities to improve column operation. For in-stance, it greatly helps operators to reach production objectives.It also provides a better environment to conduct experiments forstudying the effect of operating conditions on metallurgical results,since steady-state operation is more easily reached and main-tained. From a plant practice standpoint, a steady pulp level oper-ation also relates to a great extent to using surge capacity toattenuate high frequency throughput uctuations whereverpossible.

Bias and gas hold-up are generally not supervised with greataccuracy. The passive sonar technology recently introduced inmineral processing plants (OKeefe et al., 2007; OKeefe et al.,

526 J. Bouchard et al. /Minerals E2008) seems to be mature enough now to solve the gas hold-upmonitoring issue. The technology also offers a great potential forbias steady-state estimation since it can be adapted as well toreconciled (using Bilmat Real-TimeTMfor instance) values over the

moving window would greatly improve accuracy.On-line stream analysers are widely used to monitor the metal-

lurgical performance. However, only seldom an explicit grade orrecovery closed-loop control is achieved. Off-the-shelf expert sys-tems are available to do so, but a common plant practice is to man-ually adjust reagent addition when not ratio controlled from thecircuit head grade and/or manipulate gas rate and froth depth(for instance at Xstrata Nickel Raglan and Strathcona concentra-tors). The effect of wash water does not seem to be as clearly under-stood even though the wash water ow-rate is often monitored.

The use of simple correlations obtained from in-plant empiricalstudies (using design of experiment approach) is not a panacea, butit may partly make up for the lack of measurements and provides arst quantitative basis to guide process operation improvements.The same idea may also be used to link critical operating variablesto the metallurgical performance. If the limitations of such an ap-proach are well understood, for instance regarding the validityrange and the necessity of recalibration, it may be used in off-lineor even real-time optimisation strategies. Lestage et al. (2002) pre-sented a RTO application for a grinding circuit based on linearempirical models. Such a successful methodology could be trans-posed to otation columns.

Implementing a rigorous optimisation plan requires invest-ments involving nancial (purchase of a simulator, hiring of a con-sulting rm, etc.), human and time resources (for implementationand the strict minimum maintenance). However, the reward, as-sessed in terms of

lower production costs (reagent consumption, etc.), better metallurgical performance (grade and recovery), lower product quality variability, benets on personnel (availability, training on new technolo-gies, etc.)

fewer environmental impacts, etc.

may exceed original expectations and the payback period tends tobe much faster than in the case of major capital investments (fewweeks to few months). This last point can partly be explained bythe fact that tens and even hundreds of thousands of dollars ofcomputer equipment, controllers, DCSs, PLCs, and sensors arealready available in mineral processing plants and, in most cases,only their simplest features are being used and the most powerfulones are often left on the shelf, mainly due to the lack of humanresources. In other words, many control wares have already beenpaid off, but their potential has not been fully exploited.

More advanced control and supervision techniques may even-tually be used to improve otation column operation. For instance,nonlinear controllers based on phenomenological models couldenhance the range of validity, performance, robustness, and per-haps reduce the recalibration needs of control systems. Multivari-ate statistics could also be used to enhance monitoring anddiagnosis capabilities for otation column operations as recentlysuggested by Bergh et al. (2005) and Bergh and Acosta (2008).

6. Conclusion

The modelling and control of column otation has received par-monitor concentrate ow-rates if the velocity requirements aremet. It must be emphasized that the steady-state assumption canbecome acceptable when considering a sufciently long time oper-

neering 22 (2009) 519529ticular attention from the mineral processing community since al-most three decades. An overview of the literature pertaining to this

Engield shows that much has been achieved, but also that some tech-nologies still remain to be transferred to industry. A signicant ef-fort to bring modelling capabilities to process engineers is thedevelopment of a commercial Windows-based simulator. Follow-ing the example of JKMRC and its commercial branch JKTech, fruit-ful collaborations between academics and practitioners shouldhelp speed up developments in other areas such as on-line sensorsand process control. For many plants, important gains can be madewith the simple application of standard control techniques forintermediate process variables (froth depth, bias, ow rates, etc.).Finally, the use of multivariate statistics for on-line monitoringand phenomenological dynamic modelling are current researchinterests showing great potential. New technologies and revivedworks will probably guide future investigative efforts.

Acknowledgements

The authors wish to thank Simon Garipy (Algosys) and Pr. CarlDuchesne (Universit Laval) for fruitful discussions and exchangeson plant practice and MIA, respectively.

References

Alexander, D., Bilney, T., Schwartz, S., 2005. Flotation performance improvement atPlacer Dome Kanowna Belle Gold Mine. In: Proceedings 2005 37th AnnualMeeting of the Canadian Mineral Processors. CIM, Ottawa, Canada, pp. 171201.

Alford, R.A., 1992. Modelling of single otation column stages and column circuits.International Journal of Mineral Processing 36, 155174.

Ameluxen, R., Llerena, R., Dustan, P., Huls, B., 1988. Mechanics of column otationoperation. In: Sastry, K. (Ed.), SME Annual Meeting Column Flotation88.Society of Mining, Metallurgy and Exploration, Phoenix, Arizona, pp. 149155.

Arizmendi-Morquecho, A., Garibay, P., Uribe, A.S., Nava, F.A., 2002. On-line solidshold-up measurement in mineral slurries by the standard addition method.Minerals Engineering 15 (6164).

Banisi, S., Finch, J., 1994. Reconciliation of bubble size estimation methods usingdrift ux analysis. Minerals Engineering 7 (12), 15551559.

Barrire, P.-A., Dumont, F., Desbiens, A., 2001. Using semi-physical models for bettercontrol. Part 2: nonlinear control of a pilot otation column. In: InternationalFederation of Automatic Control (IFAC) Symposium on Automation in Mining,Mineral and Metal Processing. IFAC, Tokyo, Japan, pp. 131136.

Bartolacci, G., Pelletier, P., Tessier Jr., J., Duchesne, C., Boss, P.-A., Fournier, J., 2006.Application of numerical image analysis to process diagnosis and physicalparameter measurement in mineral processes part I: otation control basedon froth textural characteristics. Minerals Engineering 19, 734747.

Bartolacci, G., Ourriban, M., Knuutila, D., Lockhart, A., Finch, J.A., Lau, C.H., Fortin, A.,Goyette, G., 2008. The link between pulp zone and hydrodynamiccharacteristics and froth stability in a 125 m3 otation column. In: 40thAnnual Meeting of the Canadian Mineral Processors, Ottawa, Ontario, Canada,pp. 311332.

Bergh, L., Acosta, S., 2008. On-line fault detection on a pilot otation column usinglinear PCA models. In: Automining 2008, Santiago, Chile, pp. 5766.

Bergh, L., Yianatos, J., 1993. Control alternatives for otation columns. MineralsEngineering 6 (6), 631642.

Bergh, L., Yianatos, J., 1994. Experimental studies on otation column dynamics.Minerals Engineering 7 (2/3), 345355.

Bergh, L., Yianatos, J., 1995. Dynamic simulation of operating variables in otationcolumns. Minerals Engineering 8 (6), 603613.

Bergh, L., Yianatos, J., 1996. Hierarchical control strategy in columns at El Teniente.In: Gomez, C.O., Finch, J.A. (Eds.), Column96 Proceedings of the InternationalSymposium on Column Flotation. Mineral Sciences and Engineering Section ofthe Metallurgical Society of CIM and Canadian Mineral Processors Division ofCIM, Montral, Qubec, pp. 369380.

Bergh, L., Yianatos, J., 1999. Supervisory control experience on large industrialotation columns. In: Hodouin, D., Bazin, C., Desbiens, A. (Eds.), Proceedings ofthe International Symposium on Control and Optimization in Minerals, Metalsand Materials Processing. MetSoc, Qubec, Canada, pp. 299310.

Bergh, L., Yianatos, J., 2003. Flotation column automation: state of the art. ControlEngineering Practice 11, 6772.

Bergh, L., Yianatos, J., Acua, C., 1995. Hierarchical control strategy for otationcolumns. Minerals Engineering 8 (12), 15831591.

Bergh, L., Yianatos, J., Leiva, C., 1998. Fuzzy supervisory control of otation columns.Minerals Engineering 11 (8), 739748.

Bergh, L., Yianatos, J., Len, A., 2005. Multivariate methods applied to otationcolumns. Minerals Engineering 18, 721723.

Berton, A., Hodouin, D., 2003. Linear and bilinear fault detection and diagnosisbased on energy and mass balance equations. Control Engineering Practice 11,103113.

J. Bouchard et al. /MineralsBouchard, J., Desbiens, A., del Villar, R., 2005a. Optimization-free constrainednonlinear control mineral processing applications. In: 16th IFAC WorldCongress, Praha, Czech Republic, We-A22-T0/1.Bouchard, J., Desbiens, A., del Villar, R., 2005b. Recent advances in bias and frothdepth control in otation columns. Minerals Engineering 18, 709720.

Bouchard, J., Desbiens, A., del Villar, R., Chirinos, J., 2006. Column otationsimulation: a dynamic framework. In: International Conference on MineralProcess Modelling, Simulation and Control, Sudbury, Ontario, pp. 259275.

Carvalho, M.T., Duro, F., 2002. Control of a otation column using fuzzy logicinference. Fuzzy Sets and Systems 125, 121133.

Carvalho, T., Duro, F., Fernandes, C., 1999. Dynamic characterisation of columnotation process laboratory case study. Minerals Engineering 12 (11), 13391346.

Chen, F., Gomez, C., Finch, J., 2001. Bubble size measurement in otation machines.Minerals Engineering 14 (4), 427432.

Chuk, O.D., Mut, V., Nez, E., Gutierrez, L., 2001. Multivariable predictive control offroth depth and gas holdup in column otation. In: International Federation ofAutomatic Control (IFAC) Symposium on Automation in Mining, Mineral andMetal Processing. IFAC, Tokyo, Japan, pp. 8791.

Chuk, O., Ciribeni, V., Gutierrez, L., 2005. Froth collapse in otation columns: aprevention method using froth density estimation and fuzzy expert systems.Minerals Engineering 18, 495504.

Cienski, T., Cofn, V., 1981. Column otation operation at Mines Gaspe molibdenumcircuit. In: 13th Annual Meeting of the Canadian Mineral Processors. CanadianMineral Processors Division of the Canadian Institute of Mining, Metallurgy andPetroleum, Ottawa, Ontario, pp. 240262.

Cruz, E.B., 1997. A comprehensive dynamic model of the column otation unitoperation. Ph.D. Thesis, Department of mining and minerals engineering,Virginia Polytechnique Institute and State University, Blacksburg, Virginia.

Deglon, D., Sawyerr, F., OConnor, C., 1999. A model to relate the otation rateconstant and the bubble surface area ux in mechanical otation cells. MineralsEngineering 12 (3), 291308.

del Villar, R., Prez, R., Diaz, G., 1995a. Improving pulp level detection in a otationcolumn using a neural network algorithm. In: Proceedings 27th AnnualMeeting of the Canadian Mineral Processors. Canadian Mineral ProcessorsDivision of the Canadian Institute of Mining, Metallurgy and Petroleum, Ottawa,Ontario, pp. 83100.

del Villar, R., Prez, R., Diaz, G., 1995b. Improving the three-pressure transducermethod of level detection in otation columns. In: Casali, A., Dobby, G., Molina,M., Thoburn, W. (Eds.), Proceedings of Copper 95 Cobre 95 InternationalConference, vol. 2. IIMCH, MetSoc, TMS, Santiago, Chile, pp. 247260.

del Villar, R., Grgoire, M., Pomerleau, A., 1999. Automatic control of a laboratoryotation column. Minerals Engineering 12 (3), 291308.

Desbiens, A., Bouchard, J., 2004. Constrained nonlinear predictive control based onIMC-optimization. In: 11th International Federation of Automatic Control (IFAC)Symposium on Automation in Mining, Mineral and Metal Processing, Nancy,France, Thu-C1.

Desbiens, A., Pomerleau, A., Hodouin, D., 1996. Frequency-based tuning of SISOcontrollers for two-by-two processes. IEE Proceedings on control theory andapplications 143 (1), 4956.

Desbiens, A., del Villar, R., Milot, M., 1998. Identication and gain-scheduled controlof a pilot otation column. In: International Federation of Automatic Control(IFAC) Symposium on Automation in Mining, Mineral and Metal Processing.IFAC, Cologne, Germany, pp. 337342.

Dobby, G.S., Yianatos, J.B., Finch, J.A., 1988. Estimation of bubble diameter inotation columns from drift ux analysis. Canadian Metallurgical Quarterly 27(2), 8590.

Duchesne, C., Bouajila, A., Bartolacci, G., Pelletier, P., Breau, Y., Fournier, J., Girard, D.,2003. Application of multivariate image analysis (MIA) to predict concentrategrade in froth otation processes. In: Proceedings 2003 35th Annual Meetingof the Canadian Mineral Processors. CIM, Ottawa, Canada, pp. 511526.

Dumont, F., Barrire, P.-A., Desbiens, A., del Villar, R., 2001. Using semi-physicalmodels for better control. Part 1: modelling of a pilot otation column. In:International Federation of Automatic Control (IFAC) Symposium on Automationin Mining, Mineral and Metal Processing. IFAC, Tokyo, Japan, pp. 137142.

Finch, J.A., Dobby, G.S., 1990. Column Flotation. Pergamon Press, Oxford, UK.Finch, J., Gomez, C., Hardie, C., Leichtle, G., Filippone, R., Leroux, D., 1999. Bubble

surface area ux: a parameter to characterize otation cells. In: 31th AnnualMeeting of the Canadian Mineral Processors, Ottawa, Canada, pp. 199209.

Finch, J., Xiao, J., Hardie, C., Gomez, C., 2000. Gas dispersion properties: bubblesurface area ux and gas holdup. Minerals Engineering 13 (4), 365372.

Gomez, C., Finch, J., 2002. Gas dispersion measurements in otation machines. CIMBulletin 95 (1066), 7378.

Gomez, C.O., Finch, J.A., 2007. Gas dispersion measurements in otation cells.International Journal of Mineral Processing 84, 5158.

Gomez, C.O., Tavera, F., Finch, J.A., Prez, R., del Villar, R., 1995. Continuous gasholdup measurement in otation columns. In: Proceedings 27th AnnualMeeting of the Canadian Mineral Processors. Canadian Mineral ProcessorsDivision of the Canadian Institute of Mining, Metallurgy and Petroleum, Ottawa,Ontario, pp. 202216.

Gorain, B., Franzidis, J., Malanpig, E., 1995a. Studies on impeller type, impeller speedand air ow rate in an industrial scale otation cell part I: effect on bubblesize distribution. Minerals Engineering 8 (6), 615635.

Gorain, B., Franzidis, J., Malanpig, E., 1995b. Studies on impeller type, impeller speedand air ow rate in an industrial scale otation cell part II: effect on gasholdup. Minerals Engineering 8 (12), 15571570.

neering 22 (2009) 519529 527Gorain, B., Franzidis, J., Malanpig, E., 1996. Studies on impeller type, impeller speedand air ow rate in an industrial scale otation cell part III: effect onsupercial gas velocity. Minerals Engineering 9 (6), 639654.

ngiGorain, B., Franzidis, J., Malanpig, E., 1997. Studies on impeller type, impeller speedand air ow rate in an industrial scale otation cell part IV: effect bubblesurface area ux on otation performance. Minerals Engineering 10 (4), 364379.

Gorain, B., Franzidis, J., Malanpig, E., 1999. The empirical prediction of bubblesurface area ux in mechanical otation cells from cell design and operatingdata. Minerals Engineering 12 (3), 309322.

Grau, R., Heiskanen, K., 2002. Visual technique for measuring bubble size inotation machines. Minerals Engineering 15, 507513.

Grau, R., Heiskanen, K., 2003. Gas dispersion measurements in otation cell.Minerals Engineering 16, 10811089.

Gupta, S., Liu, P.-H., Svoronos, S., 1999. Hybrid rst-principles/neural networksmodels for column otation. AIChE Journal 45 (3), 557566.

Harris, M., Runge, K., Morrison, R., 2002. JKSimFloat as a practical tool for otationprocess design and optimization. In: Mular, A., Halbe, D., Barratt, D. (Eds.),Mineral Processing Plant Design & Control. SME Publications, pp. 461478.

Heiskanen, K., 2000. On the relationships between otation rate and bubble surfacearea ux. Minerals Engineering 13 (2), 141149.

Henson, M., 1998. Nonlinear model predictive control: current status and futuredirections. Computers & Chemical Engineering 23, 187202.

Hernandez-Aguilar, J., Gomez, C., Finch, J., 2002. A technique for directmeasurement of bubble size distributions in industrial otation cells. In:34th Annual Meeting of the Canadian Mineral Processors, Ottawa, Canada(Paper 24).

Hernandez-Aguilar, J., Thorpe, R., Martin, C.J., 2006. Experience in using gasdispersion measurements to understand and modify metallurgicalperformance. In: Proceedings 2006 38th Annual Meeting of the CanadianMineral Processors. CIM, Ottawa, Canada, pp. 387402.

Hirajima, T., Takamori, T., Tsunekawa, T., Matsubara, T., Oshima, K., Imai, T., Sawaki,K., Kubo, S., 1991. The application of fuzzy logic to control concentrate grade incolumn otation at Toyoha Mines. In: Agar, G., Huls, B., Hyma, D. (Eds.),Column91 Proceedings of an International Conference on Column Flotation,vol. 2. Canadian Institute of Mining, Metallurgy and Petroleum, Sudbury,Ontario, pp. 375407.

Hyma, D., Salama, A., 1993. Design and implementation of a process control systemfor column otation. CIM Bulletin 86 (973), 5054.

Ityokumbul, M., Salama, A., Al Taweel, A., 1995. Estimation of bubble size inotation columns. Minerals Engineering 8 (1/2), 7789.

Karr, C., 1996. Adaptive process control using biological paradigms. Journal ofNetwork and Computer Applications 19, 2144.

Kho, C.-J., Sohn, H.-J., 1989. Column otation of talc. International Journal of MineralProcessing 27, 157167.

Kosick, G., Dobby, G.S., Young, P., 1991. Columnex: a powerful and affordablecontrol system for column otation. In: Agar, G., Huls, B., Hyma, D. (Eds.),Column91 Proceedings of an International Conference on Column Flotation,vol. 2. Canadian Institute of Mining, Metallurgy and Petroleum, Sudbury,Ontario, pp. 359373.

Lee, K.Y., Pate, W.T., Oblad, A.E., Herbst, J.A., 1991. Methodology for selecting acontrol strategy for a column otation unit. In: Agar, G., Huls, B., Hyma, D. (Eds.),Column91 Proceedings of an International Conference on Column Flotation,vol. 2. Canadian Institute of Mining, Metallurgy and Petroleum, Sudbury,Ontario, pp. 422436.

Lestage, R., Pomerleau, A., Desbiens, A., 1999. Improved constrained cascade controlfor parallel processes. Control Engineering Practice 7, 969974.

Lestage, R., Pomerleau, A., Hodouin, D., 2002. Constrained real-time optimization ofa grinding circuit using steady-state linear programming supervisory control.Powder Technology 124, 254263.

Li, H., 2003. tude exprimentale des paramtres de mise lchelle de colonnes deottation. Ph.D. Thesis, Dpartement de gnie des mines, de la mtallurgie etdes matriaux, Universit Laval, Qubec.

Liu, J.J., MacGregor, J.F., 2008. Froth-based modeling and control of otationprocesses. Minerals Engineering 21, 642651.

Liu, J., McGregor, J., Duchesne, C., Bartolacci, G., 2005. Flotation froth monitoringusing multiresolutional multivariate image analysis. Minerals Engineering 18,6576.

Luttrell, G., Yoon, R., 1991. A otation column simulator based on hydrodynamicprinciples. International Journal of Mineral Processing 33, 355368.

Luttrell, G.H., Adel, G.T., Yoon, R.-H., 1987. Modeling of column otation. In: SMEAnnual Meeting, Denver, Colorado (preprint number 87130).

Luttrell, G., Mankosa, M., Yoon, R.-H., 1993. Design and scale-up criteria for columnotation. In: XVIII International mineral Processing Congress, Sydney, pp. 785791.

Maldonado, M., Desbiens, A., del Villar, R., 2007a. Decentralized control of a pilototation column: a 3 3 system. In: 6th International Copper Conference,Toronto, Canada, vol. 2, pp. 241254.

Maldonado, M., Desbiens, A., del Villar, R., Quispe, R., 2007b. Towards theoptimization of otation columns using predictive control. In: IFAC MMM07on Automation in Mining, Minerals and Metal Processing. Quebec City, Quebec,Canada, pp. 7580.

Maldonado, M., Desbiens, A., del Villar, R., 2008a. An update on the estimation of thefroth depth using conductivity measurements. Minerals Engineering 21, 935939.

Maldonado, M., Desbiens, A., del Villar, R., Girgin, H., Gomez, C., 2008b. On-line

528 J. Bouchard et al. /Minerals Eestimation of bubble size distributions using Gaussian mixture models. In:Kuyvenhoven, R., Gomez, C., Casali, A., (Eds.), V International Mineral ProcessingSeminar Procemin 2008, Santiago, Chile, pp. 389398.Maldonado, M., Desbiens, A., del Villar, R., Chirinos, J., 2008c. On-line biasestimation using conductivity measurements. Minerals Engineering 21, 851855.

Mauro, F., Grundy, M., 1984. The application of otation columns at Lornex MiningCorporation Ltd. In: 9th District Sixth Meeting. CIM, B.C., Canada (p. paper no.23).

McKay, J., Ynchausti, R., 1996. Expert supervisory control of otation columns. In:Gomez, C.O., Finch, J.A. (Eds.), Column96 Proceedings of the InternationalSymposium on Column Flotation. Mineral Sciences and Engineering Section ofthe Metallurgical Society of CIM and Canadian Mineral Processors Division ofCIM, Montral, Qubec, pp. 353367.

Milot, M., Desbiens, A., del Villar, R., Hodouin, D., 2000. Identication andmultivariable nonlinear predictive control of a pilot otation column. In: XXIInternational Mineral Processing Congress. IFAC, pp. 137142.

Moys, M.H., Finch, J.A., 1988a. Developments in the control of otation columns.International Journal of Mineral Processing 23, 265268.

Moys, M.H., Finch, J.A., 1988b. The measurement and control of level in otationcolumn. In: Sastry, K. (Ed.), SME Annual Meeting Column Flotation88. Societyof Mining, Metallurgy and Exploration, Phoenix, Arizona, pp. 103112.

Neethling, S.J., 2008. Simple approximations for estimating froth recovery.International Journal of Mineral Processing 89, 4452.

Neethling, S., Cilliers, J., 2001. Simulation of the effect of froth washing on otationperformance. Chemical Engineering Science 56, 63036311.

Neethling, S., Cilliers, J., 2002a. The entrainment of gangue into a otation froth.International Journal of Mineral Processing 64, 123134.

Neethling, S., Cilliers, J., 2002b. Solid motion modeling in owing froths. ChemicalEngineering Science 57, 607615.

Nesset, J.E., Gomez, C.O., Finch, J.A., Hernandez-Aguilar, J., Difeo, A., 2005. The use ofgas dispersion measurements to improve otation performance. In:Proceedings 2005 37th Annual Meeting of the Canadian Mineral Processors.CIM, Ottawa, Canada, pp. 401421.

Nguyen, A.V., Harvey, P.A., Jameson, G.J., 2003. Inuence of gas ow rate andfrothers on water recovery in a froth column. Minerals Engineering 16, 11431147.

Nicol, S., Roberts, T., Bensley, C., Kidd, G., Lamb, R., 1988. Column otation ofultrane coal: experience at BHP-Utah Coal Limiteds Riverside mine. In: Sastry,K. (Ed.), SME Annual Meeting Column Flotation88. Society of Mining,Metallurgy and Exploration, Phoenix, Arizona, pp. 711.

Nez, E., Chirinos, J., Desbiens, A., del Villar, R., Duchesne, C., 2006a. Multivariablepredictive control of a pilot otation column. part 1: on-line sensors for frothdepth and air hold-up. In: International Conference on Mineral ProcessModelling, Simulation and Control, Sudbury, Ontario, Canada, pp. 277290.

Nez, E., Desbiens, A., del Villar, R., Duchesne, C., 2006b. Multivariable predictivecontrol of a pilot otation column. Part 2: identication and control. In:International Conference on Mineral Process Modelling, Simulation and Control,Sudbury, Ontario, Canada, pp. 291301.

OConnor, C., Mills, P., Cilliers, J., 1995. Prediction of large scale column otationcells using pilot plant data. The Chemical Engineering Journal 59, 16.

OKeefe, C., Viega, J., Fernald, M., 2007. Application of passive sonar technology tomineral processing and oil sands applications if you can measure it, you canmanage it. In: 39th Annual Meeting of the Canadian Mineral Processors,Ottawa, Ontario, Canada, pp. 429457.

OKeefe, C., Poplawski, J., Maron, R., 2008. Application of non-intrusive sonar array-based technology to solve unique and difcult measurement situations. In: 40thAnnual Meeting of the Canadian Mineral Processors, Ottawa, Ontario, Canada,pp. 401419.

teyaka, B., Soto, H., 1995. Modelling of negative bias column for coarse particlesotation. Minerals Engineering 8 (1/2), 91100.

Pal, R., Masliyah, J., 1990. Process dynamics and control of a pilot otation column.Canadian Metallurgical Quarterly 30 (2), 8794.

Pate, W.T., Herbst, J.A., 1989. Dynamic simulation and control of column otationunits. In: Chandler, S., Klimpel, K. (Eds.), Advances in coal and mineralprocessing using otation. SME, Littelton, CO, USA, pp. 315321.

Prez, R., del Villar, R., 1996. Measurement of bias and water entrainment inotation columns using conductivity. In: Gomez, C.O., Finch, J.A. (Eds.),Column96 Proceedings of the International Symposium on ColumnFlotation. Mineral Sciences and Engineering Section of the MetallurgicalSociety of CIM and Canadian Mineral Processors Division of CIM, Montral,Qubec, pp. 327338.

Prez-Garibay, R., del Villar, R., 1999. On-line gas hold-up measurement in otationcolumns. Canadian Metallurgical Quarterly 38 (2), 141148.

Persechini, M., Jota, F., Peres, A., 2000. Dynamic model of a otation column.Minerals Engineering 13 (1415), 14651481.

Persechini, M., Peres, A., Jota, F., 2004. Control strategy for a column otationprocess. Control Engineering Practice 12, 963976.

Pu, M., Gupta, Y., Taweel, A.A., 1991. Model predictive control of otation columns.In: Agar, G., Huls, B., Hyma, D. (Eds.), Column91 Proceedings of anInternational Conference on Column Flotation, vol. 2. Canadian Institute ofMining, Metallurgy and Petroleum, Sudbury, Ontario, pp. 467478.

Randall, E.W., Goodall, C.M., Fairlamb, P.M., Dold, P.L., OConnor, C.T., 1989. Amethod for measuring the sizes of bubbles in two- and three-phase systems.Journal of Physics E: Scientic Instruments 22, 827833.

Rodrigues, R., Rubio, J., 2003. New basis for measuring the size distribution of

neering 22 (2009) 519529bubbles. Minerals Engineering 16, 757765.Rubinstein, J.B., 1995. Column Flotation Process. Designs and Practices. Gordon

and Breach Science Publishers, Amsterdam B.V.

Sastry, K.V., Lofftus, D.D., 1988. Mathematical modeling and computer simulation ofcolumn otation. In: Sastry, K.V.S. (Ed.), Column Flotation88. SME, Littleton, CO,USA, pp. 5768.

Schwarz, S., Alexander, D., 2006a. Gas dispersion measurements in industrialotation cells. Minerals Engineering 19, 554560.

Schwarz, S., Alexander, D., 2006b. JKSimFloat V6:1plus: improving otation circuitperformance by simulation. In: International Conference on Mineral ProcessModelling, Simulation and Control, Sudbury, Ontario, Canada, pp. 3547.

Schwarz, S., Crnkovic, I., Alexander, D., 2008. Flotation circuit analysis at ZinifexCentury Mine. In: 40th Annual Meeting of the Canadian Mineral Processors,Ottawa, Ontario, Canada, pp. 297310.

Skogestad, S., Postlethwaite, I., 2005. Multivariable Feedback Control Analysis andDesign. second ed.. Wiley.

Stevenson, P., 2007. Hydrodynamic theory of rising foam. Minerals Engineering 20,282289.

Stevenson, P., Stevanov, C., Jameson, G.J., 2003. Liquid overow from a column ofrising aqueous froth. Minerals Engineering 16, 10451053.

Tavera, F., Escudero, R., 2002. Gas hold-up and solids hold-up in otation columns:on-line measurement based on electrical conductivity. Transactions of theInstitutions in Mining and Metallurgy, Section C: Mineral Processing andExtractive Metallurgy 111, C94C99.

Tavera, F., Gomez, C., Finch, J., 1998. Estimation of gas holdup in froths by electricalconductivity: application of the standard addition method. MineralsEngineering 11 (10), 941947.

Tuteja, R., Spottiswood, D., Misra, V., 1994. Mathematical models of the columnotation process a review. Minerals Engineering 7 (12), 14591472.

Uribe-Salas, A., Gomez, C.O., Finch, J.A., 1991. Bias detection in otation columns. In:Agar, G., Huls, B., Hyma, D. (Eds.), Column91 Proceedings of an InternationalConference on Column Flotation, vol. 2. Canadian Institute of Mining,Metallurgy and Petroleum, Sudbury, Ontario, pp. 391407.

Vieira, S., Sousa, J., Duro, F., 2005. Fuzzy modelling strategies applied to a columnotation process. Minerals Engineering 18, 725729.

Xu, M., Finch, J., 1990. Simplication of bubble size estimation in a bubble swarm.Journal of Colloid and Interface Science 140 (1), 298299.

Yianatos, J.B., Finch, J.A., Dobby, G.S., Xu, M., 1988. Bubble size estimation in abubble swarm. Journal of Colloid and Interface Science 126 (1), 3744.

Yianatos, J., Bergh, L., CortTs, G., 1998. Froth zone modelling of an industrialotation column. Minerals Engineering 11 (5), 423435.

Zhou, Z., Egiebor, N., Plitt, L., 1993. Frother effects on bubble size estimation in aotation column. Minerals Engineering 6 (1), 5597.

J. Bouchard et al. /Minerals Engineering 22 (2009) 519529 529

Column flotation simulation and control: An overviewIntroductionProcess descriptionModellingPrediction of recoveryDynamic behaviourSoft sensors

Process controlIntermediate level controlControl strategies based on metallurgical objectives

Current practice, research trends & future applicationsCurrent practice and challengesSteady-state simulation: metallurgical performanceSensor development and applicationsDynamic modelling and simulationProcess control myths and reality

ConclusionAcknowledgementsReferences