The long way toward multivariate predictive control of flotation processes

Journal of Process Control 21 (2011) 226–234

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The long way toward multivariate predictive control of flotation processes L.G. Bergh ∗ , J.B. Yianatos Automation and Supervision Centre for Mineral Industry, Santa Maria University, Valparaiso, Chile

a r t i c l e

i n f o

Article history: Received 26 April 2010 Received in revised form 2 November 2010 Accepted 3 November 2010 Available online 15 December 2010 Keywords: Flotation Modeling Control Predictive control Expert control

a b s t r a c t Flotation processes are very complex, and after more than one hundred years of history, there are few reports on applications of novel techniques in monitoring and control of flotation units, circuits and global plants. On the other hand, the successful application of multivariate predictive control on other processes is well known. In this paper, an analysis on how the characteristics of flotation processes, the quality of measurements of key variables, and the general lack of realistic dynamic models, are delaying the appropriate use of predictive control. In this context, the applications of multivariate statistics, such as PCA, to model the relationship between operating data for on-line diagnosis and fault detection and to build causal models are discussed. Also the use of PLS models to predict target variables for control purposes, is presented. Results, obtained at pilot and industrial scales, are discussed, introducing new ideas on how to obtain more valuable information from the usual available operating data of the plant, and particularly from froth images. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction McKee [1] reported the state of flotation control as follows. The development of robust and lasting automatic control systems for flotation circuits has proved difficult. Reasons for this include the inherent complexity and unpredictability of the response of most flotation circuits to upset conditions, unclear expectations of what can be achieved by a control system, unrealistic objectives for control systems and excessive complexity of the actual control strategies. However, the interest in developing control systems has persisted because the benefits to be gained in terms of improved metallurgical performance are substantial. Since early 1990s, it was generally accepted that stabilizing control must precede optimization, and the focus has shifted to a range of increasingly sophisticated approaches to achieve stabilization by the use of various model based control strategies. A recent development is the application of expert systems as the crucial role and knowledge of operators are being appreciated. After 10 years, Hodouin et al. [2], reported: developments in the mineral process industry have been made in hardware (sensors, data transmission systems, computer platforms) as well as in software (data management, process models, control algorithms). However, problems inherent to the high level of complexity of the processed material are still there, leaving process engineers with more questions than answers. Some critical aspects in a control

∗ Corresponding author. Tel.: +56 32 2654229. E-mail address: [email protected] (L.G. Bergh). 0959-1524/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jprocont.2010.11.001

strategy are: measurement instrumentation, data reconciliation, pattern recognition, fault detection and diagnosis, soft sensors, process, and controller performance monitoring. The successful application of knowledge-based control strategies for grinding and flotation processes depends mainly on the quality of information and the process knowledge. Hodouin et al. [2] also emphasize that mineral processing optimization and control cannot be performed without a minimum amount of information on the input disturbances (the material properties), the process states, and the final product quality. This is in fact the bottleneck of mineral process control. The operating strategy efficiency is totally dependent upon the quality of the information used, since, on the one hand, it is used to build the knowledge encapsulated in the models which the control strategy is based on, and, on the other hand, it is the input to the real-time optimization and control algorithms. Measurement of ore composition, particle size distribution, and flow rates is central in the control of mineral processing operations. Instrumentation is available, as well as for less ore specific properties such as levels, motor power, rotation speed, pH, and slurry density. However, the quality of these measurements depends heavily on maintenance programs. Furthermore, essential properties such as grindability, mineral texture, liberation degree, surface activity, slurry rheology, grinding media size distribution, bubble size distribution, and loading are extremely difficult to measure and even to infer from other measurements. According to the industrial point of view of Thwaites [3], optimum flotation performance relies on good level control, air sparging, and flow control, as well as precise reagents addition. Significant opportunities are found in flotation operations by atten-

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tion to these fundamental controls. Flotation is the process area of significant upgrading of commodity minerals/metals. In Section 2 a brief summary of model predictive control is presented, highlighting under which conditions a successful implementation will be expected. Then in Section 3, some characteristics of flotation plants are discussed. In Section 4, the control strategies for flotation plants are discussed, focusing on the problems usually found in both the regulatory and the supervisory controls. The role of disturbances, instrumentation, process interaction and maintenance programs are discussed for regulatory control. The problems related to estimation of target variables, process and instrumentation constraints, the availability of process models, and the role of peripheral tools are discussed for the implementation of supervisory control. The discussion is centered on what else has to be done to meet the requirements needed for model predictive control, and to understand why so far the most common approach to flotation control is knowledge based control (expert and fuzzy systems). 2. Model predictive control Model predictive control (MPC) is defined as the family of controllers in which there is a direct use of an explicit and separately identifiable process model to predict the future response of the plant [4,5]. MPC has found wide acceptance in industrial applications mainly because it can be operated without expert intervention for long periods of time and because of their flexible constraint handling capability. These are significant advantages in the context of the overall operating objectives of the process industries. It is a fact that in practice the plant operating point that satisfies the overall economic goals of the process will lie close to the intersection of constraints. Therefore, in order to be successful, any control system must anticipate constraint violations and correct them in a systematic way: violations must not be allowed while keeping the operation close to these constraints [4]. 2.1. Historical development of MPC The current interest of the process industry in MPC appeared with the application reports of “model predictive heuristic control” [6], and “dynamic matrix control” (DMC) [7]. In both algorithms an explicit dynamic model of the plant is used to predict the effect of future actions of the manipulated variables on the output. The future changes of the manipulated variables are determined by optimization with the objective of minimizing the predicted error subject to operating constraints. The optimization is repeated at each sampling time based on updated information (measurements) from the plant. Thus, in the context of MPC the control problem including the relative importance of the different objectives, the constraints, etc. is formulated as a dynamic optimization problem. It constitutes one of the first examples of large-scale dynamic optimization applied routinely in real time in the process industries. More than 15 years after model predictive control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the on-line optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for non-linear systems but for practical applications many questions remain, including the reliability and efficiency of the on-line computation scheme. To deal with model uncertainty ‘rigorously’ an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage.

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Among the main research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, non-linear state estimation, and batch system control. Many practical problems like control objective prioritization and symptom-aided diagnosis can be integrated systematically and effectively into the MPC framework by expanding the problem formulation to include integer variables yielding a mixed-integer quadratic or linear program. Efficient techniques for solving these problems are available [8]. 2.2. Present situation of MPC The infinite prediction horizon of the LQG algorithm endows the algorithm with powerful stabilizing properties. For the case of a perfect model, it was shown to be stabilizing for any reasonable real plant as long as Q is positive semi definite and R is positive definite. However, the low impact of LQG on control technology developments in process industries was mainly attributed to constraints, process nonlinearities, model uncertainty, unique performance criteria, and cultural reasons [5]. This environment led to the industrial development of a more general model based control methodology in which the dynamic optimization problem is solved online at each control execution. Process inputs are computed so as to optimize future plant behavior over a time interval known as the prediction horizon. In the general case any desired objective function can be used. Plant dynamics are described by an explicit process model which can take, in principle, any required mathematical form. Process input and output constraints are included directly in the problem formulation so that future constraint violations are anticipated and prevented. The first input of the optimal input sequence is injected into the plant and the problem is solved again at the next time interval using updated process measurements. In addition to developing more flexible control technology, new process identification technology was developed to allow quick estimation of empirical dynamic models from test data, substantially reducing the cost of model development. This new methodology for industrial process modeling and control is what we now refer to as MPC technology. 2.3. Implementation requirements for MPC A detailed comparison between different MPC algorithms can be found in [4,8]. All of them have at least the following requirements to be implemented: (i) Local objectives must be under regulatory control with acceptable performance. (ii) Target variables must be measured or estimated with a frequency related to process dynamics, with high quality and availability. (iii) To minimize the variance of target variables, process constraints should be explicitly stated. (iv) A dynamic model (or at least a static model) between local regulatory control set points and target variables should be known. This model should be valid in a well established area of operation. (v) Existence of complementary mechanisms to promote robustness to process-model mismatch and instrumentation faults. The next question is to know what are the characteristics of a flotation plant, how well the local objectives can be achieved by regulatory controls, what are the problems associated with the estimation of target variables, what are the process and instrumentation constraints, which kind of models are available and which complementary mechanism can be used to promote robustness

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Rougher

Feed

Tailings

Rougher

Prerougher

Tailings

Feed PR cleaner

Concentrate

Regrinding

Regrinding Concentrate

Cleaner

Cleaner

Scavenger

Scavenger

Fig. 1. Layout of a typical flotation plant.

Fig. 2. Prerougher and Rougher split.

to process-model mismatch and instrumentation faults. In other words, how far is the state of art of flotation plant control from a successful application of MPC.

Prerougher tailing is fed to the Rougher circuit. Usually the Rougher tailings are subject to economical constraints (forced to be at least below a target). Now a new target must be chosen: the concentrate grade of the Prerougher circuit. The selection of this grade will influence the feed to the Rougher, and therefore will allow splitting the mineral separation between the two circuits. If the feed grade to the plant changes very often (for example a sudden increment in grade), then there may occur that the Prerougher capacity is not enough to pull out all the concentrate mass. In this case, one can add to the Prerougher circuit the first banks of the Rougher circuit.

3. General description of flotation plants The separation of minerals by flotation processes is so complex that an adequate final product can never be achieved in one single stage. Several consecutive cell arrays form a circuit and more than a circuit is needed to achieve high metal recoveries at commercial metal grades.

4. Control strategies for flotation plants 3.1. Typical flotation plant A typical flotation plant, shown in Fig. 1, is composed at least for the following circuits: Rougher, Regrinding, Cleaner, and Scavenger. The output of the grinding plant is fed to the Rougher circuit. Usually pulp level control is available for each bank of the circuit. Air flow rates may be controlled or have no regulation, depending on cell design. The collected Rougher concentrates are sent to a regrinding stage and after classifying the undersize stream is fed to the Cleaning circuit. This circuit is generally composed by flotation columns operating in parallel. Froth depth, wash water and air flow rates usually are under control. The collective column concentrates form part of the final concentrate. The tailings from both columns are fed to a Scavenger circuit. Again, usually pulp level control for each bank is available and air flow rate control depends on cell design. This concentrate is returned to the regrinding stage, while the tailings join the collective Rougher tailings to form the final tailings.

The overall control strategy of a flotation plant relies first on good control of local objectives (pulp levels, flow rates), usually implemented as a distributed control system (DCS). When these local objectives are satisfactory achieved, then the next level is to be able to modify the operation of each circuit (Rougher, Cleaners, Scavenger) in order to obtain specific concentrate and tailing grades. This demands the capability of changing the set points of the local controllers in such a manner that the operation of the circuit is corrected every time. Then the specific knowledge on how the target variables are related to the local inputs is needed. If this second level of control is possible, then to satisfy the overall target of the plant (final concentrate grade in a specific band and plant recovery over a minimum value) one needs to know what to ask of each circuit. Which is the best combination of circuit targets to maximize the benefits? How will it depend on the feed characteristics and plant constrains? 4.1. Regulatory control

3.2. Modified circuits Sometimes, it may be convenient to treat separately the concentrate of the first cells of a Rougher circuit from the concentrate obtained in the last cells [1]. In this case the Rougher is broken in two circuits: a Prerougher and a Rougher. The motivation for such an array is to add flexibility for plant operation. This new degree of freedom attempts to adapt the plant layout to the time variant characteristics of the feed and the process constraints presented in every circuit. This alternative plant layout is shown in Fig. 2. The Prerougher concentrate is fed to a Prerougher cleaner circuit. This last concentrate forms part of the final concentrate of the plant, while the tailings are pumped to the regrinding stage. The

In this section the role of process disturbances, available instrumentation and process dynamics characteristics on regulatory control is discussed. A brief summary of the main control algorithms used in flotation plants are presented. Finally, how maintenance programs may constraint the benefits of stabilizing control is discussed. 4.1.1. Disturbances The main disturbances coming into the Rougher circuit are the feed characteristics, such as feed rate, solid percent, particle size and surface composition distribution, grades of valuable metals, and mineralogical species. These characteristics are a result of pre-

L.G. Bergh, J.B. Yianatos / Journal of Process Control 21 (2011) 226–234

Reactives

Air

Air

Air

FC FC

Air

FC FC

LC

FC

AI

LC AI

FI AI

Feed

Tailings

Concentrate Fig. 3. Typical distributed control of a flotation circuit.

vious mining and grinding stages, and usually very little is done to modify these characteristics to favor flotation operation. 4.1.2. Instrumentation Usually, pulp level control, precise chemical reagent addition, air, pulp, and water flow rate controls are achieved in most flotation plants. Fig. 3 shows a common P&ID for a flotation circuit, while Fig. 4 illustrates the case of a flotation column. Sensors for measuring local target and actuators (control valves and peristaltic pumps) are available with reasonable performance. 4.1.3. Process interaction Some difficulties have been observed in the coordination of pulp level control in a circuit such as the one illustrated in Fig. 3, when it is composed by several banks. The main disturbance for these controllers is the change in feed flow rates to each process unit. Feed forward–feedback control schemes [9,10] have been proposed and successfully tested in plants to deal with this coordination problem, when the quality of measurements and actuators are well maintained. In general, for given controller set points the plant operation is stable. Bergh and Yianatos [11] have presented a general discussion about column flotation control, covering process and instrumentation issues. Dynamic interaction between the three classic controllers, shown in Fig. 4, is expected from a physical analysis of the system, and from experimentally obtained dynamic models

229

[12]. The computation of the relative gain array presented by Persechini et al. [13], leading almost to an identity matrix, is valid only for steady state. One alternative to deal with this problem in a DCS structure is to perform some detuning decoupling. For example, the bias control can only be attempted if the froth depth control is stable on its target. 4.1.4. Control algorithms Apart from distributed PID control of local objectives, several studies have been conducted at this level. For example, gain scheduled control, fuzzy control, dynamic matrix control, generalized predictive control, global predictive control, and others, have been implemented and tested in flotation columns. A complete discussion on this can be found in Bouchard et al. [14]. Even when the improvement in local control performance has been demonstrated using more complex control techniques, the important problem of how to select the best set points of these local targets to optimize the global performance of the process units and the whole plant still remains unsolved. In other words, model predictive control has not been used in any of its formulations to directly control the metallurgic performance of one unit. Control strategies based on metallurgical objectives have been implemented as expert systems to supervise the column operation by manipulating froth depth, air flow rate and wash water flow rate set points [15–17]. Besides illustrating the benefits of improving control strategies, the latter papers show the overall work associated with industrial implementations, including a pre-diagnosis step to detect and correct operation and maintenance problems. 4.1.5. Maintenance Plant operation on target can be stable if the quality of measurements and actuators can be assured by adequate maintenance programs. Problems with wash water and process air distributions will change the relationship between these local set points and the principal targets as concentrate grade and recovery. The use of gas hold up on-line measurement and control has been proposed and applications on pilot columns have demonstrated its benefits [18,19]. However, in a three phase system, which includes solids, it is difficult to maintain the quality of the measurement. Moreover, assuring a certain gas hold up is not synonymous with having the right bubble size distribution, and therefore, once again the relationship between hold up and concentrate grade is not unique. One can conclude that regulatory control of local objectives is not always achieved with acceptable performance.

FC

4.2. Supervisory control

Wash water AI

Feed

Concentrate LC

FC

Air

Tailings Fig. 4. Typical distributed control of a flotation column.

Concentrate and tailings grades represent the main target variables in a flotation unit and plant. Process recovery is a steady state concept and therefore it can only be used when this condition is achieved or when large periods of data are considered. 4.2.1. Target variables estimation X-ray fluorescence has been the universal method for online solid composition measurement in mineral processing plants. Equipment vendors now offer more efficient, compact, flexible, and reliable devices. The sampling device as well as the technique for presenting the sample at the analyzer window is critical, since the very small quantity of ore to be analyzed must be representative of tons of an inherently heterogeneous material. Usually, several process streams are multiplexed to one XRF detector in order to minimize the investment. These complex procedures may produce significant time delay in grade estimation, as it is compared with the process time constant of a flotation unit. Furthermore, the accuracy and reliability of the estimation is strongly related to the quality of the calibration method. These

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characteristics put a lot of constraints in building reliable dynamic models between the local set points of the regulatory control and the target variables. This has been a motivation to research on how to use some related properties of the froth to these target variables. The long sampling interval of XRF has been reduced also by reflectance spectrum analysis of the slurries [20]. After improving flotation fundamental measurements and controls, and the consolidation of on-line XRF analyzers, the introduction of flotation cameras has been a major issue. New variables, such as froth texture, froth velocity and bubble size, were available to the control engineer. In the flotation field, many investigations have been made for froth image utilization [21–24]. However, the captured information is quite complex and requires the development of correlation equations with process variables that have to be controlled. These authors found a large uncertainty in the grade predictions because of the influence of external sources of variations, such as light brightness, camera position. Even when these factors were studied and their effect practically eliminated, no models are currently useful to predict grades. Bergh and Niada [25] proposed to jointly study the froth characteristics with the state of operating variables to find the correlation between these variables through the principal component analysis technique. Other studies of froth image analysis relating air recovery and bubble loading to describe flotation bank performance can be found in Barbian et al. [26]. Interesting sensors are under development for flotation columns for measuring the air hold-up, the location of the froth–pulp interface, and the water split bias [18,19]. However, no industrial applications have claimed a significant improvement on the overall column control. This is mainly due to the difficulties found in maintaining the quality of these estimations over time, and the lack of reliable relationships between these intermediate objectives and the target metallurgical variables. 4.2.2. Process and instrumentation constraints The usual practice in flotation control was to ignore the constraint issue at the design stage and then to consider it in an ad hoc way during the implementation. Since each process unit is unique one cannot exploit the population factor as in other industries (e.g. aerospace). That is, one cannot afford extreme expenses in designing an ad hoc control system that one knows will not work in another process and therefore its cost cannot be spread over a large number of applications. The design and maintenance costs of ad hoc control systems usually more than offset their profitability. In conclusion, economics demand that the control systems must be designed, when possible, with transparent specification of performance criteria such as process constraints. In this sense, MPC methodology currently can reflect most directly many performance criteria of relevance to the process industries, and is capable of utilizing any available process model. This is the primary reason for the success of these techniques in numerous applications in the chemical process industries. Other common constraints often found in flotation plants are the operation and instrumentation problems that have to be detected and solved prior to the implementation of any control strategy, as was discussed in [16,17]. On stream analyzers usually provide grade information every 10–20 min, depending on the complexity of the process [20]. Most disturbances coming into the process units typically occur at high frequency, making extremely difficult to capture from the experimental data the information needed to obtain dynamic models of the process. 4.2.3. Models The theory of MPC has matured considerably. However, according to the practitioners, what limits the performance and

applicability of MPC are not the deficiencies of the control algorithm, but difficulties in modeling, sensing, state estimation, fault detection, diagnosis, etc. [8]. Model development is by far the most critical and timeconsuming step in implementing a MPC. It is estimated that, in a typical commissioning project, modeling efforts can take up to 90% of the cost and time. Unlike the linear case, however, there is no established method to construct a non-linear model through a plant test. Recognition of the need has made empirical modeling of non-linear systems a focal research topic within the process control community. In Chile, there are more than one thousand cameras installed from different suppliers. Faster dynamics (typically less than 1 min), as compared to XRF technology (10–20 min), open the possibility of building better flotation models, and therefore the use of predictive control. A wide review of the fundamentals of process flotation modeling in mechanical cells has been presented by King [27] and in flotation columns by Finch and Dobby [28] and Rubinstein [29]. King [27] brings the issue that flotation models do not generally incorporate variables such as pH, pulp Eh, and chemical reagent (collector, frother) concentration. Pyke et al. [30] presented a general flotation model describing the flotation process fundamentals (particle–bubble attachment and detachment in a turbulent regime). Recently, Koh and Schwarz [31] reported a CFD simulation of the particle–bubble attachment process, where they showed that the bubble surface area flux Sb is one of the flotation parameters that constrain the transport at the level of the pulp–froth interface. The recent findings in flotation modeling related to air recovery is discussed by Neethling and Cilliers [32]. All these approaches are commonly used for design and simulation of flotation circuits but not for control purposes. A common alternative, in the absence of mathematical models, is to use the cumulative process knowledge and operators experience to build a supervisory expert control system. In some sense, basic knowledge-based rules are applicable to most flotation processes. However, process constraints usually vary from plant to plant. Moreover, control decisions depend drastically on infrequent on-stream analyzer measurements, making it almost impossible to consider the process dynamics. Therefore, most expert systems are designed to supervise the process by making changes on local set points of regulatory controls from one steady state to another [11,17]. Fuzzy logic has become a powerful tool to choose most precisely the control actions [33,34], but the frequency of decisions has not changed. 4.2.4. Complementary tools When a good process model is available, the benefits of MPC can be sustained over a long period of time if a mechanism to detect an abnormality and diagnose its root cause is available. The results can be communicated to engineers and can also be used to adapt control parameters. Harris et al. [35] and other researchers have proposed performance measures for existing loops. 4.2.4.1. Application of statistical methods in fault detection. Failure and fault detection is a complementary area to process control, allowing for higher levels of operational prediction and performance optimization. The successful example of the application of multivariate statistical analysis in smelters to alert operators when furnace run out conditions are being approached, is discussed by King [36]. This system is based on principal component analysis (PCA) models. This kind of applications to flotation processes are discussed later in this paper. A more general approach using multivariate statistics have been proposed by MacGregor and his coworkers [37–39]. Successful application of principal component analysis (PCA) and partial least

L.G. Bergh, J.B. Yianatos / Journal of Process Control 21 (2011) 226–234

squares (PLS) models have been reported for different kinds of chemical processes [37] and particularly for flotation processes [25,40,41]. 4.2.4.2. PCA method. The key feature of principal component analysis (PCA) method is its ability to mathematically project high dimensional process and quality data into smaller dimensional, summary data sets via the development of linear models. The practical value of the PCA modeling method is that this technique allows for the systematic examination and interpretation of the model outputs. Examination of the model outputs can provide insight into the operation of an industrial process during monitoring and quality assurance activities. With PCA, the systematic interpretation of dominant patterns in the data and the isolation of the most important contributors to these patterns are possible. This allows the classification of data relationships according to normal and abnormal operation. Some of these numerous advantages the PCA method has over traditional monitoring and prediction technologies are: provision for data dimension reduction and robustness to highly correlated, noisy and missing data [38]. The concept of a latent variable model is that the true dimension of a process is not defined by the number of measured variables, but by the underlying phenomena that drive the process. The latent variables themselves are modeled as mathematical combinations of the measured variables and describe directions of variation in the original data. A latent variable model can contain much fewer dimensions than the original data, it can provide a useful simplification of large data sets, and it can allow better interpretation of the measured data during analysis [39]. In a typical industrial data analysis application, k process variables, x1 , x2 , . . . , xk , are measured simultaneously and are combined into a vector associated with each observation of the k variables. If N observations are made, an (N × k) matrix X, can be constructed, where each of the rows correspond to an observation of the k variables, and each of the columns correspond to a specific variable over the N observation. On-line tests can be implemented based on the following criteria: (i) It is a normal operation if the new set of data satisfies the PSE and T2 test. (ii) It is an abnormal operation if the T2 test is failed. If the PSE test is passed then the model is considered to adequately represents the process. If the PSE test is also failed then either the model is no longer appropriate or a measurement problem occurred. (iii) If only T2 test is satisfied then a measurement problem or a lack of fit of the PCA model occurred. In this way a diagnosis of the operation can be accomplished for steady state data. Furthermore, the residuals are informative of the principal process variables affecting the abnormal situation. 4.2.4.3. Case study. A pilot column [40] was operated for the air–water (and frother) system coupled with an on-line steady state model to predict output stream grades. The convenience of the approach of combining on-line process measurements and models to empirically test strategies for process control, monitoring and diagnosis, was recently discussed by Bergh [42]. A flotation column model structure was developed, following Finch and Dobby [28]. Following Fig. 5, first the gas holdup, the bias rate and the kinetic constants for each mineralogical species are estimated from empirical models, depending on operating variables such as feed flow rate, gas flow rate, wash water flow rate and froth depth. Then, dispersion number, residence times, froth and collection recovery are estimated. Finally concentrate and tailings

231

Concentrate grade Tailings grade

Design parameters:

Recovery

Diameter, high,

Bias rate

geometry…

Gas holdup

Feed characteristics: froth depth air flow rate water flow rate

Process

species, density, solid

Metallurgic

percentage, particle size,

Simulator

grades, kinetic

Fig. 5. Flotation column simulator structure.

grades are predicted. The empirical model parameters were fitted using experimental data. More details can be found in Bergh et al. [33]. The column control is similar to that shown in Fig. 4. There are three tertiary control loops: air flow rate, tailings flow rate and wash water flow rate. Feed flow rate is also measured and controlled. A hydro dynamical supervisory control is implemented to control gas hold up in cascade with air flow rate, froth depth in cascade with tailings flow rate and bias in cascade with wash water flow rate. All the operating variables are measured and communicated to a PLC, where the DCS has been implemented. All signals are communicated to a PC network, where the monitoring and hydro dynamical supervisory control is running under Intouch software. In the PC network, the steady state test is performed on-line. When the process reaches a steady state, the predicting model is solved on-line to estimate the concentrate and the tailing grades. All data is displayed on PC screen. The original X matrix consisted of sixteen variables, shown in Table 1, and 2550 observations of steady state data. The experiments were designed to cover the maximum possible variation of the main independent variables, and were conducted under closed loop control. The data was processed using PLS Toolbox from Eigenvector Research. A PCA model was built from 1800 sets of data corresponding to a normal condition. A model with 6 latent variables was found to explain at least 92% of the variance in the centered and scaled pretreated data. For monitoring the process the Hotelling T2 limit

Table 1 Operating and quality variables considered. No.

Variable

Tag

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Froth depth Gas hold up Dp/cell low Dp/cell high Pressure to air control valve Pressure to tailings control valve Bias superficial velocity Air superficial velocity Tailings superficial velocity Feed superficial velocity Wash water superficial velocity Cu recovery Concentrate Cu grade Feed particle size d80 Feed Cu grade Feed solid percentage

z E PL PH PA PT Jb Jg Jt Jf Jw R CCG D FCG S

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150

Froth depth [cm]

8

PSE

6 4 2 0 0

200

400

600

100 50 0 0

200

Sample number

Hotelling

30

Fig. 8. Froth depth over the whole period.

10 0

200

400

600

Sample number 33

90

80

29

75 70

27 Concentrate grade

Recovery %

85

31

Conc. grade

600

20

0

65

Recovery

25

60 0

200

400

600

Sample number Fig. 6. Operating condition test A.

was found to be 12.6, while the PSE (prediction squared error) limit was 3.81. Experiments were carried on to test when the process is out of control and an abnormal operating condition is met. Two results are presented: when the process is at steady state and during the transient period. One example is shown in Fig. 6, where the T2 and PSE test has been followed for over 600 samples, taken every 5 (s). One can see that most of the time the PSE test is satisfied, while T2 test is failed at intervals 130–200, 300–430 and 480–560. On these same periods, the concentrate grade is too low and recovery is high or concentrate grade is too high and recovery is low, then an abnormal operation has been detected. To identify which variables are causing this, the individual contribution to the T2 residuals, for sample 512, are shown in Fig. 7 (the nomenclature is described in Table 1). One can see that the main contributions were the froth depth and the high and low dp/cells. All variables consistently showed that the problem is due to a low froth depth, causing high recovery and low concentrate grade. Fig. 8 shows the froth depth changes during the whole period. If the froth depth were change from 50 to 100 cm, as is shown at sample 600, the column operation is driven back to a normal condition, as can be seen from the previous figures. When only the PSE residuals test fails, the device measuring the isolated variable must be recalibrated or replaced. Several tests were carried out on to find the sensitivity of the monitoring test

to the extension of the fail, measured in percentage of error. Errors less than 5% on pressure to control valves, 7% on dp/cells, 15% on flow meters and 10% on virtual measurements of concentrate grade were detected. These error limits were found for a large number of different operating conditions. One example is shown in Fig. 9 for the virtual measurement of copper concentrate grade. The same PCA model was used to test abnormal operation either because of decision based on failed sensors or process variable deviations. The PCA model relies on the selected data. If the data collected represents a narrow band of operation around the targets, it may be expected that abnormal conditions, as a result of a combination of process variable deviations, will be easily detected. A model built on such selected data will be less useful to identify measurements problems. The model used in this work was based on data corresponding to a wide operation zone, favoring the detection of sensor failures. Other approach to be tested is the use of different PCA models, based on different data, for each purpose. The example of the application of multivariate statistics analysis in flotation of a Rougher circuit is presented in Bergh and Niada [25]. The PCA model was built based on operating variables and image characteristics at steady state, and may be used to alert operators of abnormal operating conditions, indicating the most probable inputs that cause the problem. Similarly the application of multivariate statistics to flotation columns was previously discussed [40]. A PCA model was used to detect and isolate instrumentation faults and abnormal operating conditions. These PCA models can be effectively used as part of a supervisory control strategy, especially when control decisions are infrequently made, that is the case when steady state PCA models are used. 4.2.4.4. Soft sensors. Other area of application of multivariate statistics is in estimating (soft sensors) the values of unmeasured variables. PLS models have been built to predict concentrate grades based on operating variables and froth characteristics [43]. More work is under development and some new results will be available soon. 4.2.5. Some advances in flotation control As mentioned earlier, literature on flotation control using machine vision is very limited. Ylinen et al. [44] reported basic test 15

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E PL PH PA PT Jb Jf Jg Jt Jw R CCG D FCG S Fig. 7. Contributions to abnormal operation A.

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results from zinc rougher flotation circuits. Image features included in their control strategy were the red color of froth, bubble collapse rate, and froth bubble size. Xanthate and CuSO4 addition rates were used as manipulated variables. In [44], the applicability of those image variables in flotation control was demonstrated through real plant tests. A continuation of this work can be found in Kaartinen et al. [45]. FrothmasterTM is the first commercial machine vision system to report flotation control tests [46]. A simple rule-based master controller included one image variable (froth speed) and three manipulated variables (level, frother addition rate, and aeration rate). Control results showed that the quality of concentrate obtained could be stabilized when froth speed was controlled. Froth velocity has been used as a more direct indicator of concentrate mass pull, to adjust pulp level. An example of this kind of control application is described by Supomo et al. [47]. Although it is very limited, the literature regarding froth-based flotation control confirms the possibility of the use of image features in controlling flotation processes. Froth image features reflect important process characteristics and respond to changes in manipulated variables. Therefore, by employing image features as process outputs, it is possible to build a causal process model that can predict image features from the given values of manipulated variables, and furthermore any model-based control technique can be applied to froth-based flotation control using the causal model. The use of a model-based control technique will provide better control performance compared to simple PID or rule-based controllers [48,49]. Liu and MacGregor [48] discussed and illustrated a new method for froth-based flotation modeling and control that can be used as part of comprehensive flotation control systems. The new method is based on the causal process model predicting future froth appearances (e.g. bubble size distribution, clear windows, and black holes) from the given values of manipulated variables and observed values of the process variables. With this model, the new values of manipulated variables for achieving specified froth appearances can be obtained via optimization. The novelty of this approach consisted that instead of using a concentrate grade as a target variable, the method used the scores of a PCA model, whose values represent a froth appearance [50,51]. Since this model was obtained from operating data and image characteristics, no grade measurements are needed. Simulation using the steady state causal model provided control performance that was very satisfactory in achieving a specified froth appearance. It is important to note, that froth appearance represents a time variant target that strongly depends on feed characteristics. Therefore, a new target represented by a new froth appearance must be set, based on the available grades of relevant streams. When a dynamic process model is used to predict future froth status within a fixed time horizon, then an optimizer can find sequences of the manipulated variables, which is essentially MPC.

5. Conclusions MPC is ideally the solution for high quality control. However, to be applicable without losing its benefits, good measurements, acceptable regulatory control of local objectives (DCS), reliable dynamic models, explicitly stated process constraints and new methods to promote robustness are needed. Flotation processes have weaknesses in most of those aspects. Regulatory control of local objectives in flotation plants presents at least the following problems. First, maintenance programs to assure quality of measurements and actuators are insufficient. Second, a higher interaction of flotation, comminution and mining processes is needed, in order to decrease the important effect of time variant disturbances coming into the flotation plants. Finally,

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a better knowledge of process dynamics, to effectively handle process interactions in DCS, is needed. Supervisory control of flotation plants, on top of stabilizing control, has been implemented in the form of sub-optimal expert systems. The major drawback of this approach is the difficulties found in replicating a particular solution from one plant to another plant. However, this approach presents the advantage of flexibility, where the lack of accuracy and availability of key measurements such as grades can be considered in the control strategy, as well as the particular inclusion of some operating constraints. In the last years several contributions are decreasing the actual gap. The use of multivariate statistics may open new opportunities to deal with infrequent grade measurements, and to obtain more valuable information from the thousands of cameras that have been installed around the world. Froth image analysis and reflectance spectroscopy analysis can be integrated with operating variables to build better and more useful models. Statistical methods seems to provide a general framework to build models in latent variables related to froth characteristics at short sampling intervals, and as a complementary tool to better identify different operating scenarios and to opportunely detect faults in key instrumentation. All these advances may lead to create the minimum conditions necessary to successfully implement MPC algorithms. However, most work has to be done to assure that the theoretical benefits of MPC are not lost with the actual plant constraints. Acknowledgements The authors would like to thanks Santa Maria University (Project 271068), Conicyt (Project Fondecyt 1100854), and NEIM, Project P07-087-F, ICM-Mideplan for their financial support. References [1] D.J. McKee, Automatic flotation control – a review of 20 years of effort, Minerals Engineering 4 (1991) 653–666. [2] D. Hodouin, S.-L. Jamsa-Jounela, M.T. Carvalho, L.G. Bergh, State of the art and challenges in mineral processing control, Control Engineering Practice 9 (2001) 995–1005. [3] P. Thwaites, Process control in metallurgical plants – from an Xstrata perspective, Annual Reviews in Control 31 (2007) 221–239. [4] C.E. Garcia, D.M. Prett, M. Morari, Model predictive control: theory and practice – a survey, Automatica 25 (1989) 335–348. [5] S.J. Qin, T.A. Badgwell, A survey of industrial model predictive control technology, Control Engineering Practice 11 (2003) 733–764. [6] C.R. Cutler, B.L. Ramaker, Dynamic matrix control – a computer control algorithm, in: AICHE, National Meeting, Houston, TX, April, 1979. [7] D.M. Prett, R.D. Gillette, Optimization and constrained multivariable control of a catalytic cracking unit, in: Proceedings of the Joint Automatic Control Conference, San Francisco, CA, 1980. [8] M. Morari, J.H. Lee, Model predictive control: past, present and future, Computers and Chemical Engineering 23 (1999) 667–682. [9] S.-L Jamsa-Jounela, M. Dietrich, K. Halmevaara, O. Tiili, Control of pulp levels in flotation cells, Control Engineering Practice 11 (2003) 73–81. [10] B. Stenlund, A. Medvedev, Level control of cascade coupled flotation tanks, Control Engineering Practice 10 (2002) 443–448. [11] L.G. Bergh, J.B. Yianatos, Flotation column automation: state of the art, Control Engineering Practice 11 (2003) 67–72. [12] L.G. Bergh, J.B. Yianatos, Experimental studies in flotation column dynamics, Minerals Engineering 7 (1994) 345–355. [13] M. Persechini, F. Jota, F. Peres, Dynamic model of a flotation column, Minerals Engineering 13 (2000) 1465–1481. [14] J. Bouchard, A. Desbiens, R. del Villar, E. Nunez, Column flotation simulation and control: an overview, Minerals Engineering 22 (2009) 519–529. [15] J. Mckay, R. Inchausti, Expert supervisory control of flotation columns, in: C.O. Gomez, J.A. Finch (Eds.), Column’96, Proceedings of the International Symposium on Column Flotation, Montreal, Canada, 1996, pp. 353–367. [16] L.G. Bergh, J.B. Yianatos, Hierarchical control strategy in columns at El Teniente, in: C.O. Gomez, J.A. Finch (Eds.), Column’96, Proceedings of the International Symposium on Column Flotation, Montreal, Canada, 1996, pp. 369–380. [17] L.G. Bergh, J.B. Yianatos, Supervisory control experience on large industrial flotation columns, in: D. Hodouin, C. Bazin, A. Desbiens (Eds.), Proceedings of the International Symposium, Control and Optimization in Minerals, Metals, and Materials Processing, Quebec, Canada, 1999, pp. 299–310.

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[41] G. Bartolacci, P. Pelletier, J. Tessier Jr., C. Duchense, P.-A. Bosse, J. Fournier, Application of numerical image analysis to process diagnosis and physical parameter measurement in mineral process – part I: flotation control based on froth textural characteristics, Minerals Engineering 19 (2006) 734–747. [42] L.G. Bergh, Combining on-line process measurements and models to empirically test strategies for process monitoring, diagnosis and control, in: Proceedings IFAC 12th Symposium on Automation in Mining Mineral Metal Processing, Québec City, Canada, August 21–23, 2007, pp. 363–368. [43] V. Nakagawa, L.G. Bergh, Soft sensor based on PLS in a flotation circuit, in: Internal Research Report (in Spanish), Chemical Engineering Department, Santa Maria University, 2008. [44] R. Ylinen, J. Miettunen, M. Molander, E.-R. Siliamaa, Vision and model-based control of flotation, in: S.-L. Jamsa-Jounela, E. Vapaavuori (Eds.), Proceedings IFAC Workshop on Future Trends in Automation in Mineral and Metal Processing, Finland, August 22–24, 2000, pp. 475–480. [45] J. Kaartinen, J. Hätönen, H. Hyötyniemi, J. Miettunen, Machine-vision-based control of zinc flotation – a case study, Control Engineering Practice 14 (2006) 1455–1466. [46] N. Brown, P. Bourke, S. Ronkainen, M. van Olst, Improving flotation plant performance at Cadia by controlling and optimizing the rate of froth recovery using Outokumpu FrothmasterTM , in: Proceedings of 33rd Annual Meeting of Canadian Mineral Processors, Ottawa, Canada, 2001, pp. 25–36. [47] A. Supomo, E. Yap, X. Zheng, G. Banini, J. Mosher, A. Partanen, PT Freeport Indonesia’s mass-pull control strategy for rougher flotation, Minerals Engineering 21 (2008) 808–816. [48] J. Liu, J.F. MacGregor, Froth-based modeling and control of flotation processes, Minerals Engineering 21 (2008) 642–651. ˜ [49] F. Nunez, A. Cipriano, Visual information model based predictor for froth speed control in flotation process, Minerals Engineering 22 (2009) 366–371. [50] J. Liu, J.F. MacGregor, C. Duchesne, G. Bartolacci, Monitoring of flotation processes using multiresolutional multivariate image analysis, Minerals Engineering 18 (2005) 65–76. [51] J. Liu, J.F. MacGregor, On the extraction of spectral and spatial information from images, Chemometrics and Intelligent Laboratory Systems 85 (2007) 119–130. Professor Bergh is chemical engineer from Santa Maria University (1976), holds a M.Eng. (1983) and a Ph.D. (1987) from McMaster University, Canada. He gives courses in the undergraduate and graduate chemical engineering programs in the area of process control and applied statistics. He is author of a great number of scientific publications, and he is very active in the organization and participation of international conferences on the subject. He is the vicechair of the international technical committee of the IFAC chapter of Automation on MMM processes and he has participated as consultor for the mineral industry in Chile and abroad. Professor Yianatos is chemical engineer from PUCV (1974), holds a M.Sc. (1979) from lÉcole Polytecnique, Montreal University, Canada, and a Ph.D. (1987) from McGuill University, Canada. He gives courses in the undergraduate and graduate chemical engineering programs in the area of flotation. He is author of a great number of scientific publications, and he is very active in the organization and participation of international conferences on the subject. He is a member of the editorial committee of Minerals Engineering and he has participated as consultor for the mineral industry in Chile and abroad.