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Hierarchical control strategy for flotation columns
Minerals Engineering, Vol. 8, No. 12, pp. 1583--1591, 1995
Pergamon
0892--6875(95)00120.4
Copyright © 1995 Elsevier Science Lid Printed in Great Britain. All rights reserved 0892--6875/95 $9.50+0.00
HIERARCHICAL CONTROL STRATEGY FOR FLOTATION COLUMNS
]L,. G. BERGH, J. B. YIANATOS and C. P. ACUI~IA Chemical Engineering Department, Santa Maria University, Valparaiso, Chile
(Received 16 June 1995; accepted 31 July 1995)
ABSTRACT
An integral solution to the control problem has to deal with problems associated with instrumentation, process modelling, control strategies and control algorithms. The term "hierarchical" control is used here to mean the intelligent integration of available knowledge, control algorithms and logic rules of decision. The selection of information, algorithms and rules is based on the experimental and theoretical knowledge of the column flo~!ation process. The software support was designed and implemented in object oriented computer prograrmm,s. This technique allowed the implementation of a combination of control techniques, algorithms and heuristics, in the form of a control strategy. This strategy has shown to fit well with processes exhibiting complex dynamic characteristics. The hierarchical control was developed and tested in a pilot and an industrial flotation column including the following general aspects: coordination of distributed conventional control loops, verification and diagnosis of sensors, on-line predictive estimation of operating variables and diagnosis of common operating problems. Keywords Flotation columns; instrumentation; modelling; hierarchical control
INTRODUCTION To achieve a stable operation and consequently metallurgic benefits, process control systems have to be implemented. The primary objectives, as indices of process productivity and product quality, are the recovery and the concentrate grade. However, their estimation on-line is expensive and usually shows lack of accuracy. Therefore, it is common practice to substitute these control objectives for secondary ones, such as the froth depth, the gas holdup in the upper part of the collection zone and the bias in the froth [1]. This control is known as a stabilizing strategy. The first problem associated with stabilizing control is to obtain accurate measurements. Conventional sensors used to estimate these variables produce large calibration errors (from 10 to 100%). This fact has motivated the stud), of different approaches, usually referred to as non conventional, to improve the quality of these estimations and to include complementary information [2].
P,~sterpresentationat MineralsEngineering '95, St Ives, Cornwall,England, June 1995
1583
1584
L.G. Berghet
al.
Other problems associated with the control of flotation columns are the high interaction among the variables and the strong nonlinearities presented in the relationships between them. Studies conducted in a pilot column [3,4] have experimentally shown these effects. These characteristics largely constrain the proper work of distributed conventional PID control.
EXPERIMENTAL EQUIPMENT Experiences on dynamic modelling, conventional distributed control and distributed control supervised by logic rules, were performed on a 10 cm diameter and 10 m high pilot flotation column. The instrumentation to measure air mass flowrate, tailings flowrate and electrical conductivity profile across the pulp-froth interphase was installed and carefully calibrated. The wash water and feed flowrate were remotely regulated by variable speed peristaltic pumps. Intermediate tanks, air compressor and some auxiliary equipment completed the installation to operate the air-water system in a closed loop circuit. The data acquisition, the monitoring and control, were implemented through an Optomux serial interface, which connected the instrumentation with a PC computer. A schematic diagram of the instrumentation is illustrated in Figure 1.
I
~
Multiplexer
Conductimeter
~===~
Optomux
washwater r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
J
feed
air
. ............. ..~.:...-.--:--.~.j
P u t e r
Fig.1 Pilot column instrumentation. Further experimental work was carried out on a 1 m 2 section, 14 m high industrial flotation column, located at the molybdenite cleaning circuit at E1 Teniente. The original field instrumentation, complemented with the electrical conductivity profile device,was all connected to a PC computer through an Optomux serial interface. Step changes in the input variables----opening of tailing control valve, opening of air control valve and wash water flowrate--were implemented, to study the dynamic responses of the output variables--tailings flowrate and air flowrate. The dynamic information was used to set the PID control parameters of the basic loops, air flowrate control and tailing flowrate control. These control loops were tested and some fine tuning was experimentally made to account for nonlinearities and interactions. Froth depth control was then designed in cascade with the tailing flowrate controller, as well as the gas holdup control in cascade with the air flowrate controller. The bias, measured as the difference between the tailing and feed flowrates, was regulated by controlling the wash water flowrate. Experiences using distributed conventional control consisted basically in responses of the process to changes in the setpoint of the froth depth, bias and gas holdup controllers. Furthermore, under this control system the process was subjected to changes in feed flowrate and in the dosage of chemical reagent (frothing). The
Control strategyfor flotationcolumns
1585
most frequent ope~-ating and instrumental problems were studied, showing that further development in control strategies and instrumentation alternatives was needed.
CONTROL STRATEGIES A control strategy is defined in terms of how some selected objectives will be attempted under the constraints imposed by the process itself, the quality of the available information, and the mathematical tools and computational support available. Traditionally, once the process and on-line information concerning the state of different variables of interest are defined, an algorithmic control is used, such as the well known PID control or any other advanced model-based technique. More recently, the use of logic rules, emulating the operator think!rig, has found a fertile space to grow from off-line helping systems to truly on-line applications. The last family is known as heuristic control.
Algorithmic Control The most common strategy is to control the froth depth with the opening of the tailing valve and the manual regulation of wash water flowrate and air flowrate. In Chile 86% of the columns use this array [5]. With such a scheme there are no interactions between controllers [1]. A second strategy is to control the froth depth with the tlowrate of the wash water, and the bias (measured as the difference I~ztween the tailing and feed flowrates) with the tailing flowrate. Sometimes, a gas holdup controller is incorporated, acting on the air flowrate. Consequently, there exist three independently tuned control loops, with strong interactions between them. To achieve a reasonable operation some control loops have to be detuned. Experimental evidence [7] confirmed that significant changes in the control parameters are needed to keep the process under stable operation. Other advanced forms of algorithmic control have also been reported. For example, the application of predictive multiva:iable control [8] and adaptive control [9] have been tested at pilot scale.
Heuristic Control. In practice, different approaches to heuristic control have been implemented to flotation columns, based on different techniques. Expert systems applications have been reported in at least two plants. They are based on the information supplied by a system of three dp/cells, estimating the collection and froth zone densities. The strategy is to attempt to keep determined froth and collection densities by a selective manipulation of the air flowrate and the wash water flowrate. The froth depth is conventionally controlled, acting on the tailing flowrate [13]. A fuzzy logic control system was implemented and evaluated in Japan [11]. In this application the froth depth was controlled, manipulating the tailing flowrate in a conventional way. The concentrate and tailing grades were measured on-line and constitute the objectives of the control strategy. The main goal was to achieve a concentrate grade, by using fuzzy logic to change the setpoint of the air flowrate conventional controller. The logic rules considered changes in pH and in dosage of activated carbon, whenever the air flowrate controller setpoint was saturated. The tailing grade was used to infer the recovery, which was used to modify some of the logic rules. In general, algorithmic control strategies used successfully in others processes have been shown to be in adequate in solving the variety of control problems posed by flotation columns. In fact, conventional PID controllers, or modern model-based control algorithms (for example, minimum variance control, linear quadratic Gaussi~ta control, internal model control, adaptive control) are capable of optimizing the process operation in a very narrow operating zone. Usually, outside this zone, the advantages exhibited are lost very rapidly (lack of robustness to process-model mismatch). On the other hand, heuristic control based on logical rules (for example, fuzzy logic, expert systems, neural systems) are very efficient in preventing the process from moving away from some operating region, but they are less efficient in handling the dynamic ~-12-J
1586
L.G. Bergh et
al.
characteristics of the process near a local optimum operating point. Consequently, a manager or supervisor integrating these two disimilar control techniques can take advantage of choosing the right tool for the actual control problem [1].
HIERARCHICAL CONTROL A hierarchical control is a supervisor acting on top of the control system and its main goal is to increase the operating availability of the process under control. To achieve that, the control manager should coordinate the action of the controllers, according to the evolution of the process variables and some specific logic rules or functional relationships among them. The integration of algorithmic and heuristic tools in a strategy is heavily based on experimental evidence obtained from plant operation. This integration requires a software support developed using object oriented programming [6, 7]. The computer program is organized as follows. A master program deals with the data acquisition and control implementation according to a configuration stored in disk. Some of the data are shown on screen in the form of plant flowsheet and tendence plots, that can be modified on-line. A user interface program allows changes in control configurations, algorithms and parameters. Different areas of research and development are associated with some of the common control problems: (i)
Instrumental problems detection and operating variables prediction are critical subjects in the implementation of a robust control strategy.
(ii)
Emergency procedures and selection of the best available input information have to be considered in a flexible and integrated control strategy.
(iii)
Coordination of distributed control loops, through prioritization of control objectives and on-line selection of parameters for each control algorithm are definitively needed.
(iv)
Furthermore, if some limiting conditions are violated it will be necessary to pass the control to a set of logic rules until the process is driven to an appropriate operating region. This idea is shown schematically in Figure 2.
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~,IJI
Fig.2 Hierarchical control scheme.
I L l I~JI
Control strategy for flotation columns
(v)
i 587
It would be desirable for the system to be capable of processing the available input information in order t3 detect operating problems due to malfunction of auxiliary equipment, such as spargers or control[ valves.
In the following examples some tools, developed to be integrated in a hierarchical control strategy, are discussed. Instrumental Problems Detection
The main problem is to differentiate between expected changes in some process variable and the failure of the sensor measuring that variable. Statistics, history and process knowledge constitute the basis of inference to decide when we are in the presence of a sensor failure or a justifiable abrupt change in the estimated variable. Furthermore, in the case of failure detection, it would be wise to have the option of the supervisor selecting a second or third estimation of the variable using predicting models based on the kind of information that is still available. A second estimation is expected to produce larger estimation errors than a first one. The benefit is to keep the process under operation, even when a local optimum will become hard to achieve. An application example is the use of a second estimation of gas holdup. To estimate the gas holdup in the upper part of the collection zone a pair of electrodes was installed as part of an electrical c,anductivity device, to obtain a profile across the pulp-froth interface. Gas holdup is correlated to electrical conductivity using a non linear model of the form: el = fl (~)
(I)
where e represent.,; the local gas holdup as a function of the resistivity fl measured between the electrodes. This model is valid only when the froth depth interphase is far from the location of the electrodes. In practice this kind of model can be obtained by different techniques such as non linear regression or the use of neural network.';. Even more in both cases an adaptive scheme can be implemented to track the changes of model parameters over time. A second estimation of gas holdup can be obtained by modelling the effect of air flowrate (Fair), frother dosage (FD) and other available information such as wash water flowrate (Fwatcr ) and tailing flowrate (Frail): = f2(Fair, FD, Fwater, Ftail)
(2)
The prediction error of the second model is often sensitive to the particular operating zone and also to the feed characteristics. The accuracy of the electrical conductivity model is, in general, better than the second estimation [7]. A third and even less accurate prediction can be obtained from a simple model, depending only on the air flowrate: 83 = ~(Fai r)
(3)
Under normal operation the first and more accurate model is used to predict the gas holdup. When a failure condition is detec'ted the second model is used as the predictor if at that time all the independent variables of the models are available. If that condition is not satisfied then the third model becomes the best estimator of the gas holdul:. To obtain a bumpless transition from the wrong detected value to the most probable actual value of the estimated variable a time-weighted algorithm must be considered. The combination of an exponential filter and a soft sensor to estimate the gas holdup is schematically illustrated in Figure 3. The parameter k allows different weights to be given to each estimation when instrumental problems are detected. The result is that process instability, mainly due to large interactions between control loops, is avoided and a smooth operation can be achieved.
L.G. Bergh e t al.
1588
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Fig.3 Scheme of gas holdup prediction. Operating Problems Detection
Experiences in conventional distributed control showed that some operating problems can be opportunely detected and communicated to an operator, to take the necessary corrective actions, to avoid process shut down or significant degradation. A hierarchical control should have a routine to analyze the state of some process variables and other information in order to make a diagnosis about the operation. When an operating problem is detected a sequence of exploring actions are initiated to identify the origin of the failure. Some of the problems that can be detected are: sparger failure, column flooding (pulp overflow), deep froth, froth under the lip (no concentrate) and lack of frother. There will be cases where both a message to the operator and sometimes a corrective automatic procedure may be implemented. An application example is shown in Figure 4. In this case the investigation is about the state of the spargers, the air control valve and the air supply. The involved variables: computer signal for the opening [
Computer signal to air control valve
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Fig.4 Failure detection tree. of the air valve, gas holdup and air flowrate are checked. For each variable, a set of states are defined. One variable can be in one of the following states: high-high (HH), high (H), medium (M), low (L) and low-low
Control
strategy
for flotation columns
1589
(LL). If the signal to the air valve is not HH nor LL, then no failure is indicated. If that signal is HI-I (almost completly open) and the air flowrate and holdup measurements are working properly and both states are LL, then the failure may be: a plugged sparger, a defective air control valve or a low pressure supply. Similarly, if the signal is LL (almost completely close) and the air flowrate and the gas holdup are extremely high (HH) then the failure may be due to a broken sparger, a defective air control valve or a very high pressure supply.
Control Loops
Coordination of Local
The responses of the process variables to a change in the set point of the air flowrate controller is illustrated in Figure 5. In tlrds example the froth depth was controlled in cascade with the tailing flowrate controller. Gas holdup [%] • ,.i - [
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Fig.5 Interaction between variables under distributed control. A strong interact.ion between the expansion of the collection zone (due to the increment of gas holdup when the air flowrate !s increased) and the tailing flowrate (that changes due to the froth depth controller) can be observed. The clhange in the air flowrate produces an over reaction in the tailing flowrate controller, which is propagated, disturbing the bias (estimated as the difference between the tailing and feed flowrates). The bias controller changes the wash water flowrate and therefore introduces a second perturbation in the froth depth, and so on. A multivariable process under independent control loops will exhibit these interactions unless a heavy detuning of some control loops are performed. Alternatively, one can prioritize the control loops, temporarily inhibiting the action of some controllers, for some given conditions, or selecting a more appropriate algorithm according to the specific circumstances. Experiences in the application of conventional distributed control in flotation columns have shown a negative effect between the action of the bias and froth depth controllers. If a high priority is assigned to the froth depth control, then the bias control should be conditioned to the actual froth depth difference from its setpoint. This s'xategy is illustrated in Figure 6. Any time the froth depth is outside an alarm band (state HH or LL) the bias control is overriden, and the wash water flowrate is set to a constant value. If the froth depth is inside the alarm band, then the bias control is active. Depending on the difference between the actual bias and its setpoint, a different set of bias controller parameters, or an expert type of control is used. Besides the controller parameters settings, the levels of the alarm band for the froth depth and the levels of alarms (states) for the bias, constitute the tuning parameters of the control strategy. Using this strategy a much better overall control was achieved.
L. G. Berghet al.
1590
disturbances
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Fig.6 Hierarchical bias control loop.
CONCLUSIONS It has been experimentally shown that neither algorithmic control nor heuristic control can independently control both the stability of the process and the operation close to a local optimum. These results, obtained at pilot scale, were confirmed by industrial experience, where significant measurement errors are introduced to the general control problem. Hierarchical control is truly an alternative to solve the problem in an integral form, being able to manage information obtained on-line (directly measured or by inference) subjected to failure and error calibrations, to detect, alarm and sometimes correct operating problems, and to coordinate local conventional control loops combined with logical rules. In this way it is a powerful tool for increasing the operating availability and the product quality of complex processes, such as flotation columns. Furthermore, quality indices may be calculated and presented on-line to track the economic benefits of the operation. However, new opportunities and new control problems arise when a more flexible technique is used. Further work is needed to gain the necessary confidence for industrial applications.
ACKNOWLEDGEMENTS This work has been possible thanks to El Teniente, where some of the experiments were carried out, and to the financial support of Conicyt (Project Fondecyt 1950551 and Fondef MI-17) and the Santa Mafia University (Project 952723).
REFERENCES
1. 2. 3. 4. 5. 6.
Bergh, L.G. & Yianatos, J.B., Control Alternatives for Flotation Columns, Minerals Engineering, 6, No 6, 631 (1993). Bergh, L.G. & Yianatos, J.B., Advances on Flotation Column Dynamics and Measurements", Proceedings International Conference on Column Flotation, Sudbury, Canada, 409 (1991). Bergh, L.G. & Yianatos, J.B., Experimental Studies on Flotation Column Dynamics, Minerals Engineering, 7, No 2, 345 (1994). Bergh, L.G. & Yianatos, J.B., Dynamic Simulation of Operating Variables of Flotation Columns, Minerals Engineering, 8, No 7, (1995). Bergh, L.G. & Yianatos, J.B., Experience on Instrumentation and Control in Chilean Flotation Columns, Proceedings Mineral Processing Conference, Ostrava, Czech Republic, Junio, (1994). Acufia, C. & Bergh, L.G., SINCO: Sistema Inteligente de Control, Proceedings XI Chilean
Control strategyfor flotationcolumns
.
8. 9.
10.
11.
1591
Chemical Engineering Congress, Concepci6n, Chile, (1994). Acufia, C., Estudio de Control Jer~quico en Columnas de Flotaci6n, Chemical Engineer Thesis, Chemical Engineering Department, Santa Marfa University, Valparafso, Chile, (1994). Pu, M., Gupta, Y.P. & Al Taweel, A.M., Model Predictive Control of Flotation Columns, Proceeding International Conference on Column Flotation, Sudbury, Canada, 67 (1991). Jim6nez, C. & Bergh, L.G., Expefiencias de Controlador Adaptivo en una Columna de Flotaci6n Piloto, Chemical Engineer Thesis, Chemical Engineering Department, Santa Maria University, Valparaiso, Chile, (1994). Kosics, G.A., Dobby, G.S. & Young, P.D., ColumnEx: a Powerful and affordable Control System for Column Flotation, Proceedings International Conference on Column Flotation, Sudbury, Canada, 359 (19910. Hirajima, T., Takamori, T., Tsunekawa, M., Masubara, T., Oshima, K., Imai, T., Sawaki, K. & Kubo, S., The Aplication of Fuzzy Logic Control Concentrate Grade in Column Flotation at Toyaha Mines, Proceedings International Conference on Column Flotation, Sudbury, Canada, 375 (1991).
Pergamon
0892--6875(95)00120.4
Copyright © 1995 Elsevier Science Lid Printed in Great Britain. All rights reserved 0892--6875/95 $9.50+0.00
HIERARCHICAL CONTROL STRATEGY FOR FLOTATION COLUMNS
]L,. G. BERGH, J. B. YIANATOS and C. P. ACUI~IA Chemical Engineering Department, Santa Maria University, Valparaiso, Chile
(Received 16 June 1995; accepted 31 July 1995)
ABSTRACT
An integral solution to the control problem has to deal with problems associated with instrumentation, process modelling, control strategies and control algorithms. The term "hierarchical" control is used here to mean the intelligent integration of available knowledge, control algorithms and logic rules of decision. The selection of information, algorithms and rules is based on the experimental and theoretical knowledge of the column flo~!ation process. The software support was designed and implemented in object oriented computer prograrmm,s. This technique allowed the implementation of a combination of control techniques, algorithms and heuristics, in the form of a control strategy. This strategy has shown to fit well with processes exhibiting complex dynamic characteristics. The hierarchical control was developed and tested in a pilot and an industrial flotation column including the following general aspects: coordination of distributed conventional control loops, verification and diagnosis of sensors, on-line predictive estimation of operating variables and diagnosis of common operating problems. Keywords Flotation columns; instrumentation; modelling; hierarchical control
INTRODUCTION To achieve a stable operation and consequently metallurgic benefits, process control systems have to be implemented. The primary objectives, as indices of process productivity and product quality, are the recovery and the concentrate grade. However, their estimation on-line is expensive and usually shows lack of accuracy. Therefore, it is common practice to substitute these control objectives for secondary ones, such as the froth depth, the gas holdup in the upper part of the collection zone and the bias in the froth [1]. This control is known as a stabilizing strategy. The first problem associated with stabilizing control is to obtain accurate measurements. Conventional sensors used to estimate these variables produce large calibration errors (from 10 to 100%). This fact has motivated the stud), of different approaches, usually referred to as non conventional, to improve the quality of these estimations and to include complementary information [2].
P,~sterpresentationat MineralsEngineering '95, St Ives, Cornwall,England, June 1995
1583
1584
L.G. Berghet
al.
Other problems associated with the control of flotation columns are the high interaction among the variables and the strong nonlinearities presented in the relationships between them. Studies conducted in a pilot column [3,4] have experimentally shown these effects. These characteristics largely constrain the proper work of distributed conventional PID control.
EXPERIMENTAL EQUIPMENT Experiences on dynamic modelling, conventional distributed control and distributed control supervised by logic rules, were performed on a 10 cm diameter and 10 m high pilot flotation column. The instrumentation to measure air mass flowrate, tailings flowrate and electrical conductivity profile across the pulp-froth interphase was installed and carefully calibrated. The wash water and feed flowrate were remotely regulated by variable speed peristaltic pumps. Intermediate tanks, air compressor and some auxiliary equipment completed the installation to operate the air-water system in a closed loop circuit. The data acquisition, the monitoring and control, were implemented through an Optomux serial interface, which connected the instrumentation with a PC computer. A schematic diagram of the instrumentation is illustrated in Figure 1.
I
~
Multiplexer
Conductimeter
~===~
Optomux
washwater r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
J
feed
air
. ............. ..~.:...-.--:--.~.j
P u t e r
Fig.1 Pilot column instrumentation. Further experimental work was carried out on a 1 m 2 section, 14 m high industrial flotation column, located at the molybdenite cleaning circuit at E1 Teniente. The original field instrumentation, complemented with the electrical conductivity profile device,was all connected to a PC computer through an Optomux serial interface. Step changes in the input variables----opening of tailing control valve, opening of air control valve and wash water flowrate--were implemented, to study the dynamic responses of the output variables--tailings flowrate and air flowrate. The dynamic information was used to set the PID control parameters of the basic loops, air flowrate control and tailing flowrate control. These control loops were tested and some fine tuning was experimentally made to account for nonlinearities and interactions. Froth depth control was then designed in cascade with the tailing flowrate controller, as well as the gas holdup control in cascade with the air flowrate controller. The bias, measured as the difference between the tailing and feed flowrates, was regulated by controlling the wash water flowrate. Experiences using distributed conventional control consisted basically in responses of the process to changes in the setpoint of the froth depth, bias and gas holdup controllers. Furthermore, under this control system the process was subjected to changes in feed flowrate and in the dosage of chemical reagent (frothing). The
Control strategyfor flotationcolumns
1585
most frequent ope~-ating and instrumental problems were studied, showing that further development in control strategies and instrumentation alternatives was needed.
CONTROL STRATEGIES A control strategy is defined in terms of how some selected objectives will be attempted under the constraints imposed by the process itself, the quality of the available information, and the mathematical tools and computational support available. Traditionally, once the process and on-line information concerning the state of different variables of interest are defined, an algorithmic control is used, such as the well known PID control or any other advanced model-based technique. More recently, the use of logic rules, emulating the operator think!rig, has found a fertile space to grow from off-line helping systems to truly on-line applications. The last family is known as heuristic control.
Algorithmic Control The most common strategy is to control the froth depth with the opening of the tailing valve and the manual regulation of wash water flowrate and air flowrate. In Chile 86% of the columns use this array [5]. With such a scheme there are no interactions between controllers [1]. A second strategy is to control the froth depth with the tlowrate of the wash water, and the bias (measured as the difference I~ztween the tailing and feed flowrates) with the tailing flowrate. Sometimes, a gas holdup controller is incorporated, acting on the air flowrate. Consequently, there exist three independently tuned control loops, with strong interactions between them. To achieve a reasonable operation some control loops have to be detuned. Experimental evidence [7] confirmed that significant changes in the control parameters are needed to keep the process under stable operation. Other advanced forms of algorithmic control have also been reported. For example, the application of predictive multiva:iable control [8] and adaptive control [9] have been tested at pilot scale.
Heuristic Control. In practice, different approaches to heuristic control have been implemented to flotation columns, based on different techniques. Expert systems applications have been reported in at least two plants. They are based on the information supplied by a system of three dp/cells, estimating the collection and froth zone densities. The strategy is to attempt to keep determined froth and collection densities by a selective manipulation of the air flowrate and the wash water flowrate. The froth depth is conventionally controlled, acting on the tailing flowrate [13]. A fuzzy logic control system was implemented and evaluated in Japan [11]. In this application the froth depth was controlled, manipulating the tailing flowrate in a conventional way. The concentrate and tailing grades were measured on-line and constitute the objectives of the control strategy. The main goal was to achieve a concentrate grade, by using fuzzy logic to change the setpoint of the air flowrate conventional controller. The logic rules considered changes in pH and in dosage of activated carbon, whenever the air flowrate controller setpoint was saturated. The tailing grade was used to infer the recovery, which was used to modify some of the logic rules. In general, algorithmic control strategies used successfully in others processes have been shown to be in adequate in solving the variety of control problems posed by flotation columns. In fact, conventional PID controllers, or modern model-based control algorithms (for example, minimum variance control, linear quadratic Gaussi~ta control, internal model control, adaptive control) are capable of optimizing the process operation in a very narrow operating zone. Usually, outside this zone, the advantages exhibited are lost very rapidly (lack of robustness to process-model mismatch). On the other hand, heuristic control based on logical rules (for example, fuzzy logic, expert systems, neural systems) are very efficient in preventing the process from moving away from some operating region, but they are less efficient in handling the dynamic ~-12-J
1586
L.G. Bergh et
al.
characteristics of the process near a local optimum operating point. Consequently, a manager or supervisor integrating these two disimilar control techniques can take advantage of choosing the right tool for the actual control problem [1].
HIERARCHICAL CONTROL A hierarchical control is a supervisor acting on top of the control system and its main goal is to increase the operating availability of the process under control. To achieve that, the control manager should coordinate the action of the controllers, according to the evolution of the process variables and some specific logic rules or functional relationships among them. The integration of algorithmic and heuristic tools in a strategy is heavily based on experimental evidence obtained from plant operation. This integration requires a software support developed using object oriented programming [6, 7]. The computer program is organized as follows. A master program deals with the data acquisition and control implementation according to a configuration stored in disk. Some of the data are shown on screen in the form of plant flowsheet and tendence plots, that can be modified on-line. A user interface program allows changes in control configurations, algorithms and parameters. Different areas of research and development are associated with some of the common control problems: (i)
Instrumental problems detection and operating variables prediction are critical subjects in the implementation of a robust control strategy.
(ii)
Emergency procedures and selection of the best available input information have to be considered in a flexible and integrated control strategy.
(iii)
Coordination of distributed control loops, through prioritization of control objectives and on-line selection of parameters for each control algorithm are definitively needed.
(iv)
Furthermore, if some limiting conditions are violated it will be necessary to pass the control to a set of logic rules until the process is driven to an appropriate operating region. This idea is shown schematically in Figure 2.
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Control strategy for flotation columns
(v)
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It would be desirable for the system to be capable of processing the available input information in order t3 detect operating problems due to malfunction of auxiliary equipment, such as spargers or control[ valves.
In the following examples some tools, developed to be integrated in a hierarchical control strategy, are discussed. Instrumental Problems Detection
The main problem is to differentiate between expected changes in some process variable and the failure of the sensor measuring that variable. Statistics, history and process knowledge constitute the basis of inference to decide when we are in the presence of a sensor failure or a justifiable abrupt change in the estimated variable. Furthermore, in the case of failure detection, it would be wise to have the option of the supervisor selecting a second or third estimation of the variable using predicting models based on the kind of information that is still available. A second estimation is expected to produce larger estimation errors than a first one. The benefit is to keep the process under operation, even when a local optimum will become hard to achieve. An application example is the use of a second estimation of gas holdup. To estimate the gas holdup in the upper part of the collection zone a pair of electrodes was installed as part of an electrical c,anductivity device, to obtain a profile across the pulp-froth interface. Gas holdup is correlated to electrical conductivity using a non linear model of the form: el = fl (~)
(I)
where e represent.,; the local gas holdup as a function of the resistivity fl measured between the electrodes. This model is valid only when the froth depth interphase is far from the location of the electrodes. In practice this kind of model can be obtained by different techniques such as non linear regression or the use of neural network.';. Even more in both cases an adaptive scheme can be implemented to track the changes of model parameters over time. A second estimation of gas holdup can be obtained by modelling the effect of air flowrate (Fair), frother dosage (FD) and other available information such as wash water flowrate (Fwatcr ) and tailing flowrate (Frail): = f2(Fair, FD, Fwater, Ftail)
(2)
The prediction error of the second model is often sensitive to the particular operating zone and also to the feed characteristics. The accuracy of the electrical conductivity model is, in general, better than the second estimation [7]. A third and even less accurate prediction can be obtained from a simple model, depending only on the air flowrate: 83 = ~(Fai r)
(3)
Under normal operation the first and more accurate model is used to predict the gas holdup. When a failure condition is detec'ted the second model is used as the predictor if at that time all the independent variables of the models are available. If that condition is not satisfied then the third model becomes the best estimator of the gas holdul:. To obtain a bumpless transition from the wrong detected value to the most probable actual value of the estimated variable a time-weighted algorithm must be considered. The combination of an exponential filter and a soft sensor to estimate the gas holdup is schematically illustrated in Figure 3. The parameter k allows different weights to be given to each estimation when instrumental problems are detected. The result is that process instability, mainly due to large interactions between control loops, is avoided and a smooth operation can be achieved.
L.G. Bergh e t al.
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Experiences in conventional distributed control showed that some operating problems can be opportunely detected and communicated to an operator, to take the necessary corrective actions, to avoid process shut down or significant degradation. A hierarchical control should have a routine to analyze the state of some process variables and other information in order to make a diagnosis about the operation. When an operating problem is detected a sequence of exploring actions are initiated to identify the origin of the failure. Some of the problems that can be detected are: sparger failure, column flooding (pulp overflow), deep froth, froth under the lip (no concentrate) and lack of frother. There will be cases where both a message to the operator and sometimes a corrective automatic procedure may be implemented. An application example is shown in Figure 4. In this case the investigation is about the state of the spargers, the air control valve and the air supply. The involved variables: computer signal for the opening [
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Fig.4 Failure detection tree. of the air valve, gas holdup and air flowrate are checked. For each variable, a set of states are defined. One variable can be in one of the following states: high-high (HH), high (H), medium (M), low (L) and low-low
Control
strategy
for flotation columns
1589
(LL). If the signal to the air valve is not HH nor LL, then no failure is indicated. If that signal is HI-I (almost completly open) and the air flowrate and holdup measurements are working properly and both states are LL, then the failure may be: a plugged sparger, a defective air control valve or a low pressure supply. Similarly, if the signal is LL (almost completely close) and the air flowrate and the gas holdup are extremely high (HH) then the failure may be due to a broken sparger, a defective air control valve or a very high pressure supply.
Control Loops
Coordination of Local
The responses of the process variables to a change in the set point of the air flowrate controller is illustrated in Figure 5. In tlrds example the froth depth was controlled in cascade with the tailing flowrate controller. Gas holdup [%] • ,.i - [
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Fig.5 Interaction between variables under distributed control. A strong interact.ion between the expansion of the collection zone (due to the increment of gas holdup when the air flowrate !s increased) and the tailing flowrate (that changes due to the froth depth controller) can be observed. The clhange in the air flowrate produces an over reaction in the tailing flowrate controller, which is propagated, disturbing the bias (estimated as the difference between the tailing and feed flowrates). The bias controller changes the wash water flowrate and therefore introduces a second perturbation in the froth depth, and so on. A multivariable process under independent control loops will exhibit these interactions unless a heavy detuning of some control loops are performed. Alternatively, one can prioritize the control loops, temporarily inhibiting the action of some controllers, for some given conditions, or selecting a more appropriate algorithm according to the specific circumstances. Experiences in the application of conventional distributed control in flotation columns have shown a negative effect between the action of the bias and froth depth controllers. If a high priority is assigned to the froth depth control, then the bias control should be conditioned to the actual froth depth difference from its setpoint. This s'xategy is illustrated in Figure 6. Any time the froth depth is outside an alarm band (state HH or LL) the bias control is overriden, and the wash water flowrate is set to a constant value. If the froth depth is inside the alarm band, then the bias control is active. Depending on the difference between the actual bias and its setpoint, a different set of bias controller parameters, or an expert type of control is used. Besides the controller parameters settings, the levels of the alarm band for the froth depth and the levels of alarms (states) for the bias, constitute the tuning parameters of the control strategy. Using this strategy a much better overall control was achieved.
L. G. Berghet al.
1590
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CONCLUSIONS It has been experimentally shown that neither algorithmic control nor heuristic control can independently control both the stability of the process and the operation close to a local optimum. These results, obtained at pilot scale, were confirmed by industrial experience, where significant measurement errors are introduced to the general control problem. Hierarchical control is truly an alternative to solve the problem in an integral form, being able to manage information obtained on-line (directly measured or by inference) subjected to failure and error calibrations, to detect, alarm and sometimes correct operating problems, and to coordinate local conventional control loops combined with logical rules. In this way it is a powerful tool for increasing the operating availability and the product quality of complex processes, such as flotation columns. Furthermore, quality indices may be calculated and presented on-line to track the economic benefits of the operation. However, new opportunities and new control problems arise when a more flexible technique is used. Further work is needed to gain the necessary confidence for industrial applications.
ACKNOWLEDGEMENTS This work has been possible thanks to El Teniente, where some of the experiments were carried out, and to the financial support of Conicyt (Project Fondecyt 1950551 and Fondef MI-17) and the Santa Mafia University (Project 952723).
REFERENCES
1. 2. 3. 4. 5. 6.
Bergh, L.G. & Yianatos, J.B., Control Alternatives for Flotation Columns, Minerals Engineering, 6, No 6, 631 (1993). Bergh, L.G. & Yianatos, J.B., Advances on Flotation Column Dynamics and Measurements", Proceedings International Conference on Column Flotation, Sudbury, Canada, 409 (1991). Bergh, L.G. & Yianatos, J.B., Experimental Studies on Flotation Column Dynamics, Minerals Engineering, 7, No 2, 345 (1994). Bergh, L.G. & Yianatos, J.B., Dynamic Simulation of Operating Variables of Flotation Columns, Minerals Engineering, 8, No 7, (1995). Bergh, L.G. & Yianatos, J.B., Experience on Instrumentation and Control in Chilean Flotation Columns, Proceedings Mineral Processing Conference, Ostrava, Czech Republic, Junio, (1994). Acufia, C. & Bergh, L.G., SINCO: Sistema Inteligente de Control, Proceedings XI Chilean
Control strategyfor flotationcolumns
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8. 9.
10.
11.
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Chemical Engineering Congress, Concepci6n, Chile, (1994). Acufia, C., Estudio de Control Jer~quico en Columnas de Flotaci6n, Chemical Engineer Thesis, Chemical Engineering Department, Santa Marfa University, Valparafso, Chile, (1994). Pu, M., Gupta, Y.P. & Al Taweel, A.M., Model Predictive Control of Flotation Columns, Proceeding International Conference on Column Flotation, Sudbury, Canada, 67 (1991). Jim6nez, C. & Bergh, L.G., Expefiencias de Controlador Adaptivo en una Columna de Flotaci6n Piloto, Chemical Engineer Thesis, Chemical Engineering Department, Santa Maria University, Valparaiso, Chile, (1994). Kosics, G.A., Dobby, G.S. & Young, P.D., ColumnEx: a Powerful and affordable Control System for Column Flotation, Proceedings International Conference on Column Flotation, Sudbury, Canada, 359 (19910. Hirajima, T., Takamori, T., Tsunekawa, M., Masubara, T., Oshima, K., Imai, T., Sawaki, K. & Kubo, S., The Aplication of Fuzzy Logic Control Concentrate Grade in Column Flotation at Toyaha Mines, Proceedings International Conference on Column Flotation, Sudbury, Canada, 375 (1991).