- Email: [email protected]
Evaluation of MPC strategies for mineral grinding
16th IFAC Symposium on Automation in Mining, Mineral and Metal Processing August 25-28, 2013. San Diego, California, USA
Evaluation of MPC strategies for mineral grinding ⋆ Pablo Karelovic ∗ Roberto Razzetto ∗∗ Aldo Cipriano ∗ ∗
College of Engineering, Pontificia Universidad Cat´ olica de Chile, Av. Vicu˜ na Mackenna 4860, Santiago, Chile (email: [email protected], [email protected]). ∗∗ Honeywell Chile, El Bosque 500, Santiago, Chile (email: [email protected]).
Abstract: Stable operation of grinding plants is of great importance as it ensures improved efficiency and mineral recovery. The majority of current control solutions in mineral grinding plants are based largely on expert control systems which aim to maximize throughput while keeping operational variables within predefined safe limits and a stable process operation. Nevertheless, these systems are not without disadvantages: they tend to systematize bad operational practices; there are no clear procedures to tune them and they exhibit poor response to unmeasured disturbances. Strategies based on predictive control, on the other hand, allow the handling of operational constrains, unmeasured disturbances and coupling of operational variables. Additionally, they are comparably easier to tune and are less sensitive to modeling errors. This paper presents a comparative analysis of three control strategies applied to a mineral grinding plant. The tested controllers are: (i) single centralized MPC, (ii) decentralized MPC for SAG mills and ball mills and (iii) multi-level control with a higher optimization layer and a lower decentralized MPC regulatory layer. These three control strategies are implemented using various Honeywell’s Profit Suite software applications and the comparative analysis is performed through simulation. In order to analyze the strategies, several performance indices are defined. Keywords: Process control; Integrated plant control; Supervisory control; Multivariable predictive control; Comminution. 1. INTRODUCTION The grinding process is the step on a concentrator operation where the ore is broken down into smaller pieces, preparing the ore and determining its characteristics for the following separation stages. This process is of great importance as the product particle size has a great impact on the recovery rate of the valuable mineral. A stable operation of grinding plants ensures improved efficiency, which results in a greater economic benefit. Furthermore, grinding mill circuits are the most energy-intensive processes, typically accounting for approximately 50% of the total cost of the operation. For the previous reasons, it is of great interest to develop control strategies and techniques in order to accomplish economical and technical objectives. These control objectives typically are to maintain some percentage of the product particle size below a reference value, while keeping power consumption as low as possible and other operational variables (such as bearing pressure, water sump level, hydrocyclone pressure, etc.) under predefined constrains. Among the most frequent control technologies implemented in grinding circuits, according to a recent survey (Wei and Craig, 2009), are PID control and expert ⋆ Aldo Cipriano would like to thank the Fondecyt project 1120047, ”Distributed Hybrid Model Predictive Control for Mineral Processing”.
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systems. PID control, which is discussed by Pomerleau et al. (2000), shows considerably low levels of satisfaction regarding its performance in grinding circuits, which is probably due to the fact that this process is inherently multivariate. Typical expert systems aim to replicate the knowledge of operators. While these systems seem like and intuitive and straightforward solution, they have some disadvantages: bad practices may be systematized if their effects are not understood properly, there are no direct methods for developing tuning procedures and they respond poorly to disturbances. On the other hand, strategies based on predictive control exhibit better results in controlling highly interacting system such as a grinding plant, as they allow the handling of operational constrains, unmeasured disturbances and coupling of operational variables. This article presents an evaluation of various control strategies based on predictive control. The performance of each strategy is tested through changes in the reference of controlled variables, particularly product size distribution, and changes in ore hardness and feed size distribution. To perform these tests, a dynamic simulator of a grinding plant was developed and calibrated with plant data. The grinding plant modeled (Figure 1) is divided into two stages. In the primary stage, fresh ore is fed into a SAG mill, along with the necessary water. Then, the product is classified in a vibratory screen. The oversized ore is 10.3182/20130825-4-US-2038.00066
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
sent to a pebble crusher, which feeds back into the SAG mill. The undersized ore, on the other hand, continues to the secondary stage. In the secondary stage, the product of the previous stage is split into three lines through a distribution box. In each line, the pulp is sent to from the distribution box to a sump, from where is pumped to a hydrocyclone battery. The hydrocyclone underflow is fed into a ball mill, which feeds back into the sump. The final product of this grinding plant is the hydrocyclone overflow.
Fig. 1. Simulated grinding plant. The organization of this article is as follows. The control problem and the strategies are described in Section 2. Results obtained with each strategy are displayed in Section 3. A comparative analysis of the previous results obtained through dynamic simulation is presented in Section 4. Finally, conclusions and discussions are presented in Section 5. 2. CASE STUDY
Table 1 shows all the manipulated, controlled and disturbance variables included in the simulator. Table 1. Manipulated, controlled and disturbance variables
MVs
CVs
DVs
To measure the performance of these strategies, the grinding plant simulator is subjected to different scenarios of operation: normal operation, change in ore hardness, change in feed size distribution and change in the reference value of product particle size (defined as the percentage of product retained by a 65 mesh sieve). After each strategy is tested in the previous scenarios, several indices are calculated in order to do a comparative analysis of each strategy’s performance. Given that the control objectives proposed for these controllers are to minimize specific energy consumption, maximize the tonnage of ore processed and minimize the error between the product particle size and its reference, the performance indices are chosen to measure the degree of fulfillment of these objectives. Thus, the selected indices are: • Mean tonnage of ore processed • Specific energy consumption • Root-mean-square (RMS) error in product particle size Specific energy consumption and RMS error are calculated using (1) and (2), respectively. Ptotal (1) F v u N test X u 1 2 t (y(k) − yref ) (2) Ntest − Ndist + 1 k=Ndist
As previously stated, the main goal of this article is to develop a comparative analysis of three different control strategies applied to a grinding plant using a dynamic simulator. The simulator, developed in MATLAB/Simulink, represents the plant shown in Figure 1 and is composed of unit operations interrelated through their input and output streams. The unit operations included in the simulator are: SAG mill, vibratory screen, pebble crusher, sump, centrifugal pump, hydrocyclone battery and ball mill. Stockpile and belt feeders are not included in the simulator, so the effects of segregation in the feed are not modeled. Nonetheless, several particle size distributions for the feed are available to simulate disturbances.
SAG circuit Fresh ore feed Water-to-ore ratio Mill speed Mill hold-up Mill power consumption Tonnage of pebbles Tonnage of product Feed size distribution Ore hardness
The mathematical models used to represent each unit operation in the plant are based on the models developed by Austin et al. (1987), Orellana (2010) and Salazar et al. (2009). The parameters of each model were calibrated using data from various sources. Therefore, the simulator is not intended to represent a specific plant, but is designed to exhibit a behavior that is qualitatively close to reality.
Balls circuit Sump water feed Pump speed Product particle size Sump level Hydrocyclone pressure Sump slurry density Product of SAG circuit
where Ptotal is the total power consumption of the plant, F is the tonnage flow of mineral processed, y(k) is the product particle size, yref is the reference for the product particle size, Ndist is the sample number where the disturbance is applied and Ntest is the total number of samples. The three control strategies evaluated are described as follows. 2.1 Single centralized MPC control For this strategy, both primary and secondary stages (i.e. the whole grinding plant) are modeled as a single system. Manipulated variables for this controller are fresh ore feed to the SAG mill, water-to-ore ratio and SAG mill speed for the first stage; sump water feed and pump speed for each line of the second stage. Controlled variables are SAG mill hold-up, SAG mill power consumption, tonnage of pebbles produced and tonnage of product for the first stage; product particle size, sump level, hydrocyclone pressure and sump slurry density for each line of the second stage. Feed size distribution and ore hardness are treated as unmeasured disturbances. 2.2 Decentralized MPC control In this strategy, the primary stage and each line of the secondary stage of the grinding plant are modeled as in-
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IFAC MMM 2013 August 25-28, 2013. San Diego, USA
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dependent systems, and a MPC controller is developed for each one of this models. Manipulated variables, controlled variables and unmeasured disturbances are the same as in the previous strategy. Additionally, the tonnage of processed mineral in the primary stage is used as a measured disturbance for each line of the secondary stage.
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For this strategy, a multi-level controller is designed. The lower regulatory layer is the same as the previous decentralized control strategy, and a new higher optimization layer is developed as a way to coordinate the operation of the controllers in the regulatory layer. This higher layer performs an optimization of the steady-state model of the plant, thus determining the optimum values of operational variables. These values are then sent to the lower regulatory level, which drives the plant to the optimal operating point.
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Fig. 2. Simulation results for change in feed size distribution with decentralized MPC control strategy.
3. RESULTS
For the decentralized MPC control strategy operating under normal conditions with soft ore and a medium feed size distribution, the secondary stage controllers are able to keep the product particle size in the reference value of 30%, while the primary stage controller is able to maximize the tonnage processed (limited to 730 ton/h to prevent an overload in the SAG mill) and maintain a specific energy consumption of 37.76 kWh/ton. Figure 2 shows the results obtained when there is a change in feed size distribution, from fine ore to coarse ore, with a feed of hard ore. It can be seen that the product particle size drifts from its reference value at the time of the disturbance, but the secondary stage controller is able to return it. As in normal operation, the primary stage controller is able to maximize the tonnage processed at 730 ton/h. Specific energy consumption is decreased from an initial value of 39 to 37.81 kWh/ton, which seems counterintuitive, but can be explained as pebble production in the SAG mill is decreased, which decreases power consumption. Thus, specific energy consumption is decreased. Figure 3 shows the results obtained when there is a change in ore hardness, from soft ore to hard ore, with a medium feed size distribution. Again, it can be seen that the product particle size drifts from its reference value at the time of the disturbance and the secondary stage controller is able to return it. Processed tonnage is maximized and there is an increase on the specific energy consumption, from 37.76 to 37.84 kWh/ton, due to the increase in ore hardness. Finally, Figure 4 shows the results obtained when there is a step change in the reference value for the product particle size. It can be seen that the secondary stage controller is able to follow the new reference in product particle size. 232
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3.1 Decentralized MPC control
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In this section, results for the three proposed strategies are presented.
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Fig. 3. Simulation results for change in ore hardness in the grinding plant with decentralized MPC control strategy. Meanwhile, processed tonnage is maximized and there is an increase on the specific energy consumption, from 37.76 to 37.92 kWh/ton. Table 2 shows the performance indices for this strategy. PI 1 is equivalent to mean tonnage of ore processed (measured in ton/h), PI 2 is equivalent to specific energy consumption (measured in kWh/ton) and PI 3 is equivalent to RMS error in product particle size. Table 2. Performance indices for the decentralized MPC control strategy Index
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IFAC MMM 2013 August 25-28, 2013. San Diego, USA
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Fig. 4. Simulation results for change in product particle size reference with decentralized MPC control strategy. 3.2 Centralized MPC control For the centralized MPC control strategy operating under normal conditions with soft ore and a medium feed size distribution, the specific energy consumption is 37.23 kWh/ton, which is lower than the value obtained in the previous strategy. Meanwhile, product particle size is kept at its reference value and feed tonnage is maximized. Figure 5 shows the results obtained for the centralized MPC control strategy when there is a change in feed size distribution, from fine ore to coarse ore. As in the previous strategy, the controller is able to return the product particle size to its reference value. Meanwhile, specific energy consumption is lowered to 37.42 kWh/ton.
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Fig. 6. Simulation results for change in ore hardness in the grinding plant with centralized MPC control strategy. Finally, Figure 7 shows the results obtained when there is a step change in the reference value for the product particle size. 40
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Table 3 shows the performance indices for this strategy. Table 3. Performance indices for the centralized MPC control strategy
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730 37.22 –
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730 37.41 1.41
730 37.40 1.24
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Fig. 5. Simulation results for change in feed size distribution with centralized MPC control strategy. Figure 6 shows the results obtained when there is a change in ore hardness, from soft ore to hard ore. These results for product particle size do not exhibit an appreciable difference with those obtained in the decentralized strategy (Figure 3). Meanwhile, specific energy consumption stabilizes at 37.41 kWh/ton. 233
3.3 Multi-level control For the multi-level control strategy operating under normal conditions with soft ore and a medium feed size distribution, the specific energy consumption is 37.76 kWh/ton,
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
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Table 4. Performance indices for the multi-level control strategy
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Index
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PI 1 PI 2 PI 3
730 37.76 –
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730 37.92 1.42
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Figure 9 shows the results obtained when there is a change in ore hardness, from soft ore to hard ore. These results do not exhibit an appreciable difference with those obtained in the decentralized strategy.
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As show by the results obtained in section 3, the three strategies tested are able to process the same tonnage (the maximum permitted) in all the scenarios. This indicates that the remaining manipulated variables are sufficient to deal with the disturbances and meet the objectives proposed.
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Regarding the RMS error, the centralized solution shows the best performance when there is a change in feed size distribution or particle size reference, and the worst performance when there is a change in ore hardness. Multilevel control shows a slight overall improvement over the decentralized solution, except when there is a change in ore hardness, where the results are practically the same.
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4. COMPARATIVE ANALYSIS
The best performance, in terms of specific energy consumption, is provided by the centralized strategy. The decentralized solution, on the other hand, exhibits a marginally worse performance in comparison to the centralized solution. Multi-level control shows virtually no improvement over the decentralized solution.
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Fig. 10. Simulation results for change in product particle size reference with multi-level control strategy.
Fig. 8. Simulation results for change in feed size distribution with multi-level control strategy.
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Figure 8 shows the results obtained for the multi-level control strategy when there is a change in feed size distribution, from fine ore to coarse ore. Despite de disturbance, the controller is able to return the product particle size to its reference value. Meanwhile, specific energy consumption stabilizes at a value of 37.82 kWh/ton.
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which is the same as the value obtained in the decentralized strategy. Meanwhile, product particle size is kept at its reference value and feed tonnage is maximized.
Fig. 9. Simulation results for change in ore hardness in the grinding plant with multi-level control strategy. Finally, Figure 10 shows the results obtained when there is a step change in the reference value for the product particle size. Table 4 shows the performance indices for this strategy. 234
It should be noted that the previous results do not reflect the technical complexity of implementing each solution. It could be argued that although the centralized solution exhibits the best performance, from a technical point of view it is the most complex to implement. To obtain the models employed by the centralized controller, it is necessary to perform plant-wide testing, which would require disturbing the normal operation of the plant for a period of time. On the other hand, due to the modularity of the decentralized solution, it would be necessary to test only one section of the plant at a time, which would
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
lower the impact on the overall production. Moreover, the decentralized models can be rearranged and recombined if there is a modification in the structure of the plant or if it is necessary to design a controller for a different plant. The previous reasons could make the decentralized strategy, in some cases, the preferred alternative, especially when the results obtained are not significantly worse than the ones obtained with a centralized strategy. 5. CONCLUSIONS In this paper the results of a comparative analysis of control strategies in a mineral grinding plant have been presented. Three different strategies were tested. These strategies were based on predictive control and implemented using Honeywell’s Profit Suite software applications. The results show that the centralized strategy exhibits the best overall performance of the three strategies tested. Furthermore, the results show that the performance of a decentralized strategy can be improved, albeit marginally, with the addition of an optimization layer in a multi-level control scheme, or others distributed control alternatives, such as multi-agent systems. Future work will focus on the design, development and testing of different alternatives of distributed control; and the comparison of these schemes with an expert control module which will work in conjunction with existing controllers to handle special disturbances which are too great to be handled by the controllers, such as overload of the SAG mill or blockage of the pulp line (Cort´es and Cerda, 2010). Furthermore, the effects of segregation in the stockpile and belt feeders will be modeled for future implementations of the dynamic simulator. REFERENCES Austin, L., Menacho, J., and Pearcy, F. (1987). A general model for semi-autogenous and autogenous milling. In APCOM 87. Proceeding of Twentieth International Symposium on the Application of Computers and Mathematics in the Mineral Industries, volume 2, 107–126. Cort´es, G. and Cerda, J. (2010). SAG & secondary grinding multivariable predictive control coordinated: Divisi´on Codelco Norte. In Proceedings of the 2nd International Congress of Automation in the Mining Industry, 18–27. Orellana, R. (2010). Modelo, control y simulador de planta de molienda semiautgena y molienda secundaria. Thesis for degree of Engineer, Universidad de Chile. Pomerleau, A., Hodouin, D., Desbiens, A., and Gagnon, E. (2000). A survey of grinding circuit control methods: from decentralized PID controllers to multivariable predictive controllers. Powder Technology, 108(2–3), 103– 115. Salazar, J., Magne, L., Acu˜ na, G., and Cubillos, F. (2009). Dynamic modelling and simulation of semi-autogenous mills. Minerals Engineering, 22(1), 70–77. Wei, D. and Craig, I.K. (2009). Grinding mill circuits - A survey of control and economic concerns. International Journal of Mineral Processing, 90(1–4), 56–66.
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Evaluation of MPC strategies for mineral grinding ⋆ Pablo Karelovic ∗ Roberto Razzetto ∗∗ Aldo Cipriano ∗ ∗
College of Engineering, Pontificia Universidad Cat´ olica de Chile, Av. Vicu˜ na Mackenna 4860, Santiago, Chile (email: [email protected], [email protected]). ∗∗ Honeywell Chile, El Bosque 500, Santiago, Chile (email: [email protected]).
Abstract: Stable operation of grinding plants is of great importance as it ensures improved efficiency and mineral recovery. The majority of current control solutions in mineral grinding plants are based largely on expert control systems which aim to maximize throughput while keeping operational variables within predefined safe limits and a stable process operation. Nevertheless, these systems are not without disadvantages: they tend to systematize bad operational practices; there are no clear procedures to tune them and they exhibit poor response to unmeasured disturbances. Strategies based on predictive control, on the other hand, allow the handling of operational constrains, unmeasured disturbances and coupling of operational variables. Additionally, they are comparably easier to tune and are less sensitive to modeling errors. This paper presents a comparative analysis of three control strategies applied to a mineral grinding plant. The tested controllers are: (i) single centralized MPC, (ii) decentralized MPC for SAG mills and ball mills and (iii) multi-level control with a higher optimization layer and a lower decentralized MPC regulatory layer. These three control strategies are implemented using various Honeywell’s Profit Suite software applications and the comparative analysis is performed through simulation. In order to analyze the strategies, several performance indices are defined. Keywords: Process control; Integrated plant control; Supervisory control; Multivariable predictive control; Comminution. 1. INTRODUCTION The grinding process is the step on a concentrator operation where the ore is broken down into smaller pieces, preparing the ore and determining its characteristics for the following separation stages. This process is of great importance as the product particle size has a great impact on the recovery rate of the valuable mineral. A stable operation of grinding plants ensures improved efficiency, which results in a greater economic benefit. Furthermore, grinding mill circuits are the most energy-intensive processes, typically accounting for approximately 50% of the total cost of the operation. For the previous reasons, it is of great interest to develop control strategies and techniques in order to accomplish economical and technical objectives. These control objectives typically are to maintain some percentage of the product particle size below a reference value, while keeping power consumption as low as possible and other operational variables (such as bearing pressure, water sump level, hydrocyclone pressure, etc.) under predefined constrains. Among the most frequent control technologies implemented in grinding circuits, according to a recent survey (Wei and Craig, 2009), are PID control and expert ⋆ Aldo Cipriano would like to thank the Fondecyt project 1120047, ”Distributed Hybrid Model Predictive Control for Mineral Processing”.
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systems. PID control, which is discussed by Pomerleau et al. (2000), shows considerably low levels of satisfaction regarding its performance in grinding circuits, which is probably due to the fact that this process is inherently multivariate. Typical expert systems aim to replicate the knowledge of operators. While these systems seem like and intuitive and straightforward solution, they have some disadvantages: bad practices may be systematized if their effects are not understood properly, there are no direct methods for developing tuning procedures and they respond poorly to disturbances. On the other hand, strategies based on predictive control exhibit better results in controlling highly interacting system such as a grinding plant, as they allow the handling of operational constrains, unmeasured disturbances and coupling of operational variables. This article presents an evaluation of various control strategies based on predictive control. The performance of each strategy is tested through changes in the reference of controlled variables, particularly product size distribution, and changes in ore hardness and feed size distribution. To perform these tests, a dynamic simulator of a grinding plant was developed and calibrated with plant data. The grinding plant modeled (Figure 1) is divided into two stages. In the primary stage, fresh ore is fed into a SAG mill, along with the necessary water. Then, the product is classified in a vibratory screen. The oversized ore is 10.3182/20130825-4-US-2038.00066
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
sent to a pebble crusher, which feeds back into the SAG mill. The undersized ore, on the other hand, continues to the secondary stage. In the secondary stage, the product of the previous stage is split into three lines through a distribution box. In each line, the pulp is sent to from the distribution box to a sump, from where is pumped to a hydrocyclone battery. The hydrocyclone underflow is fed into a ball mill, which feeds back into the sump. The final product of this grinding plant is the hydrocyclone overflow.
Fig. 1. Simulated grinding plant. The organization of this article is as follows. The control problem and the strategies are described in Section 2. Results obtained with each strategy are displayed in Section 3. A comparative analysis of the previous results obtained through dynamic simulation is presented in Section 4. Finally, conclusions and discussions are presented in Section 5. 2. CASE STUDY
Table 1 shows all the manipulated, controlled and disturbance variables included in the simulator. Table 1. Manipulated, controlled and disturbance variables
MVs
CVs
DVs
To measure the performance of these strategies, the grinding plant simulator is subjected to different scenarios of operation: normal operation, change in ore hardness, change in feed size distribution and change in the reference value of product particle size (defined as the percentage of product retained by a 65 mesh sieve). After each strategy is tested in the previous scenarios, several indices are calculated in order to do a comparative analysis of each strategy’s performance. Given that the control objectives proposed for these controllers are to minimize specific energy consumption, maximize the tonnage of ore processed and minimize the error between the product particle size and its reference, the performance indices are chosen to measure the degree of fulfillment of these objectives. Thus, the selected indices are: • Mean tonnage of ore processed • Specific energy consumption • Root-mean-square (RMS) error in product particle size Specific energy consumption and RMS error are calculated using (1) and (2), respectively. Ptotal (1) F v u N test X u 1 2 t (y(k) − yref ) (2) Ntest − Ndist + 1 k=Ndist
As previously stated, the main goal of this article is to develop a comparative analysis of three different control strategies applied to a grinding plant using a dynamic simulator. The simulator, developed in MATLAB/Simulink, represents the plant shown in Figure 1 and is composed of unit operations interrelated through their input and output streams. The unit operations included in the simulator are: SAG mill, vibratory screen, pebble crusher, sump, centrifugal pump, hydrocyclone battery and ball mill. Stockpile and belt feeders are not included in the simulator, so the effects of segregation in the feed are not modeled. Nonetheless, several particle size distributions for the feed are available to simulate disturbances.
SAG circuit Fresh ore feed Water-to-ore ratio Mill speed Mill hold-up Mill power consumption Tonnage of pebbles Tonnage of product Feed size distribution Ore hardness
The mathematical models used to represent each unit operation in the plant are based on the models developed by Austin et al. (1987), Orellana (2010) and Salazar et al. (2009). The parameters of each model were calibrated using data from various sources. Therefore, the simulator is not intended to represent a specific plant, but is designed to exhibit a behavior that is qualitatively close to reality.
Balls circuit Sump water feed Pump speed Product particle size Sump level Hydrocyclone pressure Sump slurry density Product of SAG circuit
where Ptotal is the total power consumption of the plant, F is the tonnage flow of mineral processed, y(k) is the product particle size, yref is the reference for the product particle size, Ndist is the sample number where the disturbance is applied and Ntest is the total number of samples. The three control strategies evaluated are described as follows. 2.1 Single centralized MPC control For this strategy, both primary and secondary stages (i.e. the whole grinding plant) are modeled as a single system. Manipulated variables for this controller are fresh ore feed to the SAG mill, water-to-ore ratio and SAG mill speed for the first stage; sump water feed and pump speed for each line of the second stage. Controlled variables are SAG mill hold-up, SAG mill power consumption, tonnage of pebbles produced and tonnage of product for the first stage; product particle size, sump level, hydrocyclone pressure and sump slurry density for each line of the second stage. Feed size distribution and ore hardness are treated as unmeasured disturbances. 2.2 Decentralized MPC control In this strategy, the primary stage and each line of the secondary stage of the grinding plant are modeled as in-
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IFAC MMM 2013 August 25-28, 2013. San Diego, USA
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dependent systems, and a MPC controller is developed for each one of this models. Manipulated variables, controlled variables and unmeasured disturbances are the same as in the previous strategy. Additionally, the tonnage of processed mineral in the primary stage is used as a measured disturbance for each line of the secondary stage.
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For this strategy, a multi-level controller is designed. The lower regulatory layer is the same as the previous decentralized control strategy, and a new higher optimization layer is developed as a way to coordinate the operation of the controllers in the regulatory layer. This higher layer performs an optimization of the steady-state model of the plant, thus determining the optimum values of operational variables. These values are then sent to the lower regulatory level, which drives the plant to the optimal operating point.
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Fig. 2. Simulation results for change in feed size distribution with decentralized MPC control strategy.
3. RESULTS
For the decentralized MPC control strategy operating under normal conditions with soft ore and a medium feed size distribution, the secondary stage controllers are able to keep the product particle size in the reference value of 30%, while the primary stage controller is able to maximize the tonnage processed (limited to 730 ton/h to prevent an overload in the SAG mill) and maintain a specific energy consumption of 37.76 kWh/ton. Figure 2 shows the results obtained when there is a change in feed size distribution, from fine ore to coarse ore, with a feed of hard ore. It can be seen that the product particle size drifts from its reference value at the time of the disturbance, but the secondary stage controller is able to return it. As in normal operation, the primary stage controller is able to maximize the tonnage processed at 730 ton/h. Specific energy consumption is decreased from an initial value of 39 to 37.81 kWh/ton, which seems counterintuitive, but can be explained as pebble production in the SAG mill is decreased, which decreases power consumption. Thus, specific energy consumption is decreased. Figure 3 shows the results obtained when there is a change in ore hardness, from soft ore to hard ore, with a medium feed size distribution. Again, it can be seen that the product particle size drifts from its reference value at the time of the disturbance and the secondary stage controller is able to return it. Processed tonnage is maximized and there is an increase on the specific energy consumption, from 37.76 to 37.84 kWh/ton, due to the increase in ore hardness. Finally, Figure 4 shows the results obtained when there is a step change in the reference value for the product particle size. It can be seen that the secondary stage controller is able to follow the new reference in product particle size. 232
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In this section, results for the three proposed strategies are presented.
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Fig. 3. Simulation results for change in ore hardness in the grinding plant with decentralized MPC control strategy. Meanwhile, processed tonnage is maximized and there is an increase on the specific energy consumption, from 37.76 to 37.92 kWh/ton. Table 2 shows the performance indices for this strategy. PI 1 is equivalent to mean tonnage of ore processed (measured in ton/h), PI 2 is equivalent to specific energy consumption (measured in kWh/ton) and PI 3 is equivalent to RMS error in product particle size. Table 2. Performance indices for the decentralized MPC control strategy Index
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PI 1 PI 2 PI 3
730 37.76 –
730 37.81 1.33
730 37.84 1.23
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IFAC MMM 2013 August 25-28, 2013. San Diego, USA
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Fig. 4. Simulation results for change in product particle size reference with decentralized MPC control strategy. 3.2 Centralized MPC control For the centralized MPC control strategy operating under normal conditions with soft ore and a medium feed size distribution, the specific energy consumption is 37.23 kWh/ton, which is lower than the value obtained in the previous strategy. Meanwhile, product particle size is kept at its reference value and feed tonnage is maximized. Figure 5 shows the results obtained for the centralized MPC control strategy when there is a change in feed size distribution, from fine ore to coarse ore. As in the previous strategy, the controller is able to return the product particle size to its reference value. Meanwhile, specific energy consumption is lowered to 37.42 kWh/ton.
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Fig. 6. Simulation results for change in ore hardness in the grinding plant with centralized MPC control strategy. Finally, Figure 7 shows the results obtained when there is a step change in the reference value for the product particle size. 40
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Fig. 7. Simulation results for change in product particle size reference with centralized MPC control strategy.
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Table 3 shows the performance indices for this strategy. Table 3. Performance indices for the centralized MPC control strategy
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Index
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PI 1 PI 2 PI 3
730 37.22 –
730 37.42 0.38
730 37.41 1.41
730 37.40 1.24
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Fig. 5. Simulation results for change in feed size distribution with centralized MPC control strategy. Figure 6 shows the results obtained when there is a change in ore hardness, from soft ore to hard ore. These results for product particle size do not exhibit an appreciable difference with those obtained in the decentralized strategy (Figure 3). Meanwhile, specific energy consumption stabilizes at 37.41 kWh/ton. 233
3.3 Multi-level control For the multi-level control strategy operating under normal conditions with soft ore and a medium feed size distribution, the specific energy consumption is 37.76 kWh/ton,
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
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Table 4. Performance indices for the multi-level control strategy
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Index
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PI 1 PI 2 PI 3
730 37.76 –
730 37.82 1.19
730 37.84 1.24
730 37.92 1.42
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Figure 9 shows the results obtained when there is a change in ore hardness, from soft ore to hard ore. These results do not exhibit an appreciable difference with those obtained in the decentralized strategy.
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As show by the results obtained in section 3, the three strategies tested are able to process the same tonnage (the maximum permitted) in all the scenarios. This indicates that the remaining manipulated variables are sufficient to deal with the disturbances and meet the objectives proposed.
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Regarding the RMS error, the centralized solution shows the best performance when there is a change in feed size distribution or particle size reference, and the worst performance when there is a change in ore hardness. Multilevel control shows a slight overall improvement over the decentralized solution, except when there is a change in ore hardness, where the results are practically the same.
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4. COMPARATIVE ANALYSIS
The best performance, in terms of specific energy consumption, is provided by the centralized strategy. The decentralized solution, on the other hand, exhibits a marginally worse performance in comparison to the centralized solution. Multi-level control shows virtually no improvement over the decentralized solution.
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Fig. 10. Simulation results for change in product particle size reference with multi-level control strategy.
Fig. 8. Simulation results for change in feed size distribution with multi-level control strategy.
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Figure 8 shows the results obtained for the multi-level control strategy when there is a change in feed size distribution, from fine ore to coarse ore. Despite de disturbance, the controller is able to return the product particle size to its reference value. Meanwhile, specific energy consumption stabilizes at a value of 37.82 kWh/ton.
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which is the same as the value obtained in the decentralized strategy. Meanwhile, product particle size is kept at its reference value and feed tonnage is maximized.
Fig. 9. Simulation results for change in ore hardness in the grinding plant with multi-level control strategy. Finally, Figure 10 shows the results obtained when there is a step change in the reference value for the product particle size. Table 4 shows the performance indices for this strategy. 234
It should be noted that the previous results do not reflect the technical complexity of implementing each solution. It could be argued that although the centralized solution exhibits the best performance, from a technical point of view it is the most complex to implement. To obtain the models employed by the centralized controller, it is necessary to perform plant-wide testing, which would require disturbing the normal operation of the plant for a period of time. On the other hand, due to the modularity of the decentralized solution, it would be necessary to test only one section of the plant at a time, which would
IFAC MMM 2013 August 25-28, 2013. San Diego, USA
lower the impact on the overall production. Moreover, the decentralized models can be rearranged and recombined if there is a modification in the structure of the plant or if it is necessary to design a controller for a different plant. The previous reasons could make the decentralized strategy, in some cases, the preferred alternative, especially when the results obtained are not significantly worse than the ones obtained with a centralized strategy. 5. CONCLUSIONS In this paper the results of a comparative analysis of control strategies in a mineral grinding plant have been presented. Three different strategies were tested. These strategies were based on predictive control and implemented using Honeywell’s Profit Suite software applications. The results show that the centralized strategy exhibits the best overall performance of the three strategies tested. Furthermore, the results show that the performance of a decentralized strategy can be improved, albeit marginally, with the addition of an optimization layer in a multi-level control scheme, or others distributed control alternatives, such as multi-agent systems. Future work will focus on the design, development and testing of different alternatives of distributed control; and the comparison of these schemes with an expert control module which will work in conjunction with existing controllers to handle special disturbances which are too great to be handled by the controllers, such as overload of the SAG mill or blockage of the pulp line (Cort´es and Cerda, 2010). Furthermore, the effects of segregation in the stockpile and belt feeders will be modeled for future implementations of the dynamic simulator. REFERENCES Austin, L., Menacho, J., and Pearcy, F. (1987). A general model for semi-autogenous and autogenous milling. In APCOM 87. Proceeding of Twentieth International Symposium on the Application of Computers and Mathematics in the Mineral Industries, volume 2, 107–126. Cort´es, G. and Cerda, J. (2010). SAG & secondary grinding multivariable predictive control coordinated: Divisi´on Codelco Norte. In Proceedings of the 2nd International Congress of Automation in the Mining Industry, 18–27. Orellana, R. (2010). Modelo, control y simulador de planta de molienda semiautgena y molienda secundaria. Thesis for degree of Engineer, Universidad de Chile. Pomerleau, A., Hodouin, D., Desbiens, A., and Gagnon, E. (2000). A survey of grinding circuit control methods: from decentralized PID controllers to multivariable predictive controllers. Powder Technology, 108(2–3), 103– 115. Salazar, J., Magne, L., Acu˜ na, G., and Cubillos, F. (2009). Dynamic modelling and simulation of semi-autogenous mills. Minerals Engineering, 22(1), 70–77. Wei, D. and Craig, I.K. (2009). Grinding mill circuits - A survey of control and economic concerns. International Journal of Mineral Processing, 90(1–4), 56–66.
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