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Grinding circuit modeling and simulation of particle size control at Siilinjärvi concentrator
International Journal of Mineral Processing 96 (2010) 70–78
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International Journal of Mineral Processing j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j m i n p r o
Grinding circuit modeling and simulation of particle size control at Siilinjärvi concentrator A. Remes a,⁎, J. Aaltonen b, H. Koivo a a b
Department of Automation and Systems Technology, Aalto University School of Science and Technology, P.O. Box. 15500, 00076 Aalto, Finland Yara Suomi, Siilinjärvi Mine, P.O. Box 20, 71801 Siilinjärvi, Finland
a r t i c l e
i n f o
Article history: Received 23 October 2009 Received in revised form 7 May 2010 Accepted 9 May 2010 Keywords: Dynamic modeling Grinding Particle size control Model predictive control
a b s t r a c t Concentrator throughput can depend highly on the operation of a grinding circuit. The mill feed rate adjustments and resulting slurry particle size distribution has a great impact on performance of the following separation stage. At the Yara Siilinjärvi phosphate concentrator the aim is to avoid over coarse apatite grain size, since it declines flotation recovery, while the fresh ore feed rate should be maximized. Here, most of the recovery disturbances originate from frequent ore type changeovers. At Siilinjärvi, outlet slurry of the grinding circuit is measured with a high precision on-line laser diffraction based slurry particle size analyzer. In this study, process experiments for modeling of the grinding circuit were carried out. Then multivariablePI, fuzzy, and model predictive controls were evaluated with the simulated process. The assessment indicated increase of around 1.8% in the ore feed rate, while variation in the particle size distribution was reduced, as a result of the formulated fuzzy-MPC control scheme. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Operation of a grinding circuit affects the whole concentrator performance in terms of obtained throughput, energy efficiency and separation efficiency. Therefore, in many cases the circuit outlet slurry particle size distribution is a substantial controlled variable. The control system should be able to reject disturbances — such as changes in the feed size and grindability — while taking into account the appropriate operation limits of the manipulated variables and possible strong interactions between the variables to be controlled. A model predictive control (MPC) has an inherent structure in its control law to handle those restrictions confronted with multivariable complex processes. Nevertheless, in grinding circuits it is common to have also discrete control variables, for example, the number of valves opened in a hydrocyclone pattern. To automate those control tasks an expert system, like fuzzy reasoning, can be a more convenient solution. Model predictive control is a common strategy in process industries. However, in mineral processing it is still a relatively rare control method. A recent survey on the control of grinding circuits confirmed that the majority of them are equipped only with PID controllers; but still MPC implementations — among other multivariable control systems — exists (Wei and Craig, 2008). Different multivariable control methods of grinding circuits are widely studied in the literature, describing the applied process models and the simulation results. Niemi et al. (1997) has used industrially param-
⁎ Corresponding author. Tel.: +358 9 470 25216. E-mail address: antti.remes@tkk.fi (A. Remes). 0301-7516/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2010.05.001
eterized phenomenological and black-box models to test a model based gain matrix controller for particle size and cyclone feed density. It was concluded that it is able to eliminate steady-state control errors and interactions of variables, when setpoint changes were applied. Pomerleau et al. (2000) used mass balance based grinding circuit simulator to study the performance of various particle size and circulating load controllers, from decentralized PID (with or without decoupling) to adaptive predictive control, with setpoint and disturbance sequences. It was noted that decoupled PID performs as well as model based controllers, if the delay is relatively small. Also, the adaptive control scheme was noted to be difficult to identify when external disturbances exist. More recently, Ramasamy et al. (2005) modeled a laboratory scale milling circuit to simulate cyclone overflow particle size and mill throughput, when the feed rate and sump water were manipulated. It turned out that MPC was robust even under different operating conditions (when the model parameters are changing), whereas commonly used detuned PI multi-loop control had a very long settling time and might oscillate. The robustness of MPC in a simulated grinding setup was earlier confirmed also in Muller and de Vaal (2000), where up to 50% modeling errors were applied. At the Siilinjärvi apatite concentrator, changes in the ore type cause the majority of grinding circuit disturbances. The ore is excavated from an open pit mine, crushed and homogenized in a heap with a stacker– reclaimer system. Therefore, a characteristic is that changes in the ore type and feed size are sudden and might have strong effects on the grindability when a changeover between the heaps occurs. Any change in the ore type is often troublesome due to a preceding/simultaneous temporary change in the feed size, caused by classification at the end of the heap or in a feed ore bin, if the bin level fluctuates excessively. The
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subsequent disturbances in the circuit outlet particle size can diminish performance of the followed flotation circuit; especially recovery of overrough apatite can be poor. On the other hand, in control of the grinding circuit, the allowed circulating load sets constraints for the operation. At Siilinjärvi, the most powerful variable to control the circulating load is the number of cyclones taken in action. This obviously affects the cyclone feed pressure and thus the cyclone separation efficiency. To handle the disturbances and constraints in controlling the cyclone overflow particle size and the circulating load, finally a control system combining model based control and fuzzy control was set up and tested with various simulations. This paper presents the plant tests at the Siilinjärvi concentrator for modeling of the grinding circuit operation, and subsequent control system development studies with a simulated plant. First, the applied model predictive, fuzzy and multivariable PI control methods are briefly described. The importance of ground product particle size and ore type for the flotation performance is shortly demonstrated. Then the plant tests and the identified models for the simulator are described and, finally, the control methods are compared when disturbances, measurement noise and model mismatches are present. Also, the feasibility and advantages of the suggested MPC-fuzzy control scheme are discussed. 2. Experimental 2.1. The Siilinjärvi concentrator plant The Yara Siilinjärvi phosphate mine and phosphoric acid and fertilizer plants are located in Eastern Finland. Mining capacity at Siilinjärvi is
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around 10 Mt/a of ore. The products are: 0.8 Mt/a apatite concentrate, 0.8 Mt/a calcite concentrate and 10 kt/a mica. The produced apatite concentrate is used totally in the phosphoric acid and fertilizer plants, integrated with the mine. The main minerals in the open pit mine deposit are 10% of apatite, 20% of carbonates (calcite and dolomite) and 65% of phlogopite mica. The capacity of the concentrator depends greatly on ore type. Especially carbonates/mica ratio has a major impact on grindability; the average is around 0.3, but can vary between 0.15 and 0.7. First, the ore is crushed in a three-stage crushing section, followed by homogenization with a stacker–reclaimer system. The grinding section consists of two parallel rod mill–ball mill circuits. Next, the apatite is separated in two parallel flotation circuits and purified with a high gradient magnetic separator. Finally, dewatering is carried out by thickening and filtration. The concentrator flowsheet is shown in Fig. 1. 2.2. Effect of the ore characteristics on milling Firstly, the characteristics of different ore types, excavated from various deposit locations, were studied. The ore type affects through the process, in terms of grindability and floatability, which especially depends on the apatite grain size. Therefore, to find out the impact of the variations in the ore feed characteristics on the plant performance, a data set comprising six months hourly averages (May–Nov. 2007) were analyzed. The data consists of 52 grinding circuits' process measurements. The data set was studied by means of clustering. Prior to that, the data was compressed to five principal components (PC), explaining 78% of the original variance. In addition to data compression the use of
Fig. 1. Flowsheet of the Siilinjärvi concentrator plant.
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PC scores in clustering, instead of the original data, reduces the measurement noise. In clustering techniques, the data is classified into groups, where observations have a close distance to each other within a group. For brief introductions to principal component analysis and data clustering, see, for example, Love (2007) and Hand et al. (2001). The result of the clustering can be presented using a dendrogram graph, where the groups are linked according to the distances. Fig. 2a shows a dendrogram of the Siilinjärvi grinding section data; the number of data observations in each cluster is seen in Fig. 2b. The number of clusters was selected to be nine, since denser cluster resolution could reflect differences in process operation instead of differences in the ore feed properties. It was noted that the first clusters (1–4) and the last ones (7–9) were also in chronological order. This is consistent with a fact that summer and winter time blastings are often made from different deposits. The clustered grinding section data was further examined with concurrent metallurgical performance of the apatite flotation. The averages of feed rate, grinding energy per tons, cyclone overflow particle size, concentrate grade and recovery of each nine clusters are listed in Table 1. Grindability depends greatly on the ore type having different compositions of the apatite, carbonates and phlogopite; thus grinding energies can vary from 5 kWh/t up to 7 kWh/t. It can be judged from the data that the ore type and especially cyclone overflow particle size distribution also dictates greatly the operation performance of the flotation. For example, clusters 1 and 8 have virtually the same feed rate, grinding energy and concentrate grades. Anyhow, different ore type resulting coarser slurry particle size in cluster 8 yields notably lower recovery (decrease of 1.6% units). Also the dendrogram figure (Fig. 2a), indicates those clusters to belong to far distinct three branches. The same figure reveals clusters 2 and 3 to have close similarities in terms of the milling data. Similarly, Table 1 indicates also the particle sizes and recoveries to be close between the clusters, but the feed rate has required significant (100 t/h) adjustment indeed. Furthermore, cluster 7, having the highest average recovery, was examined in more details. Based on circa 500 observations within the cluster, a linear estimation pointed out that increase of 1%-unit of the coarse + 210 µm fraction decreases 0.4%-unit of the recovery (near the operating point: 44.5% ± 2% of + 210 µm fraction). These results motivate an exploration of the grinding circuit control potential and ore type changeover management, exploiting extensively the on-line particle size assays. 2.3. Grinding circuit experiments and dynamic modeling To find out the dynamic responses of the grinding circuit to the changes in the control variables, a series of step response experiments
Table 1 Averages of selected grinding and flotation process parameters. Ore type cluster no.
Ore feed rate (t/h)
Grinding energy (kWh/t)
COF + 210 µm (%)
COF − 20 µm (%)
Concentrate grade (%)
Recovery (%)
1 2 3 4 5 6 7 8 9
1200 1130 1230 1100 1120 1180 1170 1220 1210
5.6 5.9 5.4 6.1 6.1 5.8 6.0 5.6 5.8
42.4 43.5 42.2 47.0 51.0 46.6 44.5 52.2 49.4
12.5 13.0 12.8 10.9 10.1 10.8 11.2 9.5 9.8
36.8 36.0 36.6 36.3 36.9 37.0 36.2 36.8 36.8
87.2 86.2 86.2 87.2 87.0 86.1 88.2 85.6 86.9
was carried out while running several individual ore feed heaps. The experiments were carried out during February–March 2008, covering six days with slightly different ores. The carbonate/mica ratio varied between 0.35 and 0.49, which represents fairly typical Siilinjärvi ore characteristics. The experiments were conducted with the smaller capacity grinding circuit (J1), while the second circuit (J2) was running normally. Both primary and secondary mill slurry densities were controlled by mill water addition. The circuit product slurry density — which is a calculated quantity — was controlled by manipulating the sump water addition valve. The circuit product particle size distribution was monitored with an on-line Outotec PSI 500TM particle size analyzer. In addition, to inspect the analyzer operation, laboratory slurry samples from the analyzer calibration sampler were collected for each stabilized operation region. Fig. 3 presents the grinding circuit flowsheet with major measurements and the points (A, B and C) where the step changes were applied. The stepwise inputs were: A) Ore feed rate: from an average 500 t/h ± 50 to 100 t/h. B) Circuit product slurry density/sump water addition: from an average density 1360 kg/dm3 ± 30 to 40 kg/dm3. C) Number of cyclones in use: variations between 6 and 8. The cyclone overflow particle size fractions (%), fine −74 µm and coarse +210 µm, and also the circulating load (%) were selected to be the outputs of the circuit modeling. An example data set (26th of March 2008) of the observed plant responses are presented in Fig. 4. The step changes were applied around times 205 min and 340 min (step A: feed rate), 490 min (step B: slurry density) and 655 min (step C: cyclone pressure). The main observations for the particle size responses can be summarized as follows: higher ore feed rate as well as higher circuit product density (decrease in sump water addition) increases the coarse
Fig. 2. a) Dendrogram of clustered six month hourly average grinding section dataset, b) number of observations in each cluster.
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Fig. 3. Grinding circuit (J1) flowsheet and locations of the step input actuators A–C.
fraction, while higher cyclone pressure (decrease in number of the cyclones in use) temporarily coarsens the slurry, but, finally, it ends up slightly finer. However, the variables have strong interactions together. For example, in Fig. 4, changes in the ore feed rate affect the cyclone feed pressure — which finally influences the particle size slightly opposite to the original change in the feed rate. The grinding circuit models were identified and validated based on several experiment data sets. The final on-line implemented models were still verified with separate step test sequences, described in the next section. The resulting transfer function models are presented in Table 2. The overall model structure can be expressed as follows: 2
3 2 y1 ðsÞ G11 ðsÞ 4 y2 ðsÞ 5 = 4 G21 ðsÞ y3 ðsÞ G31 ðsÞ
32 3 u1 ðsÞ G12 ðsÞ G13 ðsÞ G22 ðsÞ G23 ðsÞ 54 u2 ðsÞ 5; u3 ðsÞ G32 ðsÞ G33 ðsÞ
ð1Þ
where y1 and y2 are particle size fractions −74 µm (%) and +210 µm (%) and y3 is circulating load (%), and the inputs are: ore feed rate (t/h) u1, circuit outlet slurry density (kg/dm3) u2 and hydrocyclone feed pressure (kPa) u3. Step responses, when +50 t/h of ore feed, +20 kg/dm3 of slurry density and +10 kPa of cyclone feed pressure are applied respectively, are shown in Fig. 5. 2.4. Model verification To verify the grinding circuit model operation, the model response calculation blocks were implemented in the plant automation system. The output simulation activated when a stepwise input threshold was exceeded. This enabled long term data gathering; in addition two model verification campaigns with auxiliary input excitations were arranged (July 2nd and October 14th, 2008). Both campaigns included five separate step changes of the inputs u1, u2 and u3, especially the
Fig. 4. Particle size − 74 µm (%) and circulating load (%) responses to manipulated variables: ore feed rate (t/h), circuit product slurry density (kg/dm3) and hydrocyclone feed pressure (bar).
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Table 2 Transfer functions of the Siilinjärvi J1 grinding circuit. Circuit outlet slurry density (kg/dm3)
Ore feed rate (t/h)
Cyclone feed pressure (kPa)
Cyclone overflow + 210 µm fraction (%)
G21 =
0:016⋅e ð1 + 6:6sÞð1 + 3:0sÞ
G22 =
0:02 ð1 + 0:001sÞð1 + 24:2sÞ
G23 =
0:016⋅ð1−113:8Þe−1s ð1 + 1:4sÞð1 + 37:3sÞ −0:015⋅ð1−141:1Þe−1:7s ð1 + 18:0sÞð1 + 1:5sÞ
Circulating load (%)
G31 =
−0:2⋅ð1 + 14:9sÞ ð1 + 3:8sÞð1 + 0:17sÞ
G32 =
−0:3⋅e−2:8s ð1 + 0:9sÞ
G33 =
−3:2 ð1 + 16:2sÞ
Cyclone overflow − 74 µm fraction (%)
G11 =
−15:4s
−0:013⋅e ð1 + 3:1sÞ
G12 =
−15:4s
particle size responses y1 and y2 were observed. Absolute deviations of the measured and 60 min ahead simulated values were compared. In addition, prediction capability was evaluated by calculating the model fit percentage (Eq. (2)) for prediction step lengths 1, 10 and 20 min. The results of both experiment days (exp. 1 and 2) are tabulated in Table 3. The formula used for the model fit number is vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 u n u u ∑ ðyðt + kÞ−⌢ B yðt + k jt ÞÞ2 C ut = 1 B C u B C Model fit % = 100⋅B1−u 2 C n t @ A ∑ yðt Þ− − y 0
ð2Þ
t =1
where y is measurements, ŷ is prediction, t is current time step and k is length of the prediction step.
−0:01 ð1 + 9:1sÞ
G13 =
Nichols method, described in Koivo and Pohjolainen (1985). Briefly summarizing, the matrices K and I are determined as follows: K=P
−1
I = εT
diagfp1 ; p2 ; …; pm g;
−1
ð4Þ
:
ð5Þ
The parameters p1…pm and ε are used for the controller tuning. Subsequently, the matrices P and T are obtained by applying separate step inputs for each m manipulated variables u and observing the rising slopes and final settlings and using the formulas: h −1 P = ˙y1 ; y˙ 2 ; …; y˙ m ½u1 ; u2 ; …; um T = ½y1 ; y2 ; …; ym ½u1 ; u2 ; …um
−1
ð6Þ ð7Þ
2.5. Applied multivariable control methods Three common multivariable control schemes were evaluated for the Siilinjärvi grinding process. The selected methods were multivariable PI control as a base case, a fuzzy control, from which earlier practices has been gained as a part of apatite flotation control, and, finally, a model predictive control, which also has embedded implementation capabilities in the current Metso DNA plant automation system. In each case, the controlled variables were the coarse size fraction (% +210 µm) and the circulating load (%). Control of the coarse fraction is important in terms of flotation recovery, and the grinding circuit circulating load in terms of stable and safe process operation. Limitations for the control were set by defining minimum and maximum allowed ore feed rates and circuit outlet slurry densities. In multivariable PI control, the controller output u is obtained from u = Ke + I e; ˙
ð3Þ
where e is control error, K and I are constant matrices for the controller proportional gain and integrator. Here, the controller was tuned using a procedure, which is analogous to a scalar case Ziegler–
The fuzzy control was constructed by defining trapezoidal membership functions for the selected input and output variables, completed with a Mamdani type rule base inference system. For an introduction to fuzzy systems, see for example Lin and Lee (1996). Omitting the detailed parameterization, operation of the designed fuzzy control logic can be summarized: • IF particle size deviation is small AND not approaching the setpoint: ∘ Change feed rate a little. ∘ IF feed rate is near the limits AND slurry density is not near the limits, change also the slurry density. • IF particle size deviation is large AND not approaching the setpoint: ∘ IF feed rate is not near the limits, change feed rate largely. ∘ IF feed rate is near the limits, change the slurry density AND feed rate a little. • IF circulating load is near the limits: ∘ AND amount of cyclones AND cyclone pressure are not in extreme values, change amount of cyclones. The rule base and fuzzy sets were carefully tuned in an iterative manner, by means of simulations, to obtain well approved input– output performance.
Fig. 5. Step responses of the grinding circuit models.
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0.68%
0.63%
horizon length, nu is the control horizon length, k is the current discrete time step, γy factors are the output weightings for the control error, γu factors are the input weightings for the control increments. A brief introduction of MPC for the process industries is available for example in Bequette (2003).
0.67%
0.97%
3. Comparison of grinding circuit control strategies
Table 3 Model validation results for two days step input experiments. Size fraction − 74 µm Mean abs. error% between 60 min simulated end values and measurement (exp. 1) Mean abs. error% between 60 min simulated end values and measurement (exp. 2) Model fit-%, prediction step = 1 (exp. 1) Model fit-%, prediction step = 10 (exp. 1) Model fit-%, prediction step = 20 (exp. 1) Model fit-%, prediction step = 1 (exp. 2) Model fit-%, prediction step = 10 (exp. 2) Model fit-%, prediction step = 20 (exp. 2)
95.6% 52.9% 26.0% 93.8% 76.6% 35.6%
Size fraction + 210 µm
96.4% 60.8% 40.7% 93.9% 78.1% 40.0%
Different control strategies were compared by simulating eight hours time periods, all with a similar set point sequence for the +210 µm (%) particle size fraction. The control performance was evaluated in terms of integrated squared error index (ISE), presenting the squared control error of the time period. To emulate the measurement conditions in reality, white noises for the particle size and circulating load (%) measurements were added. The +210 µm (%) included 0, 0.5 and 1% relative noises and the circulating load 2% relative noise.
Table 4 Model predictive control parameterization. Variable
Nominal Min/max value band
MV: hydro cyclone 76 pressure (kPa) MV: feed rate (t/h) 480 MV: product slurry 1360 3 density (kg/dm ) CV: under 74 µm 28 size fraction (%) CV: over 210 µm 48 size fraction (%) CV: circulating 200 load (%)
Min/max Weight Change rate change rate factor weight factor
50…100
±10
1
0
350…600 1320… 1390 20…40
±10 ±1
0 0
0.1 0.2
–
0
–
40…60
–
1
–
120…280
–
0
–
The third option, model predictive control (MPC) utilizes the dynamic process models to make predictions of the future process values and to calculate future controller outputs to obtain optimal output trajectory for the setpoint tracking. The respective future time windows are called prediction and control horizons. Optimality of the determined control actions is defined in terms of quadratic cost function. The cost function is minimized in each time step, while new predictions and controller outputs are calculated. This kind of MPC scheme is known as receding horizon control. Here, the applied cost function was written in form: ne
2
nu
2
J ðkÞ = ∑ γy ½yr ðk + iÞ− yˆ ðk + iÞ + ∑ γu Δuðk + j−1Þ : i=1
75
ð8Þ
j=1
The notations are: yr is the output reference (set point), ŷ is the predicted output, Δu is the control increment, ne is the prediction
3.1. Parameterization of the controllers The multivariable PI controller (3) was designed based on the identified process models (Table 2). The controlled variable was the +210 µm size fraction (y1, %), while the manipulated variables were the feed rate (u1, t/h) and the circuit outlet slurry density (u2, kg/dm3). These notations were applied in Eqs. (6) and (7); further the controller was tuned based on the ISE index when 0.5 rel.-% measurement noise for y1 was present. The resulted gain and integrator matrices (4) and (5) were: K = [5440.4 4145.1] and I = [212.4 322.6]. Operation of the fuzzy control is highly sensitive to the selected control interval. In general, higher measurement noise implies a need for a longer control interval. A control interval of 20 min was determined to be most suitable, when 0.5–1 rel-% particle size measurement noise was present. The model predictive control was implemented as a receding horizon control with one minute control interval, 10 min control horizon and 40 min prediction horizon, covering the required process stabilization time. The parameterization details for the MPC are summarized in Table 4. Selection of the weighting factor is based on the following aims: feed rate is the primary manipulated variable, slurry density is used more moderately and the hydrocyclone pressure is virtually unused (in practice, it can be only changed stepwise). The + 210 µm size fraction is the primary controlled variable; −74 µm size fraction and the circulating load may vary in the predefined limits. Operation of the MPC for a stepwise 1% increase in +210 µm particle size set point is demonstrated in Fig. 6. A new set point is reached within 40 min, while the fine fraction (%) and the circulating load (%) have decreased and also stabilized. The main
Fig. 6. Operation of the MPC when + 1% set point change is applied in the + 210 µm size fraction.
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Fig. 7. Fuzzy-MPC control scheme to control the circuit product particle size while circulating load is kept in predefined limits (MPC: DV = disturbance variable, CV = controlled variable, MV = manipulated variable).
control actions are a 40 t/h increase of the feed rate with a complementary 20 kg/dm3 increase in the slurry density. However, this control setup cannot handle large disturbances in the circulating load, due to lack of discrete cyclone pressure (number of cyclones in use) changes. These disturbances can occur when the ore type is changing drastically due to a change of the ore feed heap at the Siilinjärvi case. Finally, to utilize both the ability of the fuzzy control to automate discrete cyclone pattern control tasks, and the advantages of model based control schemes, a hybrid control system of them was set up and tested. Here, both fuzzy-MPC and fuzzy-PI controls were evaluated. Fig. 7 illustrates the fuzzy-MPC case, where the circulating load is controlled by the fuzzy system, while the particle size is controlled by MPC. The system was also provided with the feedforward information of the upcoming disturbances caused by the measured changes in the hydrocyclone feed pressure. 3.2. Results for a set point sequence tracking First, the different control schemes — PI, fuzzy, MPC and also fuzzyPI and fuzzy-MPC hybrids — were evaluated by applying a particle size setpoint sequence for a simulated process. Table 5 summarizes the results of the control performances in terms of integrated square error (ISE) index. In the circulating load control cases one change in the
Table 5 Comparison of control performances for a set point sequence tracking when the particle size measurement noise is 0, 0.5 and 1 rel.-% were applied, circulating load noise was set to 2 rel.-%. Measurement noise Particle size control No noise
Moderate
High
Controller
ISE-index
PI Fuzzy MPC PI Fuzzy MPC PI Fuzzy MPC
18.5 27.1 16.5 21.0 35.3 19.8 23.8 59.4 25.8
Particle size and circulating load control No noise Fuzzy Fuzzy-PI Fuzzy-MPC Moderate Fuzzy Fuzzy-PI Fuzzy-MPC High Fuzzy Fuzzy-PI Fuzzy-MPC
44.3 41.2 33.0 63.2 56.1 37.1 73.1 58.1 41.9
number of hydrocyclones occurs. The ISE indices indicate MPC to be good in both pure particle size control and in combination with fuzzy circulating load control. However, the performance of the multivariable PI control is nearly equal or better with high measurement noise. As an example, Fig. 8 presents the fuzzy-MPC control results for a moderate measurement noise case (Table 5) having an ISE performance index value of 37.1. Also, robustness of the model predictive control to model mismatches was evaluated. In practice, the model mismatches occur when the process equipment conditions change and when the ore types vary. Table 6 summarizes changes in the ISE performance index when a 10…30% variation in the model parameters were introduced. The applied set point sequence was the same as in Fig. 8 and Table 5. But in this case, a slightly smaller (0.2 rel.-%) particle size measurement noise was used to emphasize the effect of the varied model parameters. Impact on the ISE performance index is moderate even with the highest applied parameter change, when compared to the impact of totally other control configurations or increased measurement noise, presented in Table 5.
3.3. Control simulation with a long term process data Based on the set point tracking results shown in Table 5, the FuzzyMPC scheme was selected for long term process data simulation. The data (July 21–29, 2009) includes five separate ore heaps ran through the mill. In the original data, the ore feed was kept constantly at 480 t/h, slurry density at 1360 kg/dm3, and the number of cyclones at 7 set points. In the control simulation set up, the original measured particle size variation around the mean value was summed with the simulated result, used further in feedback control. Also, the original measured hydrocyclone pattern feed pressure and circulating load variations were fed to the control system while summed with the simulated results. Hence, the system was analogous to the scheme shown in Fig. 7 where the dotted line feedback signals include now also fluctuations obtained from the process data sequence. The set point for the coarse +210 µm fraction was set to 50.6%, which was the mean value of the process data sequence. The resulting control simulation — in addition of the original process data — for the one week data period is shown in Fig. 9. As a result of the control simulation, the mean value of the +210 µm was 50.6%, which is same as the set point. For the whole data set the hourly bases standard deviation of the coarse particle size fraction with fuzzy-MPC control was 0.36%, while in the original data it was 1.08%. However, these values include the effects of the ore type changeovers. For example, the particle size deviations within one processed ore heap (time period 45–79 h) were 0.25% for the control simulation and 0.34% for the process data. In the control simulations, the ore feed rate was an average 488.7 t/h and the circuit outlet slurry density 1352 kg/dm3.
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Fig. 8. Example of the fuzzy-MPC operation for a given set point sequence, when 0.5% particle size measurement error for + 210 µm (%) fraction is present.
Table 6 Robustness of the model predictive control at the Siilinjärvi case, when model parameters are varied and 0.2% relative particle size measurement errors are present. Case Change in process time constants
Change in process gain
Control performance (ISE)
1 2 3 4 5 6 7
0% + 10% + 30% + 30% − 10% − 30% − 30%
17.4 18.2 20.1 21.8 19.4 24.0 24.9
0% + 10% + 20% + 30% + 10% + 20% + 30%
(+4.6%) (+15.5%) (+25.3%) (+11.5%) (+37.9%) (+43.1%)
4. Discussion and conclusions This exploration covered process experiments, modeling and a feasibility study aiming for grinding circuit control improvements at
the Yara Siilinjärvi phosphate concentrator. Long term data analysis also pointed out reflections between the operation of the grinding circuit and the metallurgical performance of the apatite flotation, especially in terms of coarse fraction recovery. The survey was started by carrying out numerous step response experiments during the normal operation of the concentrator plant. Strong interactions between the process variables set challenges to the modeling task; it turned out that the most suitable model structures were transfer functions defining the input output dynamic separately for each variable. In addition, the plant automation system supported straightforward configuration of them to obtain long term verification data of the model prediction capabilities. The control development, tuning, and performance evaluation were conducted in a simulation environment, established based on the experimental dynamic models. In particle size control the model predictive and multivariable PI control gave both good results. Nevertheless, the MPC enables better handling for process constraints.
Fig. 9. Process data set of +210 µm (%) particle size fraction and circulating load (%) (dotted lines), and the simulated results (solid lines) when the feed rate (t/h), slurry density (kg/dm3) and number cyclone control actions with fuzzy-MPC set up were applied for the same data; changes of the ore heaps are indicated with triangle symbols.
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The performance of the applied fuzzy control was satisfactory. But then, from the viewpoint of long term maintenance, fuzzy control is based on readily manageable rule base. Also, fuzzy control is well suited for discrete control actions, such as valve opening and closing, used here for control of the circulating load. Therefore, a control system incorporating fuzzy and MPC control was suggested. A relatively long (one week) process data simulation with a fuzzyMPC scheme confirmed the advantages of closed loop particle size control. During the whole period the control system reduced variation of the coarse fraction 67%, and even during one feed ore heap the reduction was 26%, while keeping the circulating load in operating limits by automated manipulation of the hydrocyclone valve pattern. Moreover, the ore feed rate increased an average 1.8% within the data period. Apparently, better control of the slurry particle size distribution has a favorable impact on flotation recovery, possibly still increasing the plant capacity. The presented control system is partly based on process models identified during stable operation of the plant. In addition to changes in the ore type, segregation at the ends of the ore heaps, and also in the feed ore bin, can introduce disturbances to the circuit operation. In addition to the feedback from the product particle size measurement, the control system could be still accomplished with feed forward information of the feed ore particle size. This could reduce the disturbance effect of segregation, allowing the control system to optimize the ore type changeover yet more effectively. Overall, the control assessment presented here pointed out that model based control was robust and suitable for drastic ore type changeover management. In addition, the model predictive control system can be well operated jointly with external discrete control actions. Currently at the Siilinjärvi concentrator, the plant capacity enhancements have been started with flowsheet reconfiguration of the grinding
circuit. In future, this control assessment gives a proper insight for forthcoming grinding circuit control strategy implementations.
Acknowledgements The research project is supported by the Finnish Funding Agency for Technology and Innovation (Tekes). In addition to this, a number of Siilinjärvi plant personnel are acknowledged for good collaboration both during numerous plant visits and other meetings.
References Bequette, B.W., 2003. Process Control Modeling, Design, and Simulation. Prentice Hall, New Jersey. Hand, D., Mannila, H., Smyth, P., 2001. Principles of Data Mining. MIT Press, Cambridge. Koivo, H., Pohjolainen, S., 1985. Tuning of multivariable PI-controllers for unknown system with input delay. Automatica 21, 81–91. Lin, C.-T., Lee, G., 1996. Neural Fuzzy Systems: A Neuro-fuzzy Synergism to Intelligent Systems. Prentice Hall, Upper Saddle River. Love, J., 2007. Process Automation Handbook — A Guide to Theory and Practice. Springer, London. Muller, B., de Vaal, P.L., 2000. Development of a model predictive controller for a milling circuit. Journal of the South African Institute of Mining and Metallurgy 100, 449–453. Niemi, A.J., Tian, L., Ylinen, R., 1997. Model predictive control for grinding systems. Control Engineering Practice 5, 271–278. Pomerleau, A., Hodouin, D., Desbiens, A., Gognon, E., 2000. A survey of grinding circuit control methods: from decentralized PID controllers to multivariable predictive controllers. Powder Technology 108, 103–115. Ramasamy, M., Narayanan, S.S., Rao, Ch.D.P., 2005. Control of ball mill grinding circuit using model predictive control scheme. Journal of Process Control 273–283. Wei, D., Craig, I.K., 2008. Grinding mill circuits — a survey of control and economic concerns. Proceedings of the 17th IFAC World Congress, Seoul, Korea, Jul. 6–11, 2008, pp. 1000–1005.
Contents lists available at ScienceDirect
International Journal of Mineral Processing j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j m i n p r o
Grinding circuit modeling and simulation of particle size control at Siilinjärvi concentrator A. Remes a,⁎, J. Aaltonen b, H. Koivo a a b
Department of Automation and Systems Technology, Aalto University School of Science and Technology, P.O. Box. 15500, 00076 Aalto, Finland Yara Suomi, Siilinjärvi Mine, P.O. Box 20, 71801 Siilinjärvi, Finland
a r t i c l e
i n f o
Article history: Received 23 October 2009 Received in revised form 7 May 2010 Accepted 9 May 2010 Keywords: Dynamic modeling Grinding Particle size control Model predictive control
a b s t r a c t Concentrator throughput can depend highly on the operation of a grinding circuit. The mill feed rate adjustments and resulting slurry particle size distribution has a great impact on performance of the following separation stage. At the Yara Siilinjärvi phosphate concentrator the aim is to avoid over coarse apatite grain size, since it declines flotation recovery, while the fresh ore feed rate should be maximized. Here, most of the recovery disturbances originate from frequent ore type changeovers. At Siilinjärvi, outlet slurry of the grinding circuit is measured with a high precision on-line laser diffraction based slurry particle size analyzer. In this study, process experiments for modeling of the grinding circuit were carried out. Then multivariablePI, fuzzy, and model predictive controls were evaluated with the simulated process. The assessment indicated increase of around 1.8% in the ore feed rate, while variation in the particle size distribution was reduced, as a result of the formulated fuzzy-MPC control scheme. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Operation of a grinding circuit affects the whole concentrator performance in terms of obtained throughput, energy efficiency and separation efficiency. Therefore, in many cases the circuit outlet slurry particle size distribution is a substantial controlled variable. The control system should be able to reject disturbances — such as changes in the feed size and grindability — while taking into account the appropriate operation limits of the manipulated variables and possible strong interactions between the variables to be controlled. A model predictive control (MPC) has an inherent structure in its control law to handle those restrictions confronted with multivariable complex processes. Nevertheless, in grinding circuits it is common to have also discrete control variables, for example, the number of valves opened in a hydrocyclone pattern. To automate those control tasks an expert system, like fuzzy reasoning, can be a more convenient solution. Model predictive control is a common strategy in process industries. However, in mineral processing it is still a relatively rare control method. A recent survey on the control of grinding circuits confirmed that the majority of them are equipped only with PID controllers; but still MPC implementations — among other multivariable control systems — exists (Wei and Craig, 2008). Different multivariable control methods of grinding circuits are widely studied in the literature, describing the applied process models and the simulation results. Niemi et al. (1997) has used industrially param-
⁎ Corresponding author. Tel.: +358 9 470 25216. E-mail address: antti.remes@tkk.fi (A. Remes). 0301-7516/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2010.05.001
eterized phenomenological and black-box models to test a model based gain matrix controller for particle size and cyclone feed density. It was concluded that it is able to eliminate steady-state control errors and interactions of variables, when setpoint changes were applied. Pomerleau et al. (2000) used mass balance based grinding circuit simulator to study the performance of various particle size and circulating load controllers, from decentralized PID (with or without decoupling) to adaptive predictive control, with setpoint and disturbance sequences. It was noted that decoupled PID performs as well as model based controllers, if the delay is relatively small. Also, the adaptive control scheme was noted to be difficult to identify when external disturbances exist. More recently, Ramasamy et al. (2005) modeled a laboratory scale milling circuit to simulate cyclone overflow particle size and mill throughput, when the feed rate and sump water were manipulated. It turned out that MPC was robust even under different operating conditions (when the model parameters are changing), whereas commonly used detuned PI multi-loop control had a very long settling time and might oscillate. The robustness of MPC in a simulated grinding setup was earlier confirmed also in Muller and de Vaal (2000), where up to 50% modeling errors were applied. At the Siilinjärvi apatite concentrator, changes in the ore type cause the majority of grinding circuit disturbances. The ore is excavated from an open pit mine, crushed and homogenized in a heap with a stacker– reclaimer system. Therefore, a characteristic is that changes in the ore type and feed size are sudden and might have strong effects on the grindability when a changeover between the heaps occurs. Any change in the ore type is often troublesome due to a preceding/simultaneous temporary change in the feed size, caused by classification at the end of the heap or in a feed ore bin, if the bin level fluctuates excessively. The
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subsequent disturbances in the circuit outlet particle size can diminish performance of the followed flotation circuit; especially recovery of overrough apatite can be poor. On the other hand, in control of the grinding circuit, the allowed circulating load sets constraints for the operation. At Siilinjärvi, the most powerful variable to control the circulating load is the number of cyclones taken in action. This obviously affects the cyclone feed pressure and thus the cyclone separation efficiency. To handle the disturbances and constraints in controlling the cyclone overflow particle size and the circulating load, finally a control system combining model based control and fuzzy control was set up and tested with various simulations. This paper presents the plant tests at the Siilinjärvi concentrator for modeling of the grinding circuit operation, and subsequent control system development studies with a simulated plant. First, the applied model predictive, fuzzy and multivariable PI control methods are briefly described. The importance of ground product particle size and ore type for the flotation performance is shortly demonstrated. Then the plant tests and the identified models for the simulator are described and, finally, the control methods are compared when disturbances, measurement noise and model mismatches are present. Also, the feasibility and advantages of the suggested MPC-fuzzy control scheme are discussed. 2. Experimental 2.1. The Siilinjärvi concentrator plant The Yara Siilinjärvi phosphate mine and phosphoric acid and fertilizer plants are located in Eastern Finland. Mining capacity at Siilinjärvi is
71
around 10 Mt/a of ore. The products are: 0.8 Mt/a apatite concentrate, 0.8 Mt/a calcite concentrate and 10 kt/a mica. The produced apatite concentrate is used totally in the phosphoric acid and fertilizer plants, integrated with the mine. The main minerals in the open pit mine deposit are 10% of apatite, 20% of carbonates (calcite and dolomite) and 65% of phlogopite mica. The capacity of the concentrator depends greatly on ore type. Especially carbonates/mica ratio has a major impact on grindability; the average is around 0.3, but can vary between 0.15 and 0.7. First, the ore is crushed in a three-stage crushing section, followed by homogenization with a stacker–reclaimer system. The grinding section consists of two parallel rod mill–ball mill circuits. Next, the apatite is separated in two parallel flotation circuits and purified with a high gradient magnetic separator. Finally, dewatering is carried out by thickening and filtration. The concentrator flowsheet is shown in Fig. 1. 2.2. Effect of the ore characteristics on milling Firstly, the characteristics of different ore types, excavated from various deposit locations, were studied. The ore type affects through the process, in terms of grindability and floatability, which especially depends on the apatite grain size. Therefore, to find out the impact of the variations in the ore feed characteristics on the plant performance, a data set comprising six months hourly averages (May–Nov. 2007) were analyzed. The data consists of 52 grinding circuits' process measurements. The data set was studied by means of clustering. Prior to that, the data was compressed to five principal components (PC), explaining 78% of the original variance. In addition to data compression the use of
Fig. 1. Flowsheet of the Siilinjärvi concentrator plant.
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PC scores in clustering, instead of the original data, reduces the measurement noise. In clustering techniques, the data is classified into groups, where observations have a close distance to each other within a group. For brief introductions to principal component analysis and data clustering, see, for example, Love (2007) and Hand et al. (2001). The result of the clustering can be presented using a dendrogram graph, where the groups are linked according to the distances. Fig. 2a shows a dendrogram of the Siilinjärvi grinding section data; the number of data observations in each cluster is seen in Fig. 2b. The number of clusters was selected to be nine, since denser cluster resolution could reflect differences in process operation instead of differences in the ore feed properties. It was noted that the first clusters (1–4) and the last ones (7–9) were also in chronological order. This is consistent with a fact that summer and winter time blastings are often made from different deposits. The clustered grinding section data was further examined with concurrent metallurgical performance of the apatite flotation. The averages of feed rate, grinding energy per tons, cyclone overflow particle size, concentrate grade and recovery of each nine clusters are listed in Table 1. Grindability depends greatly on the ore type having different compositions of the apatite, carbonates and phlogopite; thus grinding energies can vary from 5 kWh/t up to 7 kWh/t. It can be judged from the data that the ore type and especially cyclone overflow particle size distribution also dictates greatly the operation performance of the flotation. For example, clusters 1 and 8 have virtually the same feed rate, grinding energy and concentrate grades. Anyhow, different ore type resulting coarser slurry particle size in cluster 8 yields notably lower recovery (decrease of 1.6% units). Also the dendrogram figure (Fig. 2a), indicates those clusters to belong to far distinct three branches. The same figure reveals clusters 2 and 3 to have close similarities in terms of the milling data. Similarly, Table 1 indicates also the particle sizes and recoveries to be close between the clusters, but the feed rate has required significant (100 t/h) adjustment indeed. Furthermore, cluster 7, having the highest average recovery, was examined in more details. Based on circa 500 observations within the cluster, a linear estimation pointed out that increase of 1%-unit of the coarse + 210 µm fraction decreases 0.4%-unit of the recovery (near the operating point: 44.5% ± 2% of + 210 µm fraction). These results motivate an exploration of the grinding circuit control potential and ore type changeover management, exploiting extensively the on-line particle size assays. 2.3. Grinding circuit experiments and dynamic modeling To find out the dynamic responses of the grinding circuit to the changes in the control variables, a series of step response experiments
Table 1 Averages of selected grinding and flotation process parameters. Ore type cluster no.
Ore feed rate (t/h)
Grinding energy (kWh/t)
COF + 210 µm (%)
COF − 20 µm (%)
Concentrate grade (%)
Recovery (%)
1 2 3 4 5 6 7 8 9
1200 1130 1230 1100 1120 1180 1170 1220 1210
5.6 5.9 5.4 6.1 6.1 5.8 6.0 5.6 5.8
42.4 43.5 42.2 47.0 51.0 46.6 44.5 52.2 49.4
12.5 13.0 12.8 10.9 10.1 10.8 11.2 9.5 9.8
36.8 36.0 36.6 36.3 36.9 37.0 36.2 36.8 36.8
87.2 86.2 86.2 87.2 87.0 86.1 88.2 85.6 86.9
was carried out while running several individual ore feed heaps. The experiments were carried out during February–March 2008, covering six days with slightly different ores. The carbonate/mica ratio varied between 0.35 and 0.49, which represents fairly typical Siilinjärvi ore characteristics. The experiments were conducted with the smaller capacity grinding circuit (J1), while the second circuit (J2) was running normally. Both primary and secondary mill slurry densities were controlled by mill water addition. The circuit product slurry density — which is a calculated quantity — was controlled by manipulating the sump water addition valve. The circuit product particle size distribution was monitored with an on-line Outotec PSI 500TM particle size analyzer. In addition, to inspect the analyzer operation, laboratory slurry samples from the analyzer calibration sampler were collected for each stabilized operation region. Fig. 3 presents the grinding circuit flowsheet with major measurements and the points (A, B and C) where the step changes were applied. The stepwise inputs were: A) Ore feed rate: from an average 500 t/h ± 50 to 100 t/h. B) Circuit product slurry density/sump water addition: from an average density 1360 kg/dm3 ± 30 to 40 kg/dm3. C) Number of cyclones in use: variations between 6 and 8. The cyclone overflow particle size fractions (%), fine −74 µm and coarse +210 µm, and also the circulating load (%) were selected to be the outputs of the circuit modeling. An example data set (26th of March 2008) of the observed plant responses are presented in Fig. 4. The step changes were applied around times 205 min and 340 min (step A: feed rate), 490 min (step B: slurry density) and 655 min (step C: cyclone pressure). The main observations for the particle size responses can be summarized as follows: higher ore feed rate as well as higher circuit product density (decrease in sump water addition) increases the coarse
Fig. 2. a) Dendrogram of clustered six month hourly average grinding section dataset, b) number of observations in each cluster.
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Fig. 3. Grinding circuit (J1) flowsheet and locations of the step input actuators A–C.
fraction, while higher cyclone pressure (decrease in number of the cyclones in use) temporarily coarsens the slurry, but, finally, it ends up slightly finer. However, the variables have strong interactions together. For example, in Fig. 4, changes in the ore feed rate affect the cyclone feed pressure — which finally influences the particle size slightly opposite to the original change in the feed rate. The grinding circuit models were identified and validated based on several experiment data sets. The final on-line implemented models were still verified with separate step test sequences, described in the next section. The resulting transfer function models are presented in Table 2. The overall model structure can be expressed as follows: 2
3 2 y1 ðsÞ G11 ðsÞ 4 y2 ðsÞ 5 = 4 G21 ðsÞ y3 ðsÞ G31 ðsÞ
32 3 u1 ðsÞ G12 ðsÞ G13 ðsÞ G22 ðsÞ G23 ðsÞ 54 u2 ðsÞ 5; u3 ðsÞ G32 ðsÞ G33 ðsÞ
ð1Þ
where y1 and y2 are particle size fractions −74 µm (%) and +210 µm (%) and y3 is circulating load (%), and the inputs are: ore feed rate (t/h) u1, circuit outlet slurry density (kg/dm3) u2 and hydrocyclone feed pressure (kPa) u3. Step responses, when +50 t/h of ore feed, +20 kg/dm3 of slurry density and +10 kPa of cyclone feed pressure are applied respectively, are shown in Fig. 5. 2.4. Model verification To verify the grinding circuit model operation, the model response calculation blocks were implemented in the plant automation system. The output simulation activated when a stepwise input threshold was exceeded. This enabled long term data gathering; in addition two model verification campaigns with auxiliary input excitations were arranged (July 2nd and October 14th, 2008). Both campaigns included five separate step changes of the inputs u1, u2 and u3, especially the
Fig. 4. Particle size − 74 µm (%) and circulating load (%) responses to manipulated variables: ore feed rate (t/h), circuit product slurry density (kg/dm3) and hydrocyclone feed pressure (bar).
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Table 2 Transfer functions of the Siilinjärvi J1 grinding circuit. Circuit outlet slurry density (kg/dm3)
Ore feed rate (t/h)
Cyclone feed pressure (kPa)
Cyclone overflow + 210 µm fraction (%)
G21 =
0:016⋅e ð1 + 6:6sÞð1 + 3:0sÞ
G22 =
0:02 ð1 + 0:001sÞð1 + 24:2sÞ
G23 =
0:016⋅ð1−113:8Þe−1s ð1 + 1:4sÞð1 + 37:3sÞ −0:015⋅ð1−141:1Þe−1:7s ð1 + 18:0sÞð1 + 1:5sÞ
Circulating load (%)
G31 =
−0:2⋅ð1 + 14:9sÞ ð1 + 3:8sÞð1 + 0:17sÞ
G32 =
−0:3⋅e−2:8s ð1 + 0:9sÞ
G33 =
−3:2 ð1 + 16:2sÞ
Cyclone overflow − 74 µm fraction (%)
G11 =
−15:4s
−0:013⋅e ð1 + 3:1sÞ
G12 =
−15:4s
particle size responses y1 and y2 were observed. Absolute deviations of the measured and 60 min ahead simulated values were compared. In addition, prediction capability was evaluated by calculating the model fit percentage (Eq. (2)) for prediction step lengths 1, 10 and 20 min. The results of both experiment days (exp. 1 and 2) are tabulated in Table 3. The formula used for the model fit number is vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 u n u u ∑ ðyðt + kÞ−⌢ B yðt + k jt ÞÞ2 C ut = 1 B C u B C Model fit % = 100⋅B1−u 2 C n t @ A ∑ yðt Þ− − y 0
ð2Þ
t =1
where y is measurements, ŷ is prediction, t is current time step and k is length of the prediction step.
−0:01 ð1 + 9:1sÞ
G13 =
Nichols method, described in Koivo and Pohjolainen (1985). Briefly summarizing, the matrices K and I are determined as follows: K=P
−1
I = εT
diagfp1 ; p2 ; …; pm g;
−1
ð4Þ
:
ð5Þ
The parameters p1…pm and ε are used for the controller tuning. Subsequently, the matrices P and T are obtained by applying separate step inputs for each m manipulated variables u and observing the rising slopes and final settlings and using the formulas: h −1 P = ˙y1 ; y˙ 2 ; …; y˙ m ½u1 ; u2 ; …; um T = ½y1 ; y2 ; …; ym ½u1 ; u2 ; …um
−1
ð6Þ ð7Þ
2.5. Applied multivariable control methods Three common multivariable control schemes were evaluated for the Siilinjärvi grinding process. The selected methods were multivariable PI control as a base case, a fuzzy control, from which earlier practices has been gained as a part of apatite flotation control, and, finally, a model predictive control, which also has embedded implementation capabilities in the current Metso DNA plant automation system. In each case, the controlled variables were the coarse size fraction (% +210 µm) and the circulating load (%). Control of the coarse fraction is important in terms of flotation recovery, and the grinding circuit circulating load in terms of stable and safe process operation. Limitations for the control were set by defining minimum and maximum allowed ore feed rates and circuit outlet slurry densities. In multivariable PI control, the controller output u is obtained from u = Ke + I e; ˙
ð3Þ
where e is control error, K and I are constant matrices for the controller proportional gain and integrator. Here, the controller was tuned using a procedure, which is analogous to a scalar case Ziegler–
The fuzzy control was constructed by defining trapezoidal membership functions for the selected input and output variables, completed with a Mamdani type rule base inference system. For an introduction to fuzzy systems, see for example Lin and Lee (1996). Omitting the detailed parameterization, operation of the designed fuzzy control logic can be summarized: • IF particle size deviation is small AND not approaching the setpoint: ∘ Change feed rate a little. ∘ IF feed rate is near the limits AND slurry density is not near the limits, change also the slurry density. • IF particle size deviation is large AND not approaching the setpoint: ∘ IF feed rate is not near the limits, change feed rate largely. ∘ IF feed rate is near the limits, change the slurry density AND feed rate a little. • IF circulating load is near the limits: ∘ AND amount of cyclones AND cyclone pressure are not in extreme values, change amount of cyclones. The rule base and fuzzy sets were carefully tuned in an iterative manner, by means of simulations, to obtain well approved input– output performance.
Fig. 5. Step responses of the grinding circuit models.
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0.68%
0.63%
horizon length, nu is the control horizon length, k is the current discrete time step, γy factors are the output weightings for the control error, γu factors are the input weightings for the control increments. A brief introduction of MPC for the process industries is available for example in Bequette (2003).
0.67%
0.97%
3. Comparison of grinding circuit control strategies
Table 3 Model validation results for two days step input experiments. Size fraction − 74 µm Mean abs. error% between 60 min simulated end values and measurement (exp. 1) Mean abs. error% between 60 min simulated end values and measurement (exp. 2) Model fit-%, prediction step = 1 (exp. 1) Model fit-%, prediction step = 10 (exp. 1) Model fit-%, prediction step = 20 (exp. 1) Model fit-%, prediction step = 1 (exp. 2) Model fit-%, prediction step = 10 (exp. 2) Model fit-%, prediction step = 20 (exp. 2)
95.6% 52.9% 26.0% 93.8% 76.6% 35.6%
Size fraction + 210 µm
96.4% 60.8% 40.7% 93.9% 78.1% 40.0%
Different control strategies were compared by simulating eight hours time periods, all with a similar set point sequence for the +210 µm (%) particle size fraction. The control performance was evaluated in terms of integrated squared error index (ISE), presenting the squared control error of the time period. To emulate the measurement conditions in reality, white noises for the particle size and circulating load (%) measurements were added. The +210 µm (%) included 0, 0.5 and 1% relative noises and the circulating load 2% relative noise.
Table 4 Model predictive control parameterization. Variable
Nominal Min/max value band
MV: hydro cyclone 76 pressure (kPa) MV: feed rate (t/h) 480 MV: product slurry 1360 3 density (kg/dm ) CV: under 74 µm 28 size fraction (%) CV: over 210 µm 48 size fraction (%) CV: circulating 200 load (%)
Min/max Weight Change rate change rate factor weight factor
50…100
±10
1
0
350…600 1320… 1390 20…40
±10 ±1
0 0
0.1 0.2
–
0
–
40…60
–
1
–
120…280
–
0
–
The third option, model predictive control (MPC) utilizes the dynamic process models to make predictions of the future process values and to calculate future controller outputs to obtain optimal output trajectory for the setpoint tracking. The respective future time windows are called prediction and control horizons. Optimality of the determined control actions is defined in terms of quadratic cost function. The cost function is minimized in each time step, while new predictions and controller outputs are calculated. This kind of MPC scheme is known as receding horizon control. Here, the applied cost function was written in form: ne
2
nu
2
J ðkÞ = ∑ γy ½yr ðk + iÞ− yˆ ðk + iÞ + ∑ γu Δuðk + j−1Þ : i=1
75
ð8Þ
j=1
The notations are: yr is the output reference (set point), ŷ is the predicted output, Δu is the control increment, ne is the prediction
3.1. Parameterization of the controllers The multivariable PI controller (3) was designed based on the identified process models (Table 2). The controlled variable was the +210 µm size fraction (y1, %), while the manipulated variables were the feed rate (u1, t/h) and the circuit outlet slurry density (u2, kg/dm3). These notations were applied in Eqs. (6) and (7); further the controller was tuned based on the ISE index when 0.5 rel.-% measurement noise for y1 was present. The resulted gain and integrator matrices (4) and (5) were: K = [5440.4 4145.1] and I = [212.4 322.6]. Operation of the fuzzy control is highly sensitive to the selected control interval. In general, higher measurement noise implies a need for a longer control interval. A control interval of 20 min was determined to be most suitable, when 0.5–1 rel-% particle size measurement noise was present. The model predictive control was implemented as a receding horizon control with one minute control interval, 10 min control horizon and 40 min prediction horizon, covering the required process stabilization time. The parameterization details for the MPC are summarized in Table 4. Selection of the weighting factor is based on the following aims: feed rate is the primary manipulated variable, slurry density is used more moderately and the hydrocyclone pressure is virtually unused (in practice, it can be only changed stepwise). The + 210 µm size fraction is the primary controlled variable; −74 µm size fraction and the circulating load may vary in the predefined limits. Operation of the MPC for a stepwise 1% increase in +210 µm particle size set point is demonstrated in Fig. 6. A new set point is reached within 40 min, while the fine fraction (%) and the circulating load (%) have decreased and also stabilized. The main
Fig. 6. Operation of the MPC when + 1% set point change is applied in the + 210 µm size fraction.
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Fig. 7. Fuzzy-MPC control scheme to control the circuit product particle size while circulating load is kept in predefined limits (MPC: DV = disturbance variable, CV = controlled variable, MV = manipulated variable).
control actions are a 40 t/h increase of the feed rate with a complementary 20 kg/dm3 increase in the slurry density. However, this control setup cannot handle large disturbances in the circulating load, due to lack of discrete cyclone pressure (number of cyclones in use) changes. These disturbances can occur when the ore type is changing drastically due to a change of the ore feed heap at the Siilinjärvi case. Finally, to utilize both the ability of the fuzzy control to automate discrete cyclone pattern control tasks, and the advantages of model based control schemes, a hybrid control system of them was set up and tested. Here, both fuzzy-MPC and fuzzy-PI controls were evaluated. Fig. 7 illustrates the fuzzy-MPC case, where the circulating load is controlled by the fuzzy system, while the particle size is controlled by MPC. The system was also provided with the feedforward information of the upcoming disturbances caused by the measured changes in the hydrocyclone feed pressure. 3.2. Results for a set point sequence tracking First, the different control schemes — PI, fuzzy, MPC and also fuzzyPI and fuzzy-MPC hybrids — were evaluated by applying a particle size setpoint sequence for a simulated process. Table 5 summarizes the results of the control performances in terms of integrated square error (ISE) index. In the circulating load control cases one change in the
Table 5 Comparison of control performances for a set point sequence tracking when the particle size measurement noise is 0, 0.5 and 1 rel.-% were applied, circulating load noise was set to 2 rel.-%. Measurement noise Particle size control No noise
Moderate
High
Controller
ISE-index
PI Fuzzy MPC PI Fuzzy MPC PI Fuzzy MPC
18.5 27.1 16.5 21.0 35.3 19.8 23.8 59.4 25.8
Particle size and circulating load control No noise Fuzzy Fuzzy-PI Fuzzy-MPC Moderate Fuzzy Fuzzy-PI Fuzzy-MPC High Fuzzy Fuzzy-PI Fuzzy-MPC
44.3 41.2 33.0 63.2 56.1 37.1 73.1 58.1 41.9
number of hydrocyclones occurs. The ISE indices indicate MPC to be good in both pure particle size control and in combination with fuzzy circulating load control. However, the performance of the multivariable PI control is nearly equal or better with high measurement noise. As an example, Fig. 8 presents the fuzzy-MPC control results for a moderate measurement noise case (Table 5) having an ISE performance index value of 37.1. Also, robustness of the model predictive control to model mismatches was evaluated. In practice, the model mismatches occur when the process equipment conditions change and when the ore types vary. Table 6 summarizes changes in the ISE performance index when a 10…30% variation in the model parameters were introduced. The applied set point sequence was the same as in Fig. 8 and Table 5. But in this case, a slightly smaller (0.2 rel.-%) particle size measurement noise was used to emphasize the effect of the varied model parameters. Impact on the ISE performance index is moderate even with the highest applied parameter change, when compared to the impact of totally other control configurations or increased measurement noise, presented in Table 5.
3.3. Control simulation with a long term process data Based on the set point tracking results shown in Table 5, the FuzzyMPC scheme was selected for long term process data simulation. The data (July 21–29, 2009) includes five separate ore heaps ran through the mill. In the original data, the ore feed was kept constantly at 480 t/h, slurry density at 1360 kg/dm3, and the number of cyclones at 7 set points. In the control simulation set up, the original measured particle size variation around the mean value was summed with the simulated result, used further in feedback control. Also, the original measured hydrocyclone pattern feed pressure and circulating load variations were fed to the control system while summed with the simulated results. Hence, the system was analogous to the scheme shown in Fig. 7 where the dotted line feedback signals include now also fluctuations obtained from the process data sequence. The set point for the coarse +210 µm fraction was set to 50.6%, which was the mean value of the process data sequence. The resulting control simulation — in addition of the original process data — for the one week data period is shown in Fig. 9. As a result of the control simulation, the mean value of the +210 µm was 50.6%, which is same as the set point. For the whole data set the hourly bases standard deviation of the coarse particle size fraction with fuzzy-MPC control was 0.36%, while in the original data it was 1.08%. However, these values include the effects of the ore type changeovers. For example, the particle size deviations within one processed ore heap (time period 45–79 h) were 0.25% for the control simulation and 0.34% for the process data. In the control simulations, the ore feed rate was an average 488.7 t/h and the circuit outlet slurry density 1352 kg/dm3.
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Fig. 8. Example of the fuzzy-MPC operation for a given set point sequence, when 0.5% particle size measurement error for + 210 µm (%) fraction is present.
Table 6 Robustness of the model predictive control at the Siilinjärvi case, when model parameters are varied and 0.2% relative particle size measurement errors are present. Case Change in process time constants
Change in process gain
Control performance (ISE)
1 2 3 4 5 6 7
0% + 10% + 30% + 30% − 10% − 30% − 30%
17.4 18.2 20.1 21.8 19.4 24.0 24.9
0% + 10% + 20% + 30% + 10% + 20% + 30%
(+4.6%) (+15.5%) (+25.3%) (+11.5%) (+37.9%) (+43.1%)
4. Discussion and conclusions This exploration covered process experiments, modeling and a feasibility study aiming for grinding circuit control improvements at
the Yara Siilinjärvi phosphate concentrator. Long term data analysis also pointed out reflections between the operation of the grinding circuit and the metallurgical performance of the apatite flotation, especially in terms of coarse fraction recovery. The survey was started by carrying out numerous step response experiments during the normal operation of the concentrator plant. Strong interactions between the process variables set challenges to the modeling task; it turned out that the most suitable model structures were transfer functions defining the input output dynamic separately for each variable. In addition, the plant automation system supported straightforward configuration of them to obtain long term verification data of the model prediction capabilities. The control development, tuning, and performance evaluation were conducted in a simulation environment, established based on the experimental dynamic models. In particle size control the model predictive and multivariable PI control gave both good results. Nevertheless, the MPC enables better handling for process constraints.
Fig. 9. Process data set of +210 µm (%) particle size fraction and circulating load (%) (dotted lines), and the simulated results (solid lines) when the feed rate (t/h), slurry density (kg/dm3) and number cyclone control actions with fuzzy-MPC set up were applied for the same data; changes of the ore heaps are indicated with triangle symbols.
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The performance of the applied fuzzy control was satisfactory. But then, from the viewpoint of long term maintenance, fuzzy control is based on readily manageable rule base. Also, fuzzy control is well suited for discrete control actions, such as valve opening and closing, used here for control of the circulating load. Therefore, a control system incorporating fuzzy and MPC control was suggested. A relatively long (one week) process data simulation with a fuzzyMPC scheme confirmed the advantages of closed loop particle size control. During the whole period the control system reduced variation of the coarse fraction 67%, and even during one feed ore heap the reduction was 26%, while keeping the circulating load in operating limits by automated manipulation of the hydrocyclone valve pattern. Moreover, the ore feed rate increased an average 1.8% within the data period. Apparently, better control of the slurry particle size distribution has a favorable impact on flotation recovery, possibly still increasing the plant capacity. The presented control system is partly based on process models identified during stable operation of the plant. In addition to changes in the ore type, segregation at the ends of the ore heaps, and also in the feed ore bin, can introduce disturbances to the circuit operation. In addition to the feedback from the product particle size measurement, the control system could be still accomplished with feed forward information of the feed ore particle size. This could reduce the disturbance effect of segregation, allowing the control system to optimize the ore type changeover yet more effectively. Overall, the control assessment presented here pointed out that model based control was robust and suitable for drastic ore type changeover management. In addition, the model predictive control system can be well operated jointly with external discrete control actions. Currently at the Siilinjärvi concentrator, the plant capacity enhancements have been started with flowsheet reconfiguration of the grinding
circuit. In future, this control assessment gives a proper insight for forthcoming grinding circuit control strategy implementations.
Acknowledgements The research project is supported by the Finnish Funding Agency for Technology and Innovation (Tekes). In addition to this, a number of Siilinjärvi plant personnel are acknowledged for good collaboration both during numerous plant visits and other meetings.
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