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An intelligent control strategy for thickening process
MINPRO-02723; No of Pages 7 International Journal of Mineral Processing xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
An intelligent control strategy for thickening process Ning Xu 1, Xu Wang ⁎,1, Junwu Zhou, Qingkai Wang, Wen Fang, Xiuyun Peng Beijing General Research Institute of Mining and Metallurgy (BGRIMM), Beijing 102600, China Beijing Key Laboratory of Automation of Mining and Metallurgy Process, Beijing 102600, China
a r t i c l e
i n f o
Article history: Received 28 September 2014 Received in revised form 19 January 2015 Accepted 23 January 2015 Available online xxxx Keywords: Thickener Modeling Process control Optimization PLS
a b s t r a c t Through the online measurement of the thickener operation parameters including feed flow rate, mud bed level, and underflow concentration, an intelligent control strategy for thickener underflow and flocculant addition is proposed based on the mass balance model and expert rules. Based on the strategy, some guidelines concerning controllers tuning are provided. The application of thickener modeling and optimization software in the wastewater treatment plant of mineral processing illustrates an optimal control operation with stable underflow concentration. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Due to its nonlinearity, long-time delay, and strong coupling characteristics with frequently varied boundary conditions, thickening process is known to be difficultly controlled. Thus the widespread thickener operation with poor standards, overflows with high fine particle contents and high variable underflows in many plants are understandable. In order to resolve these problems, a fuzzy logic controller with two basic control loops was suggested by Santos et al. (1995). One is to control underflow concentration by varying the underflow pulp flow rate and the other is to regulate overflow turbidity by adjusting the flocculant addition rate. While the effect of the interaction between the two coupled control loops was not reported. Recently, Segovia et al. (2011) mentioned a multiple-input single-output (MISO) fuzzy controller to control the sludge level and underflow concentration by adjusting the underflow flow rate. The drawback is that the effect of flocculant was not considered in the MISO fuzzy controller. On the other hand, since the development of rigorous mathematical modeling of the process of continuous sedimentation in a clarifier– thickener unit with partial differential equations (Bürger and Narváez, 2007; Garrido et al., 2003b), more advanced model-based control strategies have been proposed. Based on the sedimentation velocity of each particle affected by the time-dependent properties of the fed solids, Diehl (2008) put forward a proportional controller for controlling the inventory by calculating the mathematical model in the ideal ⁎ Corresponding author at: Beijing General Research Institute of Mining and Metallurgy (BGRIMM), Beijing 102600, China. E-mail address: [email protected] (X. Wang). 1 Equally contributed to the work.
case. Betancourt et al. (2014) suggested to using the flow rate of underflow to control the concentration and the feed property coefficient which is able to manipulate the value by modifying the flocculant concentration to control the sediment level. Since the theoretical strategies above assume that the thickener is operated under near stationary conditions and calibrated model parameters without overload, they are difficult to perform in practice. At the same time, with the phenomenological theory of sedimentation, the softwares for designing and simulating conventional industry thickeners have been developed (Garrido et al., 2003a; Burgos and Concha, 2005). The concentration profile in the thickener can be predicted by entering the solid feed rate and the required underflow concentration into the software. But there is no reported software for controlling thickening process. In this work, we proposed an intelligent thickener control strategy based on the dynamic mass balance model. The “intelligent” controller is able to calculate the optimal set point of the underflow flow rate, based on the mass flow of the fed solids in thickener and the state parameters of thickening process, and automatically adjusting the controller parameters according to the trends of state parameters. 2. Mass balance model 2.1. Process parameter online measurement Thickeners work continuously to produce a concentrated underflow and a clarified overflow. When the fed solid mass flow is determined by the upstream process, operators are used to adjusting the flow rate of underflow and flocculant to obtain the desired underflow concentration. In fact, there exist some problems in the thickener control. Mud
http://dx.doi.org/10.1016/j.minpro.2015.01.007 0301-7516/© 2015 Elsevier B.V. All rights reserved.
Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007
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bed level which makes an immediate impact on the underflow concentration is usually neglected. Online analytical instrument of overflow turbidity is replaced by manual sampling tests. Flocculant dose is adjusted according to subjective experience. What's more, thickeners often shut down due to the rakes' overloading without pressure detection. All the above factors have affected the thickening efficiency seriously. Therefore, a complete monitoring system of thickening process should at least online measure all the variables in Table 1 (see Fig. 1). By online measurement of mud bed level, solid mass flow of feed and underflow, mass balance model of thickening process can be built from the obtained historical data as the basic of optimal control. 2.2. Mass balance equations Based on mass balance, changes of the total solid mass of mud bed m are mainly depending on the solid mass flow of feeding and discharging changes. Suppose the concentration of overflow is 0, the macroscopic mass balance equation is (Betancourt et al., 2013) dmðt Þ ¼ Q F ðt ÞC F ðt Þϕ F ðt Þ−Q U ðt ÞC U ðt ÞϕU ðt Þ dt
ð1Þ
where the function of total solid mass of mud bed is mðt Þ ¼ f 1 ðLBed ðt ÞÞ f 2 ðLBed ðt Þ; ϕU ðt ÞÞ C Bed ðt Þ
ð2Þ
which involves the mud bed volume function f1(LBed (t)) and average solid mass fraction of mud bed function f2(LBed (t),ϕU (t)). Here we define V Bed ðt Þ ¼ f 1 ðLBed ðt ÞÞ
ð3Þ
ϕBed ðt Þ ¼ f 2 ðLBed ðt Þ; ϕU ðt ÞÞ
ð4Þ
where VBed is the volume of mud bed and ϕBed the average solid mass fraction of mud bed, which is obtained from the prediction model with mud bed level and underflow solid mass fraction as input variables. And the average concentration (kg/m3) of mud bed function CBed that appeared in Eq. (2) satisfies the following formula C Bed ðt Þ ¼
Fig. 1. Thickening process measurement.
2.3. Average solid mass fraction of mud bed prediction model The average solid mass fraction of mud bed prediction model can be obtained by using the partial least-squares (PLS) regression algorithm. Here, we rewrite Eq. (4) as follows y ¼ ϕBed ðt Þ ¼ f 2 ðLBed ðt Þ; ϕU ðt ÞÞ ¼ f 2 ðX Þ
ð6Þ
where the input matrix X is composed of mud bed level and underflow solid mass fraction, and the output vector y is the corresponding average solid mass fraction of mud bed. First, X is normalized processing. Then given the nonlinearity of the thickening process, X is converted to the active matrix XA. The elements aij of row i column j of XA can be obtained by 0 2 1 xi −c j B C ai j ¼ exp@− A i; j ¼ 1; 2⋯n σ 2j
ð7Þ
where xi is the input vector of row i of data samples and cj is the centered parameters which satisfies cj ¼ xj
ð8Þ
and σj is the width parameter of Gaussian function which satisfies
mbed ðt Þ V bed ðt Þ
mbed ðt Þ ¼ mbed ðt Þ ϕBed ðt Þ mbed ðt Þ ð1−ϕBed ðt ÞÞ þ ρsolid ρwater ρsolid ρwater ¼ ρwater ϕBed ðt Þ þ ρsolid ð1−ϕBed ðt ÞÞ
σj ¼ ð5Þ
3
where ρsolid is the solid density (kg/m ). Similarly, feed concentration function CF and underflow concentration function CU can be calculated from ϕF and ϕU, respectively.
Table 1 Information of online measured variables.
n 1X xi −x j : n i¼1
ð9Þ
Finally, XA and y can be decomposed as follows (Geladi and Kowalski, 1986; Qin, 1998)
T
X A ¼ TP þ Eh y ¼ XAb þ F h
ð10Þ
where b is the regression vector obtained in accordance with PLS algorithm. 3. Control objective and strategies
Icon
Symbol
Measured objects
FT (feed) DT (feed) FT (flocculant) PT LT AT DT (underflow) FT (underflow)
QF ϕF Q Floc PRake LBed TOver ϕU QU
Feed volumetric flow (m3/h) Feed solid mass fraction (%) Flocculant volumetric flow (m3/h) Rake torque (N*m) Bed level (m) Overflow turbidity (mg/l) Underflow solid mass fraction (%) Underflow volumetric flow (m3/h)
In order to maintain stable and efficient in the continuous thickening process, the controller is required to meet the following objectives. (1) Ensure stable thickener operation by minimizing “short circuit” or overloaded conditions. (2) Stabilize the underflow concentration, thereby improving the performance of downstream processes. (3) Improve the clarity of the overflow water and prevent the loss of mineral particles.
Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007
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(4) Reduce the flocculant consumption in the premise of ensuring the settling velocity. Based on the above considerations, the intelligent control strategy of thickening process was proposed. Fig. 3. Underflow control block diagram.
3.1. Flocculant addition control The best dosage of flocculant can be determined by laboratory simulation. The effects of different dosing flocculation can be evaluated from the settling velocity and the economic rationality. The set point of flocculant addition is to control the pump speed needed to deliver the required dosage. For flocculant injection, three potential control modes could be used: (1) Manual Control Mode: the operator sets the pump speed via the variable speed drive. (2) Automatic Control Mode: the operator sets the flow rate and the pump speed is adjusted automatically to maintain the specified flow. (3) Feed Forward Control Mode: the flocculant injection is managed by a feed forward control loop to control the flocculant flow by varying the pump speed. As shown in Fig. 2, the set point of the flocculant flow is adjusted in a feed forward control proportional to the solid mass flow of the thickener feed. The set point Q FlocSP (m3/h) of the flocculant flow is based on the following calculation Q Floc SP ðt Þ ¼
Q F ðt Þ ϕ F ðt Þ C F ðt Þ DRFloc SP ðt Þ FC 1000
ð11Þ
where DRFlocSP is the flocculant dose rate (g/t), and FC is the flocculant solution concentration (g/l). 3.2. Mass balance model-based methods in underflow control Thickeners are controlled as a continuous settling and thickening process, where the solids are being withdrawn at the same rate as being fed. To achieve and maintain underflow concentration, it is necessary to keep the mass balance where underflow solid rate equals to the fed solid rate. Based on the thickener mass balance model of Eq. (1), the underflow flow rate Q U is determined as Q U ðt Þ ¼
Q F ðt ÞC F ðt Þϕ F ðt Þ−dmðt Þ=dt : C U ðt ÞϕU ðt Þ
3.3. Rule-based methods in optimizing thickener control The stability of thickener operation is greatly influenced by the feed flow rate and upstream process. On the one hand, if the underflow rate is too low, it is possible to make the thickener overloaded and the mineral particle loss when the mud bed level is high enough. On the other hand, if the underflow rate is too high, thickeners will be “shortcircuited” when the mud bed is pumped out and the feed is directly discharged. To solve these problems, thickener optimal control strategies including state feedback identifier and expert system are proposed below. First, the current state of the thickener, which includes rake torque, overflow turbidity, mud bed level and underflow solid mass fraction, is identified by the state feedback identifier. Specifically, the four key parameters are identified by superimposing, thus the result is varied as shown in Fig. 4. The measured rake torque is an indication of the mud concentration and the forces needed to move the rakes. When the torque reaches to the setting threshold, operating changes are required to relieve the torque. If the torque continues up to the safe limit, the drive will be shut down to protect the mechanism. Therefore, corrective actions, such as increasing underflow rate, should be taken well in advance of reaching the safe limit to prevent overload. And by detecting turbidity of the thickener overflow, the loss of mineral particles can also be avoided. Generally, a rise in bed level or solid residence time will increase the underflow concentration and rake torque. But if the flocculation is poor, a high bed level may also be resulted though a normal torque. However, if the feed is over flocculated, the bed level may be lower than normal in spite of high torque. Second, according to the identified state, the controller searches in expert rule database extracted from above information of the thickening process, and then optimizes the set-point of underflow rate and flocculant dose rate, which takes the thickener mass balance model as the rough tuning guide and meanwhile the state parameters as the fine tuning guide (Fig. 5).
ð12Þ
Specifically, when the underflow solid mass flow is equal to the fed solid mass flow, the set point of the underflow flow rate Q USP⁎is obtained
Q U SP ðt Þ ¼
Q F ðt ÞC F ðt Þϕ F ðt Þ : C U ðt ÞϕU ðt Þ
ð13Þ
And the underflow pump speed is adjusted automatically to maintain the specified flow (Fig. 3).
Fig. 2. Control block diagram of flocculant addition.
Fig. 4. Identifier interface of thickener state feedback.
Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007
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towards the direction of thickener state parameters within the target range. 4. Application examples of optimizing thickener control The advanced thickener control software was developed based on the proposed thickener control strategy. Here are the examples of the software applied in the industrial wastewater treatment process of a copper. 4.1. Flocculant dose rate optimization
Fig. 5. Optimal control block diagram.
Specifically, if the rake torque or overflow turbidity is beyond the set range, the flow rate of underflow set-point reaches the allowed maximum value. Otherwise, the set point QUSP of underflow rate is determined from combining Eqs. (1) and (13) as
Q U SP ðt Þ ¼ Q U SP ðt Þ þ
mðt Þ−m0 1 C U ðt ÞϕU ðt Þ Δt
ð14Þ
and m0 ¼
ρsolid ρwater f 1 ðLBed SP Þ f 2 ðLBed SP; ϕU SP Þ ρwater f 2 ðLBed SP; ϕU SP Þ þ ρsolid ð1−f 2 ðLBed SP; ϕU SP ÞÞ
where m0 is the total solid mass of mud bed with the set point of mud bed level LBedSP and underflow solid mass fraction ϕUSP, and Δt is time interval related to particle sedimentation rate in the thickener. In this paper, the initial value of Δt is 0.5 h through experiments. We use 8 1 > > > ΔVu ¼ : C U ðt ÞϕU ðt Þ
ð15Þ
where K is defined as control coefficient. Eq. (14) can be rewritten as
Q U SP ðt Þ ¼ Q U SP ðt Þ þ K ΔV u :
ð16Þ
Depending on the thickener conditions, the optimization results of the set-point value of underflow rate and flocculant dose rate are list in Table 2. Finally, after the thickener controller waiting for several control cycles, if the overrun parameter of thickener state still doesn't show a downward trend, the control coefficient K will be adjusted automatically
Table 2 Expert rules of thickener control. ϕU
LBed
DRFlocSP
Q USP
On target On target On target Above target Above target Above target Below target Below target Below target
Above target On target Below target Above target On target Below target Above target On target Below target
DRFloc DRFloc DRFloc DRFloc 0.9 ∗ DRFloc 0.8 ∗ DRFloc 1.2 ∗ DRFloc 1.1 ∗ DRFloc DRFloc
Q USP⁎ + K ∗ ΔVU Q USP⁎ Q USP⁎ + K ∗ ΔVU Q USP⁎ + 1.1 K ∗ ΔVU Q USP⁎ + K ∗ ΔVU Q USP⁎ + K ∗ ΔVU Q USP⁎ + K ∗ ΔVU Q USP⁎ + K ∗ ΔVU Q USP⁎ + 0.9 K ∗ ΔVU
DRFloc is the optimum flocculant dosing proportion according to the experiment.
In order to determine the optimal ratio of flocculant dosing, the static sedimentation experiment which mimics the real environment was carried out. Static sedimentation experiment, based on the phenomenon of suspension settling partition in gravitational field, is to study the settling characteristics of the suspension by measuring changes over time in each settlement area. The test suspension with a certain concentration was prepared, fully shaken and let stand. And then the position of the interface between the settling and fining zone was recorded at set intervals, i.e., the height of the settlement area. We take the settling time as the horizontal axis and the height of the settlement area as the vertical axis. Then the relationship curve between the height and the settling time can be plotted. To make the test results be similar to the fact as possible, samples are taken from the plant with a sampler. Samples were poured into five 1000 ml cylinders as shown in Fig. 6. 32 ml, 48 ml, 64 ml, 80 ml and 96 ml of flocculant were added sequentially to the cylinders from right to left according to the density of 2 g/m3, 3 g/m3, 4 g/m3, 5 g/m3 and 6 g/m3. Then, the liquid in the five cylinders was stirred about 1 min, and stop stirring. At regular intervals, we recorded the mud–water interface level and observed sedimentation. Based on the settlement experiment data, the relationship curve between the height of the compression zone and the settling time was plotted. As can be seen from Fig. 7, after 5 min, the settling velocity of the cylinder of 2 g/m3 was significantly decreased, while there was no significant difference among other cylinders. Considering the sedimentation rate and economic factor, the optimal ratio of flocculant dosing was 3 g/m3. 4.2. Identification of the average solid mass fraction of mud bed prediction model parameters In order to build the thickener mass balance model, we first need to identify the parameters of average solid mass fraction of mud bed prediction mode through experiments. By adjusting the flow rate of the thickener underflow, the values of underflow solid mass fraction and mud bed level were recorded per 1 h. Meanwhile, the values of average solid mass fraction of mud bed were obtained from sampling tests using the developed sludge samplers (Fig. 8). 40 groups of valid data were obtained during the 5 days of sampling experiment. Of which, 30 groups were used to train the model and the other 10 groups were used to test the model. The model prediction curve of average solid mass fraction of mud bed is shown in Fig. 9. In this paper, the relative mean square error (RMSE) is used to evaluate model prediction accuracy. The RMSE of the prediction model is 7.45%. 4.3. Application of advanced thickener control software On the basis of the original control system, the function of thickener modeling and optimization could be achieved by adding a computer equipped with the advanced thickener control software designed in C/S structure.
Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007
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Fig. 6. Static sedimentation experiment.
Operation data of the thickener was collected from the programmable logic controller (PLC) and then transferred into the data server. The data was prepared and filtered by the Pre-handling Data Module and then saved to the historical database. The thickener model was created by the Model-Training Module using the data from the historical database. The control parameters were calculated by the Optimized Module and sent back to the control system. The designed modeling and optimization system takes into account the large number of data, and some modules also require manual operation. Thus the offline and online parts are included in the system and associated with parameters. In order to reduce the coupling between modules, the parameter configuration module is designed which stores the parameters into the database. Fig. 10 shows the window of advanced thickener control software. The software operations include the following aspects: in the upper right corner of the software interface, we can configure the mass balance model parameters by selecting the number of the thickener
model, set the size parameters of the thickener by selecting the number of device type, and give the process parameters by selecting the number of technological parameters. In addition, the range of the flow rate of underflow can be adjusted in the upper right corner. The state variables such as mud bed level and underflow solid mass fraction of the thickener can be selected to add to the control strategy according to the actual situation. And we may configure control range of the state variables in the bottom interface. The two curves in the middle reflect the changes between set point (SP) and process value (PV) of the flow rate of underflow. Here are examples of the application of the advanced thickener control software to optimize the thickener control. In the following examples, since the range of feed concentration change is small and uncontrollable in actual thickening process, we choose feed volumetric flow as the main input variable. And we observe and discuss how the intelligent control strategy of the flow rate of underflow works to have an effect on the mud bed level and underflow solid mass fraction with K = 2 (Eq. (16)). In the first example, the control effect of thickener controller is discussed, when a large decrease in the feed volumetric flow leads to the underflow solid mass fraction less than the lower limit. When the test began, the feed volumetric flow reduced quickly, and consequently the underflow solid mass fraction was lower than the control target after 1 h. Then the controller was triggered immediately to reduce the set point of the flow rate of underflow based on mass balance model to increase the mud bed level gradually, which made the underflow solid mass fraction recovery within the control range smoothly (Fig. 11). The second example discusses the control effect of thickener controller when an increased change in the feed volumetric flow results in the mud bed level above the upper limit. After the test was started, feed volumetric flow increased quickly leading to the mud bed level above the control target after the second hour. Then the controller
Fig. 7. Static settling characteristic curve.
Fig. 8. Developed sludge samplers.
Fig. 9. Model prediction curve.
Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007
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Fig. 10. Advanced thickener control software interface.
was triggered immediately to increase the set point of the flow rate of underflow on the basis of mass balance model to decrease the mud bed level gradually, so that the mud bed level recovered to the control range smoothly. Subsequently, the controller judged whether the current underflows solid mass fraction within the target range. If it was within the allowable target range, the set point of the flow rate of underflow was determined by the mass balance model; otherwise the controller would continue to change the set point of the flow rate of underflow as the first example (Fig. 12).
In the third example, the intelligent controller and the conventional PID controller are compared. Two parallel thickeners in the industrial wastewater treatment process of a copper were selected as subjects, and the conventional PID controller and intelligent controller were used to the first and the second thickener, respectively. At start, feed volumetric flow is evenly distributed to the two thickeners. Due to the ignored effect of the feed volumetric flow fluctuation, underflow solid mass fraction of the thickener using conventional single-loop PID control was also in a sharp fluctuation. Meanwhile, because of the serious lag of the thickening process, underflow solid mass fraction controlled with the single-loop PID controller directly
Fig. 11. Example 1: Dynamic behavior of the thickener under a reduce change in the feed volumetric flow for controller.
Fig. 12. Example 2: Dynamic behavior of the thickener under an increased change in the feed volumetric flow for controller.
Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007
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5. Conclusion In this work, we have illustrated the use of intelligent strategy for underflow and flocculant addition control based on the thickener mass balance model and the expert rules. In addition, the advanced modeling and optimization software for thickener were developed. The control strategy has been proven to be effective through the practical application in the mineral processing industrial wastewater treatment plant with high promotional value for a widely used thickener.
References
Fig. 13. The control curve of underflow solid mass fraction.
would cause abnormalities of other state variables. For example, mud bed level exceeded the safe upper limit with danger of the mineral particle loss, forcing the operator to make manual intervention, which also indirectly caused a wide change in the underflow solid mass fraction. Compared with the first thickener, underflow solid mass fraction of the second thickener was stable within the range of 22% to 25% which met thickening process requirement indicators. The average solid mass fraction of 24 h of continuous operation of the control system was 24.7%. There was an average increase of 3.1% percent compared with conventional PID control (Fig. 13). What's more, the mud bed level was always controlled within safe limits, which ensured the efficient and stable operation.
Betancourt, F., Concha, F., Sbárbaro, D., 2013. Simple mass balance controllers for continuous sedimentation. Comput. Chem. Eng. 54, 34–43. Betancourt, F., Bürger, R., Diehl, S., Farås, S., 2014. Modeling and controlling clarifier– thickeners fed by suspensions with time-dependent properties. Miner. Eng. 62, 91–101. Bürger, R., Narváez, A., 2007. Steady-state, control, and capacity calculations for flocculated suspensions in clarifier–thickeners. Int. J. Miner. Process. 84, 274–298. Burgos, R., Concha, F., 2005. Further development of software for the design and simulation of industrial thickeners. Chem. Eng. J. 111, 135–144. Diehl, S., 2008. A regulator for continuous sedimentation in ideal clarifier–thickener units. J. Eng. Math. 60, 265–291. Garrido, P., Burgos, R., Concha, F., Bürger, R., 2003a. Software for the design and simulation of gravity thickeners. Miner. Eng. 16, 85–92. Garrido, P., Concha, F., Bürger, R., 2003b. Settling velocities of particulate systems: 14. Unified model of sedimentation, centrifugation and filtration of flocculated suspensions. Int. J. Miner. Process. 72, 57–74. Geladi, P., Kowalski, B.R., 1986. Partial least-squares regression: a tutorial. Anal. Chim. Acta 185, 1–17. Qin, S.J., 1998. Recursive PLS algorithms for adaptive data modeling. Comput. Chem. Eng. 22, 503–514. Santos, R.R., Meech, J.A., Ramos, L.T.S., 1995. Thickener operations at Carajas using a fuzzy logic controller. IEEE International Conference on Systems, Man and Cybernetics: Intelligent Systems for the 21st Century vol. 2. Vancouver, BC, Canada, pp. 1636–1639. Segovia, J.P., Concha, F., Sbárbaro, D., 2011. On the control of sludge level and underflow concentration in industrial thickeners. Preprints of the 18th IFAC World Congress, Milano, Italy vol. 2, pp. 8571–8576.
Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007
Contents lists available at ScienceDirect
International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
An intelligent control strategy for thickening process Ning Xu 1, Xu Wang ⁎,1, Junwu Zhou, Qingkai Wang, Wen Fang, Xiuyun Peng Beijing General Research Institute of Mining and Metallurgy (BGRIMM), Beijing 102600, China Beijing Key Laboratory of Automation of Mining and Metallurgy Process, Beijing 102600, China
a r t i c l e
i n f o
Article history: Received 28 September 2014 Received in revised form 19 January 2015 Accepted 23 January 2015 Available online xxxx Keywords: Thickener Modeling Process control Optimization PLS
a b s t r a c t Through the online measurement of the thickener operation parameters including feed flow rate, mud bed level, and underflow concentration, an intelligent control strategy for thickener underflow and flocculant addition is proposed based on the mass balance model and expert rules. Based on the strategy, some guidelines concerning controllers tuning are provided. The application of thickener modeling and optimization software in the wastewater treatment plant of mineral processing illustrates an optimal control operation with stable underflow concentration. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Due to its nonlinearity, long-time delay, and strong coupling characteristics with frequently varied boundary conditions, thickening process is known to be difficultly controlled. Thus the widespread thickener operation with poor standards, overflows with high fine particle contents and high variable underflows in many plants are understandable. In order to resolve these problems, a fuzzy logic controller with two basic control loops was suggested by Santos et al. (1995). One is to control underflow concentration by varying the underflow pulp flow rate and the other is to regulate overflow turbidity by adjusting the flocculant addition rate. While the effect of the interaction between the two coupled control loops was not reported. Recently, Segovia et al. (2011) mentioned a multiple-input single-output (MISO) fuzzy controller to control the sludge level and underflow concentration by adjusting the underflow flow rate. The drawback is that the effect of flocculant was not considered in the MISO fuzzy controller. On the other hand, since the development of rigorous mathematical modeling of the process of continuous sedimentation in a clarifier– thickener unit with partial differential equations (Bürger and Narváez, 2007; Garrido et al., 2003b), more advanced model-based control strategies have been proposed. Based on the sedimentation velocity of each particle affected by the time-dependent properties of the fed solids, Diehl (2008) put forward a proportional controller for controlling the inventory by calculating the mathematical model in the ideal ⁎ Corresponding author at: Beijing General Research Institute of Mining and Metallurgy (BGRIMM), Beijing 102600, China. E-mail address: [email protected] (X. Wang). 1 Equally contributed to the work.
case. Betancourt et al. (2014) suggested to using the flow rate of underflow to control the concentration and the feed property coefficient which is able to manipulate the value by modifying the flocculant concentration to control the sediment level. Since the theoretical strategies above assume that the thickener is operated under near stationary conditions and calibrated model parameters without overload, they are difficult to perform in practice. At the same time, with the phenomenological theory of sedimentation, the softwares for designing and simulating conventional industry thickeners have been developed (Garrido et al., 2003a; Burgos and Concha, 2005). The concentration profile in the thickener can be predicted by entering the solid feed rate and the required underflow concentration into the software. But there is no reported software for controlling thickening process. In this work, we proposed an intelligent thickener control strategy based on the dynamic mass balance model. The “intelligent” controller is able to calculate the optimal set point of the underflow flow rate, based on the mass flow of the fed solids in thickener and the state parameters of thickening process, and automatically adjusting the controller parameters according to the trends of state parameters. 2. Mass balance model 2.1. Process parameter online measurement Thickeners work continuously to produce a concentrated underflow and a clarified overflow. When the fed solid mass flow is determined by the upstream process, operators are used to adjusting the flow rate of underflow and flocculant to obtain the desired underflow concentration. In fact, there exist some problems in the thickener control. Mud
http://dx.doi.org/10.1016/j.minpro.2015.01.007 0301-7516/© 2015 Elsevier B.V. All rights reserved.
Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007
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bed level which makes an immediate impact on the underflow concentration is usually neglected. Online analytical instrument of overflow turbidity is replaced by manual sampling tests. Flocculant dose is adjusted according to subjective experience. What's more, thickeners often shut down due to the rakes' overloading without pressure detection. All the above factors have affected the thickening efficiency seriously. Therefore, a complete monitoring system of thickening process should at least online measure all the variables in Table 1 (see Fig. 1). By online measurement of mud bed level, solid mass flow of feed and underflow, mass balance model of thickening process can be built from the obtained historical data as the basic of optimal control. 2.2. Mass balance equations Based on mass balance, changes of the total solid mass of mud bed m are mainly depending on the solid mass flow of feeding and discharging changes. Suppose the concentration of overflow is 0, the macroscopic mass balance equation is (Betancourt et al., 2013) dmðt Þ ¼ Q F ðt ÞC F ðt Þϕ F ðt Þ−Q U ðt ÞC U ðt ÞϕU ðt Þ dt
ð1Þ
where the function of total solid mass of mud bed is mðt Þ ¼ f 1 ðLBed ðt ÞÞ f 2 ðLBed ðt Þ; ϕU ðt ÞÞ C Bed ðt Þ
ð2Þ
which involves the mud bed volume function f1(LBed (t)) and average solid mass fraction of mud bed function f2(LBed (t),ϕU (t)). Here we define V Bed ðt Þ ¼ f 1 ðLBed ðt ÞÞ
ð3Þ
ϕBed ðt Þ ¼ f 2 ðLBed ðt Þ; ϕU ðt ÞÞ
ð4Þ
where VBed is the volume of mud bed and ϕBed the average solid mass fraction of mud bed, which is obtained from the prediction model with mud bed level and underflow solid mass fraction as input variables. And the average concentration (kg/m3) of mud bed function CBed that appeared in Eq. (2) satisfies the following formula C Bed ðt Þ ¼
Fig. 1. Thickening process measurement.
2.3. Average solid mass fraction of mud bed prediction model The average solid mass fraction of mud bed prediction model can be obtained by using the partial least-squares (PLS) regression algorithm. Here, we rewrite Eq. (4) as follows y ¼ ϕBed ðt Þ ¼ f 2 ðLBed ðt Þ; ϕU ðt ÞÞ ¼ f 2 ðX Þ
ð6Þ
where the input matrix X is composed of mud bed level and underflow solid mass fraction, and the output vector y is the corresponding average solid mass fraction of mud bed. First, X is normalized processing. Then given the nonlinearity of the thickening process, X is converted to the active matrix XA. The elements aij of row i column j of XA can be obtained by 0 2 1 xi −c j B C ai j ¼ exp@− A i; j ¼ 1; 2⋯n σ 2j
ð7Þ
where xi is the input vector of row i of data samples and cj is the centered parameters which satisfies cj ¼ xj
ð8Þ
and σj is the width parameter of Gaussian function which satisfies
mbed ðt Þ V bed ðt Þ
mbed ðt Þ ¼ mbed ðt Þ ϕBed ðt Þ mbed ðt Þ ð1−ϕBed ðt ÞÞ þ ρsolid ρwater ρsolid ρwater ¼ ρwater ϕBed ðt Þ þ ρsolid ð1−ϕBed ðt ÞÞ
σj ¼ ð5Þ
3
where ρsolid is the solid density (kg/m ). Similarly, feed concentration function CF and underflow concentration function CU can be calculated from ϕF and ϕU, respectively.
Table 1 Information of online measured variables.
n 1X xi −x j : n i¼1
ð9Þ
Finally, XA and y can be decomposed as follows (Geladi and Kowalski, 1986; Qin, 1998)
T
X A ¼ TP þ Eh y ¼ XAb þ F h
ð10Þ
where b is the regression vector obtained in accordance with PLS algorithm. 3. Control objective and strategies
Icon
Symbol
Measured objects
FT (feed) DT (feed) FT (flocculant) PT LT AT DT (underflow) FT (underflow)
QF ϕF Q Floc PRake LBed TOver ϕU QU
Feed volumetric flow (m3/h) Feed solid mass fraction (%) Flocculant volumetric flow (m3/h) Rake torque (N*m) Bed level (m) Overflow turbidity (mg/l) Underflow solid mass fraction (%) Underflow volumetric flow (m3/h)
In order to maintain stable and efficient in the continuous thickening process, the controller is required to meet the following objectives. (1) Ensure stable thickener operation by minimizing “short circuit” or overloaded conditions. (2) Stabilize the underflow concentration, thereby improving the performance of downstream processes. (3) Improve the clarity of the overflow water and prevent the loss of mineral particles.
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(4) Reduce the flocculant consumption in the premise of ensuring the settling velocity. Based on the above considerations, the intelligent control strategy of thickening process was proposed. Fig. 3. Underflow control block diagram.
3.1. Flocculant addition control The best dosage of flocculant can be determined by laboratory simulation. The effects of different dosing flocculation can be evaluated from the settling velocity and the economic rationality. The set point of flocculant addition is to control the pump speed needed to deliver the required dosage. For flocculant injection, three potential control modes could be used: (1) Manual Control Mode: the operator sets the pump speed via the variable speed drive. (2) Automatic Control Mode: the operator sets the flow rate and the pump speed is adjusted automatically to maintain the specified flow. (3) Feed Forward Control Mode: the flocculant injection is managed by a feed forward control loop to control the flocculant flow by varying the pump speed. As shown in Fig. 2, the set point of the flocculant flow is adjusted in a feed forward control proportional to the solid mass flow of the thickener feed. The set point Q FlocSP (m3/h) of the flocculant flow is based on the following calculation Q Floc SP ðt Þ ¼
Q F ðt Þ ϕ F ðt Þ C F ðt Þ DRFloc SP ðt Þ FC 1000
ð11Þ
where DRFlocSP is the flocculant dose rate (g/t), and FC is the flocculant solution concentration (g/l). 3.2. Mass balance model-based methods in underflow control Thickeners are controlled as a continuous settling and thickening process, where the solids are being withdrawn at the same rate as being fed. To achieve and maintain underflow concentration, it is necessary to keep the mass balance where underflow solid rate equals to the fed solid rate. Based on the thickener mass balance model of Eq. (1), the underflow flow rate Q U is determined as Q U ðt Þ ¼
Q F ðt ÞC F ðt Þϕ F ðt Þ−dmðt Þ=dt : C U ðt ÞϕU ðt Þ
3.3. Rule-based methods in optimizing thickener control The stability of thickener operation is greatly influenced by the feed flow rate and upstream process. On the one hand, if the underflow rate is too low, it is possible to make the thickener overloaded and the mineral particle loss when the mud bed level is high enough. On the other hand, if the underflow rate is too high, thickeners will be “shortcircuited” when the mud bed is pumped out and the feed is directly discharged. To solve these problems, thickener optimal control strategies including state feedback identifier and expert system are proposed below. First, the current state of the thickener, which includes rake torque, overflow turbidity, mud bed level and underflow solid mass fraction, is identified by the state feedback identifier. Specifically, the four key parameters are identified by superimposing, thus the result is varied as shown in Fig. 4. The measured rake torque is an indication of the mud concentration and the forces needed to move the rakes. When the torque reaches to the setting threshold, operating changes are required to relieve the torque. If the torque continues up to the safe limit, the drive will be shut down to protect the mechanism. Therefore, corrective actions, such as increasing underflow rate, should be taken well in advance of reaching the safe limit to prevent overload. And by detecting turbidity of the thickener overflow, the loss of mineral particles can also be avoided. Generally, a rise in bed level or solid residence time will increase the underflow concentration and rake torque. But if the flocculation is poor, a high bed level may also be resulted though a normal torque. However, if the feed is over flocculated, the bed level may be lower than normal in spite of high torque. Second, according to the identified state, the controller searches in expert rule database extracted from above information of the thickening process, and then optimizes the set-point of underflow rate and flocculant dose rate, which takes the thickener mass balance model as the rough tuning guide and meanwhile the state parameters as the fine tuning guide (Fig. 5).
ð12Þ
Specifically, when the underflow solid mass flow is equal to the fed solid mass flow, the set point of the underflow flow rate Q USP⁎is obtained
Q U SP ðt Þ ¼
Q F ðt ÞC F ðt Þϕ F ðt Þ : C U ðt ÞϕU ðt Þ
ð13Þ
And the underflow pump speed is adjusted automatically to maintain the specified flow (Fig. 3).
Fig. 2. Control block diagram of flocculant addition.
Fig. 4. Identifier interface of thickener state feedback.
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towards the direction of thickener state parameters within the target range. 4. Application examples of optimizing thickener control The advanced thickener control software was developed based on the proposed thickener control strategy. Here are the examples of the software applied in the industrial wastewater treatment process of a copper. 4.1. Flocculant dose rate optimization
Fig. 5. Optimal control block diagram.
Specifically, if the rake torque or overflow turbidity is beyond the set range, the flow rate of underflow set-point reaches the allowed maximum value. Otherwise, the set point QUSP of underflow rate is determined from combining Eqs. (1) and (13) as
Q U SP ðt Þ ¼ Q U SP ðt Þ þ
mðt Þ−m0 1 C U ðt ÞϕU ðt Þ Δt
ð14Þ
and m0 ¼
ρsolid ρwater f 1 ðLBed SP Þ f 2 ðLBed SP; ϕU SP Þ ρwater f 2 ðLBed SP; ϕU SP Þ þ ρsolid ð1−f 2 ðLBed SP; ϕU SP ÞÞ
where m0 is the total solid mass of mud bed with the set point of mud bed level LBedSP and underflow solid mass fraction ϕUSP, and Δt is time interval related to particle sedimentation rate in the thickener. In this paper, the initial value of Δt is 0.5 h through experiments. We use 8 1 > >
ð15Þ
where K is defined as control coefficient. Eq. (14) can be rewritten as
Q U SP ðt Þ ¼ Q U SP ðt Þ þ K ΔV u :
ð16Þ
Depending on the thickener conditions, the optimization results of the set-point value of underflow rate and flocculant dose rate are list in Table 2. Finally, after the thickener controller waiting for several control cycles, if the overrun parameter of thickener state still doesn't show a downward trend, the control coefficient K will be adjusted automatically
Table 2 Expert rules of thickener control. ϕU
LBed
DRFlocSP
Q USP
On target On target On target Above target Above target Above target Below target Below target Below target
Above target On target Below target Above target On target Below target Above target On target Below target
DRFloc DRFloc DRFloc DRFloc 0.9 ∗ DRFloc 0.8 ∗ DRFloc 1.2 ∗ DRFloc 1.1 ∗ DRFloc DRFloc
Q USP⁎ + K ∗ ΔVU Q USP⁎ Q USP⁎ + K ∗ ΔVU Q USP⁎ + 1.1 K ∗ ΔVU Q USP⁎ + K ∗ ΔVU Q USP⁎ + K ∗ ΔVU Q USP⁎ + K ∗ ΔVU Q USP⁎ + K ∗ ΔVU Q USP⁎ + 0.9 K ∗ ΔVU
DRFloc is the optimum flocculant dosing proportion according to the experiment.
In order to determine the optimal ratio of flocculant dosing, the static sedimentation experiment which mimics the real environment was carried out. Static sedimentation experiment, based on the phenomenon of suspension settling partition in gravitational field, is to study the settling characteristics of the suspension by measuring changes over time in each settlement area. The test suspension with a certain concentration was prepared, fully shaken and let stand. And then the position of the interface between the settling and fining zone was recorded at set intervals, i.e., the height of the settlement area. We take the settling time as the horizontal axis and the height of the settlement area as the vertical axis. Then the relationship curve between the height and the settling time can be plotted. To make the test results be similar to the fact as possible, samples are taken from the plant with a sampler. Samples were poured into five 1000 ml cylinders as shown in Fig. 6. 32 ml, 48 ml, 64 ml, 80 ml and 96 ml of flocculant were added sequentially to the cylinders from right to left according to the density of 2 g/m3, 3 g/m3, 4 g/m3, 5 g/m3 and 6 g/m3. Then, the liquid in the five cylinders was stirred about 1 min, and stop stirring. At regular intervals, we recorded the mud–water interface level and observed sedimentation. Based on the settlement experiment data, the relationship curve between the height of the compression zone and the settling time was plotted. As can be seen from Fig. 7, after 5 min, the settling velocity of the cylinder of 2 g/m3 was significantly decreased, while there was no significant difference among other cylinders. Considering the sedimentation rate and economic factor, the optimal ratio of flocculant dosing was 3 g/m3. 4.2. Identification of the average solid mass fraction of mud bed prediction model parameters In order to build the thickener mass balance model, we first need to identify the parameters of average solid mass fraction of mud bed prediction mode through experiments. By adjusting the flow rate of the thickener underflow, the values of underflow solid mass fraction and mud bed level were recorded per 1 h. Meanwhile, the values of average solid mass fraction of mud bed were obtained from sampling tests using the developed sludge samplers (Fig. 8). 40 groups of valid data were obtained during the 5 days of sampling experiment. Of which, 30 groups were used to train the model and the other 10 groups were used to test the model. The model prediction curve of average solid mass fraction of mud bed is shown in Fig. 9. In this paper, the relative mean square error (RMSE) is used to evaluate model prediction accuracy. The RMSE of the prediction model is 7.45%. 4.3. Application of advanced thickener control software On the basis of the original control system, the function of thickener modeling and optimization could be achieved by adding a computer equipped with the advanced thickener control software designed in C/S structure.
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Fig. 6. Static sedimentation experiment.
Operation data of the thickener was collected from the programmable logic controller (PLC) and then transferred into the data server. The data was prepared and filtered by the Pre-handling Data Module and then saved to the historical database. The thickener model was created by the Model-Training Module using the data from the historical database. The control parameters were calculated by the Optimized Module and sent back to the control system. The designed modeling and optimization system takes into account the large number of data, and some modules also require manual operation. Thus the offline and online parts are included in the system and associated with parameters. In order to reduce the coupling between modules, the parameter configuration module is designed which stores the parameters into the database. Fig. 10 shows the window of advanced thickener control software. The software operations include the following aspects: in the upper right corner of the software interface, we can configure the mass balance model parameters by selecting the number of the thickener
model, set the size parameters of the thickener by selecting the number of device type, and give the process parameters by selecting the number of technological parameters. In addition, the range of the flow rate of underflow can be adjusted in the upper right corner. The state variables such as mud bed level and underflow solid mass fraction of the thickener can be selected to add to the control strategy according to the actual situation. And we may configure control range of the state variables in the bottom interface. The two curves in the middle reflect the changes between set point (SP) and process value (PV) of the flow rate of underflow. Here are examples of the application of the advanced thickener control software to optimize the thickener control. In the following examples, since the range of feed concentration change is small and uncontrollable in actual thickening process, we choose feed volumetric flow as the main input variable. And we observe and discuss how the intelligent control strategy of the flow rate of underflow works to have an effect on the mud bed level and underflow solid mass fraction with K = 2 (Eq. (16)). In the first example, the control effect of thickener controller is discussed, when a large decrease in the feed volumetric flow leads to the underflow solid mass fraction less than the lower limit. When the test began, the feed volumetric flow reduced quickly, and consequently the underflow solid mass fraction was lower than the control target after 1 h. Then the controller was triggered immediately to reduce the set point of the flow rate of underflow based on mass balance model to increase the mud bed level gradually, which made the underflow solid mass fraction recovery within the control range smoothly (Fig. 11). The second example discusses the control effect of thickener controller when an increased change in the feed volumetric flow results in the mud bed level above the upper limit. After the test was started, feed volumetric flow increased quickly leading to the mud bed level above the control target after the second hour. Then the controller
Fig. 7. Static settling characteristic curve.
Fig. 8. Developed sludge samplers.
Fig. 9. Model prediction curve.
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Fig. 10. Advanced thickener control software interface.
was triggered immediately to increase the set point of the flow rate of underflow on the basis of mass balance model to decrease the mud bed level gradually, so that the mud bed level recovered to the control range smoothly. Subsequently, the controller judged whether the current underflows solid mass fraction within the target range. If it was within the allowable target range, the set point of the flow rate of underflow was determined by the mass balance model; otherwise the controller would continue to change the set point of the flow rate of underflow as the first example (Fig. 12).
In the third example, the intelligent controller and the conventional PID controller are compared. Two parallel thickeners in the industrial wastewater treatment process of a copper were selected as subjects, and the conventional PID controller and intelligent controller were used to the first and the second thickener, respectively. At start, feed volumetric flow is evenly distributed to the two thickeners. Due to the ignored effect of the feed volumetric flow fluctuation, underflow solid mass fraction of the thickener using conventional single-loop PID control was also in a sharp fluctuation. Meanwhile, because of the serious lag of the thickening process, underflow solid mass fraction controlled with the single-loop PID controller directly
Fig. 11. Example 1: Dynamic behavior of the thickener under a reduce change in the feed volumetric flow for controller.
Fig. 12. Example 2: Dynamic behavior of the thickener under an increased change in the feed volumetric flow for controller.
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5. Conclusion In this work, we have illustrated the use of intelligent strategy for underflow and flocculant addition control based on the thickener mass balance model and the expert rules. In addition, the advanced modeling and optimization software for thickener were developed. The control strategy has been proven to be effective through the practical application in the mineral processing industrial wastewater treatment plant with high promotional value for a widely used thickener.
References
Fig. 13. The control curve of underflow solid mass fraction.
would cause abnormalities of other state variables. For example, mud bed level exceeded the safe upper limit with danger of the mineral particle loss, forcing the operator to make manual intervention, which also indirectly caused a wide change in the underflow solid mass fraction. Compared with the first thickener, underflow solid mass fraction of the second thickener was stable within the range of 22% to 25% which met thickening process requirement indicators. The average solid mass fraction of 24 h of continuous operation of the control system was 24.7%. There was an average increase of 3.1% percent compared with conventional PID control (Fig. 13). What's more, the mud bed level was always controlled within safe limits, which ensured the efficient and stable operation.
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Please cite this article as: Xu, N., et al., An intelligent control strategy for thickening process, Int. J. Miner. Process. (2015), http://dx.doi.org/ 10.1016/j.minpro.2015.01.007