Study of Energy Consumption of a Bucket Conveyor in a Jig Concentrator Plant in a Hard Coal Mine

: The subject of the discussion is oriented toward limiting the energy consumption of the bucket conveyor used in jig concentrator plants by controlling its speed. A method of predictive control of the bucket conveyor speed is presented. It allows for reducing the energy consumption due to appropriate selection of bucket movement speed to ensure the nominal ﬁlling of buckets along the entire length of the conveyor. This approach enables limiting the idling speed of the conveyor, extend its life, and also reduce the electricity consumption of the entire system. Experimental studies, carried out at the “So´snica” Coal Mine working facility, conﬁrmed that the use of a predictive algorithm for controlling the bucket conveyor speed and adapting the bucket speed to the current load decreased in energy consumption n by 9.6%, with 80% of the ﬁlling conveyor.


Introduction
Reducing electricity consumption, not only in the industrial sector [1,2], but also in mining significantly reduces production costs, and consequently the profit of the company and its competitiveness. In hard coal mining, the availability and efficiency of mining and processing machines are of fundamental importance as they directly affect the mine production capacity. Rational use of electricity and extending the life of machines can reduce mining costs, which in turn translates into the profitability of mines and their competitiveness on the market. Therefore, mining companies are determined to improve the efficiency of their transport machinery and equipment in the scope not only of their capacity in relation to mining, but also in the scope of effective use of transport machinery and equipment. Issues related to the energy demand of transport equipment, especially lifting mechanisms, in the context of energy saving, are the subject of research and tests conducted by many authors. Bucket conveyors are efficient machines to transport the dry materials under large elevation angles. In [3], the authors made a complete mechanical description of a bucket conveyor. The authors in [4] developed a method of the influence of a lifting height and weight of the lifted load on the drive overload and duty cycle power consumption. In [5], they presented a model of a crane that enabled the identification of dynamic factors caused by lifting the load off the ground. The dynamic forces and energy consumption of payload lifting were defined using simulation tests on an experimentally verified model. Energy efficiency was also analyzed as a key indicator in the design and the operation phase of a lifting mechanism including conveyors. In [6], the authors presented new approaches to strength and optimization estimates according to the operational criteria for mining machines. In the mining industry, bucket conveyors are used primarily for the transport and drainage of waste products and semi-finished products in the coal enrichment process from pulsating jigs ( Figure 1) [7,8]. The influence of the pulsation the coal enrichment process from pulsating jigs ( Figure 1) [7,8]. The influence of the pulsation cycle for the parameters of the flow of water and the layers of the bed are among the most important parameters in the preparation process of the jig [9,10]. In these conveyors, the material is transported-at large elevation angles-in specific quantities that directly depend on the volume of the installed buckets [11]. One of the characteristic features of the bucket conveyor, working as a part of the jig unit, is a variability of its load, resulting from the variability of the gravimetric composition of the enriched material (spoil) [12]. In the event of an increase in the amount of material fed onto the conveyor, the speed should always be increased immediately, in order to adapt to new loading conditions and to prevent excessive material accumulation in its loading zone. Material, accumulated in this zone, may cause emergency stopping of the conveyor, which will consequently stop the entire jig concentrator plant. Currently, the majority of bucket conveyors, used in the mining industry, work at a constant speed or at a speed manually controlled by the operator [13,14]. However, attempts have been made to automate the conveyor operation control process by using the echo sounder signal located above the moving buckets [8,15]. However, the disadvantage of this solution is that in the event of a rapid increase in the amount of bottom material directed to the conveyor, the conveyor may become blocked due to overfilling [16]. As the conveyors operate in a water environment up to half of their height, the echo sounder is mounted at a considerable distance from the loading zone [17,18]. Therefore, the signal sent from the echo sounder does not contain information about the amount of material in this zone, and its excess is the most common reason for blocking the conveyor. It is therefore necessary to develop a method of controlling the conveyor that would allow for it to be adapted to the flow rate of the product-rock material from the jig [19,20]-and thus ensure continuity of operation by preventing overfilling of the buckets and ensure optimal use of conveyor feed energy [21]. Electricity consumption is most effective when the conveyor is operated at a nominal load [22]. On one hand, such a solution can reduce electricity consumption, and on the other hand, extend the life of the conveyors (wear of components depends on the travel speed and working time).

Research and Methods of Process Parameters Identification
The subject of analysis was the "Komag" bucket conveyor used in the "Sośnica" Coal Mine in Gliwice, Poland, the diagram of which is shown in Figure 2. In these conveyors, the material is transported-at large elevation angles-in specific quantities that directly depend on the volume of the installed buckets [11]. One of the characteristic features of the bucket conveyor, working as a part of the jig unit, is a variability of its load, resulting from the variability of the gravimetric composition of the enriched material (spoil) [12]. In the event of an increase in the amount of material fed onto the conveyor, the speed should always be increased immediately, in order to adapt to new loading conditions and to prevent excessive material accumulation in its loading zone. Material, accumulated in this zone, may cause emergency stopping of the conveyor, which will consequently stop the entire jig concentrator plant. Currently, the majority of bucket conveyors, used in the mining industry, work at a constant speed or at a speed manually controlled by the operator [13,14]. However, attempts have been made to automate the conveyor operation control process by using the echo sounder signal located above the moving buckets [8,15]. However, the disadvantage of this solution is that in the event of a rapid increase in the amount of bottom material directed to the conveyor, the conveyor may become blocked due to overfilling [16]. As the conveyors operate in a water environment up to half of their height, the echo sounder is mounted at a considerable distance from the loading zone [17,18]. Therefore, the signal sent from the echo sounder does not contain information about the amount of material in this zone, and its excess is the most common reason for blocking the conveyor. It is therefore necessary to develop a method of controlling the conveyor that would allow for it to be adapted to the flow rate of the product-rock material from the jig [19,20]-and thus ensure continuity of operation by preventing overfilling of the buckets and ensure optimal use of conveyor feed energy [21]. Electricity consumption is most effective when the conveyor is operated at a nominal load [22]. On one hand, such a solution can reduce electricity consumption, and on the other hand, extend the life of the conveyors (wear of components depends on the travel speed and working time).

Research and Methods of Process Parameters Identification
The subject of analysis was the "Komag" bucket conveyor used in the "Sośnica" Coal Mine in Gliwice, Poland, the diagram of which is shown in Figure 2. To determine the theoretical capacity of the bucket conveyor, the following equation should be used [8]: where -bucket capacity (m 3 ); -bucket spacing (m); -bulk density of transported material (kg/m 3 ); -linear velocity of buckets movement (m/s); and -bucket filling coefficient (0-1). The capacity of the bucket conveyor working in jig concentrator plants depends on the linear speed of the bucket movement, among other things. Two rated speeds are most commonly used: 0.2 m/s and 0.28 m/s, respectively. Each change in the rotational speed of the motor driving the conveyor translates into an immediate change in the speed of movement of the buckets transporting the material. At a constant stream of the output product from the jig, it will immediately change the amount of material on the conveyor.
In reality, the filling of the bucket conveyor (weight of material) y 1 (t) depends on both its speed u 2 (t) and the flow rate of the product removed from the jig. A change in the product flow rate is the main disturbance that affects the weight of material currently on the conveyor. The measurement of the opening of the jig flap u 1 (t) will identify this disturbance, and the control system, actively correcting the conveyor speed, will maintain a constant weight of material on the conveyor. Due to the fact that the material discharged from the jig is fed to the conveyor with a certain delay, the calculations take into account the shift of the output signal in relation to the input signal by the time needed to cover this path. This time was determined when the jig was stopped, measuring the time from the change in the opening of the discharge slot to the moment when the material appeared in the loading zone of the conveyor. In the paper, we decided to use a predictive automatic To determine the theoretical capacity of the bucket conveyor, the following equation should be used [8]: where V-bucket capacity (m 3 ); a-bucket spacing (m); γ-bulk density of transported material (kg/m 3 ); v-linear velocity of buckets movement (m/s); and Ψ-bucket filling coefficient (0-1). The capacity of the bucket conveyor working in jig concentrator plants depends on the linear speed of the bucket movement, among other things. Two rated speeds are most commonly used: 0.2 m/s and 0.28 m/s, respectively. Each change in the rotational speed of the motor driving the conveyor translates into an immediate change in the speed of movement of the buckets transporting the material. At a constant stream of the output product from the jig, it will immediately change the amount of material on the conveyor.
In reality, the filling of the bucket conveyor (weight of material) y 1 (t) depends on both its speed u 2 (t) and the flow rate of the product removed from the jig. A change in the product flow rate is the main disturbance that affects the weight of material currently on the conveyor. The measurement of the opening of the jig flap u 1 (t) will identify this disturbance, and the control system, actively correcting the conveyor speed, will maintain a constant weight of material on the conveyor. Due to the fact that the material discharged from the jig is fed to the conveyor with a certain delay, the calculations take into account the shift of the output signal in relation to the input signal by the time needed to cover this path. This time was determined when the jig was stopped, measuring the time from the change in the opening of the discharge slot to the moment when the material appeared in the loading zone of the conveyor. In the paper, we decided to use a predictive automatic Energies 2021, 14, 5706 4 of 10 control system and search for the MISO (multi input single output) process model, the structure of which is shown in Figure 3. ergies 2021, 14, x FOR PEER REVIEW control system and search for the MISO (multi input single output) structure of which is shown in Figure 3. In order to obtain information about the object of control, measu were carried out using a working industrial object, enabling the regist ing parameters: degree of opening of the discharge slots in two comp linear speed of moving conveyor buckets, and power absorbed from the conveyor drive. Additionally, in order to determine the degree of on the basis of the power absorbed from the power grid, the power co veyor motor in the time intervals when the conveyor operated withou speed range was also registered.
Tests identifying these parameters were carried out in two stage the opening of the jig discharge slots u 1 (t) was changed and the load erating at a constant speed u 2 (t) = const. was recorded. The second stag at changing the conveyor speed u 2 (t) at the constant opening of the j the frequency of 0.5 Hz, in the range u 2 (t) ϵ (0.12-0.20 m/s). The con orded in the form of electrical power consumed by the motor from th was converted into the weight of the material on the conveyor y 1 (t). Th recording of parameters, the jig was fed with a capacity of about 125 It was assumed that the time delay of the output signal, which measuring the time from the moment of opening the jig discharge sl ance of material in the loading zone of the conveyor, is constant and a Figure 4a-c shows the waveforms of input and output variables use identifying the object parameters [22].
(a) In order to obtain information about the object of control, measurement experiments were carried out using a working industrial object, enabling the registration of the following parameters: degree of opening of the discharge slots in two compartments of the jig, linear speed of moving conveyor buckets, and power absorbed from the power grid by the conveyor drive. Additionally, in order to determine the degree of the conveyor filling on the basis of the power absorbed from the power grid, the power consumed by the conveyor motor in the time intervals when the conveyor operated without any load in the full speed range was also registered.
Tests identifying these parameters were carried out in two stages. In the first stage, the opening of the jig discharge slots u 1 (t) was changed and the load of the conveyor operating at a constant speed u 2 (t) = const. was recorded. The second stage of the tests aimed at changing the conveyor speed u 2 (t) at the constant opening of the jig discharge slots at the frequency of 0.5 Hz, in the range u 2 (t) (0.12-0.20 m/s). The conveyor load was recorded in the form of electrical power consumed by the motor from the power grid, which was converted into the weight of the material on the conveyor y 1 (t). Throughout the entire recording of parameters, the jig was fed with a capacity of about 125 kg/s. It was assumed that the time delay of the output signal, which was determined by measuring the time from the moment of opening the jig discharge slot until the appearance of material in the loading zone of the conveyor, is constant and amounts to n k = 16 s. Figure 4a-c shows the waveforms of input and output variables used for the process of identifying the object parameters [22].
The initial tests also determined the conveyor energy performance (i.e., the dependence of energy consumption on the conveyor load), which is shown in Figure 5.
The simple regression equation e p = f (w) takes the form [22]: The monitoring of the bucket conveyor's energy consumption was carried out on different days and at different times. Ten measurement groups were registered, ∆t = 3600 s each. During the tests, the degree of opening of the jig discharge slots u 1 and electric energy Energies 2021, 14, 5706 5 of 10 E p taken by the conveyor motor from the power grid were measured, at a constant rated motor speed. On the basis of the obtained results, the average and maximum electricity consumption values were determined and are summarized in Table 2. at changing the conveyor speed u 2 (t) at the constant opening of the jig discharge slots at the frequency of 0.5 Hz, in the range u 2 (t) ϵ (0.12-0.20 m/s). The conveyor load was recorded in the form of electrical power consumed by the motor from the power grid, which was converted into the weight of the material on the conveyor y 1 (t). Throughout the entire recording of parameters, the jig was fed with a capacity of about 125 kg/s. It was assumed that the time delay of the output signal, which was determined by measuring the time from the moment of opening the jig discharge slot until the appearance of material in the loading zone of the conveyor, is constant and amounts to n k = 16 s. Figure 4a-c shows the waveforms of input and output variables used for the process of identifying the object parameters [22].  The Pearson linear correlation coefficient of input and output variables u 1 (t), u 2 (t), and y 1 (t) are summarized in Table 1. Table 1. Correlation coefficients of variables u 1 (t), u 2 (t), y 1 (t) [22].

Parameter u 1 (t) u 2 (t)
The initial tests also determined the conveyor energy performance (i.e., the dependence of energy consumption on the conveyor load), which is shown in Figure 5.  The Pearson linear correlation coefficient of input and output variables u 1 (t), u 2 (t) and y 1 (t) are summarized in Table 1. Table 1. Correlation coefficients of variables u 1 (t), u 2 (t), y 1 (t) [22].

Parameter u 1 (t) u 2 (t)
The initial tests also determined the conveyor energy performance (i.e., the depend ence of energy consumption on the conveyor load), which is shown in Figure 5.  [22]. where: e p -percentage energy consump tion; w-percentage load on the conveyor; A-energy consumption during no-load operation; and B-energy consumption when operating at full load.
The simple regression equation e p = f(w) takes the form [22]: Figure 5. Energy performance of the bucket conveyor [22]. where: e p -percentage energy consumption; w-percentage load on the conveyor; A-energy consumption during no-load operation; and B-energy consumption when operating at full load.  The average value of the bucket conveyor load in the period under consideration was 51.51%, while the average value of energy consumption at the same time was 29.9%.

Predictive Bucket Conveyor Speed Control System-Experimental Tests
The task of the proposed bucket conveyor control system is to stabilize its filling at the level of the set value and guarantee the continuity of its operation (preventing the conveyor from being overfilled). The created control system was implemented in the same bucket conveyor on which measurement tests were carried out for the identification of the process parameters. The waste material was discharged from two working compartments of the jig. In addition, two sensors were connected to the controller, measuring the degree of opening the jig discharge slots, and the operator's panel was installed to visualize the processes. The structure of the conveyor speed control system is shown in Figure 6. p rated motor speed. On the basis of the obtained results, the average and maximum electricity consumption values were determined and are summarized in Table 2. The average value of the bucket conveyor load in the period under consideration was 51.51%, while the average value of energy consumption at the same time was 29.9%.

Predictive Bucket Conveyor Speed Control System-Experimental Tests
The task of the proposed bucket conveyor control system is to stabilize its filling at the level of the set value and guarantee the continuity of its operation (preventing the conveyor from being overfilled). The created control system was implemented in the same bucket conveyor on which measurement tests were carried out for the identification of the process parameters. The waste material was discharged from two working compartments of the jig. In addition, two sensors were connected to the controller, measuring the degree of opening the jig discharge slots, and the operator's panel was installed to visualize the processes. The structure of the conveyor speed control system is shown in Figure 6.  During start-up operations, in order to guarantee continuity of work and prevent the overfilling of the conveyor, threshold opening values of the jig discharge slots were declared. If the sum of opening the discharge slots (feeding the conveyor) in both compartments exceeded 120%, or the opening of the discharge slot on one of the compartments exceeded 70%, the algorithm set the maximum conveyor speed. However, if the opening of the discharge slots in both compartments was less than 5%, the control system algorithm set the minimum conveyor speed. In other cases, the speed control was carried out using the predictive control system. The control system allowed for switching to manual control (the conveyor speed set point determined by the operator).
As part of the research experiment, whose basic task was to analyze the operation of the control method in the industrial conditions of the bucket conveyor, the power of the conveyor operating in the manual mode for 30 min at a constant speed, and then for 30 min, the power and speed of the conveyor working with the automatic regulation system on were recorded. When recording both characteristics, the jig was fed at a capacity of 125 kg/s. In order to compare the results of the quality control of the material weight on the conveyor, its distributions were compiled when the conveyor was operated without the speed mode control and in the speed-controlled mode. Figure 7 presents a graph of the distribution of the material weight change on the conveyor, while the mean values and standard deviations of the waveforms are presented in Table 3.
As part of the research experiment, whose basic task was to analyze the operation of the control method in the industrial conditions of the bucket conveyor, the power of the conveyor operating in the manual mode for 30 min at a constant speed, and then for 30 min, the power and speed of the conveyor working with the automatic regulation system on were recorded. When recording both characteristics, the jig was fed at a capacity of 125 kg/s. In order to compare the results of the quality control of the material weight on the conveyor, its distributions were compiled when the conveyor was operated without the speed mode control and in the speed-controlled mode. Figure 7 presents a graph of the distribution of the material weight change on the conveyor, while the mean values and standard deviations of the waveforms are presented in Table 3. Table 3. Weight of material on the conveyor without and with the control system [22].

Variant
Without

Energy Consumption Analysis of the Conveyor Drive System
During the experimental tests, the main emphasis was placed on the analysis of the impact of the control algorithm developed on the basis of the energy consumption of the bucket conveyor working in the jig unit.
Using Equation (2), the electricity consumption for transporting 1000 kg of material can be calculated and the function of efficiency can be presented using Equation ( where: -energy consumed at rated operating conditions of the conveyor motor in one hour (kWh); -rated conveyor capacity, = 2·105 (kg/h); Figure 7. Distribution of the change in the material weight of the bucket conveyor: (a) without speed control, (b) with speed control [22]. Table 3. Weight of material on the conveyor without and with the control system [22].

Energy Consumption Analysis of the Conveyor Drive System
During the experimental tests, the main emphasis was placed on the analysis of the impact of the control algorithm developed on the basis of the energy consumption of the bucket conveyor working in the jig unit.
Using Equation (2), the electricity consumption for transporting 1000 kg of material can be calculated and the function of efficiency can be presented using Equation (3) [8]: where: E zn -energy consumed at rated operating conditions of the conveyor motor in one hour (kWh); W zn -rated conveyor capacity, W zn = 2 × 105 (kg/h); e p -energy consumption (%); and w-conveyor load (%). Figure 8 shows the unit electricity consumption as a function of efficiency.
Based on the carried out calculations, it was found that the conveyor working at full load (loading) consumed 0.053 kWh to transport 1000 kg of material, and when working with a load of 10%, the electricity consumption increased up to 0.138 kWh. 1 Figure 8. Unit electricity consumption as a function of efficiency [22].
As part of the verification work, a comparative analysis of the electricity consumption of the bucket conveyor motor operating in four modes was carried out: Mode 1-with automatic control system (measurements in industrial conditions); Mode 2-with continuous control (set value M z = 3520 kg, which corresponds to 80% loading)-theoretical considerations); Mode 3-with continuous control (set value M z = 4400 kg, which corresponds to 100% loading-theoretical considerations); and Mode 4-with constant rated speed (theoretical considerations). As part of the tests, the bucket conveyor energy performance was monitored. Measurements were carried out on different days and at different times. Ten measurement cycles were recorded, ∆t = 3600 s each, in which the electric power P consumed from the power grid by the conveyor motor and the linear speed of bucket movement were recorded. For each group of measurements, the electricity consumption E p as well as the average percentage conveyor speed v p were determined using the equation: where: u 2 -bucket linear speed (m/s); and v zn -rated linear conveyor speed (v zn = 0.2 m/s). Taking into account the nominal revolutions of the conveyor drive motor, n n = 985 rpm, its average revolutions n at ∆t were also calculated. The calculation results are presented in Table 4. Table 4. Energy consumption and revolutions of the conveyor motor divided into individual tests [22].

No.
E p (kWh) v p (%) n (rpm)  Table 5 summarizes the basic operating parameters of the bucket conveyor in the four motor speed modes under analysis.  Experimental tests have shown that in the case of conveyor speed continuous control as a function of capacity and its full filling, energy consumption can be reduced by 15.3%. An implementation of the proposed algorithm reduced energy consumption by 9.6%. The decrease in electricity consumption of the conveyor was primarily due to the set value of 80% of the conveyor loading and the restrictions imposed on speed control. Comparing the obtained consumption and taking into account the load set point, the control error was 1.9%.

Results
The article presents a method of controlling the bucket conveyor speed. Verification tests focused primarily on the impact of the method on the energy consumption of the conveyor. The main assumption of the developed method was to reduce idling, extend the conveyor life, and reduce electricity consumption by achieving such a speed of the bucket conveyor movement that ensures nominal filling of buckets along the entire length of the conveyor. The application justification of this method was confirmed in experimental tests carried out at the "Sośnica" Mine in Gliwice, Poland, which showed a reduction in electricity consumption by 9.6%, at the conveyor filling of 80%. Verification tests focused primarily on the impact of the method on the energy consumption of the conveyor. This is related to the short-term character of such tests. However, savings are also expected with regard to extending the life of the conveyor. In the "Budryk" Mine in Poland, an algorithm in a similar form extended the time between overhauls by more than six months. In addition, it was found that the adopted structure of the control system with a simplified model mapped the object dynamics well enough. The conducted simulation tests confirmed the possibility of using the process of identification and pre-control to implement the tasks of identification and control of a complex system with delays in control paths. In addition, thanks to the use of information from process operators, it allowed for the stabilization of the conveyor load and the rationalization of the process. The verification studies focused primarily on the impact of the method on the energy consumption of the conveyor. This is related to the short-term nature of such research. Nevertheless, savings are also expected in terms of extended conveyor life.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.