Precision weighing control of coal mine paste backfilling weighing system

Abstract

Coal mine paste backfilling (CMPB) technology is developed rapid recently as a sustainable and green mining technology. As the application of paste technology matures gradually, it is developing towards fine research, aiming at improving filling quality and reducing filling cost. To increase feeding speed and improve weighing accuracy of the coal mine paste backfilling weighing system (CMPBWS), the mathematical weighing progress model of CMPBWS is established and the weighing control system is optimized based on the adaptive iterative algorithm. The weighing process is divided into three stages, which are the rapid feeding stage, the lower feeding stage, and the prediction feeding stage. The weighing speed of each stage is controlled with different ways. The adaptive iterative learning control method (AILCM) is introduced and used in the prediction feeding stage. The advance stop value is dynamically modified by the AILCM. The numerical simulation study shows that the actual value is much closer to the set value after several iterations by the AILCM. With the method proposed in the paper, the weighing accuracy and feeding speed of CMPBW are both improved.

Keywords

Paste backfilling weighing system feeding speed weighing accuracy adaptive iterative learning control advance stop value

1. Introduction

The technology of coal mine paste backfilling (CMPB) technology is a new green technology to deliver paste filling-materials through pipeline to underground with help of the industrial filling pump or dead weight [1, 2, 3, 4]. Paste filling materials are a mixture of fly ash, poor soil, coal gangue, slag, sand and other solid wastes around the coal mine with a certain proportion [5, 6, 7]. With the coal mine backfilling technology, the utilizing of gangue and other solid waste solid, control of coal face roof, reducing mining subsidence and protecting the ground construction are effectively combined [8, 9, 10, 11, 12, 13]. Besides, the adverse influence on environment is improved, ecological environment is protected effectively. As the application of paste technology matures gradually, it is developing towards fine research, aiming at improving filling quality and reducing filling cost. The coal mine paste backfilling weighing system (CMPBWS) is a very important system in the CMPB system. The CMPBWS has a direct impact on the filling performance. The CMPBWS is a dynamic weighing control system (DWCS), and is always controlled with the high/low speed weighing method. However, the traditional control method in the CMPBWS causes some disadvantages. Most of the time, the high weighing precision of filling materials is achieved with the loss of feeding speed. In the process of weighing, accurate weighing and weight speed cannot achieve requirement at the same time [14, 15].

To achieve better results in the DWCS, many studies have been done. In some DWCS, inching weighing is chosen. When feed-materials weight is reached a certain extent, the inching weighing is used for compensation feeding. In that way, the actual material weight is closer to the given value. However, the use of inching weighing causes dynamic weighing with low productivity, and frequent electric damage to equipment and other problems [16, 17, 18, 19]. To improve weighing speed, in some DWCS, the weighing process is divided into two stages, that is, the coarse stage and the fine stage. In the coarse stage, the higher feeding speed is used to shorten the weighing time. When the amount of feeding-materials are up to 80% or 90% of the required quantity, the fine stage is started. In the fine stage, a slower speed is given to improve the weighing accuracy. With the two stage control, the weighing speed is increased, but the weighing accuracy of this method needs to be improved. To solve the contradiction between the rapid speed and high accurate weighing, the twolevel weighing control mode is designed, that is, high/low speed weighing and inching weighing [20, 21]. However, the speed and the accuracy of weighing still cannot meet the requirements simultaneously. To improve weighing accuracy and feeding speed of CMPBWS, the optimization method based on artificial neural network is also proposed by researchers [22]. However, there is still an improvement in this method.

To obtain better control weighing speed and weighing precision, the adaptive iterative learning control method (AILCM) is proposed and used in the paper. The basic idea of adaptive iterative learning control method is that through repeated training to make control output infinitely approximate expected output. With the adaptive iterative learning control method, it can obtain better results than the previous method. Firstly, the mathematical model of weighing process is established. Then, the weighing process is divided into three stages. The weighing speed is adjusted in different stages. The AILCM is introduced and used in the prediction feeding stage. Finally, the numerical simulation study is carried out. The simulation results show that the actual value is much closer to the set value after several iterations by the proposed method.

2. Modeling and analysis

2.1 Weighing process analysis

The paste feeding-materials are conveyed by the spiral conveyor to the weighing hopper, then the feeding-materials weight value is measured by the weighing sensor which is equipped under the hopper and the real-time weight signal is sent to the CMPBWS. The speed of the spiral conveyor is controlled by the system. When the weight meets the requirements, the spiral conveyor is stopped feeding. However, the materials in the air do not reach the weighing hopper. The weight measured by the weighing sensor is further increased after the left materials fall on the hopper. When the materials in the air completely drop on the hopper, the actual weight is obtained. With the feeding process, it can be seen that when to stop the spiral conveyor is crucial to obtain precision weight. The conveying capacity flow $Q$ of the spiral conveyor can be calculated with the following formula [23].

$\displaystyle Q=15\pi(D^{2}-d^{2})\cdot L\cdot n\cdot\phi\cdot\rho\cdot C\cdot\eta$ (1)

where, $D$ is blade diameter of spiral conveyor (m); $d$ is diameter of rotation shaft (m); $L$ is Pitch (m); $n$ is revolve speed of spiral conveyor (r/min); $\rho$ is material density (t/m ${}^{3}$ ); $\phi$ is filling factor of material; $C$ is inclination coefficient of spiral conveyor; $\eta$ is efficiency between theoretical value and actual value.

For a certain CMPBWS, system parameters of $D,d,L,\phi,\rho,C$ are constant. Then, the spiral conveyor capacity flow $Q$ is mainly determined by speed $n$ and efficiency $\eta$ . The efficiency $\eta$ of a particular material is generally stable. In that case, the spiral conveying capacity flow $Q$ is only affected by the revolve speed $n$ .

2.2 Weighing process modelling

Time sequence of the spiral conveyor is seen in Fig. 1. As shown in Fig. 1, the spiral conveyor operating time is from 0 to $T2$ . The time period of the material falling into the hopper is from $T1$ to $T3$ . The feeding-materials during the period of $T2$ to $T3$ is called the lag materials in the air.

During the period of $T1$ to $T3$ , the added feeding-materials weight in unit time of the weighing hopper is defined in Eq. (2).

$\displaystyle\frac{dW(t)}{dt}=BSV$ (2)

where, $W(t)$ is the actual weight in the weighing hopper (Kg); $B$ is specific gravity of material in the air (Kg/m ${}^{3}$ ); $V$ is instantaneous velocity of the material falls to the weighing hopper (m/s); $S$ is the cross sectional area of the spiral conveyor outlet (m ${}^{2}$ ).

Figure 1.

Time sequence of spiral conveyor.

The distance from the outlet of spiral conveyor to the bottom of the weighing hopper is $H_{0}$ . The actual height of paste filling-materials in the weighing hopper is $h(t)$ . After more and more filling-materials dropped into weighing hopper, the actual height in weighing hopper is gradually increased. The height is proportional to filling material weight, that is,

$\displaystyle h(t)=k_{p}\cdot W(t)$ (3)

where $k_{p}$ is the coefficient of proportionality (m/kg).

Given $G=15\pi(D^{2}-d^{2})\cdot L\cdot\phi\cdot\rho\cdot C\cdot\eta$ , at any time $t$ during $T1$ to $T3$ , the conveying capacity $Q(t)$ of feeding-materials conveying from the spiral conveyor is:

$\displaystyle Q(t)=G\cdot n\cdot(t+T1)$ (4)

Then, the weight of the feeding-materials in the air is $W_{0}(t)=Q(t)-W(t)$ .

At any time $t$ , the distance between the spiral conveyor outlet and the material surface of the hopper is $h^{\prime}(t)=H_{0}-h(t)=H_{0}-k_{p}\cdot W(t)$ , then the specific gravity $B(t)$ at any time $t$ of the feeding-materials in the air is obtained.

$\displaystyle B(t)=\frac{Q(t)-W(t)}{S[H_{0}-k_{p}\cdot W(t)]}$ (5)

According to the law of freely falling body, the instantaneous velocity $V$ of filling-materials from the spiral conveyor outlet to the weighing hopper is,

$\displaystyle V=\sqrt{2g[H_{0}-k\cdot W(t)]}$ (6)

Thus, the mathematical model of dynamic filling-materials weight in unit time can be derived as follows,

$\displaystyle\frac{dW(t)}{dt}=BSV=\frac{Q(t)-W(t)}{S[H_{0}-k_{p}\cdot W(t)]}% \cdot S\cdot\sqrt{2g[H_{0}-k_{p}\cdot W(t)]}=\sqrt{2g}\frac{Gn(t)-W(t)}{\sqrt{% H_{0}-k_{p}\cdot W(t)}}$ (7)

Set $u$ as the input speed of spiral conveyor, the dynamic weighing process is controlled by the input speed $u$ . There is a time lag $\tau$ between $u$ and $W(t)$ , and $\tau$ is determined by $h^{\prime}(t)$ . Therefore, the mathematical model of dynamic feeding-materials weight can be rewritten as follows.

$\displaystyle\frac{dW(t)}{dt}=\sqrt{2g}\frac{G\cdot u(t-\tau)\cdot(t+T1)-W(t)}% {\sqrt{H_{0}-k_{p}\cdot W(t)}}$ (8)

where $t$ is the time of the material falls into the hopper, $G\cdot u(t-\tau)\cdot(t+T1)$ is the conveying capacity of material fed out of the spiral conveyor.

From the mathematical model of dynamic filling-materials weight above, it can be seen that, besides the inherent characteristic parameters of the system, the actual weight $W(t)$ is also a function of the time $t$ and the input speed $u$ of the spiral conveyor. Most parameters are fixed value parameters, such as $D$ , $d$ , $L$ , $\phi$ , $\rho$ , $k_{p}$ , $C$ . These parameters are related to the spiral conveyor itself and the installation conditions. These values above can be obtained by measurements. The conveying efficiency $\eta$ is a random variable, which is determined by many factors, such as the inclination angle of the conveyor, the material characteristics and the humidity of the environment. From these analysis, it is obvious that the weighing model is a time delay, uncertainty and nonlinearity model.

3. Adaptive iterative learning control of weighing process

From the analysis and mathematical modelling in Section 2, it is seen that the CMPBWS is a dynamic and nonlinearity system. The traditional control method is difficult to get the satisfactory result. To improve the control precision and reduce weighing error, the AILCM is proposed.

3.1 Method

The idea of iterative learning control is first proposed by Japanese scholar Uchiyama in 1978, which was made groundbreaking research by Arimoto et al. in 1984 [24]. Arimoto and his collaborators proposed two basic learning laws: the D type learning law and the P type learning law, which were the basis of the iterative learning law. Later, PD type, PID type, higher order learning algorithm and algorithm with forgetting factors were proposed. D type, P type is the most basic learning law. The basic principle of the iterative learning control method is as follows [25, 26]. The dynamic process of the controlled object is shown in Eq. (9).

$\displaystyle\left\{\begin{array}[]{l}x(t)=f[t,x(t),u(t)]\\ y(t)=g[t,x(t),u(t)]\\ \end{array}\right.$ (9)

where, $x(t)\in R^{n-1}$ , $y(t)\in R^{m-1}$ , $u(t)\in R^{l-1}$ are the system state, the output and the input variable of the system respectively, $f[t,x(t),u(t)]$ and $g[t,x(t),u(t)]$ are the vector functions which corresponding dimension structure and the parameters of which are unknown.

In a given time $t\in[0,T]$ , the initial state $x_{k}(0)$ and expected output $y_{d}(t)$ is given, after repeated iterative learning under a certain rule, the input variable $u(t)$ is changed to $u_{k}(t)$ , the expected output $y(t)$ is changed to $y_{k}(t)$ . Therefore, after $k$ iterations, Eq. (9) is changed to Eq. (10).

$\displaystyle\left\{\begin{array}[]{l}x_{k}(t)=f[t,x_{k}(t),u_{k}(t)]\\ y_{k}(t)=g[t,x_{k}(t),u_{k}(t)]\\ \end{array}\right.$ (10)

The tracking error after $k$ iterations is $e_{k}(t)=y_{d}(t)-y_{k}(t)$ . In Iterative learning process, current input variable $u_{k}(t)$ and output error $e_{k}(t)$ is used to construct learning law, then, the below Eq. (11) is obtained.

$\displaystyle u_{k+1}(t)=L[y_{k}(t),e_{k}(t)]$ (11)

Iterative learning control basic structure is shown in Fig. 2. After each iteration, a new input value is calculated and as the input value of the next iteration. New iterative learning control process and correction information is stored in the memory system. After several iterations, tracking error $e_{k}(t)$ is very small and the input variable $u(t)$ is adaptively changed to a new value, and the iteration process is stopped.

Figure 2.

Iterative learning control basic structure.

3.2 Adaptive iterative learning control of weighing process

Iterative learning control (iterated learning control) is an intelligent control method based on quality. The idea comes from a deep understanding of the knowledge of experiential learning. Its basic idea is that through repeated training to improve control input to make control output infinitely approximate expected output.

It is known that the CMPBWS is a nonlinear, time lag and uncertainty mathematical system. To use the intelligent control method of AILCM, the process of weighing needs to do further analysis. The dynamic stage of the weighing process is shown in Fig. 3.

Seen from Fig. 3, to further improve the efficiency, the weighing process is divided into three stages. The three stages are the weighing of the rapid feeding stage, the lower feeding stage, and the prediction feeding stage. With AILCM to control the weighing model, the advance stop value $U$ of spiral conveyor is corrected in real-time with the current actual weight and set weight deviation as the feedback.

In the rapid feeding stage, $u$ is defined as input value, $y$ is output value, representing a spiral conveyor weighing speed and material capacity, respectively. The set weighing value is $R$ . When $y\leqslant w_{1}$ , $u\leqslant u_{\max}$ , the difference between the weight of $y$ and the set weight $R$ is larger, the maximum speed is input to obtain maximum efficiency.

In the lower feeding stage, when $y\geqslant w_{1}$ , the lower speed weighing is input. In order to improve the weighing accuracy, the control speed is reduced in this stage, that is $u=u_{L}$ , $w_{1}\leqslant y\leqslant w_{2}$ .

Figure 3.

The dynamic stage of the batching process. Notes: $R$ is the set weight, $W$ is the output weight.

Figure 4.

Control system Structure.

In the prediction feeding stage, if the continuous adjustment speed is adopted, it will take a long time to reach the set weight $R$ , the weighing efficiency is very low. To improve the weighing accuracy, AILCM is used to control advance stop value $U$ of spiral conveyor. The final weight of feeding-materials is come up with iterative learning control, that is, when $w_{2}\leqslant y<R$ , $u=u_{\textit{con}}$ .

The advance stop value $U$ of spiral conveyor is regarded as control input value to distinguish from the other two stages. The AILCM is used to dynamically modify the advance stop value $U$ . Its initial value is $U_{0}$ , $U_{0}\in(0,R)$ . $U_{0}$ is generally 10% or 15% of $R$ . For each weighing, the spiral conveyor is stopped when the weight reached $R-U_{0}$ . After the remaining material falls into the weighing hopper, a final weighing value $W_{0}$ is obtained, and the error $e_{0}=W_{0}-R$ is generated which is used to generate a new input value $U$ . Therefore, $U_{k}$ is the advance stop value after $k$ times of weighing. $W_{k}$ is the actual weight after $k$ times iteration. The error after $k$ times of weighing is $e_{k}=W_{k}-R$ . The control value of the $k+$ 1 weighing is described by Eq. (12).

$\displaystyle U_{k+1}=U_{k}+g(k)e_{k}=U_{k}+g(k)(W_{k}-R)$ (12)

$g(k)$ is the weighted factor of the $k$ iteration. In the same learning law, the big iteration will make the convergence rate too fast, which may cause the output shock. To optimize the effect of iteration, learning factors $g(k)$ can be selected according to the value of $e_{k}$ under selected range, that is, $0<g(k)\leqslant$ 1.

Figure 5.

Output tracking of delay time 0.5 s (20 iteration results).

Figure 6.

The weight error of iteration learning (20 iteration results).

4. Simulation and discussion

The numerical simulation with MATLAB software is applied in a CMPBWS. The system parameters of the weighing system is $k_{p}=$ 0.001 kg/m, $\rho=$ 0.6 kg/m ${}^{3}$ , $H_{0}=$ 2.5 m, $L=$ 273 mm, $D=$ 273 mm, $d=$ 50 mm, $\phi=$ 0.45, $C=$ 0.65, $\eta=$ 0.9, spiral conveyor outlet diameter is 300 mm, lag time $\tau=$ 0.5 s.

Assuming that 140 Kg is needed for fly ash, spiral conveyor speed $u$ is 100 r/min at the beginning. When the weight is close to 80 kg, the speed is slowly reduced to 60 r/min. When the weight is reached 120 kg, the adaptive iterative learning is applied. The structure of the control system is shown in Fig. 4. In Fig. 4, the module Input is expected input control value, Controller is an adaptive iterative learning controller, and the module Plant is the controlled object. The random interference factors is introduced in the model.

The advanced open loop PD type learning law is used with sampling time $h=$ 0.05 s. To calculate conveniently, the fixed learning factor $L$ is 0.8, $\Gamma$ is 0.4. After the two stages, filling-materials weight has reached 120 kg, the left 20 kg is controlled by the AILCM. At the end of the second stage, feeding speed is maintained at 60 r/min, which is used as the input value of the third stage. The Eq. (12) of iterative learning control algorithm is used, the variable gain learning factor is shown in Eq. (13). The simulation of fixed time delay 0.5 s is obtained. The results are shown in Figs 5 and 6.

$\displaystyle g(k)=\left\{\begin{array}[]{l}0.8,e_{k}\geqslant 2\\ 0.5,0\leqslant e_{k}<2\\ \end{array}\right.$ (13)

Seen from Fig. 5, it is obvious that, at the beginning, the actual output weight in the weighing hopper is higher than the expect value. After 4 iterations, the output weight is closer to the expect weight. After 20 iterations, the actual weight is very close to the expect output weight. Seen from Fig. 6, it is obvious that at the beginning of iterative learning, the weight error is rather big. However, the weight error is much smaller after 20 iterations.

Compared with the traditional method, the adaptive iterative learning can obtain better output values after several iterations.

5. Conclusions

In this paper, the AILCM is proposed to improve weighing accuracy and increase the weighing speed. The mathematical model of weighing progress is established and the CMPBWS is optimized. The weighing process is divided into three stages, which are the rapid feeding stage, the lower feeding stage, and the prediction feeding stage. The weighing speed of each stage is controlled with different ways. The AILCM is used in the prediction feeding stage. The advance stop value is dynamically modified by the AILCM. The numerical simulation with MATLAB software is applied in a CMPBWS. The simulation results show that the actual value is much closer to the set value after several iterations by the AILCM. With the method proposed in the paper, the weighing accuracy and feeding speed of CMPBW are both improved.

Footnotes

Acknowledgments

The authors acknowledge the High Technology Research and Development Program of Hebei Province (16394102D, 17211906D).

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