The direct-fired system with duplex inlet and outlet ball mill has strong hysteresis and nonlinearity. The original control system is difficult to meet the requirements. Model predictive control (MPC) method is designed for delay problems, but, as the most commonly used rolling optimization method, particle swarm optimization (PSO) has the defects of easy to fall into local minimum and non-adjustable parameters. Firstly, a LS-SVM model of mill output is established and is verified by simulation in this paper. Then, a particle similarity function is proposed, and based on this function a parameter adaptive particle swarm optimization algorithm (HPAPSO) is proposed. In this new method, the weights and acceleration coefficients of PSO are dynamically adjusted. It is verified by two common test functions through Matlab software that its convergence speed is faster and convergence accuracy is higher than standard PSO. Finally, this new optimization algorithm is combined with MPC for solving control problem of mill system. The MPC based on HPAPSO (HPAPSO-MPC) algorithms is compared with MPC based on PAPSO (PAPSO-MPC) and PID control method through simulation experiments. The results show that HPAPSO-MPC method is more accurate and can achieve better regulation performance than PAPSO-MPC and PID method.
Direct-fired system with duplex inlet and outlet ball mills is widely used in large thermal power plants because of its strong adaptability of coal and wide range of load regulation. But, due to its complex operation mechanism, a mechanism model is difficult to be established, and, because of its strong hysteresis and nonlinear, the control effect is difficult to meet production needs.
Many scholars have done a lot of researches on the control of ball mills. Aiming at the multivariable system of ball mill, Chen et al. [
Model predictive control (MPC) is designed for the delay system. It does not need the accurate mathematical model of controlled device [
Although MPC has been used in industry for a long time, its optimization algorithm limits its application and has become the subject of many scholars. Genetic algorithm (GA), simulated annealing (SA), and particle swarm optimization (PSO) have been used as optimization algorithms in many applications of MPC [
A variant of PSO algorithm named Comprehensive Learning PSO (CLPSO) was introduced in [
In this paper, the LS-SVM model of duplex inlet and outlet ball mill system is established and verified by experiments. Then, a parametric adaptive particle swarm optimization algorithm based on particle similarity function is proposed and is named HPAPSO. In this method, a particle similarity function is put forward firstly, and based on this function the dynamic adjustment algorithm of weights and acceleration coefficients of particle swarm optimization is presented. This version of PSO has the advantages of more effective exploration of the search space, easier to lead to the global optimum, and more effective in avoiding premature convergence. At last, the HPAPSO method is combined with MPC, named HPAPSO-MPC, and is applied to solve the control problem of duplex inlet and outlet ball mill system.
The system structure of duplex inlet and outlet ball mill system is shown in Figure
Structure of duplex inlet and outlet ball mill system.
It is difficult to establish an accurate mechanism model for duplex inlet and outlet ball mill system because of its characteristics of large lag and strong nonlinearity. Least squares support vector machines (LS-SVM), as an efficient machine learning algorithm, have been used more and more widely in many fields. Its advantages of small sample learning make up for the inferior of unreliable sample information about duplex inlet and outlet ball mill system. Therefore, the LS-SVM model of mill output is adopted as the control model in this paper.
From the front analysis, there are many factors influencing the mill output, mainly as follows: ventilation quantity, hot air door opening, speed of coal feeder, mill current, mill outlet temperature, fineness of pulverized coal, ball load, diameter and proportion of steel ball, coal properties, length of mill, diameter of the cylinder, speed of mill, and so forth. If all the above factors are used as input variables of the model, the learning speed will be seriously affected. Therefore, through the grey relational analysis of the factors, five of them are chosen as input parameters, and they are as follows: hot air door opening, mill current, mill outlet temperature, fineness of pulverized coal, and mill speed [
The radial basis kernel function (RBF) with better generalization ability is selected as follows:
It is very important to select two parameters in the modeling of LS-SVM for pulverizing system; they are regularization parameter
Based on the above selection of input parameters, the LS-SVM model of mill output is established and is shown in Figure
LS-SVM model of mill output in pulverizing system.
In the input layer, mill current is used to represent the coal storage in grinding. There are two measuring points are arranged on both sides of the mill, and the average value of the two points is taken as the level signal. The fineness of pulverized coal is difficult to be measured on-line directly, but it is mainly affected by the quantity of air supply, the amount of coal and the speed of the mill, so it can be represented by these three variables indirectly.
A coal mill pulverizing system of 300 MW units in a power plant was continuously sampled with a sampling period of 5 s. According to the input and output parameters of LS-SVM model, 200 sets of measured data were obtained. There is no direct on-line measurement value of mill output in power plant, so there is no actual value used to compare with the predicted value. Consider that the mill output of direct-fired system is basically equal to the quantity of coal feed under steady condition, and in the field the quantity of coal feed is often used to express the fuel quantity into furnace, that is the mill output. Therefore, under the steady condition, the quantity of coal feed represents the actual value of mill output and is used to verify the model output. The above data are normalized, and the first 100 groups of data are used as training samples, the latter 100 groups are used as test samples. The two parameters of model are selected as follows:
The LS-SVM model established in this paper is compared with the usual neural network model by simulation. The comparisons between the predicted value and the measured value of coal feed are shown in Figures
Statistical analysis of predicted value errors using two models (at 80% rated load).
Maximum absolute error | Mean relative error | Mean square error | |
---|---|---|---|
Neural network model | 1.20 | 0.0237 | 0.3509 |
LS-SVM model | 0.87 | 0.0035 | 0.2748 |
Comparison between actual value and predicted value of neural network model (at 80% rated load).
Comparison between actual value and predicted value of LS-SVM model (at 80% rated load).
The experimental results show the following: the errors between model output and actual value, such as the maximum absolute error, the mean relative error, and the mean square error are all smaller when the model is established by LS-SVM algorithm than by neural network algorithm. Therefore, the model based on LS-SVM algorithm is more reliable.
The basic idea of PSO algorithm is as follows. Each individual is regarded as a particle without volume (or point) in
where
The inertia weight
The acceleration factor
Through the above analysis, we can see that the standard PSO algorithm will be difficult to meet the needs of the control optimization for duplex inlet and outlet ball mill system. So, a parameter adaptive particle swarm optimization algorithm based on particle similarity function (HPAPSO) is proposed in this paper.
The parameters adjustment of PSO will directly affect its optimization performance, and the regulation has a certain rule. They are closely related to population distribution and location of individual particles. Particles are more and more similar in iteration. So, the parameters can be adjusted by the degree of particle similarity. A particle similarity function is proposed in this paper as follows:
where
In the standard PSO algorithm, the weights of all particles are uniformly adjusted without considering the differences between them. If the optimal location has been found in the early stage but was jumped out of the best position because its weight is too large, then the search efficiency will be reduced. For this reason, an improved PSO algorithm is designed to dynamically adjust the inertia weight according to the similarity degree of each particle and the expected particle position. Formula is as follows:
where
For acceleration factors
where
Through the concept of similarity, the inertia weight and the two acceleration factors are adaptively adjusted. That is HPAPSO algorithm improved from PSO, which can effectively balance the global and local search ability and improve the search accuracy of the algorithm.
In order to verify the performance of the improved algorithm, the Matlab software is used, and two common test functions are used to test and verify the algorithm. The convergence rate and average optimal fitness are calculated. The PSO test results are used to compare the superiority of the improved algorithm. The test functions are as follows:
In this case,
Figures
Sphere function optimization results.
Griewank function optimization results.
For the direct-fired system with duplex inlet and outlet ball mill, HPAPSO optimization algorithm is adopted to realize the predictive control of mill output, which can make it to meet the load demand of the unit at any time. The basic structure of control system is shown in Figure
The MPC control structure of direct-fired system.
In nonlinear model predictive control of pulverizing system, HPAPSO optimization algorithm presented in this paper needs to define a particle as follows:
The following objective function (
In (
HPAPSO gives the particles location at each iteration. After obtaining the future input information in (
In order to verify the effect of predictive control system based on HPAPSO algorithm proposed in this paper, the research team set up an experimental platform of direct-fired system with duplex inlet and outlet ball mill. The scene of the experimental platform is shown in Figure
Experimental platform of duplex inlet and outlet ball mill system.
Taking into account the space of experimental site, the installation of various test instruments, and the consumption of pulverized coal in the experiment, the platform is a model designed according to the proportion of 1:10. According to the principle of similarity, the prototype is reduced according to geometric size. The normal temperature air was selected as the cold primary air. The air after heating was adopted as the hot primary and then determines the relevant physical quantities. The specific parameters are shown in Tables
Design parameters list of platform.
Parameters | Value |
---|---|
Scale k | 1/10 |
Main pipe diameter/mm | 90 |
Branch pipe diameter/mm | 70 |
coarse powder separator diameter/mm | 300 |
Maximum flow velocity/m/s | 35 |
Minimum flow velocity/m/s | 18 |
Maximum air quantity/m3/s | 0.135 |
Minimum air quantity/m3/s | 0.069 |
Maximum differential pressure/ |
10.9 |
Main technical parameters of mill.
Parameters | Value |
---|---|
Mill outlet temperature/°C | 60~80 |
Specifications for steel balls/mm | 20/15/10/5 |
Various steel ball proportion/% | 20/30/30/20 |
Mill speed/(r |
20 |
Milling capacity/(t |
5 |
Fineness of pulverized coal |
10 |
Rated current/A | 14.2 |
Power rating/kW | 16 |
The historical data used in this part of the simulation experiment are from the above experimental platform. In order to analyze and compare the control effect more comprehensively, PID control method, MPC based on PAPSO (from [
Through the comparison of experience and simulation, a group of PID parameters with better effect are selected as follows: P = 0.8, I = 0.4, D = 1.1; the parameters value of PAPSO are selected as follows:
In order to compare the control effect, the same parameters HPAPSO with PAPSO algorithm have the same values. The other parameters of HPAPSO are selected as follows: acceleration factors
Figure
Output of PID control system.
Output of PAPSO-MPC.
Output of HPAPSO-MPC.
The comparisons of two control algorithms about mill output are shown in Table
Comparisons of dynamic and static performances of three control methods.
Performance parameter | PID | PAPSO-MPC | HPAPSO-MPC |
---|---|---|---|
Overshoot % | 20.9 | 10.2 | 4 |
Adjustment time/s | 85 | 50 | 30 |
Rise time/s | 45 | 20 | 10 |
Pure delay time/s | 5 | 5 | 0 |
Mean relative error | 0.0620 | 0.0306 | 0.0156 |
Mean square error | 0.1139 | 0.0573 | 0.0390 |
Steady-state error/% | 1.8 | 1.2 | 0.5 |
Per iteration optimization time/s | - | 0.849 | 1.36 |
From Figures
At the same time, it can be seen that each iteration time (1.36s) of HPAPSO-MPC is longer than that of PAPSO-MPC (0.849s). It shows that the above results of HPAPSO-MPC are obtained at the expense of calculation amount and computation time, and they will also increase as the input dimension of the system increases. Nevertheless, as for the large time-delay and strongly nonlinear system of mill, as long as the sampling period (5s) is longer than the time required for each iteration (1.36s), it does not affect the control effect.
The operation mechanism of duplex inlet and outlet ball mill system is complex, it is difficult to establish a mechanism model, and it has strong hysteresis and nonlinearity, so the control effect is difficult to meet the production needs. Firstly, this paper established the LS-SVM model of mill output, and, based on the dynamic adjustment of weights and acceleration coefficients of PSO, proposed a HPAPSO algorithm. Then the new optimization algorithm is combined with MPC for solving control problem of mill system. Through the simulation experiment, we can see that adopting HPAPSO-MPC method is more accurate and can achieve better regulation performance than PID and PAPSO-MPC method. So it can better meet the needs of industrial production.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The authors gratefully acknowledge the financial support of the Natural Science Foundation of Hunan Province of China (Grant no. 2018JJ3552), the Key Laboratory of Renewable Energy Electric-Technology of Hunan Province (Changsha University of Science & Technology) (Grant no. 2018ZNDL001), the Key Laboratory of Renewable Energy Electric-Technology of Hunan Province (Grant no. 2016ZNDL005), the Open Fund of Innovation Platform of Hunan Provincial Education Department of China (Grant no. 17K002), the Natural Science Foundation of China (Grant no. 51706022), and the Natural Science Foundation of Hunan Province of China (Grant no. 15JJ4007).