WO2019205216A1 - 一种基于rbf神经网络预测控制的双进双出球磨机控制系统及控制方法 - Google Patents

一种基于rbf神经网络预测控制的双进双出球磨机控制系统及控制方法 Download PDF

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WO2019205216A1
WO2019205216A1 PCT/CN2018/088157 CN2018088157W WO2019205216A1 WO 2019205216 A1 WO2019205216 A1 WO 2019205216A1 CN 2018088157 W CN2018088157 W CN 2018088157W WO 2019205216 A1 WO2019205216 A1 WO 2019205216A1
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control
double
model
controlled
rbf
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French (fr)
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吕剑虹
索明琛
蔡戎彧
于吉
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东南大学
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B02—CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
    • B02C—CRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
    • B02C17/00—Disintegrating by tumbling mills, i.e. mills having a container charged with the material to be disintegrated with or without special disintegrating members such as pebbles or balls
    • B02C17/18—Details
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B02—CRUSHING, PULVERISING, OR DISINTEGRATING; PREPARATORY TREATMENT OF GRAIN FOR MILLING
    • B02C—CRUSHING, PULVERISING, OR DISINTEGRATING IN GENERAL; MILLING GRAIN
    • B02C25/00—Control arrangements specially adapted for crushing or disintegrating

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  • the invention relates to a thermal energy engineering and automatic control system and method, in particular to a control system and a control method for a double-inlet and double-out ball mill based on RBF neural network predictive control.
  • the double-inlet and double-out ball mill pulverized coal preparation system can use 15% to 25% of the electricity consumption of the plant, and has huge energy-saving potential. Therefore, the optimization of the milling system is studied. Control to improve the operating efficiency of the system is of great significance for energy-saving renovation.
  • the double-inlet and double-out ball mill mechanism is a multivariable and large-lag time-varying nonlinear system. If traditional PID control is used, it will not achieve the desired effect, so we need to explore other better control schemes.
  • the present invention proposes a control system and a control method for a double-inlet and double-out ball mill based on RBF neural network predictive control for the large hysteresis nonlinear characteristic of a double-inlet double-out ball mill mechanism powder system.
  • the present invention provides a dual-input and double-out ball mill control system based on RBF neural network predictive control, the control system including a prediction controller based on an RBF neural network model, a control amount initialization module, and a controlled object,
  • the controlled object is a double-input and double-out ball mill model, and the double-input double-out ball mill model output is continuously discretized to generate discrete controlled quantity, and the discrete controlled quantity and the controlled quantity current set value input control quantity are initialized.
  • the initial value of the control quantity output by the module, the control quantity initialization module, the discrete controlled quantity of the double-input double-out ball mill model output, and the current set value of the controlled quantity are input to the predictive controller, and the predictive controller outputs the discrete control vector via the zero order
  • the retainer is converted to a continuous control output to the double-inlet and double-out ball mill model.
  • said control amount initialization module includes an RBF neural network model for future controlled quantity prediction and an RBF neural network inverse model for control quantity prediction, said prediction controller adopting RBF for future controlled quantity prediction Neural network model.
  • the invention also provides a control method for a double-inlet and double-out ball mill control system based on the above-mentioned RBF neural network predictive control, comprising the following steps:
  • the predictive controller and the control quantity initialization module use the trained RBF neural network forward model RBF for, x and RBF neural network inverse model RBF inv to predict and control the controlled object.
  • the control object model, that is, the double-inlet and double-out ball mill model is:
  • F L is the cold air flow and F H is the hot air flow.
  • C 1 is the specific heat capacity of the primary wind
  • T L is the cold primary wind temperature
  • T H is the hot primary wind temperature
  • T in is the primary air temperature of the grinding inlet
  • B air is the bypass wind flow
  • L air For the load wind flow
  • W air is the primary air flow
  • ⁇ mc is the raw coal moisture
  • Q is the total current consumed by the running coal mill
  • F incoal is the coal supply
  • ⁇ L is the cold damper opening
  • ⁇ H is the hot damper opening.
  • T out is the grinding outlet temperature
  • F outcoal is the grinding outlet pulverized coal flow rate
  • the parameter to be identified of the double-input and double-out ball mill model is obtained by a prediction error minimization method, and the weighted prediction error norm is used as an objective function, and the formula is as follows:
  • K 1 is the number of data sample groups input and output of the double-input double-out ball mill model
  • K 2 is the number of output variables
  • e i (t) is the i-th controlled quantity at the t-th time of the double-input double-out ball mill model.
  • N i 1, 2, L, 14
  • the RBF neural network is composed of three layers of input, hidden and output, and the hidden layer includes L nodes, and the input layer of the RBF neural network forward model RBF for, x takes the discrete control quantity as an input.
  • the variables are assigned to L hidden layer nodes, all hidden layer nodes corresponding to the center vector representing the RBF center in the input space, and the input variable ⁇ l (v k ) of the lth hidden node corresponds to the kth control amount v k and hidden
  • the Euclidean distance between the node center vectors c l is composed of three layers of input, hidden and output, and the hidden layer includes L nodes, and the input layer of the RBF neural network forward model RBF for, x takes the discrete control quantity as an input.
  • the variables are assigned to L hidden layer nodes, all hidden layer nodes corresponding to the center vector representing the RBF center in the input space, and the input variable ⁇ l (v k ) of the lth hidden node corresponds to the
  • v i,k represents the value of the i-th component of the k-th control quantity
  • c i,l represents the value of the i-th component of the center vector of the lth hidden layer node
  • K is the input and output training sample used
  • the number, that is, the combination of the control amount and the controlled quantity of the double-inlet and double-out ball mill model, the activation function used here is a Gaussian function, which produces the output of each hidden node:
  • ⁇ l is the width of the Gaussian function of the lth hidden node, calculated by the P-nearest neighbor algorithm;
  • the response x(k) of the network output layer corresponding to the kth input is a weighted linear combination of the output of the hidden layer node :
  • x(k) is the response of the network output layer corresponding to the kth input, ie the kth controlled quantity
  • W is the L ⁇ M weight matrix
  • g k [g( ⁇ 1 ), g( ⁇ 2 ), L
  • g( ⁇ L )] is the output line vector of the L hidden layer nodes of the kth input
  • the fuzzy mean algorithm is used to calculate the number of hidden layer nodes and the position center c l , using standard linear regression to solve the right Value matrix W, establishes the system's discrete dynamic RBF forward model RBF for , x ;
  • the neural network input layer takes the discrete controlled quantity as the input variable, and the network output layer responds to v k .
  • the prediction controller formulates an optimization problem at each discrete time point k, and obtains a control quantity v that drives the controlled quantity to the set value of the corresponding controlled quantity by solving the performance index function ( k);
  • the performance indicator function consists of two parts, one part is the model prediction output value The minimization of the difference from the set value ⁇ (k), and the other part is the minimization of the control movement within the control range:
  • ⁇ and ⁇ are error and motion suppression coefficients
  • h c and h p are control range and prediction range
  • E(k) is the modeling error, that is, the difference between the current output and the predicted output of the previous moment:
  • the modeling error is considered to be the same throughout the prediction range, and the control amount is limited by the defined lower limit v min and upper limit v max over the entire control range:
  • v deltabound is a set threshold
  • the discrete control quantity generated by the prediction controller can be converted into a continuous control quantity output to the controlled object by the zero-order holder, and the continuous control quantity is:
  • v(t) v(kT), kT ⁇ t ⁇ (k+1)T;
  • T is the sampling period
  • the control quantity initialization module uses the RBF neural network inverse model RBF inv to solve the initial value of the control quantity by recursive relationship, and transmits the initial value of the control quantity to the predictive controller, RBF nerve
  • the input of the network inverse model RBF inv is the controlled quantity x(k), and the output is the control quantity v(k).
  • the model associates the current controlled quantity set value ⁇ (k) with the current controlled quantity x(k) to Current control amount v(k):
  • v(k) RBF inv (x(k), ⁇ (k));
  • control amount initialization process is as follows:
  • x(k) [x 1 (k), x 2 (k), L, x N (k)]: the current state vector of the system, ie the controlled quantity;
  • ⁇ (k) the controlled amount set value
  • h c the size of the prediction control range
  • the control quantity initial value V init (k) is transmitted to the predictive controller, and the predictive controller is calculated to solve the performance index function, and the control quantity v(k) is transmitted to the controlled object for control at each moment, and then k+ 1 time is the base point for the optimal control amount calculation at the next moment to achieve rolling optimization.
  • a control system for double-input and double-out ball mill based on RBF neural network predictive control of the present invention through predictive control, can effectively control actions in advance, so that the system's milling output can track command changes well and stabilize the milling output. Key parameters to improve the reliability of the operation of the milling system;
  • the control quantity initialization function module proposed by the invention can predict the initial value of the control quantity at the current time, and send the initial value of the control quantity to the initial value of the optimization problem solution, which greatly improves the online optimization of the prediction control. Compared with the traditional optimization method, the time required to solve the optimization problem is greatly reduced, the speed and accuracy of the control system are improved, and the robustness is good.
  • Figure 1 is a schematic view of a control system of the present invention
  • Figure 2 is a schematic view of the control method of the present invention.
  • 3 to 5 are diagrams showing the effect of predictive control according to an embodiment of the present invention.
  • Figure 1 shows a schematic diagram of a dual-inlet and double-out ball mill control system based on RBF neural network predictive control.
  • the predictive controller (MPC controller) is used as a feedback loop controller, and the RBF neural network is used in the control quantity initialization loop.
  • the method performs the calculation of the initial value of the control amount.
  • Predictive control technology can ensure that the controlled system can improve the rapid adjustment of the powder system of the double-inlet and double-out ball milling mechanism under the premise of stability and safety, so that the milling output can track the command changes well and adjust the milling output. In order to maintain the stability of the system, improve the speed and accuracy of the system adjustment.
  • the predictive controller establishes the RBF prediction model by using the historical data of the double-input and double-out ball mill operation through the RBF neural network method; the control quantity initialization model is established by the RBF neural network using the historical data of the double-input and double-out ball mill operation.
  • the control system includes a prediction controller based on the RBF neural network model, a control quantity initialization module, and a controlled object, and the controlled object is a double-inlet and double-out ball mill model, and the double-input double-out ball mill model output is continuously controlled and discrete.
  • the discrete controlled quantity, the discrete controlled quantity and the controlled quantity current set value input control quantity initializing module After the generation, the discrete controlled quantity, the discrete controlled quantity and the controlled quantity current set value input control quantity initializing module, the initial quantity of the control quantity output by the control quantity initializing module, the discrete controlled quantity of the double-input double-out ball mill model output and The current set value of the controlled quantity is input to the predictive controller, and the predictive controller output discrete control vector is converted into a continuous control quantity output by the zero-order retainer to the double-input double-out ball mill model.
  • the control quantity initialization module includes an RBF neural network model and an RBF neural network inverse model for future controlled quantity prediction, and the prediction controller adopts an RBF neural network model for future controlled quantity prediction.
  • the invention establishes a three-input and three-output model for the controlled object (double-inlet and double-out ball mill), and the three inputs are coal supply quantity, cold air door opening degree and hot air door opening degree respectively, and the three outputs are material level and grinding respectively.
  • a control system and predictive control method for double-input and double-out ball mill based on RBF neural network predictive control is proposed for the controlled object.
  • the RBF forward model of double-entry and double-out ball mill is established by RBF neural network algorithm as the predictive control predictive model.
  • the initial value of the control quantity is calculated by using the control quantity initialization module of the forward and reverse models of the RBF neural network of the controlled object, and the initial value of the control quantity is transmitted to the predictive controller (MPC controller), and the online optimization calculation of the predictive control is solved.
  • the RBF neural network predictive controller is designed for the double-inlet and double-out ball mill (controlled object).
  • the controller used in the control system is the predictive controller (MPC controller), which sets the set value of the material level and the grinding outlet respectively.
  • the set value of the temperature and the set value of the pulverized coal flow rate at the grinding outlet and the actual values of the three are sent to the prediction controller and the control quantity initialization module based on the RBF neural network model, and the predictive controller solves the coal supply amount and the cold damper.
  • the optimal control sequence of opening degree and hot damper opening degree, and the control of the current time of the optimal control sequence is applied to the established three-input and three-output model of double-input and double-out ball mill to obtain the material level, the grinding outlet temperature and the grinding outlet pulverized coal.
  • the output of the flow, the same calculation is repeated at the next moment to realize online scrolling optimization predictive control.
  • FIG. 2 is a block diagram showing a control method of a dual-inlet and double-out ball mill control system based on RBF neural network predictive control according to the embodiment.
  • the method detects the control quantity of the controlled object of the double-input double-out ball mill and the data sample of the controlled time history 2000 times as the RBF learning sample, and establishes the RBF neural network forward model RBF for, x and the offline double-out ball mill offline.
  • the inverse model RBF inv is used as a predictive model for the MPC controller (predictive controller) and the control quantity initialization module.
  • the controlled quantity of the current time of the double-input and double-out ball mill is detected and discretized to obtain x(k), which is used together with the current set value ⁇ (k) of the controlled vector as the input of the control quantity initialization module, and is calculated by the control quantity initializing module.
  • the control quantity initial value V init (k), and x(k) and ⁇ (k) are input as the MPC controller, and the discrete control quantity v(k) is obtained by calculation, and the continuous control quantity v(t is obtained by the zero-order holding element. ), passed to the controlled object of the double-inlet and double-out ball mill to achieve control.
  • the controlled object model (double-input and double-out ball mill model) is a three-input three-output model.
  • the three inputs are the coal volume F incoal , the cold damper opening ⁇ L , and the hot damper opening ⁇ H .
  • the mathematical model of the double-input and double-out ball mill is as follows:
  • F L is the cold air flow rate (kg/s) and F H is the hot air flow rate (kg/s).
  • the maximum wind flow (kg/s) for the cold damper The maximum wind flow (kg/s) of the hot damper
  • C 1 is the specific heat capacity of the primary air (J/(kg ⁇ K))
  • T L is the cold primary air temperature (°C)
  • T H is the hot primary air temperature (°C)
  • T in is the primary air temperature (°C) of the grinding inlet
  • B air is the bypass air flow (kg/s)
  • L air is the load air flow (kg/s)
  • W air is the primary air flow (kg/s).
  • ⁇ mc is the raw coal moisture (dimensionless)
  • Q is the total amount of current consumed by the running coal mill (A)
  • F incoal is the coal supply (kg/ s)
  • ⁇ L is the cold damper opening (dimensionless)
  • ⁇ H is the hot damper opening (dimensionless)
  • L coal is the material level (Pa)
  • T out is the grinding outlet temperature (°C)
  • F outcoal is the grinding
  • PEM prediction error minimization method
  • K 1 is the number of data sample groups input and output of the double-input and double-out ball mill model for model parameter identification, which is 2000 in the embodiment
  • K 2 is the number of output variables of the double-input and double-out ball mill model, in this embodiment 3, that is, 3 controlled quantities: material level, temperature, coal powder amount
  • e i (t) is the measured output value x i (t) of the i-th controlled quantity at the tth moment of the double-input double-out ball mill model
  • the predicted output value of the controlled amount of the double-input and double-out ball mill model Difference
  • N i 1, 2, L, 15
  • the control quantity of the controlled object of the double-input double-out ball mill and the data sample of the controlled time history 2000 time are detected as the RBF learning sample, that is, the training sample set.
  • the training sample set includes 2000 sets of training samples, each group corresponding to one moment of input and output, that is, 6 variable values (feed volume F incoal , cold damper opening ⁇ L , hot damper opening ⁇ H , level L coal
  • feed volume F incoal feed volume F incoal , cold damper opening ⁇ L , hot damper opening ⁇ H , level L coal
  • the grinding outlet temperature T out and the grinding outlet pulverized coal flow rate F outcoal are a set of training samples.
  • the prediction model used in the prediction controller is the double-input and double-out ball mill RBF neural network forward model RBF for, x ,
  • RBF neural network consists of three layers of input, hidden and output, the input and output layers are all three nodes, hidden layer Including L nodes, the input layer of the RBF neural network forward model RBF for, x assigns the discrete control quantity of the controlled object model as input variables to L hidden layer nodes, and all hidden layer nodes correspond to the representation input space.
  • the input variable ⁇ l (v k ) of the lth hidden node corresponds to the Euclidean distance between the kth control amount v k and the hidden layer node center vector c l :
  • v i,k represents the value of the i-th component of the k-th control quantity
  • c i,l represents the value of the i-th component of the l-th hidden node center vector
  • K is the number of input and output training samples used.
  • v k [F incoal (k), ⁇ L (k), ⁇ H (k)]
  • the activation function used here is a Gaussian function that produces the output of each hidden layer node:
  • ⁇ l is the width of the Gaussian function of the lth hidden node, which is calculated by the P-nearest neighbor algorithm.
  • the response x(k) of the network output layer corresponding to the kth input is a weighted linear combination of hidden node outputs:
  • x(k) is the response of the network output layer corresponding to the kth input (control amount), ie the kth controlled quantity
  • W is the L ⁇ M weight matrix
  • g k [g( ⁇ 1 ) , g( ⁇ 2 ), L, g( ⁇ L )] are output line vectors for the L hidden layer nodes of the kth input.
  • the fuzzy mean (FM) algorithm is used to calculate the number of hidden nodes (58) and the position center c l , and the weighted matrix W is solved by standard linear regression to establish the system's discrete dynamic RBF forward model RBF for, x .
  • the neural network input layer takes the discrete controlled quantity as the input variable, and the network output layer responds to v k .
  • the steps are consistent with the RBF neural network forward model RBF for, x .
  • the predictive controller and the control quantity initialization module use the trained RBF neural network forward model RBF for, x and RBF neural network inverse model RBF inv to predict and control the controlled object;
  • the predictive controller formulates an optimization problem at each discrete time point k, and obtains a control amount that drives the controlled quantity to the corresponding set value by solving the performance index function.
  • the performance indicator function consists of two parts, one is the minimization of the difference between the model's predicted output value and the set value ⁇ (k), and the other is the minimization of the control movement within the control range:
  • ⁇ and ⁇ are error and motion suppression coefficients
  • h c and h p are control range and prediction range
  • E(k) is the modeling error, that is, the difference between the current controlled output and the predicted output of the last time controlled:
  • the modeling errors are considered to be the same throughout the prediction range.
  • the control amount is limited by the defined lower limit v min and upper limit v max over the entire control range:
  • v deltabound is set by the operator using the experience value according to the specific situation.
  • the discrete control quantity generated by the predictive controller can be converted into a continuous control quantity output to the controlled object by the zero-order holding element, and the continuous control quantity is:
  • T is the sampling period
  • the following control quantity initialization module based on the RBF neural network forward model and the inverse model is used to solve the initial value of the control quantity by recursive relationship, and the initial value of the control quantity is transmitted to the predictive controller.
  • the discrete dynamic RBF inverse model of double-input and double-out ball mill is solved by the above RBF neural network method, which is expressed as RBF inv , whose input is the controlled quantity x(k) of the double-inlet and double-out ball mill model, and the output is controlled by the double-inlet and double-out ball mill model.
  • the quantity v(k) the model associates the current controlled quantity set value ⁇ (k) with the current controlled quantity x(k) to the current control quantity v(k):
  • control amount initialization process is as follows:
  • x(k) [x 1 (k), x 2 (k), L, x N (k)]: the current state vector of the system, ie the controlled quantity;
  • ⁇ (k) the controlled amount set value
  • h c predicts the size of the control range, that is, the jurisdiction of the predictive control, and calculates the next few time steps.
  • the control quantity initial value V init (k) is transmitted to the predictive controller, and the predictive controller is calculated to solve the performance index function, and the control quantity v(k) is transmitted to the controlled object for control at each moment, and then k+ 1 time is the base point for the optimal control amount calculation at the next moment to achieve rolling optimization.
  • the controlled quantity curve using the predictive control scheme of the present invention is shown in FIGS. 3 to 5.
  • the above simulation test shows that the double-inlet and double-out ball mill control system based on the RBF neural network predictive control of the present embodiment can effectively solve the problem of large lag of the milling output, the material level, the grinding outlet temperature and the grinding outlet of the double-input and double-out ball mill.
  • the pulverized coal flow rate can quickly respond to the set value change, the overshoot is small, the stability is good, and it is maintained within the safe operating range. The economy and safety of the double-inlet and double-out ball mill operation are guaranteed.

Abstract

一种基于RBF神经网络预测控制的双进双出球磨机控制系统及控制方法，控制系统包括基于RBF神经网络模型的预测控制器、控制量初始化模块以及被控对象，被控对象为双进双出球磨机模型，其输出连续被控量经离散化后生成的离散被控量和被控量当前设定值输入控制量初始化模块和预测控制器，控制量初始化模块输出控制量初始值输入给预测控制器，预测控制器输出离散控制向量经零阶保持器转换为连续控制量输出给双进双出球磨机模型。控制方法采用RBF神经网络正向模型和RBF神经网络逆向模型实现对被控对象的预测控制。该方法可以对系统进行提前控制和调节，适用于大滞后系统的控制，被控量响应快、超调量小，同时具有良好的鲁棒性。

Description

一种基于RBF神经网络预测控制的双进双出球磨机控制系统及控制方法 技术领域
本发明涉及热能动力工程及自动控制系统和方法，特别是涉及一种基于RBF神经网络预测控制的双进双出球磨机控制系统及控制方法。
背景技术
随着对火电机组节能改造工程的推进，降低煤耗以及减少厂用电当下已经成为节能方向的热门研究课题。作为常见电厂大型重要组成系统之一的双进双出球磨机煤粉制备系统，其用电量可以达到厂用电的15％～25％，有巨大的节能潜力，因此通过研究制粉系统的优化控制从而提高系统的运行效率对于节能改造具有重要意义。双进双出球磨机制粉系统是一个多变量大滞后时变非线性系统，若采用传统PID控制，达不到理想的效果，因此需要我们探索其他更好的控制方案。
发明内容
发明目的：本发明针对双进双出球磨机制粉系统的大滞后非线性特性提出了一种基于RBF神经网络预测控制的双进双出球磨机控制系统及控制方法。
技术方案：本发明提供了一种基于RBF神经网络预测控制的双进双出球磨机控制系统，所述控制系统包括基于RBF神经网络模型的预测控制器、控制量初始化模块以及被控对象，所述被控对象为双进双出球磨机模型，所述双进双出球磨机模型输出连续被控量经离散化后生成离散被控量，离散被控量和被控量当前设定值输入控制量初始化模块，控制量初始化模块输出的控制量初始值、双进双出球磨机模型输出的离散被控量和被控量当前设定值均输入给预测控制器，预测控制器输出离散控制向量经零阶保持器转换为连续控制量输出给双进双出球磨机模型。
优选的，所述控制量初始化模块包括用于未来被控量预测的RBF神经网络模型和用于控制量预测的RBF神经网络逆模型，所述预测控制器采用用于未来被控量预测的RBF神经网络模型。
本发明还提供了一种基于上述RBF神经网络预测控制的双进双出球磨机控制系统的控制方法，包括以下步骤：
(1)建立被控对象模型，即双进双出球磨机模型；
(2)检测被控对象的控制量及被控量M个历史时刻值作为训练样本集；
(3)采用训练样本集分别训练RBF神经网络正向模型RBF for,x和RBF神经网络逆向模型RBF inv；
(4)预测控制器和控制量初始化模块采用训练得到的RBF神经网络正向模型RBF for,x和RBF神经网络逆向模型RBF inv对被控对象进行预测控制。
进一步的，所述步骤(1)中被控对象的控制量为v＝[F incoal,μ L,μ H]，被控量为x＝[L coal,T out,F outcoal]，建立的被控对象模型，即双进双出球磨机模型为：
Figure PCTCN2018088157-appb-000001
其中，F L为冷风流量，F H为热风流量，
Figure PCTCN2018088157-appb-000002
为冷风门最大风流量，
Figure PCTCN2018088157-appb-000003
为热风门最大风流量，C 1为一次风的比热容，T L为冷一次风温度，T H为热一次风温度,T in为磨入口一次风温度，B air为旁路风流量，L air为负荷风流量，W air为一次风流量，
Figure PCTCN2018088157-appb-000004
为磨煤机内部水分的蒸发量，θ mc为原煤水分，Q为运行磨煤机所消耗的电流总量，F incoal为给煤量，μ L为冷风门开度，μ H为热风门开度，
Figure PCTCN2018088157-appb-000005
为料位，T out为磨出口温度，F outcoal为磨出口煤粉流量，N i是双进双出球磨机模型的待辨识参数，i＝1,2,L,15；被控对象的控制量为μ H。
更进一步的，所述双进双出球磨机模型的待辨识参数是通过预测误差最小化方法来辨识获得的，该方法以加权的预测误差范数作为目标函数，公式如下：
Figure PCTCN2018088157-appb-000006
其中，K 1为双进双出球磨机模型输入输出的数据样本组数，K 2为输出变量个数，e i(t)是双进双出球磨机模型第t个时刻第i个被控量的实测输出值x i(t)和双进双出球磨机模型被控量的预测输出值
Figure PCTCN2018088157-appb-000007
之差：
Figure PCTCN2018088157-appb-000008
求解N i(i＝1,2,L,14)需要满足的约束条件是：
e≤1。
进一步的，所述步骤(3)中RBF神经网络由输入、隐藏和输出三层组成，隐藏层包含了L个节点，RBF神经网络正向模型RBF for,x的输入层将离散控制量作为输入变量分配给L个隐藏层节点，所有隐藏层节点对应于表示输入空间中RBF中心的中心向量，第l个隐藏节点的输入变量μ l(v k)对应于第k个控制量v k和隐藏节点中心向量c l之间的欧几里得距离：
Figure PCTCN2018088157-appb-000009
其中，v i,k表示与第k个控制量中第i个分量的值，c i,l表示第l个隐层节点中心向量中第i个分量的值，K为采用的输入输出训练样本数，即双进双出球磨机模型的控制量和被控量的组合数，这里采用的激活函数是高斯函数，产生每个隐藏节点的输出：
Figure PCTCN2018088157-appb-000010
其中，σ l是第l个隐藏节点的高斯函数的宽度，通过P-最近邻居算法计算得到；对应于第k个输入的网络输出层的响应x(k)是隐藏层节点输出的加权线性组合：
x(k)＝g kgW；
其中，x(k)为对应于第k个输入的网络输出层的响应，即第k个被控量，W是L×M权值矩阵，g k＝[g(μ 1),g(μ 2),L,g(μ L)]是关于第k个输入的L个隐藏层节点的输出行向 量，采用模糊均值算法计算隐藏层节点的数量和位置中心c l，采用标准线性回归求解权值矩阵W，建立系统的离散动态RBF正向模型RBF for, x；
通过建立的双进双出球磨机离散动态正向模型RBF for, x，被控量的下一个预测值 表示为当前被控量x(k)和控制量v(k)的函数：
Figure PCTCN2018088157-appb-000012
训练RBF神经网络逆向模型RBF inv时，神经网络输入层将离散被控量作为输入变量，网络输出层的响应为v k。
进一步的，所述步骤(4)中预测控制器在每个离散时间点k处制定优化问题，通过求解性能指标函数得到将被控量驱动到相应被控量的设定值的控制量v(k)；性能指标函数由两部分组成，一部分是模型预测输出值
Figure PCTCN2018088157-appb-000013
与设定值ω(k)之差的最小化，另一部分是控制范围内控制移动的最小化：
Figure PCTCN2018088157-appb-000014
其中，Θ和Ω是误差和移动抑制系数，h c和h p是控制范围和预测范围，Δv＝v(k+i)-v(k+i-1)是两个后续控制动作之差；最小化问题通过一系列约束来描述，约束如下：
Figure PCTCN2018088157-appb-000015
其中，E(k)为建模误差，即当前输出与上一时刻预测输出的差：
E(k)＝x(k)-RBF for,x(x(k-1),v(k-1))；
在整个预测范围内，认为建模误差是相同的，在整个控制范围内，控制量受定义的下限值v min和上限v max的限制：
v min≤v(k+i)≤v max,1≤i≤h c；
对于两个连续控制量的值，有如下约束：
|v(k+i)-v(k+i-1)|≤v deltabound；
其中，v deltabound为设定阈值；
控制时域的最后控制量保持不变直到预测时域结束：
Δv(k+i)＝0,h c+1≤i≤h p；
预测控制器产生的离散控制量可以通过零阶保持器转换为连续控制量输出给被控对象，该连续控制量为：
v(t)＝v(kT),kT≤t＜(k+1)T；
其中，T是采样周期。
更进一步的，为求解性能指标函数最优解，控制量初始化模块采用RBF神经网络逆向模型RBF inv，通过递推关系求解控制量初始值，并将控制量初始值传送给预测控制器，RBF神经网络逆向模型RBF inv的输入为被控量x(k)，输出为控制量v(k)，该模型将当前被控量设定值ω(k)和当前被控量x(k)关联到当前控制量v(k)：
v(k)＝RBF inv(x(k),ω(k))；
控制量初始化过程如下所示：
输入：
x(k)＝[x 1(k),x 2(k),L,x N(k)]：系统当前状态向量，即被控量；
ω(k)：被控量设定值；
h c：预测控制范围大小；
输出：
Figure PCTCN2018088157-appb-000016
控制量初始值；
(1)当i＝1:h c执行以下操作；
(2)设置
Figure PCTCN2018088157-appb-000017
(3)将
Figure PCTCN2018088157-appb-000018
和ω(k)反馈给逆向模型RBF inv，求解在一个采样周期内驱动被控对象输出变为被控量设定值ω(k)的控制量预测值
Figure PCTCN2018088157-appb-000019
(4)设置
Figure PCTCN2018088157-appb-000020
(5)将
Figure PCTCN2018088157-appb-000021
和
Figure PCTCN2018088157-appb-000022
反馈给正向模型RBF for,x，预测系统未来状态
Figure PCTCN2018088157-appb-000023
即系统被控量预测值；
(6)若i＜h c，返回步骤(2)继续执行；若i＝h c，则结束；
将控制量初始值V init(k)传送给预测控制器，预测控制器经计算求解性能指标函数，在每一个时刻将控制量v(k)传送给被控对象实施控制作用，再以k+1时刻为基点进行下一时刻的最优控制量计算，实现滚动优化。
有益效果：与现有技术相比，本发明具有以下优点：
(1)本发明的一种基于RBF神经网络预测控制的双进双出球磨机控制系统，通过预测控制，可以有效地提前控制动作，使得系统制粉出力能够良好地跟踪指令变化，稳定制粉出力的关键参数，提高制粉系统运行的可靠性；
(2)本发明提出的控制量初始化功能模块可以预测求解当前时刻的控制量初始值，并将控制量初始值送入预测控制器作为优化问题求解的初始值，极大提升了预测控制在线优化速度，与传统优化求解方法相比，解决优化问题所需时间大大减少，提升了控制系统的快速性与准确性，同时具有良好的鲁棒性。
附图说明
图1是本发明的控制系统示意图；
图2是本发明的控制方法示意图；
图3～图5为本发明实施例预测控制效果图。
具体实施方式
下面结合附图和具体实施例对本发明的技术方案进行详细的说明。
如图1所示为一种基于RBF神经网络预测控制的双进双出球磨机控制系统示意图，预测控制器(MPC控制器)用作反馈回路的控制器，在控制量初始化回路中采用RBF神经网络方法进行控制量初始值计算。通过预测控制技术能够保证被控系统在稳定性和安全性的前提下，提升双进双出球磨机制粉系统调节的快速性，使制粉出力良好地跟踪指令变化，并在制粉出力调节过程中，保持系统的稳定性，提高系统调节速度和准确性。预测控制器通过RBF神经网络方法利用双进双出球磨机运行的历史数据建立RBF预测模型；通过RBF神经网络利用双进双出球磨机运行的历史数据建立控制量初始化模型。 具体为：该控制系统包括基于RBF神经网络模型的预测控制器、控制量初始化模块以及被控对象，被控对象为双进双出球磨机模型，双进双出球磨机模型输出连续被控量经离散化后生成离散被控量，离散被控量和被控量当前设定值输入控制量初始化模块，控制量初始化模块输出的控制量初始值、双进双出球磨机模型输出的离散被控量和被控量当前设定值均输入给预测控制器，预测控制器输出离散控制向量经零阶保持器转换为连续控制量输出给双进双出球磨机模型。控制量初始化模块包括用于未来被控量预测的RBF神经网络模型和RBF神经网络逆模型，预测控制器采用用于未来被控量预测的RBF神经网络模型。
本发明针对被控对象(双进双出球磨机)建立了一个三输入三输出模型，三个输入分别是给煤量、冷风门开度、热风门开度，三个输出分别是料位、磨出口温度及磨出口煤粉流量。针对该被控对象提出了一种基于RBF神经网络预测控制的双进双出球磨机控制系统及预测控制方法，采用RBF神经网络算法建立双进双出球磨机的RBF正向模型作为预测控制的预测模型，通过采用了被控对象RBF神经网络正向及逆向模型的控制量初始化模块计算控制量初始值，并将控制量初始值传送给预测控制器(MPC控制器)，解决了预测控制在线优化计算负担大的问题。针对双进双出球磨机(被控对象)进行基于RBF神经网络预测控制器设计，该控制系统所采用的控制器为预测控制器(MPC控制器)，分别将料位的设定值、磨出口温度的设定值和磨出口煤粉流量的设定值以及三者的实际值送入到基于RBF神经网络模型的预测控制器与控制量初始化模块，预测控制器求解得到给煤量、冷风门开度及热风门开度的最优控制序列，并取最优控制序列当前时刻的控制作用于建立的双进双出球磨机三输入三输出模型，得到料位、磨出口温度及磨出口煤粉流量的输出，下一个时刻重复同样计算，实现在线滚动优化预测控制。
如图2所示为本实施例的一种基于RBF神经网络预测控制的双进双出球磨机控制系统的控制方法框图。该方法通过检测双进双出球磨机被控对象的控制量及被控量历史2000个时刻的数据样本作为RBF学习样本，建立双进双出球磨机离线的RBF神经网络正向模型RBF for,x及逆向模型RBF inv，并作为MPC控制器(预测控制器)及控制量初始化模块的预测模型。检测双进双出球磨机当前时刻的被控量并离散化得到x(k)，与被控向量当前设定值ω(k)共同作为控制量初始化模块的输入，经控制量初始化模块计算求解得到控制量初始值V init(k)，与x(k)及ω(k)作为MPC控制器输入，经计算求解得到离 散控制量v(k),经零阶保持元件得到连续控制量v(t),传递给双进双出球磨机被控对象实现控制作用。
具体包括以下步骤：
(1)建立被控对象模型，即双进双出球磨机模型；
被控对象模型(双进双出球磨机模型)为一三输入三输出模型，三个输入分别是给煤量F incoal、冷风门开度μ L、热风门开度μ H，三个输出分别是料位L coal、磨出口温度T out、磨出口煤粉流量F outcoal，针对该研究对象，即本例的控制量为v＝[F incoal,μ L,μ H]，被控量为x＝[L coal,T out,F outcoal]。建立的双进双出球磨机数学模型如下：
Figure PCTCN2018088157-appb-000024
其中，F L为冷风流量(kg/s)，F H为热风流量(kg/s)，
Figure PCTCN2018088157-appb-000025
为冷风门最大风流量(kg/s)，
Figure PCTCN2018088157-appb-000026
为热风门最大风流量(kg/s)，C 1为一次风的比热容(J/(kg·K))，T L为冷一次风温度(℃)，T H为热一次风温度(℃)，T in为磨入口一次风温度(℃)，B air为旁路风流量(kg/s)，L air为负荷风流量(kg/s)，W air为一次风流量(kg/s)，
Figure PCTCN2018088157-appb-000027
为磨煤机内部水分的蒸发量(kg/s)，θ mc为原煤水分(无量纲)，Q为运行磨煤机所消耗的电流总量(A)，F incoal为给煤量(kg/s)，μ L为冷风门开度(无量纲)，μ H为热风门开度(无量纲)，L coal为料位(Pa)，T out为磨出口温度(℃)，F outcoal为磨出口煤粉流量(kg/s)，N i是模型的待辨识参数，i＝1,2,…,15。
上述待辨识参数是通过预测误差最小化方法(PEM)来辨识获得的，该方法以加权的预测误差范数作为目标函数，计算公式为：
Figure PCTCN2018088157-appb-000028
其中，K 1为用于模型参数辨识的双进双出球磨机模型输入输出的数据样本组数，本实施例中为2000，K 2为双进双出球磨机模型输出变量个数，本实施例中为3，即3个被控量：料位、温度、煤粉量；e i(t)是双进双出球磨机模型第t个时刻第i个被控量的实测输出值x i(t)和双进双出球磨机模型被控量的预测输出值
Figure PCTCN2018088157-appb-000029
之差：
Figure PCTCN2018088157-appb-000030
这里求解N i(i＝1,2,L,15)需要满足的约束条件是：
e≤1        (4)。
(2)检测被控对象的控制量及被控量N个历史时刻值作为训练样本集；
检测双进双出球磨机被控对象的控制量及被控量历史2000个时刻的数据样本作为RBF学习样本，即训练样本集。该训练样本集包括2000组训练样本，每一组对应一个时刻的输入输出，即6个变量值(给煤量F incoal、冷风门开度μ L、热风门开度μ H，料位L coal、磨出口温度T out、磨出口煤粉流量F outcoal)为一组训练样本。
(3)采用训练样本集分别训练RBF神经网络正向模型RBF for,x和RBF神经网络逆向模型RBF inv；
预测控制器中所采用的预测模型为双进双出球磨机RBF神经网络正向模型RBF for,x，RBF神经网络由输入、隐藏和输出三层组成，输入输出层均为3个节点，隐藏层包含了L个节点，RBF神经网络正向模型RBF for,x的输入层将被控对象模型的离散控制量作为输入变量的数据分配给L个隐藏层节点，所有隐藏层节点对应于表示输入空间中RBF中心的中心向量，第l个隐藏节点的输入变量μ l(v k)对应于第k个控制量v k和隐藏层节点中心向量c l之间的欧几里得距离：
Figure PCTCN2018088157-appb-000031
其中，v i,k表示与第k个控制量中第i个分量的值，c i,l表示第l个隐藏节点中心向量中第i个分量的值，K为采用的输入输出训练样本数，本实施例中为6000，即采用双进双出球磨机历史运行数据进行RBF神经网络训练样本的组数，每组包含一个时刻的所有输入输出6个量。v k＝[F incoal(k),μ L(k),μ H(k)]，这里采用的激活函数是高斯函数，产生每个隐藏层节点的输出：
Figure PCTCN2018088157-appb-000032
其中，σ l是第l个隐藏节点的高斯函数的宽度，通过P-最近邻居算法计算得到。对应于第k个输入的网络输出层的响应x(k)是隐藏节点输出的加权线性组合：
x(k)＝g kgW        (7)；
其中，x(k)为对应于第k个输入(控制量)的网络输出层的响应，即第k个被控量，W是L×M权值矩阵，g k＝[g(μ 1),g(μ 2),L,g(μ L)]是关于第k个输入的L个隐藏层节点的输出行向量。采用模糊均值(FM)算法计算隐藏节点的数量(58个)和位置中心c l，采用标准线性回归求解权值矩阵W，建立系统的离散动态RBF正向模型RBF for,x。
通过建立的双进双出球磨机离散动态正向RBF模型，被控量的下一个预测值
Figure PCTCN2018088157-appb-000033
表示为当前被控量x(k)和控制量v(k)的函数：
Figure PCTCN2018088157-appb-000034
训练RBF神经网络逆向模型RBF inv时，神经网络输入层将离散被控量作为输入变量，网络输出层的响应为v k。其步骤与RBF神经网络正向模型RBF for,x一致。
(4)预测控制器和控制量初始化模块采用训练得到的RBF神经网络正向模型RBF for,x和RBF神经网络逆向模型RBF inv对被控对象进行预测控制；
预测控制器在每个离散时间点k处制定优化问题，通过求解性能指标函数得到将被控量驱动到相应设定值的控制量。性能指标函数由两部分组成，一部分是模型预测输出 值与设定值ω(k)之差的最小化，另一部分是控制范围内控制移动的最小化：
Figure PCTCN2018088157-appb-000035
其中，Θ和Ω是误差和移动抑制系数，h c和h p是控制范围和预测范围，Δv＝v(k+i)-v(k+i-1)是两个后续控制动作之差；最小化问题通过一系列约束来描述，约束如下：
Figure PCTCN2018088157-appb-000036
其中，E(k)为建模误差，即当前被控量输出与上一时刻被控量预测输出的差：
E(k)＝x(k)-RBF for,x(x(k-1),v(k-1))       (11)；
在整个预测范围内，认为建模误差是相同的。在整个控制范围内，控制量受定义的下限值v min和上限v max的限制：
v min≤v(k+i)≤v max,1≤i≤h c    (12)；
对于两个连续控制量的值，有如下约束：
|v(k+i)-v(k+i-1)|≤v deltabound  (13)；
其中，v deltabound由操作人员利用经验值根据具体情况进行设定。
控制时域的最后控制量保持不变直到预测时域结束：
Δv(k+i)＝0,h c+1≤i≤h p  (14)；
预测控制器产生的离散控制量可以通过零阶保持元件转换为连续控制量输出给被控对象，该连续控制量为：
v(t)＝v(kT),kT≤t＜(k+1)T  (15)；
其中T是采样周期。
为求解性能指标函数最优解，采用以下基于RBF神经网络正向模型及逆向模型的控制量初始化模块，通过递推关系求解控制量初始值，并将控制量初始值传送给预测控制器。双进双出球磨机离散动态RBF逆向模型通过上述RBF神经网络方法求解表示为RBF inv，其输入为双进双出球磨机模型的被控量x(k)，输出为双进双出球磨机模型的控 制量v(k)，该模型将当前被控量设定值ω(k)和当前被控量x(k)关联到当前控制量v(k)：
v(k)＝RBF inv(x(k),ω(k))   (16)；
控制量初始化过程如下所示：
输入：
x(k)＝[x 1(k),x 2(k),L,x N(k)]：系统当前状态向量，即被控量；
ω(k)：被控量设定值；
h c：预测控制范围大小，即预测控制的管辖范围，对未来几个时间步骤进行计算。
输出：
Figure PCTCN2018088157-appb-000037
：控制量初始值；
(1)当i＝1:h c执行以下操作；
(2)设置
Figure PCTCN2018088157-appb-000038
(3)将
Figure PCTCN2018088157-appb-000039
和ω(k)反馈给逆向模型RBF inv，求解在一个采样周期内驱动被控对象输出变为被控量设定值ω(k)的控制量预测值
Figure PCTCN2018088157-appb-000040
(4)设置
Figure PCTCN2018088157-appb-000041
(5)将
Figure PCTCN2018088157-appb-000042
和
Figure PCTCN2018088157-appb-000043
反馈给正向模型RBF for,x，预测系统未来状态
Figure PCTCN2018088157-appb-000044
即系统被控量预测值；
(6)若i＜h c，返回步骤(2)继续执行；若i＝h c，则结束；
将控制量初始值V init(k)传送给预测控制器，预测控制器经计算求解性能指标函数，在每一个时刻将控制量v(k)传送给被控对象实施控制作用，再以k+1时刻为基点进行下一时刻的最优控制量计算，实现滚动优化。
下面以某电厂600MW超(超)临界机组建立的双进双出球磨机制粉系统为例，采用 本发明改进的预测控制系统，详细说明本发明内容。双进双出球磨机模型参数辨识结果如表1所示，预测控制器参数设置如表2所示。
表1 辨识得到的模型参数
Figure PCTCN2018088157-appb-000045
表2 预测控制器参数设置
Figure PCTCN2018088157-appb-000046
仿真试验中磨煤机制粉出力的控制指令先在T＝50s由F outcoal＝14kg/s，L coal＝557.28Pa，T out＝94.5℃，调至F outcoal＝15kg/s，L coal＝580Pa，T out＝95℃，然后在T＝1000s由F outcoal＝15kg/s，L coal＝580Pa，T out＝95℃，调至F outcoal＝13kg/s，L coal＝550Pa，T out＝90℃。采用本发明的预测控制方案的被控量曲线如图3～图5所示。
由控制曲线图可以看出，双进双出球磨机仿真模型的制粉出力跟踪控制指令展现了良好的快速性及准确性，并且具有良好的鲁棒性。
以上仿真试验表明：本实施例的基于RBF神经网络预测控制的双进双出球磨机控制系统，能有效解决制粉出力大滞后的问题，双进双出球磨机的料位、磨出口温度及磨出口煤粉流量都能快速地响应设定值变化，超调小，稳定性好，并且维持在安全运行范围内，双进双出球磨机运行的经济性和安全性均得到保障。

Claims (8)

  1. 一种基于RBF神经网络预测控制的双进双出球磨机控制系统，其特征在于：所述控制系统包括基于RBF神经网络模型的预测控制器、控制量初始化模块以及被控对象，所述被控对象为双进双出球磨机模型，所述双进双出球磨机模型输出连续被控量经离散化后生成离散被控量，离散被控量和被控量当前设定值输入控制量初始化模块，控制量初始化模块输出的控制量初始值、双进双出球磨机模型输出的离散被控量和被控量当前设定值均输入给预测控制器，预测控制器输出离散控制向量经零阶保持器转换为连续控制量输出给双进双出球磨机模型。
  2. 根据权利要求1所述的一种基于RBF神经网络预测控制的双进双出球磨机控制系统，其特征在于：所述控制量初始化模块包括用于未来被控量预测的RBF神经网络模型和用于控制量预测的RBF神经网络逆模型，所述预测控制器采用用于未来被控量预测的RBF神经网络模型。
  3. 一种基于权利要求1-2任一项所述的基于RBF神经网络预测控制的双进双出球磨机控制系统的控制方法，其特征在于，包括以下步骤：
    (1)建立被控对象模型，即双进双出球磨机模型；
    (2)检测被控对象的控制量及被控量M个历史时刻值作为训练样本集；
    (3)采用训练样本集分别训练RBF神经网络正向模型RBF for,x和RBF神经网络逆向模型RBF inv；
    (4)预测控制器和控制量初始化模块采用训练得到的RBF神经网络正向模型RBF for,x和RBF神经网络逆向模型RBF inv对被控对象进行预测控制。
  4. 根据权利要求3所述的一种基于RBF神经网络预测控制的双进双出球磨机控制系统的控制方法，其特征在于，所述步骤(1)中被控对象的控制量为v＝[F incoal,μ L,μ H]，被控量为x＝[L coal,T out,F outcoal]，建立的被控对象模型，即双进双出球磨机模型为：
    Figure PCTCN2018088157-appb-100001
    其中，F L为冷风流量，F H为热风流量，
    Figure PCTCN2018088157-appb-100002
    为冷风门最大风流量，
    Figure PCTCN2018088157-appb-100003
    为热风门最大风流量，C 1为一次风的比热容，T L为冷一次风温度，T H为热一次风温度,T in为磨入口一次风温度，B air为旁路风流量，L air为负荷风流量，W air为一次风流量，
    Figure PCTCN2018088157-appb-100004
    为磨煤机内部水分的蒸发量，θ mc为原煤水分，Q为运行磨煤机所消耗的电流总量，F incoal为给煤量，μ L为冷风门开度，μ H为热风门开度，L coal为料位，T out为磨出口温度，F outcoal为磨出口煤粉流量，N i是双进双出球磨机模型的待辨识参数，i＝1,2,L,15；被控对象的控制量为μ H。
  5. 根据权利要求4所述的一种基于RBF神经网络预测控制的双进双出球磨机控制系统的控制方法，其特征在于，所述双进双出球磨机模型的待辨识参数是通过预测误差最小化方法来辨识获得的，该方法以加权的预测误差范数作为目标函数，公式如下：
    Figure PCTCN2018088157-appb-100005
    其中，K 1为双进双出球磨机模型输入输出的数据样本组数，K 2为输出变量个数，e i(t)是双进双出球磨机模型第t个时刻第i个被控量的实测输出值x i(t)和双进双出球磨机模型被控量的预测输出值
    Figure PCTCN2018088157-appb-100006
    之差：
    Figure PCTCN2018088157-appb-100007
    求解N i(i＝1,2,L,14)需要满足的约束条件是：
    e≤1。
  6. 根据权利要求3所述的一种基于RBF神经网络预测控制的双进双出球磨机控制系统的控制方法，其特征在于，所述步骤(3)中RBF神经网络由输入、隐藏和输出三层组成，隐藏层包含了L个节点，RBF神经网络正向模型RBF for,x的输入层将离散控制量作为输入变量分配给L个隐藏层节点，所有隐藏层节点对应于表示输入空间中RBF中心的中心向量，第l个隐藏节点的输入变量μ l(v k)对应于第k个控制量v k和隐藏节点中心向量c l之间的欧几里得距离：
    Figure PCTCN2018088157-appb-100008
    其中，v i,k表示与第k个控制量中第i个分量的值，c i,l表示第l个隐层节点中心向量中第i个分量的值，K为采用的输入输出训练样本数，即双进双出球磨机模型的控制量和被控量的组合数，这里采用的激活函数是高斯函数，产生每个隐藏节点的输出：
    Figure PCTCN2018088157-appb-100009
    其中，σ l是第l个隐藏节点的高斯函数的宽度，通过P-最近邻居算法计算得到；对应于第k个输入的网络输出层的响应x(k)是隐藏层节点输出的加权线性组合：
    x(k)＝g kgW；
    其中，x(k)为对应于第k个输入的网络输出层的响应，即第k个被控量，W是L×M权值矩阵，g k＝[g(μ 1),g(μ 2),L,g(μ L)]是关于第k个输入的L个隐藏层节点的输出行向量，采用模糊均值算法计算隐藏层节点的数量和位置中心c l，采用标准线性回归求解权值矩阵W，建立系统的离散动态RBF正向模型RBF for,x；
    通过建立的双进双出球磨机离散动态正向模型RBF for,x，被控量的下一个预测值
    Figure PCTCN2018088157-appb-100010
    表示为当前被控量x(k)和控制量v(k)的函数：
    Figure PCTCN2018088157-appb-100011
    训练RBF神经网络逆向模型RBF inv时，神经网络输入层将离散被控量作为输入变量，网络输出层的响应为v k。
  7. 根据权利要求3所述的一种基于RBF神经网络预测控制的双进双出球磨机控制系统的控制方法，其特征在于，所述步骤(4)中预测控制器在每个离散时间点k处制定优化问题，通过求解性能指标函数得到将被控量驱动到相应被控量的设定值的控制量v(k)；性能指标函数由两部分组成，一部分是模型预测输出值
    Figure PCTCN2018088157-appb-100012
    与设定值ω(k)之差的最小化，另一部分是控制范围内控制移动的最小化：
    Figure PCTCN2018088157-appb-100013
    其中，Θ和Ω是误差和移动抑制系数，h c和h p是控制范围和预测范围，Δv＝v(k+i)-v(k+i-)1是两个后续控制动作之差；最小化问题通过一系列约束来描述，约束如下：
    Figure PCTCN2018088157-appb-100014
    其中，E(k)为建模误差，即当前输出与上一时刻预测输出的差：
    E(k)＝x(k)-RBF for,x(x(k-1),v(k-1))；
    在整个预测范围内，认为建模误差是相同的，在整个控制范围内，控制量受定义的下限值v min和上限v max的限制：
    v min≤v(k+i)≤v max,1≤i≤h c；
    对于两个连续控制量的值，有如下约束：
    |v(k+i)-v(k+i-1)|≤v deltabound；
    其中，v deltabound为设定阈值；
    控制时域的最后控制量保持不变直到预测时域结束：
    Δv(k+i)＝0,h c+1≤i≤h p；
    预测控制器产生的离散控制量可以通过零阶保持器转换为连续控制量输出给被控 对象，该连续控制量为：
    v(t)＝v(kT),kT≤t＜(k+1)T；
    其中，T是采样周期。
  8. 根据权利要求7所述的一种基于RBF神经网络预测控制的双进双出球磨机控制系统的控制方法，其特征在于：为求解性能指标函数最优解，控制量初始化模块采用RBF神经网络逆向模型RBF inv，通过递推关系求解控制量初始值，并将控制量初始值传送给预测控制器，RBF神经网络逆向模型RBF inv的输入为被控量x(k)，输出为控制量v(k)，该模型将当前被控量设定值ω(k)和当前被控量x(k)关联到当前控制量v(k)：
    v(k)＝RBF inv(x(k),ω(k))；
    控制量初始化过程如下所示：
    输入：
    x(k)＝[x 1(k),x 2(k),L,x N(k)]：系统当前状态向量，即被控量；
    ω(k)：被控量设定值；
    h c：预测控制范围大小；
    输出：
    Figure PCTCN2018088157-appb-100015
    控制量初始值；
    (1)当i＝1:h c执行以下操作；
    (2)设置
    Figure PCTCN2018088157-appb-100016
    (3)将
    Figure PCTCN2018088157-appb-100017
    和ω(k)反馈给逆向模型RBF inv，求解在一个采样周期内驱动被控对象输出变为被控量设定值ω(k)的控制量预测值
    Figure PCTCN2018088157-appb-100018
    (4)设置
    Figure PCTCN2018088157-appb-100019
    (5)将
    Figure PCTCN2018088157-appb-100020
    和
    Figure PCTCN2018088157-appb-100021
    反馈给正向模型RBF for,x，预测系统未来状态
    Figure PCTCN2018088157-appb-100022
    即系统被控量预测值；
    (6)若i＜h c，返回步骤(2)继续执行；若i＝h c，则结束；
    将控制量初始值V init(k)传送给预测控制器，预测控制器经计算求解性能指标函数，在每一个时刻将控制量v(k)传送给被控对象实施控制作用，再以k+1时刻为基点进行下一时刻的最优控制量计算，实现滚动优化。
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