CN100552574C

CN100552574C - Machine group loading forecast control method based on flow model

Info

Publication number: CN100552574C
Application number: CNB2008101147313A
Authority: CN
Inventors: 刘民; 董明宇; 吴澄
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2008-06-11
Filing date: 2008-06-11
Publication date: 2009-10-21
Anticipated expiration: 2028-06-11
Also published as: CN101334637A

Abstract

A flow model-based load forecasting control method for machine groups, which belongs to the fields of automatic control, information technology and advanced manufacturing, specifically relates to the complex production and manufacturing process with two bottleneck processes and each bottleneck process has multiple groups of machine groups. The predictive control method for the load of each machine group in the subsequent bottleneck process is characterized in that it includes the following steps: timing sampling of the load of the machine group in the subsequent bottleneck process, determining the expected value of the load of the machine group in the subsequent bottleneck process, and determining the load of the machine group in the subsequent bottleneck process d The first-order predictive control model is established and the control parameters of the front-end bottleneck process machine group are obtained. The present invention establishes a load prediction control model for each machine group in the subsequent bottleneck process based on the flow model and an adaptive neuro-fuzzy reasoning system, and takes the minimum sum of the squares of the differences between the actual load and the expected load of each machine group in the subsequent bottleneck process as the optimal control target. The Lagrangian relaxation method gives the task output rate of each machine group in the front bottleneck process to improve production performance.

Description

Flow Model-Based Predictive Control Method for Machine Group Load

技术领域 technical field

本发明属于自动控制、信息技术和先进制造领域。具体涉及一类具有前后两道瓶颈工序且每道瓶颈工序存在多组机器组的复杂生产制造过程中对瓶颈工序各机器组的负载预测控制方法。The invention belongs to the fields of automatic control, information technology and advanced manufacturing. In particular, it relates to a load prediction control method for each machine group in the bottleneck process in a complex manufacturing process with two bottleneck processes before and after and each bottleneck process has multiple sets of machine groups.

背景技术 Background technique

在一类具有前后两道瓶颈工序且每道瓶颈工序存在多组机器组的复杂生产制造过程中，由于在两道瓶颈工序间存在大规模的在制品加工流动现象，若对前道瓶颈工序中机器组任务输出率缺乏有效控制，将使得后道瓶颈工序各机器组负载无法到达期望值，影响了生产性能。因此，在上述生产制造过程中，根据前、后道瓶颈工序内各机器组的加工能力及后道瓶颈工序内各机器组的期望负载，以后道瓶颈工序各机器组实际负载与期望负载差的平方和最小为优化控制目标，确定前道瓶颈工序各机器组中任务输出率，以控制后道瓶颈工序各机器组负载，从而提高生产性能。目前，常规的机器负载控制方法大多为启发式控制方法，如当前后道瓶颈工序中某个机器组负载较大时，则在前道瓶颈工序中减少流向该机器组的任务量，但由于两道瓶颈工序间存在中间非瓶颈工序的加工延迟，而上述启发式预测控制方法缺乏对后道瓶颈工序机器组负载有效的预测机制，因而采用上述方法难以实现对后道瓶颈工序机器组负载的有效控制。In a complex manufacturing process with two bottleneck processes and each bottleneck process has multiple sets of machine groups, due to the large-scale processing flow phenomenon between the two bottleneck processes, if the front bottleneck process The lack of effective control of the task output rate of the machine group will make the load of each machine group in the subsequent bottleneck process unable to reach the expected value, which will affect the production performance. Therefore, in the above manufacturing process, according to the processing capacity of each machine group in the front and rear bottleneck processes and the expected load of each machine group in the subsequent bottleneck process, the difference between the actual load and the expected load of each machine group in the subsequent bottleneck process The minimum sum of squares is the optimal control target, and the task output rate of each machine group in the front bottleneck process is determined to control the load of each machine group in the subsequent bottleneck process, thereby improving production performance. At present, most of the conventional machine load control methods are heuristic control methods. For example, when a certain machine group has a large load in the front and back bottleneck processes, the task flow to the machine group will be reduced in the front bottleneck process. However, due to the two There is a processing delay of the intermediate non-bottleneck process between the bottleneck processes, and the above heuristic predictive control method lacks an effective prediction mechanism for the machine group load of the subsequent bottleneck process, so it is difficult to achieve an effective control of the machine group load of the subsequent bottleneck process by using the above method. control.

发明内容 Contents of the invention

为了解决上述复杂生产制造过程中后道瓶颈工序各机器组负载控制方法的不足，本发明提供一种具有前后两道瓶颈工序且每道瓶颈工序存在多组机器组的复杂生产制造过程中基于流模型的机器组负载预测控制方法(简称为AFFC)。在本发明中，流模型主要用于考察单位时间内各机器组加工和完成的负载量(即生产任务加工时间总和)，由于上述复杂生产过程中两道瓶颈工序间的工序是非瓶颈工序(下文简称为中间工序)，生产任务经过中间工序时其等待时间与加工时间相比小得多(可忽略)，所以从流模型的角度看，生产负载从前道瓶颈工序(下文简称为前道工序)流入中间工序后，仅需经过一定的延迟时间后，即可从中间工序流向后道瓶颈工序(下文简称为后道工序)(如图2所示)。本发明基于流模型建立后道工序机器组负载1阶预测控制模型，在此基础上采用ANFIS(自适应神经模糊推理系统)建立后道工序机器组负载d阶非线性预测控制模型，其输入为当前时刻前道工序任务输出率，输出为d时刻后的后道工序机器组负载，在上述预测控制模型基础上，根据d时刻后的后道工序各机器组负载期望值及前后道工序各机器组加工能力，确定前道工序各机器组的任务输出率，使得后道工序机器组实际负载与期望负载之差的平方和最小，从而提高后道瓶颈工序生产性能。In order to solve the shortcomings of the load control method of each machine group in the subsequent bottleneck process in the above-mentioned complex manufacturing process, the present invention provides a flow-based Model's Fleet Load Forecast Control Method (AFFC for short). In the present invention, the flow model is mainly used to investigate the loads processed and completed by each machine group per unit time (that is, the sum of the processing time of the production task), because the operation between the two bottleneck procedures in the above-mentioned complex production process is a non-bottleneck operation (hereinafter referred to as the intermediate process), when the production task passes through the intermediate process, its waiting time is much smaller than the processing time (negligible), so from the perspective of the flow model, the production load starts from the front bottleneck process (hereinafter referred to as the front process) After flowing into the intermediate process, only after a certain delay time, it can flow from the intermediate process to the subsequent bottleneck process (hereinafter referred to as the subsequent process) (as shown in Figure 2). The present invention establishes the first-order predictive control model of the machine group load in the subsequent process based on the flow model, and uses ANFIS (adaptive neuro-fuzzy inference system) to establish the d-order nonlinear predictive control model of the machine group load in the subsequent process on this basis, and its input is The task output rate of the previous process at the current moment, the output is the load of the machine group of the subsequent process after time d, based on the above predictive control model, according to the expected value of the load of each machine group of the subsequent process after time d and the load of each machine group of the previous and subsequent processes Processing capacity, to determine the task output rate of each machine group in the previous process, so that the sum of the squares of the difference between the actual load and the expected load of the machine group in the subsequent process is minimized, thereby improving the production performance of the bottleneck process in the subsequent process.

基于流模型的机器组负载预测控制方法，其特征在于所述方法是在机器组负载预测控制计算机上依次按以下步骤实现的：The machine group load forecasting control method based on the flow model is characterized in that the method is realized in the following steps sequentially on the machine group load forecasting control computer:

步骤(1)：初始化，设定以下参变量Step (1): Initialize, set the following parameters

采样时间间隔，每隔时间间隔T给出前道工序中各机器组任务输出率，所述机器组由加工能力相似的多台机器组成，而采样时刻则用k表示；Sampling time interval, every time interval T gives the task output rate of each machine group in the previous process, the machine group is composed of multiple machines with similar processing capabilities, and the sampling time is represented by k;

机器组加工能力，是在单位时间内机器组所能完成的加工任务的加工时间总和，前道工序中机器组i的加工能力用u_i表示，i＝1，…，m，用矩阵表示为U＝[u₁，u₂，…，u_m]^T，后道工序中机器组j的加工能力用v_j表示，j＝1，…，n，用矩阵表示为V＝[v₁，v₂，…，v_n]^T，m和n分别为前、后道工序中机器组的数目；The processing capacity of the machine group is the sum of the processing time of the processing tasks that the machine group can complete within a unit of time. The processing capacity of the machine group i in the previous process is represented by u _i , i=1,...,m, expressed as a matrix U=[u ₁ , u ₂ ,..., u _m ] ^T , the processing capacity of the machine group j in the subsequent process is represented by v _j , j=1,..., n, expressed as V=[v ₁ , v ₂ ,...,v _n ] ^T , m and n are the number of machine groups in the previous and subsequent processes respectively;

前道工序机器组任务输出率，前道工序机器组i基于生产工艺约束在k采样时刻加工完成的任务被安排到后道工序由机器组j加工的比例，用c_ij(k)表示，用矩阵表示为：The task output rate of the machine group in the previous process is the ratio of the tasks processed by the machine group i in the previous process at the k sampling time based on the production process constraints to be processed by the machine group j in the subsequent process, expressed by c _ij (k), expressed by The matrix is expressed as:

$C C {((k k))}^{n no \times \times m m} = = {[[{C C}_{11} ((k k)),, {C C}_{22} ((k k)),, . . . . . .,, {C C}_{n no} ((k k))]]}^{T T}$

$= = [[{C C}^{11} ((k k)),, {C C}^{22} ((k k)),, . . . . . .,, {C C}^{m m} ((k k))]]$

$= = [\begin{matrix} {c c}_{1111} ((k k)) & {c c}_{21 twenty one} ((k k)) & . . . . . . & {c c}_{m m 11} ((k k)) \\ {c c}_{1212} ((k k)) & {c c}_{22 twenty two} ((k k)) & . . . . . . & {c c}_{m m 22} ((k k)) \\ . . & . . & . . \\ . . & . . & . . . . . . & . . \\ . . & . . & . . \\ {c c}_{11 n no} ((k k)) & {c c}_{22 n no} ((k k)) & . . . . . . & {c c}_{mn mn} ((k k)) \end{matrix}]$

其中0≤c_ij≤1且 $Σ_{j = 1}^{n} c_{ij} = 1,$ i＝1，…，m；j＝1，…，n；where 0≤c _ij ≤1 and $Σ_{j = 1}^{no} c_{ij} = 1,$ i=1,...,m; j=1,...,n;

机器组负载，工序中某个机器组前等待加工任务的加工时间总和，后道工序机器组j在k时刻的负载表示为y_j(k)，用矩阵表示为Y(k)^n×1＝[y₁(k)，y₂(k)，…，y_n(k)]^T；Machine group load, the sum of the processing time of a certain machine group in the process waiting for processing tasks, the load of the subsequent process machine group j at time k is expressed as y _j (k), expressed as Y(k) ^n×1 = [y ₁ (k), y ₂ (k), ..., y _n (k)] ^T ;

后道工序中机器组j在k时刻的机器负载期望值表示为y_j ^r(k)，用矩阵表示为In the subsequent process, the machine load expectation value of machine group j at time k is expressed as y _j ^r (k), expressed as a matrix

${Y Y}^{r r} {((k k))}^{n no \times \times 11} = = {[[{y the y}_{11}^{r r} ((k k)),, {y the y}_{22}^{r r} ((k k)),, . . . . . . {y the y}_{n no}^{r r} ((k k))]]}^{T T};;$

中间工序的加工延迟时间用d表示，其是指任务从前道工序加工完毕开始，通过中间工序的加工，到达后道工序所用的平均时间单位，含等待时间；The processing delay time of the intermediate process is represented by d, which refers to the average time unit used by the task to reach the subsequent process from the completion of the previous process through the processing of the intermediate process, including the waiting time;

给定的控制周期用T_all表示；The given control period is represented by T _all ;

控制周期T_all内后道工序机器组j的总负载用Load_j表示；The total load of the subsequent process machine group j in the control period T _all is represented by Load _j ;

步骤(2)：用机器组负载信息采集装置采集机器组负载实时信息，机器组负载信息采集装置由PLC采集装置、嵌入式系统采集装置、DCS系统采集装置中的一种或它们的组合构成；Step (2): collect the real-time information of the load information of the machine group with the load information collection device of the machine group, the load information collection device of the machine group is composed of one or a combination of the PLC collection device, the embedded system collection device, and the DCS system collection device;

步骤(3)：所述的机器组负载预测控制计算机从所述采集装置中读取机器组负载实时信息，依次按以下步骤进行机器组负载预测控制：Step (3): The computer load prediction control computer of the machine group reads the real-time information of the machine group load from the acquisition device, and performs the load prediction control of the machine group according to the following steps successively:

步骤(3.1)：按下式确定各采样间隔时间内后道工序各机器组负载期望值y_j ^r(k)，Step (3.1): Determine the expected load value y _j ^r (k) of each machine group in the subsequent process within each sampling interval according to the following formula,

${y the y}_{j j}^{r r} ((k k)) = = \frac{{Load load}_{j j}}{{T T}_{all all} / / T T},, j j = = 11,, . . . . . .,, n no$

步骤(3.2)：按下式建立后道工序机器组负载预测控制问题：Step (3.2): Establish the load forecasting control problem of the machine group in the subsequent process according to the following formula:

$J J ((k k + + d d + + 11)) = = \frac{11}{22} [[Y Y ((k k + + d d + + 11)) - - {Y Y}^{r r} ((k k + + d d + + 11)) {]]}^{T T} \cdot &Center Dot; [[Y Y ((k k + + d d + + 11)) - - {Y Y}^{r r} ((k k + + d d + + 11))]]$

$+ + \frac{11}{22} {Σ Σ}_{i i = = 11}^{m m} {C C}^{i i} {((k k))}^{T T} \cdot \cdot {C C}^{i i} ((k k))$

求控制律C(k)，使得min{J(k+d+1)}，其中对所有i满足ACⁱ(k)＝1，A＝[1，1，…，1]^1×m；Find the control law C(k) such that min{J(k+d+1)}, where AC ⁱ (k)=1 is satisfied for all i, A=[1,1,...,1] ^1×m ;

步骤(3.3)：按下述步骤建立后道工序机器组负载预测控制模型Step (3.3): Follow the steps below to establish the load forecasting control model of the machine group in the subsequent process

步骤(3.3.1)：建立后道工序机器组负载1阶预测控制模型Step (3.3.1): Establish a first-order predictive control model for the machine group load in the subsequent process

y_j(k+1)＝max{y_j(k)-v_jT+[c_1j(k-d)u₁+…+c_mj(k-d)u_m]T，0}y _j (k+1)=max{y _j (k)-v _j T+[c _1j (kd)u ₁ +...+c _mj (kd)u _m ]T, 0}

＝max{y_j(k)-Tv_j+TC_j(k-d)U，0}，j＝1，…，n=max{y _j (k)-Tv _j +TC _j (kd)U, 0}, j=1, . . . , n

步骤(3.3.2)：采用具有L条模糊规则的自适应神经模糊推理系统ANFIS建立后道工序机器组负载d阶预测控制模型Step (3.3.2): Use the adaptive neuro-fuzzy inference system ANFIS with L fuzzy rules to establish a d-order predictive control model for the machine group load in the subsequent process

即：Right now:

$Y Y {((k k + + d d + + 11))}^{n no \times \times 11} = = {X x}^{n no \times \times 11} + + {Σ Σ}_{q q = = 00}^{d d} {N N}_{q q}^{n no \times \times n no} \cdot \cdot [[{C C}^{11} ((k k - - d d + + q q)),, . . . . . .,, {C C}^{m m} ((k k - - d d + + q q)) {]]}^{n no \times \times m m} \cdot \cdot {U u}^{m m \times \times 11}$

$= = {X x}^{n no \times \times 11} + + {Σ Σ}_{q q = = 00}^{d d} {N N}_{q q}^{n no \times \times n no} \cdot &Center Dot; {Σ Σ}_{i i = = 11}^{m m} {u u}_{i i} {C C}^{i i} ((k k - - d d + + q q))$

其中：X^n×1＝[E₁，E₂，…，E_n]^T， $E_{j} = Σ_{l = 1}^{L} h_{l} (k) \cdot [α^{l} (y_{j} (k) - {Tv}_{j}) + β^{l}]$ Where: X ^n×1 = [E ₁ , E ₂ ,..., E _n ] ^T , ${E.}_{j} = Σ_{l = 1}^{L} h_{l} (k) \cdot [α^{l} ({the y}_{j} (k) - {Tv}_{j}) + β^{l}]$

q＝0，1，…，d， $F_{jq} = T \cdot Σ_{l = 1}^{L} h_{l} (k) γ_{q}^{l},$ q=0,1,...,d, $f_{jq} = T \cdot Σ_{l = 1}^{L} h_{l} (k) γ_{q}^{l},$

h_l(k)＝f_l(y_j(k)-Tv_j，TC_j(k-d)U，…，TC_j(k-1)U)是ANFIS输入为y_j(k)-Tv_j，TC_j(k-d)U，…，TC_j(k-1)U时第l条模糊规则的激发值，f_l为模糊规则激发值计算函数，其为第l条模糊规则中ANFIS各输入变量所对应模糊数的隶属度函数的乘积，其中，上述模糊数的隶属度函数采用钟形函数，钟形函数中的参数即为ANFIS中待定的前件参数，而ANFIS中待定的后件参数为α^l，γ₀ ^l，γ₁ ^l，…，γ_d ^l，β^l；h _l (k)=f _l (y _j (k)-Tv _j , TC _j (kd)U, ..., TC _j (k-1)U) is ANFIS input as y _j (k)-Tv _j , TC _j (kd)U,..., TC _j (k-1)U is the excitation value of the l-th fuzzy rule, f _l is the calculation function of the excitation value of the fuzzy rule, which corresponds to each input variable of ANFIS in the l-th fuzzy rule The product of the membership function of fuzzy numbers, wherein, the membership function of the above-mentioned fuzzy numbers adopts a bell-shaped function, and the parameters in the bell-shaped function are the undetermined antecedent parameters in ANFIS, and the undetermined consequent parameters in ANFIS are α ^l ,γ ₀ ^l ,γ ₁ ^l ,…,γ _d ^l ,β ^l ;

步骤(3.3.3)：采用如下步骤确定ANFIS中的前件参数和后件参数；Step (3.3.3): adopt the following steps to determine the antecedent parameters and subsequent parameters in ANFIS;

步骤(3.3.3.1)：对所有j＝1，2，…，n，随机产生C_j(k)的值，并按步骤(3.3.1)所述公式计算y_j(k+1)值，从而产生若干用于训练ANFIS的输入输出训练数据集，其中，输入数据为Y(k)，C(k-d)，…，C(k-1)，输出数据为Y(k+d+1)；Step (3.3.3.1): For all j=1, 2, ..., n, randomly generate the value of C _j (k), and calculate the value of y _j (k+1) according to the formula described in step (3.3.1), Thereby produce some input and output training datasets for training ANFIS, wherein, the input data is Y(k), C(kd),..., C(k-1), and the output data is Y(k+d+1);

步骤(3.3.3.2)：采用步骤(3.3.2.1)生成的训练数据集及ANFIS经典学习算法，确定ANFIS中待定的前件参数和后件参数；Step (3.3.3.2): Using the training data set generated in step (3.3.2.1) and the ANFIS classic learning algorithm, determine the undetermined antecedent parameters and subsequent parameters in ANFIS;

步骤(3.4)：根据步骤(3.3)得到的后道工序机器组负载d阶预测控制模型，采用拉格朗日松弛方法按下式计算最佳控制率C(k)，其中Cⁱ(k)为：Step (3.4): According to the d-order predictive control model of the machine group load in the subsequent process obtained in step (3.3), the Lagrange relaxation method is used to calculate the optimal control rate C(k) according to the following formula, where C ⁱ (k) for:

${C C}^{i i} ((k k)) = = {u u}_{i i} ((\frac{{A A}^{T T} A A}{{AA AAA}^{T T}} - - I I)) \cdot &Center Dot; {[[I I - - (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i}^{22})) · &Center Dot; \overset{&OverBar; &OverBar;}{N N} ((\frac{{A A}^{T T} A A}{{AA AAA}^{T T}} - - I I))]]}^{-1 -1} \cdot &Center Dot; [[\overset{&OverBar; &OverBar;}{X x} + + (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i})) \cdot &Center Dot; \frac{\overset{&OverBar; &OverBar;}{N N} {A A}^{T T}}{{AA AAA}^{T T}}]] + + \frac{{A A}^{T T}}{{AA AAA}^{T T}},,$

其中：I为单位矩阵， $\overset{&OverBar;}{X} = N_{d}^{T} [X + Σ_{q = 0}^{d - 1} (Σ_{i = 1}^{m} u_{i} C^{i} (k - d + q)) - Y^{r} (k + d + 1)],$ $\overset{&OverBar;}{N} = N_{d}^{T} N_{d}$ Among them: I is the identity matrix, $\overset{&OverBar;}{x} = N_{d}^{T} [x + Σ_{q = 0}^{d - 1} (Σ_{i = 1}^{m} u_{i} C^{i} (k - d + q)) - Y^{r} (k + d + 1)],$ $\overset{&OverBar;}{N} = N_{d}^{T} N_{d}$

根据上述基于流模型的机器组负载预测控制方法，本发明做了大量的仿真试验，从仿真结果中可看出，本发明对具有前后两道瓶颈工序且每道瓶颈工序存在多组机器组的复杂生产制造过程后道瓶颈工序机器组负载控制具有很好的效果。According to the above-mentioned machine group load prediction control method based on the flow model, the present invention has done a large number of simulation tests, as can be seen from the simulation results, the present invention has two bottleneck processes before and after and each bottleneck process has multiple sets of machine groups The load control of the bottleneck process machine group in the complex manufacturing process has a very good effect.

附图说明 Description of drawings

图1：机器组负载预测控制硬件系统结构图，图中由机器组负载信息采集装置采集机器组负载实时信息，并传给机器组负载预测控制计算机。ANFIS训练计算机可根据生产历史数据对ANFIS进行训练，得到后道工序机器组负载预测控制模型参数。机器组负载预测控制计算机接收机器组负载预测控制模型参数值和机器组负载实时信息，采用拉格朗日松弛方法，求得前道工序机器组预测控制参数(任务输出率)。Figure 1: The structural diagram of the machine group load prediction control hardware system. In the figure, the machine group load information collection device collects the real-time information of the machine group load and transmits it to the machine group load prediction control computer. The ANFIS training computer can train ANFIS according to the production history data, and obtain the parameters of the load forecasting control model of the machine group in the subsequent process. The machine group load predictive control computer receives the machine group load predictive control model parameter values and the real-time information of the machine group load, and uses the Lagrangian relaxation method to obtain the machine group predictive control parameters (task output rate) of the previous process.

图2：前后道工序内机器组任务流之间的关系示意图，其中m为前道工序的机器组总数；n为后道工序的机器组总数；d为中间工序的平均加工延迟时间。Figure 2: Schematic diagram of the relationship between the machine group task flow in the preceding and following processes, where m is the total number of machine groups in the previous process; n is the total number of machine groups in the subsequent process; d is the average processing delay time in the intermediate process.

图3：预测控制方法的流程图，其中根据设置的采样时间，软件每隔采样时间进行一次机器组负载预测控制，并调整前道工序的机器组任务输出率；同时，随着样本数据的增加，每隔一定时间通过训练ANFIS对机器组负载预测控制模型参数进行修正，使得机器组负载预测控制模型更能体现复杂生产过程现状。Figure 3: The flow chart of the predictive control method, in which, according to the set sampling time, the software performs predictive control of the load of the machine group every sampling time, and adjusts the task output rate of the machine group in the previous process; at the same time, with the increase of sample data , by training the ANFIS at regular intervals to correct the parameters of the machine group load predictive control model, so that the machine group load predictive control model can better reflect the status quo of the complex production process.

图4：(a)、(b)、(c)分别为实验1中后道工序各机器组负载期望值、采用AFFC方法得到的后道工序机器组负载实际值和采用HFC方法得到的后道工序机器组负载实际值，其中y₁ ^r(k)，y₂ ^r(k)分别为后道工序两个机器组在k时刻的负载期望值；y₁(k)，y₂(k)分别为采用AFFC和HFC控制方法进行机器组负载控制的后道工序两个机器组在k时刻的实际负载值。Figure 4: (a), (b), and (c) respectively represent the expected load value of each machine group in the subsequent process in Experiment 1, the actual load value of the machine group in the subsequent process obtained by the AFFC method, and the subsequent process obtained by the HFC method The actual value of the load of the machine group, where y ₁ ^r (k), y ₂ ^r (k) are the expected load values of the two machine groups in the subsequent process at time k; y ₁ (k), y ₂ (k) are respectively AFFC and HFC control methods carry out the actual load value of the two machine groups at time k in the subsequent process of machine group load control.

图5：(a)、(b)、(c)分别为实验2中后道工序各机器组负载期望值、采用AFFC方法得到的后道工序机器组负载实际值和采用HFC方法得到的后道工序机器组负载实际值，其中y₁ ^r(k)，…，y₅ ^r(k)分别为后道工序各个机器组在k时刻的负载期望值；y₁(k)，…，y₅(k)分别为采用AFFC和HFC控制方法进行机器组负载控制的后道工序各个机器组在k时刻的实际负载值。Figure 5: (a), (b), and (c) respectively represent the expected load value of each machine group in the subsequent process in Experiment 2, the actual load value of the machine group in the subsequent process obtained by the AFFC method, and the subsequent process obtained by the HFC method The actual value of the load of the machine group, where y ₁ ^r (k), ..., y ₅ ^r (k) are the expected load values of each machine group in the subsequent process at time k; y ₁ (k), ..., y ₅ (k) are the actual load values of each machine group at time k in the subsequent process of machine group load control using AFFC and HFC control methods, respectively.

具体实施方式 Detailed ways

本发明的机器组负载预测控制方法依赖于机器组负载预测控制硬件系统，由机器组负载预测控制软件实现。其硬件系统由机器组负载信息采集装置、ANFIS训练计算机和机器组负载预测控制计算机组成(结构图见图1)。ANFIS训练计算机可根据生产历史数据对ANFIS进行训练，得到机器组负载预测控制模型参数。机器组负载预测控制计算机接收机器组预测控制模型的相关参数值(来自ANFIS训练计算机)和机器组负载实时信息，运行本发明提出的机器组负载预测控制方法，并输出预测控制参数(前道工序各机器组任务输出率)。The machine group load predictive control method of the present invention relies on the machine group load predictive control hardware system, and is realized by the machine group load predictive control software. Its hardware system is composed of machine group load information collection device, ANFIS training computer and machine group load prediction control computer (see Figure 1 for the structure diagram). The ANFIS training computer can train ANFIS according to the production history data, and obtain the parameters of the machine group load forecasting control model. The machine group load predictive control computer receives the relevant parameter value (from the ANFIS training computer) of the machine group predictive control model and the real-time information of the machine group load, runs the machine group load predictive control method proposed by the present invention, and outputs the predictive control parameter (the previous process task output rate of each machine group).

以下对本发明提出的上述基于流模型的机器组负载预测控制方法所涉及的步骤进行详细说明：The steps involved in the above-mentioned flow model-based machine group load forecasting control method proposed by the present invention are described in detail below:

第一步：后道工序各机器组负载的定时采样测量，它依次含有以下步骤：The first step: timing sampling measurement of the load of each machine group in the subsequent process, which contains the following steps in turn:

第1.1步，安装机器组负载采集装置，采集各机器组负载实时信息。Step 1.1, install the machine group load collection device to collect real-time load information of each machine group.

第1.2步，由机器组负载预测控制软件从机器组负载采集装置中读取相应的机器组In step 1.2, the machine group load prediction control software reads the corresponding machine group from the machine group load collection device

负载实时信息。Load real-time information.

第二步：后道工序各机器组负载期望值的确定The second step: Determination of the load expectation of each machine group in the subsequent process

为使各机器组负载在整个给定控制周期内保持均衡，将各机器组在给定控制周期内的总负载平均分配到各个采样间隔时间内，即：In order to keep the load of each machine group balanced throughout the given control cycle, the total load of each machine group in a given control cycle is evenly distributed to each sampling interval time, that is:

${y the y}_{j j}^{r r} ((k k)) = = \frac{{Load load}_{j j}}{{T T}_{all all} / / T T},, j j = = 11,, . . . . . .,, n no;;$

也可根据生产需要预先直接给定控制周期内每一采样时刻的后道工序机器组负载期望值。It is also possible to pre-determine directly the load expectation value of the subsequent process machine group at each sampling moment in the control cycle according to production needs.

第三步：后道工序机器组负载流模型的建立。The third step: the establishment of the load flow model of the machine group in the subsequent process.

后道工序机器组负载模糊预测控制问题可描述为：The problem of fuzzy predictive control of the machine group load in the subsequent process can be described as:

令 $J (k + d + 1) = \frac{1}{2} [Y (k + d + 1) - Y^{r} (k + d + 1)]^{T} \cdot [Y (k + d + 1) - Y^{r} (k + d + 1)]$ make $J (k + d + 1) = \frac{1}{2} [Y (k + d + 1) - Y^{r} (k + d + 1)]^{T} &Center Dot; [Y (k + d + 1) - Y^{r} (k + d + 1)]$

$+ + \frac{11}{22} {Σ Σ}_{i i = = 11}^{m m} {C C}^{i i} {((k k))}^{T T} \cdot &Center Dot; {C C}^{i i} ((k k)) - - - - - - ((11))$

求控制律C(k)，使得min{J(k+d+1)}，其中对所有i满足ACⁱ(k)＝1，A＝[1，1，…，1]^1×m。即在满足相关约束的前提下，确定前道工序机器组的任务输出率C(k)，使得在k+d+1时刻的后道工序机器组负载Y(k+d+1)与其负载期望值Y^r(k+d+1)之差的平方和最小，同时也使得Cⁱ(k)的变化最小。Find the control law C(k) such that min{J(k+d+1)}, where AC ⁱ (k)=1 for all i, A=[1, 1, . . . , 1] ^1×m . That is, under the premise of satisfying the relevant constraints, determine the task output rate C(k) of the machine group in the previous process, so that the load Y(k+d+1) of the machine group in the subsequent process and its load expectation value at the moment k+d+1 The sum of squares of the differences of Y ^r (k+d+1) is minimized, which also minimizes the change of C ⁱ (k).

第四步：后道工序机器组负载d阶预测控制模型的建立；The fourth step: the establishment of the d-order predictive control model of the machine group load in the subsequent process;

依据Little’s定理，基于后道工序加工能力、前道工序加工能力和前道工序任务输出率等，可建立用于后道工序机器组负载预测的如下流模型(机器组负载1阶预测控制模型)：According to Little's theorem, based on the processing capacity of the subsequent process, the processing capacity of the previous process, and the task output rate of the previous process, the following flow model for the load prediction of the machine group in the subsequent process can be established (the first-order predictive control model of the machine group load) :

＝max{y_j(k)-Tv_j+TC_j(k-d)U，0}，j＝1，…，n (2)=max{y _j (k)-Tv _j +TC _j (kd)U, 0}, j=1, . . . , n (2)

由于式(2)为非线性模型，很难求得y_j(k+d+1)的解析表达式，本发明采用ANFIS获得Y(k+d+1)与Y(k)和C(k)的非线性映射关系。ANFIS是在模糊推理系统的基础框架中引入自适应节点，形成的多层前馈神经网络，ANFIS的参数集合是其每个节点中参数集合的总和。Because formula (2) is a nonlinear model, it is difficult to obtain the analytical expression of y _j (k+d+1), the present invention adopts ANFIS to obtain Y(k+d+1) and Y(k) and C(k ) nonlinear mapping relationship. ANFIS is a multi-layer feed-forward neural network formed by introducing adaptive nodes into the basic framework of the fuzzy reasoning system. The parameter set of ANFIS is the sum of the parameter sets in each node.

设ANFIS中有L条规则，则对于规则1可表示如下：Assuming that there are L rules in ANFIS, then rule 1 can be expressed as follows:

如果y_j(k)-Tv_j是

并且T·C_j(k-d)·U是

并且T·C_j(k-d+1)·U是

…，并且T·C_j(k-1)·U是

那么If y _j (k)-Tv _j is

and T C _j (kd) U is

and T·C _j (k-d+1)·U is

…, and T C _j (k-1) U is

So

${y the y}_{j j}^{l l} ((k k + + d d + + 11)) = = {α α}^{l l} ((y the y ((k k)) - - {Tv Tv}_{j j})) + + T T [[{γ γ}_{00}^{l l} {C C}_{j j} ((k k - - d d)) + + {γ γ}_{11}^{l l} {C C}_{j j} ((k k - - d d + + 11)) + + . . . . . . + + {γ γ}_{d d}^{l l} {C C}_{j j} ((k k))]] U u + + {β β}^{l l} - - - - - - ((33))$

其中

为第1条模糊规则中每个ANFIS输入变量所对应的模糊数，其隶属度函数采用钟形函数，即：in

is the fuzzy number corresponding to each ANFIS input variable in the first fuzzy rule, and its membership function adopts a bell-shaped function, namely:

${μ μ}_{{\underset{~ ~}{A A}}_{lj lj}} ((x x)) = = \frac{{b b}_{lj lj}}{11 + + {| | \frac{x x - - {c c}_{lj lj}}{{a a}_{lj lj}} | |}^{22}},, j j = = 1,2 1,2,, . . . . . .,, d d + + 11,,$

钟形函数中的参数a_lj，b_lj，c_lj，j＝1，2，…，d+1即为第1条模糊规则中的前件参数，而α^l，γ₀ ^l，γ₁ ^l，…，γ_d ^l，β^l为第1条模糊规则中的后件参数。The parameters a _lj , b _lj , c _lj , j=1, 2, ..., d+1 in the bell-shaped function are the antecedent parameters in the first fuzzy rule, and α ^l , γ ₀ ^l , γ ₁ ^l ,..., γ _d ^l , β ^l are the consequential parameters in the first fuzzy rule.

第1条模糊规则的输出可写成The output of the first fuzzy rule can be written as

${y the y}_{j j}^{l l} ((k k + + d d + + 11)) = = {α α}^{l l} (({y the y}_{j j} ((k k)) - - {Tv Tv}_{j j})) + + T T (({Σ Σ}_{q q = = 00}^{d d} {γ γ}_{q q}^{l l} {C C}_{j j} ((k k - - d d + + q q)))) U u + + {β β}^{l l} - - - - - - ((44))$

令h_l(k)＝f_l(y_j(k)-Tv_j，TC_j(k-d)U，…，TC_j(k-1)U)为ANFIS输入为y_j(k)-Tv_j，TC_j(k-d)U，…，TC_j(k-1)U时第l条模糊规则的激发值，其中f_l为模糊规则激发值计算函数 $f_{l} (x_{1}, x_{2}, . . . {, x}_{d + 1}) = Π_{j = 1}^{d + 1} μ_{{\underset{&OverBar;}{A}}_{lj}} (x_{j}),$ 则L条模糊规则的综合输出为：Let h _l (k)=f _l (y _j (k)-Tv _j , TC _j (kd)U, ..., TC _j (k-1)U) for ANFIS input as y _j (k)-Tv _j , When TC _j (kd)U,...,TC _j (k-1)U, the excitation value of the l-th fuzzy rule, where f _l is the calculation function of the excitation value of the fuzzy rule $f_{l} (x_{1}, x_{2}, . . . {, x}_{d + 1}) = Π_{j = 1}^{d + 1} μ_{{\underset{&OverBar;}{A}}_{lj}} (x_{j}),$ Then the comprehensive output of L fuzzy rules is:

${y the y}_{j j} ((k k + + d d + + 11))$

$= = {Σ Σ}_{l l = = 11}^{L L} {h h}_{l l} ((k k)) \cdot &Center Dot; {y the y}_{j j}^{l l} ((k k + + d d + + 11))$

$= = {Σ Σ}_{l l = = 11}^{L L} {h h}_{l l} ((k k)) \cdot &Center Dot; [[{α α}^{l l} (({y the y}_{j j} ((k k)) - - {Tv Tv}_{j j})) + + {β β}^{l l}]] + + {Σ Σ}_{l l = = 11}^{L L} {h h}_{l l} ((k k)) \cdot \cdot [[T T (({Σ Σ}_{q q = = 00}^{d d} {γ γ}_{q q}^{l l} {C C}_{j j} ((k k - - d d + + q q)))) U u]]$

所以有： $y_{j} (k + d + 1) = E_{j} + Σ_{q = 0}^{d} F_{jq} C_{j} (d - d + q) U, j = 1, . . ., n - - - (6)$ F: ${the y}_{j} (k + d + 1) = {E.}_{j} + Σ_{q = 0}^{d} f_{jq} C_{j} (d - d + q) u, j = 1, . . ., no - - - (6)$

令X^n×1＝[E₁，E₂，…，E_n]^T，Let X ^{n × 1} = [E ₁ , E ₂ , . . . , E _n ] ^T ,

则有：Then there are:

$Y Y {((k k + + d d + + 11))}^{n no \times \times 11} = = {X x}^{n no \times \times 11} + + {Σ Σ}_{q q = = 00}^{d d} {N N}_{q q}^{n no \times \times n no} \cdot \cdot C C {((k k - - d d + + q q))}^{n no \times \times m m} \cdot \cdot {U u}^{m m \times \times 11} - - - - - - ((77))$

即：Right now:

$Y Y {((k k + + d d + + 11))}^{n no \times \times 11} = = {X x}^{n no \times \times 11} + + {Σ Σ}_{q q = = 00}^{d d} {N N}_{q q}^{n no \times \times n no} \cdot &Center Dot; [[{C C}^{11} ((k k - - d d + + q q)),, . . . . . .,, {C C}^{m m} ((k k - - d d + + q q)) {]]}^{n no \times \times m m} \cdot &Center Dot; {U u}^{m m \times \times 11}$

$= = {X x}^{n no \times \times 11} + + {Σ Σ}_{q q = = 00}^{d d} {N N}_{q q}^{n no \times \times n no} \cdot &Center Dot; {Σ Σ}_{i i = = 11}^{m m} {u u}_{i i} {C C}^{i i} ((k k - - d d + + q q)) - - - - - - ((88))$

式(8)即是Y(k)的d阶预测控制模型表达式，其中U，V为常数矩阵，d，T为常量。Equation (8) is the d-order predictive control model expression of Y(k), where U, V are constant matrices, and d, T are constants.

采用以下方法确定式(8)中ANFIS中的前件参数和后件参数：Use the following method to determine the antecedent parameters and subsequent parameters in ANFIS in formula (8):

对所有j＝1，2，…，n，随机产生C_j(k)的值，并由式(2)算出y_j(k+1)值，从而产生若干用于训练ANFIS的输入输出训练数据集，输入数据为Y(k)，C(k-d)，…，C(k-1)，输出数据为Y(k+d+1)。基于上述训练数据集，使用ANFIS的经典学习算法(即采用BP反向传播学习方法对ANFIS中的前件参数进行学习，再采用最小二乘法对ANFIS中的后件参数进行更新)，该经典学习算法可使用MATLAB 6.0中的ANFIS训练软件包实现)，确定式(8)中的ANFIS前件参数和后件参数，从而最终得到Y(k)的d阶预测控制模型。For all j=1, 2,..., n, the value of C _j (k) is randomly generated, and the value of y _j (k+1) is calculated by formula (2), thereby producing some input and output training data for training ANFIS Set, the input data is Y(k), C(kd), ..., C(k-1), and the output data is Y(k+d+1). Based on the above training data set, using the classic learning algorithm of ANFIS (that is, using the BP backpropagation learning method to learn the antecedent parameters in ANFIS, and then using the least square method to update the subsequent parameters in ANFIS), the classic learning algorithm The algorithm can be implemented using the ANFIS training software package in MATLAB 6.0), determine the ANFIS antecedent parameters and subsequent parameters in formula (8), and finally obtain the d-order predictive control model of Y(k).

第五步：前道工序机器组C(k)的求取。Step 5: Calculation of the machine group C(k) in the previous process.

根据第四步得到的Y(k)的d阶预测控制模型，采用拉格朗日松弛方法，求解第三步描述的机器组负载预测控制问题，求得最佳的控制参数C(k)。According to the d-order predictive control model of Y(k) obtained in the fourth step, the Lagrangian relaxation method is used to solve the machine load predictive control problem described in the third step, and the optimal control parameter C(k) is obtained.

1)采用拉格朗日(Lagrange)松弛方法将上述问题中的约束松弛。对于式(1)，将约束松弛后可得：1) The constraints in the above problem are relaxed by using the Lagrange relaxation method. For formula (1), after relaxing the constraint, we can get:

$\overset{&OverBar; &OverBar;}{J J} ((k k + + d d + + 11)) = = \frac{11}{22} [[Y Y ((k k + + d d + + 11)) - - {Y Y}^{r r} ((k k + + d d + + 11)) {]]}^{T T} \cdot &Center Dot; [[Y Y ((k k + + d d + + 11)) - - {Y Y}^{r r} ((k k + + d d + + 11))]]$

$+ + \frac{11}{22} {Σ Σ}_{i i = = 11}^{m m} {C C}^{i i} {((k k))}^{T T} \cdot &Center Dot; {C C}^{i i} ((k k)) + + {Σ Σ}_{i i = = 11}^{m m} {λ λ}_{i i} ((A A {C C}^{i i} ((k k)) - - 11)) - - - - - - ((99))$

其中λ_i，i＝1，2，…，m为用于松弛约束的拉格朗日算子。Wherein λ _i , i=1, 2, . . . , m is a Lagrangian operator used to relax constraints.

2)对于松弛后的式(9)，求关于给定i的Cⁱ(k)的偏导数并令偏导数为0，有：2) For the relaxed formula (9), find the partial derivative of C ⁱ (k) with respect to a given i and let the partial derivative be 0, we have:

$\frac{&PartialD; &PartialD; \overset{&OverBar; &OverBar;}{J J} ((k k + + d d + + 11))}{&PartialD; &PartialD; {C C}^{i i} ((k k))} = = \frac{{&PartialD; &PartialD; ((Y Y ((k k + + d d + + 11)) - - {Y Y}^{r r} ((k k + + d d + + 11))))}^{T T}}{{&PartialD; &PartialD; C C}^{i i} ((k k))} ((Y Y ((k k + + d d + + 11)) - - {Y Y}^{r r} ((k k + + d d + + 11))))$

$- - {C C}^{i i} ((k k)) + + {λ λ}_{i i} {A A}^{T T} = = 00,, i i = = 11,, . . . . . .,, m m - - - - - - ((1010))$

将式(8)代入式(10)，化简可得：Substituting formula (8) into formula (10), it can be simplified to get:

$\frac{&PartialD; &PartialD; \overset{&OverBar; &OverBar;}{J J} ((k k + + d d + + 11))}{{&PartialD; &PartialD; C C}^{i i} ((k k))} = = {u u}_{i i} {N N}_{d d}^{T T} [[X x + + {N N}_{d d} (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i} {C C}^{i i} ((k k)))) + + {Σ Σ}_{q q = = 00}^{d d - - 11} {N N}_{q q} (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i} {C C}^{i i} ((k k - - d d + + q q)))) - - {Y Y}^{r r} ((k k + + d d + + 11))]]$

$+ + {C C}^{i i} ((k k)) + + {λ λ}_{i i} {A A}^{T T} = = 00,, i i = = 11,, . . . . . .,, m m - - - - - - ((1111))$

3)对于松弛后的式(9)，求关于λ_i的偏导数并令偏导数为0，有：3) For the relaxed formula (9), find the partial derivative with respect to λ _i and let the partial derivative be 0, we have:

ACⁱ(k)＝1，i＝1，…，m (12)AC ⁱ (k)=1, i=1, . . . , m (12)

4)令 $\overset{&OverBar;}{X} = N_{d}^{T} [X + Σ_{q = 0}^{d - 1} (Σ_{i = 1}^{m} u_{i} C^{i} (k - d + q)) - Y^{r} (k + d + 1)], \overset{&OverBar;}{N} = N_{d}^{T} N_{d},$ 4) order $\overset{&OverBar;}{x} = N_{d}^{T} [x + Σ_{q = 0}^{d - 1} (Σ_{i = 1}^{m} u_{i} C^{i} (k - d + q)) - Y^{r} (k + d + 1)], \overset{&OverBar;}{N} = N_{d}^{T} N_{d},$

$S S = = \overset{&OverBar; &OverBar;}{X x} + + \overset{&OverBar; &OverBar;}{N N} (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i} {C C}^{i i} ((k k)))) - - - - - - ((1313))$

则式(11)可表示为：Then formula (11) can be expressed as:

u_iS+Cⁱ(k)+λ_iA^T＝0，i＝1，…，m (14)u _i S+C ⁱ (k)+λ _i A ^T =0, i=1,..., m (14)

对式(14)两边左乘A，可得：Multiply A on the left side of both sides of formula (14), we can get:

u_iAS+ACⁱ(k)+λ_iAA^T＝0，i＝1，…，m (15)u _i AS+AC ⁱ (k)+λ _i AA ^T =0, i=1,...,m (15)

将式(12)代入式(15)，既有：Substituting formula (12) into formula (15), we have:

${λ λ}_{i i} = = \frac{- - 11}{{AA AAA}^{T T}} (({u u}_{i i} AS AS + + 11)),, i i = = 11,, . . . . . .,, m m - - - - - - ((1616))$

再将式(16)代入式(13)，则：Then substitute formula (16) into formula (13), then:

${u u}_{i i} S S + + {C C}^{i i} ((k k)) + + \frac{{- - A A}^{T T}}{{AA AAA}^{T T}} (({u u}_{i i} AS AS + + 11)) = = 00,, i i = = 11,, . . . . . .,, m m$

从而：thereby:

${C C}^{i i} ((k k)) = = {u u}_{i i} ((\frac{{A A}^{T T} A A}{{AA AAA}^{T T}} - - I I)) S S + + \frac{{A A}^{T T}}{{AA AAA}^{T T}} - - - - - - ((1717))$

其中I为m阶单位矩阵。where I is the identity matrix of order m.

将式(17)代入式(13)，有：Substituting formula (17) into formula (13), we have:

$S S = = \overset{&OverBar; &OverBar;}{X x} + + \overset{&OverBar; &OverBar;}{N N} (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i} {C C}^{i i} ((k k)))) = = \overset{&OverBar; &OverBar;}{X x} + + \overset{&OverBar; &OverBar;}{N N} [[{Σ Σ}_{i i = = 11}^{m m} {u u}_{i i}^{22} ((\frac{{A A}^{T T} A A}{{AA AAA}^{T T}} - - I I)) S S + + {Σ Σ}_{i i = = 11}^{m m} {u u}_{i i} \frac{{A A}^{T T}}{{AA AAA}^{T T}}]]$

$= = \overset{&OverBar; &OverBar;}{X x} + + (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i}^{22})) \cdot &Center Dot; \overset{&OverBar; &OverBar;}{N N} ((\frac{{A A}^{T T} A A}{{AA AAA}^{T T}} - - I I)) S S + + (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i})) \cdot &Center Dot; \frac{\overset{&OverBar; &OverBar;}{N N} {A A}^{T T}}{{AA AAA}^{T T}}$

即： $[I - (Σ_{i = 1}^{m} u_{i}^{2}) \cdot \overset{&OverBar;}{N} (\frac{A^{T} A}{{AA}^{T}} - I)] S = \overset{&OverBar;}{X} + (Σ_{i = 1}^{m} u_{i}) \cdot \frac{\overset{&OverBar;}{N} A^{T}}{{AA}^{T}}$ Right now: $[I - (Σ_{i = 1}^{m} u_{i}^{2}) \cdot \overset{&OverBar;}{N} (\frac{A^{T} A}{{AAA}^{T}} - I)] S = \overset{&OverBar;}{x} + (Σ_{i = 1}^{m} u_{i}) &Center Dot; \frac{\overset{&OverBar;}{N} A^{T}}{{AAA}^{T}}$

$S S = = [[I I - - (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i}^{22})) \cdot &Center Dot; \overset{&OverBar; &OverBar;}{N N} ((\frac{{A A}^{T T} A A}{{AA AAA}^{T T}} - - I I)) {]]}^{- - 11} \cdot &Center Dot; [[\overset{&OverBar; &OverBar;}{X x} + + (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i})) \cdot &Center Dot; \frac{\overset{&OverBar; &OverBar;}{N N} {A A}^{T T}}{{AA AAA}^{T T}}]] - - - - - - ((1818))$

最后，将式(18)代入式(17)，可求得使机器组负载预测控制问题控制目标最小的控制律C(k)：Finally, substituting Equation (18) into Equation (17), the control law C(k) that minimizes the control objective of the machine load predictive control problem can be obtained:

${C C}^{i i} ((k k)) = = {u u}_{i i} ((\frac{{A A}^{T T} A A}{{AA AAA}^{T T}} - - I I)) \cdot &Center Dot; [[I I - - (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i}^{22})) \cdot &Center Dot; \overset{&OverBar; &OverBar;}{N N} ((\frac{{A A}^{T T} A A}{{AA AAA}^{T T}} - - I I)) {]]}^{- - 11} \cdot \cdot [[\overset{&OverBar; &OverBar;}{X x} + + (({Σ Σ}_{i i = = 11}^{m m} {u u}_{i i})) \cdot \cdot \frac{\overset{&OverBar; &OverBar;}{N N} {A A}^{T T}}{{AA AAA}^{T T}}]] + + \frac{{A A}^{T T}}{{AA AAA}^{T T}},,$

i＝1，…，m。i=1,...,m.

本发明提出的基于流模型的机器组负载预测控制方法流程图如图3所示。The flow chart of the load forecasting control method for machine groups based on the flow model proposed by the present invention is shown in FIG. 3 .

根据上述所提出的基于流模型的机器组负载预测控制方法，本发明做了大量的仿真试验，由于篇幅所限，采用如下两个较难预测控制的实验用以验证本发明提出的机器组负载预测控制方法的有效性，实验参数见表1：According to the flow model-based machine group load prediction control method proposed above, the present invention has done a large number of simulation tests. Due to space limitations, the following two experiments that are difficult to predict and control are used to verify the machine group load proposed by the present invention. The effectiveness of the predictive control method, the experimental parameters are shown in Table 1:

表1仿真实验参数Table 1 Simulation experiment parameters

本发明设计了用于与AFFC方法相比较的启发式方法(HFC：Heuristic Flow Control)，该方法可描述如下：用当前时刻后道工序机器组负载与负载期望值之间的差Diff(k)＝[Y^r(k)-Y(k)]＝[π₁，π₂，…，π_n]^T来调节C(k)，即如果π_j大于零，则增加C_j(k)中各个元素的值；反之，如果π_j小于零，则减少C_j(k)中各个元素的值，从而可减少Y^r(k)与Y(k)的差，但在增加和减少C_j(k)时，应满足约束A·C(k)＝A。具体方法是：对Diff(k)中的元素从大到小重新排列。如果π_j是前n/2个大的元素之一，则C_j(k)＝C_j(k-1)+0.1·I；反之，如果π_j是后n/2个大的元素之一，则C_j(k)＝C_j(k-1)-0.1·I。The present invention has designed the heuristic method (HFC: Heuristic Flow Control) that is used to compare with AFFC method, and this method can be described as follows: Use the difference Diff(k)= [Y ^r (k)-Y(k)]=[π ₁ , π ₂ ,…, π _n ] ^T to adjust C(k), that is, if π _j is greater than zero, then increase each element in C _j (k) On the contrary, if π _j is less than zero, then reduce the value of each element in C _j (k), so that the difference between Y ^r (k) and Y(k) can be reduced, but the increase and decrease of C _j (k) , the constraint A·C(k)=A should be satisfied. The specific method is: rearrange the elements in Diff(k) from large to small. If π _j is one of the first n/2 large elements, then C _j (k)=C _j (k-1)+0.1·I; otherwise, if π _j is one of the last n/2 large elements , then C _j (k)=C _j (k-1)-0.1·I.

在数值仿真中分别用AFFC和HFC方法对C(k)进行调节。图4和图5分别表示上述两个实验的数值仿真结果。In numerical simulation, C(k) is adjusted by AFFC and HFC methods respectively. Figure 4 and Figure 5 represent the numerical simulation results of the above two experiments respectively.

图4(b)和5(b)中的Y(k)较好地跟踪了图4(a)和5(a)中期望值Y^r(k)的变化(最大误差分别是5％和1.79％)，并且是收敛的。而图4(c)和5(c)中的Y(k)虽可反映出图4(a)和5(a)中Y^r(k)的变化趋势，但与Y^r(k)的误差随控制时间的增大而越来越大(曲线不收敛)。可见本发明提出的AFFC对跟踪后道工序机器组负载期望值是有效的。HFC方法的缺点是未引入对后道工序机器组负载的预测机制，而仅根据后道工序机器组负载当前状态对C(k)进行调节，且调节方法较简单，使得跟踪误差较大。Y(k) in Figures 4(b) and 5(b) tracks well the variation of the expected value Y ^r (k) in Figures 4(a) and 5(a) (maximum errors are 5% and 1.79% respectively ), and is convergent. While Y(k) in Figure 4(c) and 5(c) can reflect the variation trend of Y ^r (k) in Figure 4(a) and 5(a), but the error with Y ^r (k) As the control time increases, it becomes larger and larger (the curve does not converge). It can be seen that the AFFC proposed by the present invention is effective for tracking the load expectation value of the machine group in the subsequent process. The disadvantage of the HFC method is that it does not introduce a prediction mechanism for the load of the machine group in the subsequent process, but only adjusts C(k) according to the current state of the load of the machine group in the subsequent process, and the adjustment method is relatively simple, resulting in a large tracking error.

在数值仿真中分别用AFFC和HFC方法对C(k)进行调节。图4和图5分别表示了上述两个实验的数值仿真结果。In numerical simulation, C(k) is adjusted by AFFC and HFC methods respectively. Figure 4 and Figure 5 respectively represent the numerical simulation results of the above two experiments.

本发明的实施案例为某大型色织生产企业，该企业的生产主要包括松纱、复板、染色、络筒、整经、浆纱、穿综、插筘和织布等九道工序，其中染色工序和织布工序是该企业生产过程中的瓶颈工序。在染色和织布工序间有络筒、整经、浆纱、穿综和插筘工序，上述工序的生产能力均较大，生产任务仅需经过一定的延时(工艺加工时间)即可经过这些工序。可见，该色织生产过程符合本发明描述的复杂生产过程情况，可通过控制染色工序任务的输出率控制织布工序中各个机器组的加工负载。The implementation case of the present invention is a certain large-scale yarn-dyed production enterprise. The production of this enterprise mainly includes nine processes such as loose yarn, double board, dyeing, winding, warping, sizing, drafting, reed insertion and weaving. The dyeing process and the weaving process are the bottleneck processes in the production process of the enterprise. There are winding, warping, sizing, drawing-in and reeding processes between the dyeing and weaving processes. The production capacity of the above-mentioned processes is relatively large, and the production tasks can be completed only after a certain delay (processing time). these processes. It can be seen that the yarn-dyed production process conforms to the complex production process described in the present invention, and the processing load of each machine group in the weaving process can be controlled by controlling the output rate of the dyeing process task.

首先按照本说明书的要求在织布工序安装机器组负载预测控制硬件系统。First, install the load forecasting control hardware system of the machine group in the weaving process according to the requirements of this manual.

其次，从该色织生产的生产管理系统中读取最近1个月的生产数据，按照本说明书提供的方法建立ANFIS的训练数据，共计10000条。并使用这些训练数据对ANFIS进行训练，建立织布工序机器组负载预测控制的d阶模型。在确定采样周期时，根据该色织生产企业的实际生产情况，确定采样周期T＝2小时，同时由于染色和织布间的中间工序的加工延迟时间基本在10小时左右，所以该预测控制模型的阶数d＝5。Secondly, read the production data of the last month from the production management system of the yarn-dyed production, and establish ANFIS training data according to the method provided in this manual, with a total of 10,000 pieces. And use these training data to train the ANFIS, and establish the d-order model of the load forecasting control of the machine group in the weaving process. When determining the sampling period, according to the actual production situation of the yarn-dyed production enterprise, determine the sampling period T = 2 hours, and because the processing delay time of the intermediate process between dyeing and weaving is basically about 10 hours, so the predictive control model The order d=5.

之后，根据织布工序中的23个机器组的加工能力，使用本说明书提供的机器组负载期望值确定方法确定上述23个机器组的加工负载期望值。Afterwards, according to the processing capabilities of the 23 machine groups in the weaving process, use the method for determining the expected load of the machine groups provided in this manual to determine the expected processing loads of the above 23 machine groups.

最后，预测控制软件根据本说明书给出的染色工序中各机器组的任务输出率求取方法，在获取织布工序各机器组负载实时信息的基础上，自动给出染色工序各机器组的任务输出率。Finally, the predictive control software automatically gives the tasks of each machine group in the dyeing process on the basis of obtaining the real-time load information of each machine group in the weaving process according to the calculation method of the task output rate of each machine group in the dyeing process given in this manual. output rate.

基于流模型的机器组负载预测控制方法可很好地对织布工序机器组负载进行控制。The machine group load prediction control method based on the flow model can well control the machine group load in the weaving process.

Claims

Based on the machine group loading forecast control method of flow model, it is characterized in that 1, described method realizes successively according to the following steps on machine group load estimation control computer:

Step (1): initialization, set following parameter

Sampling time interval provides each machine group task output rating in the preceding working procedure every time interval T, and described machine group is made up of many similar machines of working ability, and sampling instant is then represented with k;

Machine group working ability is summation process time of the processing tasks that can finish in unit interval inner machine group, the working ability u of machine group i in the preceding working procedure _iExpression, i=1 ..., m is expressed in matrix as U=[u ₁, u ₂..., u _m] ^T, the working ability v of machine group j in the later process _jExpression, j=1 ..., n is expressed in matrix as V=[v ₁, v ₂..., v _n] ^T, m and n are respectively the number of machine group in the forward and backward procedure;

Preceding working procedure machine group task output rating, preceding working procedure machine group i constrains in the task that the k sampling instant machines based on production technology and is arranged to the ratio of later process by machine group j processing, uses c _Ij(k) expression is expressed in matrix as:

$C {(k)}^{n \times m} = {[C_{1} (k), C_{2} (k), \cdot \cdot \cdot, C_{n} (k)]}^{T}$

$= [C^{1} (k), C^{2} (k), \cdot \cdot \cdot, C^{m} (k)]$

$= [\begin{matrix} c_{11} (k) & c_{21} (k) & \cdot \cdot \cdot & c_{m 1} (k) \\ c_{12} (k) & c_{22} (k) & \cdot \cdot \cdot & c_{m 2} (k) \\ \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot \cdot \cdot & \cdot \\ \cdot & \cdot & \cdot \\ c_{1 n} (k) & c_{2 n} (k) & \cdot \cdot \cdot & c_{mn} (k) \end{matrix}]$

0≤c wherein _Ij≤ 1 and $Σ_{j = 1}^{n} c_{ij} = 1,$ i＝1，…，m；j＝1，…，n；

The load of machine group, summation process time of wait processing tasks before certain machine group in the operation, later process machine group j is shown y at k loading liquifier constantly _j(k), be expressed in matrix as Y (k) ^{N * 1}=[y ₁(k), y ₂(k) ..., y _n(k)] ^T

Machine group j is expressed as y in k machine loading expectation value constantly in the later process _j ^r(k), be expressed in matrix as $Y^{r} {(k)}^{n \times 1} = {[y_{1}^{r} (k), y_{2}^{r} (k), \cdot \cdot \cdot, y_{n}^{r} (k)]}^{T};$

The processing of middle operation represents that it is meant task from the preceding working procedure completion of processing time delay with d, by the processing of middle operation, arrive the used averaging time unit of later process, contains the stand-by period;

Given control cycle T _AllExpression;

Control cycle T _AllThe total load Load of interior later process machine group j _jExpression;

Step (2): gather machine group load real-time information with machine group load information harvester, machine group load information harvester is constituted by a kind of in PLC harvester, embedded system harvester, the DCS system acquisition device or they;

Step (3): the read machine group load real-time information from described harvester of described machine group load estimation control computer, carry out the control of machine group load estimation successively according to the following steps:

Step (3.1): determine each sampling interval each machine group load expectation value y of later process in the time by following formula _j ^r(k),

$y_{j}^{r} (k) = \frac{{Load}_{j}}{T_{all} / T},$ j＝1，…，n

Step (3.2): set up later process machine group load estimation control problem by following formula:

$J (k + d + 1) = \frac{1}{2} {[Y (k + d + 1) - Y^{r} (k + d + 1)]}^{T} \cdot] [Y (k + d + 1) - Y^{r} (k + d + 1)]$

$+ \frac{1}{2} Σ_{i = 1}^{m} C^{i} {(k)}^{T} \cdot C^{i} (k)$

Ask control law C (k), make min{J (k+d+1), wherein all i are satisfied AC ⁱ(k)=1, A=[1,1 ..., 1] ^{1 * m}

Step (3.3): set up later process machine group load estimation controlling models by following step

Step (3.3.1): set up later process machine group load 1 rank predictive control model

y _j(k+1)＝max{y _j(k)-v _jT+[c _1j(k-d)u ₁+…+c _mj(k-d)u _m]T，0}

＝max{y _j(k)-Tv _j+TC _j(k-d)U，0}，j＝1，…，n ，

Step (3.3.2): adopt Adaptive Neuro-fuzzy Inference ANFIS to set up later process machine group load d rank predictive control model with L bar fuzzy rule

That is:

$Y {(k + d + 1)}^{n \times 1} = X^{n \times 1} + Σ_{q = 0}^{d} N_{q}^{n \times n} \cdot {[C^{1} (k - d + q), \cdot \cdot \cdot, C^{m} (k - d + q)]}^{n \times m} \cdot U^{m \times 1}$

$= X^{n \times 1} + Σ_{q = 0}^{d} N_{q}^{n \times n} \cdot Σ_{i = 1}^{m} u_{i} C^{i} (k - d + q)$

Wherein: X ^{N * 1}=[E ₁, E ₂..., E _n] ^T, $E_{j} = Σ_{l = 1}^{L} h_{l} (k) \cdot [α^{l} (y_{j} (k) - {Tv}_{j}) + β^{l}]$

q＝0，1，…，d， $F_{jq} = T \cdot Σ_{l = 1}^{L} h_{l} (k) γ_{q}^{l},$

h _l(k)=f _l(y _j(k)-Tv _j, TC _j(k-d) U ..., TC _j(k-1) be that ANFIS is input as U),

y _j(k)-Tv _j, TC _j(k-d) U ..., TC _j(k-1) excitation values of l bar fuzzy rule during U, f _lBe fuzzy rule excitation values computing function, it is the product of the membership function of the corresponding fuzzy number of each input variable of ANFIS in the l bar fuzzy rule, wherein, the membership function of above-mentioned fuzzy number adopts bell shaped function, parameter in the bell shaped function is former piece parameter undetermined among the ANFIS, and consequent parameter undetermined is α among the ANFIS ^l, γ ₀ ^l, γ ₁ ^l..., γ _d ^l, β ^l

Step (3.3.3): the employing following steps are determined former piece parameter and the consequent parameter among the ANFIS;

Step (3.3.3.1): to all j=1,2 ..., n produces C at random _j(k) value, and (3.3.1) described formula calculates y set by step _j(k+1) value, thus some input and output training datasets that are used to train ANFIS produced, wherein, the input data are Y (k), C (k-d) ..., C (k-1), output data is Y (k+d+1);

Step (3.3.3.2): the training dataset and the classical learning algorithm of ANFIS that adopt step (3.3.2.1) to generate, determine former piece parameter undetermined among the ANFIS and consequent parameter;

Step (3.4):, adopt the Lagrange relaxation method to be calculated as follows Optimal Control rate C (k), wherein C according to the later process machine group load d rank predictive control model that step (3.3) obtains ⁱ(k) be:

$C^{i} (k) = u_{i} (\frac{A^{T} A}{{AA}^{T}} - I) \cdot {[I - (Σ_{i = 1}^{m} u_{i}^{2}) \cdot \overset{&OverBar;}{N} (\frac{A^{T} A}{{AA}^{T}} - I)]}^{- 1} \cdot [\overset{&OverBar;}{X} + (Σ_{i = 1}^{m} u_{i}) \cdot \frac{\overset{&OverBar;}{N} A^{T}}{{AA}^{T}}] + \frac{A^{T}}{{AA}^{T}},$

Wherein: I is a unit matrix, $\overset{&OverBar;}{X} = N_{d}^{T} [X + Σ_{q = 0}^{d - 1} (Σ_{i = 1}^{m} u_{i} C^{i} (k - d + q)) - Y^{r} (k + d + 1)],$ $\overset{&OverBar;}{N} = N_{d}^{T} N_{d} .$