CN104330972A

CN104330972A - Comprehensive prediction iterative learning control method based on model adaptation

Info

Publication number: CN104330972A
Application number: CN201410601343.3A
Authority: CN
Inventors: 熊智华; 陈宸; 公衍海
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2014-10-30
Filing date: 2014-10-30
Publication date: 2015-02-04

Abstract

本发明涉及一种基于模型自适应综合预测迭代学习控制方法，属于间歇式生产加工过程的产品质量跟踪控制技术领域。该方法对于大多数批次加工制造生产过程，针对该生产过程带有随机噪声情况和收敛速度较慢的情况，适用于间歇式生产加工过程的产品质量跟踪控制。本发明利用提出的基于模型自适应的综合预测迭代学习控制算法，可以在一定程度上克服间歇过程模型误差问题，加快算法的收敛速度，应用范围很广。本方法可以克服由现实环境和加工手段给生产过程带来的噪声。本方法构思巧妙，简单实用，可广泛应用于工业生产线间歇生产过程的高精度控制。The invention relates to a model-based self-adaptive comprehensive prediction iterative learning control method, which belongs to the technical field of product quality tracking control in intermittent production and processing processes. For most batch processing and manufacturing processes, the method is suitable for the product quality tracking control of batch production and processing processes for the production process with random noise and slow convergence speed. The invention utilizes the proposed comprehensive predictive iterative learning control algorithm based on model self-adaptation, which can overcome the intermittent process model error problem to a certain extent, accelerate the convergence speed of the algorithm, and has a wide range of applications. The method can overcome the noise brought to the production process by the actual environment and processing means. The method is ingenious in conception, simple and practical, and can be widely used in the high-precision control of the intermittent production process of industrial production lines.

Description

A Comprehensive Predictive Iterative Learning Control Method Based on Model Adaptation

技术领域technical field

本发明涉及一种基于模型自适应综合预测迭代学习控制方法，尤其针对该生产过程带有随机噪声情况和收敛速度较慢的情况，属于间歇式生产加工过程的产品质量跟踪控制技术领域。The invention relates to a model-based adaptive comprehensive prediction iterative learning control method, especially for the production process with random noise and slow convergence speed, and belongs to the technical field of product quality tracking control in intermittent production and processing processes.

背景技术Background technique

间歇式生产过程(Batch Process)是一种生产按批次进行操作，并且批次之间存在一定的间歇时间的生产方式。它广泛存在于国民生产如生物制品、药品生产、精细化工、半导体集成电路等各个领域，在小批量、多品种和高附加值的工业产品中占据主导地位。为了确保产品的高质量及其质量的稳定性和，过程控制显得尤为重要。然而一方面，间歇过程通常具有不连续性、非稳态性、强非线性和时变性等特点，建立间歇过程的精确模型非常困难，传统的控制方法一般并不能起到良好的效果；另一方面，在间歇过程生产中配方不变时，生产过程基本上是重复运行的，在每个批次运行周期内控制变量和产品质量都是沿着一定的操作变化轨迹运行，具有较强的重复性。此外，在实际的生产过程中，由于现实环境和加工手段不可避免的给生产过程带来干扰或噪声，在精度要求较高的产品加工中，过程噪声可能给最终的产品质量带来严重的影响。The batch production process (Batch Process) is a production method that operates in batches, and there is a certain intermittent time between batches. It widely exists in various fields of national production such as biological products, pharmaceutical production, fine chemicals, semiconductor integrated circuits, etc., and occupies a dominant position in small-batch, multi-variety and high value-added industrial products. In order to ensure the high quality of products and the stability and quality of their products, process control is particularly important. However, on the one hand, the batch process usually has the characteristics of discontinuity, instability, strong nonlinearity, and time-varying nature, so it is very difficult to establish an accurate model of the batch process, and traditional control methods generally cannot achieve good results; on the other hand, On the one hand, when the formula is unchanged in the batch process production, the production process is basically repeated operation, and the control variables and product quality are running along a certain operation change track in each batch operation cycle, which has a strong repeatability sex. In addition, in the actual production process, the actual environment and processing methods will inevitably bring interference or noise to the production process. In the processing of products with high precision requirements, the process noise may have a serious impact on the final product quality. .

迭代学习控制(Iterative Learning Control,ILC)非常适合于这一类具有周期性、重复运行特性的生产过程的控制，其思想出发点是对于在有限时间区间上重复执行相同控制任务的系统，其性能可以通过对以往重复过程的学习来得到改善。迭代学习控制算法期望利用前一个或多个批次的信息来更新下一批次的输入轨迹，使得输出轨迹尽快地收敛于期望的目标轨迹。Iterative Learning Control (ILC) is very suitable for the control of this kind of production process with periodic and repetitive operation characteristics. Improvement is achieved by learning from past repetitions. The iterative learning control algorithm expects to use the information of the previous batch or batches to update the input trajectory of the next batch, so that the output trajectory can converge to the desired target trajectory as soon as possible.

对于大多数的间歇被控过程，对象具体知识的取得并非易事，有时甚至是不可能的，如：间歇过程的运行批次有限使得输入输出数据有限；处于初始若干批次重复运行阶段，数据相关度较高；过程具有较强的非线性，无法用线性过程拟合；建模成本较高等，在这些情况下不可能建立精确的系统模型或是建立的模型有较大的偏差。同时由于间歇过程的本身有可能在多次重复运行的过程中运行状态发生变化或者由于外部干扰给使得模型在运行过程中发生改变。从而给控制算法的参数选择带来困扰，因此单纯的迭代学习控制算法难以直接使用，或者使用效果不佳，经过多个批次依然难以达到预期的控制目的。For most intermittent controlled processes, it is not easy to obtain object-specific knowledge, and sometimes it is even impossible. For example, the limited batches of intermittent processes make the input and output data limited; The correlation is high; the process has a strong nonlinearity, which cannot be fitted by a linear process; the modeling cost is high, etc. In these cases, it is impossible to establish an accurate system model or the established model has a large deviation. At the same time, due to the batch process itself, the operating state may change during repeated operations or the model may change during the operation due to external interference. This brings trouble to the parameter selection of the control algorithm, so the simple iterative learning control algorithm is difficult to use directly, or the use effect is not good, and it is still difficult to achieve the expected control purpose after multiple batches.

此外，即使能获得相比较为精确的过程模型，若在被控过程存在干扰或噪声，迭代学习控制效果可能由于控制算法在批次上积分作用变差从而达不到预期目的。大多数当前的迭代学习算法都假设过程噪声不存在进而讨论算法性质，但是在实际生产过程中，过程噪声往往难以避免，在一定过程噪声的情况下如何设计过程控制算法来保证间歇过程产品质量有待解决。In addition, even if a relatively accurate process model can be obtained, if there is interference or noise in the controlled process, the effect of iterative learning control may not achieve the expected purpose due to the deterioration of the integral function of the control algorithm on the batch. Most of the current iterative learning algorithms assume that the process noise does not exist and then discuss the properties of the algorithm. However, in the actual production process, the process noise is often unavoidable. How to design a process control algorithm to ensure the product quality of the batch process under the condition of certain process noise remains to be seen. solve.

模型预测控制(Model Predictive Control,MPC)是一种反馈先进控制算法，基于过程模型和以往的系统输入预测将来系统的输出，并在此基础上通过优化方法修正当前的输入。模型预测控制对于过程模型不确定性和存在过程噪声的被控过程有较好的控制效果。因此在迭代学习控制方法中结合模型预测控制是一条解决上述问题的理所当然的途径。Model predictive control (Model Predictive Control, MPC) is a feedback advanced control algorithm, which predicts the output of the future system based on the process model and the past system input, and on this basis corrects the current input through the optimization method. Model predictive control has a good control effect on the controlled process with process model uncertainty and process noise. Therefore, combining model predictive control in iterative learning control method is a natural way to solve the above problems.

总体而言，在参数无法选择导致传统迭代学习算法收敛速度较慢或是存在过程噪声的情况下，如何设计恰当的整合迭代学习控制方法是一个非常值得研究的问题。In general, how to design an appropriate integrated iterative learning control method is a problem worthy of research when the parameters cannot be selected, resulting in slow convergence speed or process noise in the traditional iterative learning algorithm.

发明内容Contents of the invention

本发明的目的是提供一种基于模型自适应的综合预测迭代学习控制方法，该方法针对间歇过程收敛较慢或过程中存在噪声的问题，能够很好控制间歇过程最终产品质量。该方法计算简单，计算耗时较少，具有较好的推广性。The purpose of the present invention is to provide a comprehensive predictive iterative learning control method based on model self-adaptation, which can control the final product quality of the batch process well for the problems of slow convergence or noise in the batch process. This method is simple to calculate, takes less time to calculate, and has better generalization.

本发明提出的基于模型自适应的综合预测迭代学习控制方法，方法包括以下步骤：The comprehensive predictive iterative learning control method based on model self-adaptation proposed by the present invention comprises the following steps:

1)与实际生产过程相结合，设置一个批次生产的数据采集和存储环节，该环节可以利用生产企业现有的工业控制计算机、PLC等设备；1) Combined with the actual production process, set up a batch production data collection and storage link, which can use the existing industrial control computer, PLC and other equipment of the production enterprise;

2)根据采集到的生产历史数据库中以往的生产过程数据，在进行数据预处理后采用适当的方法建立生产过程的简单数学模型；2) According to the past production process data in the collected production history database, after data preprocessing, adopt an appropriate method to establish a simple mathematical model of the production process;

3)数据采集环节采集得到工业生产线中产品加工的输入输出数据，并根据目标跟踪轨迹计算跟踪误差曲线；3) The data acquisition link collects the input and output data of product processing in the industrial production line, and calculates the tracking error curve according to the target tracking trajectory;

4)依据步骤3)得到的跟踪误差，采用综合预测迭代学习控制算法计算下一批次的实时控制量；4) According to the tracking error obtained in step 3), the real-time control quantity of the next batch is calculated by using the comprehensive prediction iterative learning control algorithm;

5)在新的批次开始时，根据新的运行数据自适应地更新生产过程的模型；5) When a new batch starts, adaptively update the model of the production process according to the new operating data;

6)在每个新的采样点，实施步骤4)，实现对输出目标轨迹的有效跟踪。6) At each new sampling point, implement step 4) to achieve effective tracking of the output target trajectory.

上述控制方法中的所述步骤2)中，建立生产过程的数学模型方法如下：In the described step 2) in the above-mentioned control method, the mathematical model method of setting up the production process is as follows:

①根据历史数据库中以往的生产过程数据，在进行数据预处理后采用适当的方法建立过程数学模型：①According to the previous production process data in the historical database, use appropriate methods to establish the process mathematical model after data preprocessing:

假定某时刻输入样本集U＝(u₁,u₂,...,u_m)^T∈R^m，表示m个监测传感器在某个时刻的历史数据，m表示监测传感器的个数，R^m表示m维列向量；u_j表示在样本U中，第j个传感器数据的单个样本数据值，j＝1,2,...,m；该时刻的输出样本集为Y＝(y₁,y₂,...,y_n)^T∈Rⁿ，表示n个监测传感器在某个时刻的历史数据，n表示监测传感器的个数，Rⁿ表示n维列向量；y_j表示在样本Y中，第j个传感器数据的单个样本数据值，j＝1,2,...,n，假设采取N组历史数据，得到的输入数据总样本集如下：Q_u＝{U₁,...,U_m}，输入数据总样本集为：Q_y＝{Y₁,...,Y_m}，分别求得输入输出数据集的均值和方差，按照设定的数据限剔除不符合要求的样本点，最终得到总的样本集Q，在数据处理过程中，数据预处理的关键在于不合理数据的剔除和数据的归一化处理；Assume that the input sample set U=(u ₁ ,u ₂ ,...,u _m ) ^T ∈ R ^m at a certain time, represents the historical data of m monitoring sensors at a certain time, m represents the number of monitoring sensors, R ^m Represents an m-dimensional column vector; u _j represents the single sample data value of the jth sensor data in the sample U, j=1,2,...,m; the output sample set at this moment is Y=(y ₁ , y ₂ ,...,y _n ) ^T ∈ R ⁿ , represents the historical data of n monitoring sensors at a certain moment, n represents the number of monitoring sensors, R ⁿ represents n-dimensional column vector; y _j represents the , the single sample data value of the jth sensor data, j=1,2,...,n, assuming that N sets of historical data are taken, the total sample set of input data obtained is as follows: Q _u ={U ₁ ,.. .,U _m }, the total sample set of input data is: Q _y ＝{Y ₁ ,...,Y _m }, respectively obtain the mean and variance of the input and output data sets, and eliminate the unqualified according to the set data limit In the process of data processing, the key to data preprocessing lies in the elimination of unreasonable data and the normalization of data;

②建立数学模型。假定过程模型能用以下的离散方程表示：②Establish a mathematical model. Assume that the process model can be represented by the following discrete equations:

y(t)+a₁·y(t-1)+...+a_p·y(t-p)＝b₁·u(t-1)+...+b_q·u(t-q)+v(t) (1)y(t)+a ₁ ·y(t-1)+...+a _p ·y(tp)＝b ₁ ·u(t-1)+...+b _q ·u(tq)+v (t) (1)

将数据样本集Q中的数据分别代入离散方程的两端，采用最小二乘等适当方法取得离散方程中参数的近似值并找到离散方程的状态空间实现，以此作为间歇过程的数学模型，其得到的近似状态空间模型为：Substitute the data in the data sample set Q into both ends of the discrete equation respectively, use least squares and other appropriate methods to obtain the approximate values of the parameters in the discrete equation and find the state space realization of the discrete equation, and use this as the mathematical model of the batch process, which can be obtained The approximate state-space model for is:

$\{\begin{matrix} x x ((t t + + 11)) = = A A \cdot &Center Dot; x x ((t t)) + + B B \cdot &Center Dot; u u ((t t)) \\ y the y ((t t)) = = C C \cdot &Center Dot; x x ((t t)) + + d d ((t t)) \end{matrix} - - - - - - ((22))$

考虑到间歇过程的重复性质，记k为批次方向，则间歇过程的状态空间模型可以表述为：Considering the repetitive nature of the batch process, record k as the batch direction, then the state space model of the batch process can be expressed as:

$\{\begin{matrix} x x ((t t + + 11,, k k)) = = A A \cdot &Center Dot; x x ((t t,, k k)) + + B B \cdot &Center Dot; u u ((t t,, k k)) \\ y the y ((t t,, k k)) = = C C \cdot &Center Dot; x x ((t t,, k k)) + + d d ((t t,, k k)) \end{matrix} - - - - - - ((33))$

假定一个批次中采样点为N个，令第k个批次的输入输出轨迹分别为U_k＝[u_k(0),u_k(1),...,u_k(N-1)]^T、Y_k＝[y_k(1),y_k(2),...,y_k(N)]^T，可得过程的离散模型为：Assuming that there are N sampling points in a batch, let the input and output trajectories of the kth batch be U _k ＝[u _k (0),u _k (1),...,u _k (N-1) ] ^T , Y _k ＝[y _k (1),y _k (2),...,y _k (N)] ^T , the discrete model of the process can be obtained as:

Y_k＝GU_k+d_k (4)Y _k =GU _k +d _k (4)

其中：in:

$G G = = [\begin{matrix} {g g}_{1,0 1,0} & 00 & . . . . . . & 00 \\ {g g}_{2,0 2,0} & {g g}_{2,1 2,1} & . . . . . . & 00 \\ . . & . . \\ . . & . . & . . . . . . & 00 \\ . . & . . \\ {g g}_{N N,, 00} & {g g}_{N N,, 11} & . . . . . . & {g g}_{N N,, N N - - 11} \end{matrix}] &Element; &Element; {R R}^{N N \times \times N N},, {g g}_{i i,, j j} = = C C \cdot \cdot {A A}^{i i - - j j} \cdot &Center Dot; B B - - - - - - ((55))$

由此得到生产过程的数学模型。A mathematical model of the production process is thus obtained.

上述控制方法的步骤4)中，采用综合预测迭代学习控制算法计算下一批次的控制量方法如下：In the step 4) of the above-mentioned control method, the method of calculating the control quantity of the next batch using the comprehensive predictive iterative learning control algorithm is as follows:

①取控制律为：① Take the control law as:

$\begin{matrix} {u u}_{k k} ((t t)) = = {u u}_{k k}^{ILC ILC} ((t t)) + + {u u}_{k k}^{MPC MPC} ((t t)) \\ {u u}_{k k}^{ILC ILC} ((t t)) = = {u u}_{k k - - 11} ((t t)) + + {K K}^{ILC ILC} \cdot \cdot {e e}_{k k - - 11} ((t t + + 11)) \end{matrix} - - - - - - ((66))$

其中为迭代学习控制量，为预测控制量，综合预测迭代学习控制算法目的旨在找到使得下个批次间歇过程的输出更接近目标轨迹；in For the iterative learning control quantity, In order to predict the control quantity, the purpose of the comprehensive predictive iterative learning control algorithm is to find Make the output of the next batch batch process closer to the target trajectory;

②根据系统的离散模型，系统的预测输出为：② According to the discrete model of the system, the predicted output of the system is:

${\overset{^^}{Y Y}}_{k k}^{ILC ILC} ((_{t t + + m m}^{t t + + 11} | | t t)) = = {G G}_{pt pt} \cdot &Center Dot; {U u}_{k k} ((t t - - 11)) + + {G G}_{mt mt} \cdot &Center Dot; {U u}_{k k}^{ILC ILC} ((_{t t + + m m - - 11}^{t t} | | t t - - 11)) - - - - - - ((77))$

其中：in:

$\begin{matrix} {G G}_{pt pt} = = [\begin{matrix} {g g}_{t t + + 1,0 1,0} & {g g}_{t t + + 1,1 1,1} & . . . . . . & {g g}_{t t + + 11,, t t - - 11} & 00 & . . . . . . & 00 \\ {g g}_{t t + + 2,0 2,0} & {g g}_{t t + + 2,1 2,1} & . . . . . . & {g g}_{t t + + 22,, t t - - 11} & 00 & . . . . . . & 00 \\ . . & . . & . . & . . & . . & . . & . . \\ {g g}_{N N,, 00} & {g g}_{N N,, 11} & . . . . . . & {g g}_{N N,, t t - - 11} & 00 & . . . . . . & 00 \end{matrix}] &Element; &Element; {R R}^{((N N - - t t)) \times \times N N} \\ {G G}_{mt mt} = = [\begin{matrix} {g g}_{t t + + 11,, t t} & 00 & . . . . . . & 00 \\ {g g}_{t t + + 22,, t t} & {g g}_{t t + + 22,, t t + + 11} & . . . . . . & 00 \\ . . & . . & . . & . . \\ {g g}_{N N,, t t} & {g g}_{N N,, t t + + 11} & . . . . . . & {g g}_{N N,, N N - - 11} \end{matrix}] &Element; &Element; {R R}^{((N N - - t t)) \times \times ((N N - - t t))} \end{matrix} - - - - - - ((88))$

则跟踪误差可以由下式估计：Then the tracking error can be estimated by the following formula:

${\overset{^^}{E E.}}_{k k} ((_{t t + + m m}^{t t + + 11} | | t t)) = = {Y Y}_{d d} ((_{t t + + m m}^{t t + + 11} | | t t)) - - {G G}_{pt pt} \cdot \cdot {U u}_{k k} ((t t - - 11)) - - {G G}_{mt mt} \cdot \cdot (({U u}_{k k}^{ILC ILC} ((_{t t + + m m - - 11}^{t t} | | t t - - 11)) + + {U u}_{k k}^{MPC MPC} ((_{t t + + m m - - 11}^{t t} | | t t - - 11)))) - - - - - - ((99))$

③引入模型预测控制考虑以下准则函数：③The introduction of model predictive control considers the following criterion function:

$\underset{{U u}_{k k}^{MPC MPC} ((_{t t + + m m - - 11}^{t t} | | t t - - 11))}{min min} {J J}_{k k} ((_{t t + + m m}^{t t} | | t t)) = = {(({\overset{^^}{E E.}}_{k k} ((_{t t + + m m}^{t t + + 11} | | t t))))}^{T T} Q Q {\overset{^^}{E E.}}_{k k} ((_{t t + + m m}^{t t + + 11} | | t t)) + + {(({U u}_{k k}^{MPC MPC} ((_{t t + + m m - - 11}^{t t} | | t t - - 11))))}^{T T} {RU RU}_{k k}^{MPC MPC} ((_{t t + + m m - - 11}^{t t} | | t t - - 11)) - - - - - - ((1010))$

④由上式计算解析解可得控制律为：④ From the analytical solution of the above formula, the control law can be obtained as:

${U u}_{k k}^{MPC MPC} ((_{t t + + m m - - 11}^{t t} | | t t - - 11)) = = {[[{G G}_{mt mt}^{T T} Q Q {G G}_{mt mt} + + R R]]}^{- - 11} {G G}_{mt mt} Q Q {\overset{^^}{E E.}}_{k k}^{ILC ILC} ((_{t t + + m m}^{t t + + 11} | | t t)) - - - - - - ((1111))$

其中： ${\hat{E}}_{k}^{ILC} (_{t + m}^{t + 1} | t) = Y_{d} (F_{t + m}^{t + 1} | t) - G_{pt} \cdot U_{k} (t - 1) - G_{mt} \cdot U_{k}^{ILC} (_{t + m - 1}^{t} | t - 1),$ 在每个时间点t，应用解析解的第一项作为当前的输入修正量。in: ${\hat{E.}}_{k}^{ILC} (_{t + m}^{t + 1} | t) = Y_{d} (f_{t + m}^{t + 1} | t) - G_{pt} \cdot u_{k} (t - 1) - G_{mt} &Center Dot; u_{k}^{ILC} (_{t + m - 1}^{t} | t - 1),$ At each time point t, the first term of the analytical solution is applied as the current input modifier.

在每个批次内，随着时间t的变化，控制律的详细算法流程如下：In each batch, with the change of time t, the detailed algorithm flow of the control law is as follows:

①根据系统的近似模型，选择迭代学习律及其控制参数；① According to the approximate model of the system, select the iterative learning law and its control parameters;

②在新的批次开始时，根据新的批次运行数据自适应更新系统模型，计算迭代学习控制量，并设定时间t＝1；② At the beginning of a new batch, adaptively update the system model according to the new batch operation data, calculate the iterative learning control amount, and set the time t=1;

③在每个批次中的时刻t，实时计算预测控制修正量；③ At time t in each batch, calculate the predictive control correction amount in real time;

④如果t＜N，令t＝t+1并返回③，否则令k＝k+1，返回②。④If t<N, set t=t+1 and return to ③, otherwise set k=k+1 and return to ②.

本发明提出的基于模型自适应的综合预测迭代学习控制方法，由于采取以上技术方案，具有以下优点：The comprehensive predictive iterative learning control method based on model self-adaptation proposed by the present invention has the following advantages due to the adoption of the above technical scheme:

1、本发明利用提出的基于模型自适应的综合预测迭代学习控制算法，可以在一定程度上克服间歇过程模型误差问题，加快算法的收敛速度，应用范围很广。1. The present invention utilizes the proposed comprehensive predictive iterative learning control algorithm based on model self-adaptation, which can overcome the intermittent process model error problem to a certain extent, accelerate the convergence speed of the algorithm, and have a wide range of applications.

2、本方法可以克服由现实环境和加工手段给生产过程带来的噪声。本方法构思巧妙，简单实用，可广泛应用于工业生产线间歇生产过程的高精度控制。2. This method can overcome the noise brought to the production process by the actual environment and processing means. The method is ingenious in conception, simple and practical, and can be widely used in the high-precision control of the intermittent production process of industrial production lines.

具体实施方式Detailed ways

本发明提出的自适应整合预测迭代学习控制方法，包括以下步骤：The adaptive integrated predictive iterative learning control method proposed by the present invention comprises the following steps:

所述步骤2)中，建立生产过程的数学模型方法如下：Described step 2) in, set up the mathematical model method of production process as follows:

①根据历史数据库中以往的生产过程数据，在进行数据预处理后采用适当的方法建立过程数学模型。①According to the previous production process data in the historical database, use appropriate methods to establish process mathematical models after data preprocessing.

假定某时刻输入样本集U＝(u₁,u₂,...,u_m)^T∈R^m，表示m个监测传感器在某个时刻的历史数据，m表示监测传感器的个数，R^m表示m维列向量；u_j表示在样本U中，第j个传感器数据的单个样本数据值，j＝1,2,...,m；该时刻的输出样本集为Y＝(y₁,y₂,...,y_n)^T∈Rⁿ，表示n个监测传感器在某个时刻的历史数据，n表示监测传感器的个数，Rⁿ表示n维列向量；y_j表示在样本Y中，第j个传感器数据的单个样本数据值，j＝1,2,...,n。假设采取N组历史数据，得到的输入数据总样本集如下：Q_u＝{U₁,...,U_m}，输入数据总样本集为：Q_y＝{Y₁,...,Y_m}。分别求得输入输出数据集的均值和方差，按照设定的数据限剔除不符合要求的样本点。最终得到总的样本集Q。在数据处理过程中，数据预处理的关键在于不合理数据的剔除和数据的归一化处理。Assume that the input sample set U=(u ₁ ,u ₂ ,...,u _m ) ^T ∈ R ^m at a certain time, represents the historical data of m monitoring sensors at a certain time, m represents the number of monitoring sensors, R ^m Represents an m-dimensional column vector; u _j represents the single sample data value of the jth sensor data in the sample U, j=1,2,...,m; the output sample set at this moment is Y=(y ₁ , y ₂ ,...,y _n ) ^T ∈ R ⁿ , represents the historical data of n monitoring sensors at a certain moment, n represents the number of monitoring sensors, R ⁿ represents n-dimensional column vector; y _j represents the Among them, the single sample data value of the jth sensor data, j=1,2,...,n. Assuming that N sets of historical data are taken, the total sample set of input data obtained is as follows: Q _u ={U ₁ ,...,U _m }, and the total sample set of input data is: Q _y ={Y ₁ ,...,Y _m }. Calculate the mean and variance of the input and output data sets respectively, and eliminate the sample points that do not meet the requirements according to the set data limit. Finally, the total sample set Q is obtained. In the process of data processing, the key to data preprocessing lies in the elimination of unreasonable data and the normalization of data.

$\{\begin{matrix} x x ((t t + + 11)) = = A A \cdot &Center Dot; x x ((t t)) + + B B \cdot \cdot u u ((t t)) \\ y the y ((t t)) = = C C \cdot &Center Dot; x x ((t t)) + + d d ((t t)) \end{matrix} - - - - - - ((22))$

$\{\begin{matrix} x x ((t t + + 11,, k k)) = = A A \cdot &Center Dot; x x ((t t,, k k)) + + B B \cdot \cdot u u ((t t,, k k)) \\ y the y ((t t,, k k)) = = C C \cdot \cdot x x ((t t,, k k)) + + d d ((t t,, k k)) \end{matrix} - - - - - - ((33))$

Y_k＝GU_k+d_k (4)Y _k =GU _k +d _k (4)

其中：in:

$G G = = [\begin{matrix} {g g}_{1,0 1,0} & 00 & . . . . . . & 00 \\ {g g}_{2,0 2,0} & {g g}_{2,1 2,1} & . . . . . . & 00 \\ . . & . . \\ . . & . . & . . . . . . & 00 \\ . . & . . \\ {g g}_{N N,, 00} & {g g}_{N N,, 11} & . . . . . . & {g g}_{N N,, N N - - 11} \end{matrix}] &Element; &Element; {R R}^{N N \times \times N N},, {g g}_{i i,, j j} = = C C \cdot \cdot {A A}^{i i - - j j} \cdot \cdot B B - - - - - - ((55))$

所述步骤4)中，采用综合预测迭代学习控制算法计算下一批次的控制量方法如下：Described step 4) in, adopt comprehensive predictive iterative learning control algorithm to calculate the control quantity method of next batch as follows:

①取控制律为：① Take the control law as:

其中为迭代学习控制量，为预测控制量。综合预测迭代学习控制算法目的旨在找到使得下个批次间歇过程的输出更接近目标轨迹。in For the iterative learning control quantity, is the predictive control quantity. The purpose of the comprehensive predictive iterative learning control algorithm is to find Make the output of the next batch batch process closer to the target trajectory.

${\overset{^^}{Y Y}}_{k k}^{ILC ILC} ((_{t t + + m m}^{t t + + 11} | | t t)) = = {G G}_{pt pt} \cdot \cdot {U u}_{k k} ((t t - - 11)) + + {G G}_{mt mt} \cdot \cdot {U u}_{k k}^{ILC ILC} ((_{t t + + m m - - 11}^{t t} | | t t - - 11)) - - - - - - ((77))$

其中：in:

其中： ${\hat{E}}_{k}^{ILC} (_{t + m}^{t + 1} | t) = Y_{d} (F_{t + m}^{t + 1} | t) - G_{pt} \cdot U_{k} (t - 1) - G_{mt} \cdot U_{k}^{ILC} (_{t + m - 1}^{t} | t - 1),$ 在每个时间点t，应用解析解的第一项作为当前的输入修正量。in: ${\hat{E.}}_{k}^{ILC} (_{t + m}^{t + 1} | t) = Y_{d} (f_{t + m}^{t + 1} | t) - G_{pt} \cdot u_{k} (t - 1) - G_{mt} \cdot u_{k}^{ILC} (_{t + m - 1}^{t} | t - 1),$ At each time point t, the first term of the analytical solution is applied as the current input modifier.

在步骤4)中，关键在于各个控制参数的选取、控制算法，以及在批次开始前采用自适应的方法对模型进行修正。In step 4), the key lies in the selection of each control parameter, the control algorithm, and the use of an adaptive method to correct the model before the batch starts.

Claims

1., based on an integrated forecasting iterative learning control method for model adaptation, it is characterized in that the method comprises the following steps:

1) combine with actual production process, arrange a batch of data acquisition of producing and store link, this link can utilize the equipment such as the existing industrial control computer of manufacturing enterprise, PLC;

2) according to production process data in the past in the production history database that collects, after carrying out data prediction, the simple mathematical model of suitable method establishment production run is adopted;

3) data acquisition link collects the inputoutput data of Product processing in industrial production line, and according to target following trajectory calculation tracking error curve;

4) according to step 3) tracking error that obtains, adopt integrated forecasting Iterative Learning Control Algorithm to calculate the real-time controlled quentity controlled variable of next batch;

5) when starting for new batch, the model of production run is upgraded adaptively according to new service data;

6) at each new sampled point, implementation step 4), realize the effective tracking to exporting target trajectory.

2. a kind of integrated forecasting iterative learning control method based on model adaptation as claimed in claim 1, is characterized in that: described step 2) in, the mathematical model method setting up production run is as follows:

1. according to production process data in the past in historical data base, after carrying out data prediction, suitable method establishment process mathematical model is adopted:

Assuming that certain moment input amendment collection U=(u ₁, u ₂..., u _m) ^t∈ R ^m, represent that m monitoring sensor is in historical data sometime, m represents the number of monitoring sensor, R ^mrepresent m dimensional vector; u _jrepresent in sample U, the single sampled data values of a jth sensing data, j=1,2 ..., m; The output sample in this moment integrates as Y=(y ₁, y ₂..., y _n) ^t∈ R ⁿ, represent that n monitoring sensor is in historical data sometime, n represents the number of monitoring sensor, R ⁿrepresent n dimensional vector; y _jrepresent in sample Y, the single sampled data values of a jth sensing data, j=1,2 ..., n, supposes to take N group historical data, and the total sample set of input data obtained is as follows: Q _u={ U ₁..., U _m, the total sample set of input data is: Q _y={ Y ₁..., Y _m, try to achieve average and the variance of inputoutput data collection respectively, reject undesirable sample point according to the data limit of setting.Finally obtain total sample set Q, in data processing, the key of data prediction is the rejecting of unreasonable data and the normalized of data;

2. founding mathematical models.Assuming that process model can represent with following discrete equation:

y(t)+a ₁·y(t-1)+...+a _p·y(t-p)＝b ₁·u(t-1)+...+b _q·u(t-q)+v(t) (1)

Data in set of data samples Q are substituted into respectively the two ends of discrete equation, the proper method such as least square is adopted to obtain the approximate value of parameter in discrete equation and find the state space realization of discrete equation, in this, as the mathematical model of batch process, the approximation state spatial model that it obtains is:

\{\begin{matrix} x (t + 1) = A \cdot x (t) + B \cdot u (t) \\ y (t) = C \cdot x (t) + d (t) \end{matrix} - - - (2)

Consider the repetitive nature of batch process, note k is a batch direction, then the state-space model of batch process can be expressed as:

\{\begin{matrix} x (t + 1, k) = A \cdot x (t, k) + B \cdot u (t, k) \\ y (t, k) = C \cdot x (t, k) + d (t, k) \end{matrix} - - - (3)

Assuming that sampled point is N number of in one batch, the input and output track of individual batch of kth is made to be respectively U _k=[u _k(0), u _k(1) ..., u _k(N-1)] ^t, Y _k=[y _k(1), y _k(2) ..., y _k(N)] ^t, the discrete model that can obtain process is:

Y _k＝GU _k+d _k(4)

Wherein:

G = [\begin{matrix} g_{1,0} & 0 & . . . & 0 \\ g_{2,0} & g_{2,1} & . . . & 0 \\ . & . \\ . & . & . . . & 0 \\ . & . \\ g_{N, 0} & g_{N, 1} & . . . & g_{N, N - 1} \end{matrix}] &Element; R^{N \times N}, g_{i, j} = C \cdot A^{i - j} \cdot B - - - (5)

Obtain the mathematical model of production run thus.

3., as claimed in claim 1 based on the integrated forecasting iterative learning control method of model adaptation, it is characterized in that: described step 4) in, adopt the controlled quentity controlled variable method of integrated forecasting Iterative Learning Control Algorithm calculating next batch as follows:

1. getting control law is:

u_{k} (t) = u_{k}^{ILC} (t) + u_{k}^{MPC} (t)

(6)

u_{k}^{ILC} (t) = u_{k - 1} (t) + K^{ILC} \cdot e_{k - 1} (t + 1)

Wherein for iterative learning controlled quentity controlled variable, for PREDICTIVE CONTROL amount, integrated forecasting Iterative Learning Control Algorithm object is intended to find make the output of next batch of batch process closer to target trajectory;

2. according to the discrete model of system, the prediction of system exports and is:

{\hat{Y}}_{k}^{ILC} (_{t + m}^{t + 1} | t) = G_{pt} \cdot U_{k} (t - 1) + G_{mt} \cdot U_{k}^{ILC} (_{t + m - 1}^{t} | t - 1) - - - (7)

Wherein:

G_{pt} = [\begin{matrix} g_{t + 1,0} & g_{t + 1,1} & . . . & g_{t + 1, t - 1} & 0 & . . . & 0 \\ g_{t + 2,0} & g_{t + 2,1} & . . . & g_{t + 2, t - 1} & 0 & . . . & 0 \\ . & . & . & . & . & . & . \\ g_{N, 0} & g_{N, 1} & . . . & g_{N, t - 1} & 0 & . . . & 0 \end{matrix}] &Element; R^{(N - t) \times N}

(8)

G_{mt} = [\begin{matrix} g_{t + 1, t} & 0 & . . . & 0 \\ g_{t + 2, t} & g_{t + 2, t + 1} & . . . & 0 \\ . & . & . & . \\ g_{N, t} & g_{N, t + 1} & . . . & g_{N, N - 1} \end{matrix}] &Element; R^{(N - t) \times (N - t)}

Then tracking error can be estimated by following formula:

{\hat{E}}_{k} (_{t + m}^{t + 1} | t) = Y_{d} (_{t + m}^{t + 1} | t) - G_{pt} \cdot U_{k} (t - 1) - G_{mt} \cdot (U_{k}^{ILC} (_{t + m - 1}^{t} | t - 1) + U_{k}^{MPC} (_{t + m - 1}^{t} | t - 1)) - - - (9)

3. introduce Model Predictive Control and consider following criterion function:

\min_{U_{k}^{MPC} (_{t + m - 1}^{t} | t - 1)} J_{k} (_{t + m}^{t} | t) = {({\hat{E}}_{k} (_{t + m}^{t + 1} | t))}^{T} {\hat{E}}_{k} (_{t + m}^{t + 1} | t) + {(U_{k}^{MPC} (_{t + m - 1}^{t} | t - 1))}^{T} {RU}_{k}^{MPC} (_{t + m - 1}^{t} | t - 1) - - - (10)

4. can obtain control law by above formula calculating analytic solution is:

U_{k}^{MPC} (_{t + m - 1}^{t} | t - 1) = {[G_{mt}^{T} {QG}_{mt} + R]}^{- 1} G_{mt} Q {\hat{E}}_{k}^{ILC} (_{t + m}^{t + 1} | t) - - - (11)

Wherein:

{\hat{E}}_{k}^{ILC} (_{t + m}^{t + 1} | t) = Y_{d} (_{t + m}^{t + 1} | t) - G_{pt} \cdot U_{k} (t - 1) - G_{mt} \cdot U_{k}^{ILC} (_{t + m - 1}^{t} | t - 1),

At each time point t, the Section 1 of analytic application solution is as current Introduced Malaria amount.

4., as claimed in claim 3 based on the integrated forecasting iterative learning control method of model adaptation, it is characterized in that: in each batch, along with the change of time t, the detailed algorithm flow process of control law is as follows:

1. according to the approximate model of system, iterative learning control law and controling parameters thereof is selected;

2. when starting for new batch, according to new batch service data adaptive updates system model, iterative learning controlled quentity controlled variable is calculated, and setting-up time t=1;

3. the moment t in each batch, real-time computational prediction controls correction;

If 4. t < N, makes t=t+1 and returns 3., otherwise making k=k+1, returning 2..