CN103034122A

CN103034122A - Multi-model adaptive controller and control method based on time series

Info

Publication number: CN103034122A
Application number: CN2012104961155A
Authority: CN
Inventors: 王昕�; 黄淼; 牟金善
Original assignee: Shanghai Jiao Tong University
Current assignee: Shanghai Jiao Tong University
Priority date: 2012-11-28
Filing date: 2012-11-28
Publication date: 2013-04-10

Abstract

The invention discloses a multi-model self-adaptive controller and control method based on time series. The controller is mainly composed of a multi-model set, a switching mechanism and a controller. The multi-model set is used to identify changes in the system and includes several Local linear model, a weighted model and two adaptive models, the local linear model is used to cover all the variation range of the system model, the weighted model is used to identify the slow change of the system operating point, the adaptive model is used to improve the control accuracy, and the switching mechanism Select the optimal model to achieve control. The controller and control method not only have good transient performance and fast control speed, but also can greatly reduce the number of models under similar control effects.

Description

Multi-model adaptive controller and control method based on time series

技术领域 technical field

本发明涉及一种非线性被控对象，具体涉及基于时间序列的多模型自适应控制方法在非线性系统中的应用。 The invention relates to a nonlinear controlled object, in particular to the application of a time series-based multi-model adaptive control method in a nonlinear system. the

背景技术 Background technique

随着社会科技与经济的发展，生产工业的自动化程度不断提高，大多数的流程工业都实现了生产控制设备的集成化和系统化。大型工业控制系统以其设备的多样性和复杂性为特点，这种系统存在大量不确定性和强非线性，快时变，多工况等特点。在这种情况下，以往的控制方法因为无法达到良好的控制性能，而导致生产效率低下、生产资料的浪费。 With the development of social technology and economy, the degree of automation of the production industry has been continuously improved, and most process industries have realized the integration and systematization of production control equipment. Large-scale industrial control systems are characterized by the diversity and complexity of their equipment. This system has a large number of uncertainties, strong nonlinearity, fast time-varying, and multiple working conditions. In this case, the previous control methods cannot achieve good control performance, resulting in low production efficiency and waste of production materials. the

对于这种数学模型事先难以确定，或模型经常变化的复杂系统，反馈控制、最优控制等都不能很好的解决其控制问题。针对对象特性参数变化范围较大的情况，自适应控制算法可以不断测量被控对象状态、性能或参数的变化，通过决策来改变自适应控制器的结构，参数或根据自适应律来改变控制作用，从而克服或降低系统受外来干扰或内部参数变动所带来的对控制性能的影响，以保证系统在某种意义下的最优状态。自适应控制作为现代控制理论的一个重要分支，在控制方案、控制系统结构、稳定性、收敛性等方面都有了突破性的进展。尽管自适应控制方法能够处理一定范围内的系统参数变化，但对于复杂的工业过程来说，系统的故障或子系统动态变化引起的系统参数大幅度跳变或者被控对象从一个工况突然变化到其它工况的情况下，由于系统的自适应模型无法适应剧烈的变化，易导致控制性能的恶化。 For such a complex system whose mathematical model is difficult to determine in advance or whose model changes frequently, feedback control and optimal control cannot solve the control problems well. For the situation where the characteristic parameters of the object vary in a large range, the adaptive control algorithm can continuously measure the state, performance or parameter changes of the controlled object, and change the structure of the adaptive controller through decision-making, and change the control function according to the parameters or according to the adaptive law , so as to overcome or reduce the influence of the system on the control performance caused by external disturbance or internal parameter changes, so as to ensure the optimal state of the system in a certain sense. As an important branch of modern control theory, adaptive control has made breakthroughs in control scheme, control system structure, stability, convergence and so on. Although the adaptive control method can handle system parameter changes within a certain range, for complex industrial processes, system failures or subsystem dynamic changes cause large jumps in system parameters or sudden changes in the controlled object from a working condition In the case of other working conditions, because the adaptive model of the system cannot adapt to drastic changes, it is easy to lead to the deterioration of control performance. the

发明内容 Contents of the invention

针对上述现有技术中存在的技术问题，本发明提供一种基于时间序列的多模型自适应控制器及控制方法。该方法利用系统的时间序列和方向导数来辨识系统工作点的缓慢变化，通过系统数据间的时间与空间关系来对多模型集进行优化，从而达到减少模型数量，提高系统辨识精度和系统控制性能的目的。 Aiming at the technical problems existing in the above-mentioned prior art, the present invention provides a multi-model adaptive controller and control method based on time series. This method uses the time series and directional derivatives of the system to identify the slow change of the system operating point, and optimizes the multi-model set through the time and space relationship between the system data, so as to reduce the number of models, improve the system identification accuracy and system control performance. the goal of. the

为达到上述目的，本发明所采用的技术方案如下： In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

一种基于时间序列的多模型自适应控制控制器，主要由多模型集、控制器和切换机构三部分组成，其中，多模型集用来对系统进行逼近，对系统的参数及工作点的变化进行辨识，切换机构用来在多模型集中选择一个与被控对象最为接近的模型，以实现对被控对象的精确辨识，控制器是由切换机构选出的最优模型设计而来，从而实现对系统的最优控制。 A multi-model adaptive control controller based on time series is mainly composed of three parts: a multi-model set, a controller and a switching mechanism. For identification, the switching mechanism is used to select a model that is closest to the controlled object in the multi-model set to achieve accurate identification of the controlled object. The controller is designed from the optimal model selected by the switching mechanism to achieve optimal control of the system. the

所述多模型集包括多个线性局部模型、一个线性加权模型和两个全局线性自适应模型。 The multi-model set includes a plurality of linear local models, a linear weighted model and two global linear adaptive models. the

建立线性局部模型需要对系统的已知数据利用模糊核聚类自适应算法(Kernel Fuzzy Clustering Method with Self-adaption,KFCMA)来对系统数据进行聚类处理，将系统数据按照聚类隶属度划分成若干个子集，再对各个子集，利用递推最小二乘法(Recursive Least Squares,RLS)建立局部线性模型。 To establish a linear local model, it is necessary to use the Kernel Fuzzy Clustering Method with Self-adaption (KFCMA) to cluster the known data of the system, and divide the system data into Several subsets, and then for each subset, use the recursive least squares method (Recursive Least Squares, RLS) to establish a local linear model. the

在每一个采样时刻，将新获得的系统输入输出数据根据其与各聚类中心的距离分类到最近的聚类中去。利用系统数据的时间序列及新数据点到其它聚类中心的方向导数来判断系统工作点的变化趋势。并利用新数据点所在的聚类局部模型与趋势聚类局部模型来建立一个局部加权模型。 At each sampling moment, the newly obtained system input and output data are classified into the nearest cluster according to their distance from each cluster center. Use the time series of system data and the directional derivatives from new data points to other cluster centers to judge the changing trend of system operating points. A local weighted model is established by using the cluster local model where the new data point is located and the trend cluster local model. the

多模型集中还包括两个全局的自适应模型，其中一个为自由的自适应模型，另一个为可重新赋值的自适应模型。这两个模型用来在线性局部模型的基础上，根据系统的实时变化来更新模型参数，从而得到更好的辨识精度。 The multi-model set also includes two global adaptive models, one of which is a free adaptive model and the other is a reassignable adaptive model. These two models are used to update the model parameters according to the real-time changes of the system on the basis of the linear local model, so as to obtain better identification accuracy. the

系统的切换机构包括一个适当定义的性能指标，在每一个采样时刻，计算各个模型的性能指标值，由切换机构选出性能指标值最小的模型作为最优模型。 The switching mechanism of the system includes a properly defined performance index. At each sampling moment, the performance index value of each model is calculated, and the model with the smallest performance index value is selected by the switching mechanism as the optimal model. the

一种基于时间序列的多模型自适应控制方法，用于设计上述的多模型自适应控制器，该控制方法所包含的步骤如下： A time series-based multi-model adaptive control method for designing the above-mentioned multi-model adaptive controller, the steps included in the control method are as follows:

S1：用KFCMA算法对先验数据聚类，得聚类数c； S1: Use the KFCMA algorithm to cluster the prior data to obtain the number of clusters c;

S2：根据RLS方法对各类建立局部模型； S2: Build local models for various types according to the RLS method;

S3：初始化两个全局自适应模型； S3: Initialize two global adaptive models;

S4：寻找局部模型M_k和M_h，计算α₁,α₂，得到线性加权模型； S4: Find local models M _k and M _h , calculate α ₁ , α ₂ , and obtain a linear weighted model;

S5：各模型的性能指标

选择性能指标的值较小的模型； S5: Performance indicators of each model

Select a model with a smaller value of the performance index;

S6：设计控制器产生控制输入u(t)； S6: Design the controller to generate control input u(t);

S7：在每个采样周期重复S4-S6。 S7: Repeat S4-S6 in each sampling period. the

本发明技术所带来的有益效果如下： The beneficial effects brought by the technology of the present invention are as follows:

本发明的基于时间序列的多模型自适应控制器及控制方法，利用系统数据的时间和空间的关系来建立多模型集，这使得多模型集对系统的工作点发生变化时的辨识程度得到了大大提高，从而设计出的控制器可以更好的实现对系统的控制。与现有的其他多模型自适应控制器相比，能够减小系统的暂态误差，提高系统暂态性能和稳态性能。 The multi-model self-adaptive controller and control method based on time series of the present invention utilizes the time and space relationship of system data to establish a multi-model set, which makes the recognition degree of the multi-model set when the working point of the system changes is obtained. Greatly improved, so that the designed controller can better realize the control of the system. Compared with other existing multi-model adaptive controllers, it can reduce the transient error of the system and improve the transient performance and steady-state performance of the system. the

附图说明 Description of drawings

图1是本发明所公开的多模型自适应控制器的系统结构框图； Fig. 1 is the system structural block diagram of multi-model adaptive controller disclosed by the present invention;

图2(1)和2(2)分别是在单个自适应控制器下系统的输出曲线和输入曲线； Figures 2(1) and 2(2) are the output and input curves of the system under a single adaptive controller, respectively;

图3(1)和3(2)是在传统的多模型自适应控制器下系统的输出曲线和输入曲线； Figure 3(1) and 3(2) are the output curve and input curve of the system under the traditional multi-model adaptive controller;

图4(1)和(2)分别为本发明的控制器下系统的输出曲线和输入曲线。 Figure 4 (1) and (2) are respectively the output curve and the input curve of the system under the controller of the present invention. the

具体实施方式 Detailed ways

下面结合附图和具体实施例对本发明的技术方案作详细说明，本实施例在以本发明技术方案为前提下进行实施，给出了详细的实施方式和具体的操作过程，但本发明的保护范围不限于下述的实施例。 The technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation methods and specific operating procedures are provided, but the protection of the present invention The scope is not limited to the examples described below. the

如图1所示，本发明所针对的被控对象为如下的离散时间非线性系统，该非线性系统可分为线性部分和非线性部分： As shown in Figure 1, the controlled object targeted by the present invention is the following discrete-time nonlinear system, which can be divided into a linear part and a nonlinear part:

$\{\begin{matrix} x x ((t t + + 11)) = = Ax Ax ((t t)) + + Bu Bu ((t t)) + + F f ((x x ((t t)),, u u ((t t)))) \\ y the y ((t t)) = = Cx Cx ((t t)) + + G G ((x x ((t t)))) \end{matrix} - - - - - - ((11))$

式中，u(t),y(t)∈R分别是系统的输入和输出序列，x(t)∈Rⁿ是系统状态向量，F(·),H(·)是高阶函数。 In the formula, u(t), y(t)∈R are the input and output sequences of the system respectively, x(t)∈R ⁿ is the system state vector, F(·), H(·) are higher-order functions.

式(1)可以表示为如下形式： Formula (1) can be expressed as the following form:

$y the y ((t t + + d d)) = = {Σ Σ}_{j j = = 00}^{{n no}_{a a} - - 11} {a a}_{j j} y the y ((t t - - j j)) + + {Σ Σ}_{l l = = 00}^{{n no}_{b b} - - 11} {b b}_{l l} u u ((t t - - l l)) + + f f ((\cdot &Center Dot;)) - - - - - - ((22))$

$= = {θ θ}^{T T} ω ω ((t t)) + + f f ((ω ω ((t t))))$

式中，n_a、n_b分别为输出、输入变量的阶次，d为系统的时延，ω(t)=[y(t),…,y(t-n_a+1),u(t),…,u(t-n_b+1)]^T是回归向量。

是参数向量，f(·)是高阶非线性函数。 In the formula, n _a and n _b are the order of the output and input variables respectively, d is the time delay of the system, ω(t)=[y(t),…,y(tn _a +1),u(t) ,...,u(tn _b +1)] ^T is the regression vector.

is a parameter vector, and f(·) is a higher-order nonlinear function.

本发明控制方法的多模型集由模型M₁…M_c+3组成。该多模型集由基于时间序列的方法来建立。M₁…M_c是c个局部线性模型，分别对应c个系统数据的聚类。M_c+1，M_c+3是系统的全局自适应模型，M_c+2是系统的局部加权模型。其建立方法如下： The multi-model set of the control method of the present invention is composed of models M ₁ ...M _c+3 . The multi-model ensemble is built by a time-series-based approach. M ₁ ... M _c are c local linear models, corresponding to the clustering of c system data respectively. M _c+1 and M _c+3 are global adaptive models of the system, and M _c+2 is a local weighted model of the system. Its establishment method is as follows:

首先产生若干个随机信号输入给被控对象，得到对应的对象输出。由得到的输入和输出数据对构建数据样本集X={x₁,x₂,…,x_m}，其中x_t=[y(t),…,y(t-n_a+1),u(t),…,u(t-n_b+1),y(t+d)]是每一个随机输入和其对应的输出，采用模糊核聚类自适应算法(Kernel Fuzzy Clustering Method with Self-Adaption,KFCMA)，KFCMA算法具有自动寻找到最优的聚类数c、模糊划分矩阵U和每个聚类的聚类中心P={p₁,p₂,…,p_c}的能力。选择如下函数作为聚类的目标函数。 Firstly, several random signals are generated to be input to the controlled object, and the corresponding object output is obtained. Construct the data sample set X={x ₁ ,x ₂ ,…,x _m } from the obtained input and output data pairs, where x _t =[y(t),…,y(tn _a +1),u(t ),...,u(tn _b +1), y(t+d)] is each random input and its corresponding output, using the Kernel Fuzzy Clustering Method with Self-Adaption (KFCMA) , the KFCMA algorithm has the ability to automatically find the optimal number of clusters c, the fuzzy partition matrix U and the cluster center P={p ₁ ,p ₂ ,…,p _c } of each cluster. Select the following function as the objective function for clustering.

$\{\begin{matrix} J J ((U u,, P P)) = = {Σ Σ}_{i i = = 11}^{m m} {Σ Σ}_{j j = = 11}^{c c} {μ μ}_{ij ij}^{A A} {| | | | {x x}_{i i} - - {p p}_{j j} | | | |}^{22} = = {Σ Σ}_{i i = = 11}^{m m} {Σ Σ}_{j j = = 11}^{c c} {μ μ}_{ij ij}^{A A} {d d}_{ij ij}^{22} \\ \begin{matrix} s the s . . t t . . & U u &Element; &Element; {M m}_{fc fc} \end{matrix} \end{matrix} - - - - - - ((33))$

式中，

0≤μ_ij≤1,i＝1,2,…m,j=1,2,…,c,A>1是权重指数，μ_ij为X集中第j个数据对第i个聚类中心的隶属度。 In the formula,

0≤μ _ij ≤1, i=1,2,...m,j=1,2,...,c, A>1 is the weight index, μ _ij is the value of the jth data in the X set to the ith cluster center Membership.

根据隶属度矩阵U中每个数据最大的隶属度对数据进行严格划分，使每一个数据都属于唯一一个聚类。对于每个聚类采用递推最小二乘（Recursive Least Square，RLS）回归方法得到针对每个聚类的线性局部模型M₁,…,M_c: Strictly divide the data according to the maximum membership degree of each data in the membership degree matrix U, so that each data belongs to only one cluster. For each cluster, the Recursive Least Square (RLS) regression method is used to obtain the linear local model M ₁ ,...,M _c for each cluster:

$M_{i} : {\hat{y}}_{i} (t + d) = {\hat{θ}}_{i}^{T} (t) ω (t),$ i=1,…,c (4) $m_{i} : {\hat{the y}}_{i} (t + d) = {\hat{θ}}_{i}^{T} (t) ω (t),$ i=1,...,c (4)

式中， ${\hat{θ}}_{i} (t) = {[{\hat{a}}_{i, 0} (t), . . ., {\hat{a}}_{i, n_{a} - 1} (t), {\hat{b}}_{i, 0} (t), . . ., {\hat{b}}_{i, n_{b} - 1} (t)]}^{T}$ 是利用RLS方法得到的线性系数。 In the formula, ${\hat{θ}}_{i} (t) = {[{\hat{a}}_{i, 0} (t), . . ., {\hat{a}}_{i, {no}_{a} - 1} (t), {\hat{b}}_{i, 0} (t), . . ., {\hat{b}}_{i, {no}_{b} - 1} (t)]}^{T}$ is the linear coefficient obtained by using the RLS method.

建立自由的全局线性自适应模型M_c+1： Build a free global linear adaptive model M _c+1 :

${M m}_{c c + + 11} : : {\overset{^^}{y the y}}_{c c + + 11} ((t t + + d d)) = = {\overset{^^}{θ θ}}_{c c + + 11}^{T T} ((t t)) ω ω ((t t)) - - - - - - ((55))$

式中， ${\hat{θ}}_{c + 1} (t) = {[{\hat{a}}_{c + 1,0} (t), . . ., {\hat{a}}_{c + 1, n_{a} - 1} (t), {\hat{b}}_{c + 1,0} (t), . . ., {\hat{b}}_{c + 1, n_{b} - 1} (t)]}^{T}$ 是需要估计的模型的参数，

是模型的估计输出。 In the formula,

{\hat{θ}}_{c + 1} (t) = {[{\hat{a}}_{c + 1,0} (t), . . ., {\hat{a}}_{c + 1, {no}_{a} - 1} (t), {\hat{b}}_{c + 1,0} (t), . . ., {\hat{b}}_{c + 1, {no}_{b} - 1} (t)]}^{T}

are the parameters of the model to be estimated,

is the estimated output of the model.

模型M_c+1的自适应律为： The adaptive law of model M _c+1 is:

${\overset{^^}{θ θ}}_{c c + + 11} ((t t)) = = {\overset{^^}{θ θ}}_{c c + + 11} ((t t - - 11)) - - \frac{{a a}_{c c + + 11} ((t t)) {e e}_{c c + + 11} ((t t)) ω ω ((t t - - 11))}{11 + + {| | | | ω ω ((t t - - 11)) | | | |}^{22}} - - - - - - ((66))$

式中， $e_{c + 1} (t) = {\hat{y}}_{c + 1} (t) - y (t),$ $a_{c + 1} (t) = \{\begin{matrix} 1 & if | e_{c + 1} (t) | > 2 Δ \\ 0 & otherwise \end{matrix} .$ In the formula, $e_{c + 1} (t) = {\hat{the y}}_{c + 1} (t) - the y (t),$ $a_{c + 1} (t) = \{\begin{matrix} 1 & if | e_{c + 1} (t) | > 2 Δ \\ 0 & otherwise \end{matrix} .$

建立线性加权模型M_c+2 Establish a linear weighted model M _c+2

${M m}_{c c + + 22} : : {\overset{^^}{y the y}}_{c c + + 22} ((t t + + d d)) = = {\overset{^^}{θ θ}}_{c c + + 22}^{T T} ((t t)) ω ω ((t t)) - - - - - - ((77))$

式中，

α₁,α₂是线性加权系统，且满足α₁,α₂≥0，α₁+α₂=1，

的确定方法介绍如下： In the formula,

α ₁ , α ₂ are linear weighted systems, and satisfy α ₁ , α ₂ ≥ 0, α ₁ + α ₂ =1,

The determination method is described as follows:

由于非线性系统具有多个工作点，当其受到外界的扰动或输入信号变化时，系统可能会由一个工作点转移到另一个工作点。常规的多模型集只针对系统的输出信号进行处理，对工作点的变化不敏感且处理具有很大的滞后性，这使得当系统工作点发生变化时，系统暂态误差增大。 Since the nonlinear system has multiple operating points, when it is disturbed by the outside or the input signal changes, the system may shift from one operating point to another. The conventional multi-model set only processes the output signal of the system, which is insensitive to the change of the operating point and has a large lag in processing, which makes the transient error of the system increase when the operating point of the system changes. the

为了解决这一问题，本发明从工作点变化的预测角度，利用系统的方向导数和系统的时间序列来判断系统工作点的变化趋势，改变了控制器被动切换的传统状态，实现了良好的系统辨识。 In order to solve this problem, the present invention uses the directional derivative of the system and the time series of the system to judge the change trend of the system operating point from the perspective of predicting the change of the operating point, changes the traditional state of passive switching of the controller, and realizes a good system identify. the

下面介绍具体的实施步骤：在第一个采样时刻，系统将产生一个新的数据向量x_m+1。计算它与各聚类中心p_j的距离d_m+1,j=||x_m+1-p_j||,j=1,2,…,c 。根据d_m+1,k=mind_m+1,j=min(||x_m+1-p_j||)，j=1,2,…,c，得到新数据点隶属于的聚类k。利用系统梯度方向l的方向导数

来表征系统下一时刻的运动趋势，按照如下步骤确定加权系数和模型参数。 The specific implementation steps are introduced below: at the first sampling moment, the system will generate a new data vector x _m+1 . Calculate the distance d _m+1,j =||x _m+1 -p _j ||,j=1,2,…,c between it and each cluster center p _j . According to d _m+1,k =mind _m+1,j =min(||x _m+1 -p _j ||), j=1,2,...,c, get the cluster k to which the new data point belongs . Using the directional derivative of the system gradient direction l

To characterize the motion trend of the system at the next moment, the weighting coefficient and model parameters are determined according to the following steps.

1：计算系统的方向导数

l_j是沿着数据点到其他所有聚类的中心的方向向量，标志着系统在该方向上的变化趋势。计算

选出与系统下一时刻输出最接近的聚类h。计算系统梯度与方向l_h的夹角余弦

如果(cos<l,l_h>)≥0，则说明系统的梯度近似指向聚类h；否则，说明系统的梯度方向背离h； 1: Calculate the directional derivative of the system

l _j is the direction vector along the data point to the center of all other clusters, which marks the trend of the system in this direction. calculate

Select the cluster h closest to the output of the system at the next moment. Calculate the cosine of the angle between the system gradient and the direction l _h

If (cos<l,l _h >)≥0, it means that the gradient of the system is approximately pointing to cluster h; otherwise, it means that the gradient direction of the system deviates from h;

2：计算l_t，t-1=x_t-x_t-1表征系统上一时刻的方向变化，如果l_t，t-1与数据到方向向量l_k的夹角余弦

则说明当前系统正在背离其所在的聚类，否则，说明系统并不会逃离其所在聚类； 2: Calculate l _{t, t-1} = x _t -x _t-1 to represent the direction change of the system at the last moment, if l _{t, t-1} and the cosine of the angle between the data and the direction vector l _k

It means that the current system is departing from its cluster, otherwise, it means that the system will not escape from its cluster;

3：如果有(cos<l,l_h>)≥0与(cos<l_t，t-1,l_k>)<0，则说明系统的工作点可能由第k个聚类变化到第h个聚类，则模型M_k和M_h加权得到新的模型M_c+2，且

分别为模型M_k和M_h的参数。 3: If (cos<l, l _h >)≥0 and (cos<l _{t, t-1} , l _k >)<0, it means that the operating point of the system may change from the kth cluster to the hth cluster clusters, the model M _k and M _h are weighted to obtain a new model M _c+2 , and

are the parameters of the models M _k and M _h respectively.

建立系统的可重新赋值的全局自适应模型M_c+3，当模型处于M_c+3时，参数按照如下自适应律进行更新： Establish a reassignable global adaptive model M _c+3 of the system. When the model is in M _c+3 , the parameters are updated according to the following adaptive law:

${\overset{^^}{θ θ}}_{c c + + 33} ((t t)) = = {\overset{^^}{θ θ}}_{c c + + 33} ((t t - - 11)) - - \frac{{a a}_{c c + + 33} ((t t)) {e e}_{c c + + 33} ((t t)) ω ω ((t t - - 11))}{11 + + {| | | | ω ω ((t t - - 11)) | | | |}^{22}} - - - - - - ((88))$

否则，把所选最优模型的参数值直接赋给

Otherwise, directly assign the parameter values of the selected optimal model to

图1所示，系统还包括了一个切换机构，该切换机构用来在多模型集中选择一个模型，来设计控制器，以实现对系统的控制。 As shown in Figure 1, the system also includes a switching mechanism, which is used to select a model in the multi-model set to design a controller to control the system. the

该切换机构包含一个切换指标，对每一个模型按照下述公式分别计算切换指标的值： The switching mechanism contains a switching index, and the value of the switching index is calculated for each model according to the following formula:

${J J}_{j j} ((t t)) = = {Σ Σ}_{l l = = 11}^{t t} \frac{{a a}_{j j} ((l l)) (({e e}_{j j}^{22} ((l l)) - - 44 {Δ Δ}^{22}))}{22 ((11 + + {| | | | ω ω ((l l - - 11)) | | | |}^{22}))} + + h h {Σ Σ}_{l l = = k k - - N N + + 11}^{t t} ((11 - - {a a}_{j j} ((l l)))) {e e}_{j j}^{22} ((l l)) - - - - - - ((99))$

其中j=1,2,…c+3，

N是一个整数，

a_{j} (k) = \{\begin{matrix} 1 & if | e_{j} (t) | > 2 Δ \\ 0 & otherwise \end{matrix},

h≥0是一个常数。 where j=1,2,...c+3,

N is an integer,

a_{j} (k) = \{\begin{matrix} 1 & if | e_{j} (t) | > 2 Δ \\ 0 & otherwise \end{matrix},

h≥0 is a constant.

若J_i(t)=minJ_j(t)，则将系统的模型切换到最优的第i个模型上去。 If J _i (t)=minJ _j (t), then switch the model of the system to the optimal i-th model.

根据切换机构选择的最优模型，设计如下的控制器： According to the optimal model selected by the switching mechanism, the following controller is designed:

$u u ((t t)) = = \frac{11}{{\overset{^^}{b b}}_{00}^{((i i))} ((t t))} (({y the y}^{* *} ((t t + + d d)) - - {\overset{^^}{\overset{&OverBar; &OverBar;}{θ θ}}}_{i i} ((t t)) \overset{&OverBar; &OverBar;}{ω ω} ((t t)))) - - - - - - ((1010))$

其中i＝1,…,c+3, $\overset{&OverBar;}{ω} (t) = {[y (y), . . ., y (t - n_{a} + 1), u (t - 1), . . ., u (t - n_{b} + 1)]}^{T},$ where i=1,...,c+3, $\overset{&OverBar;}{ω} (t) = {[the y (the y), . . ., the y (t - {no}_{a} + 1), u (t - 1), . . ., u (t - {no}_{b} + 1)]}^{T},$

${\overset{^^}{\overset{&OverBar; &OverBar;}{θ θ}}}_{i i} = = {[[{a a}_{i i,, 00},, . . . . . .,, {a a}_{i i,, n no - - 11},, {b b}_{i i,, 11},, . . . . . .,, {b b}_{i i,, n no - - 11}]]}^{T T} . .$

图2(1)和2(2)分别是在单个自适应控制器下系统输出曲线和输入曲线。可以看出，系统的输出的跟踪性能不是很好，跟踪的速度缓慢，瞬态误差大，输入频繁而存在剧烈的震荡。 Figure 2(1) and 2(2) are the system output curve and input curve under a single adaptive controller, respectively. It can be seen that the tracking performance of the output of the system is not very good, the tracking speed is slow, the transient error is large, and the input is frequent and there is severe vibration. the

图3(1)和3(2)是在传统的多模型自适应控制系统的输出曲线和输入曲线。该控制器具有2500个参数在参数空间均匀选择的固定模型。可以看出，其输出曲线暂态误差小于单个自适应控制器。 Fig. 3(1) and 3(2) are the output curves and input curves in the traditional multi-model adaptive control system. The controller has a fixed model with 2500 parameters chosen uniformly in the parameter space. It can be seen that the transient error of its output curve is smaller than that of a single adaptive controller. the

图4(1)和(2)分别为本发明的控制系统的输入和输出曲线。多模型自适应控制器有19个局部线性模型，并根据上述算法的实时更新。可以清楚的看到，控制性能和控制效果与图3是类似的，但只有19的模型，大大减少了模型数量，减少了计算量。 Figure 4 (1) and (2) are the input and output curves of the control system of the present invention respectively. The multi-model adaptive controller has 19 local linear models and is updated in real time according to the above algorithm. It can be clearly seen that the control performance and control effect are similar to those in Figure 3, but there are only 19 models, which greatly reduces the number of models and the amount of calculation. the

Claims

1. the multi-model Adaptive Control device of a time-based sequence, it is characterized in that, this controller mainly is comprised of multi-model collection, switching mechanism and controller three parts, wherein, the multi-model collection is used for system is approached, the parameter of system and the variation of working point are carried out identification, switching mechanism is used for concentrating the model of selecting one to approach the most with controlled device at multi-model, to realize the accurate identification to controlled device, controller is the optimization model design of being selected by switching mechanism, realizes the optimum control to system.

2. multi-model Adaptive Control device according to claim 1 is characterized in that, described multi-model collection comprises several linear partial models, a local weighted model of linearity and two overall adaptive models.

3. multi-model Adaptive Control device according to claim 2, it is characterized in that, described several Local Linear Models are by the fuzzy kernel clustering adaptive algorithm system data to be carried out clustering processing, system data is divided into several subsets according to the cluster degree of membership, utilizes least square method of recursion to set up Local Linear Model to each subset again.

4. multi-model Adaptive Control device according to claim 2, it is characterized in that, the local weighted model of described linearity is the relation by analytic system data time and space, by time series and the common prognoses system changing operate-point of the directional derivative trend of system, two Local Linear Model weightings that search out obtain.

5. multi-model Adaptive Control device according to claim 4, it is characterized in that, described two Local Linear Models are in each sampling instant, with system's inputoutput data of newly obtaining according to the distance classification of itself and each cluster centre in nearest cluster, utilize the time series of system data and new data point to judge the variation tendency of system works point to the directional derivative of other cluster centre, obtain cluster partial model and the trend cluster partial model at new data point place.

6. adaptive controller according to claim 3, it is characterized in that, one of them of described two overall adaptive models is overall adaptive model freely, another is again the adaptive model of assignment, namely when system model switches each time, if switch to a partial model or freely on the adaptive model time, then use the again parameter of the adaptive model of assignment of its parameter value initialization.

7. multi-model Adaptive Control device according to claim 1, it is characterized in that, described switching mechanism comprises predefined performance index, in each sampling instant, calculate the performance index value of each model, select the model of performance index value minimum as optimization model by switching mechanism.

8. the multi-model Adaptive Control method of a time-based sequence is characterized in that, is used for the arbitrary described multi-model Adaptive Control device of design claim 1 to 7, and the step that this control method comprises is as follows:

S1: to the priori data cluster, get cluster numbers c with the KFCMA algorithm;

S2: according to the RLS method to all kinds of partial models of setting up;

S3: two overall adaptive models of initialization;

S4: seek partial model M _kAnd M _h, calculate α ₁, α ₂, obtain linear weighted model;

S5: the performance index of each model

Selectivity refers to the model that target value is less;

S6: CONTROLLER DESIGN produces control inputs u (t);

S7: repeat S4-S6 in each sampling period.