CN114995149B - Hydraulic position servo system improved chaos variable weight sparrow search parameter identification method - Google Patents

Hydraulic position servo system improved chaos variable weight sparrow search parameter identification method Download PDF

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CN114995149B
CN114995149B CN202210665775.5A CN202210665775A CN114995149B CN 114995149 B CN114995149 B CN 114995149B CN 202210665775 A CN202210665775 A CN 202210665775A CN 114995149 B CN114995149 B CN 114995149B
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李俊红
严俊
蒋一哲
陈楠
程赟
张泓睿
储杰
褚云琨
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Abstract

本发明提供了一种液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法，属于液压位置伺服系统辨识技术领域。解决了液压位置伺服系统进行分析和控制时给液压位置伺服系统建立的数学模型，辨识所建立模型的参数和时间延迟的技术问题。其技术方案为：包括以下步骤：步骤1)建立液压位置伺服系统的单输入单输出模型；步骤2)构建液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法的辨识流程，对所有参数和时间延迟进行估计。本发明的有益效果为：本发明提出的液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法有较快的收敛速度和较高的收敛精度，能较好地适用于对液压位置伺服系统时滞反馈非线性模型的建模和参数辨识。

Figure 202210665775

The invention provides an improved chaotic variable-weight sparrow search parameter identification method for a hydraulic position servo system, which belongs to the technical field of hydraulic position servo system identification. The technical problem of establishing a mathematical model for the hydraulic position servo system and identifying parameters and time delays of the established model is solved when the hydraulic position servo system is analyzed and controlled. The technical solution is: including the following steps: Step 1) Establishing a single input and single output model of the hydraulic position servo system; Step 2) Constructing the hydraulic position servo system to improve the identification process of the chaotic variable weight sparrow search parameter identification method, for all parameters and time Latency is estimated. The beneficial effects of the present invention are: the improved chaotic variable weight sparrow search parameter identification method for the hydraulic position servo system proposed by the present invention has faster convergence speed and higher convergence accuracy, and can be better applied to the time lag of the hydraulic position servo system Modeling and parameter identification for feedback nonlinear models.

Figure 202210665775

Description

液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法Improved chaotic variable weight sparrow search parameter identification method for hydraulic position servo system

技术领域Technical Field

本发明涉及技术领域，尤其涉及一种液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法。The invention relates to the technical field, and in particular to an improved chaotic variable weight sparrow search parameter identification method for a hydraulic position servo system.

背景技术Background Art

随着军工产品和民用工业的发展，对于液压位置伺服系统的要求越来越高。液压位置伺服系统不仅需要能够快速动作，并且精度要求也越来越高。为了更好地对液压位置伺服系统进行分析和控制，需要给液压位置伺服系统建立相应的数学模型，同时辨识所建立模型的参数和时间延迟。经过几十年计算机技术的发展，开发了许多辨识方法，例如遗传算法、蚁群算法和鲸鱼优化算法。遗传算法具有较强的全局搜索能力，但该算法局部搜索能力较弱，往往只能得到次优解。蚁群算法收敛速度快，但需设置的参数多且搜索随机性大，导致在实际生产中不能达到令人满意的辨识效果；鲸鱼算法能够在单目标优化问题上表现不错，但这种方法在多目标搜索上的效果差强人意，而且易陷入局部最优，导致数值估计误差较大。With the development of military products and civilian industries, the requirements for hydraulic position servo systems are getting higher and higher. The hydraulic position servo system not only needs to be able to move quickly, but also has higher and higher precision requirements. In order to better analyze and control the hydraulic position servo system, it is necessary to establish a corresponding mathematical model for the hydraulic position servo system and identify the parameters and time delay of the established model. After decades of development of computer technology, many identification methods have been developed, such as genetic algorithms, ant colony algorithms, and whale optimization algorithms. Genetic algorithms have strong global search capabilities, but the local search capabilities of this algorithm are weak, and often only suboptimal solutions can be obtained. The ant colony algorithm has a fast convergence speed, but many parameters need to be set and the search is highly random, resulting in unsatisfactory identification effects in actual production; the whale algorithm can perform well on single-objective optimization problems, but this method is unsatisfactory in multi-objective search, and it is easy to fall into local optimality, resulting in large numerical estimation errors.

发明内容Summary of the invention

本发明的目的在于提供一种液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法，本发明提出的液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法是一种群智能优化算法，它具有更快的收敛速度和更高的收敛精度，能较好地适用于对液压位置伺服系统的参数辨识。The purpose of the present invention is to provide an improved chaotic variable weight sparrow search parameter identification method for a hydraulic position servo system. The improved chaotic variable weight sparrow search parameter identification method for a hydraulic position servo system proposed in the present invention is a swarm intelligence optimization algorithm, which has a faster convergence speed and higher convergence accuracy, and can be better applied to parameter identification of a hydraulic position servo system.

为了实现上述发明目的，本发明采用技术方案具体为：一种液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法，具体包括以下步骤：In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically: a method for identifying parameters of a hydraulic position servo system by improving chaotic variable weight sparrow search, which specifically includes the following steps:

步骤1)构建液压位置伺服系统的时滞反馈非线性辨识模型。Step 1) Construct a time-delay feedback nonlinear identification model of the hydraulic position servo system.

步骤2)构建液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法的辨识流程。Step 2) Construct the identification process of the improved chaotic variable weight sparrow search parameter identification method for the hydraulic position servo system.

第一步：初始化麻雀搜索算法，采用改进的Circle混沌映射初始化麻雀种群；Step 1: Initialize the sparrow search algorithm and use the improved Circle chaos map to initialize the sparrow population;

第二步：收集液压位置伺服系统的给定电压信号作为输入数据，液压位置伺服系统的负载位移数据作为输出数据；Step 2: Collect the given voltage signal of the hydraulic position servo system as input data, and the load displacement data of the hydraulic position servo system as output data;

第三步：计算麻雀群体中个体适应度，对所有麻雀个体适应度进行排序，找出全局最优适应度值和全局最差适应度值，然后计算初始全局最优位置；Step 3: Calculate the individual fitness of the sparrow group, sort the fitness of all sparrows, find the global optimal fitness value and the global worst fitness value, and then calculate the initial global optimal position;

第四步：令迭代变量k＝1，计算麻雀的初始位置；Step 4: Set the iteration variable k = 1 and calculate the initial position of the sparrow;

第五步：基于线性递减权重法计算当前的惯性权重值，更新发现者位置；Step 5: Calculate the current inertia weight value based on the linear decreasing weight method and update the discoverer's position;

第六步：更新跟随者的位置；Step 6: Update the follower's position;

第七步：更新警戒者的位置；Step 7: Update the position of the sentinel;

第八步：计算麻雀种群适应度并进行重新排序，更新麻雀种群位置；Step 8: Calculate the fitness of the sparrow population and re-sort it, and update the position of the sparrow population;

第九步：对于所有麻雀，计算群体最佳麻雀位置；Step 9: For all sparrows, calculate the best sparrow position in the group;

第十步：从群体最佳位置中分离提取出参数向量和时延的估计值；Step 10: Separate and extract the parameter vector and the estimated value of the delay from the group's best position;

第十一步：将迭代变量k值加1，重复上述过程。Step 11: Add 1 to the iteration variable k and repeat the above process.

作为本发明提供的基于改进Circle混沌线性变权麻雀搜索算法的液压位置伺服系统时滞反馈非线性模型辨识方法进一步优化方案，所述步骤1)的具体建模步骤如下：As a further optimization scheme of the time-delay feedback nonlinear model identification method of the hydraulic position servo system based on the improved Circle chaos linear variable weight sparrow search algorithm provided by the present invention, the specific modeling steps of step 1) are as follows:

(1-1)构建液压位置伺服系统的时滞反馈非线性模型：(1-1) Construct a time-delay feedback nonlinear model of the hydraulic position servo system:

Figure BDA0003691605780000021
Figure BDA0003691605780000021

Figure BDA0003691605780000022
Figure BDA0003691605780000022

Figure BDA0003691605780000023
Figure BDA0003691605780000023

Figure BDA0003691605780000024
Figure BDA0003691605780000024

其中，r(t)为输入量，y(t)为输出量，

Figure BDA0003691605780000025
为反馈通道输出，v(t)是一个均值为零、方差为σ2满足高斯分布的白噪声；定义x(t)，u(t)和w(t)为不可测的中间变量；τ是反馈非线性系统时滞，z为后移算子:z-1y(t)＝y(t-1)，A(z)，B(z)是关于z的多项式，描述为如下形式：Among them, r(t) is the input, y(t) is the output,
Figure BDA0003691605780000025
is the feedback channel output, v(t) is a white noise with zero mean and variance σ2 that satisfies Gaussian distribution; x(t), u(t) and w(t) are defined as unmeasurable intermediate variables; τ is the time lag of the feedback nonlinear system, z is the backshift operator: z -1 y(t) = y(t-1), A(z), B(z) are polynomials about z, described as follows:

Figure BDA0003691605780000026
Figure BDA0003691605780000026

Figure BDA0003691605780000027
Figure BDA0003691605780000027

将系统的非线性部分可以用传递函数表示为：The nonlinear part of the system can be expressed by the transfer function as:

Figure BDA0003691605780000028
Figure BDA0003691605780000028

其中，未知参数γi(i＝1,2,...,m)是非线性函数的系数，m是非线性块的参数个数。Among them, the unknown parameters γ i (i＝1,2,...,m) are the coefficients of the nonlinear function, and m is the number of parameters of the nonlinear block.

将公式两边同乘以A(z)得到：Multiplying both sides of the formula by A(z) yields:

A(z)y(t)＝q-τB(z)u(t)+v(t) (8)A(z)y(t)＝q -τ B(z)u(t)+v(t) (8)

可表示为：It can be expressed as:

Figure BDA0003691605780000031
Figure BDA0003691605780000031

其中噪声模型输出w(t)和前馈通道输出x(t)为：The noise model output w(t) and the feedforward channel output x(t) are:

Figure BDA0003691605780000032
Figure BDA0003691605780000032

Figure BDA0003691605780000033
Figure BDA0003691605780000033

反馈非线性系统模型可以表示为：The feedback nonlinear system model can be expressed as:

Figure BDA0003691605780000034
Figure BDA0003691605780000034

(1-2)将线性子系统的参数向量a、b以及非线性部分的参数向量γ定义为：(1-2) The parameter vectors a and b of the linear subsystem and the parameter vector γ of the nonlinear part are defined as:

Figure BDA0003691605780000035
Figure BDA0003691605780000035

那么整个模型的参数向量θ表示为：Then the parameter vector θ of the entire model is expressed as:

Figure BDA0003691605780000036
Figure BDA0003691605780000036

对应的信息向量

Figure BDA0003691605780000037
表示为：The corresponding information vector
Figure BDA0003691605780000037
It is expressed as:

Figure BDA0003691605780000038
Figure BDA0003691605780000038

Figure BDA0003691605780000039
Figure BDA0003691605780000039

其中：in:

Figure BDA00036916057800000310
Figure BDA00036916057800000310

Figure BDA00036916057800000311
Figure BDA00036916057800000311

Figure BDA0003691605780000041
Figure BDA0003691605780000041

其中：in:

f(y(t))＝[f1(y(t)),f2(y(t)),...,fm(y(t))]∈R1×m f(y(t))＝[f 1 (y(t)), f 2 (y(t)),..., f m (y(t))]∈R 1×m

根据上述定义，系统的非线性部分

Figure BDA0003691605780000042
表示为：According to the above definition, the nonlinear part of the system
Figure BDA0003691605780000042
It is expressed as:

Figure BDA0003691605780000043
Figure BDA0003691605780000043

(1-3)然后我们得到描述的液压位置伺服系统的时滞反馈非线性模型：(1-3) Then we get the time-delay feedback nonlinear model of the hydraulic position servo system described:

Figure BDA0003691605780000044
Figure BDA0003691605780000044

然后我们得到液压位置伺服系统的时滞反馈非线性模型为：Then we get the time-delay feedback nonlinear model of the hydraulic position servo system as:

Figure BDA0003691605780000045
Figure BDA0003691605780000045

作为本发明提供的液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法的进一步优化方案，所述步骤2)构建液压位置伺服系统改进混沌变权麻雀搜索参数辨识流程的具体步骤如下：As a further optimization scheme of the improved chaotic variable weight sparrow search parameter identification method for the hydraulic position servo system provided by the present invention, the specific steps of step 2) constructing the improved chaotic variable weight sparrow search parameter identification process for the hydraulic position servo system are as follows:

(2-1)设置麻雀个数为N，每个麻雀包含na+nb+m个变量，通过(18)，采用改进的Circle混沌映射初始化麻雀种群。设置Xn为当前麻雀的位置，Xn+1为更新后的麻雀位置，最大迭代次数为T、预警值为ST、发现者PD和警戒者SD比例及wmax、wmin，wk为惯性权重，wmax和wmin分别为线性权重的最大值和最小值。(2-1) Set the number of sparrows to N, each sparrow contains n a +n b +m variables, and use the improved Circle chaotic map to initialize the sparrow population through (18). Set X n to the current position of the sparrow, X n+1 to the updated position of the sparrow, the maximum number of iterations to T, the warning value to ST, the ratio of the discoverer PD and the vigilant SD, and w max , w min , w k to be the inertia weight, w max and w min to be the maximum and minimum values of the linear weight respectively.

原Circle混沌映射表达式为：The original Circle chaos map expression is:

Figure BDA0003691605780000051
Figure BDA0003691605780000051

改进之后的Circle混沌映射表达式为：The improved Circle chaos mapping expression is:

Figure BDA0003691605780000052
Figure BDA0003691605780000052

(2-2)收集液压位置伺服系统的给定电压信号输入数据和负载位移输出数据{r(t)，y(t)}。构造形式输出堆积向量Y(l)如下式(19)：(2-2) Collect the given voltage signal input data and load displacement output data {r(t), y(t)} of the hydraulic position servo system. The output stacking vector Y(l) is constructed as follows (19):

Y(l)＝[y(l),y(l-1),...,y(1)]T∈Rl (19)Y(l)＝[y(l),y(l-1),...,y(1)] T ∈R l (19)

构造ψ(l,τ)为信息堆积向量如式(20)：Construct ψ(l,τ) as the information accumulation vector as shown in formula (20):

Figure BDA0003691605780000053
Figure BDA0003691605780000053

其中，l为数据长度。Where l is the data length.

(2-3)通过(21)计算麻雀群体中个体适应度，对所有麻雀个体适应度进行排序，找出全局最优适应度值fg和全局最差适应度值fw，然后通过(22)计算初始全局最优位置

Figure BDA0003691605780000054
(2-3) Calculate the individual fitness of the sparrow group through (21), sort the fitness of all sparrows, find the global optimal fitness value fg and the global worst fitness value fw , and then calculate the initial global optimal position through (22)
Figure BDA0003691605780000054

Figure BDA0003691605780000055
Figure BDA0003691605780000055

Figure BDA0003691605780000056
Figure BDA0003691605780000056

(2-4)设迭代变量k＝1，开始迭代，个体的初始位置是

Figure BDA0003691605780000057
(2-4) Let the iteration variable k = 1, start the iteration, and the initial position of the individual is
Figure BDA0003691605780000057

Figure BDA0003691605780000058
Figure BDA0003691605780000058

(2-5)基于线性递减权重法通过(24)计算wk，通过式子(25)将发现者位置更新为

Figure BDA0003691605780000059
(2-5) Based on the linear decreasing weight method, w k is calculated by (24), and the discoverer position is updated by equation (25) as
Figure BDA0003691605780000059

Figure BDA00036916057800000510
Figure BDA00036916057800000510

Figure BDA00036916057800000511
Figure BDA00036916057800000511

其中，k为迭代变量；

Figure BDA0003691605780000061
表示在第k代中第i只麻雀在第j维的位置，随机数ξ∈[0,1]，
Figure BDA0003691605780000062
为第k代种群全局最优适应度，Q是服从正态分布的随机数，L是一个每个元素均为1的1×d维的矩阵；R2表示报警值，ST表示安全阈值。Among them, k is the iteration variable;
Figure BDA0003691605780000061
represents the position of the i-th sparrow in the j-th dimension in the k-th generation, the random number ξ∈[0,1],
Figure BDA0003691605780000062
is the global optimal fitness of the kth generation population, Q is a random number that obeys the normal distribution, L is a 1×d-dimensional matrix in which each element is 1; R 2 represents the alarm value, and ST represents the safety threshold.

(2-6)根据(26)更新跟随者位置

Figure BDA0003691605780000063
(2-6) Update the follower position according to (26)
Figure BDA0003691605780000063

Figure BDA0003691605780000064
Figure BDA0003691605780000064

其中，

Figure BDA0003691605780000065
表示第k代适应度值最差的个体位置，
Figure BDA0003691605780000066
表示第k+1代中适应度最佳的个体位置。A表示1×d的矩阵，矩阵中每个元素预设为-1或1，并且A+＝AT(AAT)-1。in,
Figure BDA0003691605780000065
Indicates the position of the individual with the worst fitness value in the kth generation,
Figure BDA0003691605780000066
represents the position of the individual with the best fitness in the k+1th generation. A represents a 1×d matrix, each element in the matrix is preset to -1 or 1, and A + = AT (AA T ) -1 .

(2-7)根据(27)更新警戒者位置

Figure BDA0003691605780000067
(2-7) Update the position of the sentinel according to (27)
Figure BDA0003691605780000067

Figure BDA0003691605780000068
Figure BDA0003691605780000068

其中，

Figure BDA0003691605780000069
表示第k代中全局最优位置，β作为步长控制参数，是服从均值为0，方差为1的正态分布的随机数，λ表示麻雀移动的方向同时也是步长控制参数，并且λ∈[-1,1]。ε设置为常数，用以避免分母为0。fi表示当前个体的适应度值，fg和fw表示目前全局最优和最差个体的适应度值。in,
Figure BDA0003691605780000069
represents the global optimal position in the kth generation, β is the step length control parameter, which is a random number that follows a normal distribution with a mean of 0 and a variance of 1, λ represents the direction in which the sparrow moves and is also the step length control parameter, and λ∈[-1,1]. ε is set to a constant to avoid the denominator being 0. fi represents the fitness value of the current individual, and fg and fw represent the fitness values of the current global optimal and worst individuals.

(2-8)计算麻雀种群适应度并进行重新排序，并更新麻雀种群位置；(2-8) Calculate the fitness of the sparrow population, re-sort it, and update the position of the sparrow population;

(2-9)通过(28)将

Figure BDA00036916057800000610
和
Figure BDA00036916057800000611
从
Figure BDA00036916057800000612
中分离出来。通过(29)计算信息向量
Figure BDA00036916057800000613
然后由(30)形成信息矩阵
Figure BDA00036916057800000614
(2-9) through (28)
Figure BDA00036916057800000610
and
Figure BDA00036916057800000611
from
Figure BDA00036916057800000612
The information vector is calculated by (29):
Figure BDA00036916057800000613
Then the information matrix is formed by (30)
Figure BDA00036916057800000614

Figure BDA00036916057800000615
Figure BDA00036916057800000615

Figure BDA00036916057800000616
Figure BDA00036916057800000616

Figure BDA00036916057800000617
Figure BDA00036916057800000617

(2-10)通过(31)计算参数向量

Figure BDA0003691605780000071
和通过(32)计算信息向量
Figure BDA0003691605780000072
然后由(33)形成信息矩阵
Figure BDA0003691605780000073
(2-10) Calculate the parameter vector through (31)
Figure BDA0003691605780000071
And the information vector is calculated by (32)
Figure BDA0003691605780000072
Then the information matrix is formed by (33)
Figure BDA0003691605780000073

Figure BDA0003691605780000074
Figure BDA0003691605780000074

Figure BDA0003691605780000075
Figure BDA0003691605780000075

Figure BDA0003691605780000076
Figure BDA0003691605780000076

(2-11)对于所有麻雀，根据(34)计算最佳麻雀位置

Figure BDA0003691605780000077
(2-11) For all sparrows, calculate the optimal sparrow position according to (34)
Figure BDA0003691605780000077

Figure BDA0003691605780000078
Figure BDA0003691605780000078

(2-12)通过(35)(36)(37)(38)从最优位置

Figure BDA0003691605780000079
中提取
Figure BDA00036916057800000710
和
Figure BDA00036916057800000711
(2-12) through (35)(36)(37)(38) from the optimal position
Figure BDA0003691605780000079
Extract
Figure BDA00036916057800000710
and
Figure BDA00036916057800000711

Figure BDA00036916057800000712
Figure BDA00036916057800000712

Figure BDA00036916057800000713
Figure BDA00036916057800000713

Figure BDA00036916057800000714
Figure BDA00036916057800000714

Figure BDA00036916057800000715
Figure BDA00036916057800000715

其中，g代表参数顺序，

Figure BDA00036916057800000716
和
Figure BDA00036916057800000717
分别为参数向量a，b和γ的估计值，
Figure BDA00036916057800000718
为时间延迟τ的估计值。Among them, g represents the parameter order,
Figure BDA00036916057800000716
and
Figure BDA00036916057800000717
are the estimated values of the parameter vectors a, b and γ, respectively.
Figure BDA00036916057800000718
is the estimated value of the time delay τ.

(2-13)将迭代变量k增加1并返回到步骤(2-5)。当k达到最大迭代次数T时，终止迭代并获得参数向量

Figure BDA00036916057800000719
和时间延迟
Figure BDA00036916057800000720
(2-13) Increase the iteration variable k by 1 and return to step (2-5). When k reaches the maximum number of iterations T, the iteration is terminated and the parameter vector is obtained.
Figure BDA00036916057800000719
and time delay
Figure BDA00036916057800000720

本发明辨识方法计算准确，辨识精度高，适用于液压位置伺服系统时滞反馈非线性模型的参数估计。The identification method of the invention has accurate calculation and high identification precision and is suitable for parameter estimation of a time-delay feedback nonlinear model of a hydraulic position servo system.

与现有技术相比，本发明的有益效果为：Compared with the prior art, the present invention has the following beneficial effects:

(1)本发明建立了液压位置伺服系统时滞反馈非线性参数辨识的模型，将液压位置伺服系统的给定电压信号作为输入数据，液压位置伺服系统的负载位移数据作为输出数据；利用改进Circle混沌线性变权麻雀搜索算法对该模型参数进行辨识。由图5可以看出该算法可以很好的辨识模型内部参数。(1) The present invention establishes a model for the time-delay feedback nonlinear parameter identification of the hydraulic position servo system, taking the given voltage signal of the hydraulic position servo system as input data and the load displacement data of the hydraulic position servo system as output data; the improved Circle chaos linear variable weight sparrow search algorithm is used to identify the model parameters. As shown in Figure 5, the algorithm can well identify the internal parameters of the model.

(2)相比麻雀搜索算法和粒子群优化算法，改进Circle混沌线性变权麻雀搜索算法采用改进的Circle混沌图对种群进行初始化，增加种群多样性，提高算法的全局搜索能力和收敛速度；在发现者麻雀的位置更新做了改进，使得降低了群体智能算法容易早熟的风险，避免算法后期容易在全局最优解附近发生振荡现象。改进后的麻雀搜索算法能够更好的辨识带未知时滞的反馈非线性系统，且辨识的精度也较高；同时，也说明本辨识方法对于液压伺服系统有较好的适用性。(2) Compared with the sparrow search algorithm and the particle swarm optimization algorithm, the improved Circle chaos linear variable weight sparrow search algorithm uses the improved Circle chaos graph to initialize the population, increase the population diversity, and improve the global search ability and convergence speed of the algorithm; the position update of the discoverer sparrow is improved, which reduces the risk of premature maturity of the swarm intelligence algorithm and avoids the oscillation phenomenon near the global optimal solution in the later stage of the algorithm. The improved sparrow search algorithm can better identify feedback nonlinear systems with unknown time delays, and the identification accuracy is also high; at the same time, it also shows that this identification method has good applicability to hydraulic servo systems.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

附图用来提供对本发明的进一步理解，并且构成说明书的一部分，与本发明的实施例一起用于解释本发明，并不构成对本发明的限制。The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

图1为本发明中液压位置伺服系统的组成分布图；其中Ui为输入电压信号，Uf为反馈电压信号，ΔU为误差信号，xp为负载位移。FIG1 is a composition distribution diagram of the hydraulic position servo system of the present invention; wherein U i is the input voltage signal, U f is the feedback voltage signal, ΔU is the error signal, and x p is the load displacement.

图2为本发明中液压位置伺服系统组成原理图。FIG. 2 is a schematic diagram showing the composition of the hydraulic position servo system of the present invention.

图3为本发明中液压位置伺服系统时滞反馈非线性模型结构示意图。FIG. 3 is a schematic diagram of the structure of a time-delay feedback nonlinear model of the hydraulic position servo system in the present invention.

图4为本发明中基于液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法的整体流程图。FIG. 4 is an overall flow chart of the improved chaotic variable weight sparrow search parameter identification method based on the hydraulic position servo system in the present invention.

图5为本发明实施例中参数估计误差δ随迭代次数k变化的示意图。FIG. 5 is a schematic diagram showing how parameter estimation error δ varies with the number of iterations k in an embodiment of the present invention.

具体实施方式DETAILED DESCRIPTION

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。当然，此处所描述的具体实施例仅用以解释本发明，并不用于限定本发明。In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

实施例Example

将所提出的液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法应用于某液压伺服系统，该系统的组成分布图参见图1。本发明实施例给出了给定电压信号输入和负载位移输出的关系，该液压伺服系统的非线性和线性环节由以下函数表示：The proposed improved chaotic variable weight sparrow search parameter identification method for hydraulic position servo system is applied to a hydraulic servo system, and the composition distribution diagram of the system is shown in Figure 1. The embodiment of the present invention provides the relationship between the given voltage signal input and the load displacement output. The nonlinear and linear links of the hydraulic servo system are represented by the following functions:

Figure BDA0003691605780000081
Figure BDA0003691605780000081

A(z)＝1+a1z-1+a2z-2＝1+0.80z-1+0.34z-2 A(z)＝1+a 1 z -1 +a 2 z -2 ＝1+0.80z -1 +0.34z -2

B(z)＝b1z-1+b2z-2＝0.44z-1+0.67z-2 B(z)＝b 1 z -1 +b 2 z -2 =0.44z -1 +0.67z -2

参数向量的真实值如下所示：The true value of the parameter vector is as follows:

θ＝[a1,a2,b1,b2,γ1,γ2,τ]Τ＝[0.80,0.34,0.44,0.67,0.14,0.11,1.00]Τ θ=[a 1 , a 2 , b 1 , b 2 , γ 1 , γ 2 , τ] Τ = [0.80, 0.34, 0.44, 0.67, 0.14, 0.11, 1.00] Τ

定义

Figure BDA0003691605780000091
为θ的估计，参数估计误差
Figure BDA0003691605780000092
definition
Figure BDA0003691605780000091
is the estimate of θ, the parameter estimation error
Figure BDA0003691605780000092

辨识过程中采用MATLAB软件，根据系统的输入输出数据，建立液压伺服系统的时滞反馈非线性模型。During the identification process, MATLAB software is used to establish a time-delay feedback nonlinear model of the hydraulic servo system based on the input and output data of the system.

本实例的液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法，具体步骤如下：The improved chaotic variable weight sparrow search parameter identification method of the hydraulic position servo system in this example has the following specific steps:

(1)构建液压位置伺服系统的时滞反馈非线性辨识模型，具体步骤如下：(1) Construct a time-delay feedback nonlinear identification model for the hydraulic position servo system. The specific steps are as follows:

第一步：构建液压位置伺服系统的时滞反馈非线性模型的结构，参加图3。Step 1: Construct the structure of the time-delay feedback nonlinear model of the hydraulic position servo system, see Figure 3.

第二步：根据此模型，构建液压位置伺服系统的时滞反馈非线性模型表达式如下：Step 2: Based on this model, the time-delay feedback nonlinear model expression of the hydraulic position servo system is as follows:

Figure BDA0003691605780000093
Figure BDA0003691605780000093

Figure BDA0003691605780000094
Figure BDA0003691605780000094

Figure BDA0003691605780000095
Figure BDA0003691605780000095

Figure BDA0003691605780000096
Figure BDA0003691605780000096

其中，r(t)为输入量，y(t)为输出量，

Figure BDA0003691605780000097
为反馈通道输出，v(t)是一个均值为零、方差为σ2满足高斯分布的白噪声；定义x(t)，u(t)和w(t)为不可测的中间变量；τ是反馈非线性系统时滞，z为后移算子:z-1y(t)＝y(t-1)，A(z)，B(z)是关于z的多项式，描述为如下形式：Among them, r(t) is the input, y(t) is the output,
Figure BDA0003691605780000097
is the feedback channel output, v(t) is a white noise with zero mean and variance σ2 that satisfies Gaussian distribution; x(t), u(t) and w(t) are defined as unmeasurable intermediate variables; τ is the time lag of the feedback nonlinear system, z is the backshift operator: z -1 y(t) = y(t-1), A(z), B(z) are polynomials about z, described as follows:

Figure BDA0003691605780000098
Figure BDA0003691605780000098

Figure BDA0003691605780000099
Figure BDA0003691605780000099

其中，多项式因子ai和bj是待估计的参数，分母的阶数na和分子的阶数nb是已知的。将系统的非线性部分可以用传递函数表示为：Among them, the polynomial factors a i and b j are the parameters to be estimated, and the order of the denominator na and the order of the numerator n b are known. The nonlinear part of the system can be expressed by the transfer function as:

Figure BDA00036916057800000910
Figure BDA00036916057800000910

其中，γi(i＝1,2,...,m)是需要辨识的非线性函数的系数，m是非线性块的参数个数。Wherein, γ i (i=1, 2, ..., m) is the coefficient of the nonlinear function to be identified, and m is the number of parameters of the nonlinear block.

将公式两边同乘以A(z)得到：Multiplying both sides of the formula by A(z) yields:

A(z)y(t)＝q-τB(z)u(t)+v(t) (8)A(z)y(t)＝q -τ B(z)u(t)+v(t) (8)

可表示为：It can be expressed as:

Figure BDA0003691605780000101
Figure BDA0003691605780000101

其中噪声模型输出w(t)和前馈通道输出x(t)为：The noise model output w(t) and the feedforward channel output x(t) are:

Figure BDA0003691605780000102
Figure BDA0003691605780000102

Figure BDA0003691605780000103
Figure BDA0003691605780000103

反馈非线性系统模型可以表示为：The feedback nonlinear system model can be expressed as:

Figure BDA0003691605780000104
Figure BDA0003691605780000104

将线性子系统的参数向量a、b以及非线性部分的参数向量γ定义为：The parameter vectors a and b of the linear subsystem and the parameter vector γ of the nonlinear part are defined as:

Figure BDA0003691605780000105
Figure BDA0003691605780000105

那么整个模型的参数向量θ表示为：Then the parameter vector θ of the entire model is expressed as:

Figure BDA0003691605780000106
Figure BDA0003691605780000106

对应的信息向量

Figure BDA0003691605780000107
表示为：The corresponding information vector
Figure BDA0003691605780000107
It is expressed as:

Figure BDA0003691605780000108
Figure BDA0003691605780000108

Figure BDA0003691605780000109
Figure BDA0003691605780000109

其中：in:

Figure BDA00036916057800001010
Figure BDA00036916057800001010

Figure BDA00036916057800001011
Figure BDA00036916057800001011

Figure BDA0003691605780000111
Figure BDA0003691605780000111

其中：in:

f(y(t))＝[f1(y(t)),f2(y(t)),...,fm(y(t))]∈R1×m f(y(t))＝[f 1 (y(t)), f 2 (y(t)),..., f m (y(t))]∈R 1×m

根据上述定义，系统的非线性部分

Figure BDA0003691605780000112
表示为：According to the above definition, the nonlinear part of the system
Figure BDA0003691605780000112
It is expressed as:

Figure BDA0003691605780000113
Figure BDA0003691605780000113

得到描述的液压位置伺服系统的时滞反馈非线性模型：The time-delay feedback nonlinear model of the hydraulic position servo system described is obtained:

Figure BDA0003691605780000114
Figure BDA0003691605780000114

第三步：得到液压位置伺服系统的时滞反馈非线性模型为：Step 3: The time-delay feedback nonlinear model of the hydraulic position servo system is obtained as:

Figure BDA0003691605780000115
Figure BDA0003691605780000115

(2)构建液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法的辨识流程。(2) Construct the identification process of the improved chaotic variable weight sparrow search parameter identification method for the hydraulic position servo system.

第一步：初始化麻雀搜索算法，采用改进的Circle混沌映射初始化麻雀种群；Step 1: Initialize the sparrow search algorithm and use the improved Circle chaos map to initialize the sparrow population;

第二步：收集液压位置伺服系统的给定电压信号作为输入数据，液压位置伺服系统的负载位移数据作为输出数据；Step 2: Collect the given voltage signal of the hydraulic position servo system as input data, and the load displacement data of the hydraulic position servo system as output data;

第三步：计算麻雀群体中个体适应度，对所有麻雀个体适应度进行排序，找出全局最优适应度值和全局最差适应度值，然后计算初始全局最优位置；Step 3: Calculate the individual fitness of the sparrow group, sort the fitness of all sparrows, find the global optimal fitness value and the global worst fitness value, and then calculate the initial global optimal position;

第四步：令迭代变量k＝1，计算麻雀的初始位置；Step 4: Set the iteration variable k = 1 and calculate the initial position of the sparrow;

第五步：基于线性递减权重法计算当前的惯性权重值，更新发现者位置；Step 5: Calculate the current inertia weight value based on the linear decreasing weight method and update the discoverer's position;

第六步：更新跟随者的位置；Step 6: Update the follower's position;

第七步：更新警戒者的位置；Step 7: Update the position of the sentinel;

第八步：计算麻雀种群适应度并进行重新排序，更新麻雀种群位置；Step 8: Calculate the fitness of the sparrow population and re-sort it, and update the position of the sparrow population;

第九步：对于所有麻雀，计算群体最佳麻雀位置；Step 9: For all sparrows, calculate the best sparrow position in the group;

第十步：从群体最佳位置中分离提取出参数向量和时延的估计值；Step 10: Separate and extract the parameter vector and the estimated value of the delay from the group's best position;

第十一步：将迭代变量k值加1，重复上述过程。Step 11: Add 1 to the iteration variable k and repeat the above process.

(3)参见图4，构建出液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法如下：(3) Referring to FIG4 , the improved chaotic variable weight sparrow search parameter identification method of the hydraulic position servo system is constructed as follows:

Figure BDA0003691605780000121
Figure BDA0003691605780000121

Figure BDA0003691605780000122
Figure BDA0003691605780000122

Figure BDA0003691605780000123
Figure BDA0003691605780000123

Figure BDA0003691605780000124
Figure BDA0003691605780000124

Figure BDA0003691605780000125
Figure BDA0003691605780000125

Figure BDA0003691605780000126
Figure BDA0003691605780000126

Figure BDA0003691605780000127
Figure BDA0003691605780000127

Figure BDA0003691605780000128
Figure BDA0003691605780000128

Figure BDA0003691605780000131
Figure BDA0003691605780000131

Figure BDA0003691605780000132
Figure BDA0003691605780000132

Figure BDA0003691605780000133
Figure BDA0003691605780000133

Figure BDA0003691605780000134
Figure BDA0003691605780000134

Figure BDA0003691605780000135
Figure BDA0003691605780000135

Figure BDA0003691605780000136
Figure BDA0003691605780000136

Y(l)＝[y(l),y(l-1),...,y(1)]T (31)Y(l)＝[y(l),y(l-1),...,y(1)] T (31)

Figure BDA0003691605780000137
Figure BDA0003691605780000137

Figure BDA0003691605780000138
Figure BDA0003691605780000138

Figure BDA0003691605780000139
Figure BDA0003691605780000139

Figure BDA00036916057800001310
Figure BDA00036916057800001310

参见图4，所述液压位置伺服系统改进混沌变权麻雀搜索参数辨识方法的辨识流程的具体步骤如下：Referring to FIG. 4 , the specific steps of the identification process of the improved chaotic variable weight sparrow search parameter identification method of the hydraulic position servo system are as follows:

(1)设置麻雀个数为N，每个麻雀包含na+nb+m个变量，通过(17)采用改进的Circle混沌映射初始化麻雀种群，设置Xn为当前麻雀的位置，Xn+1为更新后的麻雀位置，最大迭代次数为T、预警值为ST、发现者PD和警戒者SD比例及wmax、wmin。其中wk为惯性权重，wmax和wmin分别为线性权重的最大值和最小值；(1) Set the number of sparrows to N, each sparrow contains n a +n b +m variables, and initialize the sparrow population using the improved Circle chaotic map through (17), set X n to be the current position of the sparrow, X n+1 to be the updated position of the sparrow, the maximum number of iterations to T, the warning value to ST, the ratio of the discoverer PD to the vigilant SD, and w max , w min . Where w k is the inertia weight, w max and w min are the maximum and minimum values of the linear weight respectively;

(2)设置数据长度l，收集液压位置伺服系统的给定电压信号输入数据和负载位移输出数据{r(t)，y(t)}。通过(31)构造输出堆积向量形式Y(l)和信息堆积向量ψ(l,τ)；(2) Set the data length l, collect the given voltage signal input data and load displacement output data {r(t), y(t)} of the hydraulic position servo system. Construct the output stacking vector form Y(l) and the information stacking vector ψ(l,τ) through (31);

(3)通过(18)计算麻雀群体中个体适应度，对所有麻雀个体适应度进行排序，找出全局最优适应度值fg和全局最差适应度值fw，然后计算初始全局最优位置

Figure BDA00036916057800001311
(3) Calculate the individual fitness of the sparrow group through (18), sort the fitness of all sparrows, find the global optimal fitness value fg and the global worst fitness value fw , and then calculate the initial global optimal position
Figure BDA00036916057800001311

(4)设迭代变量k＝1，开始迭代，个体的初始位置是

Figure BDA00036916057800001312
(4) Assume that the iteration variable k = 1 and start the iteration. The initial position of the individual is
Figure BDA00036916057800001312

(5)基于线性递减权重法通过式(19)计算wk，通过式(20)将发现者位置更新为

Figure BDA00036916057800001313
(5) Based on the linear decreasing weight method, w k is calculated by equation (19), and the discoverer position is updated by equation (20) as
Figure BDA00036916057800001313

(6)通过式(21)更新跟随者位置

Figure BDA0003691605780000141
(6) Update the follower position through equation (21)
Figure BDA0003691605780000141

(7)通过式(22)更新警戒者位置

Figure BDA0003691605780000142
(7) Update the position of the sentinel through equation (22)
Figure BDA0003691605780000142

(8)计算麻雀种群适应度并进行重新排序，并更新麻雀种群位置；(8) Calculate the fitness of the sparrow population, re-rank it, and update the position of the sparrow population;

(9)通过式(23)将

Figure BDA0003691605780000143
和
Figure BDA0003691605780000144
从
Figure BDA0003691605780000145
中分离出来，通过(24)计算信息向量
Figure BDA0003691605780000146
然后由(25)形成信息矩阵
Figure BDA0003691605780000147
(9) Through formula (23),
Figure BDA0003691605780000143
and
Figure BDA0003691605780000144
from
Figure BDA0003691605780000145
Separate it from the original data and calculate the information vector through (24)
Figure BDA0003691605780000146
Then the information matrix is formed by (25)
Figure BDA0003691605780000147

(10)通过式(26)计算参数向量

Figure BDA0003691605780000148
和通过(27)计算信息向量
Figure BDA0003691605780000149
然后由(28)形成信息矩阵
Figure BDA00036916057800001410
(10) Calculate the parameter vector by equation (26)
Figure BDA0003691605780000148
And the information vector is calculated by (27)
Figure BDA0003691605780000149
Then the information matrix is formed by (28)
Figure BDA00036916057800001410

(11)对于所有麻雀，根据(29)计算最佳麻雀位置

Figure BDA00036916057800001411
通过式(30)将
Figure BDA00036916057800001412
和
Figure BDA00036916057800001413
从
Figure BDA00036916057800001414
分离；(11) For all sparrows, calculate the optimal sparrow position according to (29)
Figure BDA00036916057800001411
Through formula (30)
Figure BDA00036916057800001412
and
Figure BDA00036916057800001413
from
Figure BDA00036916057800001414
separation;

(12)通过(32)(33)(34)(35)从最优位置

Figure BDA00036916057800001415
中提取
Figure BDA00036916057800001416
和
Figure BDA00036916057800001417
(12) Through (32)(33)(34)(35) from the optimal position
Figure BDA00036916057800001415
Extract
Figure BDA00036916057800001416
and
Figure BDA00036916057800001417

(13)将迭代变量k增加1并返回到步骤(2-5)，当k达到最大迭代次数T时，终止迭代并获得参数向量

Figure BDA00036916057800001418
和
Figure BDA00036916057800001419
(13) Increase the iteration variable k by 1 and return to step (2-5). When k reaches the maximum number of iterations T, terminate the iteration and obtain the parameter vector
Figure BDA00036916057800001418
and
Figure BDA00036916057800001419

其中各变量定义如下：The variables are defined as follows:

定义输入量为r(t)，输出量为y(t)；定义v(t)是一个均值为零、方差为σ2满足高斯分布的白噪声；定义x(t)和w(t)为不可测的中间变量；定义θ作为参数向量；

Figure BDA00036916057800001420
作为信息向量；l为数据长度，ψ(l)为信息堆积向量，Y(l)为输出堆积向量；Define the input as r(t) and the output as y(t); define v(t) as a white noise with a mean of zero and a variance of σ 2 that satisfies a Gaussian distribution; define x(t) and w(t) as unmeasurable intermediate variables; define θ as a parameter vector;
Figure BDA00036916057800001420
as the information vector; l is the data length, ψ(l) is the information accumulation vector, and Y(l) is the output accumulation vector;

设置麻雀个数为N，每个麻雀包含na+nb+m个变量，最大迭代次数T，预警值ST，发现者比例PD，警戒者比例SD，w为惯性权重，wmax和wmin分别为线性权重的最大值和最小值。Set the number of sparrows to N, each sparrow contains n a +n b +m variables, the maximum number of iterations T, the warning value ST, the proportion of discoverers PD, the proportion of vigilants SD, w is the inertia weight, w max and w min are the maximum and minimum values of the linear weight respectively.

k为迭代变量；

Figure BDA00036916057800001421
表示在第k代中第i只麻雀在第j维的位置，随机数ξ∈[0,1]，
Figure BDA00036916057800001422
为第k代种群全局最优适应度，Q是服从正态分布的随机数，L是一个每个元素均为1的1×d维的矩阵；R2表示报警值，ST表示安全阈值。k is the iteration variable;
Figure BDA00036916057800001421
represents the position of the i-th sparrow in the j-th dimension in the k-th generation, the random number ξ∈[0,1],
Figure BDA00036916057800001422
is the global optimal fitness of the kth generation population, Q is a random number that obeys the normal distribution, L is a 1×d-dimensional matrix in which each element is 1; R 2 represents the alarm value, and ST represents the safety threshold.

Figure BDA00036916057800001423
表示第k代适应度最差的个体位置，
Figure BDA00036916057800001424
表示第k+1代中适应度最佳的个体位置。A表示1×d的矩阵，矩阵中每个元素预设为-1或1，并且A+＝AT(AAT)-1。
Figure BDA00036916057800001423
represents the position of the individual with the worst fitness in the kth generation,
Figure BDA00036916057800001424
represents the position of the individual with the best fitness in the k+1th generation. A represents a 1×d matrix, each element in the matrix is preset to -1 or 1, and A + = AT (AA T ) -1 .

Figure BDA0003691605780000151
表示第k代中全局最优位置，β作为步长控制参数，是服从均值为0，方差为1的正态分布的随机数，λ表示麻雀移动的方向同时也是步长控制参数，并且λ∈[-1,1]。ε设置为常数，用以避免分母为0。fi表示当前个体的适应度值，fg和fw表示目前全局最优和最差个体的适应度值。
Figure BDA0003691605780000151
represents the global optimal position in the kth generation, β is the step length control parameter, which is a random number that follows a normal distribution with a mean of 0 and a variance of 1, λ represents the direction in which the sparrow moves and is also the step length control parameter, and λ∈[-1,1]. ε is set to a constant to avoid the denominator being 0. fi represents the fitness value of the current individual, and fg and fw represent the fitness values of the current global optimal and worst individuals.

定义

Figure BDA0003691605780000152
为参数向量θ在第k次迭代的估计值，
Figure BDA0003691605780000153
为时间延迟τ在第k次迭代的估计值，定义
Figure BDA0003691605780000154
为信息向量
Figure BDA0003691605780000155
在第k次迭代的估计值，定义
Figure BDA0003691605780000156
为信息堆积向量ψ(l)在第k次迭代的估计值；definition
Figure BDA0003691605780000152
is the estimated value of the parameter vector θ at the kth iteration,
Figure BDA0003691605780000153
is the estimated value of the time delay τ at the kth iteration, and is defined as
Figure BDA0003691605780000154
is the information vector
Figure BDA0003691605780000155
At the kth iteration, the estimated value is defined as
Figure BDA0003691605780000156
is the estimated value of the information accumulation vector ψ(l) at the kth iteration;

定义

Figure BDA0003691605780000157
为参数向量
Figure BDA0003691605780000158
的个体最优解，
Figure BDA0003691605780000159
为时间延迟
Figure BDA00036916057800001510
的个体最优值；定义
Figure BDA00036916057800001511
为信息向量
Figure BDA00036916057800001512
的个体最优；定义
Figure BDA00036916057800001513
为信息堆积向量
Figure BDA00036916057800001514
的个体最优；g代表参数顺序，
Figure BDA00036916057800001515
和
Figure BDA00036916057800001516
分别为参数向量a、b和γ的估计值，
Figure BDA00036916057800001517
为时间延迟τ的估计值；definition
Figure BDA0003691605780000157
is the parameter vector
Figure BDA0003691605780000158
The individual optimal solution of
Figure BDA0003691605780000159
For time delay
Figure BDA00036916057800001510
The individual optimal value of
Figure BDA00036916057800001511
is the information vector
Figure BDA00036916057800001512
The individual optimum of
Figure BDA00036916057800001513
Stacking vectors for information
Figure BDA00036916057800001514
The individual optimality; g represents the order of parameters,
Figure BDA00036916057800001515
and
Figure BDA00036916057800001516
are the estimated values of parameter vectors a, b and γ, respectively.
Figure BDA00036916057800001517
is the estimated value of the time delay τ;

以上所述仅为本发明的较佳实施例，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. The method for identifying the search parameters of the chaos variable-weight sparrow by using the hydraulic position servo system is characterized by comprising the following steps of:
step 1), constructing a time-lag feedback nonlinear identification model of a hydraulic position servo system;
step 2), constructing an identification flow of an improved chaos variable weight sparrow search parameter identification method of a hydraulic position servo system; the method comprises the following steps:
2-1) initializing a sparrow search algorithm, and initializing a sparrow population by adopting improved Circle chaotic mapping;
2-2) collecting a given voltage signal of the hydraulic position servo system as input data and load displacement data of the hydraulic position servo system as output data;
2-3) calculating individual fitness in the sparrow group, sorting all the individual fitness of the sparrows, finding out a global optimal fitness value and a global worst fitness value, and then calculating an initial global optimal position;
2-4) making the iteration variable k=1, and calculating the initial position of the sparrow;
2-5) calculating a current inertia weight value based on a linear decreasing weight method, and updating the position of the finder;
2-6) updating the location of the follower;
2-7) updating the position of the alerter;
2-8) calculating the fitness of the sparrow population, reordering, and updating the position of the sparrow population;
2-9) for all sparrows, calculating the group best sparrow position;
2-10) separating and extracting parameter vectors and estimated values of time delay from the optimal positions of the groups;
2-11) adding 1 to the iteration variable k value, and repeating the process;
the modeling step of the step 1) is as follows:
(1-1) constructing a time lag feedback nonlinear model of the hydraulic position servo system:
Figure FDA0004209444910000011
Figure FDA0004209444910000012
Figure FDA0004209444910000013
Figure FDA0004209444910000014
wherein r (t) is input quantity, y (t) is output quantity,
Figure FDA0004209444910000015
for feedback channel output, v (t) is zero in mean and sigma in variance 2 White noise satisfying gaussian distribution; defining x (t), u (t) and w (t) as non-measurable intermediate variables;τ is feedback nonlinear system time lag, z is a backward operator, z -1 y (t) =y (t-1), a (z), B (z) is a polynomial about z, described as follows:
Figure FDA0004209444910000021
Figure FDA0004209444910000022
the nonlinear part of the system can be expressed as a transfer function:
Figure FDA0004209444910000023
wherein the unknown parameter gamma i (i=1, 2,., m) is the coefficient of the nonlinear function, m is the number of parameters of the nonlinear block;
the formula is obtained by multiplying both sides of the formula by A (z):
A(z)y(t)＝q -τ B(z)u(t)+v(t) (8)
can be expressed as:
Figure FDA0004209444910000024
wherein the noise model output w (t) and the feedforward tract output x (t) are:
Figure FDA0004209444910000025
Figure FDA0004209444910000026
the feedback nonlinear system model is expressed as:
Figure FDA0004209444910000027
(1-2) defining the parameter vectors a, b of the linear subsystem and the parameter vector γ of the nonlinear section as:
Figure FDA0004209444910000028
the parameter vector θ of the entire model is expressed as:
Figure FDA0004209444910000029
corresponding information vector
Figure FDA00042094449100000210
Expressed as:
Figure FDA0004209444910000031
Figure FDA0004209444910000032
wherein ：
Figure FDA0004209444910000033
Figure FDA0004209444910000034
Figure FDA0004209444910000035
wherein ：
f(y(t))＝[f 1 (y(t)),f 2 (y(t)),...,f m (y(t))]∈R 1×m
according to the above definition, the nonlinear part of the system
Figure FDA0004209444910000036
Expressed as:
Figure FDA0004209444910000037
(1-3) then deriving a described time-lapse feedback nonlinear model of the hydraulic position servo system:
Figure FDA0004209444910000041
then, a time lag feedback nonlinear model of the hydraulic position servo system is obtained as follows:
Figure FDA0004209444910000042
the step 2) of constructing a hydraulic position servo system improved chaos variable weight sparrow search parameter identification process comprises the following steps:
(2-1) setting the number of sparrows to N, each sparrow comprising N a +n b +m variables, by equation (18), using modified Circle chaotic map to initialize sparrow population, setting X n X is the current sparrow position n+1 For the updated sparrow position, the maximum iteration number is T, the early warning value is ST, the ratio of the finder PD to the alerter SD and the ratio of the finder PD to the alerter SD are w max 、w min ，w k Is the inertial weight, w max and wmin Respectively a maximum value and a minimum value of the linear weight;
the original Circle chaotic mapping expression is:
Figure FDA0004209444910000043
the modified Circle chaotic mapping expression is as follows:
Figure FDA0004209444910000044
(2-2) collecting given voltage signal input data and load displacement output data { r (t), Y (t) } of the hydraulic position servo system, and constructing an output pile-up vector Y (l) as follows (19):
Y(l)＝[y(l),y(l-1),...,y(1)] T ∈R l (19)
the information pile-up vector ψ (l, τ) is constructed as in equation (20):
Figure FDA0004209444910000045
wherein l is the data length;
(2-3) calculating individual fitness in the sparrow group through (21), sequencing all the individual fitness of the sparrows, and finding out a global optimal fitness value f g And a global worst fitness value f w Then calculate the initial global optimum position by (22)
Figure FDA0004209444910000051
Figure FDA0004209444910000052
Figure FDA0004209444910000053
(2-4) setting an iteration variable k=1, starting iteration, the initial position of the individual being
Figure FDA0004209444910000054
Figure FDA0004209444910000055
(2-5) calculating w by (24) based on a linearly decreasing weight method k Updating the finder position to be by the formula (25)
Figure FDA0004209444910000056
Figure FDA0004209444910000057
Figure FDA0004209444910000058
Wherein k is an iteration variable;
Figure FDA0004209444910000059
representing the position of the ith sparrow in the j-th dimension in the k-th generation, and the random number xi [0,1 ]]，
Figure FDA00042094449100000510
For the k generation population global optimum fitness, Q is a random number obeying normal distribution, L is a 1 x d-dimensional matrix with each element being 1; r is R 2 Representing an alarm value, and ST representing a safety threshold;
(2-6) updating follower position according to (26)
Figure FDA00042094449100000511
Figure FDA00042094449100000512
wherein ,
Figure FDA00042094449100000513
the individual position representing the worst k-th generation fitness value,/->
Figure FDA00042094449100000514
Represents the individual position of the best fitness in the k+1th generation, A represents a 1×d matrix in which each element is preset to-1 or 1, and A + ＝A T (AA T ) -1 ；
(2-7) updating the alerter position according to (27)
Figure FDA00042094449100000515
Figure FDA00042094449100000516
wherein ,
Figure FDA00042094449100000517
the global optimal position in the kth generation is represented, beta is taken as a step control parameter, is a random number obeying normal distribution with the mean value of 0 and the variance of 1, lambda represents the direction of sparrow movement and is also taken as the step control parameter, and lambda epsilon [ -1, 1)]Epsilon is set to be constant to avoid denominator of 0, f i Indicating the fitness value of the current individual, f g and fw The fitness value of the current global optimum and worst individuals is represented; />
(2-8) calculating the fitness of the sparrow population, reordering, and updating the position of the sparrow population;
(2-9) passing (28)
Figure FDA0004209444910000061
and
Figure FDA0004209444910000062
From->
Figure FDA0004209444910000063
By (29) calculating the information vector +.>
Figure FDA0004209444910000064
Then form an information matrix from (30)>
Figure FDA0004209444910000065
Figure FDA0004209444910000066
Figure FDA0004209444910000067
Figure FDA0004209444910000068
(2-10) calculating a parameter vector by (31)
Figure FDA0004209444910000069
And calculating an information vector by (32)>
Figure FDA00042094449100000610
Then form an information matrix from (33)>
Figure FDA00042094449100000611
Figure FDA00042094449100000612
Figure FDA00042094449100000613
Figure FDA00042094449100000614
(2-11) for all the sparrows, the optimal sparrow position is calculated according to (34)
Figure FDA00042094449100000615
Figure FDA00042094449100000616
(2-12) from the optimal position by (35) (36) (37) (38)
Figure FDA00042094449100000617
Extract->
Figure FDA00042094449100000618
and
Figure FDA00042094449100000619
Figure FDA00042094449100000620
Figure FDA00042094449100000621
Figure FDA00042094449100000622
Figure FDA00042094449100000623
Wherein g represents the parameter order,
Figure FDA00042094449100000624
and
Figure FDA00042094449100000625
Estimated values of parameter vectors a, b and gamma, respectively,/->
Figure FDA00042094449100000626
An estimated value of the time delay τ;
(2-13) increasing the iteration variable k by 1 and returning to step (2-5), terminating the iteration and obtaining the parameter vector when k reaches the maximum number of iterations T
Figure FDA0004209444910000071
And time delay->
Figure FDA0004209444910000072
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