CN103399490B

CN103399490B - A kind of carbon fibre precursor wet method coagulation bath temperature control technique that study is controlled based on immunological memory

Info

Publication number: CN103399490B
Application number: CN201310332913.9A
Authority: CN
Inventors: 丁永生; 徐楠; 郝矿荣; 任立红; 王华平
Original assignee: Donghua University
Current assignee: Donghua University
Priority date: 2013-08-01
Filing date: 2013-08-01
Publication date: 2016-05-18
Anticipated expiration: 2033-08-01
Also published as: CN103399490A

Abstract

The present invention proposes a carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control. The process route is that the polyacrylonitrile stock solution is extruded through the spinneret into the coagulation bath water tank, and the coagulation liquid temperature in the coagulation bath water tank is determined by The temperature detection element detects in real time and feeds back to the controller. The controller calculates the current control amount according to the current and historical data of the set value input, control amount and feedback output, and outputs it to the controlled object to heat the coagulation bath. Finally Make the actual temperature of the coagulation bath reach the set temperature. The controller is an intelligent temperature controller based on immune memory learning, which simulates the immune recognition, response and memory mechanism of the human immune system, improves the traditional iterative learning control algorithm, and uses interference as an antigen to identify, eliminate and Feature memory, when the same disturbance reappears, the control system can respond quickly and control accurately, further improving the stability and anti-interference of the control system.

Description

A carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control

技术领域technical field

本发明属于自动控制技术领域，特别是涉及一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺。The invention belongs to the technical field of automatic control, in particular to a carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control.

背景技术Background technique

碳纤维是一种具有很高强度和模量的耐高温纤维，是化纤中的高端品种。碳纤维最大的特点在于又轻又坚硬，因此用途非常广泛。在碳纤维的生产过程中，国内外专家一致认为，作为碳纤维原丝的聚丙烯腈纤维的质量是制约碳纤维性能的重要因素。因此，如何进一步提高聚丙烯腈原丝的品质受到了国内外学者的广泛关注。Carbon fiber is a high-temperature-resistant fiber with high strength and modulus, and it is a high-end variety of chemical fibers. The biggest feature of carbon fiber is that it is light and hard, so it has a wide range of uses. In the production process of carbon fiber, experts at home and abroad agree that the quality of polyacrylonitrile fiber as carbon fiber precursor is an important factor restricting the performance of carbon fiber. Therefore, how to further improve the quality of polyacrylonitrile precursor has been widely concerned by scholars at home and abroad.

聚丙烯腈原丝的生产工艺对环境、设备的控制精度要求非常高，一点微小的干扰都会造成原丝纤维的品质不均匀，从而影响碳纤维复丝的品质。然而，像碳纤维原丝生产这样的复杂的工业生产过程中，工艺中往往存在许多无法用准确的数学模型表达的物理、化学过程机理，例如在粘弹性流体凝固过程中的扩散、凝结与形变等。这些过程相互影响相互制约，无法建立精确的数学模型，往往只能通过建立近似的模型，或采用经验公式等拟合模型，进行控制系统设计。这便会给基于模型的传统控制系统引入较大误差，导致无法在这些复杂的化工过程中实现高精度的控制。The production process of polyacrylonitrile precursors has very high requirements on the control accuracy of the environment and equipment. A slight disturbance will cause the quality of the precursor fibers to be uneven, thereby affecting the quality of carbon fiber multifilaments. However, in complex industrial production processes such as the production of carbon fiber precursors, there are often many physical and chemical process mechanisms that cannot be expressed by accurate mathematical models, such as diffusion, coagulation and deformation during the solidification of viscoelastic fluids. . These processes interact and restrict each other, and it is impossible to establish an accurate mathematical model. Often, the control system can only be designed by establishing an approximate model or using a fitting model such as an empirical formula. This will introduce large errors to the traditional model-based control system, resulting in the inability to achieve high-precision control in these complex chemical processes.

近几年来，数据驱动、生物智能控制等技术在过程控制领域得到了广泛的应用，并在实践中取得了比传统方法更加优越的性能。数据驱动控制是指利用被控对象的在线或离线的输入输出数据以及由数据的处理而获得的知识来设计控制器的方法。数据驱动控制策略从存储的大量的生产、设备和过程数据挖掘隐含着的工艺和设备等信息，直接基于数据设计控制器而不尝试对对象建模，能够有效的解决无法建模或模型引入误差的问题。生物智能控制技术是从对自然界中各种生物，尤其是人类的智能行为的研究而衍生出的控制策略。例如，人体免疫系统对外来入侵病原的消除过程等。生物智能算法在控制精度和抗干扰能力了等方面均优于传统的控制算法。In recent years, technologies such as data-driven and biological intelligent control have been widely used in the field of process control, and have achieved superior performance compared to traditional methods in practice. Data-driven control refers to the method of using the online or offline input and output data of the controlled object and the knowledge obtained from data processing to design the controller. The data-driven control strategy mines hidden process and equipment information from a large amount of stored production, equipment and process data, and designs the controller directly based on the data without attempting to model the object, which can effectively solve the problem of failure to model or model introduction error problem. Biological intelligence control technology is a control strategy derived from the study of various organisms in nature, especially the intelligent behavior of human beings. For example, the process of eliminating foreign invading pathogens by the human immune system. Biological intelligence algorithms are superior to traditional control algorithms in terms of control accuracy and anti-interference ability.

因此，将数据驱动、生物智能控制等方法引入碳纤维原丝生产过程的控制系统中，基于对数据的学习优化提高生产控制系统的抗干扰能力，对产出质量稳定、指标优越的高性能原丝具有一定的指导意义。Therefore, data-driven, biological intelligent control and other methods are introduced into the control system of the carbon fiber precursor production process, and the anti-interference ability of the production control system is improved based on the learning and optimization of data, which is beneficial to the high-performance precursor with stable output quality and superior indicators. It has certain guiding significance.

发明内容Contents of the invention

本发明的目的是提出一种相对于传统控制能够进一步提高被控对象稳定性的控制策略，并实现于聚丙烯腈基碳纤维原丝凝固过程的温度控制系统，增强系统的抗干扰能力，提高凝固过程环境温度稳定性，提高初生纤维的性能及品质。The purpose of the present invention is to propose a control strategy that can further improve the stability of the controlled object compared with traditional control, and realize the temperature control system in the solidification process of polyacrylonitrile-based carbon fiber precursors, enhance the anti-interference ability of the system, and improve the stability of solidification. The temperature stability of the process environment improves the performance and quality of the primary fiber.

为实现上述目的，本发明采取的技术方案是：一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，其工艺路线为聚丙烯腈原液经喷丝板挤出进入凝固浴水槽，凝固浴水槽中凝固液的温度由温度检测元件实时检测并反馈至控制器，控制器根据设定值输入、控制量以及输出反馈的当前和历史数据进行当前的控制量计算，并输出至被控对象，对凝固浴进行加热，最终使凝固浴实际温度达到设定温度，所述的控制器为基于免疫记忆学习的智能温度控制器；所述的基于免疫记忆学习的智能温度控制器由迭代学习控制器、迭代学习存储单元、免疫识别模块、免疫应答模块和免疫记忆模块组成，所述的免疫识别模块模拟人体特异性免疫过程中免疫系统识别特定抗原的机理，将控制系统中出现的干扰作为抗原，对抗原进特异性识别；所述的抗原Ag_i定义为：In order to achieve the above object, the technical solution adopted by the present invention is: a carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control, the process route is that the polyacrylonitrile stock solution is extruded through the spinneret into the coagulation bath water tank The temperature of the coagulation liquid in the coagulation bath tank is detected in real time by the temperature detection element and fed back to the controller. The controller calculates the current control amount according to the current and historical data of the set value input, control amount and output feedback, and outputs it to the control object, the coagulation bath is heated, and finally the actual temperature of the coagulation bath reaches the set temperature, and the controller is an intelligent temperature controller based on immune memory learning; the intelligent temperature controller based on immune memory learning is composed of iterative It is composed of a learning controller, an iterative learning storage unit, an immune recognition module, an immune response module and an immune memory module. The immune recognition module simulates the mechanism of the immune system recognizing specific antigens in the specific immune process of the human body, and will control the interference that occurs in the system. As an antigen, the antigen is specifically recognized; the antigen Ag _i is defined as:

${Ag Ag}_{i i} = = {{r r,, u u,, e e,, y the y}},, i i = = 11,, ... ...,, {Num Num}_{m m a a x x}^{i i m m},,$

其中，in,

r＝{r(t),r(t-1),...,r(t-n)}；r={r(t),r(t-1),...,r(t-n)};

r(t)是t时刻系统输入，r(t-1)是t-1时刻系统输入，r(t-n)是t-n时刻系统输入；r(t) is the system input at time t, r(t-1) is the system input at time t-1, and r(t-n) is the system input at time t-n;

u＝{u(t),u(t-1),...,u(t-n)}；u={u(t),u(t-1),...,u(t-n)};

u(t)是t时刻控制器的输出，u(t-1)是t-1时刻控制器的输出，u(t-n)是t-n时刻控制器的输出；u(t) is the output of the controller at time t, u(t-1) is the output of the controller at time t-1, u(t-n) is the output of the controller at time t-n;

e＝{e(t),e(t-1),...,e(t-n)}；e={e(t),e(t-1),...,e(t-n)};

e(t)是t时刻系统误差，e(t-1)是t-1时刻系统误差，e(t-n)是t-n时刻系统误差；e(t) is the systematic error at time t, e(t-1) is the systematic error at time t-1, and e(t-n) is the systematic error at time t-n;

y＝{y(t),y(t-1),...,y(t-n)}；y={y(t),y(t-1),...,y(t-n)};

y(t)是t时刻系统输出，y(t-1)是t-1时刻系统输出，y(t-n)是t-n时刻系统输出；y(t) is the system output at time t, y(t-1) is the system output at time t-1, and y(t-n) is the system output at time t-n;

n—抗原长度；n—antigen length;

—免疫记忆模块最大存储容量； —The maximum storage capacity of the immune memory module;

i—抗原编号，i为常数， i—antigen number, i is a constant,

所述的特异性识别是指根据出现干扰的时刻的r、u、e和y的值识别与之相同的Ag_i；The specific recognition refers to the recognition of the same Ag _i according to the values of r, u, e and y at the moment when the interference occurs;

所述的免疫应答模块模拟人体特异性免疫过程中的免疫应答机理，对抗原出现的不同情况，初次出现或者再次出现，做出不同的应答机制，即初次应答及再次应答，并输出与抗原匹配的抗体；所述的抗体Ab_i定义为：The immune response module simulates the immune response mechanism in the specific immune process of the human body, and makes different response mechanisms for different situations of antigen appearance, whether it appears for the first time or reappears, that is, the first response and the second response, and outputs the antigen matching Antibody; The antibody Ab _i is defined as:

${Ab Ab}_{i i} = = {u u}_{i i}^{i i m m},, i i = = 11,, ... ...,, {Num Num}_{m m a a x x}^{i i m m}$

其中，in,

${u u}_{i i}^{i i m m} = = {{{u u}_{i i}^{i i m m} ((11)),, ... ...,, {u u}_{i i}^{i i m m} ((m m))}};;$

u_i ^im(m)是针对抗原Ag_i出现后第m时刻的免疫控制量；u _i ^im (m) is the amount of immune control at the m moment after the appearance of antigen Ag _i ;

m—抗体长度；m—antibody length;

所述的抗原与抗体的匹配关系定义为：The matching relationship between the antigen and the antibody is defined as:

{Ag_i,Ab_i}；{Ag _i ,Ab _i };

所述的免疫记忆模块模拟人体特异性免疫过程中的免疫记忆机理，对抗原的特异性及其匹配的抗体按照所述的匹配关系进行存储记录，并供免疫识别模块和免疫应答模块进行访问、查询和读取；所述的免疫记忆模块是一个线性存储器，当存储器剩余容量不足以存储新的数据时，根据查找访问概率自动删除访问概率最低的数据，然后存储新的数据。The immune memory module simulates the immune memory mechanism in the specific immune process of the human body, stores and records the specificity of the antigen and its matching antibody according to the matching relationship, and provides access to the immune recognition module and immune response module, Inquiry and reading: the immune memory module is a linear memory, when the remaining capacity of the memory is not enough to store new data, automatically delete the data with the lowest access probability according to the search access probability, and then store new data.

所述的一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，所述的被控对象为凝固浴蒸汽加热设备以及凝固浴水槽；所述的凝固浴蒸汽加热设备根据控制量控制蒸汽阀门开度，让适量的高温蒸汽进入没入凝固浴水槽中的管道，蒸汽通过管壁与凝固液发生热量交换，致使凝固液温度升高。所述的凝固浴蒸汽加热设备在凝固浴温度低于设定的温度并且偏差达到设定温度的δ％时开始工作，直到凝固浴温度达到设定的温度时停止工作，这之间的过程称为换热器的一次工作。其中δ∈[0,100]为工艺精度系数，根据实际工艺要求选取。The carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control, the controlled object is the coagulation bath steam heating equipment and the coagulation bath water tank; the coagulation bath steam heating equipment according to the control amount Control the opening of the steam valve so that an appropriate amount of high-temperature steam enters the pipe submerged in the coagulation bath tank, and the steam exchanges heat with the coagulation liquid through the pipe wall, resulting in an increase in the temperature of the coagulation liquid. The coagulation bath steam heating equipment starts to work when the coagulation bath temperature is lower than the set temperature and the deviation reaches δ% of the set temperature, and stops working until the coagulation bath temperature reaches the set temperature. The process between them is called One job for the heat exchanger. Among them, δ∈[0,100] is the process precision coefficient, which is selected according to the actual process requirements.

所述的一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，所述的迭代学习控制器和迭代学习存储单元依据迭代学习控制算法建立，所述迭代学习控制器将换热器的一次工作作为一次迭代过程，根据一定的学习律，通过在不断的迭代中学习控制系统的历史数据，以不断的提高控制效果；所述的学习律为任何已有的迭代学习律。The carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control, the iterative learning controller and the iterative learning storage unit are established according to the iterative learning control algorithm, and the iterative learning controller will exchange heat One operation of the controller is an iterative process, and according to a certain learning law, the historical data of the control system is learned in continuous iterations to continuously improve the control effect; the learning law is any existing iterative learning law.

具体的迭代学习算法及其PID型学习率为：The specific iterative learning algorithm and its PID learning rate are:

${u u}_{k k + + 11} = = {u u}_{k k} + + {Φe Φe}_{k k} + + Ψ Ψ &Integral; &Integral; {e e}_{k k} d d t t + + Γ Γ {\overset{\cdot \cdot}{e e}}_{k k}$

所述的一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，其特征在于，所述基于免疫记忆学习的智能温度控制器的算法具体流程如下：The carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control is characterized in that the algorithm specific flow of the intelligent temperature controller based on immune memory learning is as follows:

1)特异性识别：1) Specific recognition:

a.由免疫识别模块实时监控所述的r(t)、e(t)及u(t)三个信号，实时监测并判断当前时刻是否出现干扰；当满足以下条件：a. The three signals of r(t), e(t) and u(t) are monitored in real time by the immune identification module, and it is monitored in real time and judged whether there is interference at the current moment; when the following conditions are met:

e(t)≥(|u(t)-u(t-1)|+r(t))·ε_im，e(t)≥(|u(t)-u(t-1)|+r(t))·ε _im ,

此时，即认为出现干扰，启动免疫应答模块以及免疫记忆模块；At this time, it is considered that there is interference, and the immune response module and the immune memory module are activated;

其中ε_im为干扰灵敏度系数，ε_im过大则免疫识别对较小的误差不响应，控制精度不高；ε_im过小则会产生大量抗原，计算速度较慢；ε_im可在实际应用多次尝试，适当选择。Among them, ε _im is the interference sensitivity coefficient. If ε _im is too large, the immune recognition will not respond to small errors, and the control accuracy will not be high; if ε _im is too small, a large number of antigens will be generated, and the calculation speed _will be slow; Tries, chooses appropriately.

b.将该干扰时刻的r、u、e和y记为一个抗原Ag_i，并对该抗原的特异性进行识别，即，通过在免疫记忆模块中进行搜索查找，若查找到同样的抗原记录则获得该抗原编号，并认为该抗原再次入侵，若查找不到则作为一种新的抗原赋予新的编号并认为抗原初次入侵；b. Record r, u, e and y at the time of interference as an antigen Ag _i , and identify the specificity of the antigen, that is, by searching in the immune memory module, if the same antigen record is found The antigen number is obtained, and the antigen is considered to invade again. If it cannot be found, a new number is assigned as a new antigen and the antigen is considered to be the first invasion;

c.将经过抗原特异性识别获得的抗原编号，以及初次或是再次入侵的认定，传达给免疫应答模块，启动免疫应答模块；c. Communicate the antigen number obtained through antigen-specific recognition, as well as the initial or re-invasion identification, to the immune response module, and start the immune response module;

2)应答：2) Answer:

启动免疫应答模块的应答算法分为初次应答和再次应答两种情况，抗原初次入侵采用初次应答，抗原再次入侵采用再次应答。The response algorithm for starting the immune response module is divided into two situations: initial response and re-response. The initial response is used for the initial invasion of the antigen, and the re-response is used for the re-invasion of the antigen.

所述的初次应答包括以下步骤：The initial response includes the following steps:

①采用所述的迭代学习控制器的迭代学习控制算法及其学习律对出现的抗原引起的输出误差进行消除，控制器输出相应的控制量以减小输出误差并最终使输出误差趋于零。同时，将此误差消除过程中控制器输出的控制量u记为与该抗原匹配的免疫控制量其中u＝{u(t),u(t+1),...,u(t+m)}；①Use the iterative learning control algorithm of the iterative learning controller and its learning law to eliminate the output error caused by the antigen, and the controller outputs the corresponding control amount to reduce the output error and finally make the output error tend to zero. At the same time, record the control quantity u output by the controller during the error elimination process as the immune control quantity matching the antigen where u={u(t),u(t+1),...,u(t+m)};

②误差消除后，将本次初次出现的抗原Ag_i及其匹配的抗体Ab_i按照所述的匹配关系{Ag_i,Ab_i}存储至免疫记忆模块；② After the error is eliminated, store the antigen Ag _i and its matching antibody Ab _i that appear for the first time in the immune memory module according to the matching relationship {Ag _i , Ab _i };

所述的再次应答包括以下步骤：Described answering again comprises the following steps:

⑴根据免疫识别模块在免疫记忆模块中查找到的抗原的抗体匹配关系，读取与该抗原匹配的抗体的记录，即，获得控制器针对该抗原上一次出现时的免疫控制量 (1) According to the antibody matching relationship of the antigen found by the immune recognition module in the immune memory module, read the record of the antibody matching the antigen, that is, obtain the immune control amount of the controller for the last appearance of the antigen

⑵将上一步骤(1)中获得的抗体与实时的迭代学习控制器的输出进行结合，形成针对当前抗原的控制输出，并根据学习律做进一步更新，输出至被控对象；所述的结合定义为：(2) Combine the antibody obtained in the previous step (1) with the output of the real-time iterative learning controller to form a control output for the current antigen, and further update it according to the learning law, and output it to the controlled object; the combination defined as:

${u u}_{k k}^{' '} ((t t)) = = α α \cdot \cdot {u u}_{k k} ((t t)) + + ((11 - - α α)) \cdot \cdot {u u}_{i i}^{i i m m}$

其中，in,

下标k的数据表示为第k次迭代过程中的数据，k+1表示为第k+1次迭代过程中的数据；(在第2、3条中增加了“迭代过程”的说明及其表示的工艺过程。)The data with subscript k means the data in the kth iteration process, and k+1 means the data in the k+1th iteration process; (the description of "iterative process" and its Indicated process.)

u_k(t)—迭代学习控制器第k次迭代过程中t时刻输出的控制量；u _k (t)—the output control quantity of the iterative learning controller at time t during the kth iteration;

α—平滑参数，α∈[0,1]；α—smoothing parameter, α∈[0,1];

u′_k(t)—第k次迭代过程中t时刻免疫应答模块输出；u′ _k (t)—the output of the immune response module at time t during the kth iteration;

所述的更新定义为：The update is defined as:

${u u}_{k k + + 11} ((t t)) = = {u u}_{k k}^{' '} ((t t)) + + {Φe Φe}_{k k} ((t t)) + + Ψ Ψ &Integral; &Integral; {e e}_{k k} ((t t)) d d t t + + Γ Γ {\overset{\cdot \cdot}{e e}}_{k k} ((t t))$

其中，in,

u_k+1(t)—第k+1次迭代过程中t时刻控制器的输出；u _k+1 (t)—the output of the controller at time t during the k+1th iteration;

Φ,Ψ,Γ—PID型学习律参数；Φ,Ψ,Γ—PID type learning law parameters;

—对时间的导数； — derivative with respect to time;

⑶抗原消除后，将更新的控制量u_k+1(t)记为该抗原Ag_i的匹配抗体Ab_i，并按匹配关系{Ag_i,Ab_i}存储至免疫记忆模块中，替换更新前的与Ag_i匹配的抗体。(3) After the antigen is eliminated, record the updated control amount u _k+1 (t) as the matching antibody Ab _i of the antigen Ag _i , and store it in the immune memory module according to the matching relationship {Ag _i ,Ab _i }, replacing the updated Antibodies that match Ag _i .

有益效果Beneficial effect

本发明由于采取以上技术方案，其具有以下优点：The present invention has the following advantages due to the adoption of the above technical scheme:

1.本发明的主体控制方案是基于迭代学习的数据驱动控制方案，该方法无需建立被控对象模型，仅通过不断的学习历史数据达到不断的提高控制效果。该算法具有很高的智能性，在实际应用中具有良好的效果。1. The main control scheme of the present invention is a data-driven control scheme based on iterative learning. This method does not need to establish a controlled object model, and only continuously improves the control effect by continuously learning historical data. The algorithm has high intelligence and has good effect in practical application.

2.本发明采用了免疫识别、记忆与应答机制改进传统的迭代学习算法，通过模拟免疫系统自主的对入侵的病毒有效的消除过程，弥补了传统迭代学习在学习过程中存在的不分数据好坏统统学习的缺点，减少了传统算法对干扰的累积，进一步提高了系统的抗干扰能力，提高了控制效果。2. The present invention adopts the immune recognition, memory and response mechanism to improve the traditional iterative learning algorithm, and by simulating the immune system's autonomous and effective elimination process of the invading virus, it makes up for the traditional iterative learning that does not distinguish data during the learning process. The shortcomings of all learning can reduce the accumulation of interference by traditional algorithms, further improve the anti-interference ability of the system, and improve the control effect.

3.本发明设计的免疫识别、记忆与应答算法，也是根据历史数据进行自主学习的算法，无论对于随机出现的干扰或是反复出现的干扰，都能够很好的有针对性的进行消除。3. The immune recognition, memory and response algorithm designed by the present invention is also an algorithm for self-learning based on historical data, which can effectively eliminate random interference or repeated interference.

附图说明Description of drawings

图1是控制系统结构框图Figure 1 is a block diagram of the control system

图2是设备示意图Figure 2 is a schematic diagram of the device

图3是一次迭代控制流程图Figure 3 is an iterative control flow chart

图4是系统添加的随机性干扰数据图Figure 4 is a graph of random interference data added by the system

图5是系统输出仿真结果图Figure 5 is a graph of the system output simulation results

图6是控制误差仿真结果图Figure 6 is a graph of control error simulation results

图7是系统添加的重复性干扰数据图Figure 7 is a diagram of repetitive interference data added by the system

图8是针对重复性干扰控制效果图Figure 8 is an effect diagram for repetitive interference control

图9为图8中的局部放大图Figure 9 is a partial enlarged view of Figure 8

其中1为凝固浴补水入口；2为缓冲挡板；3为喷丝板；4为凝固液；5为聚丙烯腈细流；6为溢流口；7为蒸汽入口；8为蒸汽换热管道；9为蒸汽出口。Among them, 1 is the water inlet of coagulation bath; 2 is buffer baffle; 3 is spinneret; 4 is coagulation liquid; 5 is polyacrylonitrile trickle; 6 is overflow; 7 is steam inlet; 8 is steam heat exchange pipe ; 9 is the steam outlet.

具体实施方式detailed description

下面结合具体实施方式，进一步阐述本发明。应理解，这些实施例仅用于说明本发明而不用于限制本发明的范围。此外应理解，在阅读了本发明讲授的内容之后，本领域技术人员可以对本发明作各种改动或修改，这些等价形式同样落于本申请所附权利要求书所限定的范围。The present invention will be further described below in combination with specific embodiments. It should be understood that these examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art may make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of the present application.

本发明的一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，其工艺路线为聚丙烯腈原液经喷丝板挤出进入凝固浴水槽，凝固浴水槽中凝固液的温度由温度检测元件实时检测并反馈至控制器，控制器根据设定值输入、控制量以及输出反馈的当前和历史数据进行当前的控制量计算，并输出至被控对象，对凝固浴进行加热，最终使凝固浴实际温度达到设定温度，所述的控制器为基于免疫记忆学习的智能温度控制器；所述的基于免疫记忆学习的智能温度控制器由迭代学习控制器、迭代学习存储单元、免疫识别模块、免疫应答模块和免疫记忆模块组成。所述的基于免疫记忆学习的智能温度控制器结构框图如图1所示。A carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control of the present invention, its process route is that the polyacrylonitrile stock solution is extruded into the coagulation bath water tank through the spinneret, and the temperature of the coagulation liquid in the coagulation bath water tank is determined by The temperature detection element detects in real time and feeds back to the controller. The controller calculates the current control quantity according to the current and historical data of the set value input, control quantity and output feedback, and outputs it to the controlled object to heat the coagulation bath. Finally The actual temperature of the coagulation bath reaches the set temperature, and the controller is an intelligent temperature controller based on immune memory learning; the intelligent temperature controller based on immune memory learning consists of an iterative learning controller, an iterative learning storage unit, an immune It consists of recognition module, immune response module and immune memory module. The structural block diagram of the intelligent temperature controller based on immune memory learning is shown in FIG. 1 .

所述的一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，所述的被控对象为凝固浴蒸汽加热设备以及凝固浴水槽；所述的凝固浴水槽及其蒸汽加热设备示意图如图2所示。聚丙烯腈原液经过喷丝板3进入所述的凝固浴水槽，形成聚丙烯腈细流5。所述的凝固浴蒸汽加热设备根据控制量控制蒸汽阀门开度，让适量的高温蒸汽由蒸汽入口7进入没入凝固浴水槽中的蒸汽换热管道8，蒸汽通过管壁与凝固液4发生热量交换，致使凝固液4温度升高。最后蒸汽通过蒸汽出口9排出。所述的凝固浴蒸汽加热设备在凝固浴温度低于设定的温度并且偏差达到设定温度的δ％时开始工作，直到凝固浴温度达到设定的温度时停止工作，这之间的过程称为换热器的一次工作。其中δ∈[0,100]为工艺精度系数，根据实际工艺要求选取。The carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control, the controlled object is the coagulation bath steam heating equipment and the coagulation bath water tank; the coagulation bath water tank and its steam heating equipment The schematic diagram is shown in Figure 2. The polyacrylonitrile stock solution enters the coagulation bath tank through the spinneret 3 to form a polyacrylonitrile trickle 5 . The coagulation bath steam heating device controls the opening of the steam valve according to the control amount, so that an appropriate amount of high-temperature steam enters the steam heat exchange pipe 8 submerged in the coagulation bath water tank from the steam inlet 7, and the steam exchanges heat with the coagulation liquid 4 through the pipe wall , causing the temperature of the coagulation liquid 4 to rise. Finally the steam is discharged through the steam outlet 9. The coagulation bath steam heating equipment starts to work when the coagulation bath temperature is lower than the set temperature and the deviation reaches δ% of the set temperature, and stops working until the coagulation bath temperature reaches the set temperature. The process between them is called One job for the heat exchanger. Among them, δ∈[0,100] is the process precision coefficient, which is selected according to the actual process requirements.

所述的一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，所述的迭代学习控制器和迭代学习存储单元依据迭代学习控制算法建立，所述迭代学习控制器将换热器的一次工作作为一次迭代过程，根据一定的学习律，通过在不断的迭代中学习控制系统的历史数据，以不断的提高控制效果；所述的学习律为任何已有的迭代学习律。The carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control, the iterative learning controller and the iterative learning storage unit are established according to the iterative learning control algorithm, and the iterative learning controller will exchange heat A work of the controller is an iterative process, and according to a certain learning law, the historical data of the control system is learned in continuous iterations to continuously improve the control effect; the learning law is any existing iterative learning law.

所述的一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，所述的免疫识别模块模拟人体特异性免疫过程中免疫系统识别特定抗原的机理，将控制系统中出现的干扰作为抗原，对抗原进特异性识别；所述的抗原Ag_i定义为：The carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control, the immune recognition module simulates the mechanism of the immune system recognizing specific antigens in the specific immune process of the human body, and will control the interference that occurs in the system As an antigen, the antigen is specifically recognized; the antigen Ag _i is defined as:

其中，in,

r＝{r(t),r(t-1),...,r(t-n)}；r={r(t),r(t-1),...,r(t-n)};

u＝{u(t),u(t-1),...,u(t-n)}；u={u(t),u(t-1),...,u(t-n)};

e＝{e(t),e(t-1),...,e(t-n)}；e={e(t),e(t-1),...,e(t-n)};

y＝{y(t),y(t-1),...,y(t-n)}；y={y(t),y(t-1),...,y(t-n)};

n—抗原长度；n—antigen length;

i—抗原编号，i为常数， i—antigen number, i is a constant,

其中，in,

m—抗体长度；m—antibody length;

{Ag_i,Ab_i}；{Ag _i ,Ab _i };

所述的一种基于免疫记忆学习控制的碳纤维原丝湿法凝固浴温度控制工艺，其特征在于，所述基于免疫记忆学习的智能温度控制器的算法流程如图3所示，具体流程如下：The carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control is characterized in that the algorithm flow of the intelligent temperature controller based on immune memory learning is shown in Figure 3, and the specific flow is as follows:

1)特异性识别：1) Specific recognition:

d.由免疫识别模块实时监控所述的r(t)、e(t)及u(t)三个信号，实时监测并判断当前时刻是否出现干扰；当满足以下条件：d. The three signals of r(t), e(t) and u(t) are monitored in real time by the immune recognition module, and it is monitored in real time and judged whether there is interference at the current moment; when the following conditions are met:

e(t)≥(|u(t)-u(t-1)|+r(t))·ε_im，e(t)≥(|u(t)-u(t-1)|+r(t))·ε _im ,

e.将该干扰时刻的r、u、e和y记为一个抗原Ag_i，并对该抗原的特异性进行识别，即，通过在免疫记忆模块中进行搜索查找，若查找到同样的抗原记录则获得该抗原编号，并认为该抗原再次入侵，若查找不到则作为一种新的抗原赋予新的编号并认为抗原初次入侵；e. Record r, u, e and y of the interference moment as an antigen Ag _i , and identify the specificity of the antigen, that is, by searching in the immune memory module, if the same antigen record is found The antigen number is obtained, and the antigen is considered to invade again. If it cannot be found, a new number is assigned as a new antigen and the antigen is considered to be the first invasion;

f.将经过抗原特异性识别获得的抗原编号，以及初次或是再次入侵的认定，传达给免疫应答模块，启动免疫应答模块；f. Communicate the antigen number obtained through antigen-specific recognition, and the identification of initial or re-invasion to the immune response module, and start the immune response module;

2)应答：2) Answer:

③采用所述的迭代学习控制器的迭代学习控制算法及其学习律对出现的抗原引起的输出误差进行消除，控制器输出相应的控制量以减小输出误差并最终使输出误差趋于零。同时，将此误差消除过程中控制器输出的控制量u记为与该抗原匹配的免疫控制量其中u＝{u(t),u(t+1),...,u(t+m)}；③ Using the iterative learning control algorithm of the iterative learning controller and its learning law to eliminate the output error caused by the antigen, the controller outputs the corresponding control amount to reduce the output error and finally make the output error tend to zero. At the same time, record the control quantity u output by the controller during the error elimination process as the immune control quantity matching the antigen where u={u(t),u(t+1),...,u(t+m)};

④误差消除后，将本次初次出现的抗原Ag_i及其匹配的抗体Ab_i按照所述的匹配关系{Ag_i,Ab_i}存储至免疫记忆模块；④ After the error is eliminated, store the antigen Ag _i and its matching antibody Ab _i in the immune memory module according to the matching relationship {Ag _i , Ab _i };

⑷根据免疫识别模块在免疫记忆模块中查找到的抗原的抗体匹配关系，读取与该抗原匹配的抗体的记录，即，获得控制器针对该抗原上一次出现时的免疫控制量 (4) According to the antibody matching relationship of the antigen found by the immune recognition module in the immune memory module, read the record of the antibody matching the antigen, that is, obtain the immune control amount of the controller for the last occurrence of the antigen

⑸将上一步骤(1)中获得的抗体与实时的迭代学习控制器的输出进行结合，形成针对当前抗原的控制输出，并根据学习律做进一步更新，输出至被控对象；(5) Combine the antibody obtained in the previous step (1) with the output of the real-time iterative learning controller to form a control output for the current antigen, and further update it according to the learning law, and output it to the controlled object;

所述的结合定义为：Said binding is defined as:

其中，in,

α—平滑参数，α∈[0,1]；α—smoothing parameter, α∈[0,1];

所述的更新定义为：The update is defined as:

其中，in,

Φ,Ψ,Γ—PID型学习律参数；Φ,Ψ,Γ—PID type learning law parameters;

抗原消除后，将更新的控制量u_k+1(t)记为该抗原Ag_i的匹配抗体Ab_i，并按匹配关系{Ag_i,Ab_i}存储至免疫记忆模块中，替换更新前的与Ag_i匹配的抗体。After the antigen is eliminated, the updated control amount u _k+1 (t) is recorded as the matching antibody Ab _i of the antigen Ag _i , and stored in the immune memory module according to the matching relationship {Ag _i ,Ab _i }, replacing the updated Antibodies matching Ag _i .

以下实施例采用蒸汽换热设备为控制对象进行仿真。该设备的传递函数为：In the following embodiments, steam heat exchange equipment is used as the control object for simulation. The transfer function of the device is:

$G G ((s the s)) = = \frac{11}{((s the s + + 11)) ((3838 s the s + + 11))}$

取采样时间T_s＝1s，则对象的离散传递函数为：Take the sampling time T _s =1s, then the discrete transfer function of the object is:

$G G ((z z)) = = \frac{0.00959 0.00959 z z + + 0.006828 0.006828}{{z z}^{22} - - 1.342 1.342 z z + + 0.3583 0.3583}$

需要说明的是，对象的模型仅用于获得测试数据以及方法验证，所有数据驱动的控制算法设计中均假设对象模型未知，不对对象进行建模，直接利用数据进行控制器设计。It should be noted that the object model is only used to obtain test data and method verification. All data-driven control algorithm design assumes that the object model is unknown, and the object is not modeled, and the data is directly used for controller design.

本实施方式具体分为两个实施例，分别对随机出现的干扰以及重复性的干扰进行仿真实验，验证本发明抵抗各种干扰的能力。两个实施例中共同需要的实验相关参数如表一、表二所示。This implementation mode is specifically divided into two embodiments, and simulation experiments are respectively performed on randomly occurring interference and repetitive interference to verify the ability of the present invention to resist various interferences. The relevant experimental parameters commonly required in the two embodiments are shown in Table 1 and Table 2.

表一.免疫记忆与应答算法参数Table 1. Immune memory and response algorithm parameters

表二.实验参数Table 2. Experimental parameters

表二中，T_s—采样时间；T_l—单次迭代时长；K—迭代次数；T_set—凝固浴设定温度。In Table 2, T _s —sampling time; T _l —single iteration time; K—iteration number; T _set —set temperature of coagulation bath.

本实施方式的控制目标函数y_d定义为：The control objective function y _d of this embodiment is defined as:

${y the y}_{d d} = = \{\begin{matrix} {T T}_{s the s e e t t} s the s i i n no ((66 π π \cdot &Center Dot; 1010^{- - 33} t t)),, & t t \leq \leq 0.5 0.5 / / 66 \cdot &Center Dot; 1010^{33} = = 83. 83. \overset{\cdot &Center Dot;}{33} \\ {T T}_{s the s e e t t},, & t t > > 83. 83. \overset{\cdot \cdot}{33} \end{matrix} . .$

实施例一Embodiment one

本实施例在系统中添加随机性干扰，干扰幅值为控制目标的±10％以内的随机值，干扰出现频率为1％，某次随机干扰数据如图4所示。In this embodiment, random interference is added to the system. The amplitude of the interference is a random value within ±10% of the control target, and the occurrence frequency of the interference is 1%. The data of a certain random interference is shown in FIG. 4 .

本实施例同时对传统的迭代学习控制工艺以及本发明控制工艺进行仿真实验，并对比二者直接的结果。其中，本发明的仿真过程根据发明内容中的具体控制工艺步骤进行仿真。二者对比的控制效果如图5所示。In this embodiment, simulation experiments are carried out on the traditional iterative learning control process and the control process of the present invention at the same time, and the direct results of the two are compared. Wherein, the simulation process of the present invention is simulated according to the specific control process steps in the content of the invention. The control effect of the two comparisons is shown in Figure 5.

从图5和图6中可以看出，本发明的控制工艺相比传统的控制工艺能够更好的消除干扰造成的误差，进一步提高控制系统的稳定性。图5为系统输出仿真结果图，图6为控制误差仿真结果图。It can be seen from FIG. 5 and FIG. 6 that, compared with the traditional control process, the control process of the present invention can better eliminate errors caused by interference, and further improve the stability of the control system. Fig. 5 is a diagram of the simulation result of the system output, and Fig. 6 is a diagram of the simulation result of the control error.

实施例二Embodiment two

在对凝固浴中凝固液的控制工艺中，温度和浓度是两个同时进行控制的参数，因此，在凝固液温度控制工艺中，必须考虑浓度控制过程给温度参数带来的干扰。由于浓度控制也是重复性的控制过程，因此，本实施例模拟浓度控制对温度造成的影响，将其作为重复性干扰添加至温度控制系统中。In the control process of the coagulation liquid in the coagulation bath, temperature and concentration are two parameters that are controlled at the same time. Therefore, in the process of controlling the temperature of the coagulation liquid, the interference caused by the concentration control process to the temperature parameter must be considered. Since the concentration control is also a repetitive control process, this embodiment simulates the influence of the concentration control on the temperature and adds it as a repetitive disturbance to the temperature control system.

浓度控制相关设备如图2所示，常温水通过凝固浴补水入口1进入凝固浴水槽，缓冲挡板2起到缓和液体流动波动的作用，同时为保证液位稳定，在凝固浴末端设有溢流口6，将多余的凝固液4排出。每一次补水会导致凝固液温度的下降，该温度变化过程如图6所示。将该温度变化添加至系统中，并且在每一次迭代中反复出现，成为一种重复性干扰。Concentration control related equipment is shown in Figure 2. Normal temperature water enters the coagulation bath water tank through the coagulation bath replenishment inlet 1, and the buffer baffle 2 plays the role of easing the fluctuation of the liquid flow. The orifice 6 discharges the excess coagulation liquid 4 . Each water replenishment will cause the temperature of the coagulation liquid to drop, and the temperature change process is shown in Figure 6. Adding this temperature change to the system, and recurring with each iteration, becomes a repetitive disturbance.

系统对重复性干扰的控制效果如图8和图9所示，其中图9为图8中的局部放大。本实施例同样对比了传统的迭代学习控制工艺以及本发明的控制工艺，仿真计算过程按照发明内容中的具体计算步骤。通过二者的仿真结果，可以看出，在重复性干扰的问题上，本发明的控制工艺的控制性能也明显优于传统的控制工艺。The control effect of the system on repetitive interference is shown in Figure 8 and Figure 9, where Figure 9 is a partial enlargement of Figure 8. This embodiment also compares the traditional iterative learning control process with the control process of the present invention, and the simulation calculation process follows the specific calculation steps in the content of the invention. From the simulation results of the two, it can be seen that the control performance of the control technology of the present invention is also obviously better than that of the traditional control technology on the problem of repetitive interference.

Claims

1. A carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control, its process route is that the polyacrylonitrile stock solution is extruded into the coagulation bath water tank through the spinneret, and the temperature of the coagulation liquid in the coagulation bath water tank is determined by the temperature The detection element detects in real time and feeds back to the controller. The controller calculates the current control quantity according to the current and historical data of the set value input, control quantity and output feedback, and outputs it to the controlled object to heat the coagulation bath. Finally, the The actual temperature of the coagulation bath reaches the set temperature, and it is characterized in that: the controller is an intelligent temperature controller based on immune memory learning; the intelligent temperature controller based on immune memory learning is composed of iterative learning controller, iterative learning storage Unit, immune recognition module, immune response module and immune memory module; the immune recognition module simulates the mechanism of the immune system to recognize specific antigens in the process of human specific immunity, and uses the interference in the control system as an antigen to carry out specific Sex recognition; The antigen Ag _i is defined as:

{Ag Ag}_{i i} = = {{r r,, u u,, e e,, y the y}},, i i = = 11,, ... ...,, {Num Num}_{m m a a x x}^{i i m m},,

in,

r={r(t),r(t-1),...,r(t-n)};

r(t) is the system input at time t, r(t-1) is the system input at time t-1, and r(t-n) is the system input at time t-n;

u={u(t),u(t-1),...,u(t-n)};

u(t) is the output of the controller at time t, u(t-1) is the output of the controller at time t-1, u(t-n) is the output of the controller at time t-n;

e={e(t),e(t-1),...,e(t-n)};

e(t) is the systematic error at time t, e(t-1) is the systematic error at time t-1, and e(t-n) is the systematic error at time t-n;

y={y(t),y(t-1),...,y(t-n)};

y(t) is the system output at time t, y(t-1) is the system output at time t-1, and y(t-n) is the system output at time t-n;

n—antigen length;

—The maximum storage capacity of the immune memory module;

i—antigen number, i is a constant,

The specific recognition refers to the recognition of the same Ag _i according to the values of r, u, e and y at the moment when the interference occurs;

The immune response module simulates the immune response mechanism in the specific immune process of the human body, and makes different response mechanisms for different situations of antigen appearance, whether it appears for the first time or reappears, that is, the first response and the second response, and outputs the antigen matching Antibody; The antibody Ab _i is defined as:

{Ab Ab}_{i i} = = {u u}_{i i}^{i i m m},, i i = = 11,, ... ...,, {Num Num}_{m m a a x x}^{i i m m}

in,

{u u}_{i i}^{i i m m} = = {{{u u}_{i i}^{i i m m} ((11)),, ... ...,, {u u}_{i i}^{i i m m} ((m m))}};;

u _i ^im (m) is the amount of immune control at the m moment after the appearance of antigen Ag _i ;

m—antibody length;

The matching relationship between the antigen and the antibody is defined as:

{Ag _i ,Ab _i };

The immune memory module simulates the immune memory mechanism in the specific immune process of the human body, stores and records the specificity of the antigen and its matching antibody according to the matching relationship, and provides access to the immune recognition module and immune response module, Inquiry and reading: the immune memory module is a linear memory, when the remaining capacity of the memory is not enough to store new data, automatically delete the data with the lowest access probability according to the search access probability, and then store new data.

2. a kind of carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control according to claim 1, is characterized in that, described controlled object is coagulation bath steam heating equipment and coagulation bath water tank; The coagulation bath steam heating equipment described above controls the opening of the steam valve according to the control amount, so that an appropriate amount of high-temperature steam enters the pipeline submerged in the coagulation bath tank, and the steam exchanges heat with the coagulation liquid through the pipe wall, causing the temperature of the coagulation liquid to rise; The coagulation bath steam heating equipment starts to work when the coagulation bath temperature is lower than the set temperature and the deviation reaches δ% of the set temperature, and stops working until the coagulation bath temperature reaches the set temperature. The process between this is called changing One-time work of the heater; where δ∈[0,100] is the process accuracy coefficient, which is selected according to the actual process requirements.

3. a kind of carbon fiber precursor wet coagulation bath temperature control process based on immune memory learning control according to claim 1, is characterized in that, described iterative learning controller and iterative learning storage unit are established according to iterative learning control algorithm , the iterative learning controller takes one job of the heat exchanger as an iterative process, and according to a certain learning law, learns the historical data of the control system in continuous iterations to continuously improve the control effect; the learning law for any existing iterative learning law.

4. a kind of carbon fiber precursor wet method coagulation bath temperature control technology based on immune memory learning control according to claim 1, it is characterized in that, the algorithm flow of described intelligent temperature controller based on immune memory learning is as follows:

1) Specific recognition:

a. The three signals of r(t), e(t) and u(t) are monitored in real time by the immune identification module, and it is monitored in real time and judged whether there is interference at the current moment; when the following conditions are met:

e(t)≥(|u(t)-u(t-1)|+r(t))·ε _im ,

At this time, it is considered that there is interference, and the immune response module and the immune memory module are activated;

Where _εim is the interference sensitivity coefficient, if _εim is too large, the immune recognition will not respond to small errors, and the control accuracy will not be high;

If ε _im is too small, a large number of antigens will be generated, and the calculation speed will be slow; ε _im can be tried many times in practical applications, and it can be selected appropriately;

b. Record r, u, e and y at the time of interference as an antigen Ag _i , and identify the specificity of the antigen, that is, by searching in the immune memory module, if the same antigen record is found The antigen number is obtained, and the antigen is considered to invade again. If it cannot be found, a new number is assigned as a new antigen and the antigen is considered to be the first invasion;

c. Communicate the antigen number obtained through antigen-specific recognition, as well as the initial or re-invasion identification, to the immune response module, and start the immune response module;

2) Answer:

The response algorithm for starting the immune response module is divided into two situations: initial response and re-response. The initial response is used for the initial invasion of the antigen, and the re-response is used for the re-invasion of the antigen;

The initial response includes the following steps:

①Using the iterative learning control algorithm of the iterative learning controller and its learning law to eliminate the output error caused by the antigen, the controller outputs the corresponding control amount to reduce the output error and finally make the output error tend to zero; At the same time, record the control quantity u output by the controller during the error elimination process as the immune control quantity matching the antigen where u={u(t),u(t+1),...,u(t+m)};

② After the error is eliminated, store the antigen Ag _i and its matching antibody Ab _i that appear for the first time in the immune memory module according to the matching relationship {Ag _i , Ab _i };

Described answering again comprises the following steps:

(1) According to the antibody matching relationship of the antigen found by the immune recognition module in the immune memory module, read the record of the antibody matching the antigen, that is, obtain the immune control amount of the controller for the last appearance of the antigen

(2) Combine the antibody obtained in the previous step (1) with the output of the real-time iterative learning controller to form a control output for the current antigen, and further update it according to the learning law, and output it to the controlled object;

Said binding is defined as:

{u u}_{k k}^{' '} ((t t)) = = α α \cdot \cdot {u u}_{k k} ((t t)) + + ((11 - - α α)) \cdot \cdot {u u}_{i i}^{i i m m}

in,

The data of the subscript k represents the data in the k-th iteration process, and k+1 represents the data in the k+1-th iteration process;

u _k (t)—the output control quantity of the iterative learning controller at time t during the kth iteration;

α—smoothing parameter, α∈[0,1];

u′ _k (t)—the output of the immune response module at time t during the kth iteration;

The update is defined as:

{u u}_{k k + + 11} ((t t)) = = {u u}_{k k}^{' '} ((t t)) + + {Φe Φe}_{k k} ((t t)) + + Ψ Ψ &Integral; &Integral; {e e}_{k k} ((t t)) d d t t + + Γ Γ {\overset{\cdot \cdot}{e e}}_{k k} ((t t))

in,

u _k+1 (t)—the output of the controller at time t during the k+1th iteration;

Φ,Ψ,Γ—PID type learning law parameters;

— derivative with respect to time;

(3) After the antigen is eliminated, record the updated control amount u _k+1 (t) as the matching antibody Ab _i of the antigen Ag _i , and store it in the immune memory module according to the matching relationship {Ag _i ,Ab _i }, replacing the updated Antibodies that match Ag _i .