Robust H∞ control based on fuzzy hyperbolic model with time-delay
Fuzzy Logic and Systems
Fuzzy Logic and SystemsFuzzy logic is a fascinating concept that has gained popularity in various fields, including artificial intelligence, control systems, and decision-making processes. Unlike traditional binary logic, which operates based on precise values of true or false, fuzzy logic allows for degrees of truth, making it moreadaptable to real-world scenarios where uncertainties and ambiguities exist. One of the key advantages of fuzzy logic is its ability to handle imprecise data and vague boundaries. In many real-life situations, such as weather forecasting or medical diagnosis, information is often incomplete or uncertain. Fuzzy logic provides a framework for reasoning with this fuzzy information, allowing for more nuanced and flexible decision-making. In the field of artificial intelligence, fuzzy logic plays a crucial role in mimicking human reasoning and decision-making processes. By incorporating fuzzy logic into AI systems, researchers can develop more intelligent and adaptive algorithms that can learn from experience and make decisions based on uncertain or incomplete information. This is particularlyuseful in applications such as natural language processing, image recognition, and autonomous systems. From a control systems perspective, fuzzy logic offers a more intuitive and user-friendly approach to designing controllers for complex systems. Traditional control systems rely on precise mathematical models and algorithms, which can be challenging to implement in systems with nonlinear dynamics or uncertain parameters. Fuzzy logic controllers, on the other hand, can capture the expertise and intuition of human operators, making them more robust and adaptable to changing conditions. Despite its many advantages, fuzzy logic is not withoutits limitations. One common criticism is its lack of formal mathematical rigor compared to traditional logic systems. Critics argue that the subjective nature of fuzzy logic can lead to inconsistencies and ambiguity in decision-making processes. Additionally, designing fuzzy systems can be complex and time-consuming, requiring domain expertise and careful tuning of parameters. In conclusion, fuzzy logic isa powerful tool that offers a more flexible and intuitive approach to reasoningand decision-making in complex and uncertain environments. By allowing for degrees of truth and uncertainty, fuzzy logic can capture the nuances of human reasoning and behavior, making it a valuable tool in artificial intelligence, controlsystems, and other applications. While it may not be suitable for all situations, fuzzy logic has proven to be a valuable addition to the toolkit of researchers and practitioners in various fields.。
Fuzzy Systems and Control
Fuzzy Systems and Control Fuzzy systems and control are an essential part of modern engineering and technology. They are used in a wide range of applications, from controlling industrial processes to managing traffic flow in cities. The concept of fuzzylogic is based on the idea that many real-world problems are too complex to be described by precise mathematical models. Instead, they require a more flexible approach that can deal with uncertainty and imprecision.One of the key advantages of fuzzy systems is their ability to handle uncertainty. In traditional control systems, inputs and outputs are defined by precise mathematical models. However, in the real world, there are often many factors that can affect these inputs and outputs, such as noise, variability, and measurement errors. Fuzzy systems are designed to cope with these uncertainties by using a range of linguistic variables to describe the system's behavior. This allows them to produce more robust and reliable control outputs, even in the face of unpredictable events.Another important advantage of fuzzy systems is their ability to deal with imprecision. In many situations, it is difficult to define precise rules for how a system should behave. For example, in a traffic management system, it is notalways clear how drivers will respond to changing road conditions. Fuzzy systems allow engineers to define rules in a more flexible way, using linguistic variables such as "slow," "moderate," and "fast." This allows the system to adapt to changing conditions and produce more accurate and responsive control outputs.Fuzzy systems are also highly adaptable and can be used in a wide range of applications. They are used in industrial automation, robotics, and process control, as well as in more specialized areas such as medical diagnosis and financial forecasting. This versatility is due to the fact that fuzzy systems can be easily customized to suit different requirements. They can be designed tohandle different types of inputs, such as temperature, pressure, or flow rate, and can be programmed to produce different types of outputs, such as motor control signals or alarm signals.Despite their many advantages, fuzzy systems are not without their limitations. One of the main challenges is designing the system's rules and membershipfunctions. These must be carefully chosen to ensure that the system produces accurate and reliable outputs. This can be a time-consuming and complex process, requiring a deep understanding of the system's behavior and the factors that affect it. In addition, fuzzy systems can be difficult to debug and maintain, particularly if the rules and membership functions are poorly designed.Another limitation of fuzzy systems is their reliance on human expertise. In order to design an effective fuzzy system, engineers must have a deep understanding of the system they are working with and the factors that affect it. This can be a significant challenge, particularly in complex systems where there are many interacting variables. In addition, the process of designing a fuzzy system can be highly subjective, with different engineers producing different results based on their own expertise and experience.In conclusion, fuzzy systems and control are an important part of modern engineering and technology. They offer a flexible and adaptable approach to control and are used in a wide range of applications. However, they also present significant challenges, particularly in terms of designing the system's rules and membership functions and relying on human expertise. Despite these limitations, fuzzy systems are likely to play an increasingly important role in the future of engineering and technology, as they offer a powerful tool for dealing with uncertainty and imprecision in complex systems.。
离散随机奇异系统的零和博弈及H∞控制
离散随机奇异系统的零和博弈及H∞控制周海英【摘要】针对噪声依赖于状态的It(o)型离散随机奇异系统,讨论其在有限时域下的零和博弈及基于博弈方法的H..控制问题.在最优控制(单人博弈)的基础上,利用配方法,得到了离散随机奇异系统鞍点均衡策略的存在等价于相应的耦合Riccati代数方程存在解,并给出了最优解的形式.进一步地,根据博弈方法应用于鲁棒控制问题的思路,得到离散随机奇异系统H∞控制问题的最优策略,最后根据动态投入产出问题的特性,建立相应的博弈模型,得到动态投入产出问题的均衡策略.【期刊名称】《南昌大学学报（理科版）》【年(卷),期】2017(041)006【总页数】5页(P519-523)【关键词】离散随机奇异系统;零和博弈;耦合Riccati代数方程;鞍点均衡策略【作者】周海英【作者单位】广州航海学院港口与航运管理系,广东广州 510725【正文语种】中文【中图分类】F224.32奇异系统由于其广泛的应用背景,自产生以来，得到了广泛研究 [1-4]。
随着研究的深入，随机奇异系统由于能更好的模拟现实实际，近年来，引起了众多研究者的兴趣。
在随机奇异系统的稳定性、最优控制及鲁棒控制方面都有不少成果。
Yan Z等研究了伊腾型随机广义系统的稳定性问题[5]。
Zhang W等研究了广义随机线性系统的稳定性问题[6]；Jin H等研究了随机奇异系统的虑波问题[7]。
文献[8]把神经网络法应用于随机奇异系统不定线性二次控制问题中，得到了相应的Riccati微分方程；高明等研究了离散随机Markov跳跃系统的广义Lyapunov方程解的性质[9]；张庆灵等在研究随机奇异系统的稳定性的基础上，得到了连续随机奇异系统线性二次最优控制的Riccati方程[10]。
Xing等研究了不确定广义随机线性系统的H∞鲁棒控制问题[11]。
Zhang和Zhao Y等研究了广义随机线性系统的H∞鲁棒控制问题[12-13] ；Shu Y等研究不确定连续时间奇异系统的稳定性和最优控制问题 [14]。
变体辅助的无人机栖落机动模糊控制设计
第52卷第6期2020年12月Vol.52No.6Dec.2020南京航空航天大学学报Journal of Nanjing University of Aeronautics&Astronautics变体辅助的无人机栖落机动模糊控制设计岳珵，何真，王无天（南京航空航天大学自动化学院，南京，211106）摘要：无人机（Unmanned aerial vehicle，UAV）的栖落机动是一种大幅度的俯仰运动，易引起升降舵操纵力矩饱和。
本文以变体方式增强无人机的俯仰操纵能力，并研究其对应的控制设计方法。
首先对栖落机动建立了纵向动力学模型，并通过采用轨迹线性化和张量积变换方法转换得到T⁃S模糊模型。
基于Lyapunov稳定理论和平方和方法，设计了满足控制输入约束的栖落机动多项式模糊控制器。
对非变体与变体下的栖落机动控制过程进行了仿真，结果验证了控制律的有效性，并且表明变体辅助的无人机具有更强的操纵性能，能提高栖落机动中升降舵的抗饱和能力。
关键词：栖落机动；变体飞行器；T⁃S模糊模型；平方和；飞行控制中图分类号：V249文献标志码：A文章编号：1005⁃2615（2020）06⁃0871⁃10Fuzzy Control Design for Perching Maneuvers of Morphing UAVsYUE Cheng，HE Zhen，WANG Wutian（College of Automation Engineering，Nanjing University of Aeronautics&Astronautics，Nanjing，211106，China）Abstract:A perching maneuver is a kind of fierce pitching.An unmanned aerialvehicle（UAV）may probably be caught in saturation of the control moment of its elevators during such a process.A morphing mechanism is introduced to strengthen the capability of pitching control，and its corresponding controllers is discussed. Dynamic models of the longitudinal motion are generated at the beginning，and then T-S fuzzy models are obtained by trajectory linearization and tensor product transformation.According to Lyapunov stability theory and sum-of-square approach，polynomial fuzzy controllers meeting the constraints of control inputs are designed.After that，simulations of perching tasks are launched for both the rigid UAV and the morphing one.The results of simulations demonstrate that the morphing UAV has got its edge in maneuverability over the rigid one，and is more capable of suppressing the saturation of elevators.Key words:perching maneuver；morphing aircraft；T-S fuzzy model；sum of squares；flight control在栖落机动过程中，无人机拉大迎角增大阻力进行减速，最终以较低的动能降落在预定地点[1⁃4]。
基于模糊控制的全位移平衡机器人设计
收稿日期：２０２２－０４－１６基金项目：山东省自然科学基金项目（ＺＲ２０２０ＭＦ０９３）；山东省研究生教育优质课程（ＳＤＹＫＣ２００２６）；中石油重大科技合作项目（ＺＤ２０１９ １８３ ００３）引用格式：刘恒，李哲，杨明辉，等．基于模糊控制的全位移平衡机器人设计［Ｊ］．测控技术，２０２３，４２（７）：１０２－１０９．ＬＩＵＨ，ＬＩＺ，ＹＡＮＧＭＨ，ｅｔａｌ．ＤｅｓｉｇｎｏｆＦｕｌｌＤｉｓｐｌａｃｅｍｅｎｔＢａｌａｎｃｉｎｇＲｏｂｏｔＢａｓｅｄｏｎＦｕｚｚｙＣｏｎｔｒｏｌ［Ｊ］．Ｍｅａｓｕｒｅｍｅｎｔ＆ＣｏｎｔｒｏｌＴｅｃｈｎｏｌｏｇｙ，２０２３，４２（７）：１０２－１０９．基于模糊控制的全位移平衡机器人设计刘 恒，李 哲，杨明辉，邓晓刚，曹玉苹（中国石油大学（华东）控制科学与工程学院，山东青岛 ２６６５８０）摘要：设计了一种模糊控制的四轮全位移平衡机器人，通过ＳｏｌｉｄＷｏｒｋｓ改进设计了基于麦克纳姆轮的全位移平衡底盘、双轴云台等机械结构。
以ＡｌｔｉｕｍＤｅｓｉｇｎｅｒ为开发平台设计了ＳＴＭ３２Ｆ４０５核心板主控，外设电路设计主要包括：ＩＣＭ２０９４８传感器电路、ＣＡＮ通信差分电路等。
使用Ｓｉｍｕｌｉｎｋ对算法进行仿真验证，云台控制算法使用了串级ＰＩＤ控制，底盘通过ＨＩ２２０陀螺仪传感器结合模糊控制算法实现平衡及运动。
最终制作出了实体机器人并对模糊控制算法进行了验证，与传统ＰＩＤ算法相比，基于模糊控制的平衡机器人在响应速度、鲁棒性、稳定性等方面均有一定的提升。
相比于传统四轮机器人，制作的平衡机器人能够更好地通过狭小的空间，对环境的适应性更强。
关键词：模糊控制；视觉识别；全位移；平衡机器人中图分类号：ＴＰ２４２．６ 文献标志码：Ａ 文章编号：１０００－８８２９（２０２３）０７－０１０２－０８ｄｏｉ：１０．１９７０８／ｊ．ｃｋｊｓ．２０２２．０８．２９８ＤｅｓｉｇｎｏｆＦｕｌｌＤｉｓｐｌａｃｅｍｅｎｔＢａｌａｎｃｉｎｇＲｏｂｏｔＢａｓｅｄｏｎＦｕｚｚｙＣｏｎｔｒｏｌＬＩＵＨｅｎｇ牞ＬＩＺｈｅ 牞ＹＡＮＧＭｉｎｇｈｕｉ牞ＤＥＮＧＸｉａｏｇａｎｇ牞ＣＡＯＹｕｐｉｎｇ牗ＣｏｌｌｅｇｅｏｆＣｏｎｔｒｏｌＳｃｉｅｎｃｅａｎｄＥｎｇｉｎｅｅｒｉｎｇ牞ＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＰｅｔｒｏｌｅｕｍ牗ＥａｓｔＣｈｉｎａ牘牞Ｑｉｎｇｄａｏ２６６５８０牞Ｃｈｉｎａ牘Ａｂｓｔｒａｃｔ牶Ａｆｏｕｒ ｗｈｅｅｌｆｕｌｌｄｉｓｐｌａｃｅｍｅｎｔｂａｌａｎｃｉｎｇｒｏｂｏｔｗｉｔｈｆｕｚｚｙｃｏｎｔｒｏｌｉｓｄｅｓｉｇｎｅｄ．ＴｈｒｏｕｇｈＳｏｌｉｄＷｏｒｋｓ牞ｍｅｃｈａｎｉｃａｌｓｔｒｕｃｔｕｒｅｓｓｕｃｈａｓｆｕｌｌｄｉｓｐｌａｃｅｍｅｎｔｂａｌａｎｃｉｎｇｃｈａｓｓｉｓａｎｄｂｉａｘｉａｌｈｅａｄａｒｅｄｅｓｉｇｎｅｄｂａｓｅｄｏｎＭｃ Ｎａｍｗｈｅｅｌ．ＳＴＭ３２Ｆ４０５ｃｏｒｅｂｏａｒｄｍａｉｎｃｏｎｔｒｏｌｉｓｄｅｓｉｇｎｅｄｗｉｔｈＡｌｔｉｕｍＤｅｓｉｇｎｅｒａｓｔｈｅｄｅｖｅｌｏｐｍｅｎｔｐｌａｔ ｆｏｒｍ牞ａｎｄｔｈｅｐｅｒｉｐｈｅｒａｌｃｉｒｃｕｉｔｄｅｓｉｇｎｍａｉｎｌｙｉｎｃｌｕｄｅｓ牶ＩＣＭ２０９４８ｓｅｎｓｏｒｃｉｒｃｕｉｔ牞ＣＡＮｃｏｍｍｕｎｉｃａｔｉｏｎｄｉｆｆｅｒ ｅｎｔｉａｌｃｉｒｃｕｉｔ牞ｅｔｃ．Ｓｉｍｕｌｉｎｋｉｓｕｓｅｄｔｏｓｉｍｕｌａｔｅａｎｄｖｅｒｉｆｙｔｈｅａｌｇｏｒｉｔｈｍ牞ｔｈｅｇｉｍｂａｌｃｏｎｔｒｏｌａｌｇｏｒｉｔｈｍｕｓｅｓｃａｓ ｃａｄｅＰＩＤｃｏｎｔｒｏｌ牞ａｎｄｔｈｅｃｈａｓｓｉｓｉｓｂａｌａｎｃｅｄａｎｄｋｉｎｅｍａｔｉｃｂｙｕｓｉｎｇｔｈｅＨＩ２２０ｇｙｒｏｓｃｏｐｅｓｅｎｓｏｒｃｏｍｂｉｎｅｄｗｉｔｈｆｕｚｚｙｃｏｎｔｒｏｌａｌｇｏｒｉｔｈｍ．Ｆｉｎａｌｌｙ牞ａｓｏｌｉｄｒｏｂｏｔｉｓｐｒｏｄｕｃｅｄａｎｄｔｈｅｆｕｚｚｙｃｏｎｔｒｏｌａｌｇｏｒｉｔｈｍｉｓｖｅｒｉｆｉｅｄ．Ｃｏｍ ｐａｒｅｄｗｉｔｈｔｈｅｔｒａｄｉｔｉｏｎａｌＰＩＤａｌｇｏｒｉｔｈｍ牞ｔｈｅｂａｌａｎｃｅｄｒｏｂｏｔｈａｓｃｅｒｔａｉｎｉｍｐｒｏｖｅｍｅｎｔｉｎｒｅｓｐｏｎｓｅｓｐｅｅｄ牞ｒｏｂｕｓｔ ｎｅｓｓａｎｄｓｔａｂｉｌｉｔｙ．Ｃｏｍｐａｒｅｄｗｉｔｈｔｈｅｔｒａｄｉｔｉｏｎａｌｆｏｕｒ ｗｈｅｅｌｒｏｂｏｔ牞ｔｈｅｂａｌａｎｃｉｎｇｒｏｂｏｔｃａｎｂｅｔｔｅｒｐａｓｓｔｈｒｏｕｇｈｔｈｅｓｍａｌｌｓｐａｃｅａｎｄｈａｓｓｔｒｏｎｇｅｒａｄａｐｔａｂｉｌｉｔｙｔｏｔｈｅｅｎｖｉｒｏｎｍｅｎｔ．Ｋｅｙｗｏｒｄｓ牶ｆｕｚｚｙｃｏｎｔｒｏｌ牷ｖｉｓｕａｌｒｅｃｏｇｎｉｔｉｏｎ牷ｆｕｌｌｄｉｓｐｌａｃｅｍｅｎｔ牷ｂａｌａｎｃｅｄｒｏｂｏｔ随着世界经济和科技的高速发展以及人口数量的不断增多，人类对于各类资源的需求与日俱增，促使各国纷纷开始对未知风险的领域与地区进行资源的勘探与开发。
水轮机调速器的模糊B 样条基函数神经网络控制
【82】第３１卷第６期２００９－０６水轮机调速器的模糊Ｂ样条基函数神经网络控制A hydraulic turbine speed governor using fuzzy B-spline function neural networks controller何 江ＨＥ Ｊｉａｎｇ（长沙市产商品质量监督检验所，长沙 ４１００１３）摘 要：水轮机调速器是控制水轮机输出机械功率的关键设备，是水轮发电机组控制的重要内容。
针对非线性复杂时变的水轮机调速器，本文研究了一种模糊Ｂ样条基函数神经网络控制器。
该智能控制器是一种模糊逻辑与神经网络控制器的结合，集中了二者的优点和长处。
文章分析了该控制器的结构、具体实现以及学习优化。
仿真实验表明该智能控制器的实际效果良好。
关键词：水轮机调速器；非线性控制；模糊逻辑；智能控制中图分类号：ＴＰ２７３ 文献标识码：Ｂ 文章编号：１００９－０１３４（２００９）０６－００８２－０４收稿日期：２００９－０２－２４作者简介：何江（１９７７－），男，湖南长沙人，工程师，主要从事检测技术与标准化工作。
０ 引言水轮机调节系统是一个集水力、机械、电气为一体的复杂控制对象，其基本任务是根据系统负荷的不断变化来调节水轮发电机的有功功率输出，并保持机组频率的稳定［１￣３］。
由于水流惯性带来的水锤效应，水、机、电各环节的非线性和大惯性特点，还有参数变化、负荷扰动等的影响，使得水轮发电机的调节较为复杂［４］。
近年来，模糊神经网络技术将模糊技术和神经网络技术很好地融合在一起，采用神经网络来进行模糊信息处理，使神经网络具备了定性知识的表达能力，其网络的拓扑结构和连接权值具有了明确的物理意义，使得网络的初始化变得容易，避免了网络训练陷入局部最优，保证了网络的稳定性［５，６］。
本文研究提出了一种基于模糊Ｂ样条基神经网络的水轮机调速器控制方法，该方法在充分利用了模糊神经网络构造简便、容错性好、定性知识表达能力和自学习能力强的基础上，还综合了Ｂ样条基函数优异的局部特性，进一步提高了控制器的性能。
控制专业方向介绍,英文
Application of fuzzy control in the temperature and humiditycontrol of artificial climate boxFuzzy control is a control method which based on fuzzy sets theory and it is formed by the combined of fuzzy sets theory, fuzzy technology and automatic control technology. From birth of fuzzy control, there are lots of explorative and creative research and application achievements have been obtained. Now fuzzy control idea has been a widely used method to solve problems.Although fuzzy control has been widely used in engineering applications, there are still many practical problems which have not been resolved, including the ways to access the rules of fuzzy control, how to find the parameters , fuzzy control problems in a various multivariable coupling system and the way to promote the steady-state accuracy of fuzzy control , and so on. If we want a promotion of fuzzy control,the first step is to resolve these problem.To expand the scope where the application of fuzzy control is suitable, and solve the practice control problems in a new fuzzy control methods. There are several key issues in the application.The way to access rules and optimize parameter in fuzzy control.combining with fuzzy control, simulated annealing and genetic algorithms, Aimed at this problem, a new genetic algorithm, fuzzy adaptive simulated annealing genetic algorithm, which is used to optimize parameters in fuzzy controll, is presented. and its convergence, convergence speed and the prevention of "premature" phenomenon of this new genetic algorithm are analyzed.the problems when fuzzy control solutions are used in a multivariable coupling system.We can find a fuzzy compensation to decouple, and its decoupling ability is studied. We can optimize the rules and parameters of fuzzy compensation decoupling by a genetic algorithm.The steady-state accuracy of fuzzy control is not accurate enough.For a cyclical movevment objects fuzzy-iterative learning hybrid control method is presented combined with fuzzy control method and iterative learning control method; And for a servo objects, a grey prediction fuzzy compensation controlmethod is presented combined with fuzzy control method and grey prediction control method.Artificial climate box is a laboratory equipment to simulate the natural environment such as temperature, humidity and illumination, to create local artificial climate .It can not only provide users with an ideal artificial climate experiment environment, can be used to plant germination, seedling, tissue cells, microbial cultivation, wood, textile, building materials and electronic product performance and aging experiment, the storage of chemicals and experiment and so on, also can be used for breeding of insects and small animals, water analysis of the artificial climate experiment of determining BOD, and other purposes.So the artificial climate box has been widely applied in the biological, medical, agriculture, food, material, chemical and other industries .Artificial climate box usually need to control the casing temperature, humidity and light.The light can be shined by special fluorescent lamp lighting, according to the level of control can use the switch control, implementation is simpler, and the temperature and humidity control due to the particularity of object itself has, control is more complicated, its control method need additional research.The core issue of artificial climate box is the way to control temperature and humidity accuracy and response speed, etc.We can know that when the temperature is low and heating, water for cooling and dehumidification climate crate before condensation of water will increase the internal moisture ;When the temperature is high and refrigeration would have fallen after the air humidity of refrigerator and make the humidity drop, similarly, when humidity is low and humidifying, external cold or hot and will change the internal temperature, moisture and humidity high moisture will inevitably led to the decrease of the temperature.So the temperature and humidity control is strong catenated. And different specifications of the coupling of temperature and humidity of the degree is different.And sometimes climate box need a cycle control for temperature and humidity, they have two periods that the temperature and humidity is different, and climate box, the mathematical model of temperature and humidity control and shows that they have larger delay hysteresis characteristics, to achieve fast rise, short transition time, small overshoot and the purpose of general control method is very difficult to work.As mentioned earlier, there must be a strong catenated phenomenonthe betweentemperature control and humidity control, the independent use of temperature and humidity control method of fuzzy control or others without considering their catenated phenomenon, the effect of control is bad, even can cause the phenomenon of oscillation.Due to temperature and humidity control influence each other, they again it is difficult to establish the mathematical model, and different types of artificial climate box and its catenated relationship is different, so the general solution method was less effective, here we use a simple and effective method, which adopts the method of fuzzy reasoning, according to the result of the fuzzy control output, and then to draw a decoupled to compensate the output of fuzzy reasoning, solution in front of the disaster to compensate the output and the fuzzy synthetic later for the actual output control output.So we can use the fuzzy adaptive simulated annealing genetic algorithm (FASAGA) to optimize the parameters and rules of fuzzy control.Fuzzy adaptive simulated annealing genetic algorithm (FASAGA) is a kind of improved genetic algorithm, it combines the fuzzy control, the simulated annealing algorithm and genetic algorithm.In the combination of simulated annealing mechanism and genetic algorithm, we can combine the simulated annealing mechanism to the crossover operator of genetic algorithm and the genetic operators, rather than individual simulated annealing treatment, so we can not only improved the genetic operators, also we can retain the population genetic algorithm and the characteristics of the new produce flexible, and increase the "climbing" ability of the simulated annealing algorithm.So we can combine simulated annealing algorithm and genetic algorithm in this way.。
Robust Control
Robust ControlRobust control is a branch of control theory that deals with the design of control systems that can operate effectively in the presence of uncertainties and disturbances. These uncertainties can arise from various sources, such as modeling errors, parameter variations, and external disturbances. The goal of robust control is to ensure that the system remains stable and performs satisfactorily despite these uncertainties.One of the key challenges in robust control is to design controllers that can handle uncertainties without sacrificing performance. This requires a careful balance between robustness and performance. On the one hand, a controller that is too robust may be overly conservative and result in poor performance. On the other hand, a controller that is too aggressive may be sensitive to uncertainties and result in instability or poor performance.To address this challenge, various techniques have been developed for robust control. These include H-infinity control, mu-synthesis, and robust model predictive control. These techniques differ in their approach and assumptions, but they all aim to achieve robustness while maintaining performance.H-infinity control is a popular technique for robust control that is based on the concept of optimal control. The goal of H-infinity control is to minimize the worst-case performance of the system subject to certain constraints. This approach is particularly useful when the uncertainties are bounded and can be modeled as a norm-bounded perturbation.Mu-synthesis is another technique for robust control that is based on the concept of structured uncertainty. The idea behind mu-synthesis is to design a controller that is robust to uncertainties that have a known structure. This approach is particularly useful when the uncertainties are not bounded and cannot be modeled as a norm-bounded perturbation.Robust model predictive control is a relatively new technique for robust control that is based on the concept of predictive control. The idea behind robust model predictive control is to design a controller that can handle uncertainties in the future by optimizing a sequence of control actions over a finite time horizon. This approach is particularly useful when the uncertainties are time-varying and cannot be modeled as a fixed perturbation.In addition to these techniques, there are also various tools and software packages available for robust control design. These include MATLAB, Simulink, and Robust Control Toolbox. These tools can be used to simulate and analyze the performance of robust control systems under various scenarios and uncertainties.In conclusion, robust control is an important area of control theory that deals with the design of control systems that can operate effectively in the presence of uncertainties and disturbances. This requires a careful balance between robustness and performance, which can be achieved through various techniques and tools. By incorporating robust control into the design of control systems, we can ensure that these systems remain stable and perform satisfactorily under a wide range of conditions.。
Fuzzy control system
Fuzzy control definition
Fuzzy control provides a formal methodology for representing, manipulating, and implementing a human’s heuristic knowledge about how to control a system.
Expertise method Observatio nal method Based on fuzzy model Self organic method
Fuzzification
Fuzzification This is the process that transform the crisp value to the crisp value.
Fuzzy set
xS
μ : X 0, 1
μ : X 0 , 1
Fuzzy control definition
Fuzzy set
0 xa A ( x) m a bx b m 0
0 xa b a 1 d x d c 0
• If temperature is hot, then air motor speed is blast. • If temperature is warm, then air motor speed is fast. • If temperature is cool, then air motor speed is slow. • If temperature is cold, then air motor speed is stop.
Advantages of FLC(Fuzzy Logic controller): (1) Parallel or distributed control multiple fuzzy rulescomplex nonlinear system. (2) Linguistic control. Linguistic terms-human knowledge. (3) Robust control. More than 1 control rules- a error of a rule is not fatal.
H-无穷 控制
Robust Adaptive Neural Control for a Class of Perturbed Strict Feedback Nonlinear Systems
Step i:
Robust Adaptive Neural Control for a Class of Perturbed Strict Feedback Nonlinear Systems
H-infinity control question: Designing a desired controller so that the closed-loop system is stability and the transfer matrix can be minimized
Fundamental knowledge
The practical control law:
H-infinity tracking design in indirect adaptive fuzzy control
Finally, we have
H-infinity tracking design in indirect adaptive fuzzy control
Robust Adaptive Neural Control for a Class of Perturbed Strict Feedback Nonlinear Systems
Step n:
THE END
Q&A
23
Backstepping design: step 1:
Robust Adaptive Neural Control for a Class of Perturbed Strict Feedback Nonlinear Systems
主控方案的英文
Main Control SchemeIntroductionThe main control scheme is a crucial component in various systems and devices that require centralized control and coordination. It serves as the central processing unit, coordinating and managing the functions of different components and subsystems. This document aims to provide an overview of the main control scheme, its importance, and its implementation in various applications.Importance of the Main Control SchemeThe main control scheme plays a pivotal role in ensuring the proper functioning of complex systems. It acts as the brain of the system, providing instructions and managing the flow of data and signals. Through efficient control algorithms and protocols, it facilitates seamless communication between different components, ensuring optimal performance and reliability.Key Components of the Main Control SchemeThe main control scheme comprises several key components that work together to achieve the desired control and coordination:1. Central Processing Unit (CPU)The CPU is the core component of the main control scheme. It executes program instructions, performs arithmetic and logical operations, and manages the flow of data between different components. Modern control schemes often utilize powerful CPUs capable of handling complex algorithms and processing large amounts of data in real-time.2. Input/Output (I/O) ModulesI/O modules serve as the interface between the main control scheme and external devices or subsystems. They facilitate the transfer of data, signals, and instructions between the main control scheme and various sensors, actuators, displays, and other peripherals. These modules convert analog or digital signals intoa format compatible with the CPU, allowing seamless communication and control.3. Communication ProtocolsCommunication protocols enable the main control scheme to exchange information with external devices or subsystems. These protocols define the rules and procedures for data transmission, error detection and correction, and synchronization. Common communication protocols include Ethernet, CAN(Controller Area Network), Modbus, and RS-485. The choice of protocol depends on the specific application requirements and the type of devices being controlled.4. Control AlgorithmsControl algorithms determine the behavior of the main control scheme and its interaction with the controlled system. These algorithms utilize input data and predefined rules to calculate the desired output values and generate control signals. Different algorithms, such as proportional-integral-derivative (PID) control, fuzzy logic control, or model predictive control, may be employed based on the complexity of the system and the control objectives.5. User InterfaceThe main control scheme often includes a user interface that allows operators or users to interact with the system. This interface may be a physical panel with buttons, switches, and displays, or it may be a graphical user interface (GUI) displayed on a computer screen. The user interface provides a means for monitoring system status, configuring parameters, and initiating control actions.Implementation in Various ApplicationsThe main control scheme finds applications in a wide range of industries and sectors, including:1. Industrial AutomationIn industrial automation systems, the main control scheme is used to manage and coordinate the operation of machines, production lines, and entire manufacturing plants. It ensures precise control over various processes, such as temperature, pressure, speed, and position, resulting in improved efficiency, productivity, and quality.2. Aerospace and DefenseIn aerospace and defense systems, the main control scheme is responsible for controlling critical functions, such as flight control, navigation, weapon systems, and communication. It ensures the safe and reliable operation of aircraft, spacecraft, missiles, and other defense systems.3. Energy ManagementIn energy management systems, the main control scheme coordinates the operation of power generation, transmission, and distribution facilities. It optimizes the generation mix, balances supply and demand, and monitors the performance of energy assets, contributing to efficient and sustainable energy production and consumption.4. Autonomous VehiclesIn autonomous vehicles, such as self-driving cars or drones, the main control scheme enables real-time decision-making, obstacle avoidance, and navigation. It integrates sensor data, processes information, and generates control signals to ensure safe and efficient movement.ConclusionThe main control scheme is an essential component in various systems, providing centralized control and coordination. It ensures optimal performance, reliability, and user-friendliness in a wide range of applications. By utilizing advanced hardware, efficient algorithms, and robust communication protocols, the main control scheme enables seamless interaction between different components, resulting in enhanced system performance and overall functionality.。
数学英文论文
070451 Controlling chaos based on an adaptive nonlinear compensatingmechanism*Corresponding author,Xu Shu ,email:123456789@Abstract The control problems of chaotic systems are investigated in the presence of parametric u ncertainty and persistent external distu rbances based on nonlinear control theory. B y designing a nonlinear compensating mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subject to parametric variations and external disturbances is studied as an illustrative example. From Lyapu nov stability theory, sufficient conditions for the choice of control parameters are derived to guarantee chaos control. Several groups of experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to stead y states but also to any desired periodic orbits with great immunity to parametric variations and external distu rbances.Keywords: chaotic system, nonlinear compensating mechanism, Lorenz chaotic systemPACC: 05451. IntroductionChaotic motion, as the peculiar behavior in deterministic systems, may be undesirable in many cases, so suppressing such a phenomenon has been intensively studied in recent years. Generally speaking chaos suppression and chaos synchronization[1-4 ]are two active research fields in chaos control and are both crucial in application of chaos. In the following letters we only deal with the problem of chaos suppression and will not discuss the chaos synchronization problem.Since the early 1990s, the small time-dependent parameter perturbation was introduced by Ott,Grebogi, and Y orke to eliminate chaos,[5]many effective control methods have been reported in various scientific literatures.[1-4,6-36,38-44,46] There are two lines in these methods. One is to introduce parameter perturbations to an accessible system parameter, [5-6,8-13] the other is to introduce an additive external force to the original uncontrolled chaotic system. [14-37,39-43,47] Along the first line, when system parameters are not accessible or can not be changed easily, or the environment perturbations are not avoided, these methods fail. Recently, using additive external force to achieve chaos suppression purpose is in the ascendant. Referring to the second line of the approaches, various techniques and methods have been proposed to achieve chaos elimination, to mention only a few:(ⅰ) linear state feedback controlIn Ref.[14] a conventional feedback controller was designed to drive the chaotic Duffing equation to one of its inherent multiperiodic orbits.Recently a linear feedback control law based upon the Lyapunov–Krasovskii (LK) method was developed for the suppression of chaotic oscillations.[15]A linear state feedback controller was designed to solve the chaos control problem of a class of new chaotic system in Ref.[16].(ⅱ) structure variation control [12-16]Since Y u X proposed structure variation method for controlling chaos of Lorenz system,[17]some improved sliding-mode control strategies were*Project supported by the National Natural Science Foundation of C hina (Grant No 50376029). †Corresponding au thor. E-mail:zibotll@introduced in chaos control. In Ref.[18] the author used a newly developed sliding mode controller with a time-varying manifold dynamic to compensate the external excitation in chaotic systems. In Ref.[19] the design schemes of integration fuzzy sliding-mode control were addressed, in which the reaching law was proposed by a set of linguistic rules. A radial basis function sliding mode controller was introduced in Ref.[20] for chaos control.(ⅲ) nonlinear geometric controlNonlinear geometric control theory was introduced for chaos control in Ref.[22], in which a Lorenz system model slightly different from the original Lorenz system was studied considering only the Prandtl number variation and process noise. In Ref.[23] the state space exact linearization method was also used to stabilize the equilibrium of the Lorenz system with a controllable Rayleigh number. (ⅳ)intelligence control[24-27 ]An intelligent control method based on RBF neural network was proposed for chaos control in Ref.[24]. Liu H, Liu D and Ren H P suggested in Ref.[25] to use Least-Square Support V ector Machines to drive the chaotic system to desirable points. A switching static output-feedback fuzzy-model-based controller was studied in Ref.[27], which was capable of handling chaos.Other methods are also attentively studied such as entrainment and migration control, impulsive control method, optimal control method, stochastic control method, robust control method, adaptive control method, backstepping design method and so on. A detailed survey of recent publications on control of chaos can be referenced in Refs.[28-34] and the references therein.Among most of the existing control strategies, it is considered essentially to know the model parameters for the derivation of a controller and the control goal is often to stabilize the embedded unstable period orbits of chaotic systems or to control the system to its equilibrium points. In case of controlling the system to its equilibrium point, one general approach is to linearize the system in the given equilibrium point, then design a controller with local stability, which limits the use of the control scheme. Based on Machine Learning methods, such as neural network method[24]or support vector machine method,[25]the control performance often depends largely on the training samples, and sometimes better generalization capability can not be guaranteed.Chaos, as the special phenomenon of deterministic nonlinear system, nonlinearity is the essence. So if a nonlinear real-time compensator can eliminate the effect of the system nonlinearities, chaotic motion is expected to be suppressed. Consequently the chaotic system can be controlled to a desired state. Under the guidance of nonlinear control theory, the objective of this paper is to design a control system to drive the chaotic systems not only to steady states but also to periodic trajectories. In the next section the controller architecture is introduced. In section 3, a Lorenz system considering parametric uncertainties and external disturbances is studied as an illustrative example. Two control schemes are designed for the studied chaotic system. By constructing appropriate L yapunov functions, after rigorous analysis from L yapunov stability theory sufficient conditions for the choice of control parameters are deduced for each scheme. Then in section 4 we present the numerical simulation results to illustrate the effectiveness of the design techniques. Finally some conclusions are provided to close the text.2. Controller architectureSystem differential equation is only an approximate description of the actual plant due to various uncertainties and disturbances. Without loss of generality let us consider a nonlinear continuous dynamic system, which appears strange attractors under certain parameter conditions. With the relative degree r n(n is the dimension of the system), it can be directly described or transformed to the following normal form:121(,,)((,,)1)(,,,)(,,)r r r z z z z za z v wb z v u u d z v u u vc z v θθθθθθθθ-=⎧⎪⎪⎪=⎪=+∆+⎨⎪ ++∆-+⎪⎪ =+∆+⎪=+∆⎩ (1) 1y z =where θ is the parameter vector, θ∆ denotes parameter uncertainty, and w stands for the external disturbance, such that w M ≤with Mbeingpositive.In Eq.(1)1(,,)T r z z z = can be called external state variable vector,1(,,)T r n v v v += called internal state variable vector. As we can see from Eq.(1)(,,,,)(,,)((,,)1)d z v w u a z v w b z v uθθθθθθ+∆=+∆+ ++∆- (2)includes system nonlinearities, uncertainties, external disturbances and so on.According to the chaotic system (1), the following assumptions are introduced in order to establish the results concerned to the controller design (see more details in Ref.[38]).Assumption 1 The relative degree r of the chaotic system is finite and known.Assumption 2 The output variable y and its time derivatives i y up to order 1r -are measurable. Assumption 3 The zero dynamics of the systemis asymptotically stable, i.e.,(0,,)v c v θθ=+∆ is asymptotically stable.Assumption 4 The sign of function(,,)b z v θθ+∆is known such that it is always positive or negative.Since maybe not all the state vector is measurable, also (,,)a z v θθ+∆and (,,)b z v θθ+∆are not known, a controller with integral action is introduced to compensate theinfluenceof (,,,,)d z v w u θθ+∆. Namely,01121ˆr r u h z h z h z d------ (3) where110121112100ˆr i i i r r r r i i ii r i i d k z k k k z kz k uξξξ-+=----++-==⎧=+⎪⎪⎨⎪=----⎪⎩∑∑∑ (4)ˆdis the estimation to (,,,,)d z v w u θθ+∆. The controller parameters include ,0,,1i h i r =- and ,0,,1i k i r =- . Here011[,,,]Tr H h h h -= is Hurwitz vector, such that alleigenvalues of the polynomial121210()rr r P s s h sh s h s h --=+++++ (5)have negative real parts. The suitable positive constants ,0,,1i h i r =- can be chosen according to the expected dynamic characteristic. In most cases they are determined according to different designed requirements.Define 1((,,))r k sign b z v θμ-=, here μstands for a suitable positive constant, and the other parameters ,0,,2i k i r =- can be selected arbitrarily. After011[,,,]Tr H h h h -= is decided, we can tune ,0,,1i k i r =- toachievesatisfyingstaticperformances.Remark 1 In this section, we consider a n-dimensional nonlinear continuous dynamic system with strange attractors. By proper coordinate transformation, it can be represented to a normal form. Then a control system with a nonlinear compensator can be designed easily. In particular, the control parameters can be divided into two parts, which correspond to the dynamic characteristic and the static performance respectively (The theoretic analysis and more details about the controller can be referenced to Ref.[38]).3. Illustrative example-the Lorenz systemThe Lorenz system captures many of the features of chaotic dynamics, and many control methods have been tested on it.[17,20,22-23,27,30,32-35,42] However most of the existing methods is model-based and has not considered the influence ofpersistent external disturbances.The uncontrolled original Lorenz system can be described by112121132231233()()()()x P P x P P x w x R R x x x x w xx x b b x w =-+∆++∆+⎧⎪=+∆--+⎨⎪=-+∆+⎩ (6) where P and R are related to the Prendtl number and Rayleigh number respectively, and b is a geometric factor. P ∆, R ∆and b ∆denote the parametric variations respectively. The state variables, 1x ,2x and 3x represent measures of fluid velocity and the spatial temperature distribution in the fluid layer under gravity ， and ,1,2,3i w i =represent external disturbance. In Lorenz system the desired response state variable is 1x . It is desired that 1x is regulated to 1r x , where 1r x is a given constant. In this section we consider two control schemes for system (6).3.1 Control schemes for Lorenz chaotic system3.1.1 Control scheme 1The control is acting at the right-side of the firstequation (1x), thus the controlled Lorenz system without disturbance can be depicted as1122113231231x Px Px u xRx x x x x x x bx y x =-++⎧⎪=--⎨⎪=-⎩= (7) By simple computation we know system (7) has relative degree 1 (i.e., the lowest ordertime-derivative of the output y which is directly related to the control u is 1), and can be rewritten as1122113231231z Pz Pv u vRz z v v v z v bv y z =-++⎧⎪=--⎨⎪=-⎩= (8) According to section 2, the following control strategy is introduced:01ˆu h z d=-- (9) 0120010ˆ-d k z k k z k uξξξ⎧=+⎪⎨=--⎪⎩ (10) Theorem 1 Under Assumptions 1 toAssumptions 4 there exists a constant value *0μ>, such that if *μμ>, then the closed-loop system (8), (9) and (10) is asymptotically stable.Proof Define 12d Pz Pv =-+, Eq.(8) can be easily rewritten as1211323123z d u v Rz z v v vz v bv =+⎧⎪=--⎨⎪=-⎩ (11) Substituting Eq.(9) into Eq.(11) yields101211323123ˆz h z d dv R z z v v v z v bv ⎧=-+-⎪=--⎨⎪=-⎩ (12) Computing the time derivative of d and ˆdand considering Eq.(12) yields12011132ˆ()()dPz Pv P h z d d P Rz z v v =-+ =--+- +-- (13) 0120010000100ˆ-()()ˆ=()d k z k k z k u k d u k d k z k d d k dξξξ=+ =--++ =-- - = (14)Defining ˆdd d =- , we have 011320ˆ()()dd d P h P R z P z v P v P k d=- =+- --+ (15) Then, we can obtain the following closed-loop system101211323123011320()()z h z dvRz z v v v z v bv d Ph PR z Pz v Pv P k d⎧=-+⎪=--⎪⎨=-⎪⎪=+---+⎩ (16) To stabilize the closed-loop system (16), a L yapunovfunction is defined by21()2V ςς=(17)where, ςdenotes state vector ()123,,,Tz v v d, isthe Euclidean norm. i.e.,22221231()()2V z v v dς=+++ (18) We define the following compact domain, which is constituted by all the points internal to the superball with radius .(){}2222123123,,,2U z v v d zv v dM +++≤(19)By taking the time derivative of ()V ςand replacing the system expressions, we have11223322*********01213()()(1)V z z v v v v dd h z v bv k P d R z v P R P h z d P v d P z v d ς=+++ =----++ +++-- (20) For any ()123,,,z v v d U ∈, we have: 222201230120123()()(1)V h z v b v k P dR z v PR Ph z d P v d d ς≤----+ ++++ ++ (21)Namely,12300()(1)22020V z v v dPR Ph R h R P ς⎡⎤≤- ⎣⎦++ - 0 - - 1 - 2⨯00123(1)()2Tb PR Ph P k P z v v d ⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥0 ⎢⎥2⎢⎥++⎢⎥- - - +⎢⎥⎣22⎦⎡⎤⨯ ⎣⎦(22) So if the above symmetrical parameter matrix in Eq.(22) is positive definite, then V is negative and definite, which implies that system (16) is asymptotically stable based on L yapunov stability theory.By defining the principal minor determinants of symmetrical matrix in Eq.(22) as ,1,2,3,4i D i =, from the well-known Sylvester theorem it is straightforward to get the following inequations:100D h => (23)22004RD h =-> (24)23004R b D bh =-> (25)240302001()(1)(2)821[2(1)]08P M D k P D b PR Ph PR D Pb Ph R PR Ph =+-+++--+++>(26)After 0h is determined by solving Inequalities (23) to (25), undoubtedly, the Inequalities (26) can serve effectively as the constraints for the choice of 0k , i.e.20200031(1)(2)821[2(1)]8P M b PR Ph PR D Pb Ph R PR Ph k P D ++++ ++++>- (27)Here,20200*31(1)(2)821[2(1)]8P M b PR Ph PR D Pb Ph R PR Ph P D μ++++ ++++=-.Then the proof of the theorem 1 is completed. 3.1.2 Control scheme 2Adding the control signal on the secondequation (2x ), the system under control can be derived as112211323123x P x P x x R x x x x u xx x bx =-+⎧⎪=--+⎨⎪=-⎩ (28) From Eq.(28), for a target constant 11()r x t x =,then 1()0xt = , by solving the above differential equation, we get 21r r x x =. Moreover whent →∞,3r x converges to 12r x b . Since 1x and 2x havethe same equilibrium, then the measured state can also be chosen as 2x .To determine u , consider the coordinate transform:122133z x v x v x=⎧⎪=⎨⎪=⎩ and reformulate Eq.(28) into the following normal form:1223121231231zRv v v z u vPz Pv v z v bv y z =--+⎧⎪=-⎨⎪=-⎩= (29) thus the controller can be derived, which has the same expression as scheme 1.Theorem 2 Under Assumptions 1, 2, 3 and 4, there exists a constant value *0μ>, such that if *μμ>, then the closed-loop system (9), (10) and (29) is asymptotically stable.Proof In order to get compact analysis, Eq.(29) can be rewritten as12123123z d u v P z P v vz v bv =+⎧⎪=-⎨⎪=-⎩ (30) where 2231d Rv v v z =--Substituting Eq.(9) into Eq.(30),we obtain:1012123123ˆz h z d dv P z P v v z v bv ⎧=-+-⎪=-⎨⎪=-⎩ (31) Giving the following definition:ˆdd d =- (32) then we can get22323112123212301()()()()dRv v v v v z R Pz Pv Pz Pv v v z v bv h z d =--- =--- ----+ (33) 012001000ˆ-()d k z k k z k u k d u k dξξ=+ =--++ = (34) 121232123010ˆ()()()(1)dd d R Pz Pv Pz Pv v v z v bv h z k d=- =--- --+-+ (35)Thus the closed-loop system can be represented as the following compact form:1012123123121232123010()()()(1)zh z d v Pz Pv v z v bv d R Pz Pv Pz Pv v v z v bv h z k d⎧=-+⎪⎪=-⎪=-⎨⎪=---⎪⎪ --+-+⎩(36) The following quadratic L yapunov function is chosen:21()2V ςς=(37)where, ςdenotes state vector ()123,,,Tz v v d , is the Euclidean norm. i.e.,22221231()()2V z v v dς=+++ (38) We can also define the following compact domain, which is constituted by all the points internalto the super ball with radius .(){}2222123123,,,2U z v v d zv v dM =+++≤ (39)Differentiating V with respect to t and using Eq.(36) yields112233222201230011212322321312()(1)(1)()V z z v v v v dd h z P v bv k dP R h z d P z v z v v P b v v d P v d P z v d z v d ς=+++ =----+ +++++ ++--- (40)Similarly, for any ()123,,,z v v d U ∈, we have: 2222012300112133231()(1)(1)(2V h z P v b v k dPR h z d P z v v P b d P v d d M z dς≤----+ +++++ ++++ + (41)i.e.,12300()(12)22V z v v dPR M h P h P Pς⎡⎤≤- ⎣⎦+++ - -2 - 0 ⨯ 001230(12)(1)2TP b PR M h P k z v v d ⎡⎤⎢⎥⎢⎥⎢⎥ - ⎢⎥⎢⎥⎢⎥ ⎢⎥22⎢⎥⎢⎥ +++ - - -+⎢⎥⎣22⎦⎡⎤⨯ ⎣⎦(42) For brevity, Let1001(12)[(222)82(23)]P PR M h b PR P h M P b α=++++++ ++(43) 2201[(231)(13)]8P M P b b PR h α=+-+++ (44)230201(2)[2(12)8(2)(4)]PM P b P P PR M h P b Ph P α=++ +++ ++- (45)Based on Sylvester theorem the following inequations are obtained:100D h => (46)22004PD h P =-> (47)3202PMD bD =-> (48)403123(1)0D k D ααα=+---> (49)where,1,2,3,4i D i =are the principal minordeterminants of the symmetrical matrix in Eq.(42).*0k μ>*12331D αααμ++=- (50)The theorem 2 is then proved.Remark 2 In this section we give two control schemes for controlling chaos in Lorenz system. For each scheme the control depends on the observed variable only, and two control parameters are neededto be tuned, viz. 0h and 0k . According to L yapunov stability theory, after 0h is fixed, the sufficient condition for the choice of parameter 0k is also obtained.4. Simulation resultsChoosing 10P =,28R =, and 8/3b =, the uncontrolled Lorenz system exhibits chaotic behavior, as plotted in Fig.1. In simulation let the initial values of the state of thesystembe 123(0)10,(0)10,(0)10x x x ===.x1x 2x1x 3Fig.1. C haotic trajectories of Lorenz system (a) projected on12x x -plane, (b) projected on 13x x -plane4.1 Simulation results of control the trajectory to steady stateIn this section only the simulation results of control scheme 2 are depicted. The simulation results of control scheme 1 will be given in Appendix. For the first five seconds the control input is not active, at5t s =, control signal is input and the systemtrajectory is steered to set point2121(,,)(8.5,8.5,27.1)T Tr r r x x x b =, as can be seen inFig.2(a). The time history of the L yapunov function is illustrated in Fig.2(b).t/sx 1,x 2,x 3t/sL y a p u n o v f u n c t i o n VFig.2. (a) State responses under control, (b) Time history of the Lyapunov functionA. Simulation results in the presence ofparameters ’ changeAt 9t s =, system parameters are abruptly changed to 15P =,35R =, and 12/3b =. Accordingly the new equilibrium is changedto 2121(,,)(8.5,8.5,18.1)T Tr r r x x x b =. Obviously, aftervery short transient duration, system state converges to the new point, as shown in Fig.3(a). Fig.4(a) represents the evolution in time of the L yapunov function.B. Simulation results in the presence of set pointchangeAt 9t s =, the target is abruptly changedto 2121(,,)(12,12,54)T Tr r r x x x b =, then the responsesof the system state are shown in Fig.3(b). In Fig.4(b) the time history of the L yapunov function is expressed.t/sx 1,x 2,x 3t/sx 1,x 2,x 3Fig.3. State responses (a) in the presence of parameter variations, (b) in the presence of set point changet/sL y a p u n o v f u n c t i o n Vt/sL y a p u n o v f u n c t i o n VFig.4. Time history of the Lyapunov fu nction (a) in the presence of parameter variations, (b) in the presence of set point changeC. Simulation results in the presence ofdisturbanceIn Eq.(5)external periodic disturbance3cos(5),1,2,3i w t i π==is considered. The time responses of the system states are given in Fig.5. After control the steady-state phase plane trajectory describes a limit cycle, as shown in Fig.6.t/sx 1,x 2,x 3Fig.5. State responses in the presence of periodic disturbancex1x 3Fig.6. The state space trajectory at [10,12]t ∈in the presence ofperiodic disturbanceD. Simulation results in the presence of randomnoiseUnder the influence of random noise,112121132231233xPx Px x Rx x x x u xx x bx εδεδεδ=-++⎧⎪=--++⎨⎪=-+⎩ (51) where ,1,2,3i i δ= are normally distributed withmean value 0 and variance 0.5, and 5ε=. The results of the numerical simulation are depicted in Fig.7,which show that the steady responses are hardly affected by the perturbations.t/sx 1,x 2,x 3t/se 1,e 2,e 3Fig.7. Time responses in the presence of random noise (a) state responses, (b) state tracking error responses4.2 Simulation results of control the trajectory to periodic orbitIf the reference signal is periodic, then the system output will also track this signal. Figs.8(a) to (d) show time responses of 1()x t and the tracking trajectories for 3-Period and 4-period respectively.t/sx 1x1x 2t/sx 1x1x 2Fig.8. State responses and the tracking periodic orbits (a)&( b)3-period, (c)&(d) 4-periodRemark 3 The two controllers designed above solved the chaos control problems of Lorenz chaoticsystem, and the controller design method can also beextended to solve the chaos suppression problems of the whole Lorenz system family, namely the unified chaotic system.[44-46] The detail design process and close-loop system analysis can reference to the author ’s another paper.[47] In Ref.[47] according to different positions the scalar control input added,three controllers are designed to reject the chaotic behaviors of the unified chaotic system. Taking the first state 1x as the system output, by transforming system equation into the normal form firstly, the relative degree r (3r ≤) of the controlled systems i s known. Then we can design the controller with the expression as Eq.(3) and Eq.(4). Three effective adaptive nonlinear compensating mechanisms are derived to compensate the chaotic system nonlinearities and external disturbances. According toL yapunov stability theory sufficient conditions for the choice of control parameters are deduced so that designers can tune the design parameters in an explicit way to obtain the required closed loop behavior. By numeric simulation, it has been shown that the designed three controllers can successfully regulate the chaotic motion of the whole family of the system to a given point or make the output state to track a given bounded signal with great robustness.5. ConclusionsIn this letter we introduce a promising tool to design control system for chaotic system subject to persistent disturbances, whose entire dynamics is assumed unknown and the state variables are not completely measurable. By integral action the nonlinearities, including system structure nonlinearity, various disturbances, are compensated successfully. It can handle, therefore, a large class of chaotic systems, which satisfy four assumptions. Taking chaotic Lorenz system as an example, it has been shown that the designed control scheme is robust in the sense that the unmeasured states, parameter uncertainties and external disturbance effects are all compensated and chaos suppression is achieved. Some advantages of this control strategy can be summarized as follows: (1) It is not limited to stabilizing the embeddedperiodic orbits and can be any desired set points and multiperiodic orbits even when the desired trajectories are not located on the embedded orbits of the chaotic system.(2) The existence of parameter uncertainty andexternal disturbance are allowed. The controller can be designed according to the nominal system.(3) The dynamic characteristics of the controlledsystems are approximately linear and the transient responses can be regulated by the designer through controllerparameters ,0,,1i h i r =- .(4) From L yapunov stability theory sufficientconditions for the choice of control parameters can be derived easily.(5) The error converging speed is very fast evenwhen the initial state is far from the target one without waiting for the actual state to reach the neighborhood of the target state.AppendixSimulation results of control scheme 1.t/sx 1,x 2,x 3t/sL y a p u n o v f u n c t i o n VFig.A1. (a) State responses u nder control, (b) Time history of the Lyapunov functiont/sx 1,x 2,x 3t/sx 1,x 2,x 3Fig.A2. State responses (a) in the presence of parameter variations, (b) in the presence of set point changet/sL y a p u n o v f u n c t i o n Vt/sL y a p u n o v f u n c t i o n VFig.A3. Time history of the L yapu nov fu nction (a) in the presence of parameter variations, (b) in the presence of set point changet/sx 1,x 2,x 3Fig.A4. State responses in the presence of periodic disturbanceresponsest/sx 1,x 2,x 3Fig.A5. State responses in the presence of rand om noiset/sx 1x1x 2Fig.A6. State response and the tracking periodic orbits (4-period)References[1] Lü J H, Zhou T S, Zhang S C 2002 C haos Solitons Fractals 14 529[2] Yoshihiko Nagai, Hua X D, Lai Y C 2002 C haos Solitons Fractals 14 643[3] Li R H, Xu W , Li S 2007 C hin.phys.16 1591 [4]Xiao Y Z, Xu W 2007 C hin.phys.16 1597[5] Ott E ，Greb ogi C and Yorke J A 1990 Phys.Rev .Lett. 64 1196 [6]Yoshihiko Nagai, Hua X D, Lai Y C 1996 Phys.Rev.E 54 1190 [7] K.Pyragas, 1992 Phys. Lett. A 170 421 [8] Lima,R and Pettini,M 1990 Phys.Rev.A 41 726[9] Zhou Y F, Tse C K, Qiu S S and Chen J N 2005 C hin.phys. 14 0061[10] G .Cicog na, L.Fronzoni 1993 Phys.Rew .E 30 709 [11] Rakasekar,S. 1993 Pramana-J.Phys.41 295 [12] Gong L H 2005 Acta Phys.Sin.54 3502 (in C hinese) [13] Chen L,Wang D S 2007 Acta Phys.Sin.56 0091 (in C hinese) [14] C hen G R and Dong X N 1993 IEEE Trans.on Circuits andSystem-Ⅰ:Fundamental Theory and Applications 40 9 [15] J.L. Kuang, P.A. Meehan, A.Y.T. Leung 2006 C haos SolitonsFractals 27 1408[16] Li R H, Xu W, Li S 2006 Acta Phys.Sin.55 0598 (in C hinese) [17] Yu X 1996 Int.J.of Systems Science 27 355[18] Hsun-Heng Tsai, C hyu n-C hau Fuh and Chiang-Nan Chang2002 C haos,Solitons Fractals 14 627[19] Her-Terng Yau and C hieh-Li C hen 2006 C hao ,SolitonsFractal 30 709[20] Guo H J, Liu J H, 2004 Acta Phys.Sin.53 4080 (in C hinese) [21] Yu D C, Wu A G , Yang C P 2005 Chin.phys.14 0914 [22] C hyu n-C hau Fuh and Pi-Cheng Tu ng 1995 Phys.Rev .Lett.752952[23] Chen L Q, Liu Y Z 1998 Applied Math.Mech. 19 63[24] Liu D, R en H P, Kong Z Q 2003 Acta Phys.Sin.52 0531 (inChinese)[25] Liu H, Liu D and Ren H P 2005 Acta Phys.Sin.54 4019 (inChinese)[26] C hang W , Park JB, Joo YH, C hen GR 2002 Inform Sci 151227[27] Gao X, Liu X W 2007 Acta Phys.Sin. 56 0084 (in C hinese) [28] Chen S H, Liu J, Lu J 2002 C hin.phys.10 233 [29] Lu J H, Zhang S. 2001 Phys. Lett. A 286 145[30] Liu J, Chen S H, Xie J. 2003 C haos Solitons Fractals 15 643 [31] Wang J, Wang J, Li H Y 2005 C haos Solitons Fractals 251057[32] Wu X Q, Lu JA, C hi K. Tse, Wang J J, Liu J 2007 ChaoSolitons Fractals 31 631[33] A.L.Fradkov , R .J.Evans, 2002 Preprints of 15th IF AC W orldCongress on Automatic Control 143[34] Zhang H G 2003 C ontrol theory of chaotic systems (Shenyang:Northeastern University) P38 (in C hinese)[35] Yu-Chu Tian, Moses O.Tadé, David Levy 2002Phys.Lett.A.296 87[36] Jose A R , Gilberto E P, Hector P, 2003 Phys. Lett. A 316 196 [37] Liao X X, Yu P 2006 Chaos Solitons Fractals 29 91[38] Tornambe A, V aligi P.A 1994 Measurement, and C ontrol 116293[39] Andrew Y.T.Leung, Liu Z R 2004 Int.J.Bifurc.C haos 14 2955 [40] Qu Z L, Hu,G .,Yang,G J, Qin,G R 1995 Phys.Rev .Lett.74 1736 [41] Y ang J Z, Qu Z L, Hu G 1996 Phys.Rev.E.53 4402[42] Shyi-Kae Yang, C hieh-Li Chen, Her-Terng Yau 2002 C haosSolitons Fractals 13 767。
具有广泛不确定性的模糊系统的鲁棒控制英文
控制工程C ontrol Engi neering of China Sep 12008V ol .15,S 12008年9月第15卷增刊文章编号:167127848(2008)S 120066206 收稿日期22; 收修定稿日期22 作者简介L F (62),,D q ,j ,,,f zzy ;S B K (2),,2f 李凤江(62),男,黑龙江大庆人,工程师,主要研究方向为鲁棒控制、模糊控制等;苏宝库(2),男,教授。
Delay 2dependent R obust H ∞Contr ol of FuzzySystem w ith G eneral U ncer ta intyLI Feng 2jiang 1,G ONG Cheng 2,SU Bao 2ku 2,(1.3rd Oil 2extraction Plant ,Daqi ng Oil field Limited Liability C om pany ,Daqing 163453,Chi na ;2.S pace C ontrol and Inertial Technology Res earch C enter ,Harbi n Ins tit ute of Technol ogy ,Harbin 150001,China)Abstract :T he delay 2dependent robus t control problem of T 2S f u zzy time 2delay s ystem w ith a generalized class o f uncertainty is pres ented.Both n orm b ounded uncertainty and conv ex polyhedral un certainty are in 2cluded in the generalized un certainty.A delay 2dependen t stability condition is derived by Lyapun ov 2K ra 2sovskii functi onal meth od.Based on the s tability condition ,a delay 2dependen t robust H ∞con troller ,wh ich guaran tees n ot only th e robust asy mptotic s tability of the uncertain system ,but als o the prescribed H ∞atten 2uation level for all admiss ible un certainties.The numerical ex ample sh ows the effectiveness o f the prop osed method.K ey w or ds :robus t H ∞control ;delay 2dependent ;polyhedral uncertain ty;norm b ounded uncertainty;fuzzy sys temCLC number :T P 273 Document code :A具有广泛不确定性的模糊系统的鲁棒控制李凤江1,巩 诚2,苏宝库2(1.大庆油田有限责任公司采油三厂,黑龙江大庆 163453;2.哈尔滨工业大学空间控制与惯性技术研究中心,黑龙江哈尔滨 150001)摘 要:研究了一类具有广泛不确定性的T 2S 模糊时滞系统的时滞依靠鲁棒H ∞控制问题。
杭州电子科技大学2017年博士生导师介绍周绍生
杭州电子科技大学2017年博士生导师介绍周绍生一、导师照片周绍生二、基本信息周绍生Zhou Shaosheng教授所属学院：自动化学院导师类别：博士生导师、硕士生导师研究方向：控制理论与控制工程（非线性系统、随机系统、量子系统的分析与设计、多目标优化、信号处理等）博士招生学院：自动化学院硕士招生学院：自动化学院/理学院联系方式：sszhou65@三、个人简述周绍生，男，1965年9月出生，山东省济宁人，2002年4月于东南大学自动化研究所获得博士学位。
现任IEEE控制系统协会（CSS）CEB成员，澳大利亚研究理事会（ARC）外评专家。
2015年信息学部优青评审会专家。
国家杰出青年基金通信评议专家。
至今已在IEEE TFS,IEEE TNN,IEEE TAC.,Automatica,Systems&Control Letters,Information Sciences,Quantum Information Processing,Fuzzy Sets and Systems等系统与控制学术期刊上发表论文60余篇，50篇为SCI收录，SCI 论文引用次数累计达1000余次。
主持国家基金面上项目3项，参与（排名第二）国家基金重点项目1项。
2014年获浙江省自然科学一等奖（排名第二），2010年获山东省科学技术二等奖（排名第四）。
四、学术成果（一）代表性论文1.Control design for fuzzy systems based on relaxed nonquadratic stability and H∞performance conditions.《IEEE Transactions on Fuzzy Systems》2007年第2期，排名1/3，SCI一区。
2.Exponentialε-regulation for multi-input nonlinear systems using neural networks.《IEEE Transactions on Neural Networks》2005年第6期，排名1/4，SCI一区。
Maximum Power Point Tracking
Abstract--The power available at the output of photovoltaic cells keeps changing with solar insolation and ambient temperature because photovoltaic cells exhibit a nonlinear current-voltage characteristic. So photovoltaic cells’ maximum power point varies with solar insolation and ambient temperature. With the improved efficiencies of power electronics converters, it is now possible to operate photovoltaic power systems at its maximum power point (MPP) in order to improve the overall system efficiency. This paper presents a fuzzy control method for tracking maximum power point in photovoltaic power systems and the control system is established simultaneously. In this paper, simulation model of photovoltaic system’s maximum power point tracking based on the fuzzy control method is developed in the MATLAB software. The results of simulation show that the fuzzy control algorithm significantly improves the efficiency during the tracking phase as compared to a conventional algorithm about maximum power point tracking (MPPT) in photovoltaic power systems. It is especially suitable for fast changing environmental conditions. Furthermore, the proposed algorithm is simple and can be easily implemented with any fast micro processor such as a digital signal processor.Index Terms--Fuzzy control, maximum power point tracking (MPPT), photovoltaic power systems, simulation.I. I NTRODUCTIONITH the quick development of society, the rapid trendof industrialization of nations and increased interest inenvironmental issues has recently to consideration of the use of renewable forms such as solar energy and wind energy. Photovoltaic (PV) generation is becoming increasingly important as a renewable source since it offers many advantages such as incurring no fuel costs, not being polluting, requiring little maintenance, and emitting no noise, among others [1]. PV arrays produce electric power directly from sunlight. With the advent of silicon P-N junction during the 1950s, the photoelectric current was able to produce power due to the inherent voltage drop across the junction [2]. This gives the well-known nonlinear relationship between the current and voltage of the photovoltaic cell. From this nonlinear relationship of the photovoltaic cell, it can be observed that there is a unique point, under given illumination, at whi ch the cell produces maxi mum power, the so-called Jiyong Li is with the College of Electrical Engineering, Hohai University, Nanjing, 210098 China (e-mail: ji_yong_li@).Honghua Wang is with the College of Electrical Engineering, Hohai University, Nanjing, 210098 China (e-mail: wanghonghua@). maximum power point (MPP). This point occurs when the rate of change of the power with respect to the voltage is equal to zero [3]. T he output power of PV cell varies with depending mainly on the level of solar radiation and ambient temperature corresponding to a specific weather condition. The MPP will change with external environment of PV cell. An important consideration in achieving high efficiency in PV power generation system is to match the PV source and load impedance properly for any weather conditions, thus obtaining maximum power generation. The technique process of maximum power point is been tracking which is called maximum power point tracking (MPPT).In order to gain maximum power, MPPT is an essential part of a PV generation system. Because of the nonlinear voltage-current characteristics of PV cells, the power versus voltage (P–V) curve in solar cells has more complicated nonlinear relationship when solar illumination and ambient temperature change, so the MPP is difficult to solve analytically, and therefore numerous techniques have been proposed to realize MPPT. These MPPT methods vary in complexity, sensors required, convergence speed, cost, range of effectiveness, implementation hardware, popularity, and in other respects. Some methods applied in PV system are the constant voltage method, the perturb-and-observe (P&O or hill-climbing, because hill climbing and P&O methods are different ways to envision the same fundamental method.) method, the incremental conductance method, and so on.From the power versus voltage characteristic curve of PV cell, it can be observed that the MPP is in the neighborhood of a constant voltage when solar illumination is changing and temperature’s change is omitted. So the MPP’s voltage V m can be designed to be constant. This is the constant voltage tracking (CVT) method [4]. Although the CVT method is very simple, however, the constant voltage can’t track MPP when temperature changes, so the constant voltage method is not often used in the true MPPT strategy. From the characteristic curves of PV cell, it can be seen that incrementing (decrementi ng) the voltage i ncreases (decreases) the power when operating on the left of the MPP and decreases (increases) the power when on the right of the MPP. Therefore, i f there i s an i ncrease i n power, the subsequent perturbati on should be kept the same to reach the MPP and i f there i s a decrease i n power, the perturbati on should be reversed [5]. Small perturbations are introduced in the system in order to vary the operating point such that the MPP is achieved. However, this method has several drawbacks such as slow tracking speed and oscillations about MPP, making it less favorable for rapidly changing environmental conditions. AndMaximum Power Point Tracking of Photovoltaic Generation Based on the FuzzyControl MethodJiyong Li, and Honghua WangWthis method can appear fallacious tracking when there is a sudden change in irradiance. The incremental conductance (INC) method is based on the fact that the slope of the PV array power curve is zero at the MPP, positive on the left of the MPP, and negative on the right [5], as given bydP/dV=0, at MPP dP/dV>0, left of MPP dP/dV<0, right of MPP ⎧⎪⎨⎪⎩(1) By derivation, it can be gained the relationship between the instantaneous conductance (I/V ) and the incremental conductance (ΔI /ΔV ). The MPP can be tracked by comparingI /V to ΔI /ΔV. It can be supposed thatV ref equals to V MPP at the MPP. Once the MPP is reached, the operation of the PV array is maintained at this point unless a change in ΔI is noted. The algorithm decrements or increments V ref to track the new MPP when atmospheric conditions change. However, from derivation of the INC method, it can be seen that the INC method has no consideration about change of temperature.In fact, because changes i n the env ironment have uncertai nty, changes of load and output characteri sti c of PV cell have more nonl i near feature, so above convent ional tracking methods have more difficult to track real MPP.Fuzzy control has adaptive characteristic in nature, and can achieve robust response of a system with uncertainty, parameter variation and load disturbance. It has been broadly used to control ill-defined, nonlinear or imprecise system [6]. Fuzzy logic controllers have the advantages of working with imprecise inputs, not needing an accurate mathematical model, and handling nonlinearity. Fuzzy control has been successfully applied in many fields, such as industry controls. Fuzzy control does not require accurate models of control object. To overcome the limitation of the above conventional tracking methods, fuzzy control is applied to deal with MPPT of PV generation system in this paper. With this technique, not only can the real MPP be readily tracked but also fast dynamic responses can be achieved.II. C HARACTERISTIC OF P HOTOVOLTAIC C ELLPhotovolta c cells cons st of a s l co n P-N junction that when exposed to light releases electrons arou nd a closed electrical circuit. From this premise the circuit equivalent of a PV cell can be modeled through the circuit shown in Fig. 1. Electrons from the cell are exci ted to hi gher energy levels when a collision with a photon occurs. These electrons are free to move across the junct on and create a current. Th s s modeled by the l i ght generated current source (I ph ). The intrinsic P-N junction characteristic is introduced as a diode inthe circuit equivalent [7].Fig. 1. Photovoltaic cell equivalent circuitThe photo current I ph generated in the PV cell isproportional to level of solar illumination. I is the output current of photovoltaic cell. The current (I d ) through the bypass diode varies with the junction voltage V j and the cellreverse saturation current I 0. V is the output of the photovoltaiccell. R sh and R s are the parallel and series resistances, respectively. Parallel resistance R sh is very large while the series resistance R s is small. When the number of cell in series is n s , and the number of cell in parallel is n p . There are relevant mathematical equations expressing as following:(/)0/[1]s s q V n IR s snkTp ph p shV n IR I n I n I eR ++=−−−(2) ()()1000ph sc T ref SI I C T T =+− (3) Where 11[()]300(gref qE nkT Td refT I I eT −=, 191.602210q C −=× is theelectronic charge, n is the emission coefficient of diodes, 2311.380710JK k −−=× is Boltzmann’s constant, T is ambienttemperature in Kelvin, and ref Tis reference absolute temperature. sc Iis the short current, S is the level of solar illumination, g E is the energy of the band gap for silicon which is (1~3) eV, T C is the short-circuit-current temperaturecoefficient(=0.0016A/K), do I is the reverse current of diode. And From equation (2) and (3), it is known that the characteristic of PV will be changed when S and T change. Changes in these variables S and T cause the current-voltage (I-V ) curves of photovoltaic array to change as well. As illustrated in Fig. 2, where S symbolizes the solar illumination, S variation from 200W/m 2 to 1000W/m 2 is reported, and temperature T is constant 40℃. Besides the solar illumination, another important factor influencing the characteristics of a photovoltaic module is ambient temperature, as shown in Fig. 3, where the solar illumination is constant 1000W/m 2, and temperature T is changing from 20℃ to 100℃.Fig. 2. Simulate current versus voltage curves of PV array influenced bysolar illuminationFig. 3. Simulated current versus voltage curves of PV array influencedby temperatureThe output power of a PV array is the product of current I and terminal voltage V ; thus(/)20/[1]s s q V n IR s sp ph p shV n VIR P n VI n VI eR ++=−−− (4)From above equation, it can be known that the solar illumination and ambient temperature will influence the output power of a PV module. T he output power of a PV changes with the solar illumination’s variation when temperature is constant 40℃, as shown in Fig. 4, and the characteristic ofoutput power changes with the ambient temperature’s variation when the solar illumination is constant 1000W/m 2, asshown in Fig. 5.Fig. 4. Power versus voltage curves influence by the solar illuminationFig. 5. Power versus voltage curves influence by temperatureFrom Fig. 4 and Fig. 5, it can be seen that the output power of a PV module is influenced by the solar illumination and ambient temperature. So the MPP will be change whenperipheral condition is changed. Especially, the solar illumination and temperature changes at the same time, MPP is more difficult to search by above convent i onal track i ng methods. In order to quick and accurate track MPP under any weather conditions, a new technique for tracking MPP of photovoltaic (PV) generation based on fuzzy control method is proposed in this paper.III. A N EW MPPT M ETHOD W ITH F UZZY C ONTROL In recent years, fuzzy logic controllers have been widely used for industrial processes owing to their heuristic nature associated with simplicity and effectiveness for both linear and nonlinear systems [8]. A MPP search based on fuzzy heuristic rules, which does not need any parameter information, consists of a stepwise adaptive search, leads to fast convergence and is sensorless with respect to sunlight and temperature measurements [9]. The control objective is to track and extract maximum power from the PV arrays for a given solar insolation level. The maximum power corresponding to the optimum operating point is determined for a different solar insolation level and temperature.The fuzzy controller consists of three functional blocks: A) Fuzzification, B) Fuzzy rule algorithm and C) Defuzzification. These functions are described as follows:A. FuzzificationThe fuzzy control requires that variable used in describing the control rules has to be expressed in terms of fuzzy set notations with linguistic labels. In this paper, the fuzzy control MPPT method has two input variables, namely ΔP(k) and ΔU(k), at a sampling instant k. The output variable is ΔU(k+1), which is voltage’s increase of PV array at next sampling instant k+1. The variable ΔP(k) and ΔU(k) are expressed as follows:ΔP(k)=P(k)-P(k-1) (5) ΔU(k)=U(k)-U(k-1) (6)where P(k) and U(k) are the power and voltage of PV array, respectively. So, ΔP(k) and ΔU(k) are zero at the maximum power point of a PV array.In Fig. 6, the membership functions of the input variable ΔP(k) which is assigned five fuzzy sets, including positive big(PB), positive small (PS), zero (ZE), negative small (NS), andnegative big (NB). The membership functions are denser at the center in order to provide more sensitivity against variationFig. 6. The membership function of input ΔP(k)In Fig. 7, the membership functions of the input variable ΔU(k) which is assigned three fuzzy sets, including positive (P), zero (Z), and negative(N).Fig. 7. The membership function of input ΔU(k)Fig. 8 shows the membership functions of the output variable ΔU(k+1) which is assigned seven fuzzy sets, including positive big (PB), positive middle (PM), positive small (PS), zero (ZE), negative small (NS), negativemiddle(NM), and negative big (NB). Fig. 8. The membership function of input ΔU(k+1) B. Fuzzy rule algorithmThe rule base that associates the fuzzy output to the fuzzy inputs is derived by understanding the system behavior. In this paper, the fuzzy rules are designed to incorporate thefollowing considerations keeping in view the overall trackingperformance.1) If the last change in voltage ΔU(k) has caused the powerto rise, keep moving the next change in voltage ΔU(k+1)in the same direction by tuning duty ratio of converter toachieve, otherwise, if it has caused the power to drop,move it in the opposite direction.2) Owing to the fact that the characteristic curves might change with temperature and sunlight level, leading to anoverall shift of the optimum point.3) Because the optimum point tends to satisfy the conditionəP/əU =0, the system might recognize any large plateau as a maximum power region and stop. The some rules have been identified for avoiding the stabilizing effect in a region other than that of true peak power when power is zero. 4) It is necessary to provide the system with a rule thatstabilizes the point of operation at a peak power point. Taking the above points into consideration the fuzzy rules are derived and the corresponding rule base is given in Table I.TABLE IRAs a fuzzy i nference method, Mamdani ’s method i s used with max---min operation fuzzy combination law in this paper.To satisfy different conditions and gain better tracking performance, several possible combinations of the degree of supports are with varying strengths to the corresponding rules.Fig. 9. A three-dimensional view of the fuzzy surface for MPPT C. DefuzzificationAfter the rules have been evaluated, the last step to complete the fuzzy control algorithm is to calculate the crisp output of the fuzzy control with the process of defuzzification. The well-known center of gravity method for defuzzification is used in this paper. It computes the center of gravity from the final fuzzy space, and yields a result which is highly related to all of the elements in the same fuzzy set [10]. The crisp valueof control output ΔU(k+1) is computed by the followingequation: ni i=1ni i=1w U U=w i ΔΔ∑∑ (7)Where n is the maximum number of effective rules, w i isthe weighting factor, and ΔU i is the value corresponding to themembership function of ΔU. Then, the final control voltage isobtained by adding this change to the previous value of thecontrol voltage:U(k+1)=U(k) + ΔU(k+1) (8)Using the steps mentioned above, the fuzzy controller canbe implemented in real time for MPPT.IV. S IMULATION R ESULTSAs mentioned previously, since fuzzy control is with adaptive characteristics, uncertainties and variations can be readily accommodated. In this paper, Fig. 10 illustrates aFig. 10. A control flowchart for MPPT with fuzzy controlThe CVT can’t track MPP when solar illumination changes because voltage of maximum power point (Vm) is constant, so the CVT is no t o ften used in the true MPPT strategy. The P&O metho d has several drawbacks such as slo w tracking speed and oscillations about MPP, and this method can appear fallacius tracking when there is a sudden change in irradiance. Compared to the fixed size INC MPPT method, the variable step size INC MPPT algorithm is able to improve the dynamic and steady state perfo rmance o f the PV system simultaneously.Thus, in order to verify the performance of the fuzzy control MPPT method proposed in this paper, this paper compares the perfo rmance o f the fuzzy co ntro l MPPT metho d with the variable step size INC MPPT method. According to the flowchart, the co rresponding simulation model is built inMatlab/Simulink so ftware. The specificatio ns o f PV arraymodel in simulation are listed in Table II. The simulations are configured under exactly the same conditions to compare the performances.TABLE IIPV S IMULATION M ODULE S PECIFICATIONOpen circuit voltage 20.9VShort circuit current 3.0Athe number of cell in series 15the number of cell in parallel 1Simulatio n has been perfo rme d when solar illumination changes from 400 W/m2 to 1000 W/m2 at 0.03s and changes back to 400 W/m2 at 0.1s, temperature (T) rises from 40℃ to 60℃ at 0.06s at the same time, as can be seen in Fig. 11.Fig. 11. The change of solar illumination in simulationFig. 12. The current, voltage and output power of PV array based on MPPTwith variable size step INCFig. 13. The current, voltage and output power of PV array based on MPPTwith fuzzy controlFig. 12 shows curves of current, voltage and output powerof PV array based on MPPT with the variable size step INC. And Fig. 13 illustrates curves of current, voltage and output power of PV array based on MPPT with the fuzzy control.TABLE IIIT HE T RACKING P ERFORMANCE C OMPARISON B ETWEEN V ARIABLE S TEP S IZEINC AND F UZZY C ONTROL MPPT M ETHODSMPPTMethodTracking time of PV power with circumstance step change400 1000W/m2at 0.03s40℃ 60℃at 0.06s1000 400W/m2at 0.1sVariablesize INC0.037s 0.004s 0.0025sFuzzycontrol0.032s 0.0005s 0.0004s From Fig. 12, Fig. 13, and table III, co mpare to variable step size INC MPPT metho d, it can be known that fuzzy control MPPT algo rithm can fast track MPP in vo ltage, current, and power sides. So the fuzzy control MPPT methodis able to impro ve the dynam ic and steady state performanceof the PV system simultaneously. MPPT fuzzy logic controllers have been shown to perform well under varying atmospheric conditions both solar illumination and temperature.V. C ONCLUSIONA complete fuzzy logic solar array maximum power tracking controller has been designed and simulated in the software in this paper. Simulation results show fast convergence to the MPP and minimal fluctuation about it. Fuzzy controlled the maximum power point of a PV module at given atmospheric conditions very fast and efficiently. The sudden change in atmospheric conditions shifts the maximum power point abruptly which is tracked accurately by this controller. If practically implemented, this method can increase the efficiency of the PV system by quite a large scale. Since the proposed approach requires only the measurement of PV array output current and voltage, not the measurement of solar irradiation level and temperature, it decreases the number and cost of equipment as well as the design complexity. So theproposed algorithm is simple and can be easily implemented on any fast controller such as the digital signal processor. The advantages of the fuzzy controller are that the control algorithm gives fast convergence and robust performance against parameter variation, and can accept noisy and inaccurate signals. The system was found to reliably stabilize the maximum power transfer in all operating conditions, and it is ready to be fitted in a larger installation.R EFERENCES[1]Vineeta Agarwal, and Alck Vishwakarma, "A Comparative Study ofPWM Schemes for Grid Connected PV Cell," in Proc. 2007 IEEE The 7th International Conference on Power Electronics and Drive Systems, pp. 1769-1775.[2]Cuauhtemoc Rodriguez, and Gehan A. J Amaratunga, "AnalyticSolution to the Photovoltaic Maximum Power Point Problem," IEEE Transactions on Circuit and Systems, Vol. 54, No. 9, pp. 2054–2060, September 2007.[3]J. Nelson, The Physics of Solar Cells. London, U.K.: Imperial CollegePress, 2003.[4]Z. M. Salameh, D, Fouad, and A. William, "Step-down maximum powerpoint tracker for photovoltaic systems," Solar Energy, Vol. 46, No. 5, pp.279-282, 1991.[5]Trishan Esram, and Patrick L. Chapman, "Comparison of PhotovoltaicArray Maximum Power Point Tracking Techniques," IEEE Transactions on Energy Conversion, vol. 22, No. 2, pp. 439-449, June. 2007.[6]Tsai-Fu Wu, Chien-Hsuan Chang, and Yu-Kai Chen, "A Fuzzy-Logic-Controlled Single-Stage Converter for PV-Powered Lighting System Application," IEEE Transactions on Industrial Electronics, Vol. 47, No.2, pp.287-296, April 2000.[7]Nicola Femia, Giovanni Petrone, Giovanni Spagnuolo, and MassimoVitelli, " Optimization of Perturb and Observe Maximum Power Point Tracking Method," IEEE Trans. on Power Electronic, Vol. 20, No. 4, pp.963- 972, July 2005.[8]Mummadi Veerachary, Tomonobu Senjyu, and Katsumi Uezato,"Feedforward Maximum Power Point Tracking of PV Systems Using Fuzzy Controller," IEEE Transactions on Aerospace and Electronic System, Vol. 38, No. 3, pp. 969-981, July 2002. [9]M.Godoy Simoes, and N.N.Franceschetti, "Fuzzy optimisation basedcontrol of a solar array system," IEEE Proc.-Electr. Power Appl., Vol.146, No. 5, pp.552-558, Sepetember 1999.[10]Mummadi Veerachary, Tomonobu Senjyu, and Katsumi Uezato,"Neural-Network-Based Maximum-Power-Point Tracking of Coupled-Inductor Interleaved-Boost-Converter-Supplied PV System Using Fuzzy Controller," IEEE Transactions on Induetrial Electronics, Vol. 50, No. 4, pp.749-758, August 2003.Jiyong Li was born in Zunyi in China, on December1, 1975. He received the B.S. degree in vehicleengineering from Lanzhou Jiaotong University,Lanzhou, China, and M.S. degree in systemengineering from Southwest Jiaotong University,Chengdu, China, in 1999, and 2005, respectively. Heis currently working toward the Ph.D. degree inHohai University, Nanjing, China.His employment experience included theSouthwest Jiaotong University. His special fields ofinterest included the application of control techniques, the control technology of power electronics and applications of renewable energy sources.Honghua Wang was born in taizhou in China, in1963. He received the M.S. degree in industrialautomation from South China University ofTechnology, Guangzhou, China, and Ph.D degree inElectrical engineering from Zhejiang University,Hangzhou, China, in 1992, and 1997, respectively.He is currently the professor in Hohai University,China. His research interests include powerelectronic application, motion control system,intelligent control technique, and new type dc and acdrives.。
耦合神经网络轮胎模型EPS自适应控制
耦合神经网络轮胎模型EPS自适应控制黄晨;陈龙;江浩斌;王志忠;夏天【摘要】建立了基于神经网络的轮胎模型.同时在EPS工况分类的基础上建立了工况推理准则,满足准确的判断要求,进而根据EPS所处的不同工况更改模糊PID的模糊规则,实现了多种助力特性的自适应切换.建立了整车多体动力学模型,进行了蛇形道路下的SIMPACK/Matlab联合仿真,并与基于dSPACE平台的实车试验进行对比分析.结果表明,基于该模型设计的控制策略可以有效降低驾驶员的操纵转矩和提高车辆的回正性能.【期刊名称】《农业机械学报》【年(卷),期】2013(044)010【总页数】5页(P47-51)【关键词】轮胎;EPS;神经网络;自适应控制【作者】黄晨;陈龙;江浩斌;王志忠;夏天【作者单位】江苏大学汽车与交通工程学院,镇江212013;江苏大学汽车与交通工程学院,镇江212013;江苏大学汽车与交通工程学院,镇江212013;江苏大学汽车与交通工程学院,镇江212013;江苏大学汽车与交通工程学院,镇江212013【正文语种】中文【中图分类】U461.4引言电控助力转向系统(EPS)由电动机提供助力，通过合适的综合控制方法，并设计控制器，方便地调节系统助力特性，不仅与传统的液压助力转向相比具有节能、安全、成本低和总装性好等优点，而且为助力特性的设置提供了较高的自由度，使车辆在不同车速下获得不同的静态助力特性，提高驾驶员转向时的路感，以提高操纵稳定性。
此外，它可大大改善转向的响应，使车辆在经历弯道后引起的横向摆动快速收敛［1］。
但是，当车辆在高速转弯行驶时，侧偏角处于较小的范围，轮胎侧向力呈线性变化，而在较大的侧向加速度范围内，轮胎特性为非线性，侧向力呈非线性变化，转向效果减弱［2～3］。
车辆在复杂运行工况和大量不确定因素的影响下，行驶过程中的轮胎负荷、路面附着情况、侧向力和切向力等都是变化的，需要建立更加精确的模型才能满足控制的要求［4］。
一类带有执行器故障不确定线性系统的自适应H∞控制
一类带有执行器故障不确定线性系统的自适应H∞控制彭晓易;武力兵【摘要】针对一类带有不匹配外部扰动、非线性参数不确定性和执行器故障的线性系统,提出一种基于自适应容错技术的H∞控制方案.所设计的变增益容错控制器既可以对外部扰动具有良好的抑制作用,同时也可以有效补偿系统参数不确定和未知故障的影响,进而保证闭环系统具有期望的优化性能指标.飞行控制系统的数值仿真例子表明了所提出控制方法的有效性.【期刊名称】《辽宁科技大学学报》【年(卷),期】2017(040)004【总页数】6页(P292-297)【关键词】自适应控制;H∞控制;稳定性分析;飞行器模型【作者】彭晓易;武力兵【作者单位】辽宁科技大学理学院,辽宁鞍山 114051;辽宁科技大学理学院,辽宁鞍山 114051【正文语种】中文【中图分类】TP273一直以来，容错控制是控制理论研究的热点，可以提高系统的安全性，避免不必要的经济损失和人员伤亡［1-5］。
同时，伴随容错控制的发展，鲁棒H∞扰动抑制问题［6-9］在控制领域也备受关注，其主要设计思想是抑制线性系统外部扰动到被调输出传递函数的增益，使扰动对闭环系统的影响最小化。
H∞控制理论发展近二十年，各方面理论趋于成熟，同时也在导航制导、机械电子、材料化工等领域中得到广泛应用。
尽管H∞控制技术可以有效处理外部扰动对闭环系统的影响，但是对于带有执行器故障和非线性参数不确定性线性系统的容错控制问题却无能为力，由此可见这种方法还具有一定的保守性。
近些年来，基于自适应技术的容错控制策略逐渐成为容错控制领域的主流方法，其主要特点是不需要设计故障诊断与隔离机制而直接针对带有未知故障的闭环系统进行在线容错，也进一步避免了因为故障检测阶段的误报或漏报信息导致容错设计失败的情形。
文献［10-11］分别基于鲁棒控制模式给出相应的容错控制设计方法；针对一类六自由度机器人模型，文献［12］所提出改进的鲁棒自适应控制算法提高了系统轨迹跟踪估计精度。