Adaptive System Identification Based on All PassMinimum Phase System Decomposition 1

系统辨识与自适应控制教材
系统辨识与自适应控制是一门涉及自动化控制、信号处理、人工智能等多个领域的交叉学科。

这门学科主要研究如何从系统的输入输出数据中，通过一定的方法和技术，辨识出系统的数学模型，进而实现对系统的有效控制。

系统辨识的主要方法包括：基于频率响应的方法、基于时间序列的方法、基于状态空间的方法等。

这些方法可以通过对系统的输入输出数据进行处理和分析，提取出系统的模型参数和结构。

自适应控制是一种特殊的控制系统，它可以根据环境的变化或者系统参数的变化，自动调整控制参数，以实现最优的控制效果。

自适应控制的主要方法包括：模型参考自适应控制、自校正控制、多变量自适应控制等。

系统辨识与自适应控制教材有很多种，以下是一些经典的教材：
1. 《System Identification and Adaptive Control》（第二版）- John H. Holland
2. 《Adaptive Control of Linear Systems》- Michael C. Corsini
3. 《Nonlinear System Identification and Control》- Massimo Ippolito
4. 《System Identification: Theory for the User》- Jack W. Newbold
5. 《Introduction to System Identification》- Mark H. Sager
这些教材都是系统辨识与自适应控制的经典之作，它们详细介绍了系统辨识与自适应控制的基本概念、方法和技术，以及它们在各个领域的应用。

如果您想深入学习系统辨识与自适应控制，建议阅读这些教材。

User Exploration Based Adaptation in Adaptive Learning SystemsKinshuk and Taiyu LinInformation Systems DepartmentMassey University, Palmerston North, New Zealandkinshuk@Kinshuk & Lin T. (2003). User Exploration Based Adaptation in Adaptive Learning Systems. International Journal of Information Systems in Education, 1 (1), 22-31 (ISSN 1348-236X).AbstractExploratory learning, which involves searching the information, navigating through the learning space, understanding of domain-related conceptual knowledge and acquiring skills, often requires high cognitive effort on the part of the learner. Adaptive learning systems attempt to reduce the cognitive load by tailoring the domain content to suit the needs of individual learners but it is not easy for the developers of such systems to determine the effective adaptation techniques. This paper describes the formalization of Exploration Space Control framework to provide the learning system developers an effective and practical way to employ adaptive techniques in their systems and ensure that the students explore/acquire domain concepts and skills with as less cognitive load as possible.Keywords: Adaptive learning systems, Exploration, Cognitive load, Learning space1. IntroductionIn the increasing heterogeneous student population in our academic environment, the need of adaptivity in the instructional process is becoming obvious. The ideal learning environment described by Gilbert & Han (1999) consists of many (or more exactly “infinite”) teachers, each having their unique teaching styles, and the students could choose the teacher that perfectly matches their own learning styles.Currently, there are many educational system design techniques and methods for supporting learning in adaptive systems. However, all these techniques have their strengths and weaknesses, and they do not identify with each other as a mean to support learning in an adaptive environment. There exists the necessity of a framework to provide the guidelines on how to utilise existing adaptive techniques to achieve the best results.Kinshuk et al. (2000) described the Exploration Space Control (ESC) approach to support exploratory learning in educational systems. ESC employs existing adaptive techniques to enable students to explore/acquire domain concepts and skills with as less cognitive load as possible. This paper describes the formalization of ESC to provide a mechanism by which the developers of adaptive learning systems can maximise the effects of adaptivity. A prototype system is also developed to demonstrate the result of ESC formalization.The next section will discuss the adaptivity in educational systems. Then the formalization process of ESC is discussed and concrete guidelines for the developers of adaptive learning systems are provided. Finally a prototype is demonstrated that uses the formalization.2. Adaptivity in Educational SystemsExisting educational systems are mostly based on hypermedia and multimedia technologies. Inclusion of adaptivity makes such systems more usable and suitable for a wider range of users. Brusilovsky et al. (1998) distinguished two categories of features that could be adapted in such systems: content adaptation and navigational adaptation.Adaptive navigation provides guidance on the available learning paths in a manner that is both pedagogically sound and customised to individual students. It can be implemented as direct guidance, adaptive hiding or re-ordering of links, link annotation, map adaptation (Eklund & Zeiliger, 1996), link disabling, and link removal (De Bra et al., 1999).Adaptive content presentation works at the domain content level. The information can be adapted to various details, difficulty, and media usage to meet users with different needs, background knowledge, interaction style and cognitive characteristics (Recker et al., 1995). Experiments carried out on content adaptation show that it helps the memorisation of information, and improves the overall comprehension (De Bra et al., 1999).The design of an adaptive educational system requires adaptation of both navigation and content. Exploration Space Control (ESC) integrates both adaptive content and adaptive navigation in educational systems and has been proved as an effective educational framework for design of adaptive learning systems (Kinshuk et al., 2000).3. Exploration Space Control (ESC)Exploration Space Control (ESC) supports exploratory learning in educational systems by integrating and re-organising existing adaptive techniques and combining both the adaptive content and adaptive navigational support. ESC limits the learning space to control the students’ cognitive loadat an adequate level for individual students. It facilitates adequate learning for a whole spectrum of learners by adopting two extreme approaches - active learning support and step-by-step learning support.Active learning support fits those students with better competence level and more familiarity and experience with the domain, and offers the initial exploration space as wide as possible using only those restrictions that are required to protect the students from cognitive overload, and subsequently adding or removing restrictions according to students’ progress. Step-by-step learning support works for those who are completely new to the domain area or do not have active learning styles, by starting with as restricted information space as possible and then gradually enlarging. By the combination of these two approaches, “ESC can be employed to facilitate proper learning for all types of learners” (Kinshuk et al., 2000).4. Different Control Levels in ESCThe main concept of ESC is control: to control the available learning space by adaptive navigation, and to control the presentation of the learning content by adaptive presentation. Several types of control are proposed by ESC at different levels:1.Embedding information: Information sources (e.g.multimedia resources) are selected according to individual student needs and used by the scaffolding process to create the learning space.2.Limiting information resources: The selection ofinformation resources has great effect on what the student is going to see and interact with.Multimedia resources that suit the student’s cognitive ability yield the best result.3.Limiting exploration paths: ESC supports the useof navigational adaptation to offer the suitable paths in the learning space. This approach ensures that the students are not discouraged by the complexity of the entire learning space and do not receive the material that is not appropriate for them at a particular stage of learning process.4.Limiting information to be presented: Moreinformation does not mean better understanding.For example, textual explanation that matches the abstractness and granularity currently appropriate for a student will produce better learning results than flashy multimedia presentation.5. Exploration Space Control ElementsExploration space control elements (ESCEs) are the gauges on the learning content and navigational paths that could be modified to create different versions of the same materials to suit different needs (Kinshuk et al., 2000).Path: NumberRelevanceContent: Amount (detail)ConcretenessStructurenessInformation Resources: NumberMost of the modern adaptive learning systems are built using hypermedia technology, and paths are generally presented as series of links. Theamount/detail of content affects the volume of the presentation. The concreteness determines the abstract level of the information. The structureness of information indicates the ordering, arrangement, and sequencing of the information. The elaboration theory (Reigeluth, 1992) suggested a structured approach by stating that the instruction should be organized in increasing order of complexity for optimal learning. The final category in table 1 is information resource such as text, audio, and graphics. Each media type has different impact on each individual’s learning. If there is more than one media (e.g. a textual explanation and a chart), it could make the information more explanatory and easier for future recall.6. Standardizing ESC elementsThe developers of adaptive learning systems face the difficult task to identify the most adequate adaptation techniques for a particular situation. The conversion of theoretical ESC framework into a practical formalization is aimed to provide a welding mould where the courseware content can just be cast in and the benefits of adaptivity could be ensured.Figure 1: Standardization of ESC elementsThe first step in the formalization of ESC is to standardize the ESC elements. The standardization process aims at developing a base-line on how and what to utilize about the information resources for “average students” for a particular domain. The term “average students” refers to those who have the prerequisite knowledge and appropriate background according to the domain experts.The standardization process creates a domain-dependant baseline for the display elements (figure 1). Then the Exploration Space Control Elements (ESCEs) are formulated against the selected student attributes to create domain-independent information on how to adjust the ESCEs for different student attributes. This domain-independent pedagogical information can apply to any domain, but has to utilise corresponding domain-dependant standardization. The Formalization structures the ESCEs, divided into path, content, and information resource, against the level of the student attributes. Students attributes used in this research are: working memory capacity, inductive reasoning skill, associative reasoning skill, domain experience and the domain complexity. 6.1 Working Memory Capacity Deficiencies in working memory capacity result different performances on a variety of tasks. Examples of affected tasks include natural language use (comprehension, production, etc), recognition of declarative memory, skill acquisition and so on (Byrne, 1996). An empirical study by Huai (2000) showed that students with holistic learning style also have a significantly smaller working memory, but have remarkably higher learning effect in the long run, whereas the students with serial learning style have better working memory capacity but poorer learning result in the long run. The instructional design should therefore assist the central execution unit for the formation of higher order rules, build up of the mental model and of course not to overload the storage system of the working memory. These attempts can be formalised as follows:When the working memory capacity of the learner islow:• The number of paths should decease to protectthe learners from overloading the workingmemory with complex hyperspace structure.• The relevance of the information should increaseso the learners get the important informationdirectly without going through irrelevant information.• The amount of information should decrease toprovide the learners only the important information, and protect them from informationoverload.• The concreteness of the information should increase so the learners can first grasp thefundamental rules and then generalize them togenerate higher-order rules.• The structure of the information should stayunchanged. The increase of structureness couldfacilitate the building of mental model and assistfuture recall of the learned information. But theversatile learners tend to have smaller short-termmemory than serial learners (Huai, 2000), and theincrease of structureness limits their navigationalfreedom, the primary way by which they learn.Therefore the net effect cancels out.• The number of the information resources should increase so the learners could be provided with the media resources that work best along their cognitive styles. When the working memory capacity of the learner is high: • The number of paths should increase and relevance of the information should decrease to enlarge the learning space so that more content isavailable to the learners who process morehigher-orders rules which “account for creative behaviour (unanticipated outcomes) as well as the ability to solve complex problems by making it possible to generate (learn) new rules ” (Kearsley, 2001). • The amount of information should increase to allow the learners to get the most out of the domain. • The concreteness of the information should decrease to avoid boredom for the learners resulting from too many similar examples. Learner with higher working memory capacity can generate higher-order rules faster. • The structure of the information should stay unchanged (rationale is same as for the condition of low working memory capacity). • The number of information resources should stay unchanged because there are no direct and apparent benefits. These rules are summarised in table 2. Path Content Info Res Level No Rel Amt Con Str NoLow- + - + \ + High \+ \- + - \\ (No =Number; Rel =Relevance; Amt =Amount;Con=Concreteness; Str=Structure)where"+" Æ should increase "-" Æ shoulddecrease "\+" Æ s hould slightly increase (recommend only), or could increase "\-" Æ should slightly decrease (recommend only),or could decrease Table 2: Working Memory Formalization6.2 Inductive Reasoning Skill Inductive reasoning skills relate to the ability to construct concepts from examples. When a student faces a complicated problem, (s)he looks for known patterns, and uses them to construct a temporary internal hypotheses or schema to work with (Bower & Hilgard, 1981). It is easier for students, who possess better inductive reasoning skill, to recognize a previously known pattern, and generalize higher-orderVarious ESCEs can be related to information processing speed as follows: rules. As a result, the load on working memory isreduced, and learning process is more efficient.In other words, the higher the inductive reasoningability, the easier it is to build up the mental model ofthe information learned. When learner’s information processing speed is slow: • The number of paths and amount of information should decrease so only the important points are presented to the learner. The relevance of the paths should increase for the same reason. The inductive reasoning skills can be considered in ESCE formalization as follows: When the learner’s inductive reasoning skill is poor: • The concreteness of the information and number of information resources should stay unchangedbecause there are no direct and apparent benefits. • The number of paths should increase and relevance of paths should decrease to give the learner more opportunity for observations and thus promote induction. • The structure of the information should increase to speed up the learning process. • The amount of information should increase to give detailed and step-by-step explanation to the learners, so they can see the rules/theories easierWhen learner’s information processing speed is fast: • The number of paths should increase and relevance of the paths should decrease to enlargethe information space. • The concreteness of the information should increase because more examples help the learners to understand the underlying theories. • The amount of information should increase so the learner can gain in-depth insight of the subjectmatter. • The structure of the information should increase so that it is easier for the learner to build up the mental model and see the relationships among concepts. • The concreteness and structure of the information and the number of the information resources should stay unchanged because there are no directand apparent benefits. • The number of information resources should stay unchanged because there are no direct and apparent benefits. These rules are summarised in table 4. When the learner’s inductive reasoning skill is good: • The number of paths should decrease to reduce the complexity of the hyperspace and hence enable the learners to grasp the concepts quicker. Path Content Info ResLevel No Rel Amt Con Str No Slow - + - \ \+ \ Fast+ - + \ \ \ • The relevance of paths should stay unchanged because there are no direct and apparent benefits. (No=Number; Rel=Relevance; Amt=Amount; Con=Concreteness; Str=Structure)• The amount and structure of the information, and number of information resources should decrease to speed up the learning process. Table 4: Information Processing Speed Formalization• The concreteness of the information should decrease to avoid the boredom resulting from too many similar examples. 6.4 Associative Learning SkillThese rules are summarised in table 3. Path Content Info ResLevel No Rel Amt Con Str NoPoor \+ \- + + + \Good \-\ - \- \ \ The associative learning skills link new knowledge to existing knowledge. The association process requires the pattern-matching to discover the space of existing information, analyse the relationships between the existing and newknowledge, and finally retain the new knowledge in the long-term memory (or more specifically to maintain the links to the new knowledge). In order to assist the association processes during the student’s learning, the instruction needs to assist the recall (revisit) of learned information, clearly show the relationships of concepts (new to existing), and facilitate new or creative association/insight formation by providing information of related domain area. (No=Number; Rel=Relevance; Amt=Amount;Con=Concreteness; Str=Structure)Table 3: Inductive Reasoning Skill Formalization6.3 Information Processing SpeedInformation processing speed determines how fastthe learners acquire the information correctly.Instructional designers should take into account theconsideration of learner’s information processingspeed. For example, the learner may have such a slowreading speed that (s)he is unable to hold enoughdetails in working memory to permit decoding of theoverall meaning (Bell, 2000).Various components of ESCEs can be related to associative learning skills as follows: When the learner’s associative learning skill is poor: • The number of paths should increase. More hints and information could help the learner to associate one concept to another. • The relevance of the paths should increase tospeed up the learning process.•The amount and concreteness of information should stay unchanged because there are no direct and apparent benefits.•The structure of the information should increase to enhance the development of the mental model and to accelerate the learning speed by a better-structured curriculum design. •The structure of the information should increase to help the leaner make linkages easily between concepts.• The number of information resources shouldincrease so the learners could be provided with the media that suits best to their learning style. •The number of information resources should increase. Different information resources provide different magnitude of understanding of the same concept.When the learner’s domain experience is more:• The number of paths should increase so that morecontent can be explored. When the learner’s associative learning skill is good: • The relevance of the paths should stay unchanged because there are no direct and apparent benefits.• The number of paths should decrease so as to reduce the required learning time. • The amount of information should increase so the learner can have in-depth study of the topic.• The relevance of the paths should decrease to enlarge the information space. • The concreteness of the information should decrease so that the learner could accumulatemore abstract concepts faster.• The amount and concreteness of information, and the number of information resources should stay unchanged because there are no direct and apparent benefits. • The structure of the information and the number of information resources should stay unchanged because there are no direct and apparent benefits.• The structure of the information should decrease to enable the learner to navigate more freely and hence enhance the learning speed. These rules are summarised in table 6. These rules are summarised in table 5. Path Content Info Res Level No Rel Amt Con Str No Poor + + \ \ + + Good \- - \ \ \- \ Path Content Info Res Level No Rel Amt Con Str No Little - + \- + + \+ Many + \ + \- \ \ (No=Number; Rel=Relevance; Amt=Amount; Con=Concreteness; Str=Structure) Con=Concreteness; Str=Structure) Table 6: Domain Experience Formalization6.6 Domain ComplexityTable 5: Associative Learning Skill Formalization Domain complexity is the difficulty level of the concepts in the domain. When the domain is large, it has to be more structured to maintain the comprehensibility of its concepts and the visibility of the relationships between concepts, and when the domain concepts are by themselves difficult to be learned, concepts have to be broken down into simpler ones and more supplementary information should be provided.6.5 Domain ExperienceThe domain experience is the familiarity with the domain concepts and skills. Experience can be either related to skills (operational) or concepts. Studies cited by Espinoza & Hook (1996) and Li et al. (2001) have identified user's background knowledge as a major influence on understanding the domain. Taking domain experience into consideration, those who possess more are likely to perform more active learning than those who possess less. Thus the instructional design should provide means by which the students with more experience can be satisfied and those with less experience do not get overwhelmed. Domain complexity can be related to ESCEs as follows: When the domain complexity is low: • The number of paths should increase and relevance of paths should decrease so that the learner could explore more about the details and related areas of the topic. The domain experience can be related to ESCEs as follows: When the domain experience of the learner is little: • The amount and concreteness of the information should stay unchanged because there are no directand apparent benefits. • The number of paths should decrease and relevance of the paths should increase to protect the learner from getting confused by complex hypermedia space. • The structure of the information should decrease so the learners have more freedom to navigate through the information.• The amount of information should decrease to protect the learner from cognitive overload. • The number of the information resources should decrease. There is no need to prepare too manyresources when the domain is very straightforward.• The concreteness of the information should increase so the learner could obtain concepts easier.When the domain complexity is high: • The number of paths should decrease so the learner is not carried away from the central theme of the curriculum and gets confused. • The relevance of the paths should increase so the learner gets only what is important. • The amount of information should increase in order to provide detailed explanations of the complex domain concepts. • The concreteness of the information should increase so the learner can grasp the fundamentals before advancing to the abstract. • The structure of the information should increase to facilitate the building of the mental model. • The number of information resources should increase so there are varieties of resources to suit different users.These rules are summarised in table 7.Path Content Info ResLevel No Rel Amt Con Str NoLow \+ - \ \ \- \-High \- + + + + +(No=Number; Rel=Relevance; Amt=Amount;Con=Concreteness; Str=Structure)Table 7: Domain Complexity Formalization6.7. Overall relationship of ESCEs with student attributes The relationships between various student attributes and ESCEs provide the ESC formalization matrix (table 8). Path Content Info Res Student Attributes Level No Rel Amt Con Str No Low - + - + \ + Work mem capacity High \+ \- + - \ \ Poor \+ \- + + +\ Induct reason skill Good \- \ - \- \ \ Slow - + - \ \+\ Info process speed Fast + - + \ \ \Poor + + \ \ ++ Assoc learn skill Good \- - \ \ \-\Little - + \- + +\+ Domain Experience Many + \ + \- \ \Low \+ - \ \ \-\- Domain Complexity High \- + + + ++Con=Concreteness; Str=Structure)Table 8: ESC Formalization Matrix7. Translation of ESC Formalization MatrixThe ESC Formalization matrix in table 8 containsonly qualitative information (+, -, /+, and /-). It has tobe translated into quantitative information that can becomputed to match what is needed in the instructional design. The translation follows the rules: • Standard – set to the average score of 3• Slight change (“\” sign) – add/deduct 1 point • Complete change – add/deduct 2 pointsTable 9 shows the resulting quantitative version of ESC Formalization Matrix.Path Content Info ResStudent Attributes Level No Rel Amt Con Str No Low 1 5 1 5 3 5 Std 3 3 3 3 3 3Work Mem Capacity High 4 2 5 1 4 4 Low 4 2 5 5 53 Std 3 3 3 3 3 3 Induct Reason Skill High 2 3 1 2 3 3Low 1 5 1 3 4 3 Std 3 3 3 3 3 3 Info Process Speed High 5 1 5 3 3 3 Low 5 5 3 3 5 5 Std 3 3 3 3 3 3 Assoc Learn Skill High 2 1 3 3 2 3 Low 1 5 2 3 3 4 Std 3 3 3 3 3 3 Domain Experience High 5 3 5 2 3 3 Low 4 1 3 3 2 2 Std 3 3 3 3 3 3 Domain Complexity High 2 5 5 5 5 5 (No=Number; Rel=Relevance; Amt=Amount; Con=Concreteness; Str=Structure) Table 9: ESC Formalization Matrix (quantitative)8. Correlation of ESC Matrix withConditional Page Display Elements Once the quantitative information is available on how to format the presentation of content, the next task is to correlate this information to the displayelements. A display element could be a textualparagraph (e.g. chapter overview), a link (e.g. a link toapplication area), or other media object (e.g. a chart ora video clip). Conditional display elements get displayed only when the condition is met. For example, the detailed version of “Chapter Overview” is displayed when the required concreteness (Con) is greater than 2 points, the detail of information (Amt) is greater than 4 points and the structureness (Str) of information is greater than 2, whereas the standard version only requires the Con to be greater than 2points, Amt greater than 3 points and Str greater than2 points. The entire correlation result is shown intable 10. The “+” sign means “greater than”, “-“ signmeans “less than”, for example, “Amt1+” means when the requirement of information detail has scoregreater than 1. For the display element the “/” sign indicates parent/child hierarchy, and the @ sign indicates an attribute value, for example“prerequisite/intro” indicates the introductory explanation of the prerequisite chapter.The ESC Matrix to Display Elements Correlation Table has been applied to create a prototype adaptive learning system for the topic of Marginal Costing in accounting domain.9. Prototype SystemThe architecture of the prototype system is shown in figure 2. The domain content for Marginal Costing topic in the system is stored in the eXtendible Markup Language (XML) document. A Data Type Definition (DTD) provides the validation of the correctness and completeness of the corresponding XML documents. Therefore, another teacher can create a completely different XML document for Marginal Costing if required. As long as the new XML document complies with the DTD, the whole system will just take it and use it without any extra customisation. The system uses an eXtensible Style Language (XSL) style sheet to render the display elements. XSL can transform XML page into several different views that can have different information, media types, or even different order of display, for different students.Display Elements Student State RequirementsLearningObjective Amt1+, Con1+, Str2+ Prerequisites PathNo1+, Amt1+, Str1+ Prerequisite/Intro Amt2+ ChapterOverview/@detailLevel= simple Amt1+, Con1+, Str2+ ChapterOverview/@detailLevel= standard Amt3+, Con2+, Str2+ChapterOverview/@detailLevel= high Amt4+, Con2+, Str2+Glossary/newTerm/termDefinition/@detailLevel =standard Amt1+ Glossary/newTerm/termDefinition/@detailLevel =detailed Amt2+ ChapterBody/chapterConcept/@difficultLevel =hard Amt4- ChapterBody/chapterConcept/@difficultLevel =easy Amt3+ ChapterBody/chapterConcept/conceptDefinition/@detailLevel =detailed Amt4+ ChapterBody/chapterConcept/conceptDefinition/@detailLevel =standard Amt2+ ChapterBody/chapterConcept/conceptExample/@difficultLevel =hard Amt3+, Con1+ ChapterBody/chapterConcept/conceptExample/@difficultLevel =hard Amt1+, Con1+ ChapterBody/chapterConcept/conceptExample/checkFile PathNo2+, Amt2+ ChapterBody/chapterConcept/conceptExcursion PathNo3+, Amt2+, Rel4- ChapterBody/chapterConcept/conceptGraph InfoResNo2+ Application/applicationArea/@relevance Rel1+, Amt2+, Con2+ Application/applicationArea/@relevance =high Rel3+, Amt2+, Con2+RelatedTheory/theory Rel2+, Amt1+ RelatedTheory/theory/@relevance high Rel3+ExerciseSection Amt1+ Summary Amt2+, Str3+Concreteness of Information, Str = Structure of Information; and InfoResNo = Number of Information Resource/Media)Table 10: ESC Matrix to Display Elements Correlation tableFigure 2: ESC Formalization System Architecture Final component of the prototype is ESC Formalization schema builder, which contains two modules: In-Time Student Module (ITSM) and Rendering Module (RM).In a real adaptive learning system, various student-modelling techniques are used to obtain the information about the students. Each of those techniques either requires students to provide their information explicitly or contains algorithms to perform the analysis of student behaviour. It is difficult to demonstrate in such an environment the real effects of adaptivity on different students, unless the system is used by a large number of students for significant amount of time. To circumvent this problem, the In-Time Student Module (ITSM) has documentDifferent views for。

■技术探讨与研究TECHNIQUE RESEARCH基于MRAS的永磁同步电机在线参数辨识Online Parameter Identification of Permanent Magnet Synchronous Motor Based on MRAS Runchan Liu大连交通大学刘闰婵(Runchan Liu)摘要:在永磁电机运转过程中，电机的参数会实时发生变化，而调节器不能进行参数自校正，为了获得更好的控制效果，需要对电机的参数进行在线辨识。

本文提出基于模型参考自适应(MRAS)的PMSM在线辨识方法，建立参考模型和可调模型，利用两个模型的输出量之差/通过合适的自适应律来现对PMSM参数的辨识，在线估计定子电阻、定子电感、永磁体磁链，并通过MATLAB仿真验证可行性。

关键词:永磁同步电机；在线参数辨识；模型参考自适应；参考模型；可调模型Abstract:During the operation of permanent magnet motor the parameters of the motor will change in real time,but the regulator cart perform self-correction of paramBeters.In order to obtain better control effect,the parameters of the motor n e ed to be ide ntified online.This paper proposes a model reference adaptive system(MRAS)based on PMSM on line ide n tificati o n method,which establishes a ref e re n ee model and an adjustable model,the n uses the differe n ee betwee n the output of the two models to ide n tify the PMSM parameters through an appropriate adaptive law.Stator resista nee,stator in d u eta nee,perma nent magnet flux lin kage were estimated online and verified by MATLAB simulation.Key words:PMSM;Online par a meter ide ntificati o n;MRAS;Refere n ee model;Adjustable model【中图分类号】TM351【文献标识码】B文章编号1606-5123(2020)07-0067-051引言与传统的电励磁同步电机相比，永磁同步电机具有结构简单、体积小、质量轻、运行可靠等显著优势。

动力调谐陀螺仪系统辨识方法田凌子;李醒飞;赵建远;王亚辉【摘要】针对动力调谐陀螺仪(DTG)系统辨识中,传统辨识方法(最小二乘类辨识法和频域辨识法)辨识拟合度不高的问题,提出去离群点频域辨识法.该方法结合DTG 模型结构特征和固有有色噪声特点,将去离群点思想应用于DTG模型的频域辨识.实验结果表明,去离群点频域辨识法的辨识效果优于最小二乘类辨识法和传统频域辨识法,辨识拟合度在90％以上,并且辨识结果重复性好,辨识算法稳定.在DTG系统辨识中,去离群点频域辨识法能够提高辨识拟合度.【期刊名称】《计算机应用》【年(卷),期】2014(034)012【总页数】5页(P3641-3645)【关键词】动力调谐陀螺仪;系统辨识;强有色噪声;频域辨识法;最小二乘类辨识法【作者】田凌子;李醒飞;赵建远;王亚辉【作者单位】天津大学精密仪器与光电子工程学院,天津300072;精密测试技术及仪器国家重点实验室(天津大学),天津300072;天津大学精密仪器与光电子工程学院,天津300072;精密测试技术及仪器国家重点实验室(天津大学),天津300072;天津大学精密仪器与光电子工程学院,天津300072;精密测试技术及仪器国家重点实验室(天津大学),天津300072;天津大学精密仪器与光电子工程学院,天津300072;精密测试技术及仪器国家重点实验室(天津大学),天津300072【正文语种】中文【中图分类】TP273;U666.120 引言陀螺仪作为惯性导航系统的核心部件，能够为载体提供精确的空间角位置信息［1-2］。

目前，能达到惯性级的中高精度陀螺仪仍多为工作在闭环条件下的机械式陀螺仪［3］，如液浮陀螺仪、动力调谐陀螺仪(Dynamically Tuned Gyroscope，DTG)等。

陀螺仪闭环系统在建立过程中，需要可靠的陀螺模型，以便调整控制器参数，保证整个闭环系统的性能。

传统的陀螺仪建模方法主要是机理建模［4］，然而由于陀螺仪系统结构复杂，机理建模需要忽略掉诸多因素，建模精度不高，也难以针对某个陀螺仪的实际情况进行具体分析，建模不具有普适性［4］。

第27卷㊀第9期2023年9月㊀电㊀机㊀与㊀控㊀制㊀学㊀报Electri c ㊀Machines ㊀and ㊀Control㊀Vol.27No.9Sep.2023㊀㊀㊀㊀㊀㊀新型模型参考自适应的PMSM 无差拍电流预测控制张懿,㊀徐斌,㊀魏海峰,㊀李垣江,㊀刘维亭(江苏科技大学电子信息学院,江苏镇江212100)摘㊀要:永磁同步电机(PMSM )的无差拍电流预测控制(DPCC )对参数失配非常敏感㊂在实际应用环境中,由于某些因素的影响,电机参数会失配,严重时会导致PMSM 运行故障㊂为了减小对DPCC 的影响,提出一种基于新型模型参考自适应系统(MRAS )的参数分步辨识方法㊂首先,获得定子电阻和定子电感的参数,并将其作为已知量来辨识转子磁链㊂等待参数稳定之后,再将辨识结果作为已知量用于辨识定子电感和定子电阻㊂最后,将辨识出的参数代入DPCC 进行改进㊂实验结果表明,该方法可以解决模型欠秩的问题,并且可以抑制电机参数失配对DPCC 的影响,提高动态跟踪性和鲁棒性,具有一定的工程实际意义㊂关键词:无差拍电流预测控制;参数分步辨识;动态跟踪性;鲁棒性;永磁同步电机DOI :10.15938/j.emc.2023.09.017中图分类号:TM351文献标志码:A文章编号:1007-449X(2023)09-0157-11㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀收稿日期:2022-05-25基金项目:国家自然科学基金(51977101);江苏省省重点研发计划产业前瞻性与共性关键技术重点项目(BE2018007)作者简介:张㊀懿(1982 ),女,博士,教授,研究方向为电机控制;徐㊀斌(1998 ),男,硕士研究生,研究方向为电机控制;魏海峰(1981 ),男,博士,教授,研究方向为电机控制;李垣江(1981 ),男,博士,副教授,研究方向为电机控制以及复杂控制系统;刘维亭(1966 ),男,博士,教授,研究方向为电机控制㊂通信作者:魏海峰New model reference adaptive deadbeat predictive currentcontrol of PMSMZHANG Yi,㊀XU Bin,㊀WEI Haifeng,㊀LI Yuanjiang,㊀LIU Weiting(School of Electronics and Information,Jiangsu University of Science and Technology,Zhenjiang 212100,China)Abstract :The deadbeat predictive current control (DPCC)of permanent magnet synchronous motor (PMSM)is quite sensitive to parameter mismatch.In the environment of practical application,parameter mismatch could occur in the motor due to certain factors,and serious occasions would result in the opera-tion failure of PMSM.In order to weaken the influence on the DPCC,a parameter stepwise identification method based on the new model reference adaptive system (MRAS)was proposed.Firstly,the parame-ters of stator resistance and stator inductance were acquired and used as the known quantity to identify ro-tor flux.Then the identification result was used as the known quantity to identify stator inductance and stator resistance after the parameters are stable.And finally,the identified parameters were substituted into the DPCC for improvement.The experiment result shows that the method can solve the under-rank problem of the model and can suppress the influence of motor parameter mismatch on the DPCC to im-prove the dynamic tracking and robustness.The method has a certain practical engineering significance.Keywords :deadbeat predictive current control;parameter stepwise identification;dynamic tracking;ro-bustness;permanent magnet synchronous motor0㊀引㊀言永磁同步电机(permanent magnet synchronous motor,PMSM)具有体积小㊁质量轻㊁功率高等特点,因此广泛普及于民用㊁航天及军事等领域㊂当前,电流环控制策略有:电流预测控制[1-4]㊁电流滞环控制[5-8]㊁PI电流控制[9-12]和自抗扰控制[13-14]等㊂截至目前,应用最广的是传统PI电流环控制,由于其结构简单以及低通滤波的特性,导致超调量较大,适用于滞后性和惯性比较大的场合㊂电流滞环控制的算法比较复杂,并且其开关频率受负载的影响较大,而自抗扰控制研究目前还未达到一定的深度,因此算法实现难度大㊂为了满足高精度领域的需求,无差拍电流预测控制可以让系统的电流环得到更快的响应输出,同时电流的纹波小,控制算法也容易实现,但由于无差拍电流预测控制受电机参数的影响较大,当电机参数不准确或者工作环境改变,都会导致交直轴电流出现偏差,随着转速的增大,交直轴电流偏差就会越大㊂文献[15]设计了基于Lagrange 插值的无差拍电流预测控制(deadbeat predictive current control,DPCC)算法,虽然提高了鲁棒性,但也降低了一定的动态效果㊂文献[16]提出了一种新的功率滑模趋近律,缩短系统的收敛时间,然后建立了一种改进功率滑模趋近律的非齐次扰动观测器,保证电流误差收敛至0,最后建立一种新型定子电流和扰动观测器的改进型DPCC㊂模型参数扰动的问题基本得到解决,但是计算复杂,对计算机硬件要求高㊂文献[17]在无差拍电流预测控制中引入鲁棒电流预测算法,提高了系统电流环的动态性能和稳态精度,但是研究对象只针对电感参数失配,在实际应用中,电机运行受限不只是电感参数的问题㊂文献[18]通过加入模糊前馈控制器来降低参数的敏感度,从而提高鲁棒性,但是目前只停留在仿真阶段,没有考虑实际应用环境中的电机控制,缺乏实验依据㊂文献[19]提出了一种非线性扩展状态观测器和权重因子相结合来改进DPCC的方法,估计的电流扰动和电压扰动可以分别用来校正电流参考值和输出电压,以此提高系统的鲁棒性,但设计过程较为复杂㊂文献[20]为了实现让电流误差为0,需要提供补偿给反馈电流,将引入电流预测的补偿因子来修正电压,以此提高系统的鲁棒性,但是该方法比较影响系统的动态性能㊂为了解决由于参数失配导致无差拍电流预测控制动态跟踪性和鲁棒性差的问题,本文提出一种基于新型模型参考自适应系统的参数分步辨识法㊂首先获取定子电感和定子电阻参数,将其作为已知量来辨识转子磁链㊂等到转子磁链参数稳定后,再针对定子电阻和定子电感进行辨识㊂其次,将辨识出的参数代入无差拍电流预测控制进行改进,可以有效解决参数辨识模型存在的欠秩问题,增加电机参数辨识的精确度,同时可以抑制参数失配对无差拍电流控制系统的影响,从而提高系统的动态跟踪性和鲁棒性㊂最后通过实验验证该方法的有效性㊂1㊀无差拍电流预测控制1.1㊀永磁同步电机数学模型搭建为了简化设计,因此假设PMSM满足以下理想情况:1)忽略电机的铁心饱和;2)不计涡流和磁滞损耗;3)电机电流为对称的三相正弦波㊂基于以上理想情况,永磁同步电机在d-q轴下的定子电压方程为:u d=R s i d+L dd i dd t-ωe L q i q;u q=R s i q+L qd i qd t+ωeψf+ωe L d i d㊂üþýïïïï(1)式中:u d㊁u q和i d㊁i q分别是d-q轴下的定子电压和定子电流分量;R s是定子电阻;L d㊁L q是d-q轴电感;ωe是转子电角速度;ψf是转子磁链㊂1.2㊀无差拍电流预测控制的实现采用表贴式永磁同步电机,利用其d-q轴电感相等的特性,即L d=L q=L㊂将d-q轴电流作为状态分量,得到的电流状态方程数学模型为:d i dd t=u dL-R s i dL+ωe i q;d i qd t=u qL-R s i qL-ωe i d-ωeψfL㊂üþýïïïï(2)由于电流的采样时间短,则本文采用一阶泰勒公式将电流状态方程进行离散化,即离散化的数学模型近似为:d i dd t=i d(k+1)T s-i d(k)T s;d i qd t=i q(k+1)T s-i q(k)T s㊂üþýïïïï(3)式中:i d(k)㊁i q(k)是第k时刻的d-q轴电流变量值;i d(k+1)㊁i q(k+1)是第k+1时刻的d-q轴电流变量值;T s是电流的采样时间值㊂通过将式(3)851电㊀机㊀与㊀控㊀制㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第27卷㊀代入式(2),可以计算出无差拍电流预测控制中第k +1时刻的离散化d -q 轴电流变量值控制方程为i d (k +1)i q (k +1)éëêêùûúú=M (k )i d (k )i q (k )éëêêùûúú+N u d (k )u q (k )éëêêùûúú+T (k )㊂(4)式中:M (k )=L -T s R sLωe (k )T s -ωe (k )T s L -T s R s Léëêêêêùûúúúú;N =T s L00T s L éëêêêêùûúúúú;T (k )=0-T sLψf ωe (k )()㊂无差拍电流预测控制的实际意义是为了实现控制系统下一刻的输出电流能够跟上给定电流,则需要将控制系统的给定电流值作为下一个时刻的输出电流值,因此,需要根据离散方程和d -q 轴的给定电流值计算出控制电压,以此来实现下一时刻的输出电流经过单独的电流采样周期后能够跟上给定电流㊂通过式(4)可以计算出无差拍电流预测控制中所需的d -q 轴电压控制方程为u d (k )u q (k )éëêêùûúú=N -1-M (k )i d (k )i q (k )éëêêùûúú+{i d (k +1)i q (k +1)éëêêùûúú-T (k )}㊂(5)图1为传统无差拍电流预测控制系统结构框图㊂为了实现永磁同步电机的电流无差拍,用第k时刻的d -q 轴给定电流值i ∗d (k )和i ∗q (k )去替换第k +1时刻的d -q 轴电流变量值i d (k +1)和i q (k +1),因此通过式(5)可以计算出无差拍电流预测控制中所需的d -q 轴电压控制方程为u d (k )u q (k )éëêêùûúú=N -1-M (k )i d (k )i q (k )éëêêùûúú+i ∗d (k )i ∗q (k )éëêêùûúú-T (k ){}㊂(6)在实际进行永磁同步电机控制过程中,基于电机参数准确的情况下,则在第k +1时刻的d -q 轴输出电流值将会达到给定电流值㊂若电机参数失配的情况下,则第k +1时刻的d -q 轴输出电流值将会和给定电流值出现误差㊂根据式(4)可以计算出无差拍电流预测控制中第k +1时刻的离散化d -q 轴实际电流变量值控制方程为i d (k +1)i q (k +1)éëêêùûúú=M 0(k )i d (k )i q (k )éëêêùûúú+N 0u d (k )u q (k )éëêêùûúú+T 0(k )㊂(7)式中:M 0(k )=L 0-T s R s0L 0ωe (k )T s -ωe (k )T s L 0-T s R s0L 0éëêêêêùûúúúú;N 0=T s L 000T s L 0éëêêêêùûúúúú;T 0(k )=-T sL 0ψf0ωe (k )()㊂其中:R s0是定子电阻实际值;L 0是定子电感实际值;ψf0是转子磁链实际值㊂图1㊀无差拍电流预测控制系统结构框图Fig.1㊀Structural block diagram of traditional DPCCsystem将式(6)代入式(7)可得:i d (k +1)=T s ΔR -ΔL L 0i d (k )+LL 0i ∗d(k )-ΔLL 0T s ωe (k )i q (k );i q (k +1)=T s ΔR -ΔL L 0i q (k )+LL 0i ∗q(k )+ΔLL 0T s ωe (k )i d (k )+T s ωe (k )ΔψL㊂üþýïïïïïïïïïï(8)式中:ΔR =R s -R s0;ΔL =L -L 0;Δψ=ψf -ψf0㊂当系统达到稳定时刻,可从上式看出,定子电阻和定子电感均会影响d -q 轴电流,而转子磁链只会影响q 轴电流㊂由此可见,电机参数的精度偏差会影响整个电机电流环控制的性能,因此,增加电机参951第9期张㊀懿等:新型模型参考自适应的PMSM 无差拍电流预测控制数辨识的精度就可以抑制参数失配对电机的性能影响,使得整个控制系统运行具有稳定性㊂1.3㊀无差拍电流预测控制的稳定性基于T s的开关周期很小,因此将式(8)进行Z 变换,可以得出d-q轴给定电流和实际电流的离散域闭环传递函数为i dq(z) i∗dq(z)=LL0zz-1-L L()㊂(9)通过式(9)可以看出,该系统的极点为z=1-LL0㊂由离散稳定性条件可知,系统想要稳定,极点应处于Z平面内的单位圆内,即|z|<1,则无差拍电流预测控制的稳定界限为0<L<2L0㊂(10)由式(10)可知,要使系统稳定,则定子电感值需在该范围内,假如超出该范围,则系统是不稳定的㊂2㊀新型模型参考自适应的参数分步辨识思想2.1㊀传统模型参考自适应系统的参数辨识图2为传统模型参考自适应系统(model refer-ence adaptive system,MRAS)结构框图,由参考模型㊁可调模型和自适应律共同组成㊂该系统主要实际意义在于求得一种能够实时进行动态调整的反馈自适应律,使得当前系统的闭环控制性能可以和参考模型的性能相一致,因此构造出两个模型,其中一个将不含待辨识参数的电流状态方程作为永磁同步电机参考模型,而将含待辨识参数的电流状态方程作为永磁同步电机可调模型,将这两个模型输出量作差,当得出的输出误差送入自适应律进行实时动态调整至0时,则可调模型就等效于参考模型,而待辨识参数的估算值就等效于参数的实际值㊂本文结合Popov超稳定性理论设计自适应律,该设计方法可以降低计算量,同时可以保证待辨识参数的稳定性㊂2.2㊀新型模型参考自适应系统的参数分步辨识如式(2)所示,永磁同步电机数学模型的电流状态方程是2维的,在需要辨识电机3个参数的情况下,会存在欠秩情况,从而导致电机参数的失配,影响电机的控制性能㊂因此,本文采用参数分步辨识的方法,其系统结构框图如图3所示㊂图2㊀传统模型参考自适应系统结构框图Fig.2㊀Structural block diagram of traditional MRASsystem图3㊀参数分步辨识系统结构框图Fig.3㊀Structural block diagram of parameter stepwise identification system具体的辨识过程如下:1)固定定子电阻和定子电感,以上电机参数均可从电机参数铭牌上获取;2)将不含待辨识参数的电流状态方程作为永磁同步电机参考模型,将步骤1获取到的定子电阻和定子电感参数值作为已知量代入进电流状态方程中,设计出含待辨识参数的可调模型㊂由于转子磁链只和q轴电流状态方程相关,所以只需采用q轴电流状态方程即可㊂此时只有一个未知量,方程存在唯一解,从而设计自适应律来辨识转子磁链; 3)待转子磁链辨识稳定后,将已知的转子磁链代入第二个可调模型中,用来辨识定子电阻和定子电感,此时只有2个未知量,针对2维的电流状态方程存在唯一解,再设计自适应律来辨识定子电阻和定子电感㊂061电㊀机㊀与㊀控㊀制㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第27卷㊀3㊀参数分步辨识实现3.1㊀转子磁链的辨识实现由于转子磁链只和q轴的电流方程有关,通过式(2)可得q轴的电流状态方程为d i q d t=u qL-R s i qL-ωe i d-ωeψfL㊂(11)对应的可调模型为d i^q d t=u qL-R s i^qL-ωe i d-ωeψ^fL㊂(12)由式(11)~式(12)可得一阶误差系统为d e qd t=De q-F㊂(13)式中:e q=i q-i^q;D=-R s L;F=ωe L(ψf-ψ^f)㊂为了满足该系统的全局稳定,根据Popov超稳定性理论可知,需要满足以下条件:∀t1>0,η(0,t1)=ʏt10e T F d tȡ-γ2㊂(14)式中γ2是有限正数㊂将e q和F代入式(14)可得:∀t1>0,η(0,t1)=ʏt10e T qωe L(ψf-ψ^f)d tȡ-γ2㊂(15)这里将转子磁链的自适应律设置为比例积分形式,具体形式如下:ψ^f=ʏt0g1(τ)dτ+g2(t)+ψ^f(0)㊂(16)式中ψ^f(0)为所辨识参数的初始值㊂将式(16)代入式(15)得ʏt10e qωe L[ψf-ʏt10g1(τ)dτ-g2(t)-ψ^f(0)]d tȡ-γ2㊂(17)将式(17)拆分成积分项和比例项,即:ʏt10e qωe L[ψf-ʏt0g1(τ)dτ-ψ^f(0)]d tȡ-γ21;ʏt10-e qωe L g2(t)d tȡ-γ22㊂üþýïïïï(18)式中γ21和γ22是有限正数,且γ2=γ21+γ22㊂显然式(18)成立即式(17)同样成立,令:fᶄ(t)=e qωe L;k i f(t)=ψf-ʏt0g1(τ)dτ-ψ^f(0); k p fᶄ(t)=-g2(t)㊂üþýïïïïïï(19)将式(19)代入式(18)可得:ʏt10k i f(t)fᶄ(t)d tȡ-γ21;ʏt10k p[fᶄ(t)]2d tȡ-γ22㊂üþýïïïï(20)式中k i和k p均大于0㊂由式(20)进行变换可得:ʏt10k i f(t)fᶄ(t)d t=k i2[f2(t1)-f2(0)]ȡ0;ʏt10k p[fᶄ(t)]2d tȡ0㊂üþýïïïï(21)由式(21)可知,式(18)成立,因此式(17)成立㊂即该系统全局稳定,则有:g1(τ)=-k i e qωe L;g2(t)=-k p e qωe L㊂üþýïïïï(22)因此,将式(22)代入式(16)并化简,转子磁链的自适应律为ψ^f=-k is+k p()e qωe L+ψ^f(0)㊂(23) 3.2㊀定子电阻和定子电感的辨识实现当转子磁链辨识稳定后,对定子电阻和定子电感进行辨识,通过式(2)可得参考模型为dd ti di qéëêêùûúú=-R s Lωe-ωe-R s Léëêêêêùûúúúúi di qéëêêùûúú+1L001Léëêêêêùûúúúúu du qéëêêùûúú+-ωeψf Léëêêêùûúúú㊂(24)分别令可调参数:a=R sL;b=1L㊂电流状态方程式(24)可化简为p I=AI+BU+C㊂(25)式中:I=i di qéëêêùûúú;U=u d uqéëêêùûúú;A=-aωe-ωe-aéëêêùûúú;B= b00b[];C=0-ωeψf b[];p=d d t为微分算子㊂可调模型为dd ti^di^qéëêêùûúú=-a^ωe-ωe-a^éëêêùûúúi^di^qéëêêùûúú+b^00b^éëêêùûúúu du qéëêêùûúú+-ωeψf b^éëêêùûúú㊂(26)电流状态方程式(26)可化简为p I^=A^I^+B^U+C^㊂(27)式中:I^=i^di^qéëêêùûúú;A^=-a^ωe-ωe-a^éëêêùûúú;B^=b^00b^éëêêùûúú;161第9期张㊀懿等:新型模型参考自适应的PMSM无差拍电流预测控制C ^=0-ωe ψf b ^éëêêùûúú㊂将式(25)减去式(27)得p e =Ae +ΔAI ^+ΔBU +ΔC ㊂(28)式中:e =I -I ^=e d e q éëêêùûúú=i d -i ^d i q -i^q éëêêùûúú;ΔA =A -A ^;ΔB =B -B ^;ΔC =C -C ^㊂令F =-(ΔAI ^+ΔBU +ΔC ),式(28)改写为p e =Ae -F ㊂(29)根据上述的Popov 稳定性定理,要想使反馈系统保持稳定,则需满足:∀t 1>0,η(0,t 1)=ʏt 1e TF d t ȡ-γ2㊂(30)将F =-(ΔAI ^+ΔBU +ΔC )代入式(30)得:∀t 1>0,η(0,t 1)=-ʏt 1e T (ΔAI ^+ΔBU +ΔC )d t ȡ-γ2㊂(31)将式(31)拆成如下两部分:η1=ʏt0(a -a ^)[e d i ^d+e q i ^q ]d t ȡ-γ23;η2=ʏt 0(b ^-b )[e dud+e q (u q -ωe ψf )]d t ȡ-γ24㊂üþýïïïï(32)式中γ23和γ24是有限正数,且γ2=γ23+γ24㊂显然式(32)成立即式(31)同样成立,从而设计参数自适应律,表达式为:a ^=R ^sL ^=ʏt0g 1(τ)d τ+g 2(t )+R ^sL^(0);b ^=1L ^=ʏt0f 1(τ)d τ+f 2(t )+1L ^(0)㊂üþýïïïï(33)式中R ^s L^(0)和1L^(0)均为所辨识参数的初始值㊂其余计算过程与上文一致,此处不再推导,最终得到待辨识的参数自适应律为:R ^sL^=-k ᶄis+k ᶄp ()[(i d -i ^d )i ^d +(i q -i ^q )i ^q ]+R ^s L^(0);1L ^=k ᵡi s +k ᵡp()[(i d -i ^d )u d +(i q -i ^q )u q -(i q -i ^q )ωe ψf ]+1L ^(0)㊂üþýïïïïïïïïïï(34)式中k ᶄp ,k ᶄi ,k ᵡp ,k ᵡi 均大于0㊂由式(34)可推导并化简后得出定子电阻和定子电感的自适应律为:R ^s =-k ᶄi s +k ᶄp ()[(i d -i ^d )i ^d +(i q -i ^q )i ^q ]+R ^s L^(0)k ᵡi s +k ᵡp ()[(i d -i ^d )u d +(i q -i ^q )u q -(i q -i ^q )ωe ψf ]+1L^(0);L ^=1k ᵡi s +k ᵡp ()[(i d -i ^d )u d +(i q -i ^q )u q -(i q -i ^q )ωe ψf ]+1L^(0)㊂üþýïïïïïïïï(35)㊀㊀因此,通过式(23)和式(35)辨识过程完全稳定后,则可得到定子电阻㊁定子电感和转子磁链的辨识值,该辨识值就是式(7)中定子电阻实际值R s0㊁定子电感实际值L 0和转子磁链实际值ψf0㊂4㊀实验结果及分析本文研究重点在于电机参数失配对无差拍电流预测算法的性能影响及如何进行改进㊂针对提出新型模型参考自适应系统的参数分步辨识来改进无差拍电流预测控制,通过实验的方法来验证其有效性㊂本文采用i d =0的矢量控制,图4为改进后的无差拍电流预测控制系统结构框图㊂4.1㊀实验平台搭建本次实验使用意法半导体ST 公司的STM32F417作为电机控制器的主控芯片,6个半桥臂采用安世半导体nexperia 的BUK9M35-80E,实验用400W 的表贴式永磁同步电机,其参数如表1所示,本次实验平台搭建如图5所示㊂实验过程分为三个阶段,首先进行无差拍电流预测控制器参数和电机参数不匹配的性能实验,观察电机参数失配对性能的影响;其次进行新型模型参考自适应系统的参数分步辨识实验,观察基于该方法下的参数精度;最后将新型模型参考自适应辨识好的参数给入无差拍电流预测控制进行实验,与电机参数同时失配的性能影响进行对比,得出改进后的结论㊂261电㊀机㊀与㊀控㊀制㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第27卷㊀图4㊀改进后的无差拍电流预测控制系统结构框图Fig.4㊀Structure block diagram of improved DPCC system表1㊀电机参数表Table 1㊀Motor parameters㊀㊀参数数值额定功率/W 400定子电阻/Ω0.15定子电感/mH 10.2转子磁链/Wb 0.25额定转矩/(N㊃m) 1.6极对数5额定转速/(r /min)2500图5㊀实验平台搭建Fig.5㊀Construction of experimental platform4.2㊀验证电机参数失配对无差拍电流预测控制的性能影响4.2.1㊀转子磁链单独失配的影响图6为转子磁链在0.5倍和1.5倍失配下d -q 轴电流启动响应波形㊂图6㊀转子磁链失配下d -q 轴电流启动响应波形Fig.6㊀d -q axis current start response waveform un-der rotor flux linkage mismatch实验条件给定2500r /min 的转速启动运行,其中图6(a)为ψf =0.5ψf0的d -q 轴电流启动响应波形,可以看出,由于转子磁链只和q 轴电流有关,所以对q 轴电流的影响比较大,实际电流i q 在稳态过程中出现了明显的跟踪静差㊂其中图6(b)为ψf =1.5ψf0的d -q 轴电流启动响应波形,其实验结果与361第9期张㊀懿等:新型模型参考自适应的PMSM 无差拍电流预测控制图6(a)相反,实际电流i q 在稳态过程中出现了一定的跟踪静差,实际电流i q 无法跟踪给定电流i ∗q ㊂由上述实验结果可知,转子磁链失配对d 轴电流没有实际影响,但会使q 轴电流出现跟踪静差,导致电流动态跟踪性能变差,对系统的鲁棒性存在一定的影响㊂4.2.2㊀定子电感单独失配的影响图7为定子电感在0.5倍和1.5倍失配下d -q 轴电流启动响应波形㊂实验条件给定2500r /min 的转速启动运行,其中图7(a)为L =0.5L 0的d -q 轴电流启动响应波形,可以看出,实际电流i q 跟踪给定电流i ∗q 的效果略微变差,实际电流i d 在稳态过程中出现了跟踪静差㊂其中图7(b)为L =1.5L 0的d -q 轴电流启动响应波形,实际电流i d 在稳态过程中也出现了跟踪静差㊂由上述实验结果可知,定子电感失配会略微弱化q 轴电流的动态跟踪性,对d 轴电流影响较大,同时对鲁棒性造成了一定的影响㊂图7㊀定子电感失配下d -q 轴电流启动响应波形Fig.7㊀d -q axis current start response waveform un-der stator inductance mismatch4.2.3㊀定子电阻单独失配的影响图8为定子电阻在0.5倍和1.5倍失配下d -q 轴电流启动响应波形㊂实验条件给定2500r /min 的转速启动运行,其中图8(a)为R s =0.5R s0的d -q 轴电流启动响应波形,可以看出,给定电流i ∗q 在稳态过程中略大于实际电流i q ㊂其中图8(b)为R s =1.5R s0的d -q 轴电流启动响应波形,其实验结果与图8(a)相反㊂由上述实验结果可知,定子电阻失配对系统的影响不大,动态跟踪性一般㊂图8㊀定子电阻失配下d -q 轴电流启动响应波形Fig.8㊀d -q axis current start response waveform un-der single stator resistance mismatch4.2.4㊀电机参数同时失配的影响图9为电机参数在0.5倍和1.5倍同时失配下d -q 轴电流启动响应波形,其中电机参数分别为转子磁链,定子电感和定子电阻㊂实验条件给定2500r /min 的转速启动运行,其中图9(a)为R s0=0.5R s ,ψf0=0.5ψf ,L =0.5L 0同时失配下的d -q轴电流启动响应波形,通过与图6(b)㊁图7(a)㊁图8(b)相比,实际电流i q 在稳态过程中产生了更大的跟踪静差,实际电流i d 在稳态过程中产生了一定的跟踪静差,实际电流i q 的动态跟踪性更差㊂其中图9(b)为R s0=1.5R s ,ψf0=1.5ψf ,L =1.5L 0同时失配下的d -q 轴电流启动响应波形,通过与图6(a)㊁图7(b)㊁图8(a)相比,实际电流i q 在稳态过程中产生了更大的跟踪静差,实际电流i d 在稳态过程中产生了一定的跟踪静差,实际电流i q 的动态跟踪性更差㊂由上述实验结果可知,电机参数同时461电㊀机㊀与㊀控㊀制㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第27卷㊀失配会对动态跟踪性和鲁棒性造成严重影响㊂图9㊀电机参数同时失配d -q 轴电流启动响应波形Fig.9㊀d -q axis current start response waveform un-der simultaneous motor parameters mismatch4.3㊀验证基于新型模型参考自适应的参数分步辨识精度㊀㊀图10为新型模型参考自适应的参数分步辨识波形,表2为辨识结果总结㊂实验条件给定2500r /min 的转速启动运行,由图10和表2可知,由于电机起步阶段的不稳定性,导致辨识的电机参数发生了一定的超调,但是经过调节后迅速趋于稳定㊂其中图10(a)为转子磁链辨识波形,可知转子磁链在30ms 左右开始辨识,辨识结果经过1.5ms 左右的调节时间收敛于0.25Wb 左右,得到的最大误差为3.2%㊂其中图10(b)为定子电阻和电感同时参数辨识波形,可知定子电感和电阻同时在42ms 左右开始辨识,定子电感辨识结果经过2ms 左右的调节时间收敛于10.2mH 左右,得到的最大误差为2.3%,定子电阻辨识结果经过2.7ms 左右的调节时间收敛于0.15Ω左右,得到的最大误差为2.5%㊂由上述实验结果可知,基于新型模型参考自适应的参数分步辨识算法可以在较短时间内收敛到参数给定值附近,并且最大误差很小,达到了很好的参数辨识效果㊂图10㊀新型模型参考自适应的参数分步辨识波形Fig.10㊀Parameter stepwise identification of newMRAS waveform表2㊀辨识结果总结Table 2㊀Identification result summary参数给定值浮动范围最大误差/%转子磁链0.25Wb 0.242~0.257Wb 3.2定子电感10.2mH 9.958~10.445mH 2.3定子电阻0.15Ω0.1463~0.1526Ω2.54.4㊀验证基于参数分步辨识算法下的无差拍电流预测控制性能㊀㊀图11为参数分步辨识算法下的无差拍电流预测控制波形㊂实验给定2500r /min 的转速并且带载1N ㊃m 启动,待转速稳定后突加负载至1.3N㊃m,待转速稳定后再突减负载至1N㊃m,其中图11(a)为d -q 轴电流启动响应波形,通过与图9的电机参数同时失配情况相比,可以看出,实际电流i q 能够很好地跟上给定电流i ∗q ,并且基本无静差,实际电流i d 无明显波动,一直稳定在0左右㊂其中图11(b)㊁图11(c)为突加负载和突减负载的转速和q 轴电流响应波形,可以看出,在突加或突减负载的时刻,转速有大约20r /min 左右的上下波动,但是经过25ms 左右的调节后恢复正常,实际电流i q 由于突加或突减负载上升或下降了1.2A 左右,561第9期张㊀懿等:新型模型参考自适应的PMSM 无差拍电流预测控制但是经过22ms 左右的调节后也立马稳定下来,可以看出,实际电流i q 有很好的负载突变响应和抗干扰能力㊂由上述实验结果可知,将参数分步辨识加入无差拍电流预测控制中,d -q 轴电流的跟踪静差减小,动态跟踪性能提升,并且在负载突变下,系统的鲁棒性加强,可以有效地抑制参数失配带来的影响㊂图11㊀参数分步辨识下的无差拍电流预测控制波形Fig.11㊀DPCC waveform under parameter stepwiseidentification本文的实验数据仅限于此次实验搭建的平台,而本次实验电机参数辨识开始时的超调如何减小,有待进一步研究与分析㊂5㊀结㊀论以400W 的表贴式永磁同步电机为研究对象,本文针对参数失配会导致无差拍电流预测控制的动态跟踪性和鲁棒性差的问题,提出一种基于新型模型参考自适应系统的参数分步辨识来进行改进,通过实验验证分析可以得到以下结论:1)电机参数失配会对无差拍电流预测控制产生一定的影响,包括:动态跟踪效果差㊁跟踪静差大和鲁棒性差,为后面进行改进提供了实验依据;2)通过新型模型参考自适应系统设计出参数分步辨识法,经过相关实验验证出此方法的辨识结果精度高;3)将上述得到的参数辨识结果给入设计好的无差拍电流预测控制中,可以有效地抑制参数失配带来的影响,减小了跟踪静差,提高了系统的动态跟踪效果,同时增强了系统在负载突变下的鲁棒性㊂实验结论表明,基于新型模型参考自适应系统的无差拍电流预测控制具有一定的实用性,但是本文实验中参数辨识开始时的超调如何减小,有待进一步探究㊂参考文献:[1]㊀吴迪,王影,周渊深,等.模型预测控制在永磁同步电机系统中的应用综述[J].防爆电机,2021,56(6):1.WU Di,WANG Ying,ZHOU Yuanshen,et al.Application over-view of model prediction control in PMSM system[J].Explosion-Proof Electric Machine,2021,56(6):1.[2]㊀LI Xuerong,WANG Yang,GUO Xingzhong,et al.An 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coloc abf要求的格式-范文模板及概述示例1:Coloc ABF (Alcohol Beverage and Food) 是一种要求特定格式的制度，旨在规范餐厅、酒吧和饮食场所的布局和组织。

这一制度的实施对于提升顾客体验、保证饮食业的安全性和卫生标准非常重要。

在这篇文章中，我们将讨论Coloc ABF要求的格式，并探讨其对餐饮业的影响。

首先，Coloc ABF要求的格式涉及到餐厅或饮食场所的布局。

根据要求，餐厅的布局应该合理、舒适且安全，以确保员工和顾客在其中能够顺利移动。

这意味着餐桌、座位和服务区域的设置必须符合一定的标准和规定。

此外，Coloc ABF还要求在紧急情况下能够便捷地疏散人员，这就要求餐厅应该设有适当的紧急出口和安全设施。

其次，Coloc ABF要求的格式还包括餐厅的装修和设施。

根据这一制度，餐厅的装修应该符合卫生、安全和舒适的标准，并且易于清洁和维护。

墙壁、地板和天花板等表面应该是光滑的且不易积聚灰尘和污垢。

此外，餐厅应该安装适当的照明和通风系统，确保室内空气的流通和光线的充足。

最后，Coloc ABF要求的格式还与设备和设施配备有关。

根据要求，餐厅应该配备先进的厨房设备和工具，以确保食物的质量和卫生。

此外，对于饮酒场所，Coloc ABF还要求酒吧区域的设施符合相关法规和规定，包括设置适当的酒精饮品展示、保持充足的酒精库存和配备专业的酒保人员等。

总的来说，Coloc ABF要求的格式在餐饮业中起到了至关重要的作用。

它不仅提升了顾客的体验，也保证了饮食场所的卫生和安全。

遵守这一制度可以使餐厅或饮食场所在竞争激烈的餐饮市场中脱颖而出，赢得更多的顾客信任和口碑。

因此，餐厅经营者应该认真对待Coloc ABF要求的格式，并不断更新和改进自己的设施和布局，以满足顾客的需求和期望。

示例2:撰写一篇文章时，遵循CoLoc ABF的格式要求是非常重要的。

CoLoc ABF是指一种共同居住协议书的格式，它用于规范和记录租赁房屋时的租约条款和注意事项。

自适应显式互补滤波在六旋翼飞行器中的应用刘洲;单修洋;谭芳【摘要】针对六旋翼飞行器的惯性传感器在测量过程中存在漂移的问题,提出了基于自适应显式互补滤波的姿态解算算法,并对该算法的原理和稳定性进行分析;搭建了六旋翼飞行器的实验测试装置,并进行机体的动、静态测试实验.在实验中,对自适应显式互补滤波算法、显式互补滤波算法以及陀螺仪传感器测量方法进行比较.实验结果表明:自适应显式互补滤波算法能够实现惯性传感器的解算姿态角误差收敛,且动态误差最小.%To solve the drift problem of inertial sensor of six-rotor aircraft during the measurement process,a attitude estimation algorithm based on adaptive explicit complementary filtering(AECF) is proposed.The principle and stability of the proposed algorithm are analyzed.A six-rotor aircraft experimental test device is set up to carry out static and dynamic experiment of the aircraft.Adaptive explicit complementary filtering algorithm,explicit complementary filtering algorithm and gyroscope sensor measurement are compared in the experiment.The experimental results show that the adaptive explicit complementary filtering algorithm can make the solution attitude error of sensor gradually converge and its dynamic error is the smallest.【期刊名称】《传感器与微系统》【年(卷),期】2017(036)005【总页数】4页(P157-160)【关键词】自适应显式互补滤波;六旋翼飞行器;姿态解算;惯性传感器;陀螺仪【作者】刘洲;单修洋;谭芳【作者单位】中南大学机电工程学院,湖南长沙410083;中南大学机电工程学院,湖南长沙410083;中南大学机电工程学院,湖南长沙410083【正文语种】中文【中图分类】V249六旋翼飞行器惯性测量单元IMU使用的是微机电系统(micro-electro-mechanical system,MEMS)类型传感器。

外、热红外光谱特征，大大提高了地物的分类和识别能力，在农业、林业、海洋、气象、地质、全球环境及军事遥感等诸多领域显示出巨大的应用前景。

目前，已有许多国家相继研制出或正在研制各具特色的成像光谱仪，数量达四十种之多［３－６１。

从第一代ＡＩＳ的３２个连续波段，到第二代高光谱成像仪。

航空可见光、红外光成像光谱仪（ＡＶＩＲＩＳ）的２２４个波段，光谱分辨率在不断提高，ＡＶＲＩＳ是首次测量全反射波长范围（Ｏ．４～２．５ｒｕｎ）的成像光谱仪。

美国宇航局在１９９９年底发射的中等分辨率成像光谱仪（ＭＯＤＩＳ）和高分辨率成像光谱仪（ＨＩＲｊＳ）为人类提供了更多信息。

２００１年发射的ＯｒｂＶｉｅｗ卫星能够同时提供更高空间分辨率和光谱分辨率的数据，它能获取】ｍ全色波段影像和４ｍ～５ｍ的多光谱波段以及空间分辨率为８ｍ的２００个波段的高光谱数据。

此外，许多具有高空间分辨率和高光谱分辨率的成像光谱仪正在或即将进入实用阶段，例如：美国的ＨＹＤＩＣＥ、ＳＥＢＡＳ，加拿大的ＦＬＩ、ＣＡＳＩ和ＳＦＳＩ，德国的ＲＯＳＩＳ以及澳大利亚的ＨＹＭＡＰ等。

这些传感器有的已经进入了商业运营，技术比较成熟。

特别是美国的ＨＹＤＩＣＥ和ＡＶＩＲＩＳ多次参与军方的实验，提供了大量的军事应用的第一手资料。

图ｌ—ｌ高光谱图像数据立方体示意我国在这一领域的发展也十分迅速。

中科院上海技术物理研究所于１９９７年开始研制２４４波段的推扫式（ＰＨＩ）和１２８波段的可见光／近红外、短波红外、热红外模块化成像光谱仪系统（ＯＭＩＳ）并取得了成功，特别是ＯＭＩＳ已经成功转入商业运营。

另外，中科院长春光学精密机械与物理研究所、西安光学精密机械研究所也在这一领域取得了重要的研究成果。

高光谱数据除了拥有图像数据的几何信息外，还具有光谱信息，从而构成三维的图像立方体。

如图１．１，光谱维信息可以记录地物所具有的反射、吸收和发射电磁能量的能力，这种能力是由物质的分子和原子结构确定，不同的地物类型对应于不同的谱特征，这就是光谱的“指纹效应”，如图１．２。