第9章 汽车四轮转向控制系统的仿真 [基于MATLAB的控制系统仿真及应用]
实验报告基于Matlab的控制系统仿真1
实验一 基于Matlab 的控制系统模型姓名 学号 班级机械一、实验目的1) 熟悉Matlab 的使用环境，学习Matlab 软件的使用方法和简单编程方法。
2) 学习使用Matlab 软件进行拉氏变换和拉式反变换的方法。
3) 学习使用Matlab 软件建立、转换连续系统数学模型的方法。
4) 学习使用Matlab 软件分析控制系统稳定性的方法。
二、实验原理1. 拉氏变换和反拉氏变换(1) 拉氏变换syms a w tf1=exp(-a*t)laplace(f1)f2=2laplace(f2)f3=t*exp(-a*t)laplace(f3)f4=sin(w*t)laplace(f4)f5=exp(-a*t)*cos(w*t)laplace t-t (f5)(2) 拉氏反变换syms s a wf 1=1/silaplace(f 1)f 2=1/(s+a)ilaplace(f 2)f 3=1/s^2ilaplace(f 3)f 4=w/(s^2+w^2)ilaplace(f 4)f 5=1/(s*(s+2)^2*(s+3))ilaplace(f 5)…2. 控制系统模型的建立和转化传递函数模型：112m 112+()+m m n n nb s b s b num G s den a s a s b --++==++…… 零极点增益模型：1212()()()()()()()m n s z s z s z G s k s p s p s p ---=--- (1) 建立系统传递函数模型22(1)()(2)(3)56s s s s G s s s s s ++==++++ num=[1,1,0]den=[1,5,6]Gs1=tf(num,den)(2) 建立系统的零极点模型z=[0,-1]p=[-2,-3]k=[1]Gs1=zpk(z,p,k)(3) 传递函数模型转化为零极点模型num=[1,1,0]den=[1,5,6]Gs1=tf(num,den)[z,p,k]=tf2zp(num,den)Gs2=zpk(z,p,k)(4) 零极点模型转化为传递函数模型z=[0,-1]p=[-2,-3]k=[1]Gs1=zpk(z,p,k)[num,den]=zp2tf(z',p',k)Gs2=tf(num,den)3. 用Matlab 进行传递函数部分分式展开5434321139+52s+26()1035+50s+241 2.530.5 1s+4s+3s+2s+1num s s s G s den s s s ++==++-=++++num=[1 11 39 52 26]den=[1 10 35 50 24][r,p,k]=residue(num,den)4. 连续系统稳定性分析已知传递函数，试求该系统的闭环极点并判断系统的稳定性。
电动汽车论文：四轮独立转向四轮独立驱动目标函数仿真分析MATLAB
电动汽车论文：四轮独立转向四轮独立驱动目标函数仿真分析MATLAB【提示】本文仅提供摘要、关键词、篇名、目录等题录内容。
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【摘要】车辆的操纵稳定性是评价车辆主动安全性能重要指标之一，对于如何评价车辆稳定性能，是研究车辆安全性能一个非常重要的课题。
四轮独立转向系统车辆能够很好的改善汽车横向动力学特性，本课题的研究是基于四轮独立转向系统控制策略下的操纵动力学特性，对四轮独立转向电动汽车仿真进行了分析和研究。
首先，介绍了燕山大学独立开发设计的四轮独立驱动四轮独立转向(4WID-4WIS)电动汽车硬件结构以及控制系统组成，在此车辆基础上建立整车二自由度动力学线性模型，应用Matlab软件对此线性模型进行离散化处理，得到相应矩阵参数，建立不同速度的离散化模型，为下文控制器模型设计打下基础。
其次，对整车控制器进行设计。
建立不同速度模型下离散模型目标函数，应用Fmincon函数建立控制器优化函数，通过仿真试验验证，确定横摆角速度和质心侧偏角参数最佳组合。
最后，通过仿真实验验证控制器模型正确性。
在Matlab/Simulink模块中建立整车仿真模型，对低速、中高速下直线工况、加减速工况及转向工况分别进行仿真研究，分析车辆质心侧偏角和横摆角速度响应特性变化规律，同时得出车轮转角和车轮纵向力曲线。
仿真试验结果表明，对于四轮独立转向电动车，本文所设计控制器能够很好地改善其操纵稳定性，验证了控制器正确性。
【关键词】电动汽车；四轮独立转向；四轮独立驱动；目标函数；仿真分析；MATLAB；【篇名】四轮独立转向电动汽车的转向控制仿真研究【目录】四轮独立转向电动汽车的转向控制仿真研究摘要5-6Abstract6第1章绪论9-14 1.1 课题背景及研究意义9-11 1.1.1 电动汽车9-10 1.1.2 四轮独立转向技术10-11 1.1.3 动力学仿真技术11 1.2 国内外研究现状11-13 1.2.1 国外研究现状11-12 1.2.2 国内研究现状12-13 1.3 主要研究工作13-14 1.3.1 技术路线13 1.3.2 本文主要研究内容13-14第2章硬件介绍及建立车辆动力学模型14-26 2.1 硬件介绍14-18 2.1.1 硬件介绍14-17 2.1.2 四轮独立转向控制系统17-18 2.2 建立 4WIS 二自由度动力学模型18-25 2.2.1 轮胎数学模型18-19 2.2.2 四轮独立转向线性动力学模型19-22 2.2.3 可控性和可观测性22-23 2.2.4 连续模型离散化23-25 2.3 本章小结25-26第3章控制器设计26-44 3.1 控制策略研究26-28 3.1.1 传统四轮转向汽车控制系统26-27 3.1.2 四轮独立转向控制思想27-28 3.1.3 整车控制框图28 3.2 控制器设计28-34 3.2.1 问题提出28-30 3.2.2 确定目标函数30-33 3.2.3 Fmincon 函数介绍33-34 3.3 软件介绍及确定参数34-43 3.3.1 Matlab 软件简介34 3.3.2 确定参数C1 和C34-39 3.3.3 确定参数α1 和α239-43 3.4 本章小结43-44第4章仿真试验结果及分析44-59 4.1 建立仿真系统模型44-45 4.2 仿真及分析45-57 4.2.1 直线行驶工况分析45-51 4.2.2 转向工况分析51-53 4.2.3 加速工况分析53-55 4.2.4 减速工况分析55-57 4.3 仿真试验结论57-58 4.4 本章小结58-59结论59-60参考文献60-63攻读硕士学位期间承担的科研任务与主要成果63-64致谢64-65作者简介65（英文版）Two regulations promulgated for implementation is in the party in power for a long time and the rule of law conditions, the implementation of comprehensive strictly strategic plan, implementation in accordance with the rules and discipline to manage the party, strengthen inner-party supervision of major initiatives. The two regulations supporting each other, the < code > adhere to a positive advocate, focusing on morality is of Party members and Party leading cadres can see, enough to get a high standard; < rule > around the party discipline, disciplinary ruler requirements, listed as "negative list, focusing on vertical gauge, draw the party organizations and Party members do not touch the" bottom line ". Here, the main from four square face two party rules of interpretation: the first part introduces two party Revised regulations the necessity and the revision process; the second part is the interpretation of the two fundamental principles of the revision of laws and regulations in the party; the third part introduces two party regulations modified the main changes and needs to grasp several key problems; the fourth part on how to grasp the implementation of the two regulations of the party. < code > and < Regulations > revised the necessity and revisedhistory of the CPC Central Committee the amendment to the Chinese Communist Party members and leading cadres honest politics several guidelines > and < Chinese Communist Party discipline and Punishment Regulations > column 1 by 2015 to strengthen party laws and regulations focus. Two party regulations revision work lasted a Years, pooling the wisdom of the whole party, ideological consensus, draw historical experience, respect for the wisdom of our predecessors, which reflects the unity of inheritance and innovation; follow the correct direction, grasp the limited goals, adhere to the party's leadership, to solve the masses of the people reflect a focus on the problem. The new revision of the < code > and < rule >, reflects the party's 18 and the eighth session of the third, the spirit of the fourth plenary session, reflecting the experience of studying and implementing the General Secretary Xi Jinping series of important speech, reflects the party's eighteen years comprehensive strictly practice. (a) revised two regulations of the party need of < the ICAC guidelines > in < in 1997 Leaders as members of the Communist Party of China clean politics certain criteria (Trial) > based on revised, the promulgation and implementation of January 2010, to strengthen the construction of the contingent of leading cadres play animportant role. But with the party to manage the party strictly administering the deepening, has not been able to fully meet the actual needs. Content is too complicated, "eight prohibition, 52 are not allowed to" hard to remember, and also difficult to put into practice; the second is concisely positive advocated by the lack of prohibited provisions excessive, no autonomy requirements; the third is banned terms and discipline law, both with the party discipline, disciplinary regulations repeat and Criminal law and other laws and regulations repeat; the fourth is to "clean" the theme is not prominent, not for the existing problems, and is narrow, only needle of county-level leading cadres above. < rule > is in 1997 < Chinese Communist Party disciplinary cases (Trial) > based on revision, in December 2003 the promulgation and implementation, to strengthen the construction of the party play very important role. Along with the development of the situation, which many provisions have been unable to fully meet the comprehensive strictly administering the practice needs. One is Ji law, more than half of the provisions and criminal law and other countries laws and regulations Repetition; two is the political discipline regulations is not prominent, not specific, for violation of the party constitution, damage theauthority of Party Constitution of misconduct lack necessary and serious responsibility to pursue; third is the main discipline for the leading cadres, does not cover all Party members. Based on the above situation, need to < the criterion of a clean and honest administration > and < rule > the two is likely to be more relevant regulations first amendment. By revising, really put the authority of Party discipline, the seriousness in the party tree and call up the majority of Party members and cadres of the party constitution of party compasses party consciousness. (II) two party regulations revision process the Central Committee of the Communist Party of China attaches great importance to two regulations revision . Xi Jinping, general books recorded in the Fifth Plenary Session of the eighth session of the Central Commission for Discipline Inspection, on the revised regulations < > made clear instructions. According to the central deployment, the Central Commission for Discipline Inspection from 2014 under six months begin study two regulations revision. The Standing Committee of the Central Commission for Discipline Inspection 4 review revised. Comrade Wang Qishan 14 times held a special meeting to study two regulations revision, amendment clarifies the direction, major issues of principle, path and target,respectively held a forum will listen to part of the province (area) secretary of the Party committee, Secretary of the Discipline Inspection Commission, part of the central ministries and state organs DepartmentThe first party committee is mainly responsible for people, views of experts and scholars and grassroots party organizations and Party members. Approved by the Central Committee of the Communist Party of China, on 7 September 2015, the general office of the Central Committee of the Party issued a notice to solicit the provinces (autonomous regions, municipalities) Party, the central ministries and commissions, state ministries and commissions of the Party (party), the General Political Department of the military, every 3 people organization of Party of two regulations revision opinion. Central Commission for Discipline Inspection of extensive solicitation of opinions, careful study, attracting, formed a revised sent reviewers. In October 8 and October 12, Central Committee Political Bureau Standing Committee and the Political Bureau of the Central Committee After consideration of the two regulations revised draft. On October 18, the Central Committee of the Communist Party of China formally issued two regulations. Can say, two laws amendment concentrated thewisdom of the whole party, embodies the party. Second, < code > and < Regulations > revision of the basic principles of two party regulations revision work and implement the party's eighteen, ten eight plenary, the spirit of the Fourth Plenary Session of the Eleventh Central Committee and General Secretary Xi Jinping important instructions on the revised < low political criterion > and < Regulations >, highlighting the ruling party characteristics, serious discipline, the discipline quite in front of the law, based on the current, a long-term, advance as a whole, with Bu Xiuding independent < rule > and < rule >. Main principle is: first, adhere to the party constitution to follow. The constitution about discipline and self-discipline required specific, awaken the party constitution of party compasses party consciousness, maintaining the authority of the constitution. General Secretary Xi Jinping pointed out that "no rules, no side round. Party constitution is the fundamental law, the party must follow the general rules. In early 2015 held the eighth session of the Central Commission for Discipline Inspection Fifth Plenary Session of the 16th Central Committee, Xi Jinping again pointed out that constitution is the party must follow the general rules, but also the general rules." the revision of the< code > and < rule > is Method in adhere to the regulations established for the purpose of combining rule of virtue is to adhere to the party constitution as a fundamental to follow, the constitution authority set up, wake up the party constitution and party rules the sense of discipline, the party constitution about discipline and self-discipline specific requirements. 4 second is to adhere to in accordance with the regulations governing the party and the party. The Party of rule of virtue "de", mainly refers to the party's ideals and beliefs, excellent traditional style. The revised the < code > closely linked to the "self-discipline", insisting on the positive initiative, for all members, highlight the "vital few", emphasized self-discipline, focusing on the morality, and the majority of Party members and the ideological and moral standards. The revised < > Ji method separately, Ji, Ji Yan to Method, as a "negative list", emphasizing the heteronomy, focusing on vertical gauge. Is this one high and one low, a positive reaction, the strict party discipline and practice results transformation for the integration of the whole party to observe moral and discipline requirements, for the majority of Party members and cadres provides benchmarking and ruler. Third, insist on to. In view of the problems existing in theparty at the present stage, the main problems of Party members and cadres in the aspect of self-discipline and abide by the discipline to make clearly defined, especially the party's eighteen years strict political discipline and political rules, organization and discipline and to implement the central eight provisions of the spirit against the four winds and other requirements into Disciplinary provisions. Not one pace reachs the designated position, focusing on in line with reality, pragmatic and effective. After the revision of major changes, major changes in the < code > and < rule > modified and needs to grasp several key problems (a) < code > < code > adhere to according to regulations governing the party and party with morals in combination, for at the present stage, the leadership of the party members and cadres and Party members in existing main problems of self-discipline, put forward principles, requirements and specifications, showing Communists noble moral pursuit, reflected at all times and in all over the world ethics from high from low 5 common requirements. One is closely linked to the "self-discipline", removal and no direct relation to the provisions of . the second is adhere to a positive advocate, "eight prohibition" 52 are not allowed to "about the content of the" negative list moved into synchronizationamendment < cases >. Three is for all the party members, will apply object from the leadership of the party members and cadres to expand to all Party members, fully embodies the comprehensive strictly required. The fourth is prominent key minority, seize the leadership of the party members and cadres is the key, and put forward higher requirements than the ordinary Party members. Five is to simplify, and strive to achieve concise, easy to understand, easy to remember. The revised < code > is the ruling Party since the first insists on a positive advocate forAll Party members and the self-discipline norms, moral declaration issued to all members of the party and the National People's solemn commitment. > < criterion of a clean and honest administration consists of 4 parts, 18, more than 3600 words. After the revision of the < code >, a total of eight, 281 words, including lead, specification and Party member cadre clean fingered self-discipline norms, etc. Part 3 members low-cost clean and self-discipline, the main contents can be summarized as "four must" "eight code". Lead part, reiterated on ideal and faith, fundamental purpose, the fine traditions and work style, noble sentiments, such as "four must" the principle of requirements, strong tone of self-discipline, The higher request for 6 andsupervised tenet, the foothold in permanent Bao the party's advanced nature and purity, to reflect the revised standards requirements. Members of self-discipline norms around the party members how to correctly treat and deal with the "public and private", "cheap and rot" thrifty and extravagance "bitter music", put forward the "four norms". Party leader cadre clean fingered self-discipline norms for the leadership of the party members and cadres of the "vital few", around the "clean politics", from civil servant of the color, the exercise of power, moral integrity, a good family tradition and other aspects of the leadership of the party members and cadres of the "four norms" < > < norm norm. "The Party member's self-discipline norms" and "party members and leading cadre clean fingered self-discipline norms," a total of eight, collectively referred to as the "eight". "Four must" and "eight" of the content from the party constitution and Party's several generation of leaders, especially Xi Jinping, general secretary of the important discussion, refer to the "three discipline and eight points for attention" statements, and reference some embody the Chinese nation excellent traditional culture essence of epigrams. (2) the revised regulations, the main changes in the revised Regulations > to fully adapt to thestrictly requirements, reflects the according to the regulations governing the law of recognition of deepening, the realization of the discipline construction and Jin Ju. < rule > is party a ruler, members of the basic line and follow. And the majority of Party members and cadres of Party organizations at all levels should adhere to the bottom line of thinking, fear discipline, hold the bottom line, as a preventive measure, to keep the party's advanced nature and purity. 1, respect for the constitution, refinement and discipline. Revised < rule > from comprehensive comb physical constitution began, the party constitution and other regulations of the Party of Party organizations and Party discipline requirements refinement, clearly defined in violation of the party constitution will be in accordance with regulations to give the corresponding disciplinary action. The original 10 categories of misconduct, integration specification for political discipline, discipline, honesty and discipline masses Ji Law and discipline and discipline and other six categories, the content of < rule > real return to Party discipline, for the majority of Party members and listed a "negative list. 7 2, highlighting the political discipline and political rules. > < Regulations according to the stage of the discipline of outstandingperformance, emphasizing political discipline and political rules, organization and discipline, in opposition to the party's leadership and the party's basic theory, basic line, basic program and basic experience, the basic requirement of behavior made prescribed punishment, increase the cliques, against the organization such as violation of the provisions, to ensure that the central government decrees and the Party of centralized and unified. 3, adhere to strict discipline in the law and discipline In front, Ji separated. Revised < Regulations > adhere to the problem oriented, do Ji separated. Any national law existing content, will not repeat the provisions, the total removal of 79 and criminal law, repeat the content of the public security management punishment law, and other laws and regulations. In the general reiterated that party organizations and Party members must conscientiously accept the party's discipline, die van comply with national laws and regulations; at the same time, to investigate violations of Party members and even criminal behavior of Party discipline and responsibility, > < Regulations distinguish five different conditions, with special provisions were made provisions, so as to realize the connection of Party discipline and state law. 4, reflect Wind building and anti-corruptionstruggle of the latest achievements. < rule > the party's eighteen years implement the spirit of the central provisions of the eight, against the requirements of the "four winds" and transformation for disciplinary provisions, reflecting the style construction is always on the road, not a gust of wind. In the fight against corruption out of new problems, increase the trading rights, the use of authority relatives profit and other disciplinary terms. Prominent discipline of the masses, the new against the interests of the masses and ignore the demands of the masses and other disciplinary terms and make provisions of the disposition and the destruction of the party's close ties with the masses.Discipline to protect the party's purpose. 8 of these regulations, a total of three series, Chapter 15, 178, more than 24000 words, after the revision of the regulations a total of 3 series, Chapter 11, 133, 17000 words, divided into "general" and "special provisions" and "Supplementary Provisions" Part 3. Among them, add, delete, modify the provisions of the proportion of up to nearly 90%. 1, the general general is divided into five chapters. The first chapter to the regulations of the guiding ideology, principles and scope of application of the provisions, highlight the strengthening ofthe party constitution consciousness, maintenance the authority of Party Constitution, increase the party organizations and Party members must abide by the party constitution, Yan Centralized centralized, would examine at all levels of the amended provisions implementing and maintaining Party discipline, and consciously accept the party discipline, exemplary compliance with national laws and regulations. The second chapter of discipline concept, disciplinary action types and effects of the regulations, will be a serious warning from the original a year for a year and a half; increase the Party Congress representative, by leaving the party above (including leave probation) punishment, the party organization should be terminated its representative qualification provisions. The third chapter of the disciplinary rules of use prescribed in the discipline rectifying process, non convergence, not close hand classified as severely or heavier punishment. "Discipline straighten "At least eighteen years of five years, these five years is to pay close attention to the provisions of the central eight implementation and anti -" four winds ". The fourth chapter on suspicion of illegal party disciplinary distinguish five different conditions, with special provisions were madeprovisions, to achieve effective convergence of Party and country 9 method. < rule > the provisions of Article 27, Party organizations in the disciplinary review found that party members have committed embezzlement, bribery, dereliction of duty dereliction of duty and other criminal law act is suspected of committing a crime shall give cancel party posts, probation or expelled from the party. The second is < Regulations > Article 28 the provisions of Party organizations in the disciplinary review But found that party members are stipulated in the criminal law, although not involved in a crime shall be investigated for Party discipline and responsibility should be depending on the specific circumstances shall be given a warning until expelled punishment. This situation and a difference is that the former regulation behavior has been suspected of a crime, the feeling is quite strict, and the latter for the behavior not involving crime, only the objective performance of the provisions of the criminal code of behavior, but the plot is a crime to slightly. < Regulations > the 29 provisions, Party organizations in the discipline review found that party members and other illegal behavior, affect the party's image, the damage to the party, the state and the people's interests, we should depend on the situationSeriousness given disciplinary action. The loss of Party members, seriously damaging the party's image of behavior, should be given expelled from the party. At this article is party member is in violation of the criminal law outside the other illegal acts, such as violates the public security administration punishment law, customs law, financial laws and regulations behavior. The fourth is < cases > Article 32 stipulates, minor party members and the circumstances of the crime, the people's Procuratorate shall make a decision not to initiate a prosecution, or the people's court shall make a conviction and exempted from criminal punishment shall be given within the party is removed from his post, probation or expelled from the party. Party members and crime, sheets were fined in accordance with For acts; the principal Ordinance amended the provisions of the preceding paragraph. This is the new content, in order to achieve Ji method effective convergence. Five is < > the thirty third article 10 of the provisions, the Party member due to an intentional crime is sentenced to criminal law (including probation) sheets or additional deprivation of political rights; due to negligence crime and was sentenced to three years or more (excluding three years) a penalty, shall give expelled punishment. Due to negligence crime is convictedand sentenced to three years (including three years) in prison or be sentenced to public surveillance, detention, shall in general be expelled from the party. For the individual may not be expelled from the party, should control Approval. This is followed and retained the original > < Regulations the provisions of punishment party authorization rules and report to a level party organizations. For is "party members with criminal acts, and by the criminal punishment, generally should be expelled from the party". The fifth chapter of probationary Party member of the discipline and discipline after missing members of the treatment and punishment decisions, such as the implementation of the provisions, clear the related party discipline and punishment decision made after, for duties, wages and other relevant alteration formalities for the longest time. 2, sub sub section will the original regulations of10 categories of acts of violation of discipline integration revised into 6 categories, respectively, in violation of the punishments for acts of political discipline "in violation of discipline behavior of punishment" in violation of integrity of disciplinary action points "of violation punishments for acts of mass discipline" "the violation of work discipline, punishment" in violation of discipline of life behaviorpunishment "6 chapters. 3, annex" Supplementary Provisions "clear authority making supplementary provisions of, cases of interpretative organ, as well as regulations implementation time and retroactivity etc.. 11 (3) learning understanding > < regulations needs to grasp several key problems The first problem -- about the violation of political discipline behavior > < new ordinance chapter 6 the political discipline column for the six disciplines, that is the main opposition to Party leadership and the opposition of the basic theory, basic line, basic program and basic experience, basic requirements of misconduct made provisions of the disposition, especially the eighteen since the CPC Central Committee put forward the Yan Mingzheng treatment of discipline and political rules requirements and practical achievements transformation for Discipline article, increase the false debate central policies, cliques, against the organization review, make no discipline of the principle of harmony terms. These are the party's eighteen years in comprehensive strictly Process combined with the practice of rich content. (1) false debate the central policies and undermine the Party of centralized and unified the problem is made in accordance with the provisions of the party constitution. Constitution in general programme requirementsadhere to democratic centralism is one of the requirements of the construction of the party must adhere to the four cardinal. Application of this principle is not only the party the basic organization principle and is also the mass line in party life, it requires that we must fully develop inner-party democracy, respect for the dominant position of Party members, safeguarding the Party member democratic rights, give full play to the enthusiasm and creativity of the party organizations at all levels and Party members, at the same time, also must implement the right concentration, ensure the party's mission < the chaos in unity and concerted action to ensure that the party's decision to get quickly and effectively implementing. The Party Central Committee formulated the major principles and policies, through different channels and ways, fully listen to the party organizations and Party members of the opinions and suggestions, but 12 is some people face to face not to say back blather "" will not say, after the meeting said, "" Taiwan does not say, and nonsense ", in fact, not only disrupt the people thought, some causing serious consequences, the damage to the Party of the centralized and unified, hinder the central policy implementation, but also a serious violation of the democratic system of principles. There is no doubt that shall, inaccordance with the Regulations > 4 Specified in Article 6 to give the appropriate punishment. For did not cause serious consequences, to give criticism and education or the corresponding tissue processing. (2) about the destruction of the party's unity < New Regulations > the forty eighth to fifty second article, to damage Party's unity unified and violation of political discipline, punishment situation made explicit provisions. Article 52 of the new "in the party get round group, gangs seek private gain, cliques, cultivate private forces or through the exchange of interests, for their own to create momentum and other activities to gain political capital, given a serious warning or withdraw from their party posts disposition; if the circumstances are serious, to give Leave a party to observation or expelled from the party. (3) on against the organization review of the provisions of the constitution, party loyalty honesty is party members must comply with the obligations. Members must obey the organization decision, shall not violate the organization decided encounters by asking questions to find organization, rely on the organization, shall not deceive the organization, against the organization. For example, after the investigation does not take the initiative to explain the situation, but to engage in。
基于联合仿真的四轮转向汽车控制策略研究
基于联合仿真的四轮转向汽车控制策略研究冯樱;邓召文;高伟【摘要】基于四轮转向技术和模糊控制理论,提出一种新的四轮转向汽车后轮转角控制策略,即比例前馈加模糊反馈.在ADAMS/car模块中建立四轮转向整车多体动力学模型,并基于Matlab/Simulink依据控制策略设计了四轮转向汽车控制系统,由ADAMS与Matlab的数据接口实现了控制系统与整车动力学模型联合,对四轮转向汽车进行典型行驶工况的联合仿真试验.仿真结果表明:所设计的后轮转角控制器能使车辆很好地跟随理想转向模型,提高了车辆的操纵稳定性.【期刊名称】《重庆交通大学学报（自然科学版）》【年(卷),期】2010(029)006【总页数】5页(P997-1001)【关键词】四轮转向;多体系统动力学;前馈控制;模糊控制;联合仿真【作者】冯樱;邓召文;高伟【作者单位】湖北汽车工业学院,汽车工程系,湖北,十堰,442002;湖北汽车工业学院,汽车工程系,湖北,十堰,442002;湖北汽车工业学院,汽车工程系,湖北,十堰,442002【正文语种】中文【中图分类】U461.3;TP391.9四轮转向(4WS)是汽车工业的高新技术之一，是主动底盘控制技术研究的关键。
4WS汽车通过后轮直接参与对汽车侧向及横摆运动的控制，不仅减少了转向力产生的滞后，而且能独立地控制汽车的运动轨迹与姿态，使汽车的方向角与姿态角重合，改善了车辆高速时的操纵稳定性和低速时的机动灵活性［1］。
目前，4WS所采用的控制策略基本都是基于线性二自由度模型，围绕着使车辆质心的侧偏角为0，以提高侧向稳定性。
但车辆状态和外界干扰的不确定性直接影响控制系统设计，控制性能往往难以达到设计要求［2］。
对4WS控制系统的研究已逐渐从线性向非线性领域过渡。
笔者在ADAMS中建立四轮转向的多刚体整车动力学模型，进行了四轮转向汽车控制策略研究，提出了比例前馈加模糊反馈的后轮转角控制策略，在Matlab/Simulink设计了四轮转向综合控制器，并基于ADAMS和Matlab联合仿真技术进行了仿真试验。
基于MATLAB四轮转向车辆PID控制的建模与仿真
基于MATLAB四轮转向车辆PID控制的建模与仿真
王晨
【期刊名称】《成都大学学报（自然科学版）》
【年(卷),期】2015(034)004
【摘要】以二自由度整车操纵稳定性研究为基础,建立车身零侧偏角的前馈控制策略对四轮转向车辆实施控制.在NATLAB中建立前轮转向、四轮转向车辆模型,并在角阶跃工况下进行仿真,发现其存在横摆角速度损失的缺陷,提出PID车身横摆角补偿控制策略,通过建模在角阶跃工况下仿真.结果表明:横摆角速度补偿控制策略可较好地解决车辆转向灵敏度的问题.
【总页数】4页(P404-407)
【作者】王晨
【作者单位】成都高原汽车工业有限公司,四川成都610100
【正文语种】中文
【中图分类】U463.4;TP391.92
【相关文献】
1.基于MATLAB的空调系统专家PID控制的建模与仿真 [J], 曹国庆;涂光备;安大伟;娄承芝
2.基于Matlab的无刷直流电机Fuzzy-PID控制研究及其建模仿真 [J], 丁鹏;姚平喜
3.基于模糊PID控制的交流励磁调节系统的MATLAB建模与仿真 [J], 岳夕彪;杨润生
4.基于Matlab的四轮转向车辆操纵稳定性仿真研究 [J], 王辉;喻凡
5.基于Matlab/Simulink的四轮转向车辆操纵稳定性仿真 [J], 吕红明;陈南
因版权原因，仅展示原文概要，查看原文内容请购买。
基于Matlab_Simulink和神经网络的四轮转向车辆控制研究
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基于 Matlab/Simulink 和神经网络的四轮转向车辆控制研究
四轮转向的车辆在低速时，在后轮上附加一个与前轮转角相反的转角，可 以减小车辆的转弯半径。 由阿克曼 （Ackerman） 转向模型即可得出这样的结论[3]， 即当前轮转角相同时，四轮转向车辆的转弯半径明显小于前轮转向车辆，使车 辆在低速转弯时更加灵活[4-8]。
Key words: 4WS， Nonlinear Tire， Neural Network， Handling and Stability， Simulation Analysis
基于 Matlab/Simulink 和神经网络的四轮转向车辆控制研究
第一章 绪论
1.1 四轮转向原理简介
随着汽车工业的不断发展，改善车辆的操纵稳定性，使驾乘更加舒适和安 全，是现今汽车技术的一个重要发展方向[1]。作为提高车辆操纵稳定性、主动安 全性的四轮转向技术在这种背景下应运而生，并得到了很大的发展。 四轮转向技术能使车辆在转弯时后轮直接参与对车辆侧偏角和侧向运动的 控制，不仅可以减少转向力产生的滞后，而且还能独立地控制车辆的运动轨迹 与姿态[2]。图 1.1 所示为两轮转向与四轮转向的对比[2]，其中(a)和(b)为前轮转向 情况，(c)和(d)为四轮转向情况。由图可见，四轮转向车辆的姿态得以控制，车 辆的方向角与航向角重合，提高了车辆的侧向稳定性。
基于ADAMS／MATLAB的车辆转向操控系统仿真研究
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基于MatlabSimulink的四轮转向汽车操纵动力学仿真分析
武汉理工大学课程论文基于Matlab/Simulink的四轮转向汽车操纵动力学仿真分析课程：汽车动力学学院（系）：汽车工程学院专业班级：汽研学号：学生姓名：任课教师：乔维高基于Matlab/Simulink 的四轮转向汽车操纵动力学仿真分析摘要：本文分析了四轮转向(4WS)汽车的运动特性，建立了三自由度四轮转向汽车动力学模型，并基于Matlab /Simulink 对四轮转向汽车的操纵动力学进行仿真分析，结果表明四轮转向汽车的操纵性能要优于前轮转向汽车。
关键词：汽车，四轮转向，操纵动力学，仿真分析Simulation for the Handling Dynamics of Four-wheelSteering Vehicle Based on Matlab/SimulinkAbstract:Inthispaper,themotioncharacteristicsoffour-wheelsteering(4WS)vehicle are analyzed.The three degrees of freedom simulation analysis of four-wheel steering vehicle dynamics model is established. The simulation forthe handling dynamics of four-wheel steering vehicle based on Matlab / Simulink is done, and the results show that the handling performance of four-wheel steering vehicle is better than the front wheel steering vehicle.Key words:vehicle, four-wheel steering, handling dynamics, simulation 1 引言早期的汽车均采用前轮转向方式，但传统的前轮转向汽车具有低速时有低速时转向响应慢，回转半径大，转向不灵活；高速时方向稳定性差等缺点。
基于的四轮转向汽车操纵稳定性仿真
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基于Matlab_Simulink的四轮转向车辆操纵稳定性仿真
引
言1
四轮转向[1] (Four-wheel steering, 4WS)作为一种有效
描述系统典型环节，因此十分方便地建立系统模型而不 需要花较多时间编程。并可以对系统作适当的实时修正 或者按照仿真的最佳效果来调试及整定控制系统的参 数，以提高系统的性能，减少设计系统过程中反复修改 的时间，实现高效率地开发系统的目标。本文基于 Matlab/simulink 对四轮转向车辆的控制系统进行了设计， 并对 4WS 车辆的操纵稳定性进行了仿真研究。
1 4WS 车辆运动的数学模型
理论和实验都证明 [3] ， 在正常车速范围 （一般意义 的低速到高速）的非紧急状态（ low-g，低侧向加速度） 和小操纵转角输入情况下，二自由度车辆横向运动动 力学模型的精度是足够的。 车辆状态量为质心侧偏角 â 和 横 摆 角 速 度 r， 还 研 究 与 它 们 相 关 的 侧 向 加 速 度 & + r ) ，运动方程[4]如下： a y = V (β
改善车辆操纵性能的技术，近期在高档车中应用正受到 更多重视，有在中低档车上应用的趋势。使用 4WS 技术 的主要目的有：①减少车辆质心侧偏角β；②减少车辆 横摆率与车辆横向加速度之间的相差；③增加轮胎横向 力的裕度，使其远离饱和状态。从驾驶的观点看， 4WS 车辆低速时有较小的转弯半径，这增强了车辆的低速性 能，如更加灵活或和方便于泊车；高速时 4WS 车辆由于 由较小的β角和相差，高速变道将更加平滑，操纵控制 更容易，乘客感觉更加舒适；高速紧急避让时，车体较 少甩尾，减少了车体扫过的包线面积，从而减少了碰撞 的可能性。 Matlab 作为一种面向科学和工程计算的高级计算机 语 言 ， 已 成 为 国 际 科 技 界 公 认 的 最 优 秀 应 用 软 件 [2] 。 Simulink 是 Matlab 提供的主要工具箱之一，用于可视化 的动态系统建模、仿真和分析。它采用系统模块直观地
基于MATLAB的汽车运动控制系统设计仿真
基于MATLAB的汽车运动控制系统设计仿真汽车运动控制系统是指通过电子控制单元（ECU）对汽车进行控制和管理的系统。
在汽车行驶过程中，运动控制系统可以通过调整引擎、悬挂、制动和转向等部件的工作状态，来实现对汽车行驶性能和稳定性的控制。
本文将基于MATLAB对汽车运动控制系统进行设计和仿真。
首先，需要建立汽车的动力学模型。
汽车的动力学模型包括车辆的运动学和动力学两个方面。
运动学模型描述了车辆的位置、速度和加速度之间的关系；动力学模型描述了车辆受到的作用力与车辆运动状态之间的关系。
在MATLAB中可以使用车辆动力学工具箱（Vehicle Dynamics Blockset）来建立汽车的动力学模型。
其次，需要设计车辆控制器。
车辆控制器负责根据车辆的状态和控制要求生成控制指令，并将其发送给相应的执行器。
控制器可以采用基于硬件的控制器，也可以采用基于软件的控制器。
在MATLAB中可以使用Simulink进行控制系统的建模和设计。
接下来，需要设计和实现车辆运动控制算法。
车辆运动控制算法可以包括速度控制、转向控制、制动控制等。
在MATLAB中可以使用控制系统工具箱（Control System Toolbox）和优化工具箱（Optimization Toolbox）来设计和实现车辆运动控制算法。
最后，需要对车辆运动控制系统进行仿真和验证。
在MATLAB中可以使用Simulink和Simscape进行车辆运动控制系统的仿真。
通过仿真可以评估和验证车辆控制系统的性能和稳定性，并进行必要的调整和优化。
综上所述，基于MATLAB的汽车运动控制系统设计仿真包括建立汽车动力学模型、设计车辆控制器、实现运动控制算法以及进行仿真和验证等步骤。
通过仿真和验证可以评估和优化车辆运动控制系统的性能和稳定性，为实际应用提供参考和指导。
车辆系统仿真课件PPT(MATLAB精选课程、优质学习资料)汽车制动、悬架、四轮转向控制系统仿真
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考虑轮胎受到侧向力的作用，采用Gim模型对汽车制动系统进行仿真设 计，其侧向力和回转力矩分别如下式所示：
由此建立单轮车辆制动模型的微分方程式：
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制动过程仿真模型参数如表14-1所示。
建立汽车单轮制动模型仿真框图如图14-3所示。
模型根据不同滑移率下的地面附着系数得到相应的汽车的加速度，积分后与初 始化车速得到相应的车速，运行仿真文件输出结果如图14-4~图14-7所示。
车辆系统仿真
本章讲述了汽车系统仿真，主要设计有汽车制动系统 仿真，汽车悬架的仿真，包括汽车悬架系统的方程建 立、汽车悬架系统仿真以及白噪声路面模拟输入仿真 等，汽车四轮转向系统仿真，分别考虑在低速和高速 运行情况下的四轮系统仿真，很好的解释了汽车系统 建模分析仿真，使读者了解和掌握汽车系统建模，挖 掘更深层本质。 学习目标： （1）学习和掌握汽车制动系统仿真； （2）学习和掌握汽车悬架的仿真； （3）学习和掌握汽车四轮转向系统仿真。
尤为必要。 选取三个性能指标： 车身加速度： y1 xs x2 悬架动扰度： y2 xs xt x1
轮胎动变形： y3 xr xt x3
于是得到输出方程为： Y CX
ks / ms cs / ms 0 cs / ms
C
1
0
控制系统仿真与工具(matlab)实验指导书精选全文
可编辑修改精选全文完整版控制系统仿真与工具实验指导书目录实验一熟悉MATLAB语言工作环境和特点 (1)实验二图形绘制与修饰 (4)实验三系统的时间响应分析 (8)实验四系统的时间响应分析 (12)实验五SIMULINK仿真基础 (14)实验一熟悉MATLAB语言工作环境和特点一、实验目的通过实验使学生熟悉MA TLAB语言的工作环境，并了解MATLAB语言的特点，掌握其基本语法。
二、实验设备PC机MATLAB应用软件三、实验内容本实验从入门开始，使学生熟悉MA TLAB的工作环境，包括命令窗、图形窗和文字编辑器、工作空间的使用等。
1、命令窗（1）数据的输入打开MATLAB后进入的是MA TLAB的命令窗，命令窗是用户与MATLAB做人机对话的主要环境。
其操作提示符为“》”。
在此提示下可输入各种命令并显示出相应的结果，如键入：x1=sqrt(5),x2=1.35,y=3/x2显示结果为:x1=2.2361x2=1.3500y=2.2222上命令行中两式之间用逗号表示显示结果，若用分号，则只运行而不用显示运行结果。
如键入A=[1,2,3;4,5,6;7,8,9]，则显示为说明：●直接输入矩阵时，矩阵元素用空格或逗号分隔，矩阵行用分号相隔，整个矩阵放在方括号中。
注意：标点符号一定要在英文状态下输入。
●在MA TLAB中，不必事先对矩阵维数做任何说明，存储时自动配置。
●指令执行后，A被保存在工作空间中，以备后用。
除非用户用clear指令清除它，或对它重新赋值。
●MATLAB对大小写敏感。
（2）数据的显示在MA TLAB工作空间中显示数值结果时，遵循一定的规则，在缺省的情况下，当结果是整数，MATLAB将它作为整数显示；当结果是实数，MATLAB以小数点后4位的精度近似显示。
如果结果中的有效数字超出了这一范围，MATLAB以类似于计算器的计算方法来显示结果。
也可通过键入适当的MA TLAB命令来选择数值格式来取代缺省格式。
基于MatlabSimulink环境四轮驱动混合动力汽车建模与仿真
1 前言能源危机和环境污染是当前汽车工业面临的两大主要压力。
汽车是油耗大户，又是重要的污染源。
国内汽车产品水平与国外差距很大，使汽车工业面临的压力更大。
上个世纪以来世界各国和各大汽车公司以及国内各大科研机构和高等院校纷纷致力于开发清洁节能汽车，混合动力系统已经被证明是现阶段最切实可行的清洁汽车技术。
仿真一直是汽车开发中的一个重要环节，通过合理有效的仿真可以加快汽车开发进度，节约开发成本。
伴随着混合动力技术的发展，其建模和仿真技术也在飞速发展。
2 混合动力车的建模仿真技术混合动力电动汽车仿真的研究是伴随着19世纪60年代几种样车的发展而出现的。
随着计算机技术的飞速发展，计算机仿真已经是混合合动力汽车设计开发的有力辅助工具，仿真分析有利于深入理解混合动力系统的工作过程，分析控制策略中占主要影响的动力学因素；并可用来分析整车能量消耗和评估整车性能，验证和优化设计方案。
随着研究的深入，国内外已经开发出多款混合动力汽车计算机仿真软件，用以预测一个或者多个领域的性能，如燃油经济性、排放特性、加速性能、爬坡性能。
最著名最先进的混合动力汽车软件是美国国家可回收能源实验室开发的ADVISOR，它基Matlab/Simulink的可视化模块示意图编程环境，具有很大的灵活性，可以对任何类型的混合动力电动汽车或内燃机汽车进行建模。
其它还开发出许多混合动力汽车仿真软件。
这些软件的仿真都是首先计算满足驱动循环要求的功率，然后利用各部件的传动效率计算出总线输出功率。
同时具有绘制输出数据图表或存储仿真中每一时间步长数据的功能。
混合动力系统属于既有连续环节又有时间离散环节的“采样控制系统”，模拟和分析其复杂行为的核心是建立其动态和非线性的仿真模型。
由于混合动力系统本身的复杂性，必须按目标和研究对象的不同建立仿真模型，以兼顾结果的准确性和仿真效率。
目前对混合动力电动汽车的仿真有后向仿真和前向仿真两种基本方法。
后向仿真模型以目标车速(如标准行驶循环试验工况)为输入，计算驱动系统中需要的扭矩、转速和功率。
《基于CarSim和Simulink的四轮转向汽车控制策略及其稳定性的研究》
《基于CarSim和Simulink的四轮转向汽车控制策略及其稳定性的研究》篇一一、引言随着汽车技术的快速发展，四轮转向汽车已经成为提高车辆稳定性和操控性的重要手段。
为了提高四轮转向汽车的操控性能和稳定性，研究者们一直在探索有效的控制策略。
本文基于CarSim和Simulink两款仿真软件，对四轮转向汽车的控制策略及其稳定性进行了深入研究。
二、CarSim与Simulink在四轮转向汽车研究中的应用CarSim和Simulink是两款广泛应用于汽车动力学仿真和控制系统设计的软件。
CarSim主要用于车辆动力学仿真，可以模拟各种路况和驾驶条件；而Simulink则主要用于控制系统设计和分析，可以实现对汽车控制策略的建模和仿真。
两款软件的结合使用，为四轮转向汽车的控制策略研究提供了有效的工具。
三、四轮转向汽车控制策略研究针对四轮转向汽车的控制策略，本文提出了基于模糊控制的控制策略。
该策略通过模糊控制器对四轮转向汽车的转向角度进行实时调整，以实现车辆在各种路况和驾驶条件下的稳定性和操控性。
在Simulink中建立了控制系统模型，并对控制策略进行了仿真分析。
四、四轮转向汽车稳定性分析在CarSim中建立了四轮转向汽车的虚拟模型，并通过仿真分析了车辆的稳定性和操控性。
通过对不同路况和驾驶条件下的仿真结果进行分析，发现采用基于模糊控制的四轮转向控制策略可以有效提高车辆的稳定性和操控性。
同时，通过对车辆动力学参数的优化，进一步提高了车辆的稳定性和操控性能。
五、实验验证与分析为了验证仿真结果的可靠性，我们在实际道路上进行了实验验证。
通过对比实验结果和仿真结果，发现两者基本一致，证明了基于模糊控制的四轮转向控制策略的有效性和可靠性。
同时，通过对实验数据的分析，进一步优化了控制策略和车辆动力学参数，提高了车辆的稳定性和操控性能。
六、结论本文基于CarSim和Simulink两款仿真软件，对四轮转向汽车的控制策略及其稳定性进行了深入研究。
汽车线控四轮转向执行系统的仿真与分析
汽车线控四轮转向执行系统的仿真与分析
曹宾;王振宏
【期刊名称】《新技术新工艺》
【年(卷),期】2014(000)007
【摘要】利用动力学原理，建立了汽车线控四轮转向系统中的转向执行系统数学模型，根据其并采用Simulink软件，建立了该转向执行系统的基于积分分离 PID 控制器的仿真模型。
在此基础上，采用单位阶跃作为转向执行系统的输入，求出相应的响应。
结果表明，该转向执行系统的性能满足要求，可以实现对目标信号的随动，为改善汽车的转向性能提供了依据。
【总页数】3页(P43-45)
【作者】曹宾;王振宏
【作者单位】长春理工大学机电工程学院，吉林长春 130022;长春理工大学机电工程学院，吉林长春 130022
【正文语种】中文
【中图分类】U463.4
【相关文献】
1.四轮转向汽车操纵动力学虚拟仿真分析 [J], 焦凤;陈南;秦绪柏
2.基于线控变传动比的四轮转向汽车最优控制 [J], 张庭芳;张超敏;何新毅;曲志林
3.线控四轮转向汽车平行泊车路径规划与跟踪控制 [J], 张家旭;卜纯研;王晨;赵健
4.全方位线控四轮转向电动汽车设计 [J], 卓桂荣;陈辛波;余卓平;万钢
5.四轮转向汽车操纵动力学仿真分析 [J], 张孝祖;蔡双飞
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基于MATLAB的四轮转向电动汽车横向稳定性控制仿真研究
基于MATLAB的四轮转向电动汽车横向稳定性控制仿真研究作者：文／雷敏来源：《时代汽车》 2017年第5期摘要：质心侧偏角与横摆角速度是影响电动汽车横向稳定性的重要因素。
为了提高四轮转向电动汽车的横向稳定性，本文在前轮转角前馈控制和横摆角速度反馈控制的基础上综合控制四轮转向电动汽车的横向稳定性，并在Matlab/Simulink软件进行仿真试验。
关键词：四轮转向电动汽车；横向稳定性；控制策略；Matlab/Simulink；仿真1引言随着人类生活水平的提高与汽车工业的不断发展，人们对汽车的关注重点从拥有汽车转变为汽车的质量与安全性。
汽车安全性能分主动安全性和被动安全性，其中主动安全技术占有尤其重要的地位。
汽车在转弯时容易发生侧滑、甩尾等危险，对电动汽车的横向稳定性进行控制研究非常重要。
本文以四轮转向电动汽车为研究对象。
2四轮转向电动汽车横向稳定性控制前轮转向汽车后轮不参与转向运动，如果转向时汽车的质心侧偏角数值过大，容易使汽车失去横向稳定性。
四轮转向汽车后轮也参与转向，能够有效地减小质心侧偏角，保证其横向稳定性，因此四轮转向能有效提高主动安全性。
低速行驶的汽车，通过增加后轮与前轮转向相反的转角，可减小转弯半径并提高机动性。
由于前后车轮转向角对质心侧偏角的作用相反，高速运行时的效果为质心侧偏角减小，提高了高速横向稳定性。
2.1 二自由度四轮转向模型研究对象可简化成二自由度模型。
只考虑横轴运动以及横摆这两个自由度。
由牛顿第二定律得动力学方程；假设前后轮转角很小；假设轮胎横向力为线性；假设汽车纵向速度维持不变；由轮胎侧偏角的定义可得二自由度转向模型为：2.2横向稳定性控制变量的选择电动汽车横向稳定性控制目标包括：高速运行时，要求质心侧偏角响应值控制在0附近，横摆角速度要比前轮转向控制系统的小低速运行时，要求质心侧偏角响应值较小，横摆角速度要比传统的前轮转向控制系统的大。
所以本文选择质心侧偏角与横摆角速度作为控制变量进行研究。
《基于CarSim和Simulink的四轮转向汽车控制策略及其稳定性的研究》
《基于CarSim和Simulink的四轮转向汽车控制策略及其稳定性的研究》一、引言随着汽车工业的快速发展，四轮转向技术因其出色的操控性能和稳定性已成为现代汽车的重要特征之一。
为了深入研究四轮转向汽车的控制策略及其稳定性，本文将基于CarSim和Simulink 软件平台展开研究。
CarSim作为一款专业的汽车仿真软件，能够为汽车动力学研究提供精确的模型；而Simulink则以其强大的控制系统仿真能力为依托，为四轮转向汽车的控制策略提供强有力的分析工具。
本文将通过理论分析、仿真实验等方法，探讨四轮转向汽车的控制策略及其稳定性，以期为实际车辆的设计与开发提供理论依据和指导。
二、四轮转向汽车控制策略的研究四轮转向汽车的控制策略主要涉及到前轮转向控制和后轮转向控制两部分。
前轮转向控制主要依赖于驾驶员的输入和车辆的当前状态，而后轮转向控制则需根据车辆的行驶状态和驾驶员的意图进行合理分配。
2.1 前轮转向控制策略前轮转向控制策略主要采用传统的PID控制算法，通过调整PID参数，使车辆在各种行驶工况下都能保持稳定的操控性能。
此外，还可以采用模糊控制、神经网络等智能控制算法，进一步提高前轮转向的精度和响应速度。
2.2 后轮转向控制策略后轮转向控制策略是四轮转向汽车的核心部分，其控制效果直接影响到车辆的稳定性和操控性能。
目前，常用的后轮转向控制策略包括：基于规则的控制策略、基于优化的控制策略和基于智能算法的控制策略。
其中，基于优化的控制策略通过优化车辆的操控性能指标，实现后轮转向的合理分配；而基于智能算法的控制策略则能根据车辆的行驶状态和驾驶员的意图，自适应地调整后轮转向的角度和速度。
三、基于CarSim和Simulink的仿真实验为了验证四轮转向汽车的控制策略及其稳定性，本文采用CarSim和Simulink进行联合仿真实验。
首先，在CarSim中建立四轮转向汽车的动力学模型，并设置相应的仿真参数；然后，将CarSim与Simulink进行连接，实现数据的实时交互；最后，在Simulink中搭建四轮转向汽车的控制策略模型，并进行仿真实验。
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0.41194
0.21239 B 0.85521
0.21149 D 10.67067
18
9.3.3 基于Matlab仿真
Amplitude
1、在低速（V 30km / h ）下的系统仿真
0.5
Step Response
0
-0.5
-1
-1.5
-2
-2.5
Amplitude
Step Response
8
7
6
5
4
3
2
1
00
3
6
9
12
15
Time (sec)
图9.3.4高速时横摆角速度响应曲线
4WS车辆的横摆角 速度响应迅速，很 好地实现了驾驶员 的转向意图，同时 准确地跟踪了期望 的横摆角速度。
22
由最优控制理论可知，若控制输入为
c KX R1BT LX 则性能指标J为最小
最优控制可用 c 最优反馈增益矩阵写成：
c KX [k1
得到
k2
]
r
(k1
k2r)
X ( A BK ) X Ds
16
9.3.3 基于Matlab仿真
-3
-3.50
1
2
3
4
Time (sec)
图9.3.1低速时质心侧偏角响应曲线
与2WS汽车相比，采 用最优控制的4WS车 辆的质心侧偏角瞬态 响应性能得到很大改 善，能够很快地到达 稳态值，超调量明显 减小，汽车的运动姿 态得到了很好的控制
19
9.3.3 基于Matlab仿真
1、在低速（V 30km / h）下的系统仿真
1、在低速（V 30km/ h ）下的系统仿真
图9.2.2 低速下四轮转向系统仿真模型
7
9.2.3 基于Matlab/Simulink仿真
1、在低速（V 30km/ h ）下的系统仿真
6
0.5
2WS系统
0
5
-0.5
2WS系统
4
横摆角速度反馈的4WS系统
-1
3
-1.5
-2 2
定前后轮比例控制的4WS系统
1、前轮角阶跃输入下的稳态响应 2、前轮角阶跃输入下的瞬态响应
12
9.3 基于最优控制的四轮转向系统研究
9.3.1模型的建立
前、后轮的转角可以由以下式子给出：rf
s Kcc (1 Kc )c
选取状态变量 X [ , r]T ，得到状态方程为： X AX Bc Ds
Amplitude
Step Response
1
0
-1
-2
-3
-4
-5
-6
-7
-8
0
3
6
9
12
15
Time (sec)
图9.3.3高速时质心侧偏角响应曲线
高速时，2WS汽车 的质心侧偏角比较
大，而采用最优控 制的4WS车辆可以 有效地保证质心侧 偏角接近为零。
21
9.3.3 基于Matlab仿真
1、在高速（V 90km / h）下的系统仿真
-2.5
横摆角速度反馈的4WS系统
1
-3
0
0
2
4
6
8
10
图9.2.3 低速时横摆角速度响应曲线
-3.50
2
4
6
8
10
图9.2.4 低速时质心侧偏角响应曲线
8
9.2.3 基于Matlab/Simulink仿真
2、在高速（V 90km / h ）下的系统仿真
将参数代入后，得到：
Gr
/
f
(s)
95.9422s 44.0064 8.9912s2 7.5231s 16.9434
Gr
/r
(s)
111.321s 44.0064 8.9912s2 7.5231s 16.9434
1.9016s 95.1051 G / f (s) 8.9912s2 7.5231s 16.9434
1.9177s 111.3376 G /r (s) Байду номын сангаас 8.9912s2 7.5231s 16.9434
)u2 ]L
(1 i)u (1 Ku2 )L
3
9.2.2 控制算法
图9.2.1 基于横摆角速度反馈的4WS系统控制原理图
Gr / f
(s)
a1s a0 m's2 hs
f
G / f
(s)
c1s c0 m's2 hs
f
Gr /r
(s)
b1s b0 m's2 hs
V2 2
Ou
x 得到：
L1
L2
图9.1 二自由度四轮转向汽车模型
Mu(r )
I zr Fy1Lf
Fy1 Fy2
Fy Lr
2
2
9.2.1 基于横摆角速度反馈控制的四轮转向系统研究
转角输入-横摆角速度输出的关系函数：
r(s)
a1s a0 m's2 hs
f
f
b1s b0 m's2 hs
f
r
转角输入-质心侧偏角输出的关系函数：
(s)
c1s c0 m's2 hs
f
f
d1s d0 m's2 hs
f
r
稳态横摆角速度增益：
r
f
s
[1
M L2
(1 i)u ( Lr Lf C f Cr
A
1.27433
1.71042
0.99496 1.23581
0.63716 B 0.85521
D
0.63447 10.67067
2、在低速（ V 90km/ h ）下的系统仿真
0.42478 0.995
A
1.71042
得4WS系统稳态时状态向量X对 s 的增益为：
X
s
s
(A
BK )1 D
对X 拉普拉斯变换，得：X (s) [sI A BK ]1 Ds (s)
对Y拉普拉斯变换，得: Y (s) CX (s) C[sI A BK ]1D
最后得到4WS系统的传递函数矩阵为：
输出变量 Y [ , r]T ，得到输出方程为：Y CX
C f Cr
A
MV
C f Lf Cr Lr
Iz
C f Lf Cr Lr MV 2
1
C f L2f Cr L2r
IV
C
1 0
0 1
B
C f Kc Cr (1 Kc ) MV
C
f
Lf
Kc
Cr Iz
Lr
(Kc
1)
D
Cf MV
C
fL I
f
13
9.3.2 4WS系统的可控性和能观性分析
最优控制是根据系统状态变量提供
最优反馈增益即来 c 实现的。
（1）通过判断可控性矩阵[B AB] 是否满 秩来分析控制器 对系统的可控性 （2）通过判断可控性矩阵[C CA]T 是否满 秩来分析系统是否可观测
G
/ f
(s)
s2
0.6339s 9.8231 2.5077s 3.2734
0.6392s 13.0966 G /r (s) s2 2.5077s 3.2734
稳态横摆角速度增益
r
f
s
4.4812
前后轮比例常数 i 0.844
6
9.2.3 基于Matlab/Simulink仿真
G(s) Y (s) C[sI A BK ]1 D s (s)
17
9.3.3 基于Matlab仿真
本例中选取 Kc 0.5 ，权系数 q 50 ，前轮 转角 s 为单位阶跃输入进行Matlab仿真。具 体模型数值设置如表9.3.1所示。
1、在低速（ V 30km/ h ）下的系统仿真
f
G /r
(s)
d1s d0 m's2 hs
f
4
9.2.3 基于Matlab/Simulink仿真
本例采用的汽车模型参数，见表9.2： 表9.2 汽车模型参数设置
变量名称 数值
单位 变量名称 数值
单位
M
2045 kg
Iz
5428 kg m2
Lf
1.488
m
Lr
m 1.712
Cf
-38925 N / rad
14
9.3.3 基于Matlab仿真
4WS的最优控制问题是：
在初始条件和系统参数已知的情况下， 寻找一个最优控制 ，使4WS系统工作性能指 标达到极值。
性能指标为：
J
(X
0
T QX
T c
R
c
)dt
式中
Q
q2 0
0 0
，为权矩阵，其中q、R为权系数。
15
9.3.3 基于Matlab仿真