Finite-Dimensional Vector Spaces - P. Halmos (Springer, 1987)
在学习代数学之余,值得一看的代数学书籍。里面介绍了更为丰富的代数学概念和结论。PREFACEMy purpose in this book is to treat linear transformations on finite-dimensional vector spaces by the methods of more general theories. Theidea is to emphasize the simple geometric notions common to many partsof mathematics and its applications, and to do so in a language that givesaway the trade secrets and tells the student what is in the back of the mindsof people proving theorems about integral equations and Hilbert spaces.The reader does not, however, have to share my prejudiced motivationExcept for an occasional reference to undergraduate mathematics the bookis self-contained and may be read by anyone who is trying to get a feelingfor the linear problems usually discussed in courses on matrix theory orhigher"algebra. The algebraic, coordinate-free methods do not lose powerand elegance by specialization to a finite number of dimensions, and theyare, in my belief, as elementary as the classical coordinatized treatmentI originally intended this book to contain a theorem if and only if aninfinite-dimensional generalization of it already exists, The temptingeasiness of some essentially finite-dimensional notions and results washowever, irresistible, and in the final result my initial intentions are justbarely visible. They are most clearly seen in the emphasis, throughout, ongeneralizable methods instead of sharpest possible results. The reader maysometimes see some obvious way of shortening the proofs i give In suchcases the chances are that the infinite-dimensional analogue of the shorterproof is either much longer or else non-existent.A preliminary edition of the book (Annals of Mathematics Studies,Number 7, first published by the Princeton University Press in 1942)hasbeen circulating for several years. In addition to some minor changes instyle and in order, the difference between the preceding version and thisone is that the latter contains the following new material:(1) a brief dis-cussion of fields, and, in the treatment of vector spaces with inner productsspecial attention to the real case.(2)a definition of determinants ininvariant terms, via the theory of multilinear forms. 3 ExercisesThe exercises(well over three hundred of them) constitute the mostsignificant addition; I hope that they will be found useful by both studentPREFACEand teacher. There are two things about them the reader should knowFirst, if an exercise is neither imperative "prove that.., )nor interrogtive("is it true that...?" )but merely declarative, then it is intendedas a challenge. For such exercises the reader is asked to discover if theassertion is true or false, prove it if true and construct a counterexample iffalse, and, most important of all, discuss such alterations of hypothesis andconclusion as will make the true ones false and the false ones true. Secondthe exercises, whatever their grammatical form, are not always placed 8oas to make their very position a hint to their solution. Frequently exer-cises are stated as soon as the statement makes sense, quite a bit beforemachinery for a quick solution has been developed. A reader who tries(even unsuccessfully) to solve such a"misplaced"exercise is likely to ap-preciate and to understand the subsequent developments much better forhis attempt. Having in mind possible future editions of the book, I askthe reader to let me know about errors in the exercises, and to suggest im-provements and additions. (Needless to say, the same goes for the text.)None of the theorems and only very few of the exercises are my discovery;most of them are known to most working mathematicians, and have beenknown for a long time. Although i do not give a detailed list of my sources,I am nevertheless deeply aware of my indebtedness to the books and papersfrom which I learned and to the friends and strangers who, before andafter the publication of the first version, gave me much valuable encourage-ment and criticism. Iam particularly grateful to three men: J. L. Dooband arlen Brown, who read the entire manuscript of the first and thesecond version, respectively, and made many useful suggestions, andJohn von Neumann, who was one of the originators of the modern spiritand methods that I have tried to present and whose teaching was theinspiration for this bookP、R.HCONTENTS的 FAPTERPAGRI SPACESI. Fields, 1; 2. Vector spaces, 3; 3. Examples, 4;4. Comments, 55. Linear dependence, 7; 6. Linear combinations. 9: 7. Bases, 108. Dimension, 13; 9. Isomorphism, 14; 10. Subspaces, 16; 11. Calculus of subspaces, 17; 12. Dimension of a subspace, 18; 13. Dualspaces, 20; 14. Brackets, 21; 15. Dual bases, 23; 16. Reflexivity, 24;17. Annihilators, 26; 18. Direct sums, 28: 19. Dimension of a directsum, 30; 20. Dual of a direct sum, 31; 21. Qguotient spaces, 33;22. Dimension of a quotient space, 34; 23. Bilinear forms, 3524. Tensor products, 38; 25. Product bases, 40 26. Permutations41; 27. Cycles,44; 28. Parity, 46; 29. Multilinear forms, 4830. Alternating formB, 50; 31. Alternating forms of maximal degree,52II. TRANSFORMATIONS32. Linear transformations, 55; 33. Transformations as vectors, 5634. Products, 58; 35. Polynomials, 59 36. Inverses, 61; 37. Mat-rices, 64; 38. Matrices of transformations, 67; 39. Invariance,7l;40. Reducibility, 72 41. Projections, 73 42. Combinations of pro-jections, 74; 43. Projections and invariance, 76; 44. Adjoints, 78;45. Adjoints of projections, 80; 46. Change of basis, 82 47. Similarity, 84; 48. Quotient transformations, 87; 49. Range and null-space, 88; 50. Rank and nullity, 90; 51. Transformations of rankone, 92 52. Tensor products of transformations, 95; 53. Determinants, 98 54. Proper values, 102; 55. Multiplicity, 104; 56. Triangular form, 106; 57. Nilpotence, 109; 58. Jordan form. 112III ORTHOGONALITY11859. Inner products, 118; 60. Complex inner products, 120; 61. Innerproduct spaces, 121; 62 Orthogonality, 122; 63. Completeness, 124;64. Schwarz e inequality, 125; 65. Complete orthonormal sets, 127;CONTENTS66. Projection theorem, 129; 67. Linear functionals, 130; 68. P aren, gBCHAPTERtheses versus brackets, 13169. Natural isomorphisms, 138;70. Self-adjoint transformations, 135: 71. Polarization, 13872. Positive transformations, 139; 73. Isometries, 142; 74. Changeof orthonormal basis, 144; 75. Perpendicular projections, 14676. Combinations of perpendicular projections, 148; 77. Com-plexification, 150; 78. Characterization of spectra, 158; 79. Spec-ptral theorem, 155; 80. normal transformations, 159; 81. Orthogonaltransformations, 162; 82. Functions of transformations, 16583. Polar decomposition, 169; 84. Commutativity, 171; 85. Self-adjoint transformations of rank one, 172IV. ANALYSIS....17586. Convergence of vectors, 175; 87. Norm, 176; 88. Expressions forthe norm, 178; 89. bounds of a self-adjoint transformation, 17990. Minimax principle, 181; 91. Convergence of linear transformations, 182 92. Ergodic theorem, 184 98. Power series, 186APPENDIX. HILBERT SPACERECOMMENDED READING, 195INDEX OF TERMS, 197INDEX OF SYMBOLS, 200CHAPTER ISPACES§L. FieldsIn what follows we shall have occasion to use various classes of numbers(such as the class of all real numbers or the class of all complex numbers)Because we should not at this early stage commit ourselves to any specificclass, we shall adopt the dodge of referring to numbers as scalars. Thereader will not lose anything essential if he consistently interprets scalarsas real numbers or as complex numbers in the examples that we shallstudy both classes will occur. To be specific(and also in order to operateat the proper level of generality) we proceed to list all the general factsabout scalars that we shall need to assume(A)To every pair, a and B, of scalars there corresponds a scalar a+called the sum of a and B, in such a way that(1) addition is commutative,a+β=β+a,(2)addition is associative, a+(8+y)=(a+B)+y(3 there exists a unique scalar o(called zero)such that a+0= a forevery scalar a, and(4)to every scalar a there corresponds a unique scalar -a such that十(0(B)To every pair, a and B, of scalars there corresponds a scalar aBcalled the product of a and B, in such a way that(1)multiplication is commutative, aB pa(2)multiplication is associative, a(Br)=(aB)Y,( )there exists a unique non-zero scalar 1 (called one)such that al afor every scalar a, and(4)to every non-zero scalar a there corresponds a unique scalar a-1or-such that aaSPACES(C)Multiplication is distributive with respect to addition, a(a+n)If addition and multiplication are defined within some set of objectsscalars) so that the conditions(A),B), and (c)are satisfied, then thatset(together with the given operations) is called a field. Thus, for examplethe set Q of all rational numbers(with the ordinary definitions of sumand product)is a field, and the same is true of the set of all real numberaand the set e of all complex numbersHHXERCISIS1. Almost all the laws of elementary arithmetic are consequences of the axiomsdefining a field. Prove, in particular, that if 5 is field and if a, and y belongto 5. then the following relations hold80+a=ab )Ifa+B=a+r, then p=yca+(B-a)=B (Here B-a=B+(a)(d)a0=0 c=0.(For clarity or emphasis we sometimes use the dot to indi-cate multiplication.()(-a)(-p)(g).If aB=0, then either a=0 or B=0(or both).2.(a)Is the set of all positive integers a field? (In familiar systems, such as theintegers, we shall almost always use the ordinary operations of addition and multi-lication. On the rare occasions when we depart from this convention, we shallgive ample warningAs for "positive, "by that word we mean, here and elsewherein this book, "greater than or equal to zero If 0 is to be excluded, we shall say"strictly positive(b)What about the set of all integers?(c) Can the answers to these questiong be changed by re-defining addition ormultiplication (or both)?3. Let m be an integer, m2 2, and let Zm be the set of all positive integers lessthan m, zm=10, 1, .. m-1). If a and B are in Zmy let a +p be the leastpositive remainder obtained by dividing the(ordinary) sum of a and B by m, andproduct of a and B by m.(Example: if m= 12, then 3+11=2 and 3. 11=9)a) Prove that i is a field if and only if m is a prime.(b What is -1 in Z5?(c) What is囊izr?4. The example of Z, (where p is a prime)shows that not quite all the laws ofelementary arithmetic hold in fields; in Z2, for instance, 1 +1 =0. Prove thatif is a field, then either the result of repeatedly adding 1 to itself is always dif-ferent from 0, or else the first time that it is equal to0 occurs when the numberof summands is a prime. (The characteristic of the field s is defined to be 0 in thefirst case and the crucial prime in the second)SEC. 2VECTOR SPACES35. Let Q(v2)be the set of all real numbers of the form a+Bv2, wherea and B are rational.(a)Ie(√2) a field?(b )What if a and B are required to be integer?6.(a)Does the set of all polynomials with integer coefficients form a feld?(b)What if the coeficients are allowed to be real numbers?7: Let g be the set of all(ordered) pairs(a, b)of real numbers(a) If addition and multiplication are defined by(a月)+(,6)=(a+y,B+6)and(a,B)(Y,8)=(ary,B6),does s become a field?(b )If addition and multiplication are defined by(α,月)+⑦,b)=(a+%,B+6)daB)(,b)=(ay-6a6+的y),is g a field then?(c)What happens (in both the preceding cases)if we consider ordered pairs ofcomplex numbers instead?§2. Vector spaceWe come now to the basic concept of this book. For the definitionthat follows we assume that we are given a particular field s; the scalarsto be used are to be elements of gDEFINITION. A vector space is a set o of elements called vectors satisfyingthe following axiomsQ (A)To every pair, a and g, of vectors in u there corresponds vectora t y, called the aum of a and y, in such a way that(1)& ddition is commutative,x十y=y十a(2)addition is associative, t+(y+2)=(+y)+a(3)there exists in V a unique vector 0(called the origin) such thata t0=s for every vector and(4)to every vector r in U there corresponds a unique vector -rthat c+(-x)=o(B)To every pair, a and E, where a is a scalar and a is a vector in u,there corresponds a vector at in 0, called the product of a and a, in sucha way that(1)multiplication by scalars is associative, a(Bx)=aB)=, and(2 lz a s for every vector xSPACESSFC B(C)(1)Multiplication by scalars is distributive with respect to vectorddition, a(+y=a+ ag, and2)multiplication by vectors is distributive with respect to scalar ad-dition, (a B )r s ac+ Bc.These axioms are not claimed to be logically independent; they aremerely a convenient characterization of the objects we wish to study. Therelation between a vector space V and the underlying field s is usuallydescribed by saying that v is a vector space over 5. If S is the field Rof real number, u is called a real vector space; similarly if s is Q or if gise, we speak of rational vector spaces or complex vector space§3. ExamplesBefore discussing the implications of the axioms, we give some examplesWe shall refer to these examples over and over again, and we shall use thenotation established here throughout the rest of our work.(1) Let e(= e)be the set of all complex numbers; if we interpretr+y and az as ordinary complex numerical addition and multiplicatione becomes a complex vector space2)Let o be the set of all polynomials, with complex coeficients, in avariable t. To make into a complex vector space, we interpret vectoraddition and scalar multiplication as the ordinary addition of two poly-nomials and the multiplication of a polynomial by a complex numberthe origin in o is the polynomial identically zeroExample(1)is too simple and example (2)is too complicated to betypical of the main contents of this book. We give now another exampleof complex vector spaces which(as we shall see later)is general enough forall our purposes.3)Let en,n= 1, 2,. be the set of all n-tuples of complex numbers.Ix=(1,…,轨)andy=(m1,…,n) are elements of e, we write,,bdefinitionz+y=〔1+叽,…十物m)0=(0,…,0),-inIt is easy to verify that all parts of our axioms(a),(B), and (C),52, aresatisfied, so that en is a complex vector space; it will be called n-dimenaionalcomplex coordinate space
- 2020-12-05下载
- 积分:1
基于MATLAB复调制ZOOM-FFT算法的分析和实现
基于MATLAB复调制ZOOM-FFT算法的分析和实现2006年第4期舰船电子工程121滤波;使用函数来实现傅立叶变换次复数乘法。设数字滤波器的阶数为K,滤波器系数离线生成,则滤波需要DNK次复数乘法,则总4 Matlab仿真和验证的运算量为为验证上述算法及分析过程的正确性,在MatZFFTNloN+2N+DN·K(3)中产生一个正弦组合信号3随着细化倍数的增加,基带FFT和ZFFT的运算量x(t)=30cos(2m110t)+30cos(2x11145t)都会大幅度增加;zFF只有当细化频带较窄(此时+25cos(2x112.3t)+48cos(2m113.8t)无需数字滤波)或长序列的情况下,与基带FT相+50co(2x114.5t)比才具有运算量上的优势。分别利用基带FT和ZT对其进行谱分析ZFT算法存在自身的局限性,其存在的问题仿真条件:f=2048H,F点数N=1024,细化倍数D=50。基带FFT的频率分辨率4f=2H,历如下:(1)需要存放中间数据的内存空间巨大限制ZF的频率分辨率△f=0.04H。仿真结果如图了最大细化倍数2和图3所示。(2)采用具有线性相位的FIR数字滤波器实igure(n现抗混叠滤波,由于有限阶滤波器的吉布斯效应( Gibbs effect),滤波器截止频率处的频谱不可避免020040060080010001200会出现局部失真。(3)细化倍数越高,重釆样的选抽比越高,则细化带宽越窄。当需要细化的带宽较大时,必须进5行多次细化,这势必会增加计算量。Figure(4)频率成分调整较复杂。将FT和谱分析105110115130得到的频率成分调整到所选频带的频率成分式较Frequency(Hz复杂的过程,特别是为了避免低通抗混滤波器的边图3FF幅值频谱缘误差造成的频率混叠为了比较频率细化的效果,对图中谱线作了归化处理。图2中fgme(a)为原始信号,fgme(c)6小结为基带FYT处理后的幅值谱线,fgre(d)为移频后ZFT算法的关键在于利用傅立叶变换的移频基带FFT处理后的幅值谱线。由此图可以看出,基特性将感兴趣的高频段频率移至频谱原点,降低采带FFT的几个谱峰叠加为一个谱峰,各频率成分不可分辨。图3中fge(g)为重新采样后F处理样率重新釆样,从而获取较高的频率分辨率。它对后的幅值谱线,gure(h)为频率调整到实际频率处于获得某些特殊频段而不是整个带宽的信号细微的幅值谱线。此图中,因频率分辨率降低了D倍谱结构十分有用。该算法在实际工程技术中有较zF的幅值谱线中5条谱线清晰可见,说明ZF广泛的应用效果明显。参考文獻5ZF运算量和局限性讨论[1]胡广书.数字信号处理-理论、算法与实现[M]北京:清华大学出版社,1997当采用时域抽取FFT算法时,N点DT的复数[2] Vinay K ingle, John g proakis.数字信号处理及其乘法次数为l2N,复数加法次数为NN。为MATLAB实现[M].北京:电子工业出版社,1998[3]赵霞,熊小伏,郭珂.用细化频谱技术分析断路器简单起见,仅比较两种算法的复数乘法次数。操动机构振动信号[J.电力系统自动化,2003,(12):37设频率分辨率4f=fN,细化倍数D=△/404」f。要获得4/的分辨率,基带FFT的运算量为[4]丁康,谢明,张彼德等.基于复解析带通滤波器的FrTdN)lo复调制细化谱分析原理和方法[J.振动工程学报,2001,62(D14(1):30~35采用ZF算法,在复调制时只计算重采样的[5]宗孔德.多抽样率信号处理[M].北京:清华大学点,需N次复数乘法。同样,调制系数的计算也需N出版社,19基于 MATLAB复调制Z00M-FT算法的分析和实现旧WANFANG DATA文献链接作者:王力,张冰,徐伟, Wang li, Zhang bing, Xu Wei作者单位:王力,张冰, Wang Li, Zhang bing(江苏科技大学,镇江,212003),徐伟, Xu Wei(船舶系统工程部,北京,100036)刊名:舰船电子工程英文刊名SHIP ELECTRONIC ENGINEERING年,卷(期)2006,26(4)被引用次数:次参考文献(5条)1.宗孔德多抽样率信号处理19962.丁康;谢明;张彼德基于复解析带通滤波器的复调制细化谱分析原理和方法[期刊论文]振动工程学报2001(013.赵霞;熊小伏;郭珂用细化频谱技术分析断路器操动机构振动信号[期刊论文]电力系统自动化2003(12)4.陈怀琛数字信号处理教程- MATLAB释义与实现19985.胡广书数字信号处理一理论、算法与实现1997本文读者也读过(6条江波.唐普英基于复调制的ZooⅷFFT算法在局部频谱细化中的研究与实现[期刊论文]-大众科技2010(7)2.丁康.谢明.张彼德.赵玲.张晓飞. Ding Kang. Xie ming. Zhang bide. Zhao ling. ZHANG Xiaofei基于复解析带通滤波器的复调制细化谱分析原理和方法[期刊论文]-振动工程学报2001,14(1)3.罗利春. LUo Lic- hun zoom-FFT的改进、频谱反演与时-频局部化特性[期刊论文]-电子学报2006,34(1)4.戴振华.纪海林.徐运涛.DAⅠZhen-hua. JI Hai-1in.ⅫUYun-taoZ00MFFT算法在数字音频分析仪中的实现[期刊论文]-兵工自动化2007,26(10)5.黄镔.许婧.高峰.束洪春Z0OM-FFT在水电机组振动信号分析中的应用[期刊论文]-昆明理工大学学报(理工版)2002,27(5)6.王卫江改进的自适应Zoom-FFT算法研究[期刊论文]一电子技术应用2006,32(7)证文献(10条1.程兆刚.唐力伟.张淑琴.曹洪娜基于复调制Z0OM-FFT算法下阻尼比识别的研究[期刊论文]计算机与数字工程2012(1)2.刘树强.罗天.王宁.潘栋基于 Labview的异步电机转子断条检测[期刊论文]电子设计工程2011(3)3.王文森.邱宏安高精度超声流量检测系统设计[期刊论文]电声技术2011(2)4刘树强.罗天.谭兴文基于 Labview的笼型异步电动机转子断条故障在线检测系统[期刊论文]西南大学学报:自然科学版2011(9)5.王乐.苏小敏.杜林.李春化复白噪声中复正弦波频率估计方法硏究[期刊论文]火控雷达技术2011(36.周红霞.江佩勤.伍洲基于嵌入式系统的ZFFT移频轨道检测算法[期刊论文]通信技术2010(37.焦玮琦.陈特放基于局部频谱细化的轨道移频信号高精度检测[期刊论文]机车电传动2009(28.史瑞根.姚金杰基于 Labview的数字变频FFT设计[期刊论文]现代电子技术2009(7)9武中奇.杨世武丌FT算法在铁路移频信号分析中的应用及其DSP实现[期刊论文]铁道通信信号2008(7)10.时献江.张春喜.邵俊鹏异步电机断条故障诊断的细化包络方法[期刊论文]电机与控制学报2008(2)本文链接http://d.g.wanfangdata.com.cn/periodicaljcdzgc200604033.aspx
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- 积分:1
MATLAB与控制系统仿真实践
MATLAB与控制系统仿真实践,适合学习自动制方向的用MATLAB进行仿真的人士学习和参考内容简介本书以 MATLAB R2007a为仿真平台,以清新、简洁的风格介绍了 MATLAB语言基础及基于 MATLAB的控制系统仿真。本书在结构上包括上下两篇共17章。上篇介绍 MATLAB语言基础,并简要介绍了 MATLAB GUI程序设计和 MATLAB的混合编程知识,共7章;下篇介绍控制系统的 MATLAB仿真,并提供了两个课程设计实例供学习参考,共10章全书结构清晰,内容翔实,图文并茂,以丰富的实例突岀实践性,通过紧密联系实际突出实用性。本书可作为自动控制等相关专业的教学参考用书,也可作为相关领域工程技术人员和研究人员的参考资料。书中 MATLAB语言的介绍较为全面,可供 MATLAB语言入门者学习参考。书中所给综合实例则对相关课程设计、毕业设计等有重要参考价值图书在版编目(CIP)数据MATLAB与控制系统仿真实践/赵广元编著.一北京北京航空航天大学出版社,2009.8( MATLAB开发实例系列图书)ISBN978-7-81124-787-9Ⅰ.M…·Ⅱ.赵…Ⅲ.①自动控制系统一计算机辅助计算一软件包, MATLAB7.4—教材②自动控制系统一计算机仿真一软件包, MATLAB7.4—教材Ⅳ.TP273TP391.9中国版本图书馆CIP数据核字(2009)第073080号MATLAB与控制系统仿真实践赵广元编著责任编辑陈守平刘亚军北京航空航天大学出版社出版发行北京市海淀区学院路37号(100191)发行部电话:(010)82317024传真:(010)82328026http://www.buaapress.comcnE-mail:bhpress@263.net北京市印刷有限公司印装各地书店经销开本:787mm×1092mm1/16印张:20字数:512千字2009年8月第1版2009年8月第1次印刷印数:5000册ISBN978-7-81124-787-9定价:34.00元前言MATLAB被称为 The Language of Technical computing,它面向理工科不同领域,功能强大、使用方便,而更大的优点在于它的高度开放性。正因如此, MATLAB在理工多个学科的仿真中成为首选工具。作者结合“ MATLAB语言与控制系统仿真”的教学实践与研究成果,以 MATLAB R2007a为系统仿真平台,以清新、简洁的风格编写了本书。1.本书结构与内容安排本书在结构上包括上下两篇。上篇为 MATLAB语言基础,共7章;下篇为控制系统的MATLAB仿真,共10章。上篇主要内容有: MATLAB环境认识与操作, MATLAB语言数据类型和运算符等基础知识, MATLAB的数学运算与符号运算, MATLAB语言的程序设计, MATLAB语言的二维图形、三维图形和符号函数的绘制等绘图基础。同时,以基于GUⅠ设计工具 GUIDE的开发为例简要介绍了 MATLAB GUI程序设计,初步介绍了 MATLAB的混合编程知识,并给出了应用 MATLAB Builder for Java进行混合编程的实例。下篇主要内容有:自动控制及其仿真概述;对 MATLAB仿真集成环境— Simulink的较全面介绍,包括基本操作与设置、子系统及封装技术和S函数的编写等高级应用;基于MATLAB的控制系统数学建模包括了不同函数模型的建立及各种系统模型之间的转换,方框图模型的连接化简等;分别从直接判定和图解判定两方面来进行控制系统的稳定性分析;对控制系统的时域分析分别从动态性能指标和稳态性能指标的分析岀发进行描述;对控制系统的根轧迹分析及基于根轨迹的系统校正;对控制系统的频域分析与基于频域法的校正;控制系统的PID控制器设计主要包括了PI控制器的作用分析及设计举例;非线性控制系统分析中首先给出了非线性特性模块的构建举例,之后分别对使用相平面法和描述函数法进行了仿真分析。各章的原理要点起提纲作用,也供回顾之用;同时对所使用的 MATLAB函数给出简明用法说明。最后一章以两个课程设计综合实例演示了实践教学中 MATLAB的系统仿真应用。2.本书的特点本书结构清晰,内容翔实,图文并茂,并突出以下三点:第一,适当扩展介绍 MATLAB。上篇对 MATLAB的介绍除尽可能满足控制系统仿真需要,直接为下篇做铺垫外,作为扩展还简要介绍了 MATLAB GUⅠ程序设计和 MATLAB的混合编程知识,这有利于读者更全面地认识 MATLAB。学生在其他课程的学习、参加竞赛以及毕业设计等活动中主动应用了这两部分内容,证明以适当的篇幅进行 MATLAB的扩展介绍是必要和有效的。第二,以丰富的实例突出实践。通篇以大量实例展示 MATLAB操作及其在控制系统仿真中的应用。各章中避免太多理论的重复讲解,而仅适当地对自动控制原理的已有结论作简要介绍。对于不同例题的分析有助于引导读者对自动控制原理的深入理解,避免仅作函数的使用介绍与举例。建议读者在使用本书时最好手头有一本自动控制原理的教材作参考第三,紧密联系实际突出应用。通过课程设计综合实例的介绍,突出仿真的实际应用,达到将书本知识与实际系统设计联系起来的目的。这两篇课程设计报告源于学生课程设计的优秀作品,经进一步整理完善而形成3.本书的适用对象本书可作为自动控制、机电一体化、计算机仿真等专业的大专院校学生和研究生的教学参考用书,也可作为自动控制相关领域工程技术人员和研究人员的参考资料。本书对 MATLAB语言的介绍较为全面,也可供学习使用 MATLAB语言参考。书中所给综合实例则对相关课程设计、毕业设计等有重要参考价值4.致谢本书成稿过程中,在结构安排方面得到陕西师范大学傅钢善教授的指点。对傅老师的指点与鼓励表示诚挚的谢意本书成稿后,东北大学人工智能与机器人硏究所潘峰博士仔细阅读了主体内容,提岀了诸多宝贵意见。作者已按照其意见进行了修改。在此表示感谢本书是西安邮电学院课程建设项目(院教[2007]26号)的部分成果。本门课程于2009年被评为校级优秀课程。这里对课程建设小组其他成员的不懈努力表示感谢,对教务处的大力支持表示感谢感谢西安邮电学院信息与控制系主任范九伦教授的鼓励与大力支持,感谢自动化实验室全体老师的无私帮助。本书编写过程中,郑祺、魏美荣、张爱妮等做了部分仿真实验工作,马宏宇、白建华、赵晓莉等做了大量资料查阅、文字校对工作,对他们的辛勤付出表示感谢最后特别感谢妻子马泓波博士的全力支持书中所有程序的源代码可在北京航空航天大学出版社(htp:/www.buaapres.com.cn/)下载中心下载。同时,北京航空航天大学出版社联合MATLAB中文论坛(http://wwwiLoveMatlab.cn)为本书设立了在线交流版块,网址http://www.ilOveMatlab.cn/forum156-1.html,有问必答!作者会第一时间在 MATLAB中文论坛勘误,也会根据读者要求陆续上传更多案例和相关知识链接,还会随着 MATLAB版本的升级增添必要的内容以满足读者的需求。希望这本不断“成长”的书能最大限度地解决您在学习、研究、工作中遇到的MATLAB控制系统仿真相关问题由于作者水平有限,加之时间仓促,书中的不足与疏忽之处,敬请读者批评指正编者2009年5月目录上篇 MATLAB语言基础第1章 MATLAB环境认识与操作1.1 MATLAB环境认识1.1.1命令窗口33351.1.2命令历史记录窗口1.1.3工作空间…1.1.4帮助窗口……………………………………………………………………………81.1.5图形窗口101.1.6编辑/调试窗口111.2 MATLAB notebook及其使用…111.2.1 MATLAB Notebook的启动121.2.2 Notebook的菜单命令…121.2.3输出单元的格式控制131.2.4使用M-book模板的技巧14本章小结14第2章 MATLAB语言基础152.1 MATLAB语言的常量与变量鲁·2.1.1 MATLAB语言的常量2.1.2 MATLAB语言的变量162.2 MATLAB语言的运算符……172.2.1算术运算符…172.2.2关系运算符172.2.3逻辑运算符…………………………………172.3 MATLAB语言的数据类型…2.3.1 MATLAB语言的数据类型概述8882.3.2稀疏矩阵2.3.3单元数组222.3.4结构数组252.4 MATLAB语言的基本语句结构………………………………………………284.1直接赋值语句282.4.2调用函数语句29本章小结29第3章 MATLAB的数值运算与符号运算基础3.1数组与矩阵的基本操作…···鲁··,鲁·,·,·,··鲁·鲁…303.1.1数组与矩阵的输入……………303.1.2数组与矩阵元素的操作343.1.3数组与矩阵的输出………………3.2 MATLAB的基本数值运算∴373.2.1算术运算3.2.2关系运算3.2.3逻辑运算433.2.4运算优先级443.3 MATLAB的基本符号运算453.3.1符号运算基本函数453.3.2符号代数方程求解463.3.3符号微积分运算483.3.4 Laplace变换及其反变换、Z变换及其反变换49本章小结∴51第4章 MATLAB语言的程序设计524.1 MATLAB语言的流程结构524.1.1if,else和 elseif组成的条件转移结构…524.1.2 switch,case和 otherwise组成的开关结构534.1.3 while/for循环结构544.1.4try和 catch组成的试探结构544.1.5 MATLAE程序设计举例554.2 MATLAB函数的编写584.2.1 MATLAB函数基本结构……···.··..·;···.····4.2.2 MATLAB函数编写举例3 MATLAB程序设计中的一些问题本章小结……∴65第5章 MATLAB语言的绘图基础665.1二维图形的绘制661.1绘制二维图形的基本函数及示例66图形的修饰及示例5.1.3多图绘制函数及示例特殊应用二维图形的绘制5.2三维图形的绘制805.2.1三维图形绘制函数805.2.2三维图形绘制举例805.3图形的图形化编辑………825.4符号函数绘制图形835.4.1符号函数绘制图形的函数及示例………835.4.2符号函数的图形化绘制方式84本章小结·鲁85第6章 MATLAB GUI程序设计初步866.1GUI设计工具 GUIDE简介866.1.1 GUIDE的启动866.1.2GUI界面的创建6.2GUI程序设计示例876.2.1“ Hello world”程序的设计曹·,·非876.2.2控制系统典型环节的演示程序…………………………………………………89本章小结94第7章 MATLAB的混合编程初步…………957.1 MATLAB的混合编程形式简述957.2常用 MATLAB混合编程方法957.2.1使用 MATLAB的 MATLAB Compiler957.2.2利用 MATLAB引擎( MATLAB Engine)967.2.3利用 ActiveX技术967.2.4利用MAT文件967.2.5使用MEX文件977.2.6利用 MatrixVB实现与 Visual basic的混合编程977.2.7利用 MATLAB Builder系列工具∴977.3示例— MATLABG Builder forJava应用987.3.1生成魔方矩阵的演示程序……987.3.2输出函数曲线的演示程序102本章小结…………∴…105下篇控制系统的 MATLAB仿真第8章自动控制及其仿真概述8.1自动控制系统概述8.1.1自动控制系统的基本形式及特点8.1.2自动控制系统的分类1108.1.3对自动控制系统的要求及性能评价8.2控制系统仿真概述8.2.1仿真的基本概念……………………………………………………………1108.2.2仿真的不同分类1118.2.3仿真技术的应用及发展1128.2.4计算机仿真的要素及基本步骤1132.5控制系统仿真软件本章小结….114第9章 MATLAB的仿真集成环境—— Simulink∴1159.1 Simulink概述……1159.2 Simulink的基本界面操作………1159.3 Simulink的功能模块及其操作1179.3.1 Simulink的功能模块9.3.2功能模块的基本操作1219.3.3功能模块的连接操作1249.4 Simulink仿真环境的设置1249.5子系统及封装技术1269.5.1子系统的建立……………………………………………………………………1269.5.2子系统的封装1279.6用 Simulink建立系统模型示例1299.7 Simulink的高级应用—S函数的编写1329.7.1S-函数的工作原理1329.7.2S-函数的设计实例…138本章小结……·········.···143第10章基于 MATLAB的控制系统数学建模14410.1控制系统的传递函数模型14410.1.1系统传递函数模型简述14410.1.2传递函数的 MATLAB相关函数……14510.1.3建立传递函数模型实例∴………………14610.2控制系统的零极点函数模型14910.2.1零极点函数模型简述鲁·要10.2.2零极点函数的 MATLAB相关函数14910.2.3建立零极点函数模型实例∴……………………15010.3控制系统的状态空间函数模型15310.3.1状态空问函数模型简述………………15310.3.2状态空间函数的 MATLAB相关函数15310.3.3建立状态空间函数模型实例…15410.4系统模型之间的转换15610.4.1系统模型转换的 MATLAB相关函数15610.4.2系统模型之间转换实例10.5方框图模型的连接化简16110.5.1方框图模型的连接化简简述…………………………………………………16110.5.2系统模型连接化简的 MATLAB相关函数16310.5.3系统模型连接化简实例16310.6 Simulink图形化系统建模实例…166本章小结………………167第∏1章控制系统的稳定性分析16811.1系统稳定性的 MATLAB直接判定……16911.1.1 MATLAB直接判定的相关函数16911.1.2 MATLAB直接判定实例………………16911.2系统稳定性的 MATLAB图解判定…17211.2.1 MATLAB图解判定的相关函数17211.2.2 MATLAB图解判定实例17211.3 MATLAB LTI Viewer稳定性判定实例………………174本章小结176第12章控制系统的时域分析7712.1控制系统的动态性能指标分析12.1.1控制系统的动态性能指标7712.1.2控制系统动态性能指标 MATLAB求取实例12.2控制系统的稳态性能指标分析18512.2.1系统的稳态性能指标………18512.2.2控制系统稳态性能指标 MATLAB求取实例…18512.3 MATLAB时域响应仿真的典型函数应用18812.3.1 MATLAB时域响应仿真的典型函数18812.3.2 MATLAB时域响应仿真的典型函数应用实例………………………………18812.4 MATLAB/ Simulink图形化时域分析19212.4.1 MATLAB LTI Viewer时域分析实例19212.4.2 Simulink时域分析实例194本章小结196第13章控制系统的根轨迹分析与校正19713.1控制系统的根轨迹法分析19913.1.1 MATLAB根轨迹分析的相关函数…13.1.2 MATLAB根轨迹分析实例19913.2控制系统的根轨迹法校正21113.2.1根轨迹法超前校正及基于 MATLAB的实例21213.2.2根轨迹法滞后校正及基于 MATLAE的实例……21613.3 MATLAB图形化根轨迹法分析与设计22013.3.1 MATLAB图形化根轨迹法分析与设计工具 rltool∴…∴22013.3.2基于图形化工具 rltool的系统分析与设计实例221本章小结223
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