Introduction to Modern Control Theory中英文
Introduction to Modern Control Theory
Several factors provided the stimulus for the development of modern control theory:
a. The necessary of dealing with more realistic models of system.
b. The shift in emphasis towards optimal control and optimal system design.
c. The continuing developments in digital computer technology.
d. The shortcoming of previous approaches.
e. Recognition of the applicability of well-known methods in other fields of knowledge.
The transition from simple approximate models, which are easy to work with, to more realistic models, produces two effects. First, a large number of variables must be included in the models. Second, a more realistic model is more likely to contain nonlinearities and time-varying parameters. Previously ignored aspects of the system, such as interactions with feedback through the environment, are more likely to be included.
With an advancing technological society, there is a trend towards more ambitious goals. This also means dealing with complex system with a large number of interacting components. The need for greater accuracy and efficiency has changer the emphasis on control system performance. The classical specifications in terms of percent overshoot, setting time, bandwidth, etc. have in many cases given way to optimal criteria such as mini mum energy, minimum cost, and minimum time operation. Optimization of these criteria makes it even more difficult to avoid dealing with unpleasant nonlinearities. Optimal control theory often dictates that nonlinear time-varying control laws are used, even if the basic system is linear and time-invariant.
The continuing advances in computer technology have had three principal effects on the controls field. One of these relates to the gigantic supercomputers. The size and the class of the problems that can now be modeled, analyzed, and controlled are considerably large than they were when the first
edition of this book was written.
The second impact of the computer technology has to so with the proliferation and wide availability of the microcomputers in homes and I the work place, classical control theory was dominated by graphical methods because at the time that was the only way to solve certain problems, Now every control designer has easy access to powerful computer packages for systems analysis and design. The old graphical methods have not yet disappeared, but have been automated. They survive because of the insight and intuition that they can provide, some different techniques are often better suited to a computer. Although a computer can be used to carry out the classical transform-inverse transform methods, it is used usually more efficient for a computer to integrate differential equations directly.
The third major impact of the computers is that they are now so commonly used as just another component in the control systems. This means that the discrete-time and digital system control now deserves much more attention than it did in the past.
Modern control theory is well suited to the above trends because its time-domain techniques and its mathematical language (matrices, linear vector spaces, etc.) are ideal when dealing with a computer. Computers are a major reason for the existence of state variable methods.
Most classical control techniques were developed for linear constant coefficient systems with one input and one output (perhaps a few inputs and outputs). The language of classical techniques is the Laplace or Z-transform and transfer functions. When nonlinearities ad time variations are present, the very basis for these classical techniques is removed. Some successful techniques such as phase-plane methods, describing function s, and other ad hoc methods, have been developed to alleviant this shortcoming.
However, the greatest success has been limited to low-order systems. The state variable approach of modern control theory provides a uniform and powerful method of representing systems of arbitrary order, linear or nonlinear, with time-varying or constant coefficient. It provides an ideal formulation for
computer implementation and is responsible for much of the progress in optimization theory.
Modern control theory is a recent development in the field of control. Therefore, the name is justified at least as a descriptive title. However, the foundations of modern control theory are to be found in other well-established fields. Representing a system in terms of state variables is equivalent to the approach of Hamiltonian mechanics, using generalized coordinates and generalized moment. The advantages of this approach have been well-known I classical physics for many years. The advantages of using matrices when dealing with simultaneous equations of various kinds have long been appreciated in applied mathematics. The field of linear algebra also contributes heavily to modern control theory. This is due to the concise notation, the generality of the results, and the economy of thought that linear algebra provides.
Mechanism of Surface Finish Production
There are basically five mechanisms which contribute to the production of a surface which have been machined. There are:
(1) The basic geometry of the cutting process. In, for example, single point turning the tool will advance a constant distance axially per revolution of the work piece and the resultant surface will have on it, when viewed perpendicularly to the direction of tool feed motion, a series of cusps which will have a basic form which replicates the shape of the tool in cut.
(2) The efficiency of the cutting operation. It has already been mentioned that cutting with unstable built-up-edges will produce a surface which contains hard built-up-edge fragments which will result in a degradation of the surface finish. It can also be demonstrated that cutting under adverse conditions such as apply when using large feeds small rake angles and low cutting speeds, besides producing conditions which continuous shear occurring in the shear zone, tearing takes place, discontinuous chips of uneven thickness are produced, and the resultant surface is poor. This situation is particularly noticeable when machining very ductile materials such as copper and aluminum.
(3) The stability of the machine tool. Under some combinations of cutting conditions: work piece size , method of clamping, and cutting tool rigidity relative to the machine tool structure, instability can be set up in the tool which causes it to vibrate. Under some conditions the vibration will built up and unless cutting is stopped considerable damage to both the cutting tool and work piece may occur. This phenomenon is known as chatter and in axial turning is characterized by long pitch helical bands on the work piece surface and short pitch undulations on the transient machined surface.
(4) The effectiveness of removing sward. In discontinuous chip production machining, such as milling or turning of brittle materials, it is expected that the chip (sward) will leave the cutting zone either under gravity or with the assistance of a jet of cutting fluid and that they will not influence the cut surface in any way. However, when continuous chip production is evident, unless steps ate taken to control the swarf it is likely that it will impinge on the cut surface and mark it. Inevitably, this marking beside a looking unattractive, often results in a poorer surface finishing,
(5) The effective clearance angle on the cutting tool. For certain geometries of minor cutting edge relief and clearance angles it is possible to cut on the major cutting edge and burnish on the minor cutting edge. This can produce a good surface finish but, of course, it is strictly a combination of metal cutting and metal forming and is not to be recommended as a practical cutting method. However, due to cutting tool wear, these conditions occasionally arise and lead to a marked change in the surface characteristics.
Surface Finishing and Dimensional Control
Products that have been completed to their proper shape and size frequently require some type of surface finishing to enable than to satisfactorily fulfill their function. In some cases, tit is necessary to improve the physical properties of the surface material for resistance to penetration or abrasion. In many manufacturing processes, the product surface is left with dirt, chips, grease, or other harmful material upon it. Assemblies that are made of different materials,
or from the same materials processed in different manners, many require some special surface treatment to provide uniformity of appearance.
Surface finishing many sometimes become an intermediate step processing. For instance, cleaning and polishing are usually essential before any kind of plating process. Some of the cleaning procedures are also used for improving surface smoothness on mating parts and for removing burrs and sharp corners, which might be harmful in later use. Anotherimportant need for surface finishing is for corrosion protection in a variety of environments. The type of protection procedure will depend largely upon the anticipated exposure, with due consideration to the material being protected and the economic factors involved.
Satisfying the above objectives necessitates the use of main surface-finishing methods that involve chemical change of the surface mechanical work affecting surface properties, cleaning by a variety of methods, and the application of protective coatings, organic and metallic.
In the early days of engineering, the mating of parts was achieved by machining one part as nearly as possible to the required size, machining the mating part nearly to size, and then completing its machining, continually offering the other part to it, until the desired relationship was obtained. If it was inconvenient to offer one par to the other part during machining, the final work was done at the bench by a fitter, who scraped the mating parts until the desired fit was obtained, the fitter therefore being a ‘fitter’ in the literal sense. It is obvious that the two parts would have to remain together, and in the event of one having to be replaced, the fitting would have to be done all over again. I n these days, we expect to be able to purchase a replacement for a broken part, and for it to function correctly without the need for scraping and other fitting operations.
When one part can be used ‘off the shelf’ to replace another of the same dimension and material specification, the parts are said to be interchangeable. A system of interchangeability usually lowers the production costs as there is no need for an expensive, ‘fiddling’ operation, and it benefits the customer in the event of the need to replace worn parts.
Limits and Tolerances
Machine parts are manufactured so they are interchangeable. In other words, each part of a machine or mechanism is made to a certain size and shape so it will fit into any other machine or mechanism of the same type. To make the part interchangeable, each individual part must be made to a size that will fit the mating part in the correct way. It is not only impossible, but also impractical to make many parts to an exact size. This is because machines are not perfect, and the tools become worn. A slight variation from the exact size is always allowed. The amount of this variation depends on the kind of part being manufactured. For example, a part might be made 6 in. long with a variation allowed of 0.003(th ree thousandths) in. above and below this size. Therefore, the part could be 5.997 to 6.003 in. and still be the correct size. These are known as the limits. The difference between upper and lower limits is called the tolerance.
A tolerance is the total permissible variation in the size of a part.
The basic size is that size from which limits of size are derived by the application of allowances and tolerances.
Sometimes the limit is allowed in only one direction. This is known as unilateral tolerance.
Unilateral tolerancing is a system of dimensioning where the tolerance (that is variation) is shown I only one direction from the nominal size. Unilateral tolerancing allow the changing of tolerance on a hole or shaft without seriously affecting the fit.
When the tolerance is in both directions from the basic size, it is known as a bilateral tolerance (plus and minus).
Bilateral tolerancing is a system of dimensioning where the tolerance (that is variation) is split and is shown on either side of the nominal size. Limit dimensioning is a system of dimensioning where only the maximum and minimum dimensions are shown. Thus, the tolerance is the difference between these two dimensions.
Introduction of Machining
Machining as a shape-producing method is the most universally used and the most important of all manufacturing processes. Machining is a shape-producing process in which a power-driven device causes material to be removed in chip form. Most machining is done with equipment that supports both the work piece and cutting tool although in some cases portable equipment is used with unsupported work piece.
Low setup cost for small quantities. Machining has two applications in manufacturing. For casting, forging, and pressworking, each specific shape to be produced, even one part, nearly always has a high tooling cost. The shapes that may be produced by welding depend to a large degree on the shapes of raw material that are available. By making use of generally high cost equipment but without special tooling, it is possible, by machining, to start with nearly any form of raw material, so long as the exterior dimensions are great enough, and produce any desired shape from any material. Therefore, machining is usually the preferred method for producing one or a few parts, even when the design of the part would logically lead to casting, forging or pressworking if a high quantity were to be produced.
Close accuracies, good finishes. The second application for machining is based on the high accuracies and surface finishes possible. Many of the parts machined in low quantities would be produced with lower but acceptable tolerances if produced I high quantities by some other process. On the other hand, many parts are given their general shapes by some high quantity deformation process and machined only on selected surfaces where high accuracies are needed. Internal threads, for example, are seldom produced by any means other than machining and small holes in pressworked parts may be machined following the pressworking operations.
现代的控制理论简介
下列几方面为现代控制理论发展的促进因素:
1.处理更多的现实模型系统的必要性；
2.强调向最佳的控制和最佳的系统设计的升级；
3.数字化计算机技术的持续发展；
4.当前技术的不成熟。
众所周知的方法在其它知识领域的适用性得到承认。
从容易解决的简单近似的模型到更多的现实模型的转变产生了两种效果：首先，模型必须包括很多的变量；其次，一个十分逼真的模型是尽可能的包括非线性和随时间变化的参数。早先忽略了系统的一些方面，例如很有可能的一方面就是在环境中有着反馈的交互作用。
在现代科技高度发达的社会，存在一种非常雄心的目标的趋势，这也意味着要处理有着很多相互关联成分的复杂系统，高精确度与高效率的需要改变了控制系统的执行重点。在超频百分比，时间设置，频宽等方面的典型规范，在很多情况下解决了优化标准。如最小能量、最小花费、最小时间控制，优化这些标准时很难避免和不开心的非线性打交道。即使基础系统是线性的和不随时间变化的，优化控制理论显示非线性时间变化控制也被应用到了。
不停发展的计算机技术在控制领域创造了三条最重要的影响。其中一项是有关数字化的超级计算机，较之这本书首印时期，现在能模拟，分析，控制的问题的大小和种类都要大得惊人。
计算机技术的第二个问题就是必须处理微型计算机在家庭和工作地的扩散与广泛的可靠性。古典的控制理论是以图画似的方法为主导的. 因为在时间那是唯一的解决确定的问题的途径。为了系统分析和设计,现在每一个控制设计者很容易有机会接近强大的计算机内部。老的图画似的方法不但没有消失, 并且还使其自动化了。它们之所以能生存是因为提供了洞察力与直觉，许多不同的技术经常能更适合于计算机。虽然计算机能被用于执行经典的改变-到转的改变方法，但它通常更多的有效用于直接整合微分方程。
计算机的第三个，也是最重要的方面，就是它们现在已经如此普遍地应用于控制系统，俨然其中的一员。其价格，型号和稳定性使得能够在许多系统中常规的使用。这也意味着离散的-时间和数字的系统控制现在比在它过
去更受人关注。
现代的控制理论更适合上面的趋势。因为它的时间-领域技术和它的数学的语言(公式, 线性向量空间等) 是处理计算机时的方法。计算机是状态变量方法存在的主要原因。
最多的古典的控制技术是为了发展只有一个输入和一个输出(或许少许输入和输出)线性常数系数系统。古典的技术的语言是拉普内斯或Z-改变和传送功能。就在那个时候非线性和时间变量出现了, 这些古典的技术的基础远离了.。一些成功的技术例如阶段-平面方法, 描述函数和其他的特别方法,发展并缓和了这些缺点。然而, 最大的成功被这些低级命令系统限制了。现代的控制理论的状态变量接近供应统一和强大的方法表现任意的订购的系统, 线的或非线性的, 有时间-改变或常数系数。它为形成计算机的执行提供了理论，同时也对大多数优化理论的进程负有责任。
现代的控制理论是在控制领域的最近发展。因此,这个名字至少替换了一个描述性的标题。然而,现代的控制理论的基础在其它已知领域也被发现了。用一般化坐标和一般化瞬间表现一个系统时，在相关状态变量上，其等同到
接近哈密尔敦函数机械学,这接近的优势在古典的物理学已经闻名了许多年. 应用数学领域中，在处理各种形式相类似的方程时，利用母式的优越性早已
表现出来了，线性代数学也很大程度上归功于现代的控制理论。这是由于线
性代数学所提供的简明的符号,结果的普遍性和思考的效率。
表面粗糙度的技术
在已经进行机械加工过的表面，有五种基本的影响其表面粗糙度的技术。
1、切断过程的基本几何学。例如，在单点车削时，工件每转一周，刀具
就沿轴线方向进给一个固定的距离。从垂直刀具进给的方向观察，所得到的
表面上有很多尖角，这些尖角的形状与切削刀具的形状相同。
2、切断操作的效率。已经提过的用不稳定的切削瘤切削将会加工出包含
有坚硬的切削瘤碎片在上面的表面，而这些将会导致表明粗糙度的等级降低。已经证明，在采用进给量大，前角小，切削速度低的不利情况下，除了
产生不稳定的切削瘤外，切削过程也会不稳定。同时，在切削区里进行的也
不再是切削，而是撕裂，导致厚度不均匀，不连续的切削，加工出的表面质
量差。在切削加工延展性良好的金属材料，如铜和铝时，这种情况就尤为突
出。
3、机械工具的稳定性。在许多联合切削的情况下：工件的大小，夹紧的方法，和切断工具相对于机床结构的坚硬度，不稳定性是建立在使其变化的工具上的。在某些情况下，这种变化将达到并保持很长一段时间，在另外一些情况下，这种变化将会产生，除非切断停止，否则，将肯定会同时对切断刀具和工具产生破坏。这种现象就是有名的刀振，在轴向转动被描述为在工件表面的长间距螺旋状带和段间距波动在机械加工的过渡表面。
4、刀刃的移动效率。在不连续的产品加工过程中例如易碎材料的磨或旋转，我们期望碎片在重力作用或在冷却液的喷射作用下将离开切削面域。而且怎么也不会影响切削表面。然而，在连续切削时，产品是明显的，除非逐步控制刀刃，否则他很有可能中级切削表面并在其上留下记号。不可避免，这记号在旁边样子不美的, 时常导致差的表面粗糙度。
5、切断工具的有效清除角。由于副切削刃的某种几何特征减轻和清除了角，使得在主切削面上主切削刃切削和副切削刃打磨变得可能。这样能加工出良好的表面粗糙度，但是，当然，它严格来讲，是一种金属切削和金属成型的综合，而不失被认为的一种实际的切削方法。然而，归功于切削工具的表面处理，这些情况偶尔才会出现，并导致了表面特性的标志性改变。
表面精整加工与尺寸控制
产品在被加工成它们的适当的外形和大小时，经常地需要各种的表面精整加工，使得其能够比较令人满意地履行它们的功能. 在一些情况下，通过提高材料表面的物理特性来抵抗腐蚀和磨损是非常重要的。在许多制造过程中，产品表面上都残留有污垢，碎屑，油渍以及其它有害的材料。假设那是由不同种金属材料，或是由同一种金属材料在不同的加工方式中所造成的，大多数需要一些特殊的表面处理技术来提供均匀的外表面。
有时表面精整加工也许只是中间阶段处理，例如，清洁的和磨光在任何一种电镀之前都是必不可少的工序。有些清洁程序是为了改善配合处表面的光滑程度，或是清除会对稍候工序产生有害作用的毛刺和尖角。表面精整加工的另一重要需要就是为了在各种各样的环境下防腐蚀。这种保护程序很大程度上依赖于预期的暴露，考虑到材料将被保护和其所包含的经济因素。
满意于上表面材料使应用主要表面精整技术成为必然性，而这技术包括
材料工作表面特性在化学上的改变，用各种方法清洗，以及有机的和金属的保护膜的应用。
在早期的工程中，零部件的装配是这样完成的：加工一个部件使其尽可能的达到要求的大小，加工装配部件接近大小时，也就完成了它的加工，继续提供另一部件，直到获得所要求的配合关系。如果在加工一个部件时不方便提供另一部件，那么最后的工作将交予装配工完成，它刮削装配部件直到获得要求的配合。因此，装配工也就成为了“装配工”在字面上的意思了。很显然，这两部件将必然保持在一起，最重要的是其中一个具有互换性，装配也将全部重新完成。在这期间，我们希望能更换一个已经坏掉了的零件，并且在不需要刮磨和其它装配作业的情况下就能具有原有功能。
如果一个部件能被用作为备用件去替换另一格同样尺寸和材料特性的零件，那么我们就说它具有互换性。具有互换性的系统经常可以减少其产品成本，因此，对于一种昂贵的，琐细的加工工艺没有必要存在。而且万一假使顾客有必要更换磨损了的零部件。
大批量生产的零部件都具有可互换性。也就是说，一部机器或一个系统的每一个零部件都做成确定的大小和规格，因此它们将用于装入于同类型的其它机器或系统。为了使零部件具有互换性，每个单个零件都必须做成可以与其配件能正确装配。把每个零件做成确切的大小，那不但没有必要，也是不切实际的。这是因为机器不时完美无缺的，加工工具也会在加工过程中逐渐损耗。在允许范围内稍微的尺寸变动经常是允许的。而这个变动的范围是由要进行制造的零件所决定的。例如，一个零件要做成6英寸大小，长度变化范围是±0.003英寸。因此，这个零件制成5.997英寸或者6.003英寸都符合正确的尺寸要求。这就是极限，上限尺寸与下限尺寸之间的大小就是公差。公差就是零件大小尺寸总的允许变动量。
基本尺寸就是那样的尺寸，从基本尺寸出发，应用极限和公差来得到(推导出)尺寸极限。
有时候极限允许值存在于一个方向，这就是所谓的单边公差。
单边公差标注是一种只表现在标称大小的单方向的尺寸标注制度，它允许在没有严重影响配合的前提下来改变孔或轴的公差。
当公差是基本尺寸向两侧延伸时，这时就变成了双向公差（正或负）。
双向公差标注是一种当公差在分离或者表现与标称尺寸两侧时的尺寸
标注制度。极限尺寸标注就是一种在仅仅表现出尺寸的最大值或最小值是的尺寸标注制度。因此，公差就是在这两种尺寸之间的距离。
机器加工的介绍
作为一种成型方法，机械加工得到了普遍应用并且成为了机械制造过程中最重要的部分。机械加工是一种在动力驱动下使材料以碎屑的方式分离的成型方法。尽管在某些场合，工件无支撑情况下，使用移动式装备来实现加工，但大多数的机械加工还是通过既支承工件又支承刀具的装备来完成。
小批量的安装成本。机械加工在机械制造中有两种应用形式。为铸造，锻造和压力加工等的特种成型制造，仅仅只是一个零部件，几乎经常达到了刀具的高花费。这些外形可能是焊接而成的，它很大程度上取决于可利用的原材料的外形。一般来说，通过利用高价设备而又无需特种加工条件下，几乎可以从任何种类原材料开始，借助机械加工把原材料加工成任意所要求的结构现状，只要外部尺寸足够大，那都是可能的。
严密的精度，合适的表面粗糙度。机械加工的另一个应用就是基于高精度和表面精整处理上的。对于虽低但可以接受的公差，许多小批量加工的零件可以利用其它的方法来大批量的生产。另一方面，许多零部件的外形是由在所选的需要高精度的表面经过大量的机械加工所形成的。例如内孔，很少是由除了机械加工以外的方法加工的，压力加工零件上的小孔，也许就是在压力加工操作之后的机械加工出来的。