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譯文題目： 現(xiàn)代的控制理論的簡單介紹
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20xx年 2月 27日
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 whichcontinuous 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. Another important 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(three 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 of:
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.
現(xiàn)代的控制理論的簡單介紹
下列幾方面為現(xiàn)代控制理論發(fā)展的促進因素:
1.處理更多的現(xiàn)實模型系統(tǒng)的必要性
2.強調(diào)向最佳的控制和最佳的系統(tǒng)設計的升級
3.數(shù)字化計算機技術(shù)的持續(xù)發(fā)展.
4.當前技術(shù)的不成熟.
眾所周知的方法在其它知識領(lǐng)域的適用性得到承認.
從容易解決的簡單近似的模型到更多的現(xiàn)實模型的轉(zhuǎn)變產(chǎn)生了兩種效果：首先，模型必須包括很多的變量。其次，一個十分逼真的模型是盡可能的包括非線性和隨時間變化的參數(shù)。早先的忽略了系統(tǒng)的一些方面，例如很有可能的一方面就是在環(huán)境中有著反饋的交互作用。
在現(xiàn)代科技高度發(fā)達的社會，存在一種非常雄心的目標的趨勢，這也意味著要處理有著很多相互關(guān)聯(lián)成分的復雜系統(tǒng)，高精確度與高效率的需要改變了控制系統(tǒng)的執(zhí)行重點。在超頻百分比，時間設置，頻寬等等方面的經(jīng)典規(guī)范，在很多情況下解決了優(yōu)化標準如最小能量，最小花費，最小時間控制，優(yōu)化這些標準時很難避免和不開心的非線性打交道。即使基礎(chǔ)系統(tǒng)是線性的和不隨時間變化的，優(yōu)化控制理論顯示非線性時間變化控制也被應用到了。
不停發(fā)展的計算機技術(shù)在控制領(lǐng)域創(chuàng)造了三條最重要的影響。其中一項是有關(guān)數(shù)字化的超級計算機，較之這本書首印時期，現(xiàn)在能模擬，分析，控制的問題的大小和種類都要大得驚人。
計算機技術(shù)的第二個問題就是必須處理微型計算機在家庭和工作地的擴散與廣泛的可靠性。古典的控制理論是以圖畫似的方法為主導的. 因為在時間那是唯一的解決確定的問題的途徑。為了系統(tǒng)分析和設計,現(xiàn)在每一個控制設計者很容易有機會接近強大的計算機內(nèi)部。老的圖畫似的方法不但沒有消失, 并且還使其自動化了.它們之所以能生存是因為提供了洞察力與直覺，許多不同的技術(shù)經(jīng)常能更適合于計算機。雖然計算機能被用于執(zhí)行經(jīng)典的改變-到轉(zhuǎn)的改變方法，但它通常更多的有效用于直接整合微分方程。
計算機的第三個，也是最重要的方面，就是它們現(xiàn)在已經(jīng)如此普遍地應用于控制系統(tǒng)，儼然其中的一員。其價格，型號和穩(wěn)定性使得能夠在許多系統(tǒng)中常規(guī)的使用。這也意味著離散的-時間和數(shù)字的系統(tǒng)控制現(xiàn)在比在它過去更受人關(guān)注。
現(xiàn)代的控制理論更適合上面的趨勢. 因為它的時間-領(lǐng)域技術(shù)和它的數(shù)學的語言(公式, 線性向量空間, 等等.) 是處理計算機時的方法。. 計算機是狀態(tài)變量方法存在的主要原因。
最多的古典的控制技術(shù)是為了發(fā)展只有一個輸入和一個輸出(或許少許輸入和輸出)線性常數(shù)系數(shù)系統(tǒng). 古典的技術(shù)的語言是拉普內(nèi)斯或Z-改變和傳送功能. 就在那個時候非線性和時間變量出現(xiàn)了, 這些古典的技術(shù)的基礎(chǔ)遠離了. 一些成功的技術(shù)例如階段-平面方法, 描述函數(shù), 和其他的特別方法,發(fā)展并緩和了這些缺點。然而, 最大的成功被這些低級命令系統(tǒng)限制了. 現(xiàn)代的控制理論的狀態(tài)變量接近供應統(tǒng)一和強大的方法表現(xiàn)任意的訂購的系統(tǒng), 線的或非線性的, 有時間-改變或常數(shù)系數(shù).它為形成計算機的執(zhí)行提供了理論，同時也對大多數(shù)優(yōu)化理論的進程負有責任。
現(xiàn)代的控制理論是在控制領(lǐng)域的最近發(fā)展. 因此, 這個名字至少替換了一個描述性的標題. 然而, 現(xiàn)代的控制理論的基礎(chǔ)在其它已知領(lǐng)域也被發(fā)現(xiàn)了. 用一般化坐標和一般化瞬間表現(xiàn)一個系統(tǒng)時，在相關(guān)狀態(tài)變量上，其等同到接近哈密爾敦函數(shù)機械學,. 這接近的優(yōu)勢在古典的物理學已經(jīng)聞名了許多年. 應用數(shù)學領(lǐng)域中，在處理各種形式相類似的方程時，利用母式的優(yōu)越性早已表現(xiàn)出來了，線性代數(shù)學也很大程度上歸功于現(xiàn)代的控制理論。 這是由于線性代數(shù)學所提供的簡明的符號, 結(jié)果的普遍性, 和思考的效率。
表面粗糙度的技術(shù)
在已經(jīng)進行機械加工過的表面，有五種基本的影響其表面粗糙度的技術(shù)。
1、切斷過程的基本幾何學. 例如，在單點車削時，工件每轉(zhuǎn)一周，刀具就沿軸線方向進給一個固定的距離。從垂直刀具進給的方向觀察，所得到的表面上有很多尖角，這些尖角的形狀與切削刀具的形狀相同。
2、切斷操作的效率. 已經(jīng)提過的用不穩(wěn)定的切削瘤切削將會加工出包含有堅硬的切削瘤碎片在上面的表面，而這些將會導致表明粗糙度的等級降低。已經(jīng)證明，在采用進給量大，前角小，切削速度低的不利情況下，除了產(chǎn)生不穩(wěn)定的切削瘤外，切削過程也會不穩(wěn)定。同時，在切削區(qū)里進行的也不再是切削，而是撕裂，導致厚度不均勻，不連續(xù)的切削，加工出的表面質(zhì)量差。在切削加工延展性良好的金屬材料，如銅和鋁時，這種情況就尤為突出。
3、機械工具的穩(wěn)定性。在許多聯(lián)合切削的情況下：工件的大小，夾緊的方法，和切斷工具相對于機床結(jié)構(gòu)的堅硬度，不穩(wěn)定性是建立在使其變化的工具上的。在某些情況下，這種變化將達到并保持很長一段時間，在另外一些情況下，這種變化將會產(chǎn)生，除非切斷停止，否則，將肯定會同時對切斷刀具和工具產(chǎn)生破壞。這種現(xiàn)象就是知名的刀振，在軸向轉(zhuǎn)動被描述為在工件表面的長間距螺旋狀帶和段間距波動在機械加工的過渡表面。
4、刀刃的移動效率。在不連續(xù)的產(chǎn)品加工過程中例如易碎材料的磨或旋轉(zhuǎn)，我們期望碎片在重力作用或在冷卻液的噴射作用下將離開切削面域。而且怎么也不會影響切削表面。然而，在連續(xù)切削時，產(chǎn)品是明顯的，除非逐步控制刀刃，否則他很有可能中級切削表面并在其上留下記號。不可避免，這記號在旁邊樣子不美的, 時常導致差的表面粗糙度。
5、切斷工具的有效清除角。由于副切削刃的某種幾何特征減輕和清除了角，使得在主切削面上主切削刃切削和副切削刃打磨變得可能。這樣能加工出良好的表面粗糙度，但是，當然，它嚴格來講，是一種金屬切削和金屬成型的綜合，而不失被認為的一種實際的切削方法。然而，歸功于切削工具的表面處理，這些情況偶爾才會出現(xiàn)，并導致了表面特性的標志性改變。
表面精整加工與尺寸控制
產(chǎn)品在被加工成它們的適當?shù)耐庑魏痛笮r，經(jīng)常地需要各種的表面精整加工，使得其能夠比較令人滿意地履行它們的功能. 在一些情況下，通過提高材料表面的物理特性來抵抗腐蝕和磨損是非常重要的。在許多制造過程中，產(chǎn)品表面上都殘留有污垢，碎屑，油漬以及其它有害的材料。假設那是由不同種金屬材料，或是由同一種金屬材料在不同的加工方式中所造成的，大多數(shù)需要一些特殊的表面處理技術(shù)來提供均勻的外表面。
有時表面精整加工也許只是中間階段處理，例如，清潔的和磨光在任何一種電鍍之前都是必不可少的工序。有些清潔程序是為了改善配合處表面的光滑程度，或是清除會對稍候工序產(chǎn)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為了在各種各樣的環(huán)境下防腐蝕。這種保護程序很大程度上依賴于預期的暴露，考慮到材料將被保護和其所包含的經(jīng)濟因素。
滿意于上表面材料使應用主要表面精整技術(shù)成為必然性，而這技術(shù)包括材料工作表面特性在化學上的改變，用各種方法清洗，以及有機的和金屬的保護膜的應用。
在早期的工程中，零部件的裝配是這樣完成的：加工一個部件使其盡可能的達到要求的大小，加工裝配部件接近大小時，也就完成了它的加工，繼續(xù)提供另一部件，直到獲得所要求的配合關(guān)系。如果在加工一個部件時不方便提供另一部件，那么最后的工作將交予裝配工完成，它刮削裝配部件直到獲得要求的配合。因此，裝配工也就成為了“fitter”在字面上的意思了。很顯然，這兩部件將必然保持在一起，最重要的是其中一個具有互換性，裝配也將全部重新完成。在這期間，我們希望能更換一個已經(jīng)壞掉了的零件，并且在不需要刮磨和其它裝配作業(yè)的情況下就能具有原有功能。
如果一個部件能被用作為備用件去替換另一格同樣尺寸和材料特性的零件，那么我們就說它具有互換性。具有互換性的系統(tǒng)經(jīng)?？梢詼p少其產(chǎn)品成本，因此，對于一種昂貴的，瑣細的加工工藝沒有必要存在。而且萬一假使顧客有必要更換磨損了的零部件。
大批量生產(chǎn)的零部件都具有可互換性。也就是說，一部機器或一個系統(tǒng)的每一個零部件都做成確定的大小和規(guī)格，因此它們將用于裝入于同類型的其它機器或系統(tǒng)。為了使零部件具有互換性，每個單個零件都必須做成可以與其配件能正確裝配。把每個零件做成確切的大小，那不但沒有必要，也是不切實際的。這是因為機器不時完美無缺的，加工工具也會在加工過程中逐漸損耗。在允許范圍內(nèi)稍微的尺寸變動經(jīng)常是允許的。而這個變動的范圍是由要進行制造的零件所決定的。例如，一個零件要做成6英寸大小，長度變化范圍是正負0.003英寸。因此，這個零件制成5.997英寸或者6.003英寸都符合正確的尺寸要求。這就是極限。上限尺寸與下限尺寸之間的大小就是公差。公差就是零件大小尺寸總的允許變動量。
基本尺寸就是那樣的尺寸，從基本尺寸出發(fā)，應用極限和公差來得到(推導出)尺寸極限。
有時候極限允許值存在于一個方向，這就是所謂的單邊公差。
單邊公差標注是一種只表現(xiàn)在標稱大小的單方向的尺寸標注制度，它允許在沒有嚴重影響配合的前提下來改變孔或軸的公差。
當公差是基本尺寸向兩側(cè)延伸時，這時就變成了雙向公差（正或負）。
雙向公差標注是一種當公差在分離或者表現(xiàn)與標稱尺寸兩側(cè)時的尺寸標注制度。極限尺寸標注就是一種在僅僅表現(xiàn)出尺寸的最大值或最小值是的尺寸標注制度。因此，公差就是在這兩種尺寸之間的距離。
機器加工的介紹
作為一種成型方法，機械加工得到了普遍應用并且成為了機械制造過程中最重要的部分。機械加工是一種在動力驅(qū)動下使材料以碎屑的方式分離的成型方法。盡管在某些場合，工件無支撐情況下，使用移動式裝備來實現(xiàn)加工，但大多數(shù)的機械加工還是通過既支承工件又支承刀具的裝備來完成。
小批量的安裝成本。機械加工在機械制造中有兩種應用形式。為鑄造，鍛造和壓力加工等的特種成型制造，僅僅只是一個零部件，幾乎經(jīng)常達到了刀具的高花費。這些外形可能是焊接而成的，它很大程度上取決于可利用的原材料的外形。一般來說，通過利用高價設備而又無需特種加工條件下，幾乎可以從任何種類原材料開始，借助機械加工把原材料加工成任意所要求的結(jié)構(gòu)現(xiàn)狀，只要外部尺寸足夠大，那都是可能的。
嚴密的精度，合適的表面粗糙度。機械加工的另一個應用就是基于高精度和表面精整處理上的。對于雖低但可以接受的公差，許多小批量加工的零件可以利用其它的方法來大批量的生產(chǎn)。另一方面，許多零部件的外形是由在所選的需要高精度的表面經(jīng)過大量的機械加工所形成的。例如內(nèi)孔，很少是由除了機械加工以外的方法加工的，壓力加工零件上的小孔，也許就是在壓力加工操作之后的機械加工出來的。