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1、<p> Introduction to Control System</p><p> 1 HISTORICAL PERSPECTIVE</p><p> The desire to control the forces of nature has been with man since early civilizations. Although many exampl
2、es of control systems existed in early times, it was not until the mid-eighteenth century that several steam engine, and perhaps the most noteworthy invention was the speed control flyball governor invented by James Wa
3、tt.</p><p> The period biginnign about twenty-five years before World War Two saw rapid advances in electronics and especially in circuit theory, aided by the now classical work of Nyquist in the area of st
4、ability theory, The requirements of sophisticated weapon systems, submarines, aircraft and the like gave new impetus to the work in control systems before and after the war The advent of the analog computer coupled with
5、advances in electronics saw the beginning of the establishment of control systems as a</p><p> The sputnik began the space race and large governmental expenditures in the space as well as military effort. D
6、uring this time. circuits became miniaturized and large sophisticated systems could be put together very compactly thereby allowing a computational and control advantage coupled with systems of small physical dimensions.
7、 We were now capable of designing and flying minicomputers and landing men on the moon. The post sputnik age saw much effort in system optimization and adaptive systems.</p><p> Finally, the refinement of t
8、he chip and related computer development has created an explosion in computational capability and computer-controlled devices. This has led to many innovative methods in manufacturing methods. such as computer-aided desi
9、gn and manufacturing, and the possibility of unprecedented increases in industrial productivity via the use of computer-controlled machinery, manipulators and robotics.</p><p> Today control systems is a sc
10、ience with the art still playing an important role. Much mathematical sophistication has been achieved with considerable interest in optimal control system. The modern approach, having been established as a science, is b
11、eing applied not only to the traditional control systems, but to newer problems like urban analysis, econometrics, transportation, biomedical problems, energy analysis, and a host of similar problems that affect modern m
12、an.</p><p> BIASIC CONCEPTS</p><p> Control system analysis is concerned with the study of the behavior of dynamic systems. The analysis relies upon the fundamentals of system theory where the
13、 governing differential equations assume a cause-effect relationship. A physical system may be represented as shown in Fig. where the excitation or input is x(t) and the response or output is y(t) . A simple control syst
14、em is shown in Fig. Here the output is compared to the input signal, and the difference of these two signals becomes the ex</p><p> SYSTEMS DESCRIPTION</p><p> Because control systems occur s
15、o frequently in our lives, their study is quite important. Generally, a control system is composed of several subsystems connected in such a way as to yield the proper cause-effect relationship. Since the various subsyst
16、ems can be electrical, mechanical, pneumatic, biological, etc., the complete description of the entire system requires the understanding of fundamental relationships in many different disciplines. Fortunately, the simila
17、rity in the dynamic behavior</p><p> As an example of a control system consider the simplified version of the attitude control of a spacecraft illustrated in Fig.1-4. We wish the satellite to have some spe
18、cific attitude relative to an inertial coordinate system. The actual attitude is measured by an attitude sensor on board the satellite. If the desired and actual attitudes are not the same, then the comparator sends a si
19、gnal to the valves which open and cause gas jet firings. These jet firings give the necessary corrective signal</p><p> If we have many inputs and outputs that are monitored and controlled, the block diagr
20、am appears as illustrated in Fig.1-5. Systems where several variables are monitored and controlled are called multivariable systems. Examples of multivariable systems are found in chemical processing, guidance and contro
21、l of vehicles, the national economy, urban problems.</p><p> The number of control systems that surround us is indeed very large. The essential feature of all these systems is in general the same . They all
22、 have input ,control ,output, and disturbance variables. They all describe a controller and a plant . They all have some type of a comparator. Finally, in all cases we want to drive the control system to follow a set pre
23、conceived commands. </p><p> 1.4 DESIGN, MODELING ,AND ANALYSIS</p><p> Prior to the building of a piece of hardware, a system must be designed, modeled, and analyzed. Actually the analysis
24、is an important and essential feature of the design process. In general, when we design a control system we do so conceptually. Then we generate a mathematical model which is analyzed. The results of this analysis are co
25、mpared to the performance specifications that are design a control system we do so conceptually. Then we generate a mathematical model which is analysis are compa</p><p> It is important to remember that al
26、l real control systems are nonlinear; however , many can be approximated within a useful though limited range as linear systems. Generally, this is an acceptable first approximation. A very important benefit to be deriv
27、ed by assuming linearity is that the superposition theorem applies. If we obtain the response due to two different inputs, then the response due to the combined input is equal to the sum of the individual response due to
28、 the combined input is eq</p><p> Traditionally, control system were represented by higher-order linear differential equations and the techniques of operational mathematics were employed to study these equa
29、tions. Such an approach is referred to as the classical method and is particularly useful for analyzing systems characterized by a single input and a single output. As systems began to become more complex , it became inc
30、reasingly necessary to use a digital </p><p> Computer . The work on a computer can be advantageously carried out if the system under consideration is represented by a set of first-order differential equa
31、tions and the analysis is carried out via matrix theory. This is in essence what is referred to as the state space or state variable approach . This method , although applicable to single input-output systems , finds imp
32、ortant applications in the multivariable system . Another very attractive benefit is that it enables the control system e</p><p> Regardless of the approach used in the design and analysis of a control syst
33、em , we must at least following steps:</p><p> Postulate a control system and the system specifications to be satisfied.</p><p> Generate a functional block diagram and obtain a mathematical r
34、epresentation of the system .</p><p> Analyze the system using any of the analytical or graphical methods applicable to the problem.</p><p> Check the performance (speed , accuracy, stability,
35、 or other eriterion) to see if the problem.</p><p> Finally, optimize the system parameters so that (1) is satisfied.</p><p><b> 控制系統(tǒng)的介紹 </b></p><p><b> 1. 歷史回
36、顧</b></p><p> 早在人類歷史文明出現(xiàn)之初,人們就產(chǎn)生了控制自然力的愿望。盡管歷史上出現(xiàn)過許多控制系統(tǒng)的實(shí)例,但是直到18世紀(jì)中葉才出現(xiàn)一些蒸汽驅(qū)動(dòng)的控制裝置。這就是所謂的蒸汽機(jī)時(shí)代,其中最著名的發(fā)明要數(shù)瓦特的飛球調(diào)速器。</p><p> 20世紀(jì)初,關(guān)于控制系統(tǒng)的大部分研究工作都和發(fā)電,化工等行業(yè)有關(guān),而且關(guān)于飛機(jī)自動(dòng)駕駛儀的設(shè)想也是在這一時(shí)期初形成的 。&
37、lt;/p><p> 從二戰(zhàn)前的25年開始,電子學(xué)特別是電路理論發(fā)展迅速。這也得益于奈魁斯特關(guān)于穩(wěn)定性理論方面的研究工作,這一理論到現(xiàn)在也還是經(jīng)典性上午。戰(zhàn)前和戰(zhàn)后對(duì)尖端試器系統(tǒng),潛艇。飛行器等方面的需求是對(duì)控制系統(tǒng)研究工作強(qiáng)有力的刺激因素。模擬計(jì)算機(jī)的出現(xiàn)加上電子學(xué)的進(jìn)展奠定了控制系統(tǒng)作為一門科學(xué)的基礎(chǔ)。到了50年代中期,數(shù)字計(jì)算機(jī)的發(fā)展為工程師們提供了一個(gè)新的工具,這就大大地加強(qiáng)了他們從事大型和復(fù)雜系統(tǒng)的研究能
38、力。計(jì)算機(jī)的使用開辟了數(shù)據(jù)采集,計(jì)算機(jī)控制,狀態(tài)空間法等現(xiàn)代分析方法的新紀(jì)元。</p><p> 蘇聯(lián)發(fā)射的人造地球衛(wèi)星開始了空間技術(shù)上的競爭以及政府在空間技術(shù)和軍事項(xiàng)目上的大量投資。這期間電路實(shí)現(xiàn)了小型化,又大又復(fù)雜的系統(tǒng)可以緊湊地放在一起,因此使得計(jì)算和控制上的強(qiáng)大優(yōu)勢和物理尺寸小的系統(tǒng)可以相互匹配?,F(xiàn)在我們已經(jīng)可以設(shè)計(jì)飛行用的小型計(jì)算機(jī),使人類降落在月球上。人造地球衛(wèi)星時(shí)代的后期,在系統(tǒng)最優(yōu)化和自適應(yīng)系統(tǒng)
39、方面也做了不少努力。</p><p> 最后,芯片集成度的提高及相關(guān)的計(jì)算機(jī)的開發(fā)引起了計(jì)算機(jī)能力和計(jì)算機(jī)器件的大爆炸。其結(jié)果是出現(xiàn)了許多新的制造方法,如計(jì)算機(jī)輔助設(shè)計(jì)和計(jì)算機(jī)輔助制造,而且計(jì)算機(jī)控制的機(jī)器,機(jī)械手和機(jī)器人帶來了生產(chǎn)率空前提高。</p><p> 今天,雖然生產(chǎn)工藝仍然起著重要作用,但控制系統(tǒng)已成為一門科學(xué)。由于對(duì)研究最優(yōu)控制的濃厚興趣引起了數(shù)學(xué)上的發(fā)展。已經(jīng)作為一門學(xué)
40、科建立起來的現(xiàn)代控制論,不僅用于傳統(tǒng)的控制系統(tǒng),而且也用來解決許多新的問題,如城市發(fā)展分析,計(jì)量經(jīng)濟(jì)學(xué),交通,生物醫(yī)學(xué),能源分析及其他許多類似的,對(duì)現(xiàn)代人類有影響的問題。</p><p><b> 2. 基本概念</b></p><p> 控制系統(tǒng)分析要做的是研究動(dòng)態(tài)系統(tǒng)的性能,這種分析的依據(jù)是系統(tǒng)理論中的基本原理,其中描述系統(tǒng)的微分方程都遵循因果關(guān)系。其中激勵(lì)
41、或輸入為x(t),響應(yīng)或輸出為y(t)。一個(gè)簡單的控制系統(tǒng)輸出信號(hào)和輸入信號(hào)相比較,兩者之差成為物理系統(tǒng)的激勵(lì),我們稱該系統(tǒng)具有反饋。這樣一個(gè)系統(tǒng),它的分析包括給定輸入時(shí)求取y(t),我們希望設(shè)計(jì)系統(tǒng)的特性。另一方面,如果給定輸入和輸出,我們希望設(shè)計(jì)系統(tǒng)特性,這就是所謂綜合。</p><p><b> 3. 系統(tǒng)描述</b></p><p> 由于我們生活中經(jīng)常
42、碰到控制系統(tǒng),因此對(duì)它們的研究相當(dāng)重要。一般說來,一個(gè)控制系統(tǒng)是由幾個(gè)子系統(tǒng)組合而成的,這些子系統(tǒng)互相聯(lián)接在一起,從而產(chǎn)生一定的因果關(guān)系。各種各樣的子系統(tǒng)可能是電氣的,機(jī)械的,氣動(dòng)的,生物的等等,因此為了完整地描述整個(gè)系統(tǒng),需要了解很多不同學(xué)科中的基本關(guān)系。所幸的是,不同物理系統(tǒng)的動(dòng)態(tài)性能具有相似性,這就使得這一任務(wù)變得比較容易也比較有意思了。</p><p> 作為控制系統(tǒng)的一個(gè)實(shí)例,考慮簡化的空間飛行器的姿
43、態(tài)角控制。我們希望衛(wèi)星相對(duì)某個(gè)慣性坐標(biāo)系具有指定的姿態(tài)角,實(shí)際的狀態(tài)角由衛(wèi)星上的一個(gè)姿態(tài)角傳感器測量。如果期待的姿態(tài)角和實(shí)際的姿態(tài)角不一致,則比較器送出一個(gè)信號(hào)給閥門,閥門打開使燃?xì)鈬姵霾Ⅻc(diǎn)火。這些噴射出的火焰為衛(wèi)星的動(dòng)態(tài)提供必要的糾正信號(hào),從而使衛(wèi)星處于被控制之中。用這種方法有利于把一個(gè)大系統(tǒng)分解成若干個(gè)子系統(tǒng),所以我們一次可以只研究一個(gè)子系統(tǒng)。</p><p> 如果有多個(gè)輸入和輸出需要監(jiān)控,則方框圖就像所
44、示的樣子,多個(gè)變量要監(jiān)控的系統(tǒng)稱為多變量系統(tǒng)。在化工過程,運(yùn)載器的導(dǎo)引和控制,國民經(jīng)濟(jì),城市住增長模式,郵政服務(wù)以及很多其他的社會(huì)和城市問題中都有多變量系統(tǒng)的例子。</p><p> 我們周圍控制系統(tǒng)的數(shù)量是很多,這些系統(tǒng)的基本特征總的說來是一樣的。它們都有輸入,控制,輸出和干擾對(duì)象;它們都可以描述成一個(gè)控制器加上一個(gè)被控對(duì)象;它們都有某種類型的比較器。最后,在所有情況下,我們都希望控制系統(tǒng)服從一組事先規(guī)定的指
45、令。</p><p> 1.4 設(shè)計(jì),建模及分析</p><p> 一個(gè)系統(tǒng)在硬件制造以前必須經(jīng)過設(shè)計(jì),建模和分析。實(shí)際上,分析是設(shè)計(jì)過程中重要而關(guān)鍵的一部分。一般來說,當(dāng)我們開始設(shè)計(jì)一個(gè)控制系統(tǒng)時(shí),所做的只是初步構(gòu)思,然后產(chǎn)生一個(gè)用于分析數(shù)學(xué)模型。分析的結(jié)果與將來系統(tǒng)應(yīng)該具有的性能指標(biāo)進(jìn)行比較,結(jié)論的精確度取決于用于設(shè)計(jì)的原始模型的質(zhì)量。后面第7章里,我們將闡述怎樣分析一個(gè)初步設(shè)
46、計(jì),然后修改,從而使其性能滿足系統(tǒng)的指標(biāo)。在建造系統(tǒng)以前,還要考慮的一件事是預(yù)測一個(gè)物理系統(tǒng)會(huì)呈現(xiàn)的動(dòng)態(tài)性能,即系統(tǒng)受干擾后偏離平衡狀態(tài)的自由運(yùn)動(dòng)以及受外部刺激后產(chǎn)生的響應(yīng)。我們特別關(guān)心響應(yīng)的速度即瞬態(tài)響應(yīng),響應(yīng)的精度即穩(wěn)態(tài)響應(yīng)以及穩(wěn)定性等等。所謂穩(wěn)定性是指輸出始終保持在某一合理的范圍內(nèi)。每一項(xiàng)專門要求所占的權(quán)重取決于具體應(yīng)用情況。例如,某一建筑物內(nèi)使用的空調(diào)只要維持+/—0。1度就可以令使用者滿意;但某種低溫系統(tǒng)中的溫度控制則要求把溫
47、度控制在幾分之一度之內(nèi)。對(duì)速度,精度及穩(wěn)定性的要求常常是互相矛盾的,必須做出某些折中。例如,提高精度常常使瞬態(tài)響應(yīng)變差。如果減小阻尼則會(huì)加劇系統(tǒng)振蕩,這就使系統(tǒng)需要較長時(shí)間才會(huì)達(dá)到某個(gè)穩(wěn)態(tài)值。</p><p> 別忘了,所有實(shí)際系統(tǒng)中都有非線性,但是許多系統(tǒng)在有限而適用的范圍內(nèi)都可以近似為一個(gè)線性系統(tǒng),這是很重要的。一般說來,這是一個(gè)初步的可以接受的近似。在推導(dǎo)中有了這種假設(shè)最大的好處是可以應(yīng)用疊加原理。如果我
48、們得到兩個(gè)不同輸入引起的響應(yīng),則兩個(gè)輸入合成的響應(yīng)就等于它們單獨(dú)響應(yīng)之和。另一個(gè)好處是在線性系統(tǒng)分析中可以應(yīng)用算子法。算子法可以使我們把原始微分方程化為代數(shù)方程,這樣處理起來就簡單多了。</p><p> 控制系統(tǒng)通常用高階線性微分方程來描述,用算子法來研究這些方程。這種方法稱為經(jīng)典方法,用它來分析單輸入單輸出系統(tǒng)特別有效。當(dāng)系統(tǒng)變的越來越復(fù)雜時(shí),使用數(shù)字計(jì)算機(jī)就顯得非常必要了。如果被研究的系統(tǒng)用一組一階微分方
49、程組來描述,并用矩陣?yán)碚搧矸治?,則在計(jì)算機(jī)上就很容易完成這一任務(wù)。這實(shí)際上是所謂的狀態(tài)或狀態(tài)變量法。這種方法雖然也能用于單輸入單輸出系統(tǒng),更重要的是用于多變量系統(tǒng)。這種方法的另一個(gè)誘人之處是它使控制系統(tǒng)工程師可以研究系統(tǒng)內(nèi)部的變量。</p><p> 不管在控制系統(tǒng)的設(shè)計(jì)和分析中用什么方法,我們至少要遵循下列步驟:</p><p> 以一個(gè)控制系統(tǒng)為出發(fā)點(diǎn),闡明該系統(tǒng)要滿足的指標(biāo)。&l
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