倒立擺外文翻譯

1、<p><b>　　電子與信息工程學(xué)院</b></p><p><b>　　本科畢業(yè)設(shè)計(jì)</b></p><p>　　外 文 文 獻(xiàn) 翻 譯</p><p>　　論文題目 直線式倒立擺控制系統(tǒng) </p><p>　　學(xué)生姓名 包雷

2、 </p><p>　　專 業(yè) 電氣工程及其自動(dòng)化 </p><p>　　指導(dǎo)教師 李 東 京 </p><p>　　2011年 11 月</p><p>　　The inverted pendulum</p><p>　　Key words:

3、 inverted pendulum, modeling, PID controllers, Fuzzy controllers, state space controllers</p><p>　　What is an Inverted Pendulum? Remember when you were a child and you tried to balance a broom-stick or baseb

4、all bat on your index finger or the palm of your hand? You had to constantly adjust the position of your hand to keep the object upright. An Inverted Pendulum does basically t he same thing. However, it is limited in tha

5、t it only moves in one dimension, while your hand coul d move up, down, sideways, etc. Check out the video provided to see exactly how the Inverted Pe ndulum works.</p><p>　　倒立擺是什么？還記得當(dāng)你是個(gè)孩子時(shí)你曾用你的食指或者掌心設(shè)法去平

6、衡一把掃帚柄或者棒球棍嗎？你必須不斷地調(diào)整你 的手的位置以保持對(duì)象的垂 直。一個(gè)倒立擺在本質(zhì)上就是做相同的事情。然而，它會(huì)受限制因?yàn)樗荒茉?一 定范圍內(nèi)移動(dòng)，雖然你的手可以上升、下降、斜向一邊等等。檢查錄象提供 的畫面來(lái)觀察倒立擺是如何確切 地工作的。</p><p>　　An inverted pendulum is a physical device consisting in a cylindrical

7、bar (usually of aluminum) free to oscillate around a fixed pivot. The pivot is mounted on a carriage, which in its turn can mo ve on a horizontal direction. The carriage is driven by a motor, which can exert on it a vari

8、able for ce. The bar would naturally tend to fall down from the top vertical position,which is a position of unsteady equilibrium.</p><p>　　一個(gè)倒立擺是個(gè)物理設(shè)備它包括一個(gè)圓柱體的棒子（通常是鋁的）可以在一 個(gè)支點(diǎn)周圍振蕩。這個(gè)支點(diǎn)是安在一個(gè)車架上，它的轉(zhuǎn)動(dòng)方向是水平的偏轉(zhuǎn)

9、。小 車是由一個(gè)馬達(dá)控制的，它可以運(yùn)用于一個(gè)變力。棒子會(huì)有自然的趨勢(shì)從最高的 豎直位置下落，那是一個(gè)不穩(wěn)定的平衡位置。</p><p>　　The goal of the experiment is to stabilize the pendulum (bar) on the top vertical position. This is possible by exerting on the carriage t

10、hrough the motor a force which tends to contrast the 'free' pe ndulum dynamics. The correct force has to be calculated measuring the instant values of the horiz ontal position and the pendulum angle (obtained e.g

11、. through two potentiometers).</p><p>　　實(shí)驗(yàn)的目標(biāo)是使擺（棒子）穩(wěn)定在最高的豎直位置。這是有可能的只要運(yùn)用 通過馬達(dá)的小車一個(gè)力該力可以與“自由”擺的動(dòng)力學(xué)抵消。 這個(gè)正確的力必須 通過計(jì)算測(cè)量水平偏轉(zhuǎn)的瞬時(shí)值和擺的角度（獲得兩個(gè)電位計(jì)） 。</p><p>　　The system pendulum+cart+motor can be model

12、ed as a linear system if all the parameters are k nown (masses, lengths, etc.), in order to find a controller to stabilize it. If not all the parameters ar e known, one can however try to 'reconstruct' the system

13、 parameters using measured data on the d ynamics of the pendulum.</p><p>　　系統(tǒng)擺+車+馬達(dá)可以建模成一個(gè)線形系統(tǒng)如果所有的參數(shù)都是已知的（質(zhì) 量、長(zhǎng)度等） ，為了尋找一個(gè)控制 器去穩(wěn)定住它。如果不是所有的參數(shù)都已知， 可以用多種方法去“推想”系統(tǒng)參數(shù)像用擺的動(dòng)力學(xué)的測(cè)量數(shù)據(jù)。</p><p>　　What is

14、it used for?Just like the broom-stick, an Inverted Pendulum is an inherently unstable sys tem. Force must be properly applied to keep the system intact. To achieve this, proper control theo ry is required. The Inverted P

15、endulum is essential in the evaluating and comparing of various cont rol theories.</p><p>　　倒立擺是干什么的？就好象掃帚柄，一個(gè)倒立擺是一個(gè)天生的不穩(wěn)定系統(tǒng)。 力度必須被嚴(yán)格地應(yīng)用以保持系統(tǒng)的完整性。為了實(shí)現(xiàn)它，嚴(yán)格的控制理論是必</p><p>　　須的。倒立擺在求數(shù)值和各種控制理論的比較中是必

16、要的。</p><p>　　The inverted pendulum is a traditional example (neither difficult nor trivial) of a controlled syst em. Thus it is used in simulations and experiments to show the performance of different contro

17、ller s (e.g. PID controllers, state space controllers, fuzzy controllers……).</p><p>　　倒立擺是一個(gè)控制器系統(tǒng)中的一個(gè)傳統(tǒng)的例子 （既不困難也不是沒有價(jià)值） 。 盡管它是仿真和實(shí)驗(yàn)來(lái)顯示不同控制器的性能（舉例來(lái)說(shuō) PID 控制器，狀態(tài)空間 控制器，模糊控制器） 。</p><p>　　The Real-T

18、ime Inverted Pendulum is used as a benchmark, to test the validity and the performa nce of the software underlying the state-space controller algorithm, i.e. the used operating system. Actually the algorithm is implement

19、 form the numerical point of view as a set of mutually co-oper ating tasks, which are periodically activated by the kernel, and which perform different calculation s. The way how these tasks are activated (e.g. the activ

20、ation order) is called scheduling of the tasks . I</p><p>　　實(shí)時(shí)倒立擺被作為一個(gè)基準(zhǔn)， 去測(cè)試軟件在狀態(tài)空間控制器運(yùn)算法則下的有 效性和性能，也就是實(shí)用的操作系統(tǒng)。事實(shí)上運(yùn)算法則是通過數(shù)值點(diǎn)實(shí)現(xiàn)的該數(shù) 值點(diǎn)看作一組互助的協(xié)同操作的任務(wù)，它是周期性的通過核心的活動(dòng)，它執(zhí)行不 同的計(jì)算。這些任務(wù)如何活動(dòng)的方法（舉例來(lái)說(shuō)激活命令）被稱作任務(wù)的時(shí)序安 排。很明

21、顯每個(gè)任務(wù)的時(shí)序安排對(duì)控制器的一個(gè)好的性能是至關(guān)緊要的，因此對(duì) 一個(gè)擺的穩(wěn)定性是有效的。 如此倒立擺是非常有用的在決定是否一個(gè)特殊的時(shí)序 安排的選擇比另一個(gè)好，在哪個(gè)情形下，在什么程度內(nèi)等等。</p><p>　　Modeling an inverted pendulum.Generally the inverted pendulum system is modeled as a linear system, a

22、nd hence the modeling is valid only for small oscillations of the pendulum.</p><p>　　為倒立擺建模。通常倒立擺系統(tǒng)建模成一個(gè)線形系統(tǒng)，因此模型只對(duì)小幅度 擺動(dòng)的擺才有效。</p><p>　　Prescribed trajectory tracking with certain accuracy is a

23、 main task of robotic control. The contr ol is often based on a mathematical model of the system. This model is never an exact representati on of reality, since modeling errors are inevitable. Moreover, one can use a sim

24、plified model on pu rpose. In this paper, the structured and unstructured uncertainties are of primary interest, i.e., the m odeling error due to the parameters variation and unmodeled modes, especially the friction and

25、sen</p><p>　　法定軌道通過確定的精確性是機(jī)器控制的一個(gè)主要任務(wù)。 控制通常是基于一 個(gè)系統(tǒng)的數(shù)學(xué)模型。模型不是一 個(gè)準(zhǔn)確的實(shí)體表現(xiàn)，模型的誤差是不可避免的。 此外，我們可以特意使用一個(gè)簡(jiǎn)化的模型。在這篇論文中， 構(gòu)造好的和未構(gòu)造 好的不確定因素是主要的興趣所在， 也就是說(shuō)模型的誤差導(dǎo)致參數(shù)變化和未模型 化的模式 ，尤其是摩擦力和敏感元件的力度，被忽視的時(shí)間延遲等等。</p><p

26、>　　The erroneous model and the demand for high performance require the controller to be robust. The sliding mode controllers(SMC) based on variable structure control can be used if the inaccura cies in the model struc

27、ture are bounded with known bounds. However, an SMC has some disadvan tages, related to chattering of the control input signal. Often this phenomenon is undesirable, since it causes excessive control action leading to in

28、crease wear of the actuators and to excitation of un modeled dynam</p><p>　　不正確的模型和高性能的需求要求控制器非常堅(jiān)固。滑?？刂破?SMC)是基 于變結(jié)構(gòu)控制使用的如果模型結(jié)構(gòu)中的錯(cuò)誤在已知的范圍內(nèi)躍進(jìn)。然而，一個(gè) SMC 有一些缺點(diǎn)，涉及控制輸入信號(hào)的振動(dòng)。通常這個(gè)現(xiàn)象是令人不快的，它會(huì) 引起額外的控制作用從而導(dǎo)致激勵(lì)者穿戴的增加和

29、未建模動(dòng)力學(xué)的刺激。</p><p>　　The attempts to attenuate this undesirable effect result in the deterioration of the robustness char acteristics. This is a well-known problem and widely treated in the literature. In ord

30、er to obtain s moothing in the bang-bang typed discontinuities of the sliding mode controller different schemes have been suggested.</p><p>　　削弱這個(gè)令人不快的效果的嘗試導(dǎo)致堅(jiān)固的特性的變化。這是一個(gè)眾所周 知的難題并且廣泛的在文獻(xiàn)中經(jīng)過處理。 為了在繼電器控制中獲得濾波

31、中斷滑模 控制器的方案已經(jīng)被提出了。</p><p>　　Another important issue limiting the practical applicability of SMC is the over conservative con trol law due to the upper bounds of the uncertainties. In practice most often the

32、worst case implem ented in control law does not take place and the resulting large control inputs become unnecessary and uneconomical.</p><p>　　另外一個(gè)重要的論點(diǎn)限定了 SMC 的實(shí)際應(yīng)用性就是創(chuàng)新的控制定律導(dǎo)致上 面的不確定因素的范圍。 在實(shí)踐中通常大部分最差的案例在

33、控制定律下執(zhí)行確沒 有發(fā)生并且作為結(jié)果的大的控制輸入變得不必要和不經(jīng)濟(jì)的。</p><p>　　In this paper we suggest an approach to the design of decentralized motion controllers for electr omechanical systems besides the sliding mode motion controller

34、 structure and disturbance torque estimation. The accuracy of the estimation is the critical parameter for robustness in this scheme, a s opposed to the upper bounds of the perturbations themselves. Consequently, the dri

35、ving terms of the error dynamics are reduced from the uncertainties (as in the conventional SMC) to the accurac y in the</p><p>　　在這篇論文中我們提出一個(gè)機(jī)電系統(tǒng)中分散震動(dòng)控制器的設(shè)計(jì)方法除了滑 模震動(dòng)控制器結(jié)構(gòu)和干擾轉(zhuǎn)矩的估算。 估算的精確性是這個(gè)計(jì)劃中最中堅(jiān)的評(píng)定 參數(shù)，與上面的

36、不確定的范圍正好相反。因此，在評(píng)估的精確 性中控制一些誤 差動(dòng)力學(xué)的條件減少了一些不確定性（就如同在傳統(tǒng)的 SMC 中） 。結(jié)果在沒有 超越傳統(tǒng)的控 制中是一個(gè)較好的跟蹤精度。</p><p>　　Experimental robustness properties of fuzzy controllers remain theoretically difficult to prove a nd their sy

37、nthesis is still an open problem. The non-linear structure of the final controller is derive d from all controllers at the different stages of fuzzy control, particularly from common defuzzific ation methods (such as Cen

38、tre of Area). In general, fuzzy controllers have a region-wise structure given the partition of its input space by the fuzzification stage. Local controls designed in thes</p><p>　　模糊控制裝置的實(shí)驗(yàn)的健全的性質(zhì)難以用理論去證明它們的

39、綜合仍然是一</p><p>　　個(gè)未解決的問題。最終控制器的非線性性質(zhì)來(lái)源于各級(jí)模糊控制的控制器，顯著 地逆模糊化方法（諸如中心區(qū)） 。通常，模糊控制器有一個(gè)區(qū)域勸導(dǎo)的性質(zhì)是模 糊化級(jí)數(shù)給的輸入空間。本地控制設(shè)計(jì)這些區(qū)域結(jié)合成集使最終的全球控制實(shí) 現(xiàn)。一個(gè)級(jí) 數(shù)空間的分割可以在控制器有區(qū)域勸導(dǎo)的常數(shù)參數(shù)中找到。此外， 每個(gè)模糊控制器調(diào)整參數(shù)（即形狀以及輸 入輸出的變量的值的隸屬函數(shù)）會(huì)在 同一時(shí)間在某些區(qū)域影響

40、參數(shù)的值。在特殊情況下開關(guān)線將相平面分成 一個(gè)區(qū) 域那個(gè)區(qū)域中控制是正的反之另一邊是負(fù)的， 模糊控制器可以視為一個(gè)可變結(jié)構(gòu) 的控制器。這類的模 糊控制器可以吸收到可變結(jié)構(gòu)控制器邊界層，其中穩(wěn)定性 定理存在，而是一個(gè)非線形開關(guān)面。</p><p>　　With the use of trapezoidal input membership functions and appropriate composition

41、and infere nce methods, it will be shown that it is possible to obtain rule membership functions which are reg ion-wise affine functions of the controller input variable. We propose a linear defuzzification algor ithm th

42、at keeps this region-wise affine structure and yields a piece-wise affine controller. A particu lar and systematic parameter tuning method will be given which allows turning this controller into a </p><p>　　

43、通過梯形輸入隸屬函數(shù)的使用和適當(dāng)?shù)淖鲌D法和推論方法， 這將說(shuō)明那是有 可能遵循規(guī)則區(qū)域勸導(dǎo)的輸 入變量仿射函數(shù)的隸屬函數(shù)。我們提出線形逆模糊 化算法它能這個(gè)區(qū)域勸導(dǎo)仿射結(jié)構(gòu)和產(chǎn)生一個(gè)塊仿射控制 器。一個(gè)特殊的系統(tǒng) 的參數(shù)調(diào)節(jié)方法將會(huì)被給定它允許把這個(gè)控制器調(diào)節(jié)成一個(gè)可變的結(jié)構(gòu)相似的 控制器。 我們將比較這個(gè)區(qū)域勸導(dǎo)仿射控制器和一個(gè)模糊的可變結(jié)構(gòu)的控制器 通過應(yīng)用一個(gè)倒立擺控制。</p><p>　　So far,

44、 in the application note series, we have provided several examples showing how to create fuzzy controllers with FIDE. However, these examples do not provide topics on implementation o f the designed system. In this appli

45、cation note, we use an example of an inverted pendulum to pro vide details on all aspects of fuzzy logic based system design.</p><p>　　迄今為止，在應(yīng)用筆記系列中，我們已經(jīng)提供了許多展示如何用 FIDE 創(chuàng)造 模糊控制裝置的例子。然而， 這些例子不能提供設(shè)計(jì)系統(tǒng)執(zhí)行的話題。在這應(yīng)

46、 用筆記中，我們可以用一個(gè)倒立擺的例子來(lái)提供模糊邏輯基 礎(chǔ)系統(tǒng)設(shè)計(jì)的所有 方面的細(xì)節(jié)。</p><p>　　We will begin with system design; analyzing control behavior of a two-stage inverted pendulum . We will then show how to design a fuzzy controller for the

47、 system. We will describe a control cur ve and how it differs from that of conventional controllers when using a fuzzy controller. Finally, we will discuss how to use this curve to define labels and membership functions

48、for variables, as well as how to create rules for the controller.</p><p>　　我們將從系統(tǒng)設(shè)計(jì)開始；分析二級(jí)倒立擺的控制行為。隨后我們將展示如何 為系統(tǒng)設(shè)計(jì)一個(gè)模糊控制裝 置。我們將描繪一個(gè)控制曲線當(dāng)使用模糊控制裝置 時(shí)它與一個(gè)常規(guī)控制器是如何的不同。最后，我們將討論 如何使用這個(gè)曲線去 定義標(biāo)志還有變量的隸屬函數(shù)，還有就是如何為控制器創(chuàng)立

49、一套規(guī)則。</p><p>　　In the formulation of any control problem there will typically be discrepancies between the act ual plant and the mathematical model developed for controller design.This mismatch may be due to

50、 unmodelled dynamics, variation in system parameters or the approximation of complex plant b ehavior by a straightforward model.The engineer must ensure that the resulting controller has the ability to produce the requir

51、ed performance levels in practice despite such plant/model mismatche</p><p>　　s. This has led to an intense interest in the development of so-called robust control methods which seek to solve this problem. O

52、ne particular approach to robust control controller design is the so-cal led sliding mode control methodology.</p><p>　　在任何控制問題的陳述中， 在控制的設(shè)計(jì)發(fā)展中現(xiàn)行的設(shè)備和數(shù)學(xué)模型之間 總是有著明顯的差異。這種 失諧也許應(yīng)歸于非建模動(dòng)力學(xué)中，通過一個(gè)簡(jiǎn)潔的 模型系統(tǒng)參數(shù)或者復(fù)雜設(shè)備的近似值

53、會(huì)發(fā)生變化。工程師 必須確定作為結(jié)果的 控制器在實(shí)際中有能力制造必須的性能指標(biāo)不管是設(shè)備還是模型的失諧。 這已經(jīng) 導(dǎo)致了 在所謂堅(jiān)固的操縱方法的發(fā)展產(chǎn)生一個(gè)強(qiáng)烈的興趣此方法能設(shè)法解決這 個(gè)問題。堅(jiān)固的操縱控制器設(shè)計(jì)的一 個(gè)特殊的方法就是所謂的滑?？刂品椒ā?lt;/p><p>　　Sliding mode control is a particular type of Variable Structure Contr

54、ol System (VSCS). A VSC S is characterized by a suite of feedback control laws and a decision rule. The decision rule, terme d the switching function, has as its input some measure of the current system behavior and prod

55、uc es as an output the particular feedback controller which should be used at that instant in time. A va riable structure system,which may be regarded as a combination of subsystems where each subsys tem has a f</p>

56、;<p>　　滑?？刂剖强勺兘Y(jié)構(gòu)控制系統(tǒng)（VSCS）的一個(gè)特殊的類型。一個(gè) VSCS 是 由一套反饋控制定律和一個(gè)決策規(guī)則表現(xiàn)出來(lái)的。決策規(guī)則，條件是開關(guān)方程， 將輸入估計(jì)成正確的系統(tǒng)特性并且產(chǎn)生一個(gè)輸出精確的反饋控制器使之可以 及 時(shí)地被使用。一個(gè)可變結(jié)構(gòu)系統(tǒng)，被認(rèn)為是各子系統(tǒng)的結(jié)合其中每個(gè)子系統(tǒng) 有一個(gè)確定的控制結(jié)構(gòu)并且結(jié)果是對(duì)系統(tǒng)結(jié)構(gòu) 給定的區(qū)域是適用的。介紹這個(gè) 額外的系統(tǒng)的復(fù)雜性的優(yōu)勢(shì)之一就是可以將系統(tǒng)中復(fù)合結(jié)構(gòu)

57、的有用的性質(zhì)組合 起來(lái)。此外，該系統(tǒng)可能被設(shè)計(jì)成擁有新的性質(zhì)而且不是單獨(dú)地應(yīng)用與復(fù)合結(jié)構(gòu) 的某一方面。 前蘇聯(lián)在 20 世紀(jì) 50 年代末最先開始利用這些自然的想法。</p><p>　　In sliding mode control, the VSCS is designed to drive and then constrain the system state to li e within a neighb

58、orhood of the switching function. There are two main advantages to this approac h. Firstly, the dynamic behavior of the system may be tailored by the particular choice of switchin g function. Secondly, the closed-loop re

59、sponse becomes totally insensitive to a particular class of u ncertainty. The latter invariance property clearly makes the methodology an appropriate candidate for ro</p><p>　　在滑模控制中，VSCS 被設(shè)計(jì)成操作并強(qiáng)迫系統(tǒng)狀態(tài)位于鄰近的開

60、關(guān)方程 中。這種方法有兩個(gè)主要的優(yōu)點(diǎn)：第一，系統(tǒng)的動(dòng)態(tài)性能適應(yīng)于開關(guān)方程的特殊 選擇；第二，閉環(huán)響應(yīng)完全不受不確定的特殊種類的影響。后面的恒定性質(zhì)明顯 地使方法論在堅(jiān)固的操縱方法中有一個(gè)適當(dāng)?shù)暮钸x對(duì)象。另外，立即指定性能的 能力使得滑?？刂茝脑O(shè)計(jì)觀點(diǎn)看變得有價(jià)值。</p><p>　　The sliding mode design approach consists of two components. The

61、first involves the design of a switching function so that the sliding motion satisfies design specifications. The second is conce rned with the selection of a control law which will make the switching function attractive

62、 to the sy stem state. Note that this control law is not necessarily discontinuous.</p><p>　　滑模設(shè)計(jì)處理兩種結(jié)構(gòu)組成。 第一個(gè)包括開關(guān)方程的設(shè)計(jì)所以滑行的動(dòng)作滿</p><p>　　足設(shè)計(jì)規(guī)范。第二個(gè)涉及到 控制規(guī)則的選擇該規(guī)則將使開關(guān)方程在系統(tǒng)狀態(tài)中 變得有價(jià)值。注意這個(gè)控制規(guī)則并不是必然不連

63、續(xù)的。</p><p>　　We will provide the reader with a thorough grounding in the sliding mode control area and as su ch is appropriate for the graduate with a basic knowledge of classical control theory and some kno

64、 wledge of state-space methods. From this basis, more advanced theoretical results are developed. Resulting design procedures are emphasized using Matlab files. Fully worked design examples are an additional tutorial fea

65、ture. Industrial case studies, which present the results of sliding mode co ntroller i</p><p>　　我們將提供讀者一個(gè)徹底的滑?？刂祁I(lǐng)域的基礎(chǔ)并且適合大學(xué)生使用的經(jīng) 典控制理論和一寫狀態(tài)空間方 法的知識(shí)的基礎(chǔ)知識(shí)。從這些基礎(chǔ)中，許多先進(jìn) 的理論的成果在不斷發(fā)展。因而發(fā)生的設(shè)計(jì)規(guī)程強(qiáng)調(diào)需要用 Matlab 軟件。充分 的處

66、理過的設(shè)計(jì)實(shí)例是一個(gè)額外的性質(zhì)的指示。工業(yè)的案例學(xué)習(xí)，介紹了滑模控 制執(zhí)行的 成果，被用于闡述成功的實(shí)際的理論上的應(yīng)用。</p><p>　　The “INVERTED PENDULUM, ANALYSIS, DESIGN AND IMPLEMENTATION” is a collec tion of MATLAB functions and scripts, and SIMULINK models, usefu

67、l for analyzing Inverted Pe ndulum System and designing Control System for it. This report & MATLAB-files collection are developed as a part of practical assignment on Control System Analysis, Design & Developmen

68、t p ractical problem. The assigned problem of INVERTED PENDULUM is a part of Lab Work of Co ntrol System.</p><p>　　“倒立擺、分析、設(shè)計(jì)和執(zhí)行”是由一個(gè) MATLAB 方程和內(nèi)容的收藏的，還有 SIMULINK 模型，對(duì)分析倒立 擺系統(tǒng)和設(shè)計(jì)控制系統(tǒng)是很有用的。這個(gè)報(bào)道 MATLAB 文件收藏是由少

69、量的控制系統(tǒng)分析的實(shí)際任務(wù)而發(fā)展的，設(shè)計(jì)和發(fā)展 實(shí)際問題。這分派 的倒立擺的問題是一個(gè)控制系統(tǒng)的實(shí)驗(yàn)室工作的一部分。</p><p>　　The Inverted Pendulum is one of the most important classical problems of Control Engineering. Broom Balancing (Inverted Pendulum on a cart)

70、 is a well known example of nonlinear, unstable c ontrol problem. This problem becomes further complicated when a flexible broom, in place of a ri gid broom, is employed. Degree of complexity and difficulty in its contro

71、l increases with its flexib ility. This problem has been a research interest of control engineers.</p><p>　　倒立擺是最重要最經(jīng)典的控制工程問題中的一個(gè)。帚平衡（車載的倒立擺） 是一個(gè)著名的非線形例子， 不穩(wěn)定的控制問題。這個(gè)問題越來(lái)越復(fù)雜當(dāng)一個(gè)柔 韌的帚代替一個(gè)剛硬的帚被使用。復(fù)雜的問題的真實(shí)度和 難度在

72、控制中隨著彈 性而增長(zhǎng)。這個(gè)問題已經(jīng)引起調(diào)度工程師的興趣并展開研究。</p><p>　　Control of Inverted Pendulum is a Control Engineering project based on the FLIGHT SIMUL ATION OF ROCKET OR MISSILE DURING THE INITIAL STAGES OF FLIGHT. The AIM O F

73、 THIS STUDY is to stabilize the Inverted Pendulum such that the position of the carriage on the t rack is controlled quickly and accurately so that the pendulum is always erected in its inverted pos ition during such mov

74、ements.</p><p>　　倒立擺的控制是一個(gè)控制工程的方案基于火箭的飛行模擬或者導(dǎo)彈飛行的 初始狀態(tài)。這個(gè)學(xué)習(xí)的目的是 穩(wěn)定倒立擺這樣小車的位置在軌道上被控制得快 速和準(zhǔn)確以使擺在這一裝置下始終垂直在它的倒立位置。</p><p>　　This practical exercise is a presentation of the analysis and practical i

75、mplementation of the resul ts of the solutions presented in the papers, “Robust Controller for Nonlinear & Unstable System: I nverted Pendulum” and “Flexible Broom Balancing” , in which this complex problem was analy