一級倒立擺的模糊控制畢業(yè)論文開題報告

1、<p>　　本科畢業(yè)設計(論文)開題報告</p><p>　　題目：一級倒立擺的模糊控制</p><p>　　課 題 類 型： 設計□ 實驗研究□ 論文□ </p><p>　　學 生 姓 名： </p><p>　　學 號： 3090201214</p><p>　　專

2、 業(yè) 班 級： 自動化092</p><p>　　學 院： 電氣工程學院</p><p>　　指 導 教 師： </p><p>　　開 題 時 間： 2013年3月</p><p>　　2013 年3月10日</p><p>　　一、畢業(yè)設計（論文）內(nèi)容及研

3、究意義（價值）</p><p>　　在控制理論發(fā)展的過程中，一種理論的正確性及在實際應用中的可行性，往往需要一個典型對象來驗證，并比較各種控制理論之間的優(yōu)劣，倒立擺系統(tǒng)就是這樣一個可以將理論應用于實際的理想實驗平臺。本論文在參考大量文獻的基礎上，建立了一級倒立擺系統(tǒng)的數(shù)學模型，對系統(tǒng)進行了穩(wěn)定性、可控性分析，指出一階倒立擺的開環(huán)不穩(wěn)定性。文章主要完成了：一級倒立擺動力學模型和模糊PID控制器模塊的設計，確定了輸入

4、輸出信號的論域、隸屬度函數(shù)和模糊規(guī)則，最后利用Matlab中的simulink工具箱創(chuàng)建了基于模糊控制理論的一級倒立擺系統(tǒng)的simulink仿真模型，對倒立擺系統(tǒng)進行分析。仿真結(jié)果證明模糊PID控制不僅可以穩(wěn)定倒立擺系統(tǒng)，還使小車穩(wěn)定在平衡位置附近，證明了本文設計的模糊PID控制器有良好的穩(wěn)定性、魯棒性和適應性</p><p>　　倒立擺系統(tǒng)能有效地反映諸如鎮(zhèn)定性、魯棒性、隨動性等許多控制中的關鍵問題，是檢驗各種

5、控制理論的理想模型。其典型性在于：作為實驗裝置，它本身具有成本低廉、結(jié)構(gòu)簡單、物理參數(shù)和結(jié)構(gòu)易于調(diào)整、便于模擬、形象直觀的優(yōu)點；作為被控對象，它是一個具有高階次、不穩(wěn)定、多變量、非線性和強藕合特性的不穩(wěn)定系統(tǒng)，可以有效地反映控制中的許多問題；作為檢測模型，該系統(tǒng)的特點與機器人、飛行器、起重機穩(wěn)鉤裝置等的控制有很大的相似性。對倒立擺因此對倒立擺控制機理的研究具有非常重要的理論和實踐意義。。</p><p>　　二、

6、畢業(yè)設計（論文）研究現(xiàn)狀和發(fā)展趨勢（文獻綜述）</p><p>　　1.倒立擺系統(tǒng)的研究現(xiàn)狀</p><p>　　到目前為止，人們己經(jīng)利用包括經(jīng)典控制理論、現(xiàn)代控制理論以及各種智能控制理論在內(nèi)的各種手段先后實現(xiàn)了倒立擺系統(tǒng)的穩(wěn)定控制。隨著微型計算機的發(fā)展和廣泛應用，又陸續(xù)出現(xiàn)了對一級、二級甚至多級倒立擺的穩(wěn)定控制。倒立擺系統(tǒng)是一個難以控制的不穩(wěn)定結(jié)構(gòu)，隨著級數(shù)的增加，控制難度加大。在這樣復

7、雜的控制對象面前，把人工智能的方法引入到控制系統(tǒng)中，就為解決倒立擺控制問題提出了新的方向。</p><p>　　模糊智能控制和神經(jīng)網(wǎng)絡控制是智能控制的重要方面，它們在倒立擺系統(tǒng)的控制上起到了很大的作用。程福雁等將傳統(tǒng)控制理論與模糊控制相結(jié)合實現(xiàn)了對二級倒立擺的穩(wěn)定控制。王衛(wèi)華采用專家模糊控制解決單級倒立擺的穩(wěn)定問題。張乃堯等人采用模糊雙閉環(huán)的方案，成功的對單級倒立擺進行了穩(wěn)定控制。胡叔旖、孫增沂應用基于規(guī)則的方法

8、實現(xiàn)了二級倒立擺的穩(wěn)定控制。劉妹琴、陳際達等采用遞歸神經(jīng)網(wǎng)絡控制了單級倒立擺。王琳等采用模糊小腦模型控制器仿真控制了單級倒立擺。1994年8月，北京航空航天大學自動化系張明廉教授、沈程智教授領導的人工智能小組，采用擬人智能控制模仿人面對同樣問題的解決思路，成功實現(xiàn)了單電機控制三級平面運動倒立擺的控制。李洪興教授領導的模糊系統(tǒng)與模糊信息研究中心暨復雜系統(tǒng)實時智能控制實驗室采用變論域自適應模糊控制理論，于2001年9月實現(xiàn)了三級倒立擺實物系

9、統(tǒng)控制后，又于2002年8月11日在世界上首次成功實現(xiàn)了四級倒立擺實物控制系統(tǒng)。在對倒立擺系統(tǒng)的研究過程中新的控制理論的不斷出現(xiàn)，使現(xiàn)有的控制理論得到了不斷的完善和發(fā)展。</p><p>　　2.倒立擺系統(tǒng)研究的發(fā)展趨勢</p><p>　　此前，實現(xiàn)的一級至四級倒立擺均為直線運動倒立擺。直線運動倒立擺實現(xiàn)的是在一個平面上的擺動，軌道較長、傳動環(huán)節(jié)較多、占地空間較大，實踐中常常由于傳動機構(gòu)

10、的故障或誤差，而不是控制方法本身的問題導致平衡控制失敗。隨著科學技術的發(fā)展，被控對象日趨復雜，對控制性能的要求也日趨提高，直線倒立擺已不能滿足復雜系統(tǒng)的需要，由此產(chǎn)生了圓形軌道倒立擺。圓形軌道倒立擺實現(xiàn)了上、下、左、右、前、后任何方向的擺動，與傳統(tǒng)的直線軌道倒立擺相比，圓形軌道倒立擺具有控制精度高、功能多、結(jié)構(gòu)緊湊、性價比高等優(yōu)點，所以圓形軌道倒立擺比傳統(tǒng)的直線軌道倒立擺更具有競爭力和應用價值。圓形軌道倒立擺實物系統(tǒng)控制的實現(xiàn)要比直線運

11、動倒立擺實物系統(tǒng)控制的實現(xiàn)困難得多；這不僅是因為這樣的系統(tǒng)其變量、非線性程度及不穩(wěn)定性成倍地增加，而且有關機械和電子器件的實現(xiàn)或選用會遇到瓶頸性的困難。因此，圓形軌道倒立擺實物系統(tǒng)是控制領域研究的重要課題之一。 </p><p>　　近年來，人們對倒立擺的研究越來越感興趣，倒立擺的種類也變得豐富多樣。倒立擺系統(tǒng)不僅在高科技領域中得到廣泛應用，人們還可以通過倒立擺這樣一個嚴格的控制對象，檢驗新的控制方法是

12、否有較強的處理多變量、非線性和絕對不穩(wěn)定系統(tǒng)的能力。因此，倒立擺系統(tǒng)作為控制理論研究中的一種比較理想實驗手段常常用來檢驗控制策略的效果。</p><p>　　三、畢業(yè)設計（論文）研究方案及工作計劃（含工作重點與難點及擬采用的途徑）</p><p><b>　　1、研究方案</b></p><p>　　一級倒立擺系統(tǒng)由導軌，小車和一級擺桿組成，小

13、車依靠直流電機施加的控制力，可以在導軌上左右移動，其位移和擺桿角度信息由傳感器測得，目標是使倒立擺在有限長的導軌上豎立穩(wěn)定，達到動態(tài)平衡，即不超過一個預先定義好的垂直偏離角度范圍。</p><p>　　面對一級倒立擺系統(tǒng)這樣一個非線性、不穩(wěn)定的復雜被控對象，其控制方法主要有三類：線性控制、預測控制、智能控制。智能控制方法源自于人類實踐經(jīng)驗，不需要精確的數(shù)學模型，是當前應用較廣的控制方法。在倒立擺系統(tǒng)中應用的智能控

14、制方法有：神經(jīng)網(wǎng)絡控制、模糊控制、仿人智能控制、擬人智能控制以及云模型控制。對一級倒立擺的穩(wěn)定控制而言，模糊控制方法是一種比較優(yōu)秀的解決途徑，魯棒性較好。</p><p>　　在研究倒立擺這類多變量非線性系統(tǒng)的模糊控制時，一個難題就是規(guī)則爆炸，比如一級倒立擺的控制涉及的狀態(tài)變量共有4個，每個變量的論域作7個模糊集的模糊劃分，這樣，完備的推理規(guī)則庫會包含2401個推理規(guī)則;而對于二級倒立擺有6個狀態(tài)變量，推理規(guī)則會

15、達到117649，顯然如此多的規(guī)則是不可能實現(xiàn)的。 為了解決這個問題，張乃堯等提出雙閉環(huán)的倒立擺模糊控制方案，內(nèi)環(huán)控制倒立擺的角度，外環(huán)控制倒立擺的位移。范醒哲等人將這一方法推廣到三級倒立擺控制系統(tǒng)中，并提出兩種模糊串級控制方案，用來解決倒立擺這類多變量系 統(tǒng)模糊控制時的規(guī)則爆炸問題。shulinagLei和RezaLnagari應用分級思想，將x，dx/dt,θ,dθ/dt4個狀態(tài)變量分成兩個子系統(tǒng)，分別用兩個模糊控制器控制，然后來協(xié)

16、調(diào)子系統(tǒng)之間的相互作用。本文模仿人類簡化問題的思路，將單一的復雜控制策略轉(zhuǎn)化為多級簡單控制策略嵌套，通過分離變量的方法設計控制器。</p><p><b>　　2、工作計劃</b></p><p>　　01-02周：安排畢業(yè)設計計劃，分配設計任務。</p><p>　　02-03周：了解本課題設計要求，針對倒立擺系統(tǒng)學習相關知識。</p&

17、gt;<p>　　04-05周：完成開題報告以及相關知識點的掌握，掌握倒立擺系統(tǒng)仿真的整體思路，收集整理matlab仿真所需的資料。</p><p>　　06-11周：建立級倒立擺動力學模型，完成模糊PID控制器模塊的設計，在matlab中完成仿真。</p><p>　　11-14周：完善控制效果，分析輸出結(jié)果，得出仿真結(jié)論；翻譯英文文獻資料。</p><

18、p>　　15-16周：編寫畢業(yè)設計論文和準備畢業(yè)答辯。</p><p>　　主要參考文獻（不少于10篇，期刊類文獻不少于7篇，應有一定數(shù)量的外文文獻，</p><p>　　至少附一篇引用的外文文獻（3個頁面以上）及其譯文）</p><p>　　[1]王海英.控制系統(tǒng)CAD與仿真[M].哈爾濱:東北林業(yè)大學出版社,2002.</p><p&g

19、t;　　[2]黃忠霖.控制系統(tǒng)MATLAB計算及仿真[M].2版.北京：國防工業(yè)出版社，2004.</p><p>　　[3]蔡自興.智能控制[M].北京:電子工業(yè)出版社,2004.</p><p>　　[4]周其鑒,李祖樞,陳民鈾.智能控制及其展望[J].信息與控制,2006(2):39-45.</p><p>　　[5]劉朝英，宋哲英.MATLAB在模糊控制系統(tǒng)

20、中的應用[J].計算機仿真,2001,18（3）：11-13.</p><p>　　[6]李永強，楊明忠.智能控制理論在倒立擺系統(tǒng)中應用研究[J].現(xiàn)代機械，2006，2(3)：100-103.</p><p>　　[7]倪桂杰,郭巧菊.基本模糊控制器控制規(guī)則的提取[J].自動化儀表,2002,23(3):7-10</p><p>　　[8]高飛,薛忠.模糊控制技術

21、中的幾個問題[J].西安電子科技大學學報，1998,25（3）：369-373</p><p>　　[9]Lee C C.Fuzzy Logic in Controll Systems:Fuzzy Logic.Controller-part I,Part I[J].IEEE Trans.on SMC,1990,20(2):404-435.</p><p>　　[10]Bezdek J. F

22、uzzy Models-What Are They,and Why? [J].IEEE Trans on FuzzySystems，1993,1（1）：1-6.</p><p>　　[11] Mario E. Magana and Frank Holzapfel[J].IEEE Trans on Education,1998,2(4):41-44.</p><p>　　Fuzzy-Logi

23、c Control of an Inverted Pendulum with Vision Feedback</p><p>　　Mario E. Magana and Frank Holzapfel</p><p>　　Abstract— In this paper we present an experimental setup of a fuzzy-logic controller

24、of an inverted pendulum that uses vision feedback. The experimental testbed is used at Oregon State University in senior and first-year graduate courses on automatic control systems to illustrate the usefulness and limit

25、ations of thisapproach. The results that are obtained support the claim, within certain limits, that it is possible to control an inverted pendulum using fuzzy-logic control and vision feedback.</p><p>　　Ind

26、ex Terms—Control, fuzzy logic, vision feedback.</p><p>　　I. INTRODUCTION</p><p>　　The implementation of a fuzzy-logic controller for an</p><p>　　inverted pendulum is not new. In fac

27、t, one of the first</p><p>　　applications of it was to stabilize an inverted pendulum. Our</p><p>　　approach differs from previous approaches in the way in which</p><p>　　the physic

28、al variables are measured. The fact that a human</p><p>　　being is able to stabilize an inverted pendulum of reasonable</p><p>　　length and mass, along with the knowledge of the brain’s</p>

29、;<p>　　ability to process about 25 images per second, leads one to</p><p>　　conclude that this data rate should be sufficient to control an</p><p>　　inverted pendulum using computer visio

30、n information. This</p><p>　　“l(fā)ow data rate” approach is in strong contrast to past research</p><p>　　that focused on measurement updates that are two to three</p><p>　　times faster

31、. Of special interest is the fact that in certain realworld</p><p>　　applications the position of a controlled object cannot</p><p>　　be determined with traditional methods. The introduction of&

32、lt;/p><p>　　video cameras and vision systems to process their images has</p><p>　　led to a new way to measure relevant quantities without having</p><p>　　to touch or even to come close

33、 to the object. The drawback</p><p>　　of this approach, on the other hand, is that just 60 half-frames</p><p>　　are obtained per second. This leads to problems that result</p><p>　　

34、from delays, especially in connection with fast-moving objects.</p><p>　　Therefore, one of the goals of the experiment performed in</p><p>　　our teaching and research laboratory was to explore c

35、ritical</p><p>　　limits and investigate if the speed and the versatility of the</p><p>　　fuzzy controller are sufficient to deal with them. The paper</p><p>　　describes the experime

36、ntal setup extensively so that it can</p><p>　　also be performed at other teaching and research laboratories.</p><p>　　Such a setup can be used by both electrical and mechanical</p><p

37、>　　engineering students to learn and apply fuzzy-logic control</p><p>　　techniques using nontouching sensors such as vision sensors.</p><p>　　The theoretical background of fuzzy systems with

38、regard to</p><p>　　an inverted pendulum is developed in [6] and [12], where it is</p><p>　　taken as a benchmark for binary input–output fuzzy associative</p><p>　　memory (BIOFAM) sy

39、stems. Using a similar approach as</p><p>　　described in [6], we take two states and one control variable.</p><p>　　The first fuzzy state variable is the angle that the pendulum</p><p

40、>　　shaft makes with the vertical. The second is the average</p><p>　　angular velocity . As output fuzzy variable we use</p><p>　　the motor armature current. All three variables can be either&

41、lt;/p><p>　　positive or negative and are related in the following manner:</p><p>　　If the pendulum falls to the left, the motor velocity should be</p><p>　　negative to compensate. If t

42、he pendulum successfully balances</p><p>　　in the middle, the motor current should be zero. Therefore,</p><p>　　every variable takes on a certain set of values whose range</p><p>　　

43、is limited by practical considerations that result from physical</p><p>　　and technological constraints. In the experiment we quantify</p><p>　　each set or universe of discourse into seven overl

44、apping fuzzy</p><p>　　set values. This choice is based on prior experience.</p><p>　　II. EXPERIMENTAL PLATFORM</p><p>　　The setup of the inverted pendulum fuzzy-logic control with&l

45、t;/p><p>　　vision feedback experiment consists of the following parts:</p><p>　　1) a mechanical system composed of an inverted pendulum</p><p>　　mounted on an – table, 2) a video camer

46、a and a vision</p><p>　　computer that are used as a nontouching sensor to obtain</p><p>　　the states of the system, 3) a fuzzy-logic controller that is</p><p>　　implemented on a 386

47、 personal computer using Borland C ,</p><p>　　and 4) an actuator that consists of an armature-controlled dc</p><p>　　servo-motor driven by a pulsewidth-modulated amplifier.</p><p>　

48、　A. The Mechanical System</p><p>　　A lead screw that is directly coupled to the shaft of a dc</p><p>　　motor and is guided by two steel bars using bearings drives the</p><p>　　sled.

49、 The pendulum itself consists of a 70-cm-long rod and a</p><p>　　wooden ball designed in such a way that the center of mass can</p><p>　　be assumed to be at the top of the rod. The pendulum rota

50、tes</p><p>　　in the vertical plane using low friction roller bearings. Possible</p><p>　　deviations range up to 90 , but are actually restricted to a</p><p>　　much smaller range by

51、the constraints of the system.</p><p>　　B. The Vision System</p><p>　　In order to control the system, it is necessary to measure the</p><p>　　different states. To do this, we use an

52、 Intelledex vision system</p><p>　　with a relatively low-resolution video camera. The camera is</p><p>　　equipped with a 16-mm lens with adjustable aperture to vary</p><p>　　the amo

53、unt of incident light. The vision computer is the HR</p><p>　　model with a memory management unit. It allows transferring</p><p>　　frames or single rows from the A/D buffer to the main memory<

54、;/p><p>　　without long delays. The information is evaluated and written</p><p>　　to a serial RS 232 port that is set to operate at a 38-kb/s clock</p><p><b>　　rate [4].</b>

55、</p><p>　　C. The Controller</p><p>　　The controller is implemented on a 386 personal computer</p><p>　　running at 16 MHz. The control commands are sent to a power</p><p&g

56、t;　　amplifier via a 10-V D/A converter.</p><p>　　D. The Actuator</p><p>　　This part of the system consists of a dc servomotor and a</p><p>　　power amplifier. The analog signal from

57、the D/A converter is</p><p>　　translated as a current and fed to the motor. Since the torque</p><p>　　of the dc motor is proportional to the armature current, we can</p><p>　　contro

58、l the speed of the sled with a voltage command signal.</p><p>　　III. VISION SYSTEM</p><p>　　To successfully control the inverted pendulum using vision</p><p>　　information it is nec

59、essary to separate the whole task into</p><p>　　two parts: data acquisition and control. The vision system is</p><p>　　responsible for acquiring the data and transmitting them to</p><

60、p>　　the PC that determines the control command based on these</p><p>　　values. In doing so, routines for I/O and programs to handle the</p><p>　　serial communication apart from the main contr

61、ol program are</p><p>　　needed. This task is performed using C and small assembly</p><p>　　language programs for controlling the serial communication.</p><p>　　1) Vision System Conf

62、iguration: The vision system core is</p><p>　　an Intel 386 microprocessor running at 20 MHz. Also, the</p><p>　　vision computer has a fast A/D unit that samples the RS</p><p>　　170

63、analog signal and writes the digitized data in a local</p><p>　　array that is separated from the main memory of the CPU.</p><p>　　Because the camera sends the data of each frame for 15 ms</p&

64、gt;<p>　　and pauses for 1.25 ms during the vertical blank, we use</p><p>　　this window to copy the information that we are interested</p><p>　　in to the main memory. This gives us the opp

65、ortunity to</p><p>　　manipulate the data and compute the angle and position of the</p><p>　　sled simultaneously before the next image is acquired. Since</p><p>　　this process takes

66、place during a relatively short period of</p><p>　　time, we can also transmit the position of the sled and the</p><p>　　angle over an RS 232 serial communication channel without</p><p

67、>　　losing image information.</p><p>　　The vision application program is written and compiled in</p><p>　　the host PC and then downloaded via the RS 232 into the</p><p>　　vision c

68、omputer.</p><p>　　2) Angle Computation: The video picture consists of 480</p><p>　　rows and 512 columns and a vertical blank period to allow</p><p>　　the beam to reach the upper lef

69、t corner again. The easiest</p><p>　　way to determine the angle of the pendulum is to take two</p><p>　　rows and find the position of the greatest dark/bright transition.</p><p>　　T

70、his position is represented as the column number. Since we</p><p>　　know the distance between the rows (e.g., 400 lines) and the</p><p>　　columns (e.g., 10 points) we can determine the angle by

71、using a</p><p>　　simple trigonometric function. The following figure illustrates</p><p>　　the procedure.</p><p>　　In order to have reliable values for the angle we need a high</p

72、><p>　　contrast of the video picture. To ensure this, the pendulum rod</p><p>　　is painted black and a white background is used. To detect</p><p>　　the point with the greatest black/wh

73、ite transition in a row we</p><p>　　use a linear search algorithm that compares the contrast of the</p><p>　　pixels and returns the position of the one with the greatest</p><p>　　da

74、rk value. From the coordinates, we calculate the and</p><p>　　distances and obtain the angle from</p><p>　　dist. hor.</p><p>　　dist. vert.</p><p>　　To protect the sled

75、from running into its mount, we use</p><p>　　the position given in the lower row to determine five areas</p><p>　　of the sled position. They are encoded as integer values and</p><p>

76、;　　transmitted to the control computer. The following table shows</p><p>　　the areas in pixels.</p><p>　　IV. THE FUZZY LOGIC CONTROLLER</p><p>　　The proposed fuzzy-logic controller

77、used to control the</p><p>　　experimental inverted pendulum uses conventional triangular</p><p>　　membership functions to fuzzify the data measured by the</p><p>　　vision system [9]

78、. Furthermore, the fuzzy inference engine</p><p>　　implements a set of IF-AND-THEN rules on the angular</p><p>　　V. PERFORMANCE EVALUATION</p><p>　　In order to evaluate the performa

79、nce of our fuzzy-logic</p><p>　　control system, all the acquired data are stored in a file on the</p><p>　　hard disk. To avoid delays in the output of the control signal,</p><p>　　t

80、he measured values are saved after the output command is</p><p>　　computed. The remaining time until the new angle and position</p><p>　　measurements are available at the serial port is still su

81、fficient</p><p>　　to store the old values without losing data. To be able to</p><p>　　process the data off-line, the angle information is stored with</p><p>　　a precision of 0.1 .&l

82、t;/p><p>　　We can observe in Fig. 7 that the average amplitude that</p><p>　　results from the deviation of the pendulum is about 2.7 . We</p><p>　　can also see in the same figure that

83、the system displays an</p><p>　　oscillatory behavior. The amplitude of the oscillations depends</p><p>　　on the maximum acceleration, inertia, and other factors. From</p><p>　　the s

84、ame figure, we can determine that the period of the oscillations is approximately 400 ms.</p><p>　　VI. OBSERVATIONS</p><p>　　As with every real-life design, we have also made assumptions</p&g

85、t;<p>　　that simplify the design procedure described in this paper.</p><p>　　Therefore, it is important to verify that such assumptions are</p><p>　　valid and that they do not result in a

86、n unacceptable system</p><p>　　performance.</p><p>　　Fig. 8 shows that the response delay is about 25 ms. Also,</p><p>　　during the write cycles of the PC, data are lost resulting i

87、n</p><p>　　a slight time shift. Because of this reason, the time delay of</p><p>　　25 ms can only be determined from the very beginning. The</p><p>　　sometimes-sharp changes in the

88、velocity are also caused by</p><p>　　missing measurement values. In general, we see that it takes</p><p>　　the motor about 100 ms to reverse its movement and several</p><p>　　hundre

89、d milliseconds to approach top speed.</p><p>　　Another problem with the experimental system is that of</p><p>　　precision in the data acquisition. Not only is the rate of data</p><p&g

90、t;　　measurements very slow (60 measurements per second), but</p><p>　　they are also not very exact. This results from the fact that the</p><p>　　whole field of view that we observe and in which

91、the pendulum</p><p>　　moves spans 480 pixels. Noting that two steel bars that are 60</p><p>　　cm long guide the sled, we get a maximal resolution of 1.25</p><p>　　mm/pixel. Since we

92、 calculate the angle from the trigonometric</p><p>　　relationship between the constant vertical distance and the</p><p>　　variable number of pixels in the horizontal direction, we get a</p>

93、;<p>　　resolution of about 0.25 . This means that, if the pendulum is</p><p>　　0.2 off center, such a position will go undetected.</p><p>　　Last, but not least, is the error contribution

94、due to the coarse</p><p>　　quantization of the angle. We know that fuzzy logic is based on</p><p>　　membership functions and on the technique of inference. This</p><p>　　means that

95、a value is not only a member of a particular set,</p><p>　　but also, to some degree, a member of several different sets.</p><p>　　Now, with coarse quantization we lose part of the flexibility<

96、;/p><p>　　of the fuzzy-logic system. In reality, the range of the angle</p><p>　　that is used never exceeds 5 . For larger deviations, the</p><p>　　system turned out to be too slow to

97、compensate. The output</p><p>　　values are therefore amplified to give the maximum output</p><p>　　current already in the case when the controller wants to apply</p><p>　　a positive

98、 or negative MEDIUM control force. Although we</p><p>　　implemented a matrix with 49 rules, we effectively use</p><p>　　only the core matrix. This leads to another deterioration</p><p

99、>　　of the controller performance.</p><p>　　VII. SUMMARY AND CONCLUSION</p><p>　　The proposed vision feedback fuzzy-logic controller is able</p><p>　　to keep the inverted pendulum

100、 in the upright position, though</p><p>　　for a limited time. In what follows, we will discuss modifications</p><p>　　that might lead to an improvement in the behavior of</p><p>　　t

101、he experimental system.</p><p>　　The fuzzy-logic controller implementation is entirely written</p><p>　　in Borland C . This programming language running on</p><p>　　MS-DOS 6.2 opera

102、ting system does not provide a real-time environment</p><p>　　for the experiment and results in re-entry problems</p><p>　　of subroutines. This problem could be avoided by introducing</p>

103、<p>　　real-time subroutines that are not part of the standard C</p><p>　　package. To control the inverted pendulum successfully for</p><p>　　long periods of time, we would have to make use

104、 of not only</p><p>　　the angle of the pendulum, but also the position and perhaps</p><p>　　the velocity of the sled. Using the position of the sled also will</p><p>　　in turn lead

105、to a four-dimensional fuzzy-logic control system.</p><p>　　The addition of an extra state, however, will render the manual</p><p>　　tuning approach to determine the fuzzy set values a more</p

106、><p>　　challenging task. It might even be necessary to implement</p><p>　　an adaptive fuzzy-logic controller that obtains suitable control</p><p>　　parameters after a period of “traini

107、ng” [11], [12]. This will</p><p>　　require major changes not only in the controller program, but</p><p>　　also in the data acquisition system, since the sled position is</p><p>　　no

108、t part of the present control strategy. Further problems arise</p><p>　　from the fact that we use the difference between two angles</p><p>　　as input for the angular velocity. Since the measurem