畢業(yè)設(shè)計(論文)外文參考資料及譯文封面

1、魚陵科扶羅院畢業(yè)設(shè)計（論文）外文參考資料及譯文譯文題目： Inverted Pendulum學生姓名：徐飛馬 學號：0704111030專業(yè)：07自動彳卜,所在學院：機電學院指導教師：陳麗換職稱：Mffi2011年2月24日The inverted pendulumKey words: inverted pendulum, modeling, PID controllers,LQRcontrollersWhat is an Inverted Pendulum? Remember when you were a child and you tried to balance a broom-sti

2、ck or baseball 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 the same thing. However, it is limited in that it onl y moves in one dimension, while your hand could move up, dow

3、n, sideways, etc. Che ck out the video provided to see exactly how the Inverted Pendulum works.An inverted pendulum is a physical device consisting in a cylindrical bar (usually o f aluminum) free to osc川ate around a fixed pivot. The pivot is mounted on a carriage, which in its turn can move on a ho

4、rizontal direction. The carriage is driven by a moto r, which can exert on it a variable force. The bar would naturally tend to fall down fro m the top vertical position, which is a position of unsteady equilibrium.The goal of the experiment is to stabilize the pendulum (bar) on the top vertical pos

5、 ition. This is possible by exerting on the carriage through the motor a force which ten ds to contrast the 'free* pendulum dynamics. The correct force has to be calculated me asuring the instant values of the horizontal position and the pendulum angle (obtained e.g. through two potentiometers).

6、The system pendulum+cart+motor can be modeled as a linear system if all the para meters are known (masses, lengths, etc.), in order to find a controller to stabilize it. If not all the parameters are known, one can however try to 'reconstruct* the system para meters using measured data on the dy

7、namics of the pendulum.The inverted pendulum is a traditional example (neither difficult nor trivial) of a co ntrolled system. Thus it is used in simulations and experiments to show the performan ce of different controllers (e.g. PID controllers, state space controllers, fuzzy controlle rs ).The Rea

8、l-Time Inverted Pendulum is used as a benchmark, to test the validity and t he performance of the software underlying the state-space controller algorithm, i.e. th e used operating system. Actually the algorithm is implement form the numerical poin t of view as a set of mutually co-operating tasks,

9、which are periodically activated by t he kernel, and which perform different calculations. The way how these tasks are acti vated (e.g. the activation order) is called scheduling of the tasks. It is obvious that a co rrect scheduling of each task is crucial for a good performance of the controller,

10、and h ence for an effective pendulum stabilization. Thus the inverted pendulum is very usef ul in determining whether a particular scheduling choice is better than another one, in which cases, to which extent, and so on.Modeling an inverted pendulum.Generally the inverted pendulum system is model

11、69; d as a linear system, and hence the modeling is valid only for small oscillations of the pendulum.With the use of trapezoidal input membership functions and appropriate compositio n and inference methods, it will be shown that it is possible to obtain rule membership functions which are region-w

12、ise affine functions of the controller input variable. We propose a linear defuzzification algorithm that keeps this region-wise affine structure and yields a piece-wise affine controller. A particular and systematic parameter tuning method will be given which allows turning this controller into a v

13、ariable structure-like controller. We will compare this region-wise affine controller with a Fuzzy and Varia ble Structure Controller through the application to an inverted pendulum control.We will begin with system design; analyzing control behavior of a two-stage invert ed pendulum. We will then s

14、how how to design a fuzzy controller for the system. We will describe a control curve 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 for variables, as well as how to crea

15、te rules for the c ontroller.In the formulation of any control problem there will typically be discrepancies betw een the actual plant and the mathematical model developed for controller design.This mismatch may be due to unmodelled dynamics, variation in system parameters or the approximation of co

16、mplex plant behavior by a straightforward model.The engineer must ensure that the resulting controller has the ability to produce the required perfor mance levels in practice despite such plant/model mismatches. This has led to an inte nse interest in the development of so-called robust control meth

17、ods which seek to solv e this problem. One particular approach to robust control controller design is the so-ca lied sliding mode control methodology.The Inverted Pendulum is one of the most important classical problems of Control Engineering.Broom Balancing (Inverted Pendulum on a cart) is a well k

18、nown exampl e of nonlinear, unstable control problem. This problem becomes further complicated when a flexible broom, in place of a rigid broom, is employed. Degree of complexity and difficulty in its control increases with its flexibility. This problem has been a rese arch interest of control engin

19、eers.Control of Inverted Pendulum is a Control Engineering project based on the FLIG HT SIMULATION OF ROCKET OR MISSILE DURING THE INITIAL STAGES O F FLIGHT. The AIM OF THIS STUDY is to stabilize the Inverted Pendulum such tha t the position of the carriage on the track is controlled quickly and acc

20、urately so that t he pendulum is always erected in its inverted position during such movements.This practical exercise is a presentation of the analysis and practical implementatio n of the results of the solutions presented in the paper "s, RobusCt ontroller for Nonlin ear & Unstable Syste

21、m: lnvertedPendulum and “ FlexibleBroom Balancing ” ,in whi ch this complex problem was analyzed and a simple yet effective solution was pre sented.Prescribed trajectory tracking with certain accuracy is a main task of robotic contro I. The control is often based on a mathematical model of the syste

22、m. This model is ne ver an exact representation of reality, since modeling errors are inevitable. Moreover, one can use a simplified model on purpose. In this paper, the structured and unstructur ed uncertainties are of primary interest, i.e., the modeling error due to the parameters variation and u

23、nmodeled modes, especially the friction and sensor dynamics, neglecte d time delays,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 ca n be used if the inaccuracies in the model structu

24、re are bounded with known bounds. However, an SMC has some disadvantages, related to chattering of the control input si gnal. Often this phenomenon is undesirable, since it causes excessive control action Ie ading to increase wear of the actuators and to excitation of unmodeled dynamics.The attempts

25、 to attenuate this undesirable effect result in the deterioration of the ro bustness characteristics. This is a well-known problem and widely treated in the literat ure. In order to obtain smoothing in the bang-bang typed discontinuities of the sliding mode controller different schemes have been sug

26、gested.Another important issue limiting the practical applicability of SMC is the over cons ervative control law due to the upper bounds of the uncertainties. In practice most ofte n the worst case implemented in control law does not take place and the resulting larg e control inputs become unnecess

27、ary and uneconomical.In this paper we suggest an approach to the design of decentralized motion controll ers for electromechanical systems besides the sliding mode motion controller structure and disturbance torque estimation. The accuracy of the estimation is the critical para meter for robustness

28、in this scheme, as opposed to the upper bounds of the perturbatio ns themselves. Consequently, the driving terms of the error dynamics are reduced fro m the uncertainties (as in the conventional SMC) to the accuracy in their estimates. T he result is a much better tracking accuracy without being ove

29、r conservative in controlExperimental robustness properties of fuzzy controllers remain theoretically difficu It to prove and their synthesis is still an open problem. The non-linear structure of the final controller is derived from all controllers at the different stages of fuzzy control, p articul

30、arly from common defuzzification methods (such as Centre of Area). In general , fuzzy controllers have a region-wise structure given the partition of its input space b y the fuzzification stage. Local controls designed in these regions are then combined i nto sets to make up the final global control

31、. A partition of the state space can be found for which the controller has region-wise constant parameters. Moreover, each fuzzy c ontroller tuning parameter (i.e. the shapes and the values of input or output variables membership functions) influences the values of parameters in several regions at t

32、he sa me time. In the particular case of a switching line separating the phase plane into one region where the control is positive whereas in the other it is negative, the fuzzy controiler may be seen as a variable structure controller. This kind of a fuzzy controller can be assimilated to a variabl

33、e structure controller with boundary layer such as in, for w hich stability theorems exist, but with a non-linear switching surface.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 system. We wil

34、l describe a control curve 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 label s and membership functions for variables, as well as how to create rules for the contro Iler.In the formulation of any con

35、trol problem there will typically be discrepancies betw een the actual plant and the mathematical model developed for controller design.This mismatch may be due to unmodelled dynamics, variation in system parameters or the approximation of complex plant behavior by a straightforward model.The engine

36、er must ensure that the resulting controller has the ability to produce the required perfor mance levels in practice despite such plant/model mismatches. This has led to an inte nse interest in the development of so-called robust control methods which seek to solv e this problem. One particular appr

37、oach to robust control controller design is the so-ca lied sliding mode control methodology.Sliding mode control is a particular type of Variable Structure Control System (VS CS). A VSCS is characterized by a suite of feedback control laws and a decision rule. The decision rule, termed the switching

38、 function, has as its input some measure of the current system behavior and produces as an output the particular feedback controller which should be used at that instant in time. A variable structure system,which may be regarded as a combination of subsystems where each subsystem has a fixed control

39、 s tructure and is valid for specified regions of system behavior, results. One of the adva ntages of introducing this additional complexity into the system is the ability to combi ne useful properties of each of the composite structures of the system. Furthermore, th e system may be designed to pos

40、sess new properties not present in any of the composi te structures alone. Utilization of these natural ideas began in the Soviet Union in the I ate1950&.In sliding mode control, the VSCS is designed to drive and then constrain the syste m state to lie within a neighborhood of the switching func

41、tion. There are two main ad vantages to this approach. Firstly, the dynamic behavior of the system may be tailored by the particular choice of switching function. Secondly, the closed-loop response be comes totally insensitive to a particular class of uncertainty. The latter invariance prop erty cle

42、arly makes the methodology an appropriate candidate for robust control. In ad dition, the ability to specify performance directly makes sliding mode control attractiv e from the design perspective.The sliding mode design approach consists of two components. The first involves t he design of a switch

43、ing function so that the sliding motion satisfies design specificati ons. The second is concerned with the selection of a control law which will make the switching function attractive to the system state. Note that this control law is not nece ssarily discontinuous.We will provide the reader with a

44、thorough grounding in the sliding mode control a rea and as such is appropriate for the graduate with a basic knowledge of classical con trol theory and some knowledge of state-space methods. From this basis, more advanc ed theoretical results are developed. Resulting design procedures are emphasize

45、d usin g Matlab files. Fully worked design examples are an additional tutorial feature. Indust rial case studies, which present the results of sliding mode controller implementations, are used to illustrate the successful practical application of the theory.倒立擺關(guān)鍵詞：倒立擺，模型，PID控 帶f，LQR控帝f倒立擺是什么？還記得當你是個

46、孩子時你曾用你的食指或者掌心設(shè)法去 平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象的垂直。一個 倒立擺在本質(zhì)上就是做相同的事情。然而，它會受限制因為它只能在一定范圍內(nèi)移動，雖然 你的手可以上升、下降、斜向一邊等等。檢查錄象提供 的畫面來觀察倒立擺是如何確切 地工 作的。一個倒立擺是個物理設(shè)備它包括一個圓柱體的棒子（通常是鋁的）可以在一個支點周圍振蕩。這個支點是安在一個車架上，它的轉(zhuǎn)動方向是水平的偏轉(zhuǎn)。小車是由一個馬達控 制的，它可以運用于一個變力。棒子會有自然的趨勢從最高的豎直位置下落，那是一個不 穩(wěn)定的平衡位置。實驗的目標是使擺（棒子）穩(wěn)定在最高的豎直位置。這是有可能的只

47、要運用通過馬達 的小車一個力該力可以與“自由”擺的動力學抵消。這個正確的力必須通過計算測量水平偏 轉(zhuǎn)的瞬時值和擺的角度（獲得兩個電位計）。倒立擺是干什么的？就好象掃帚柄，一個倒立擺是一個天生的不穩(wěn)定系統(tǒng)。力度必須被 嚴格地應(yīng)用以保持系統(tǒng)的完整性。為了實現(xiàn)它，嚴格的控制理論是必 須的。倒立擺在求數(shù) 值和各種控制理論的比較中是必要的。倒立擺是一個控制器系統(tǒng)中的一個傳統(tǒng)的例子（既不困難也不是沒有價值）。盡管它 是仿真和實驗來顯示不同控制器的性能（舉例來說PID控制器，狀態(tài)空間控制器，模糊控 制器）。實時倒立擺被作為一個基準，去測試軟件在狀態(tài)空間控制器運算法則下的有效性和性 能，也就是實用的操作系統(tǒng)。

48、事實上運算法則是通過數(shù)值點實現(xiàn)的該數(shù)值點看作一組互助 的協(xié)同操作的任務(wù)，它是周期性的通過核心的活動，它執(zhí)行不同的計算。這些任務(wù)如何活 動的方法（舉例來說激活命令）被稱作任務(wù)的時序安排。很明顯每個任務(wù)的時序安排對控 制器的一個好的性能是至關(guān)緊要的，因此對一個擺的穩(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特殊的時序 安排的選擇比另一個好，在哪個情形下，在什么程度內(nèi)等 等。為倒立擺建模。通常倒立擺系統(tǒng)建模成一個線形系統(tǒng)，因此模型只對小幅度擺動的擺 才有效。通過梯形輸入隸屬函數(shù)的使用和適當?shù)淖鲌D法和推論方法，這將說明那是有可能遵循規(guī) 則區(qū)域勸導的輸入變量仿射函數(shù)的隸屬函數(shù)。我們提出線形逆模

49、糊化算法它能這個區(qū)域勸導 仿射結(jié)構(gòu)和產(chǎn)生一個塊仿射控制器。一個特殊的系統(tǒng)的參數(shù)調(diào)節(jié)方法將會被給定它允許把這 個控制器調(diào)節(jié)成一個可變的結(jié)構(gòu)相似的控制器。我們將比較這個區(qū)域勸導仿射控制器和一個 模糊的可變結(jié)構(gòu)的控制器通過應(yīng)用一個倒立擺控制。我們將從系統(tǒng)設(shè)計開始；分析二級倒立擺的控制行為。隨后我們將展示如何為系統(tǒng)設(shè) 計一個模糊控制裝置。我們將描繪一個控制曲線當使用模糊控制裝置時它與一個常規(guī)控制器 是如何的不同。最后，我們將討論如何使用這個曲線去定義標志還有變量的隸屬函數(shù)，還有 就是如何為控制器創(chuàng)立一套規(guī)則。“倒立擺、分析、設(shè)計和執(zhí)行”是由一個MATLAB方程和內(nèi)容的收藏的，還有 SIMULINK模型

50、，對分析倒立擺系統(tǒng)和設(shè)計控制系統(tǒng)是很有用的。這個報道MATLAB文件 收藏是由少量的控制系統(tǒng)分析的實際任務(wù)而發(fā)展的，設(shè)計和發(fā)展實際問題。這分派的倒立擺 的問題是一個控制系統(tǒng)的實驗室工作的一部分。倒立擺是最重要最經(jīng)典的控制工程問題中的一個。帚平衡（車載的倒立擺）是一個著名 的非線形例子，不穩(wěn)定的控制問題。這個問題越來越復雜當一個柔韌的帚代替一個剛硬的帚 被使用。復雜的問題的真實度和難度在控制中隨著彈性而增長。這個問題已經(jīng)引起調(diào)度工程 師的興趣并展開研究。倒立擺的控制是一個控制工程的方案基于火箭的飛行模擬或者導彈飛行的初始狀態(tài)。這 個學習的目的是穩(wěn)定倒立擺這樣小車的位置在軌道上被控制得快速和準確以

51、使擺在這一裝置 下始終垂直在它的倒立位置。這個實際的運動是一個分析的表現(xiàn)還有實際的執(zhí)行在解決問題的結(jié)果中在本文中，“非線 形和不穩(wěn)定系統(tǒng)的堅固的控制器：倒立擺”和“柔韌的帚平衡”，其中這個復雜問題分析 和一個簡單的有效的解決方案被引出法定軌道通過確定的精確性是機器控制的一個主要任務(wù)?？刂仆ǔＪ腔谝粋€系統(tǒng)的數(shù) 學模型。模型不是一個準確的實體表現(xiàn)，模型的誤差是不可避免的。此外，我們可以特意 使用一個簡化的模型。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，也就是說模型的誤差導致參數(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，被忽視的時間延遲等等。不正確的模型和高性能的需求要求控制器非常堅固?；？刂破鳎⊿MC是基于變結(jié)構(gòu)控制使用的如果模型結(jié)構(gòu)中的錯誤在已知的范圍內(nèi)躍進。然而，一個SMC有一些缺 點，涉及控制輸入信號的振動。通常這個現(xiàn)象是令人不快的，它會引起額外的控制作用從而 導致激勵者穿戴的增加和未建模動力學的刺激。削弱