【正文】 形系統(tǒng)如果所有的參數(shù)都是已知的（質(zhì)量、長度等），為了尋找一個控制 器去穩(wěn)定住它。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。The inverted pendulum Key words: inverted pendulum, modeling, PID controllers, Fuzzy controllers, state space controllers What is an Inverted Pendulum? Remember when you were a child and you tried to balance a broomstick 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 only moves in one dimension, while your hand could move up, down, sideways, etc. Check out the video provided to see exactly how the Inverted Pendulum works. 倒立擺是什么 ？ 還記得當(dāng)你是個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。 The goal of the experiment is to stabilize the pendulum (bar) on the top vertical position. This is possible by exerting on the carriage through the motor a force which tends to contrast the 39。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)像用擺的動力學(xué)的測量數(shù)據(jù)。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。模型不是一 個準(zhǔn)確的實體表現(xiàn)，模型的誤差是不可避免的。這是一個眾所周知的難題并且廣泛的在文獻中經(jīng)過處理。 Experimental robustness properties of fuzzy controllers remain theoretically difficult to prove and their synthesis is still an open problem. The nonlinear structure of the final controller is derived from all controllers at the different stages of fuzzy control, particularly from mon defuzzification methods (such as Centre of Area). In general, fuzzy controllers have a regionwise structure given the partition of its input space by the fuzzification stage. Local controls designed in these regions are then bined into sets to make up the final global control. A partition of the state space can be found for which the controller has regionwise constant parameters. Moreover, each fuzzy controller tuning parameter (. the shapes and the values of input or output variables membership functions) influences the values of parameters in several regions at the same 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 controller may be seen as a variable structure controller. This kind of a fuzzy controller can be assimilated to a variable structure controller with boundary layer such as in, for which stability theorems exist, but with a nonlinear switching surface. 模糊控制裝置的實驗的健全的性質(zhì)難以用理論去證明它們的綜合仍然是一個未解決的問題。 With the use of trapezoidal input membership functions and appropriate position and inference methods, it will be shown that it is possible to obtain rule membership functions which are regionwise affine functions of the controller input variable. We propose a linear defuzzification algorithm that keeps this regionwise affine structure and yields a piecewise affine controller. A particular and systematic parameter tuning method will be given which allows turning this controller into a variable structurelike controller. We will pare this regionwise affine controller with a Fuzzy and Variable Structure Controller through the application to an inverted pendulum control. 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)。 analyzing control behavior of a twostage inverted pendulum. We will then show 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 c