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【正文】 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. We will begin with system design。 the system parameters using measured data on the dynamics of the pendulum. The inverted pendulum is a traditional example (neither difficult nor trivial) of a controlled system. Thus it is used in simulations and experiments to show the performance of different controllers (. PID controllers, state space controllers, fuzzy controllers....). The RealTime Inverted Pendulum is used as a benchmark, to test the validity and the performance of the software underlying the statespace controller algorithm, . the used operating system. Actually the algorithm is implement form the numerical point of view as a set of mutually cooperating tasks, which are periodically activated by the kernel, and which perform different calculations. The way how these tasks are activated (. the activation order) is called scheduling of the tasks. It is obvious that a correct scheduling of each task is crucial for a good performance of the controller, and hence for an effective pendulum stabilization. Thus the inverted pendulum is very useful in determining whether a particular scheduling choice is better than another one, in which cases, to which extent, and so on. Modeling an inverted the inverted pendulum system is modeled 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 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. We will begin with system design。 pendulum dynamics. The correct force has to be calculated measuring the instant values of the horizontal position and the pendulum angle (obtained . through two potentiometers). The system pendulum+cart+motor can be modeled as a linear system if all the parameters 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 39。 畢 業(yè) 設(shè) 計（論 文） 外 文 參 考 資 料 及 譯 文 譯文題目： Inverted Pendulum 學(xué)生姓名： 學(xué) 號： 專 業(yè)： 07 自動化 所在學(xué)院： 指導(dǎo)教師： 職 稱： 2021 年 2 月 24 日 \The inverted pendulum Key words: inverted pendulum, modeling, PID controllers, LQRcontrollers What is an Inverted Pendulum? Remember when you were a child and you tried to balan
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