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1、电子与信息工程学院 本科毕业设计外 文 文 献 翻 译 论文题目 直线式倒立摆控制系统 学生姓名 包雷 专 业 电气工程及其自动化 指导教师 李 东 京 2011年 11 月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 bro
2、om-stick 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 t he same thing. However, it is limited in that it only moves in one dimension, while your hand coul d move u
3、p, down, sideways, etc. Check out the video provided to see exactly how the Inverted Pe ndulum works. 倒立摆是什么？还记得当你是个孩子时你曾用你的食指或者掌心设法去平 衡一把扫帚柄或者棒球棍吗？你必须不断地调整你 的手的位置以保持对象的垂 直。一个倒立摆在本质上就是做相同的事情。然而，它会受限制因为它只能在 一 定范围内移动，虽然你的手可以上升、下降、斜向一边等等。检查录象提供 的画面来观察倒立摆是如何确切 地工作的。 An inverted pendulum is a physical de
4、vice consisting in a cylindrical 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 variable for ce. The bar would naturally tend to fa
5、ll down from the top vertical position,which is a position of unsteady equilibrium. 一个倒立摆是个物理设备它包括一个圆柱体的棒子（通常是铝的）可以在一 个支点周围振荡。这个支点是安在一个车架上，它的转动方向是水平的偏转。小 车是由一个马达控制的，它可以运用于一个变力。棒子会有自然的趋势从最高的 竖直位置下落，那是一个不稳定的平衡位置。 The goal of the experiment is to stabilize the pendulum (bar) on the top vertical positio
6、n. This is possible by exerting on the carriage through 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. through two potentiometers). 实验的目标是使摆（棒
7、子）稳定在最高的竖直位置。这是有可能的只要运用 通过马达的小车一个力该力可以与“自由”摆的动力学抵消。 这个正确的力必须 通过计算测量水平偏转的瞬时值和摆的角度（获得两个电位计） 。 The system pendulum+cart+motor can be modeled 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,
8、one can however try to reconstruct the system parameters using measured data on the d ynamics of the pendulum. 系统摆+车+马达可以建模成一个线形系统如果所有的参数都是已知的（质 量、长度等） ，为了寻找一个控制 器去稳定住它。如果不是所有的参数都已知， 可以用多种方法去“推想”系统参数像用摆的动力学的测量数据。 What is it used for?Just like the broom-stick, an Inverted Pendulum is an inherently un
9、stable sys tem. Force must be properly applied to keep the system intact. To achieve this, proper control theo ry is required. The Inverted Pendulum is essential in the evaluating and comparing of various cont rol theories. 倒立摆是干什么的？就好象扫帚柄，一个倒立摆是一个天生的不稳定系统。 力度必须被严格地应用以保持系统的完整性。为了实现它，严格的控制理论是必 须的。倒立摆
10、在求数值和各种控制理论的比较中是必要的。 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 controller s (e.g. PID controllers, state space controllers, fuzzy controllers). 倒立摆是一个控制器系
11、统中的一个传统的例子 （既不困难也不是没有价值） 。 尽管它是仿真和实验来显示不同控制器的性能（举例来说 PID 控制器，状态空间 控制器，模糊控制器） 。 The Real-Time 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
12、implement 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 activation order) is called scheduling of the tasks . It is obvious that a c
13、orrect scheduling of each task is crucial for a good performance of the contro ller, and hence for an effective pendulum stabilization. Thus the inverted pendulum is very useful i n determining whether a particular scheduling choice is better than another one, in which cases, to which extent, and so
14、 on. 实时倒立摆被作为一个基准， 去测试软件在状态空间控制器运算法则下的有 效性和性能，也就是实用的操作系统。事实上运算法则是通过数值点实现的该数 值点看作一组互助的协同操作的任务，它是周期性的通过核心的活动，它执行不 同的计算。这些任务如何活动的方法（举例来说激活命令）被称作任务的时序安 排。很明显每个任务的时序安排对控制器的一个好的性能是至关紧要的，因此对 一个摆的稳定性是有效的。 如此倒立摆是非常有用的在决定是否一个特殊的时序 安排的选择比另一个好，在哪个情形下，在什么程度内等等。 Modeling an inverted pendulum.Generally the inverte
15、d pendulum system is modeled as a linear system, and hence the modeling is valid only for small oscillations of the pendulum. 为倒立摆建模。通常倒立摆系统建模成一个线形系统，因此模型只对小幅度 摆动的摆才有效。 Prescribed trajectory tracking with certain accuracy is a main task of robotic control. The contr ol is often based on a mathematic
16、al model of the system. This model is never an exact representati on of reality, since modeling errors are inevitable. Moreover, one can use a simplified 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 para
17、meters variation and unmodeled modes, especially the friction and sen sor dynamics, neglected time delays, etc. 法定轨道通过确定的精确性是机器控制的一个主要任务。 控制通常是基于一 个系统的数学模型。模型不是一 个准确的实体表现，模型的误差是不可避免的。 此外，我们可以特意使用一个简化的模型。在这篇论文中， 构造好的和未构造 好的不确定因素是主要的兴趣所在， 也就是说模型的误差导致参数变化和未模型 化的模式 ，尤其是摩擦力和敏感元件的力度，被忽视的时间延迟等等。 The errone
18、ous 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 structure are bounded with known bounds. However, an SMC has some disadvan tages, related to chatteri
19、ng of the control input signal. Often this phenomenon is undesirable, since it causes excessive control action leading to increase wear of the actuators and to excitation of un modeled dynamics. 不正确的模型和高性能的需求要求控制器非常坚固。滑模控制器(SMC)是基 于变结构控制使用的如果模型结构中的错误在已知的范围内跃进。然而，一个 SMC 有一些缺点，涉及控制输入信号的振动。通常这个现象是令人不快的
20、，它会 引起额外的控制作用从而导致激励者穿戴的增加和未建模动力学的刺激。 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 order to obtain s moothing in the bang-bang typed discontinuities of the slidin
21、g mode controller different schemes have been suggested. 削弱这个令人不快的效果的尝试导致坚固的特性的变化。这是一个众所周 知的难题并且广泛的在文献中经过处理。 为了在继电器控制中获得滤波中断滑模 控制器的方案已经被提出了。 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 prac
22、tice most often the worst case implem ented in control law does not take place and the resulting large control inputs become unnecessary and uneconomical. 另外一个重要的论点限定了 SMC 的实际应用性就是创新的控制定律导致上 面的不确定因素的范围。 在实践中通常大部分最差的案例在控制定律下执行确没 有发生并且作为结果的大的控制输入变得不必要和不经济的。 In this paper we suggest an approach to the
23、design of decentralized motion controllers for electr omechanical systems besides the sliding mode motion controller 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 perturbatio
24、ns themselves. Consequently, the driving terms of the error dynamics are reduced from the uncertainties (as in the conventional SMC) to the accurac y in their estimates. The result is a much better tracking accuracy without being over conservative in control. 在这篇论文中我们提出一个机电系统中分散震动控制器的设计方法除了滑 模震动控制器结
25、构和干扰转矩的估算。 估算的精确性是这个计划中最中坚的评定 参数，与上面的不确定的范围正好相反。因此，在评估的精确 性中控制一些误 差动力学的条件减少了一些不确定性（就如同在传统的 SMC 中） 。结果在没有 超越传统的控 制中是一个较好的跟踪精度。 Experimental robustness properties of fuzzy controllers remain theoretically difficult to prove a nd their synthesis is still an open problem. The non-linear structure of the
26、 final controller is derive d from all controllers at the different stages of fuzzy control, particularly from common defuzzific ation methods (such as Centre of Area). In general, fuzzy controllers have a region-wise structure given the partition of its input space by the fuzzification stage. Local
27、 controls designed in these re gions are then combined into sets to make up the final global control. A partition of the state space can be found for which the controller has region-wise constant parameters. Moreover, each fuzzy controller tuning parameter (i.e. the shapes and the values of input or
28、 output variables membership functions) influences the values of parameters in several regions at the same time. In the particula r 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
29、as a variable structure controll er. This kind of a fuzzy controller can be assimilated to a variable structure controller with bounda ry layer such as in, for which stability theorems exist, but with a non-linear switching surface. 模糊控制装置的实验的健全的性质难以用理论去证明它们的综合仍然是一 个未解决的问题。最终控制器的非线性性质来源于各级模糊控制的控制器，显
30、著 地逆模糊化方法（诸如中心区） 。通常，模糊控制器有一个区域劝导的性质是模 糊化级数给的输入空间。本地控制设计这些区域结合成集使最终的全球控制实 现。一个级 数空间的分割可以在控制器有区域劝导的常数参数中找到。此外， 每个模糊控制器调整参数（即形状以及输 入输出的变量的值的隶属函数）会在 同一时间在某些区域影响参数的值。在特殊情况下开关线将相平面分成 一个区 域那个区域中控制是正的反之另一边是负的， 模糊控制器可以视为一个可变结构 的控制器。这类的模 糊控制器可以吸收到可变结构控制器边界层，其中稳定性 定理存在，而是一个非线形开关面。 With the use of trapezoidal
31、input membership functions and appropriate composition 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 that keeps this region-wise
32、 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 variable structure-like controller. We will compare this region-wise affine controller with a Fuzz y and Variable Structure Cont
33、roller through the application to an inverted pendulum control. 通过梯形输入隶属函数的使用和适当的作图法和推论方法， 这将说明那是有 可能遵循规则区域劝导的输 入变量仿射函数的隶属函数。我们提出线形逆模糊 化算法它能这个区域劝导仿射结构和产生一个块仿射控制 器。一个特殊的系统 的参数调节方法将会被给定它允许把这个控制器调节成一个可变的结构相似的 控制器。 我们将比较这个区域劝导仿射控制器和一个模糊的可变结构的控制器 通过应用一个倒立摆控制。 So far, in the application note series, we ha
34、ve 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 application note, we use an example of an inverted pendulum to pro vide details on all aspects of fuzzy logic based system
35、design. 迄今为止，在应用笔记系列中，我们已经提供了许多展示如何用 FIDE 创造 模糊控制装置的例子。然而， 这些例子不能提供设计系统执行的话题。在这应 用笔记中，我们可以用一个倒立摆的例子来提供模糊逻辑基 础系统设计的所有 方面的细节。 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 will descr
36、ibe 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 for variables, as well as how to create rules for the controller. 我们将从系统设计开始；分析二级倒立摆的控制行为。随后我们将展示如何 为系
37、统设计一个模糊控制装 置。我们将描绘一个控制曲线当使用模糊控制装置 时它与一个常规控制器是如何的不同。最后，我们将讨论 如何使用这个曲线去 定义标志还有变量的隶属函数，还有就是如何为控制器创立一套规则。 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 unmod
38、elled 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 required performance levels in practice despite such plant/model mismatche s. This has led t
39、o an intense interest in the development of so-called robust control methods which seek to solve this problem. One particular approach to robust control controller design is the so-cal led sliding mode control methodology. 在任何控制问题的陈述中， 在控制的设计发展中现行的设备和数学模型之间 总是有着明显的差异。这种 失谐也许应归于非建模动力学中，通过一个简洁的 模型系统参数
40、或者复杂设备的近似值会发生变化。工程师 必须确定作为结果的 控制器在实际中有能力制造必须的性能指标不管是设备还是模型的失谐。 这已经 导致了 在所谓坚固的操纵方法的发展产生一个强烈的兴趣此方法能设法解决这 个问题。坚固的操纵控制器设计的一 个特殊的方法就是所谓的滑模控制方法。 Sliding mode control is a particular type of Variable Structure Control System (VSCS). A VSC S is characterized by a suite of feedback control laws and a decisio
41、n rule. The decision rule, terme d the switching function, has as its input some measure of the current system behavior and produc 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 s
42、ubsystems where each subsys tem has a fixed control structure and is valid for specified regions of system behavior, results. On e of the advantages of introducing this additional complexity into the system is the ability to comb ine useful properties of each of the composite structures of the syste
43、m. Furthermore, the system m ay be designed to possess new properties not present in any of the composite structures alone. Util ization of these natural ideas began in the Soviet Union in the late 1950s. 滑模控制是可变结构控制系统（VSCS）的一个特殊的类型。一个 VSCS 是 由一套反馈控制定律和一个决策规则表现出来的。决策规则，条件是开关方程， 将输入估计成正确的系统特性并且产生一个输出
44、精确的反馈控制器使之可以 及 时地被使用。一个可变结构系统，被认为是各子系统的结合其中每个子系统 有一个确定的控制结构并且结果是对系统结构 给定的区域是适用的。介绍这个 额外的系统的复杂性的优势之一就是可以将系统中复合结构的有用的性质组合 起来。此外，该系统可能被设计成拥有新的性质而且不是单独地应用与复合结构 的某一方面。 前苏联在 20 世纪 50 年代末最先开始利用这些自然的想法。 In sliding mode control, the VSCS is designed to drive and then constrain the system state to li e within
45、 a neighborhood 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 response becomes totally insensitive to a particular class of u ncertaint
46、y. The latter invariance property clearly makes the methodology an appropriate candidate for robust control. In addition, the ability to specify performance directly makes sliding mode cont rol attractive from the design perspective. 在滑模控制中，VSCS 被设计成操作并强迫系统状态位于邻近的开关方程 中。这种方法有两个主要的优点：第一，系统的动态性能适应于开关方
47、程的特殊 选择；第二，闭环响应完全不受不确定的特殊种类的影响。后面的恒定性质明显 地使方法论在坚固的操纵方法中有一个适当的侯选对象。另外，立即指定性能的 能力使得滑模控制从设计观点看变得有价值。 The sliding mode design approach consists of two components. The first involves the design of a switching function so that the sliding motion satisfies design specifications. The second is conce rned wi
48、th the selection of a control law which will make the switching function attractive to the sy stem state. Note that this control law is not necessarily discontinuous. 滑模设计处理两种结构组成。 第一个包括开关方程的设计所以滑行的动作满 足设计规范。第二个涉及到 控制规则的选择该规则将使开关方程在系统状态中 变得有价值。注意这个控制规则并不是必然不连续的。 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 wledge of state-space methods. From this basis, more advanced theoretical results are develop
