毕业设计（论文）材料之二（2）
本科毕业设计(论文)开题报告
题目：一级倒立摆的模糊控制
课 题 类 型： 设计□ 实验研究□ 论文□ 学 生 姓 名：
学 号： 3090201214
专 业 班 级： 自动化092
学 院： 电气工程学院
指 导 教 师：
开 题 时 间： 20xx年3月
2013 年3月10日
一、毕业设计（论文）内容及研究意义（价值）
在控制理论发展的过程中，一种理论的正确性及在实际应用中的可行性，往往需要一个典型对象来验证，并比较各种控制理论之间的优劣，倒立摆系统就是这样一个可以将理论应用于实际的理想实验平台。本论文在参考大量文献的基础上，建立了一级倒立摆系统的数学模型，对系统进行了稳定性、可控性分析，指出一阶倒立摆的开环不稳定性。文章主要完成了：一级倒立摆动力学模型和模糊PID控制器模块的设计，确定了输入输出信号的论域、隶属度函数和模糊规则，最后利用Matlab中的simulink工具箱创建了基于模糊控制理论的一级倒立摆系统的simulink仿真模型，对倒立摆系统进行分析。仿真结果证明模糊PID控制不仅可以稳定倒立摆系统，还使小车稳定在平衡位置附近，证明了本文设计的模糊PID控制器有良好的稳定性、鲁棒性和适应性
倒立摆系统能有效地反映诸如镇定性、鲁棒性、随动性等许多控制中的关键问题，是检验各种控制理论的理想模型。其典型性在于：作为实验装置，它本身具有成本低廉、结构简单、物理参数和结构易于调整、便于模拟、形象直观的优点；作为被控对象，它是一个具有高阶次、不稳定、多变量、非线性和强藕合特性的不稳定系统，可以有效地反映控制中的许多问题；作为检测模型，该系统的特点与机器人、飞行器、起重机稳钩装置等的控制有很大的相似性。对倒立摆因此对倒立摆控制机理的研究具有非常重要的理论和实践意义。。
二、毕业设计（论文）研究现状和发展趋势（文献综述）
1.倒立摆系统的研究现状
到目前为止，人们己经利用包括经典控制理论、现代控制理论以及各种智能控制理论在内的各种手段先后实现了倒立摆系统的稳定控制。随着微型计算机的发展和广泛应用，又陆续出现了对一级、二级甚至多级倒立摆的稳定控制。倒立摆系统是一个难以控制的不稳定结构，随着级数的增加，控制难度加大。在这样复杂的控制对象面前，把人工智能的方法引入到控制系统中，就为解决倒立摆控制问题提出了新的方向。
模糊智能控制和神经网络控制是智能控制的重要方面，它们在倒立摆系统的控制上起到了很大的作用。程福雁等将传统控制理论与模糊控制相结合实现了对二级倒立摆的稳定控制。王卫华采用专家模糊控制解决单级倒立摆的稳定问题。张乃尧等人采用模糊双闭环的方案，成功的对单级倒立摆进行了稳定控制。胡叔旖、孙增沂应用基于规则的方法实现了二级倒立摆的稳定控制。刘妹琴、陈际达等采用递归神经网络控制了单级倒立摆。王琳等采用模糊小脑模型控制器仿真控制了单级倒立摆。19xx年8月，北京航空航天大学自动化系张明廉教授、沈程智教授领导的人工智能小组，采用拟人智能控制模仿人面对同样问题的解决思路，成功实现了单电机控制三级平面运动倒立摆的控制。李洪兴教授领导的模糊系统与模糊信息研究中心暨复杂系统实时智能控制实验室采用变论域自适应模糊控制理论，于20xx年9月实现了三级倒立摆实物系统控制后，又于20xx年8月11日在世界上首次成功实现了四级倒立摆实物控制系统。在对倒立摆系统的研究过程中新的控制理论的不断出现，使现有的控制理论得到了不断的完善和发展。
2.倒立摆系统研究的发展趋势
此前，实现的一级至四级倒立摆均为直线运动倒立摆。直线运动倒立摆实现的是在一个平面上的摆动，轨道较长、传动环节较多、占地空间较大，实践中常常由于传动机构的故障或误差，而不是控制方法本身的问题导致平衡控制失败。随着科学技术的发展，被控对象日趋复杂，对控制性能的要求也日趋提高，直线倒立摆已不能满足复杂系统的
需要，由此产生了圆形轨道倒立摆。圆形轨道倒立摆实现了上、下、左、右、前、后任何方向的摆动，与传统的直线轨道倒立摆相比，圆形轨道倒立摆具有控制精度高、功能多、结构紧凑、性价比高等优点，所以圆形轨道倒立摆比传统的直线轨道倒立摆更具有竞争力和应用价值。圆形轨道倒立摆实物系统控制的实现要比直线运动倒立摆实物系统控制的实现困难得多；这不仅是因为这样的系统其变量、非线性程度及不稳定性成倍地增加，而且有关机械和电子器件的实现或选用会遇到瓶颈性的困难。因此，圆形轨道倒立摆实物系统是控制领域研究的重要课题之一。
近年来，人们对倒立摆的研究越来越感兴趣，倒立摆的种类也变得丰富多样。倒立摆系统不仅在高科技领域中得到广泛应用，人们还可以通过倒立摆这样一个严格的控制对象，检验新的控制方法是否有较强的处理多变量、非线性和绝对不稳定系统的能力。因此，倒立摆系统作为控制理论研究中的一种比较理想实验手段常常用来检验控制策略的效果。
三、毕业设计（论文）研究方案及工作计划（含工作重点与难点及拟采用的途径）
1、研究方案
一级倒立摆系统由导轨，小车和一级摆杆组成，小车依靠直流电机施加的控制力，可以在导轨上左右移动，其位移和摆杆角度信息由传感器测得，目标是使倒立摆在有限长的导轨上竖立稳定，达到动态平衡，即不超过一个预先定义好的垂直偏离角度范围。 面对一级倒立摆系统这样一个非线性、不稳定的复杂被控对象，其控制方法主要有三类：线性控制、预测控制、智能控制。智能控制方法源自于人类实践经验，不需要精确的数学模型，是当前应用较广的控制方法。在倒立摆系统中应用的智能控制方法有：神经网络控制、模糊控制、仿人智能控制、拟人智能控制以及云模型控制。对一级倒立摆的稳定控制而言，模糊控制方法是一种比较优秀的解决途径，鲁棒性较好。
在研究倒立摆这类多变量非线性系统的模糊控制时，一个难题就是规则爆炸，比如一级倒立摆的控制涉及的状态变量共有4个，每个变量的论域作7个模糊集的模糊划分，这样，完备的推理规则库会包含2401个推理规则;而对于二级倒立摆有6个状态变量，推理规则会达到117649，显然如此多的规则是不可能实现的。 为了解决这个问题，张乃尧等提出双闭环的倒立摆模糊控制方案，内环控制倒立摆的角度，外环控制倒立摆的位移。范醒哲等人将这一方法推广到三级倒立摆控制系统中，并提出两种模糊串级控制方案，用来解决倒立摆这类多变量系 统模糊控制时的规则爆炸问题。shulinagLei和RezaLnagari应用分级思想，将x，dx/dt,θ,dθ/dt4个状态变量分成两个子系统，分别用两个模糊控制器控制，然后来协调子系统之间的相互作用。本文模仿人类简化问题的思路，将单一的复杂控制策略转化为多级简单控制策略嵌套，通过分离变量的方法设计控制器。
2、工作计划
01-02周：安排毕业设计计划，分配设计任务。
02-03周：了解本课题设计要求，针对倒立摆系统学习相关知识。
04-05周：完成开题报告以及相关知识点的掌握，掌握倒立摆系统仿真的整体思路，收集整理matlab仿真所需的资料。
06-11周：建立级倒立摆动力学模型，完成模糊PID控制器模块的设计，在matlab中完成仿真。
11-14周：完善控制效果，分析输出结果，得出仿真结论；翻译英文文献资料。
15-16周：编写毕业设计论文和准备毕业答辩。
主要参考文献（不少于10篇，期刊类文献不少于7篇，应有一定数量的外文文献， 至少附一篇引用的外文文献（3个页面以上）及其译文）
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[2]黄忠霖.控制系统MATLAB计算及仿真[M].2版.北京：国防工业出版社，2004.
[3]蔡自兴.智能控制[M].北京:电子工业出版社,2004.
[4]周其鉴,李祖枢,陈民铀.智能控制及其展望[J].信息与控制,2006(2):39-45.
[5]刘朝英，宋哲英.MATLAB在模糊控制系统中的应用[J].计算机仿真,2001,18（3）：11-13.
[6]李永强，杨明忠.智能控制理论在倒立摆系统中应用研究[J].现代机械，2006，2(3)：100-103.
[7]倪桂杰,郭巧菊.基本模糊控制器控制规则的提取[J].自动化仪表,2002,23(3):7-10
[8]高飞,薛忠.模糊控制技术中的几个问题[J].西安电子科技大学学报，1998,25（3）：369-373
[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.
[10]Bezdek J. Fuzzy Models-What Are They,and Why? [J].IEEE Trans on FuzzySystems，1993,1（1）：1-6.
[11] Mario E. Magana and Frank Holzapfel[J].IEEE Trans on Education,1998,2(4):41-44.
Fuzzy-Logic Control of an Inverted Pendulum with Vision Feedback
Mario E. Magana and Frank Holzapfel
Abstract— In this paper we present an experimental setup of a fuzzy-logic controller 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 limitations 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.
Index Terms—Control, fuzzy logic, vision feedback.
I. INTRODUCTION
The implementation of a fuzzy-logic controller for an
inverted pendulum is not new. In fact, one of the first
applications of it was to stabilize an inverted pendulum. Our
approach differs from previous approaches in the way in which
the physical variables are measured. The fact that a human
being is able to stabilize an inverted pendulum of reasonable
length and mass, along with the knowledge of the brain’s
ability to process about 25 images per second, leads one to
conclude that this data rate should be sufficient to control an
inverted pendulum using computer vision information. This
“low data rate” approach is in strong contrast to past research
that focused on measurement updates that are two to three
times faster. Of special interest is the fact that in certain realworld
applications the position of a controlled object cannot
be determined with traditional methods. The introduction of
video cameras and vision systems to process their images has
led to a new way to measure relevant quantities without having
to touch or even to come close to the object. The drawback
of this approach, on the other hand, is that just 60 half-frames
are obtained per second. This leads to problems that result
from delays, especially in connection with fast-moving objects.
Therefore, one of the goals of the experiment performed in
our teaching and research laboratory was to explore critical
limits and investigate if the speed and the versatility of the
fuzzy controller are sufficient to deal with them. The paper
describes the experimental setup extensively so that it can
also be performed at other teaching and research laboratories.
Such a setup can be used by both electrical and mechanical
engineering students to learn and apply fuzzy-logic control
techniques using nontouching sensors such as vision sensors.
The theoretical background of fuzzy systems with regard to
an inverted pendulum is developed in [6] and [12], where it is taken as a benchmark for binary input–output fuzzy associative memory (BIOFAM) systems. Using a similar approach as described in [6], we take two states and one control variable. The first fuzzy state variable is the angle that the pendulum shaft makes with the vertical. The second is the average angular velocity . As output fuzzy variable we use
the motor armature current. All three variables can be either positive or negative and are related in the following manner: If the pendulum falls to the left, the motor velocity should be negative to compensate. If the pendulum successfully balances in the middle, the motor current should be zero. Therefore, every variable takes on a certain set of values whose range is limited by practical considerations that result from physical and technological constraints. In the experiment we quantify each set or universe of discourse into seven overlapping fuzzy set values. This choice is based on prior experience. II. EXPERIMENTAL PLATFORM
The setup of the inverted pendulum fuzzy-logic control with vision feedback experiment consists of the following parts:
1) a mechanical system composed of an inverted pendulum mounted on an – table, 2) a video camera and a vision computer that are used as a nontouching sensor to obtain the states of the system, 3) a fuzzy-logic controller that is implemented on a 386 personal computer using Borland C , and 4) an actuator that consists of an armature-controlled dc servo-motor driven by a pulsewidth-modulated amplifier.
A. The Mechanical System
A lead screw that is directly coupled to the shaft of a dc
motor and is guided by two steel bars using bearings drives the sled. The pendulum itself consists of a 70-cm-long rod and a wooden ball designed in such a way that the center of mass can be assumed to be at the top of the rod. The pendulum rotates in the vertical plane using low friction roller bearings. Possible deviations range up to 90 , but are actually restricted to a much smaller range by the constraints of the system.
B. The Vision System
In order to control the system, it is necessary to measure the different states. To do this, we use an Intelledex vision system with a relatively low-resolution video camera. The camera is equipped with a 16-mm lens with adjustable aperture to vary the amount of incident light. The vision computer is the HR model with a memory management unit. It allows transferring frames or single rows from the A/D buffer to the main memory
without long delays. The information is evaluated and written to a serial RS 232 port that is set to operate at a 38-kb/s clock rate [4].
C. The Controller
The controller is implemented on a 386 personal computer running at 16 MHz. The control commands are sent to a power amplifier via a 10-V D/A converter.
D. The Actuator
This part of the system consists of a dc servomotor and a power amplifier. The analog signal from the D/A converter is translated as a current and fed to the motor. Since the torque of the dc motor is proportional to the armature current, we can control the speed of the sled with a voltage command signal. III. VISION SYSTEM
To successfully control the inverted pendulum using vision information it is necessary to separate the whole task into two parts: data acquisition and control. The vision system is responsible for acquiring the data and transmitting them to the PC that determines the control command based on these values. In doing so, routines for I/O and programs to handle the serial communication apart from the main control program are needed. This task is performed using C and small assembly language programs for controlling the serial communication.
1) Vision System Configuration: The vision system core is an Intel 386 microprocessor running at 20 MHz. Also, the vision computer has a fast A/D unit that samples the RS 170 analog signal and writes the digitized data in a local array that is separated from the main memory of the CPU. Because the camera sends the data of each frame for 15 ms and pauses for 1.25 ms during the vertical blank, we use this window to copy the information that we are interested in to the main memory. This gives us the opportunity to
manipulate the data and compute the angle and position of the sled simultaneously before the next image is acquired. Since this process takes place during a relatively short period of time, we can also transmit the position of the sled and the angle over an RS 232 serial communication channel without losing image information.
The vision application program is written and compiled in the host PC and then downloaded via the RS 232 into the vision computer.
2) Angle Computation: The video picture consists of 480 rows and 512 columns and a vertical blank period to allow the beam to reach the upper left corner again. The easiest
way to determine the angle of the pendulum is to take two
rows and find the position of the greatest dark/bright transition.
This position is represented as the column number. Since we
know the distance between the rows (e.g., 400 lines) and the
columns (e.g., 10 points) we can determine the angle by using a
simple trigonometric function. The following figure illustrates
the procedure.
In order to have reliable values for the angle we need a high
contrast of the video picture. To ensure this, the pendulum rod
is painted black and a white background is used. To detect
the point with the greatest black/white transition in a row we
use a linear search algorithm that compares the contrast of the
pixels and returns the position of the one with the greatest
dark value. From the coordinates, we calculate the and
distances and obtain the angle from
dist. hor.
dist. vert.
To protect the sled from running into its mount, we use
the position given in the lower row to determine five areas
of the sled position. They are encoded as integer values and
transmitted to the control computer. The following table shows
the areas in pixels.
IV. THE FUZZY LOGIC CONTROLLER
The proposed fuzzy-logic controller used to control the
experimental inverted pendulum uses conventional triangular
membership functions to fuzzify the data measured by the
vision system [9]. Furthermore, the fuzzy inference engine
implements a set of IF-AND-THEN rules on the angular
V. PERFORMANCE EVALUATION
In order to evaluate the performance of our fuzzy-logic
control system, all the acquired data are stored in a file on the
hard disk. To avoid delays in the output of the control signal,
the measured values are saved after the output command is
computed. The remaining time until the new angle and position
measurements are available at the serial port is still sufficient
to store the old values without losing data. To be able to
process the data off-line, the angle information is stored with
a precision of 0.1 .
We can observe in Fig. 7 that the average amplitude that
results from the deviation of the pendulum is about 2.7 . We
can also see in the same figure that the system displays an
oscillatory behavior. The amplitude of the oscillations depends
on the maximum acceleration, inertia, and other factors. From
the same figure, we can determine that the period of the oscillations is approximately 400 ms.
VI. OBSERVATIONS
As with every real-life design, we have also made assumptions that simplify the design procedure described in this paper. Therefore, it is important to verify that such assumptions are valid and that they do not result in an unacceptable system performance.
Fig. 8 shows that the response delay is about 25 ms. Also, during the write cycles of the PC, data are lost resulting in a slight time shift. Because of this reason, the time delay of 25 ms can only be determined from the very beginning. The sometimes-sharp changes in the velocity are also caused by missing measurement values. In general, we see that it takes the motor about 100 ms to reverse its movement and several hundred milliseconds to approach top speed.
Another problem with the experimental system is that of precision in the data acquisition. Not only is the rate of data measurements very slow (60 measurements per second), but they are also not very exact. This results from the fact that the whole field of view that we observe and in which the pendulum moves spans 480 pixels. Noting that two steel bars that are 60 cm long guide the sled, we get a maximal resolution of 1.25 mm/pixel. Since we calculate the angle from the trigonometric relationship between the constant vertical distance and the variable number of pixels in the horizontal direction, we get a resolution of about 0.25 . This means that, if the pendulum is 0.2 off center, such a position will go undetected.
Last, but not least, is the error contribution due to the coarse quantization of the angle. We know that fuzzy logic is based on membership functions and on the technique of inference. This means that a value is not only a member of a particular set, but also, to some degree, a member of several different sets. Now, with coarse quantization we lose part of the flexibility of the fuzzy-logic system. In reality, the range of the angle that is used never exceeds 5 . For larger deviations, the system turned out to be too slow to compensate. The output values are therefore amplified to give the maximum output current already in the case when the controller wants to apply a positive or negative MEDIUM control force. Although we implemented a matrix with 49 rules, we effectively use only the core matrix. This leads to another deterioration of the controller performance.
VII. SUMMARY AND CONCLUSION
The proposed vision feedback fuzzy-logic controller is able to keep the inverted pendulum in the upright position, though
for a limited time. In what follows, we will discuss modifications that might lead to an improvement in the behavior of
the experimental system.
The fuzzy-logic controller implementation is entirely written in Borland C . This programming language running on
MS-DOS 6.2 operating system does not provide a real-time environment for the experiment and results in re-entry problems
of subroutines. This problem could be avoided by introducing real-time subroutines that are not part of the standard C
package. To control the inverted pendulum successfully for
long periods of time, we would have to make use of not only the angle of the pendulum, but also the position and perhaps
the velocity of the sled. Using the position of the sled also will in turn lead to a four-dimensional fuzzy-logic control system. The addition of an extra state, however, will render the manual tuning approach to determine the fuzzy set values a more
challenging task. It might even be necessary to implement
an adaptive fuzzy-logic controller that obtains suitable control parameters after a period of “training” [11], [12]. This will
require major changes not only in the controller program, but also in the data acquisition system, since the sled position is
not part of the present control strategy. Further problems arise from the fact that we use the difference between two angles
as input for the angular velocity. Since the measurements
are noisy and have a relatively large quantization error, we
end up computing an even noisier estimate of the velocity.
Introduction of filtering techniques in the vision system can
potentially result in a better system performance because of a smaller angular velocity error.
The mechanical time constants of our experimental system
limit the response time and prevent fast changes in the
movement of the sled [1], [3], [7]. To achieve an improvement, it would be beneficial to change the design from the lead
screw – table to a belt-driven configuration that is more
responsive, has a smaller mass and less friction. Another aspect is the use of a different camera to accelerate the acquisition of data through the vision system. The Intelledex Vision System is able to give a reset pulse to the video camera. This would
make it possible to acquire more than just 60 frames per second and also decrease the response time of the system. Also we
encounter problems that result from the limited resolution of
the video camera. The fact that we have only 480 pixels for
the entire horizontal field of view leads to large quantization
errors and a low precision. It would be extremely beneficial
to improve the accuracy of the measured angle, since the precision of the input data is of great importance for the controller.
After reviewing the experimental results, it seems clear that it would be necessary to make substantial changes to
achieve a more satisfactory performance of the vision feedback fuzzy-logic control system. For example, better inference rules (perhaps adaptive) in the fuzzy-logic controller that use position and velocity information of the sled, along with a faster and more precise vision data acquisition system would certainly lengthen the time that the pendulum is kept in the upright position.