基于matlab的一级倒立摆自适应仿真-毕业论文.doc

Here and there: they had just discovered that a prisoner had escaped. At that moment, a large black car with four officers inside it, stopped at the camp gates. The officers got out and the prisoner stood to attention and saluted as they passed. When they had gone, the driver of the car came towards him. The man obviously wanted to talk. He was rather elderly with grey hair and clear blue eyes. The prisoner felt sorry for him, but there was nothing else he could do. As the man came near, the prisoner knocked him to the ground with a sharp blow. Then, jumping into the car, he drove off as quickly as he could. ？Fishermen and sailors sometimes claim to have seen monsters in the sea. Though people have often laughed at stories told by seamen, it is now known that many of these monsters which have at times been sighted are simply strange fish. Occasionally, unusual creatures are washed to the shore, but they are rarely caught out at sea. Some time ago, however, a peculiar fish was caught near Madagascar. A small fishing-boat was carried miles out to sea by the powerful fish as it pulled on the line. Realizing that this was no ordinary fish, the fisherman made every effort not to damage it in any way. When it was eventually brought to shore, it was found to be over thirteen feet long. It had a head like a horse, big blue eyes, shining silver skin, and a bright red tail, the fish, which has since been sent to a museum where it is being examined by a scientist, is called an oarfish. Such creatures have rarely been seen alive by man as they live at a depth of six hundred feet.Lesson83 After the elections 大选之后The former Prime Minister, Wentworth Lane, was defeated in the recent elections. He is now retiring from political life and has gone abroad. My friend, Crawley, has always been a fanatical opponent of Lanes Radical Progressive Party. After the elections, Crawley went to the former Prime Ministers house. When he asked if Lane lived there, the policeman on duty told him that since his defeat, the ex-Prime Minister had gone abroad. On the following day, Crawley went to the house again. The same policeman was just walking slowly past the entrance, when Crawley asked the same question. Though a little suspicious this time, the policeman gave him the same answer. The day after, Crawley went to the house once more and asked exactly the same question. This time, the policeman lost his temper. I told you yesterday and the day before yesterday, he shouted, Lane was defeated in the elections. He has retired from political life and gone to live I know, answered Crawley, but I love to hear you say it Lesson84 On strike 罢工Busmen have decided to go on strike next week. The strike is due to begin on Tuesday. No one knows how long it will last. The busmen have stated that the strike will continue until general agreement is reached about pay and working conditions. Most people believe that the strike will last for at least a week. Many owners of private cars are going to offer free rides to people on their way to work. This will relieve pressure on the trains to some extent. Meanwhile, a number of university students have volunteered to drive buses while the strike lasts. All the young men are expert drivers, but before they drive any of the buses, they will have to pass a special test. The students are going to take the test in two days time. Even so, people are going to find it difficult to get to work. But so far, the public has expressed its gratitude to the students in letters to the Press. Only one or two people have objected that the students will drive too fast!Lesson85 Never too old to learn 活到老学到老I have just received a letter from my old school informing me that my former head- master, Page, will be retiring next week. Pupils of the school, old and new, will be sending him a present to mark the occasion. All those who have contributed towards the gift will sign their names in a large album which will be sent to the headmasters home. We shall all remember Page for his patience and understanding and for the kindly encouragement he gave us when we went so unwillingly to school. A great many former pupils will be attending a farewell dinner in his next Thursday. It is a curious coincidence that the day before his retirement, Page will have been teaching for a total of forty years. After he has retired, he will devote himself to gardening. For him, this will be an entirely new hobby. But this does not matter, for, as he has often remarked, one is never too old to learn. Lesson86 Out of control 失控As the man tried to swing the speed-boat round, the steering-wheel came away in his hands. He waved desperately to his companion, who had been water-skiing for the last fifteen minutes. Both men had hardly had time to realize what was happening when they were thrown violent1y into the sea. The speed-boat had struck a buoy, but it continued to move very quickly across the water. Both men had just begun to swim towards the shore. they noticed with dismay that the speed-boat was moving in a circle. It now came straight towards them at tremendous speed. In less than a minute, it roared past them only a few feet away. After it had passed, they swam on as quickly as they could because they knew that the boat would soon return. They had just had enough time to swim out of danger when the boat again completed a circle. On this occasion, however, it had slowed down considerably. Before long, the noise dropped completely and the boat began to drift gently across the water.Lesson87 A perfect alibi 极好的不在犯罪现场的证据At the time the murder was committed, I was travelling on the 8.0 oclock train to London, said the man.Do you always catch such an early train asked the inspector.Of course I do, answered the man. I must be at work at 10.0 oclock. My employer will confirm that I was there on time. Would a later train get you to work on time? asked the inspector.I suppose it would, but I never catch a later train.At what time did you arrive at the station? eight. I bought a paper and waited for the train.And you didnt notice anything unusual. I suggest, said the inspector, that you are not telling the truth. I suggest that you did not catch the 8.0 oclock train, but that you caught the 8.25 which would still get you to work on time. You see, on the morning of the murder, the 8.0 oclock train did not run at all. It broke down at station and was taken off the line.Lesson88 Trapped in a mine 困在矿井里Six men have been trapped in a mine for seventeen hours. If they are not brought to the surface soon they may lose their lives. However, rescue operations are proving difficult. If explosives are used, vibrations will cause the roof of the mine to collapse. Rescue workers are therefore drilling a hole on the north side of the mine. They intend to bring the men up in a special capsule. If there had not been a hard layer of rock beneath the soil, they would have completed the job in a few hours. As it is, they have been drilling for sixteen hours and they still have a long way to go. Meanwhile, a microphone, which was lowered into the mine two hours ago, has enabled the men to keep in touch with the closest relatives. Though they are running out of food and drink, the men are cheerful and confident that they will get out soon. They have been told that rescue operations are progressing smoothly. If they knew how difficult it was to drill through the hard rock, they would lose heart. Lesson89 A slip of the tongue 口误People will do anything to see a free show-even if it is a bad one. When the news got round that a variety show would be presented at our local cinema by the P. and U. Bird Seed Company, we all rushed to see it. We had to queue for hours to get in and there must have been several hundred people present just before the show began. Unfortunately, the show was one of the dullest we have ever seen. Those who failed to get in need not have felt disappointed as many of the artistes who should have appeared did not come. The only funny things we heard that evening came from the advertiser at the beginning of the. He was obviously very nervous and for some minutes stood awkwardly before the microphone. As soon as he opened his mouth, everyone burst out laughing. We all know what the poor man should have said, but what he actually said was: This is Seed Bird Company. Good ladies, evening and gentlemen!lesson90 for supper ？ 晚餐吃什么？Though Brazil is one of the richest countries in the world, much of it has not yet been developed. It was mainly for this reason that the Brazilian government decided to have a new city built 600 miles north-west of Rio de Janeiro. Designed by the great architect Costa, the new city, Brasilia, replaced Rio de Janeiro as the capital of in 1960. Brasilia has been carefully planned for modern living. Its wide roads, which can take fourteen lanes of traffic, have been keptaway from living areas. Children do not have to cross busy streets to go to school. Housewives can visit-shopping on foot, for in these specially designed living areas, cars are unnecessary. At first, the government had great difficulty in persuading people to leave Rio and to settle in Brasilia. Since 1960, however, the population has been growing all the time. Brasilia has quickly established itself as the capital of the country. The idea to have the capital moved so far inland will have a great effect on the future of Brazil.Lesson91 Three men in a basket 三人同篮A pilot noticed a balloon which seemed to be making for a Royal Air Force Station nearby. He informed the station at once, but no one there was able to explain the mystery. The officer in the control tower was very angry when he heard the news, because balloons can be a great danger to aircraft. He said that someone might by spying on the station and the pilot was ordered to keep track of the strange object. The pilot managed to circle the balloon for some time. He could make out three men in a basket under it and one of them was holding field-glasses. When the balloon was over the station, the pilot saw one of the men taking photographs. Soon afterwards, the balloon began to descend and it landed near an airfield. The police were called in, but they could not arrest anyone, for the basket contained two Members of Parliament and the Commanding Officer of the station! As the Commanding Officer explained later, one half of the station did not know what the other half was! Lesson92 Asking for trouble 自找麻烦It must have been about two in the morning when I returned home. I tried to wake up my wife by ringing the door-bell, but she was fast asleep, so I got a ladder from the shed in the garden, put it against the wall, and began climbing towards the bedroom window. I was almost there when a sarcastic voice below said, I dont think the windows need cleaning at this time of the night.I looked down and nearly fell off the ladder when I saw a policeman. I immediately regretted answering in the way I did, but I said, I enjoy cleaning windows at night.So do I, answered the policeman in the same tone. Excuse me interrupting you. I hate to interrupt a man when hes busy working, but would you mind coming with me to the Well, Id prefer to stay here, I said. You see, Ive forgotten my key. He called.My key, I shouted. Fortunately, the shouting woke up my wife who opened the window just as the policeman had started to climb towards me.Lesson93 A noble gift 崇高的礼物One of the most famous monuments in the world, the Statue of Liberty, was presented to the United States of America in the nineteenth century by the people of France. The great statue, which was designed by the sculptor August Bartholdi, took ten years to complete. The第一章 绪论1.1倒立摆系统的简介1.1.1倒立摆系统的研究背景及意义倒立摆系统的最初分析研究开始于二十世纪五十年代，是一个比较复杂的不稳定、多变量、带有非线性和强耦合特性的高阶机械系统，它的稳定控制是控制理论应用的一个典型范例1。倒立摆系统存在严重的不确定性，一方面是系统的参数的不确定性，一方面是系统的受到不确定因素的干扰。通过对它的研究不仅可以解决控制中的理论问题，还将控制理论涉及的相关主要学科：机械、力学、数学、电学和计算机等综合应用。在多种控制理论与方法的研究和应用中，特别是在工程中，存在一种可行性的实验问题，将其理论和方法得到有效的验证，倒立摆系统可以此提供一个从控制理论通过实践的桥梁。近些年来，国内外不少专家、学者一直将它视为典型的研究对象，提出了很多控制方案，对倒立摆系统的稳定性和镇定问题进行了大量研究，都在试图寻找不同的控制方法实现对倒立摆的控制，以便检查或说明该方法的严重非线性和绝对不稳定系统的控制能力，其控制方法在军工、航天、机械人领域和一般工业过程中都有着广泛的用途，如精密仪器的加工、机器人行走过程中的平衡控制、火箭发射中的垂直度控制、导弹拦截控制、航空对接控制、卫星飞行中的姿态控制等方面均涉及到倒置问题。因此，从控制这个角度上讲，对倒立摆的研究在理论和方法论上均有着深远意义。倒立摆系统是一个典型的自不稳定系统，其中摆作为一个典型的振动和运动问题，可以抽象为许多问题来研究。随着非线性科学的发展，以前的采用线性化方法来描述非线性的性质，固然无可非议，但这种方法是很有局限性，非线性的一些本质特征往往不是用线性的方法所能体现的。非线性是造成混乱、无序或混沌的核心因素，造成混乱、无序或混沌并不意味着需要复杂的原因，简单的非线性就会产生非常的混乱、无序或混沌。在倒立摆系统中含有极其丰富和复杂的动力学行为，如分叉、分形和混沌动力学，这方面的问题也值得去探讨和研究。 无论哪种类型的倒立摆系统都具有如下特性2：(1)非线性倒立摆是一个典型的非线性复杂系统。实际中可以通过线性化得到系统的近似模型，线性化处理后再进行控制，也可以利用非线性控制理论对其进行控制，倒立摆的非线性控制正成为一个研究的热点。(2)不确定性主要是指建立系统数学模型时的参数误差、量测噪声以及机械传动过程中的减速齿轮间隙等非线性因素所导致的难以量化的部分。(3)欠冗余性一般的，倒立摆控制系统采用单电机驱动，因而它与冗余机构，比如说冗余机器人有较大的不同。之所以采用欠冗余的设计是要在不失系统可靠性的前提下节约经济成本或者节约有效的空间。研究者常常是希望通过对倒立摆控制系统的研究获得性能较为突出的新型控制器设计方法，并验证其有效性及控制性能。(4)耦合特性倒立摆摆杆和小车之间，以及多级倒立摆系统的上下摆杆之间都是强耦合的。这既是可以采用单电机驱动倒立摆控制系统的原因，也是使得控制系统的设计、控制器参数调节变得复杂的原因。(5)开环不稳定性倒立摆系统有两个平衡状态：垂直向下和垂直向上。垂直向下的状态是系统稳定的平衡点(考虑摩擦力的影响)，而垂直向上的状态是系统不稳定的平衡点，开环时微小的扰动都会使系统离开垂直向上的状态而进入到垂直向下的状态中。(6)约束限制由于实际机构的限制，如运动模块行程限制，电机力矩限制等。为制造方便和降低成本，倒立摆的结构尺寸和电机功率都尽量要求最小，行程限制对于倒立摆的摆起尤为突出，很容易出现小车的撞边现象。倒立摆的以上特性增加了倒立摆的控制难度，也正是由于倒立摆的这些特性，使其更具有研究价值和意义3。1.1.2 倒立摆系统的分类倒立摆系统诞生之初为单级直线形式，即仅有的一级摆杆一端自由，另一端铰接于可以在直线导轨上自由滑动的小车上。在此基础上，人们又进行拓展，产生了多种形式的倒立摆。按照基座的运动形式，主要分为三大类：直线倒立摆、环形倒立摆和平面倒立摆，每种形式的倒立摆再按照摆杆数量的不同可进一步分为一级、二级、三级及多级倒立摆等4。摆杆的级数越多，控制难度越大，而摆杆的长度也可能是变化的。多级摆的摆杆之间属于自有连接(即无电动机或其他驱动设备)。目前，直线型倒立摆作为一种实验仪器以其结构相对简单、形象直观、构件参数易于改变和价格低廉等优点，已经广泛运用于教学5。关于直线倒立摆的控制技术已经基本趋于成熟，在该领域所出的成果也相当丰富。尽管环形倒立摆的基座运动形式与直线倒立摆有所差异，但二者相同之处是基座仅有一个自由度，可以借鉴比较成熟的直线倒立摆的研究经验，所以近几年来也产生了大量的理论成果。平面倒立摆是倒摆系统中最复杂的一类，这是因为平面倒立摆的基座可以在平面内自由运动，并且摆杆可以沿平面内的任一轴线转动，使系统的非线性、耦合性、多变量等特性更加突出，从而增加了控制的难度，而且机械和电子器件发展遇到瓶颈性的困难，给平面倒立摆的工程实现也带来了一定的难度。按摆杆的材质不同，倒立摆系统分为刚体摆杆倒立摆系统和柔性倒立摆系统。在柔性倒立摆系统中，摆杆本身己经变成了非线性分布参数系统。根据研究的目的和方法不同，倒立摆系统又分为悬挂式倒立摆、球平衡系统和平行式倒立摆。其中，研究比较多的是悬挂式倒立摆。这种倒立摆开始工作时，摆杆处于自由下垂状态。控制开始时，首先使摆杆按自由振荡频率摆动，随着摆杆振荡幅度的加大，当摆杆接近于倒立摆竖直倒立位置时，自动转换控制方法，使其稳定于倒置状态。根据导轨的形状小同，倒立摆的运动轨道可以是水平的，也可以是倾斜的。倾斜倒立摆对实际机器人的步行稳定控制研究非常有意义。尽管倒立摆系统的结构形式多种多样，但是无论属于哪一种结构，就其本身而言，都是一个非线性、多变量、强耦合、绝对不稳定性系统6。1.1.3 倒立摆系统的研究现状倒立摆系统的研究具有重要的理论意义和应用价值，对其控制研究是控制领域研究的热门课题之一，国内外的专家学者对此给予了广泛的关注。倒立摆系统研究最早始于上世纪50年代，麻省理工学院(MIT)机电工程系的控制论专家根据火箭发射助推器原理设计出一级倒立摆实验装置7。1966年Schaefer和Cannon应用BangBang控制理论将一个曲轴稳定于倒置位置。其实，正式提出倒立摆概念的是60年代后期。在此基础上，世界各国专家和学者对倒立摆进行了拓展，产生了直线二级倒立摆、三级倒立摆、多级倒立摆、柔性直线倒立摆、环形倒立摆、平面倒立摆、环形并联多级倒立摆以及斜坡倒立摆等实验设备，并用不同的控制方法对其进行了控制，使研究成为了具有挑战性的课题之一。1976年Mori etc首先把倒立摆系统在平衡点附近线性化，利用状态空间方法设计比例微分控制器实现了一级倒立摆的稳定控制。1980年，Furuta etc等人基于线性化方法，实现了二级倒立摆的控制。1984年，Furuta等人应用最优状态调节器理论首次实现双电机三级倒立摆实物控制；Wattes研究了LQR(Linear Quadratic Regulator)方法控制倒立摆。80年代后期开始，较多的研究了倒立摆系统中的非线性特性，提出了一系列的基于非线性分析的控制策略。1992年，Furuta等人提出用变结构控制来控制倒立摆。1993年，Wiklund等人应用基于李亚普诺夫的方法控制了环形一级倒立摆。Bouslama利用一个简单的神经网络来学习模糊控制器的输入输出数据，设计了新型控制器。1995年，Fradkov等人提出的基于无源性的控制；Yamakita等人给出了环形二级倒立摆的实验结果；Li利用两个并行的模糊滑模来分别控制小车和摆杆偏角；Deris利用神经网络的自学习能力来整定PID控制器参数。1997年，Gordillo比较了LQR方法和基于遗传算法的控制方法，结论是传统控制方法比遗传算法控制效果更好8。国内对倒立摆的研究始于80年代，虽然起步较晚但发展迅速，取得了可喜的成果。对于单级倒立摆口钉和二级倒立摆系统的研究已经历了很长的历程，并且有很多控制成功的报道。在此基础上，三级倒立摆b53及多级倒立摆的研究也取得了很大进展，不仅在系统仿真方面，而且在实物实验中，都出现了控制成功的范例。尹征琦等成功的以模拟的降维观测器实现了二级倒立摆的控制。梁任秋等针对二级倒立摆系统给出了三种实用的数字控制器和降维观测器。1994年，北京航空航天大学教授张明廉将人工智能与自动控制理论相结合，提出“拟人智能控制理论”，实现了用单电动机控制三级倒立摆实物以及后来实现对二维单倒立摆控制。张乃尧等用双闭环模糊控制方法对倒立摆进行了控制。李祖枢等人利用拟人智能控制理论研究了二级倒立摆的起摆和控制问题。李德毅教授利用反映语言值中蕴涵的模糊性和随机性，给出云发生器的生成算法，解释多条定性推理规则同时被激活时的不确定性推理机制，利用这种智能控制方法有效地实现了单电机控制的一、二、三级倒立摆的多种不同动平衡姿态，显示其鲁棒性，并给出了详细试验结果。北京师范大学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，分别于2001年6月和2002年8月完成了四级倒立摆系统的仿真和实物实验。朱江滨等人提出了一种基于专家系统及变步长预测控制的实时非线性系统控制方法，仿真实现了二级倒立摆的摆起及稳定控制侧。王永等通过对多级倒立摆动力学分析，得到了任意级旋转倒立摆的数学模型。2005年国防科学技术大学的罗成教授等人利用基于LQR的模糊插值实现了五级倒立摆的控制。总之，倒立摆系统是检验各种控制算法、研究控制理论很有效的实验设备9。目前应用在倒立摆上的算法主要有以下几类：(1)经典控制理论：PID控制。通过对倒立摆物理模型的分析，建立倒立摆系统的动力学模型，设计PID控制器实现控制。(2)现代控制理论：状态反馈。通过对倒立摆系统物理模型的分析，建立系统的动力学模型，然后使用状态空间理论推导出状态方程和输出方程，应用状态反馈，实现对倒立摆的控制。常见的方法有：1）极点配置，2）线性二次型最优控制，3）鲁棒控制，4）状态反馈控制10。(3)模糊控制理论：主要是确定模糊规则，克服系统的非线性和不确定性实现对倒立摆的稳定控制。(4)神经网络控制理论。利用神经网络能够充分逼近复杂的非线性关系，学习与适应严重不确定系统的动态特性，与其他控制方法结合实现对倒立摆的稳定控制。(5)拟人智能控制理论。不需要了解被控对象的数学模型，凭借人的知识与直觉经验并借助计算机快速模拟控制经验，把人的思维中的定性分析与控制理论中的定量计算相互结合，从而实现对倒立摆的控制。(6)云模型控制理论。用云模型构成语言值，用语言值构成规则，形成一种定性的推理机制。这种方法不要求给出对象的精确的数学模型，而仅依据人的经验、感受和逻辑判断，将人用自然语言表达的控制经验，通过语言原子和云模型转换到语言控制规则器中，就能解决非线性问题和不确定性问题。(7)自适应控制理论。主要是为倒立摆设计出自适应控制器。(8)非线性控制理论。应用非线性控制的方法研究倒立摆的控制。(9)遗传算法。以要寻优的参数组成染色体，通过模拟生物从父代到子代，再从子代到孙代，不断地进化演变的过程来进行迭代求解的。其模拟生物界优胜劣汰的进化过程来实现参数的寻优。（10）支持向量机聆刿。提出最优超平面的概念并且与核空间相结合，以一个凸二次优化及其Wolfe对偶来构造分类问题，并且在此基础上发展成多类分类和函数回归问题。(11)变结构控制理论：滑模控制。（12）几种控制算法相结合的控制方式。充分利用各控制算法的优越性，来实现一种组合式的控制方法，比如：神经网络控制与模糊控制理论结合的方法，遗传算法与神经网络控制结合的方法，模糊控制与PID控制结合的方法，神经网络控制与预测控制算法相结合的方法，遗传算法与模糊控制理论结合的方法，支持向量机与模糊控制相结合的方法等。1.1.4 倒立摆的控制方法倒立摆系统的输入为小车的位移(即位置)和摆杆的倾斜角度期望值，计算机在每一个采样周期中采集来自传感器的小车与摆杆的实际位置信号，与期望值进行比较后，通过控制算法得到控制量，再经数模转换驱动电机实现倒立摆的实时控制。电机通过皮带带动小车在固定的轨道上运动，摆杆的一端安装在小车上，能以此点为轴心使摆杆能在垂直的平面上自由地摆动。作用力平行于轨道的方向作用于小车，使杆绕小车上的轴在竖直平面内旋转，小车沿着水平导轨运动。当没有作用力时，摆杆处于垂直的稳定的平衡位置(竖直向下)。为了使摆杆摆动或者达到竖直向上的稳定，需要给小车一个控制力，使其在轨道上被往前或朝后拉动。因此，倒立摆系统的控制原理可简述如下：用一种强有力的控制方法对小车的速度作适当的控制，从而使摆杆倒置稳定于小车正上方。倒立摆刚开始工作时，首先使小车按摆杆的自由振荡频率摆动，摆杆随之大幅度摆动。经过几次摆动后，摆杆能自动直立起来。这种被控量既有角度，又有位置，且它们之问又有关联，具有非线性、时变、多变量耦合的性质。1.2 MATLAB简介MATLAB是美国Math Works 软件公司于1984年推出的一种用于科学计算的高性能语言。它集数值计算、图形图像显示以及编程于一体, 是常用的控制系统分析与设计工具12。1990 年, MathWorks软件公司为MATLAB 提供了新的控制系统图形化模型输入与仿真工具Simulink。这是MATLAB的一个扩展软件模块。该模块提供了一个建模、分析与仿真等多种物理与数学问题的软件环境, 并为图形用户界面提供了动态系统的结构方块图模型, 从而使用户可以既快又方便地对系统进行建模、仿真, 而不必写任何代码程序。因此该工具很快就在控制工程界获得了广泛的认可,并使仿真软件进入了系统模型的图形组态阶段13。1.2.1 Simulink仿真环境介绍Simulink环境是1990年前后由Mathworks公司推出的产品，原名SimuLAB，1992年改为Simulink。其名字有两重含义，仿真(simu)与模块连接(1ink)，表示该环境可以用框图的方式对系统进行仿真14。Simulink是用来建模、分析和仿真各种动态系统的交互环境，包括连续系统、离散系统和混合系统。Simulink提供了采用鼠标拖放的方法建立系统框图模型的图形交互平台。通过Simulink提供的丰富的功能块，可以迅速地创建动态系统模型。同时Simulink还集成了Stateflow，用来建模、仿真复杂事件驱动系统的逻辑行为。另外，Simulink也是实时代码生成工具Real-Time Workshop的支持平台。控制系统仿真研究