哈工大自动控制原理大作业完整版
哈工大自动控制原理大作业
自动控制原理大作业1.题目在通常情况下，自动导航小车（AGV ）是一种用来搬运物品的自动化设备。
大多数AGV 都需要有某种形式的导轨，但迄今为止，还没有完全解决导航系统的驾驶稳定性问题。
因此，自动导航小车在行驶过程中有时会出现轻微的“蛇行”现象，这表明导航系统还不稳定。
大多数的AGV 在说明书中都声明其最大行驶速度可以达到1m/s ，但实际速度通常只有0.5m/s ,只有在干扰较小的实验室中，才能达到最高速度。
随着速度的增加，要保证小车得稳定和平稳运行将变得越来越困难。
AGV 的导航系统框图如图9所示，其中12=40ms =21ms ττ， 。
为使系统响应斜坡输入的稳态误差仅为1%，要求系统的稳态速度误差系数为100。
试设计合适的滞后校正网络，试系统的相位裕度达到50 ，并估计校正后系统的超调量及峰值时间。
()R s ()Y s2.分析与校正主要过程2.1确定开环放大倍数K100)1021.0)(104.0(lim )(lim =++==s s s sK s sG K v （s →0） 解得K=100)1021.0)(104.0(100++=s s s G s 2.2分析未校正系统的频域特性根据Bode 图：穿越频率s rad c /2.49=ω相位裕度︒---=⨯-⨯--=99.18)2.49021.0(arctan )2.4904.0(arctan 9018011γ 未校正系统频率特性曲线由图可知实际穿越频率为s rad c /5.34=ω2.3根据相角裕度的要求选择校正后的穿越频率1c ω现在进行计算：︒︒︒--=+=---55550)021.0(arctan )04.0(arctan 901801111c c ωω则取s rad c /101=ω可满足要求2.4确定滞后校正网络的校正函数 由于11201~101c ωω）（=因此取s rad c /110111==ωω）（，则由Bode 图可以列出 40)1lg(20)1lg(40)110lg(2022+=+ωω 解得s rad /1.02=ω于是1.0=β 则滞后网络传递函数为1101)(++=s s s G c ，10=T 2.5验证已校正系统的相位裕度已校正系统的开环传递函数为：)110)(1021.0)(104.0()1(100)()(++++=s s s s s s G s G c 相位裕度︒----=-⨯-⨯-+-=2.51)100(arctan )10021.0(arctan )1004.0(arctan )10(arctan 901801111γ校正后的相位裕度大于50°，满足设计要求。
哈工大自动控制原理大作业
Harbin Institute of Technology自动控制原理设计论文课程名称：自动控制原理设计题目：液压伺服系统校正院系：测控技术与仪器系班级：设计者：学号：指导教师：设计时间：哈尔滨工业大学自动控制原理大作业一、 设计任务书考虑图中所示的系统。
要求设计一个校正装置，使得稳态速度误差常数为-14秒，相位裕度为，幅值裕度大于或等于8分贝。
利用MATLAB 画出已校正系统的单位阶跃响应和单位斜坡响应曲线。
二、 设计过程1、 人工设计1）、数据计算由图可知，校正前的开环传递函数为：0222s+0.10.025(20s 1)G =0.1(s 0.14)(1)44s s s s s +=++++ 其中按频率由小到大分别含有积分环节和放大环节，-20dB/dec ；一阶微分环节，10.05/w rad s =，0dB/dec;振荡环节，22/w rad s =，-40dB/dec;稳态速度误差：0202s+0.1e ()lim (s)lim 0.025(s 0.14)ss s s sG ss s →→∞===++。
显然，此时的相位裕度和稳态速度误差都不满足要求。
为满足题目要求，可以引入超前校正，提高系统的相位裕度和稳态速度误差。
2）、校正装置传递函数 （1）、稳态速度误差常数的确定为使稳态速度误差常数为-14秒,设加入的开环放大倍数为k,加入校正装置后的稳态速度误差满足： 11e ()4k 0.025kss v ∞=== 解得K=160；将K=160带入，对应的传递函数为：0222s+0.14(20s 1)G (s)=1600.1(s 0.14)(1)44s s s s s +=++++ 则校正前（加入k=160的放大倍数后）幅值穿越频率：018.00/c w rad s =，相位裕度：o 00.1631c r =； （2）、校正装置的确定这里采用超前补偿，由前面算得k=160，故设加入的校正装置传递函数为：111G (s)T 1c aT s s +=+ 设计后要求o =50γ,则o 0-=500.163149.8369o o γγ-=；a 满足：01sin 49.83691a a -=+ 解得：a =7.33，取a =8.取1010/18.00/c w rad s w rad s =<=作为第一个转折频率，取第二个转折频率为21*80/w a w rad s ==；在伯德图上过3rad/s 处做斜率为-20dB/dec 的线。
哈工大PLC大作业
哈⼯⼤PLC⼤作业《可编程控制器》课程设计院系：天平学院专业：机械制造及其⾃动化班级：0823姓名：俊学号：0730114326指导教师：郭丽华lihuaguo2008163.⽬录⽬录………………………………………………………………第⼀章交通信号控制系统实况.................................1.1⼗字路⼝交通灯控制实际情况描述.............................1.2 结合⼗字路⼝交通灯的路况画出模拟图.........................第⼆章可编程控制器程序设计.................................2.1 ⼗字路⼝交通灯模拟控制时序图.............................2.2可编程控制器I/O端⼝分配...................................2.3程序梯形图及语句表.......................................第三章总结.................................................3.1程序调试...............................................3.2 难点分析...............................................3.3 PLC智能化控制交通灯的⽅法................................3.4 收获与体会.............................................. 参考⽂献....................................................第⼀章交通信号控制系统分析1.1⼗字路⼝交通灯控制实际情况描述（1）南北⽅向绿灯和东西⽅向的绿灯不能同时亮；如果同时亮，则应⾃动⽴即关闭信号灯系统，并⽴即发出报警信号。
自动控制大作业
自动控制大作业(总28页)--本页仅作为文档封面，使用时请直接删除即可----内页可以根据需求调整合适字体及大小--自动控制原理课程大作业班级：1302011成员：刘罡潘仕林赵奇2014 年《自动控制技术》课程大作业一、课程习题1．带飞球式调节器的瓦特蒸汽机是近代工业革命兴起的标志，同样也是一个典型的反馈控制系统，请画出该系统的组成框图，并注明下列器件的位置，并说明与每个信号相关的装置。
受控过程过程要求的输出信号传感器执行机构执行机构的输出信号调节器调节器输出信号参考信号误差信号图瓦特离心式调速器示意图解：受控过程蒸汽机运行过程要求的输出信号转速传感器履带执行机构蒸汽阀执行机构的输出信号蒸汽推力调节器调速器调节器输出信号调速器转速参考信号规定转速误差信号转速偏差2.倒立摆控制系统是一个典型的非线性、强耦合、多变量和不稳定系统。
倒立摆的控制问题就是给连接摆杆的小车施加控制力，使摆杆尽快的达到一个平衡位置，并且保证不出现过大的振荡。
当摆杆到达期望的平衡位置后，系统能克服随机扰动保持在平衡点。
如图 2 所示是一个简单的一阶倒立摆系统，这里忽略空气阻力和各种次要的摩擦力，将倒立摆系统看做是一个由小车和均匀刚性杆组成的系统。
假设系统初始状态时，摆杆垂直于小车处于平衡状态，此时摆杆受到冲激信号作用产生一个微小的偏移。
建立此时系统的控制系统数学模型。
图小车-单摆系统示意图解：1. 一阶倒立摆的微分方程模型对一阶倒立摆系统中的小车和摆杆进行受力分析，其中，N 和 P 为小车与摆杆相互作用力的水平和垂直方向的分量。
图1-2 小车及摆杆受力图分析小车水平方向所受的合力，可以得到以下方程：传感器控制器执行机构对象R C（1-1）由摆杆水平方向的受力进行分析可以得到下面等式：（1-2）即：（1-3）把这个等式代入式(1-1)中，就得到系统的第一个运动方程：（1-4）为了推出系统的第二个运动方程，我们对摆杆垂直方向上的合力进行分析，可以得到下面方程：（1-5）即：（1-6）力矩平衡方程如下：（1-7）由于所以等式前面有负号。
哈尔滨工业大学自控原理习题答案(第三章)
则根据系统框图可得
代入 ，得
另 ，得到系统的干扰输出
则误差表达式为
若积分环节加在扰动点之前则
， ,
可求得 。
若积分环节加在扰动点之后，则
, ,
可求得
由此可见在扰动点之前的前向通道加入积分环节，才能消除阶跃扰动产生的稳态误差。
3.23
设
则系统的闭环传递函数为：
误差为
将 及 得
闭环特征方程为
又因为 故系统稳定，与参数a，b无关。
若
则有系统的稳态误差
则求出待定系数为
3.29
当a=0时系统的闭环传递函数为：
则根据
得 。
当 ，根据系统的闭环传递函数为
则根据
得a=0.25
3.30
由图3.30所示的单位阶跃响应 ，可得系统的超调量和峰值时间为
又有参数间的关系：
因为系统的开环传递函数为 ，则系统的闭环传递函数为
则
得到参数为
3.34
列Routh表可得
3.12
由系统框图可知系统的开环传递函数为
因为是单位反馈，可得系统的特征方程为
如果要求闭环传递函数的特征根全部位于s=-1垂线之左，可令s=z-1，并代入特征方程，得
建立Routh表
Z3115
z21140K-27
z1 0
z040K-27
令第一列的元素全部为正，可得不等式组
解得K的取值范围为
3.14
由系统框图可以求得系统的开环传递函数为
3.1
图3.1（b）所示的单位阶跃响应具有等幅振荡特性，说明系统的阻尼比 。这与系统主反馈取“-”及内反馈取“0”相对应，因为在这种情况下该二阶系统的传递函数为
图3.1（c）所示单位阶跃响应具有发散特性，说明系统不稳定。这与系统的主反馈取“-”及内反馈取“+”相对应，因为在这种情况下，该二阶系统的传递函数为：
三轴转台内环控制系统【哈工大自动控制原理 大作业】【范本模板】
Harbin Institute of Technology三轴转台内环控制系统课程名称：自动控制原理院系：班级:设计者：学号:设计时间：2016。
1。
1哈尔滨工业大学哈尔滨工业大学一、背景描述三轴转台是应用在半实物仿真系统中，模拟被测物体姿态变化的装置.本文研究的主要内容是三轴转台的内环控制系统。
二、问题描述技术要求：最大角速度400/o s ,最大动态踪误差0.02o ss e ≤；频带宽度148c s ω-≥，相位裕度45oγ=。
固有系统传递函数： 原题如下:修改后如下:三、求解过程设，为待定的补偿装置传递函数，。
设计要求为0.02oss e ≤令0。
02=,则K=2系统开环传递函数如下:E s θ sU s + —G C s G 0 s对数幅频特性方程如下：令，得剪切频率。
相位裕度：由bode图中校正前的图像可知需采用超前补偿的方法，加入校正装置如下：可求得：,得哈尔滨工业大学所以校正后的传递函数：校正后的相位裕度：性能要求系统相位裕度为，而校正后的系统相位裕度为，符合要求. 令,得校正后的剪切频率：:校正前与校正后的系统bode图如下哈尔滨工业大学四、计算机辅助设计观察系统的单位阶跃相应曲线：哈尔滨工业大学五、校正装置电路图电路元件参数为：R2=1.3kΩ R3=6.0kΩ C1=28.1μF C2=12.8μF六、结论校正后的传递函数:哈尔滨工业大学校正后的相位裕度：:校正后的剪切频率七、设计后的心得体会经过本次大作业的设计，我深刻体会到了基础知识的重要性：熟练掌握相关基础知识有利于理解文献和软件的高级操作.哈尔滨工业大学。
哈工大PLC大作业教程文件
哈工大P L C大作业《可编程控制器》课程设计院系：天平学院专业：机械制造及其自动化班级： 0823姓名：李俊学号： 0730114326指导教师：郭丽华lihuaguo2008@目录目录………………………………………………………………第一章交通信号控制系统实况.................................1.1十字路口交通灯控制实际情况描述.............................1.2 结合十字路口交通灯的路况画出模拟图.........................第二章可编程控制器程序设计.................................2.1 十字路口交通灯模拟控制时序图.............................2.2可编程控制器I/O端口分配...................................2.3程序梯形图及语句表.......................................第三章总结.................................................3.1程序调试...............................................3.2 难点分析...............................................3.3 PLC智能化控制交通灯的方法................................3.4 收获与体会.............................................. 参考文献....................................................第一章 交通信号控制系统分析1.1十字路口交通灯控制实际情况描述（1）南北方向绿灯和东西方向的绿灯不能同时亮；如果同时亮，则应自动立即关闭信号灯系统，并立即发出报警信号。
哈工大数控大作业完美版
第一作业调研报告 (1)1.1调研内容 (1)1.2工作量与要求 (1)1.3正文 (1)The development and application of NC machine tool servo system (2)第二作业：典型曲线数字积分法插补方法 (13)2.1目的 (13)2.2要求 (13)2.3 DDA法双曲线插补的积分表达式 (13)2.4终点判别 (15)2.5插补举例 (15)第三作业：加工中心零件加工编程 (17)3.1目的和要求 (17)3.2数控机床设备 (17)3.3加工工艺制订 (19)3.4要完成的程序编写任务 (22)《数控技术》课程（2015）大作业院（系）专业姓名学号班号任课教师完成日期哈尔滨工业大学机电工程学院2015年5月数控大作业第一作业调研报告1.1调研内容请以课堂所学习的知识为基础，自主选择课程中所涉及的任一知识点进行调研。
可以调研知识点的发展脉络，也可以重点介绍该知识点的发展现状、争议与未来发展趋势。
请提交交独一无二的报告1.2工作量与要求1. 报告需用英文撰写，可计算机打印，也可手写，但最后封面需手工签名。
2. 格式请参照本科生毕业论文要求（见教务处网站），总字数不少于2000字。
3.在调研报告的最后，请列出参考的主要文献（英文学术刊物上正式发表的文献不少于5篇）或网址，并在正文中标注引用。
4. 如果出现雷同，两位同学均无成绩。
1.3正文The development and application of NC machine tool servo system Since the invention of NC machine tool in 1950s, servo system has been the indispensable component of the NC machine tool. With the rapid development of new materials, electronic power and controlling system, the servo system has evolved from the step-by-step system to DC system and then to AC system. As the blossom of AC servo technology, AC servo system will replace the DC system wholly and take up the dominant position in the family of servo system.With the electronic power conversion unit as actuator and controller as c ore , Servo system which contains the servo driver and servo motor const itutes the main part of the electric-driving and automatic control system . When working, firstly the servo system willreceive the signal from NC devices, and then drive the motion of machine tool as well as ensure the accuracy and speediness of movement under the guidance of pulse command . Usually, precision and speed of t he NC machine tool and other technical indicatorsmainly depend on the servo system itself1.The improvement and assortment of NC servo systemAt present, engineers tend to assess the quality by reference to several im portant indicators, such as precision, speed and so on. Therefore, a NC se rvo system must meet these requirements.High precisionUnlike the traditional manufacturing which can be manually handled to r egulate and compensate errors, the NC servo system has a high demand o n positioning accuracy and repeated positioning accuracyQuick repose characteristicQuick response is one of important indicators of servo system’s dynamic quality which requires the servo system following the command signal with minimum error as well as quick repose and high stability. Once receiving the instruction of manipulator, the working machine can restore the original state of equilibrium quickly after a short regulation or a disturbance from outer space.Wide speed rangeDue to the difference in work piece materials, cutting tool and process requirements, servo system must have wide speed range, so as to ensure that the CNC machine in any circumstances can get the optimal cutting condition. Thus the machine tool can satisfy the requirement of high speed machining as well as the requirement of low speed feed.The speed range is generally larger than 1 to 10000. when the machine is working in a low cutting speed which ask for a larger stable torqueoutput, NC servo system must maintain a good reliability.Good reliabilitythe usage of machine tool is frequent, usually with 24 hours' continuous work, so the servo system must have good working reliability. Servo system of NC machine tool can be divided into open loop control system and closed loop control system according to the presence of feedback test components. Drive control Unit transforms feeding instructions to perform signal needed by actuator, and then actuator convert this signal into mechanical displacement.In Open loop control system, there is no feedback detecting components and comparing control links. On the contrary, these are essential part of a closed-loop control system.The composition of servo systemServo system can be classified into the feed drive system and the spindle drive system on the basis of function and usage. Besides,the NC servo system can also be sorted into open loop control system and the closed loop control system in light of the presence of feedback detecting element.In addition, according to the difference of actuators, servo system can be divided into stepping servo system, dc servo system and ac servo system.Stepping servo systemBefore the 1960 s,the stepping servo system is based on step motor driven hydraulic servo motor or characterized by power steppingmotor as direct drive,and servo system uses open-loop control. Stepping servo system works with the pulse signal, and its speed and turning Angle depends on the frequency or the number ofInstruction pulses.Because there is no testing and feedback loop, the precision of the stepper motor step depends on the step angle, the accuracy of the gear transmission clearance and so on, its accuracy is low. stepping motor is easy to appear vibration phenomenon when working in the low frequency,and its output torque decreases with increment of speed. Because the stepping servo system is the open loop control, step motor in the start of machine with the over-high frequency or large load shows"lost" or "blocked" phenomenon and prone to appear phenomenon of high speed overshoot in the braking of the machine tool. At the same time, step motor speed accelerating from 0 to working speed requires longer time and slower speed response. But because of its simple structure, easy adjustment, and good working reliability and the low prices, the stepping system is a good choice in many many occasions of low occasions.Dc servo systemAfter 60 and 70 s, most of numerical control system adopts dc servo system. Dc servo motor has a good wide range speed performance, large output torque, and strong overload capacity. servo system also has evolved from open loop control into closed-loop control, thus in the industry as well as its related fields gains the more extensive or aboard application. However, with the rapid development of modern industry, the corresponding equivalents such as precision CNC machine tools, industrial robots make higher and higher requirements to the electrical servo system, especially the precision, reliability and other performance.The traditional dc motor uses a mechanical commutator, faced up with many problems in the application process, such as brush and commutator wear easily, maintenance work is heavy and the cost of it is high. Commutator reversing would produce sparks, the maximum speed of the motor and the application environment is limited;Dc motor has a more complex structure, higher cost,and prone to interfere other devices'work.Ac servo systemThe existence of these problems, limiting the dc servo system in high precision, high performance requires the application of servo driveoccasion.Because hard-overcoming weakness of dc motor, people have been seeking the development of ac servo motor to replace the dc motor whose advantage is limited by mechanical commutor and brush to satisfy the needs of various application fields, especially in the field of high precision and high-performance servo drive .But because the ac motor has strong coupling, nonlinear characteristics, so control is very complete and the high-performance application has been limited. Since the 1980 s, with the boom of the new technology such as electronic electricity, the modern control theory, and the breakthrough in the field of vector control algorithm, the original problems of AC motor which has bothered so many engineers has been solved, and ac servo development faster and faster.The characteristics of the ac servo systemIn addition to good stability, good rapidity,and high precision,servo motor system has a series of other advantages.with out the limitation of commutator circumferential speed and armature reactance potential numerical element, the speed limit ofAC motor can be design higher than DC motor in the same given motor. with a wide range of speed regulation, the most ac servo motor speed ratio can reach 1:50000,and high-performance servo motor speed ratio can even amount to ver 100000. Meet the numerical control machine tooldrive, wide speed range and small static rate request.good torque speed characteristicAC motor as the constant torque output, i.e. within its rated speed output rated torque, in for a constant power output above the rated speed.And torque overload capacity, can overcome the inertia moment of inertia load moment at start-up.Meet the machine tool servo system, large output torque, good dynamic accordingly, high positioning accuracy demands.The research status of domestic ac servoAc servo system consists of the ac servo system based on asynchronous motor and the ac servo system on the base of synchronous motor.At present machine mainly adopts a permanent magnet synchronous ac servo system.In the field of ac servo research, the Japan, the United States and Europe are in the forefront.In the mid 1980s, Japan yaskawa company has successfully developed the world's first ac servo drive.Then F ANUC, Mitsubishi, Panasonic and other companies have launched their own ac servo system. Most of these products from aboard companies are based on the asynchronous motor. However,domestic institutes has set up late in ac servo system with asynchronous motor,and so far there are still no products available. Many domestic researchers put much importance on the research of permanent magnet synchronous motor servo system. Huazhong university of science and technology, Beijing machine toolresearch institute, xi 'an micro motor research institute, shenyang institute of automation of Chinese academy of sciences, lanzhou electric factory etc have started out in the research of AC servo system and are expected to launch their own products. DA98 all-digital ac servo drive unit from guangzhou NC manufacturing company has already knock at the door of high-precision servo driver industry in our country, broken the monopoly of foreign countries , and initiated a new era belonging to our national brands.Ac servo signal and numerical control system interface have three different modes, which can also divided into three stages.Domestically, Guangzhou CNC DA98 which belongs to the first generation and is also a epoch-making servo drive, at the same time, it is first all-digital domestic ac servo drive unit, pulse command it accept direction. The second generation is EDB series delegated by Aston, it can not only accept pulse command signal, but also receive the signal from the speed control and torque control analog input.The third generation is networked ac servo worked servo system is the organic combination of industrial field-bus technology and full digital ac servo,which enables users to adjust the parameters according to load conditions and saves some unstable factors such as drift produced by analog circuits. Based on field bus network control technology,the servosystem the microprocessor and field bus interface in all type ac motor servo drive, form independent of intelligent digital servo control unit, it directly connected to the industrial field bus, it formed a new type of network control system based on field-bus.Reduced the number of hardware and the attachment, the structure of intelligent units on independent, to the outside world and realize data sharing between each other, but also can use other field control equipment, easy to extend.So far, the network communication server product in domestic has not yet mature.Robotics institute of Beijing university of aeronautics and astronautics development design a network based on DSP + FPGA + ASIPM ac servo control system, the principle prototype has been got preliminary validation of the three-dimensional carving machine. currently, the most server drive adopt high-speed DSP processors,which promote the movement of all kinds of advanced control algorithms in the use of new type of drive. Mostly, suppliers of servo system employ the structure of DSP + CPLD (FPGA) on the hardware. Because the DSP and CPLD (FPGA) can repeat programming,they are easy to realize modular re-configurable of the ac servo system.As long as the software for corresponding different system configurations, including the control algorithm can control and asynchronous motor, permanent magnet synchronous servo motor, brush-less dc motor, and through the reconfiguration of FPGA can also drive dc motor and three phaseinduction of stepping motor.It's for NC machine tool upgrade and innovation has left a lot of space.The development tendency of ac servoWith the constant improvement of productive forces, the ac servo system will be sophisticated in the direction of the integration, intelligent and network .integrationBy using a single and multi-function control unit, the servo system can achieve position control and speed control function through the setting of software and constitute a half closed loop feedback unit configuration or full closed loop control system of high accuracy through the external interface composition.intelligentServer intelligent control mode, such as internal programming can achieve a certain trajectory in advance and control the surrounding IO port as well as the adjustment of master-slave's following with electronic CAM, etc.networkServer implementation is distributed by network.The server's modulation could be reconstructed with low cost .conclusionThe modern NC machine tool is developing rapidly in the direction ofhigh speed and high precision.As the essential component of the NC machine tool,servo system has gradually equated to ac servo system which has several incomparable advantages compared with other servo systems. With the progress of the ac servo technology, it will gradually replace dc servo system overall.[参考文献][1]Tryling, David P.Simple servo uses.ProQuest Journal,2009.[2]J. Cao ；Z.W. Li ；Z.X. Meng.Development Of A Nc Servo System Based On Fuzzy Adaptive Control.Key engineering materials,2009.[3]Fusaomi&Nagata.Development of CAM system based on industrial robotic servo controller without using robot languag.Robotics andComputer Integrated Manufacturing,2013.[4]Mulan Wang Kaiyun Xu Chuan He Lei Zhou.Research on Servo System for CNC Machine Tool Driven by Permanent Magnet Synchronous Torque Motor.Materials Engineering and Automatic Control,2012[5]Xu, Kaiyun Li, Ning Lin, Jian He, Chuan.Development of linear servo control system for CNC machine tool based on DSP.International Conference on Mechatronic Science, Electric Engineering and Computer,2011第二作业：典型曲线数字积分法插补方法2.1目的数字积分插补方法是实现数控插补功能的重要方法之一。
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哈工大自动控制原理大
作业
HUA system office room 【HUA16H-TTMS2A-HUAS8Q8-HUAH1688】
Harbin Institute of Technology
课程设计说明书（论文）
课程名称：自控控制原理大作业
设计题目：控制系统的矫正
院系：自动化测试与控制系
班级：
设计者：
学号：
指导教师：强盛
设计时间： 2016.12.21
哈尔滨工业大学
题目8
8. 在德国柏林，磁悬浮列车已经开始试验运行，长度为 1600m的M-Bahn号实验线路系统代表了目前磁悬浮列车的发展水平。
自动化的磁悬浮列车可以在较短的时间内正常运行，而且具有较高的能量利用率。
车体悬浮控制系统的框图模型如图 8 所示，试设计一
个合适的校正网络，使系统的相位裕度满足45°≤
γ
≤55°，并估算校正后系统的阶跃响应。
图 8 题 8 中磁悬浮列车悬浮控制系统
一、人工设计
利用半对数坐标纸手工绘制系统校正前后及校正装置的Bode图，并确定出
校正装置的传递函数。
验算校正后系统是否满足性能指标要求。
1)未校正系统的开环频率特性函数应为：
γ0(γγ)=
1
γ2(γ+10)
2)未校正系统的幅频特性曲线图如下：
由图中可以得出:
γγ=√γ=0.316 rad/s
对应的相位裕度为:
γ(γγ)=180°−180°−arctan(
γγ
10
)=−1.81°
G c(s) 1
3)超前校正提供(m)=50°
4)γ−1
γ+1
=γγγ50°解得 a=7.5
5)−10γγγ=−8.75γγ,得到γγ=0.523 rad/s
6)1
γ=√γγγ=1.43 rad/s 1
γγ
=0.19 rad/s
7)γγ(γ)=1+5.3γ
1+0.7γ
二、计算机辅助设计
利用MATLAB语言对系统进行辅助设计、仿真和调试
g = tf(1,[1 10 0 0]);
gc = tf([5.3 1],[0.7 1]);
ge = tf([5.3 1],conv([0.7 1],[1 10 0 0]));
bode(g,gc,ge);
grid
legend('uncompensated','compensator','compensated') [kg,r,wg,wc]=margin(ge)
系统校正前后及校正装置的Bode图:
性能指标：
kg =18.3027 r =47.0334 wg =3.4822 wc =0.5273满足题目要求。
Simulink仿真：
plot(ScopeData(:,1),ScopeData(:,2))
title('Step Response');
xlabel('t/s')
ylabel('y')
由图可以得出：
γγ=5.49s γγ=13.1s γγ=30.7%
三、矫正装置电路图
四、设计结论
对原系统进行矫正，矫正后的相位裕度为47°
根据题目要求，设计了γγ(γ)=1+5.3γ
1+0.7γ
满足了45°≤γ≤55°的要求。
校正后由系统阶跃响应求出γγ=5.49s γγ=13.1s γγ=30.7%。
五、设计后心得体会
通过本次大作业，学会了在自动控制中应用MATLAB/SIMULINK辅助设计，并且将课程中学
到的知识在具体场景中的应用，更加深化对系统矫正知识的理解。
同时通过书本和互联网
解决了设计中遇到的各种问题，但在最后的电路图设计中，由于之前未考虑到元件的选
取，导致选型困难，在今后的设计中会进一步吸取经验，继续学习进步。