CN110415589A - A magnetic levitation demonstration instrument and its modeling method - Google Patents
A magnetic levitation demonstration instrument and its modeling method Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及教学演示仪器，尤其涉及一种磁悬浮演示仪器及其建模方法。The invention relates to a teaching demonstration instrument, in particular to a magnetic levitation demonstration instrument and a modeling method thereof.
背景技术Background technique
磁悬浮技术是集电磁学、电磁感应技术为一体的高新技术，随着电子技术、控制工程以及电磁理论等的发展，磁悬浮技术有了很大的进步。虽然磁悬浮技术有了长足的发展，但是磁悬浮概念对于学校的学生来说还是太过抽象难以理解，不利于学生掌握和应用磁悬浮知识，需要提供一种具体化的演示仪器将抽象的概念具体化，使学生更好地掌握磁悬浮的特性。Magnetic levitation technology is a high-tech integrating electromagnetics and electromagnetic induction technology. With the development of electronic technology, control engineering and electromagnetic theory, magnetic levitation technology has made great progress. Although maglev technology has made great progress, the concept of maglev is still too abstract and difficult for school students to understand, which is not conducive to students' mastering and application of maglev knowledge. It is necessary to provide a concrete demonstration instrument to concretize the abstract concept. To enable students to better grasp the characteristics of maglev.
发明内容Contents of the invention
本发明为解决教学过程中磁悬浮概念对于学生来说抽象难以理解的问题，提供了一种磁悬浮演示仪器及其建模方法，将抽象的磁悬浮概念通过演示仪器演示出来，将抽象的概念具体化，使得学生更直观更深刻的理解磁悬浮的概念，且该装置操作简单使用方便。In order to solve the problem that the concept of magnetic levitation is abstract and difficult for students to understand in the teaching process, the present invention provides a magnetic levitation demonstration instrument and its modeling method, which demonstrates the abstract concept of magnetic levitation through the demonstration instrument, and makes the abstract concept concrete. It enables students to understand the concept of magnetic levitation more intuitively and deeply, and the device is easy to operate and easy to use.
为达到上述目的，本发明的技术方案具体是这样实现的：In order to achieve the above object, the technical solution of the present invention is specifically realized in the following way:
一种磁悬浮演示仪器包括环形永久磁铁、磁性浮子、磁场检测模块、微处理器和驱动电路。其中，环形永久磁铁的内环配置多个电磁线圈，磁性浮子悬浮于多个电磁线圈的上方，磁场检测模块用于将磁场变化转换为电压信号，磁场检测模块包括至少三个磁场传感器，三个磁场传感器分别对应X、Y和Z轴三个方向，微处理器用于将电压信号转换为电流控制信号以控制驱动电路，驱动电路用于驱动电磁线圈来改变电磁场使所述磁性浮子悬浮。A magnetic levitation demonstration instrument includes an annular permanent magnet, a magnetic float, a magnetic field detection module, a microprocessor and a drive circuit. Among them, the inner ring of the annular permanent magnet is equipped with a plurality of electromagnetic coils, and the magnetic float is suspended above the plurality of electromagnetic coils. The magnetic field detection module is used to convert the change of the magnetic field into a voltage signal. The magnetic field detection module includes at least three magnetic field sensors, three The magnetic field sensors correspond to the three directions of X, Y and Z axes respectively, and the microprocessor is used to convert the voltage signal into a current control signal to control the driving circuit, and the driving circuit is used to drive the electromagnetic coil to change the electromagnetic field to make the magnetic float float.
进一步地，磁悬浮演示仪器还包括电压转换电路，用于将电压信号调节到微处理器的额定工作电压。Furthermore, the maglev demonstration instrument also includes a voltage conversion circuit, which is used to adjust the voltage signal to the rated working voltage of the microprocessor.
进一步地，电压转换电路由第一运算放大器、第二运算放大器和第三运算放大器组成，第一运算放大器、第二运算放大器和第三运算放大器的输入端分别连接三个磁场传感器的输出端，第一运算放大器、第二运算放大器和第三运算放大器的输出端分别连接微处理器。Further, the voltage conversion circuit is composed of a first operational amplifier, a second operational amplifier and a third operational amplifier, the input terminals of the first operational amplifier, the second operational amplifier and the third operational amplifier are respectively connected to the output terminals of the three magnetic field sensors, The output ends of the first operational amplifier, the second operational amplifier and the third operational amplifier are respectively connected to the microprocessor.
进一步地，微处理器包括AD转换电路和CPU，AD转换电路将电压信号转化为数字信号，CPU将数字信号转化成电流控制信号，电流控制信号控制驱动电路。Further, the microprocessor includes an AD conversion circuit and a CPU, the AD conversion circuit converts the voltage signal into a digital signal, the CPU converts the digital signal into a current control signal, and the current control signal controls the driving circuit.
进一步地，微处理器的CPU型号为STM32，CPU的A0引脚连接驱动电路的IN4引脚，微处理器的A1引脚连接驱动电路的IN3引脚，微处理器的A2引脚连接驱动电路的IN2引脚，微处理器的A3引脚连接驱动电路的IN1引脚。Further, the CPU model of the microprocessor is STM32, the A0 pin of the CPU is connected to the IN4 pin of the driving circuit, the A1 pin of the microprocessor is connected to the IN3 pin of the driving circuit, and the A2 pin of the microprocessor is connected to the driving circuit The IN2 pin of the microprocessor and the A3 pin of the microprocessor are connected to the IN1 pin of the drive circuit.
进一步地，电磁线圈为四个，驱动电路的四个输出端口OUT1、OUT2、OUT3和OUT4分别连接四个电磁线圈。Further, there are four electromagnetic coils, and the four output ports OUT1 , OUT2 , OUT3 and OUT4 of the driving circuit are respectively connected to the four electromagnetic coils.
进一步地，磁场传感器为OH49E。Further, the magnetic field sensor is OH49E.
进一步死，磁悬浮演示仪器还包括下载器，下载器的SWCLK端脚连接微处理器的SWCLK端，下载器的SWDIO端连接微处理器的SWDIO端，下载器的GND端连接微处理器的GND端。Further, the maglev demonstration instrument also includes a downloader, the SWCLK terminal of the downloader is connected to the SWCLK terminal of the microprocessor, the SWDIO terminal of the downloader is connected to the SWDIO terminal of the microprocessor, and the GND terminal of the downloader is connected to the GND terminal of the microprocessor .
本发明的另一方面还提供一种磁性浮子的建模方法，包括以下步骤：Another aspect of the present invention also provides a method for modeling a magnetic float, comprising the following steps:
1)根据力学理论，建立磁性浮子动力学模型， 1) According to the theory of mechanics, establish the dynamic model of the magnetic float,
2)根据能量转换方式建立电磁力方程， 2) Establish the electromagnetic force equation according to the energy conversion method,
3)采用滑模结构算法实现磁性浮子的控制。3) The sliding mode structure algorithm is used to realize the control of the magnetic float.
有益技术效果：Beneficial technical effects:
本发明通过提供一种磁悬浮演示仪器及其磁性浮子建模方法，解决了教学过程中磁悬浮概念对于学生来说过于抽象难以理解的问题，将抽象的磁悬浮概念具体化，使得学生能更直观更深刻的理解磁悬浮的概念，且该装置使用简单，操作方便。The present invention solves the problem that the concept of magnetic levitation is too abstract and difficult for students to understand in the teaching process by providing a magnetic levitation demonstration instrument and its magnetic float modeling method, and makes the abstract concept of magnetic levitation concrete so that students can be more intuitive and profound A good understanding of the concept of magnetic levitation, and the device is simple to use and easy to operate.
附图说明Description of drawings
为了更清楚地说明本发明的技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍。In order to illustrate the technical solutions of the present invention more clearly, the following will briefly introduce the drawings required for the description of the embodiments.
图1为本发明磁悬浮演示仪器的电路原理框图；Fig. 1 is the circuit schematic block diagram of magnetic levitation demonstration instrument of the present invention;
图2为本发明磁悬浮演示仪器的俯视图；Fig. 2 is the top view of the magnetic levitation demonstration instrument of the present invention;
图3为本发明磁悬浮演示仪器的电路结构图；Fig. 3 is the circuit structure diagram of the magnetic levitation demonstration instrument of the present invention;
图4为本发明磁悬浮演示仪器电路结构图中的Ⅰ局部放大电路图；Fig. 4 is a partial enlarged circuit diagram of I in the circuit structure diagram of the magnetic levitation demonstration instrument of the present invention;
图5为本发明磁悬浮演示仪器电路结构图中的Ⅱ局部放大电路图；Fig. 5 is the partial enlarged circuit diagram of II in the circuit structure diagram of the magnetic levitation demonstration instrument of the present invention;
图6为本发明磁悬浮演示仪器的磁性浮子建模。Fig. 6 is a modeling of the magnetic float of the magnetic levitation demonstration instrument of the present invention.
其中，1-环形永久磁铁，2-电磁线圈，3-磁场传感器，4-微处理器，5-驱动电路，6-下载器，7-第一运算放大器，8-第二运算放大器，9-第三运算放大器。Among them, 1-ring permanent magnet, 2-electromagnetic coil, 3-magnetic field sensor, 4-microprocessor, 5-drive circuit, 6-downloader, 7-first operational amplifier, 8-second operational amplifier, 9- third operational amplifier.
具体实施方式Detailed ways
下面详细描述本发明的实施例，所述实施例的示例在附图中示出，其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的，仅用于解释本发明，而不能理解为对本发明的限制。Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.
下面结合附图对本发明的实施方式进行详细说明。Embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.
一种磁悬浮演示仪器包括环形永久磁铁1、磁性浮子、磁场检测模块、微处理器4和驱动电路5，参见图1和图2，具体地，环形永久磁铁1的内环配置多个电磁线圈2，磁性浮子悬浮于多个电磁线圈2的上方，磁场检测模块用于将磁场变化转换为电压信号，磁场检测模块包括至少三个磁场传感器3，三个磁场传感器3分别对应X、Y和Z轴三个方向。微处理器4用于将电压信号转换为电流控制信号以控制驱动电路5，驱动电路5用于驱动电磁线圈2来改变电磁场使所述磁性浮子悬浮。A magnetic levitation demonstration instrument includes an annular permanent magnet 1, a magnetic float, a magnetic field detection module, a microprocessor 4 and a drive circuit 5, see Figures 1 and 2, specifically, the inner ring of the annular permanent magnet 1 is configured with a plurality of electromagnetic coils 2 , the magnetic float is suspended above a plurality of electromagnetic coils 2, the magnetic field detection module is used to convert the change of the magnetic field into a voltage signal, the magnetic field detection module includes at least three magnetic field sensors 3, and the three magnetic field sensors 3 correspond to the X, Y and Z axes respectively three directions. The microprocessor 4 is used to convert the voltage signal into a current control signal to control the drive circuit 5, and the drive circuit 5 is used to drive the electromagnetic coil 2 to change the electromagnetic field to levitate the magnetic float.
磁场传感器Magnetic field sensor
三个磁场传感器3分别测量X轴方向、Y轴方向和Z轴方向上的磁场变化量，参见图4，优选地，磁场传感器3为OH49E，OH49E是一种小型的多功能线性霍尔，其输入是磁感应强度，输出是和输入成正比的电压，0H49E只有三个引脚，一个引脚VCC端接电源正极，一个引脚GND端接地端，一个引脚OUT端为电压输出端，X轴方向的磁场传感器3的OUT端经电阻R11连接第一运算放大器7的正向输入端；Y轴方向的磁场传感器3的OUT端经电阻R23连接第二运算放大器8的正向输入端；Z轴方向的磁场传感器3的OUT端经电阻R19连接第三运算放大器9的正向输入端。磁场传感器3将变化的磁感应强度转化成与变化的磁感应强度成正比的电压信号，并将电压信号输出至电压转换电路。Three magnetic field sensors 3 respectively measure the magnetic field variation on the X-axis direction, the Y-axis direction and the Z-axis direction, see Fig. 4, preferably, the magnetic field sensor 3 is OH49E, and OH49E is a kind of small multifunctional linear Hall, its The input is the magnetic induction intensity, and the output is the voltage proportional to the input. 0H49E has only three pins, one pin VCC terminal is connected to the positive pole of the power supply, one pin GND terminal is the ground terminal, one pin OUT terminal is the voltage output terminal, and the X axis The OUT end of the magnetic field sensor 3 in the direction is connected to the positive input end of the first operational amplifier 7 through the resistor R11; the OUT end of the magnetic field sensor 3 in the Y axis direction is connected to the positive input end of the second operational amplifier 8 through the resistor R23; the Z axis The OUT terminal of the direction magnetic field sensor 3 is connected to the positive input terminal of the third operational amplifier 9 via a resistor R19. The magnetic field sensor 3 converts the changing magnetic induction into a voltage signal proportional to the changing magnetic induction, and outputs the voltage signal to the voltage conversion circuit.
电压转换电路voltage conversion circuit
优选地，磁悬浮演示仪器还包括电压转换电路，参见图4，用于将电压信号调节到微处理器的额定工作电压。电压转换电路由第一运算放大器7、第二运算放大器8和第三运算放大器9组成，具体地，第一运算放大器7的正向输入端经过电阻R11连接X轴方向磁场传感器的OUT电压输出端，第一运算放大器7的输出端连接微处理器4的A4引脚；第二运算放大器8的正向输入端经过电阻R23连接Y轴方向磁场传感器的OUT电压输出端，第二运算放大器8的输出端连接微处理器4的A5引脚；第三运算放大器9的正向输入端经过电阻R19连接Z轴方向磁场传感器的OUT电压输出端，第三运算放大器9的输出端连接微处理器4的A6引脚；运算放大器输出端的电压为输入的正向输入端电压与输入的反向输入端电压之差，这样利用运算放大器的工作原理电压转换电路把磁场传感器3输出端的1～4V的电压转换为0～3V的电压，并传输到微处理器4的输入端。Preferably, the maglev demonstration instrument further includes a voltage conversion circuit, see FIG. 4 , for adjusting the voltage signal to the rated working voltage of the microprocessor. The voltage conversion circuit is composed of a first operational amplifier 7, a second operational amplifier 8 and a third operational amplifier 9. Specifically, the positive input terminal of the first operational amplifier 7 is connected to the OUT voltage output terminal of the magnetic field sensor in the X-axis direction through a resistor R11 , the output end of the first operational amplifier 7 is connected to the A4 pin of the microprocessor 4; the positive input end of the second operational amplifier 8 is connected to the OUT voltage output end of the Y-axis direction magnetic field sensor through a resistor R23, and the second operational amplifier 8 The output end is connected to the A5 pin of the microprocessor 4; the positive input end of the third operational amplifier 9 is connected to the OUT voltage output end of the Z-axis direction magnetic field sensor through the resistor R19, and the output end of the third operational amplifier 9 is connected to the microprocessor 4 The A6 pin of the operational amplifier; the voltage at the output terminal of the operational amplifier is the difference between the voltage at the forward input terminal of the input and the voltage at the reverse input terminal of the input, so that the voltage of 1 to 4V at the output terminal of the magnetic field sensor 3 is converted by the voltage conversion circuit using the working principle of the operational amplifier. Converted to the voltage of 0 ~ 3V, and transmitted to the input of the microprocessor 4.
微处理器microprocessor
优选地，磁悬浮演示仪器还包括微处理器4，微处理器4包括AD转换电路和CPU，AD转换电路将电压信号转化为数字信号，CPU将数字信号转化成电流控制信号，电流控制信号控制驱动电路5。具体地，参见图5，微处理器4的CPU型号为STM32，CPU的A0引脚连接驱动电路5的IN4引脚，CPU的A1引脚连接驱动电路5的IN3引脚，CPU的A2引脚连接驱动电路5的IN2引脚，CPU的A3引脚连接驱动电路5的IN1引脚，STM32将由电压转换电路传送的电压信号，经过STM32内部的AD转换电路将模拟信号转换为数字信号，再采用控制算法将数字信号转化成电流控制信号，并将电流控制信号分别通过A0、A1、A2和A3端口传输到驱动电路5的IN4、IN3、IN2和IN1端口；利用下载器6，优选地，下载器6为cp2102usb，利用下载器6将编写的程序代码下载到STM32的内部，控制驱动电路5，具体地参见图5，下载器的SWCLK端脚连接微处理器的SWCLK端，下载器的SWDIO端连接微处理器的SWDIO端，下载器的GND端连接微处理器的GND端。Preferably, the maglev demonstration instrument also includes a microprocessor 4, the microprocessor 4 includes an AD conversion circuit and a CPU, the AD conversion circuit converts the voltage signal into a digital signal, the CPU converts the digital signal into a current control signal, and the current control signal controls the drive Circuit 5. Specifically, referring to FIG. 5, the CPU model of the microprocessor 4 is STM32, the A0 pin of the CPU is connected to the IN4 pin of the drive circuit 5, the A1 pin of the CPU is connected to the IN3 pin of the drive circuit 5, and the A2 pin of the CPU Connect the IN2 pin of the drive circuit 5, and connect the A3 pin of the CPU to the IN1 pin of the drive circuit 5. The STM32 converts the voltage signal transmitted by the voltage conversion circuit into a digital signal through the AD conversion circuit inside the STM32, and then uses The control algorithm converts the digital signal into a current control signal, and transmits the current control signal to the IN4, IN3, IN2 and IN1 ports of the drive circuit 5 through the A0, A1, A2 and A3 ports respectively; The device 6 is cp2102usb, use the downloader 6 to download the written program code to the inside of the STM32, and control the drive circuit 5, specifically refer to Figure 5, the SWCLK terminal of the downloader is connected to the SWCLK terminal of the microprocessor, and the SWDIO terminal of the downloader Connect the SWDIO end of the microprocessor, and connect the GND end of the downloader to the GND end of the microprocessor.
优选地，电磁线圈为四个Preferably, there are four electromagnetic coils
驱动电路Drive circuit
优选地，驱动电路5为L298N，L298N是ST公司生产的一种高电压、大电流电机驱动芯片，内含两个H桥的高电压大电流全桥式驱动器，可以用来驱动直流电动机和步进电动机和继电器线圈等感性负载。驱动电路5的四个输出端OUT1、OUT2、OUT3和OUT4分别控制四个电磁线圈2，控制电磁线圈2中电流的大小。Preferably, the drive circuit 5 is L298N. L298N is a high-voltage, high-current motor drive chip produced by ST Company. It contains a high-voltage, high-current full-bridge driver of two H-bridges, which can be used to drive DC motors and steppers. into inductive loads such as motors and relay coils. The four output terminals OUT1 , OUT2 , OUT3 and OUT4 of the driving circuit 5 respectively control the four electromagnetic coils 2 and control the magnitude of the current in the electromagnetic coils 2 .
综上所述，本发明磁悬浮演示仪器的工作原理，参见图1，具体地，磁场传感器3将电磁线圈2中磁场的变化量转化成1～4V的电压信号，1～4V的电压信号经过电压转换电路调整为微处理器4的额定工作电压0～3V，同时并通过微处理器4中的AD转换电路将电压转换电路传输来的模拟信号转化为数字信号，采用控制算法将数字信号转化成电流控制信号，电流控制信号控制驱动电路5，驱动电路5驱动电磁线圈2来改变电磁场，实现磁性浮子的悬浮。In summary, the working principle of the magnetic levitation demonstration instrument of the present invention is shown in Fig. 1. Specifically, the magnetic field sensor 3 converts the variation of the magnetic field in the electromagnetic coil 2 into a voltage signal of 1-4V, and the voltage signal of 1-4V is passed through the voltage signal. The conversion circuit is adjusted to the rated operating voltage of the microprocessor 4, 0-3V, and at the same time, the analog signal transmitted by the voltage conversion circuit is converted into a digital signal through the AD conversion circuit in the microprocessor 4, and the digital signal is converted into a digital signal by using a control algorithm. The current control signal, the current control signal controls the drive circuit 5, and the drive circuit 5 drives the electromagnetic coil 2 to change the electromagnetic field and realize the suspension of the magnetic float.
本发明的磁性浮子数学建模过程：The mathematical modeling process of the magnetic float of the present invention:
1)根据力学理论，建立磁性浮子动力学模型；1) According to the mechanics theory, establish the dynamic model of the magnetic float;
其中：m为磁浮体质量，单位为kg；x为磁极平面到磁浮体的距离，单位为m；F(x,i)为电磁力，单位为N；g为重力加速度，单位为m/s2；Where: m is the mass of the maglev, in kg; x is the distance from the magnetic pole plane to the maglev, in m; F(x,i) is the electromagnetic force, in N; g is the gravitational acceleration, in m/s 2 ;
2)根据能量转换方式建立电磁力方程；2) Establish the electromagnetic force equation according to the energy conversion method;
其中，i0磁性浮子在平衡点时的线圈电流值；i是位移x引起的控制电流；x0磁性浮子在平衡点时的位置；k为比例系数且μ0为空气导磁率；s为磁性浮子底面积；N为线圈匝数；Among them, i0 is the coil current value of the magnetic float at the balance point; i is the control current caused by the displacement x; x0 is the position of the magnetic float at the balance point; k is the proportional coefficient and μ 0 is the magnetic permeability of air; s is the area of the bottom of the magnetic float; N is the number of turns of the coil;
在平衡点位置时， When at the equilibrium point,
得到平衡点的条件， To obtain the condition of the equilibrium point,
且有，i＝0，x＝0，f＝0；And have, i=0, x=0, f=0;
将(2)式在平衡点处用泰勒公式展开并忽略二次以上项得到，Expand the formula (2) at the equilibrium point with Taylor's formula and ignore the above two terms to get,
其中， in,
最终得到磁性浮子运动方程为，Finally, the motion equation of the magnetic float is obtained as,
设则(7)式变成如下一般式，Assume Then formula (7) becomes the following general formula,
用幂次趋近率的滑模变结构算法实现磁性浮子的控制：The control of the magnetic float is realized by the sliding mode variable structure algorithm with power reaching rate:
首先，定义 First, define
其中，c1是一个大于5的常数，e＝x0-x， Among them, c 1 is a constant greater than 5, e=x 0 -x,
其次，slaw＝-k|s|αsign(s) (10)Secondly, slaw＝-k|s| α sign(s) (10)
且 and
其中，α为大于1的正整数；Wherein, α is a positive integer greater than 1;
由e＝x0-x和 By e=x 0 -x and
得到， get,
控制电流为:The control current is:
由Stm32产生PWM波控制输出电流的有效值经过驱动电路实现了磁浮体的悬浮。The effective value of PWM wave control output current generated by Stm32 realizes the levitation of the magnetic levitation body through the drive circuit.
以上的实施例仅是对本发明的优选实施方式进行描述，并非对本发明的范围进行限定，在不脱离本发明设计精神的前提下，本领域普通工程技术人员对本发明的技术方案做出的各种变形和改进，均应落入本发明的权利要求书确定的保护范围内。The above embodiments are only descriptions of preferred implementations of the present invention, and are not intended to limit the scope of the present invention. On the premise of not departing from the design spirit of the present invention, various technical solutions of the present invention can be made by ordinary engineers and technicians in the field. Variations and improvements should fall within the scope of protection defined by the claims of the present invention.
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