WO2021237910A1 - 一种基于查表法的主动磁轴承控制器的构造方法 - Google Patents
一种基于查表法的主动磁轴承控制器的构造方法 Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0444—Details of devices to control the actuation of the electromagnets
- F16C32/0451—Details of controllers, i.e. the units determining the power to be supplied, e.g. comparing elements, feedback arrangements with P.I.D. control
- F16C32/0453—Details of controllers, i.e. the units determining the power to be supplied, e.g. comparing elements, feedback arrangements with P.I.D. control for controlling two axes, i.e. combined control of x-axis and y-axis
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0444—Details of devices to control the actuation of the electromagnets
- F16C32/0451—Details of controllers, i.e. the units determining the power to be supplied, e.g. comparing elements, feedback arrangements with P.I.D. control
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Definitions
- the invention relates to the control technology of active magnetic bearings, which is suitable for the control of active magnetic bearings in high-speed compressors, wind power generation, molecular pumps and other high-speed running equipment.
- the magnetic bearing is a rotor support system that uses electromagnetic force to overcome the gravity and interference force of the rotor to achieve no mechanical contact suspension. It has the characteristics of no mechanical contact, long service life, and easy maintenance. At the same time, its stiffness and damping are adjustable and can be controlled The current in the winding flexibly adjusts the output of the electromagnetic force, and realizes the movement adjustment of the rigidity and damping of the magnetic bearing.
- many applications with high-speed rotating shafts, such as molecular pumps, wind power generation, and flywheel energy storage have increased.
- Traditional mechanical bearings will greatly reduce the service life of the equipment due to friction loss. Therefore, the application of magnetic bearings has been continuously promoted.
- Magnetic bearings can be divided into three types: active, passive, and hybrid magnetic bearings.
- Active magnetic bearings are widely used due to their simple structure and adjustable levitation force.
- the stability control of active magnetic bearings has shortcomings.
- the problem lies in the inability to obtain accurate control models, that is, current stiffness and displacement stiffness.
- the current control methods generally use fixed current stiffness coefficient and displacement stiffness coefficient.
- the displacement, current and levitation force of the active magnetic bearing are only in the working point, and its displacement, current and levitation force are approximately linear. When the displacement and current are With large changes, the model will no longer be accurate.
- the prior art generally uses fuzzy logic control, neural network control, parameter adjustment control based on advanced algorithms, etc., and the adjustment of the model is extremely limited, or the adjustment of the control only exists in the adjustment of the controller parameter. Therefore, there is an urgent need for a reasonable method that can change the model parameters with the change of the active magnetic bearing rotor displacement to achieve more precise control.
- the look-up table method has been used in various fields of control methods.
- the look-up table method is a control method in which known test or simulation data is used in control, and the corresponding results are obtained through the data on the table or interpolation calculation.
- the look-up table method is also widely used. For example, in the control of a switched reluctance motor, the flux linkage information is obtained through the position information obtained by the sensor and the control current size look-up table. Therefore, it is a feasible solution to learn from the current look-up table method and obtain accurate model parameters through the look-up table method in the control of active magnetic bearings.
- the current look-up table method has some problems: the main problem is that the establishment of a usable parameter table requires a large number of experiments or simulations and repeated verifications. This requires a lot of experimental costs and time costs. For this, how to Establishing a parameter table with high accuracy quickly is a problem worthy of study.
- the Kriging model is a regression algorithm for spatial modeling and prediction of the random field of a random process based on the covariance function.
- the Kriging model can give the best linear unbiased estimator, which is also called the spatially optimal unbiased estimator in statistics. Therefore, the Kriging model has applications in many fields such as geographic science, environmental science, and atmospheric science. In many cases, the amount of regionalization will not be stable. In this case, the Fan Kriging model needs to be used for processing. Through the Fan Kriging model, only a small amount of data can be used to obtain the parameter table of the active magnetic bearing.
- the purpose of the present invention is to overcome the current problem of inaccurate models of active magnetic bearings in the control process. It proposes a method for constructing active magnetic bearing controllers based on the look-up table method.
- the model state table is established by using the Van Kriging model.
- the table method realizes active magnetic bearing control, which can adjust the current stiffness coefficient and displacement stiffness coefficient in real time according to the displacement and current changes of the active magnetic bearing during operation.
- the technical scheme adopted in the construction method of the active magnetic bearing controller based on the look-up table method of the present invention has the following steps:
- Step (1) Establish a finite element model of the active magnetic bearing, and obtain the actual levitation force in the X and Y axis directions based on the general Kriging model on the finite element model About actual displacement eccentricity And actual control current Corresponding two Van Kriging prediction models;
- Step (2) Establish the actual levitation force based on the two Van Kriging prediction models Eccentric to actual displacement Actual control current
- the two corresponding model state tables respectively construct two corresponding look-up modules of the built-in model state table
- the active magnetic bearing controller is composed of two fuzzy adaptive PID controllers in the X and Y axis directions, two amplifier modules, two look-up modules, and two measurement modules. Adapt to the PID controller, amplifier module, and look-up module connected in series with the active magnetic bearing input, and then connect with the active magnetic bearing input after the fuzzy adaptive PID controller, amplifier module, and look-up module in the Y-axis direction are connected in series ,
- the two measurement modules in the X and Y axis respectively measure the actual displacement eccentricity of the active magnetic bearing in the X and Y axis directions Eccentric the actual displacement Enter the corresponding two look-up table modules respectively, the reference displacement x * and y * in the X and Y axis directions are respectively eccentric with the corresponding actual displacement
- the displacement errors e x and e y obtained by subtraction are respectively obtained by the corresponding fuzzy adaptive PID controller to obtain the initial control currents I x0 and I y0 , and the initial control currents I x0 and I
- step (1) select N levels of control currents and M levels of displacement eccentricity for finite element simulation to obtain N*M finite element models, and collect the X and Y axes of N*M finite element models Directional control current, displacement eccentricity, and corresponding levitation force.
- the control current and displacement eccentricity of each finite element model in the X and Y axis directions are used as independent variable data x, and the corresponding levitation force is used as dependent variable data.
- the two Van Kriging prediction models are obtained by fitting F( ⁇ ,x), with Is the regression model, z(x), with Is the error term, ⁇ is the regression coefficient of the general Kriging model, It is the regression coefficient of the pan-Kriging prediction model.
- the fuzzy adaptive PID controller in step (3) is composed of a fuzzy inference system, a proportional part, an integral part and a derivative part.
- the displacement errors e x , e y and their first-order derivative As the input of the corresponding fuzzy inference system, the fuzzy inference system outputs the proportional correction coefficient CP, the integral correction coefficient CI, and the differential correction coefficient CD.
- the proportional correction coefficient CP, the integral correction coefficient CI, and the differential correction coefficient CD are respectively associated with the corresponding proportional coefficients.
- KP, integral coefficient KI, and differential coefficient KD are multiplied to obtain the corresponding corrected proportional part, integral part and differential part.
- the displacement errors e x and e y respectively pass through the corrected proportional part, integral part and differential part.
- the corrected output of the proportional part, the integral part and the differential part are respectively summed to obtain the initial control currents I x0 and I y0 .
- the present invention constructs an accurate change model of the active magnetic bearing under different displacement eccentricities and control currents, and obtains the prediction of the actual levitation force required by the active magnetic bearing with the rotor displacement.
- Parameter table the parameter table is established quickly, which saves the cost of tabulation, and can obtain a more accurate model of the active magnetic bearing according to the actual situation, and improve the accuracy of control.
- the present invention omits the fixed displacement stiffness and current stiffness in the process, so that its applicability is expanded from the pseudo-linear region near the operating point to the nonlinear region with large displacement and current. Improved control accuracy and control range.
- the fuzzy adaptive PID control module constructed by the present invention uses the error and the error rate of change as input on the basis of the PID algorithm, and passes the current control Conditions change PID regulator parameters, use fuzzy rules for fuzzy inference, meet the requirements of PID parameter self-tuning for errors and error change rates at different times, and can achieve more accurate active magnetic bearing control.
- Figure 1 is a block diagram of the fuzzy adaptive PID controller
- FIG. 2 is a block diagram of the commonly used PID controller
- Fig. 3 is a structural block diagram of an active magnetic bearing controller constructed by the method of the present invention.
- the present invention first establishes the finite element model of the active magnetic bearing.
- the actual levitation force in the X and Y axis directions of the active magnetic bearing is obtained based on the Van Kriging model.
- Two Van Kriging prediction models in the X and Y axis directions to establish the actual levitation force Eccentric to actual displacement Actual control current
- two look-up modules with built-in model state tables are constructed respectively, and then two fuzzy adaptive PID controllers in the X and Y axis directions are constructed.
- N levels of control current and M levels of displacement eccentricity are selected, and finite element simulation is performed to obtain N*M finite element models.
- N and M are based on the control current and the air gap range and the The fineness of the model needs to be selected. Then, the data of the control current in the X and Y axis directions, the displacement eccentricity in the X and Y axis directions and the corresponding levitation force in the X and Y axis directions of the N*M finite element models are collected.
- control current and displacement eccentricity in the X and Y axis directions of each model are measured independent variable data, and the corresponding suspension force in the X and Y axis directions are dependent variable data.
- the present invention is described below taking the X-axis direction as an example, and the Y-axis direction and the X-axis direction are similar:
- ⁇ 1 , ⁇ 2 ,..., ⁇ p are regression coefficients of various orders, and f p (x) is a p-order approximate model.
- the actual levitation forces are established respectively Eccentric to actual displacement And actual control current
- the corresponding two model state tables Specifically, the following actual suspension force in the X-axis direction is established Eccentric to actual displacement And actual control current
- the model state table 1 and the actual levitation force in the Y-axis direction Eccentric to actual displacement And actual control current
- the model status table 2 The model status table 2:
- the first line is the actual displacement eccentricity in the X-axis direction
- the first column is the actual control current Actual displacement eccentricity Starting from 0 to the maximum eccentricity x max , sampling every 0.01mm, at the same time, the actual control current Start from 0 and sample every 0.1A.
- Eccentric the actual displacement And actual control current The sampled value of is brought into formula (3), and the actual levitation force under the current sampled value can be calculated Size, build model status table 1. Therefore, each actual displacement is eccentric And actual control current Corresponds to an actual levitation force
- x max is the maximum displacement in the X-axis direction
- i max is the maximum control current.
- the actual levitation force at this time is F 11 ; when the actual displacement eccentricity is 0.03mm and the actual control current is 0.2A , The actual levitation force at this time is F 34 .
- b, a are the number of samples of actual displacement eccentricity and actual control current.
- Table 2 is the actual levitation force F '11 ⁇ F' ba, y max is the maximum displacement of the Y-axis direction, i ymax is the maximum control current Y-axis direction.
- the first line is the actual displacement eccentricity in the Y-axis direction
- the first column is the actual control current
- the sampling method is the same as the sampling method in the X-axis direction, and the actual displacement is eccentric And actual control current
- the sampled value of is brought into formula (3), and the actual levitation force under the current sampled value can be calculated Size, build model status table 2.
- the interpolation method is used to calculate the corresponding actual levitation force.
- the current actual displacement eccentricity is x 0
- the actual control current is i 0.
- the positions of x 0 and i 0 in Table 1 need to be determined first.
- the displacement eccentricity is between x 1 and point x 2
- the control current is between i 1 and sampling point i 2
- the values of x 1 , x 2 , i 1 and i 2 are the displacement and current values at the sampling point.
- the actual levitation force corresponding to the sampling point ⁇ x 1 , i 1 ⁇ is F c, d
- the actual levitation force corresponding to ⁇ x 1 , i 2 ⁇ is F c, d+1 , ⁇ x 2 , i 1 ⁇
- the corresponding actual levitation force is F c+1, d , ⁇ x 2 , i 2 ⁇
- the corresponding actual levitation force is F c+1, d+1 .
- c, d are the number of rows and columns of the sampling point ⁇ x 1 , i 1 ⁇ in Table 1. Then the actual levitation force at ⁇ x 0 , i 0 ⁇ at this time can be calculated as:
- the levitation force value at this point can be calculated according to the data in Table 1.
- the model state tables 1 and 2 are respectively built into the table look-up module in the X-axis direction and the table look-up module in the Y-axis direction, respectively, to construct two table look-up modules.
- FIG. 1 shows the structure block diagram of the existing commonly used PID controller, which mainly consists of a proportional part, an integral part and a differential part.
- the proportional part is directly composed of the proportional coefficient KP
- the integral part is directly composed of the integral coefficient KI and the integral module.
- the differential part is directly composed of the differential coefficient KD and the differential module d/dt, and the three parts get the final output through the summation ⁇ .
- Figure 1 shows a fuzzy adaptive PID controller in the X-axis direction constructed by the present invention. It is composed of a fuzzy inference system, a proportional part, an integral part and a derivative part. Improved on the basis, in addition to retaining the proportional part, integral part and differential part of the PID controller in Figure 2, a fuzzy inference system is added.
- the fuzzy adaptive PID controller in the X-axis direction Take the fuzzy adaptive PID controller in the X-axis direction as an example: the displacement error e x in the X-axis direction and its first-order derivative
- the fuzzy inference system takes the displacement error e x and the first-order differential Perform calculations to output the proportional correction coefficient CP, the integral correction coefficient CI, and the differential correction coefficient CD.
- the final output of the corrected proportional part, integral part and differential part is obtained through the summation ⁇ , that is, the displacement error e x can be accurately controlled by the corrected proportional part, integral part and differential part.
- the adjustment principles for formulating the correction coefficients CP, CI, CD are as follows: When e x is large, the correction coefficient should be increased Reduce And make Keep it moderate to improve the response speed of the system, while preventing excessive overshoot; when e x is medium, use the correction coefficient to make Keep the value small, and make Moderate to reduce the overshoot, while maintaining a faster response speed of the system; when e x is small, the correction coefficient should be increased And make Keep it moderate to ensure good stability of the system, while avoiding system oscillations and enhancing the anti-interference performance of the system.
- the construction direction of the fuzzy adaptive PID controller in the Y-axis direction is the same as the construction direction of the fuzzy adaptive PID controller in the X-axis direction.
- the displacement error e y in the Y-axis direction and its first-order derivative As the input of the fuzzy inference system in the corresponding Y-axis direction, the fuzzy inference system outputs the proportional correction coefficient CP, the integral correction coefficient CI, and the differential correction coefficient CD.
- the corresponding proportional coefficient KP, integral coefficient KI, and differential coefficient KD are multiplied to obtain the corresponding corrected proportional part, integral part and differential part.
- the displacement error e y respectively passes through the corrected proportional part, integral part and differential part,
- the output of the corrected proportional part, the integral part and the differential part are respectively summed and operated to obtain the initial control current I y0 in the Y-axis direction.
- the active magnetic bearing controller consists of two fuzzy adaptive PID controllers in the X-axis and Y-axis directions, an amplifier module, a look-up module, and a measurement module, which are connected to the active magnetic
- the input end of the bearing realizes the control of the active magnetic bearing.
- the fuzzy adaptive PID controller, amplifier module, and look-up module in the X-axis direction are connected in series with the input end of the active magnetic bearing
- the fuzzy adaptive PID controller, amplifier module, and look-up module in the Y-axis direction are connected in series.
- the two measurement modules in the X and Y axis directions respectively measure the actual displacement eccentricity of the active magnetic bearing in the X and Y axis directions through displacement sensors
- the actual displacement eccentricity in the X-axis direction In the look-up module of inputting the X-axis direction, the actual displacement in the Y-axis direction is eccentric Enter the Y-axis direction in the look-up table module.
- the reference displacement x * in the X-axis direction is eccentric to the actual displacement Obtained by subtracting the displacement error e x, e x displacement error X-axis direction by a fuzzy adaptive PID controller to obtain an initial control current I x0, and obtained actual control current through the X-axis direction of the amplifier module
- the actual control current Enter the X-axis direction look-up module, the X-axis direction look-up module obtains the actual levitation force at this time according to the data in the model state table 1
- the reference displacement y * in the Y-axis direction is eccentric to the actual displacement Obtained by subtracting the displacement error e y, e y displacement error by fuzzy adaptive PID controller Y-axis direction to obtain an initial control current I y0, and obtained actual control current through an amplifier module of the Y-axis direction
- the actual control current Enter the Y-axis direction look-up module, the Y-axis direction look-up module obtains the actual levitation force at this time
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Abstract
一种基于查表法的主动磁轴承控制器的构造方法,具有以下步骤:建立主动磁轴承有限元模型,基于范Kriging模型得到主动磁轴承X、Y轴方向的实际悬浮力关于实际位移偏心和实际控制电流的X、Y轴方向的两个范Kriging预测模型,从而建立实际悬浮力与实际位移偏心、实际控制电流的X、Y轴方向的两个模型状态表,分别构造内置有模型状态表的两个查表模块,将两个模糊自适应PID控制器、相应的X、Y轴方向的两个放大器模块、两个查表模块与相应的X、Y轴方向的两个测量模块共同构成主动磁轴承控制器,实现对主动磁轴承的精确控制。
Description
本发明涉及主动磁轴承的控制技术,适用于高速压缩机、风力发电、分子泵等高速运转设备中主动磁轴承的控制,属于磁悬浮技术领域,具体是主动磁轴承控制器的构造方法。
磁轴承是利用电磁力克服转子重力和干扰力,实现无机械接触悬浮的转子支撑系统,其具有无机械接触、使用寿命长、易于维护的特点,同时,其刚度和阻尼可调,可通过控制绕组内的电流灵活的调节电磁力的输出,实现磁轴承刚度和阻尼的运动调节。目前,如分子泵、风力发电、飞轮储能等多种具有高速转轴使用的应用场合的增多,传统机械轴承由于摩擦损耗会大大降低设备的使用寿命。因此,磁轴承的应用不断推广。
磁轴承可分为主动、被动、混动磁轴承三种形式,主动磁轴承因结构简单、悬浮力可调等优点得到了较多的运用,但是目前,主动磁轴承稳定控制存在缺陷,最大的问题在于不能得到精确的控制模型,即电流刚度与位移刚度。当前一般采用的控制方法都是用的固定的电流刚度系数与位移刚度系数,但是,主动磁轴承仅在工作点时,其位移、电流与悬浮力才呈近似的线性关系,当位移与电流有较大变化时,模型将不再精确。现有技术一般使用模糊逻辑控制、神经网络控制、基于先进算法的参数调节控制等,对于模型的调整极为有限,或对控制的调节仅存在控制器参数调节上。因此,当前亟需一种合理的方法,能随主动磁轴承转子位移变化改变模型参数,实现更精确的控制。
目前,查表法在各个领域的控制方法中得到了一定的使用。查表法是一种在控制中利用已知试验或仿真数据,通过表上数据或进行插值计算获得相应结果的一种控制方法。在电气领域中,查表法也广泛被使用。例如在开关磁阻电机的控制中,通过传感器获得的位置信息以及控制电流大小查表获得磁链信息。因此,借鉴当前的查表法,在主动磁轴承的控制中通过查表法获得准确地模型参数,是一种可行的方案。但当前的查表法存在一些问题:最主要的问题是建立一个可用的参数表需要进行大量的实验或者仿真,并且反复进行验证,为此需要花费大量的实验成本以及时间成本,为此,如何快速地建立准确度较高的参数表是一个值得研究的问题。
Kriging模型是一种依据协方差函数对随机过程随机场进行空间建模和预测的回归算法。在特定的随机过程,例如固有平稳过程中,Kriging模型能够给出最优线性无偏估计,在统计学中也被称为空间最优无偏估计器。因此,Kriging模型在地理科学、环境科学、大 气科学等诸多领域中都有应用。在许多情况下,会出现区域化量不平稳的现象,此时则需要运用范Kriging模型进行处理。通过范Kriging模型,只利用较少量的数据即可得到主动磁轴承的参数表。
发明内容
本发明的目的是为了克服当前主动磁轴承在控制过程中模型不精确的问题,提出了一种基于查表法的主动磁轴承控制器的构造方法,利用范Kriging模型建立模型状态表,通过查表法实现主动磁轴承控制,能根据主动磁轴承在运行过程中的位移与电流变化,实时调节电流刚度系数与位移刚度系数。
本发明一种基于查表法的主动磁轴承控制器的构造方法采用的技术方案是具有以下步骤:
步骤(3):由X、Y轴方向的两个模糊自适应PID控制器、两个放大器模块、两个查表模块、两个测量模块构成主动磁轴承控制器,由X轴方向的模糊自适应PID控制器、放大器模块、查表模块串联后与主动磁轴承输入端相接,由Y轴方向的模糊自适应PID控制器、放大器模块、查表模块串联后与主动磁轴承输入端相接,X、Y轴方向的两个测量模块分别测得主动磁轴承X、Y轴方向的实际位移偏心
将实际位移偏心
各自分别输入对应的两个查表模块中,X、Y轴方向的参考位移x
*、y
*分别与对应的实际位移偏心
相减得到的位移误差e
x、e
y各自分别通过对应的模糊自适应PID控制器得到初始控制电流I
x0、I
y0,初始控制电流I
x0、I
y0各自分别通过对应的放大器模块得到实际控制电流
将实际控制电流
输入对应的查表模块中,两个查表模块输出对应的实际悬浮力
至主动磁轴承。
进一步地,步骤(1)中,选取N个等级的控制电流与M个等级的位移偏心进行有限元仿真,得到N*M个有限元模型,采集N*M个有限元模型的X、Y轴方向的控制电流、 位移偏心以及对应的悬浮力,将每个有限元模型的X、Y轴方向的控制电流、位移偏心作为自变量数据x,对应的悬浮力作为因变数据
分别带入一般范Kriging模型
通过拟合得到所述的两个范Kriging预测模型
F(β,x)、
和
为回归模型,z(x)、
和
是误差项,β为一般范Kriging模型回归系数,
为泛Kriging预测模型回归系数。
进一步地,步骤(3)中的模糊自适应PID控制器由模糊推理系统、比例部分、积分部分与微分部分构成,位移误差e
x、e
y及其一阶微分
作为对应的模糊推理系统的输入,模糊推理系统输出比例修正系数CP、积分修正系数CI以及微分修正系数CD,将比例修正系数CP、积分修正系数CI以及微分修正系数CD各自分别与相应的比例系数KP、积分系数KI、微分系数KD相乘,得到相应的修正后的比例部分、积分部分与微分部分,位移误差e
x、e
y各自分别通过修正后的比例部分、积分部分与微分部分,对修正后的比例部分、积分部分与微分部分的输出分别求和运算得到初始控制电流I
x0、I
y0。
本发明的有益效果是:
1、本发明基于范Kriging模型理论以及主动磁轴承悬浮控制原理,构建了主动磁轴承在不同位移偏心与控制电流下的精确变化模型,获得主动磁轴承所需实际悬浮力随转子位移变化的预测参数表,参数表建立快速,节约制表成本,可根据实际情况得到主动磁轴承更加精确模型,提高控制的精确性。
2、本发明相比传统主动磁轴承的控制,省略了过程中固定的位移刚度与电流刚度,使其适用性从工作点附近的伪线性区扩大至位移与电流都较大的非线性区域,提升了控制精度与控制范围。
3、由于模型可变的原因,普通控制器无法满足根据模型的调整的需求,本发明构造的模糊自适应PID控制模块,在PID算法的基础上以误差和误差变化率作为输入,通过当前控制条件改变PID调节器参数,利用模糊规则进行模糊推理,满足不同时刻的误差和误差变化率对PID参数自整定的要求,能实现更精确的主动磁轴承控制。
图1为模糊自适应PID控制器的构成框图;
图2为常用PID控制器的构成框图;
图3为采用本发明方法构造的主动磁轴承控制器的结构框图。
本发明首先建立主动磁轴承有限元模型,在主动磁轴承有限元模型的基础上,基于范Kriging模型得到主动磁轴承X、Y轴方向的实际悬浮力
关于实际位移偏心
和实际控制电流
的X、Y轴方向的两个范Kriging预测模型,从而建立实际悬浮力
与实际位移偏心
实际控制电流
的X、Y轴方向的两个模型状态表,基于两个模型状态表,分别构造内置有模型状态表的两个查表模块,然后构造X、Y轴方向的两个模糊自适应PID控制器,最后将两个模糊自适应PID控制器、相应的X、Y轴方向的两个放大器模块、两个查表模块与相应的X、Y轴方向的两个测量模块共同构成主动磁轴承控制器,实现对主动磁轴承的精确控制。具体方法如下:
测量所要被控的主动磁轴承的尺寸参数,在有限元软件中建立主动磁轴承的有限元模型,并通过仿真获得主动磁轴承的性能参数。在磁场强度不饱和的前提下,选取N个等级的控制电流与M个等级的位移偏心,进行有限元仿真,得到N*M个有限元模型,N与M根据控制电流与气隙范围以及所需模型的精细程度选取。然后采集N*M个有限元模型的X、Y轴方向的控制电流、X、Y轴方向的位移偏心以及对应的X、Y轴方向的悬浮力的数据。每个模型的X、Y轴方向的控制电流、位移偏心是测量自变量数据,对应的X、Y轴方向的悬浮力是因变数据。本发明以下以X轴方向为例来描述,Y轴方向和X轴方向雷同:
采集N*M个有限元模型的X轴方向的控制电流{i
11,i
12,…,i
NM}、位移偏心{x
11,x
12,…,x
NM}以及对应的悬浮力{F
11,F
12,…,F
NM}的数据。每个有限元模型的控制电流{i
11,i
12,…,i
NM}、位移偏心{x
11,x
12,…,x
NM}是测量的自变量数据,悬浮力{F
11,F
12,…,F
NM}是因变数据,自变量数据可表示为X
ij=[i
ij,x
ij]
T,因变数据表示为Y
ij=F
ij,其中i=1,2,…,N,j=1,2,…,M。
一般范Kriging模型的表达式为:
其中,
为最终结果值,也就是为因变数据,F(β,x)为回归模型,β为回归系数,x为范Kriging模型的自变量数据。z(x)是一个误差项,它服从均值为0,方差为
的正态分布,方差为
的选取根据具体应用确定,对近似模型精确度会产生影响。其中,回归模型F(β,x)表达式为:
F(β,x)=β
1f
1(x)+…+β
pf
p(x)=f(x)
Tβ (2)
β
1、β
2、…、β
p为各阶回归系数,f
p(x)为p阶近似模型。
将有限元模型的自变量数据X
ij与因变数据Y
ij分别带入一般范Kriging模型的公式(1)中,分别替代x与
通过拟合可以得到主动磁轴承的X轴方向的实际悬浮力
关于实际位移偏心
与实际控制电流
的X轴方向的范Kriging预测模型,具体表达为:
同理,得到Y轴方向的范Kriging预测模型为:
根据获得的X、Y轴方向的两个范Kriging预测模型,分别建立实际悬浮力
与实际位移偏心
和实际控制电流
的对应的两个模型状态表。具体是建立以下的X轴方向实际悬浮力
与实际位移偏心
和实际控制电流
的模型状态表1以及Y轴方向实际悬浮力
与实际位移偏心
和实际控制电流
的模型状态表2:
表1
表2
以表1为例,第一行为X轴方向上的实际位移偏心
第一列为实际控制电流
实际位移偏心
从0开始到最大偏心x
max,每隔0.01mm进行采样,同时,实际控制电流
从0开始,每隔0.1A进行采样。将实际位移偏心
与实际控制电流
的采样值带入公式(3)中,即可计算出当前采样值下的实际悬浮力
大小,建立模型状态表1。因此,每个实际位移偏心
与实际控制电流
都对应一个实际悬浮力
大小,如表1中F
11~F
ba所示,x
max为X轴方向的最大位移,i
max为最大控制电流。例如,以表1为例,当实际位移偏心为0.01mm,实际控制电流为0.1A时,此时的实际悬浮力大小为F
11;当实际位移偏心为0.03mm,实际控制电流为0.2A时,此时的实际悬浮力大小为F
34。其中b,a为实际位移偏心与实际控制电流的采样个数。同理,表2中实际悬浮力为F’
11~F’
ba,y
max为Y轴方向的最大位移,i
ymax为Y轴方向的最大控制电流。同理,对于表2,第一行为Y轴方向上的实际位移偏心
第一列为实际控制电流
采样方式与X轴方向上采样方式的相同,将实际位移偏心
与实际控制电流
的采样值带入公式(3)中,即可计算出当前采样值下的实际悬浮力
大小,建立模型状态表2。
对于实际位移偏心、实际控制电流不在采样点上的数据,采用插值法计算其对应的实际悬浮力大小。以X轴方向为例,设当前实际位移偏心为x
0,实际控制电流为i
0,此时,首先需要确定x
0与i
0在表一中的位置。假设{x
0,i
0}位移偏心位于x
1与点x
2之间,控制电流位于i
1与采样点i
2之间,其中x
1与x
2满足x
1+0.01mm=x
2;i
1与i
2满足i
1+0.1A=i
2,且x
1,x
2,i
1与i
2数值皆为采样点上的位移与电流数值。此时,采样点{x
1,i
1}对应的实际悬 浮力大小为F
c,d,{x
1,i
2}对应的实际悬浮力大小为F
c,d+1,{x
2,i
1}对应的实际悬浮力大小为F
c+1,d,{x
2,i
2}对应的实际悬浮力大小为F
c+1,d+1。c,d为采样点{x
1,i
1}在表一中的行列数。则此时{x
0,i
0}处的实际悬浮力可计算为:
举例,当实际位移偏心为0.025mm,实际控制电流为0.25A,根据表一中数据可以算该点的悬浮力值为
同理,对于Y轴方向上的实际位移偏心、实际控制电流不在采样点上的数据,采用雷同的插值法计算其对应的实际悬浮力大小。
将模型状态表1和表2各自分别内置于X轴方向上的查表模块和Y轴方向上的查表模块中,构造成两个查表模块。
构造如图1所示的模糊自适应PID控制器。由于主动磁轴承根据输入电流与当前位移的变化会导致模型存在一定的误差,普通控制器无法满足根据模型的调整的需求,故本发明采用模糊自适应PID控制器进行控制。图2所示为现有常用的PID控制器的结构框图,其主要包括比例部分、积分部分与微分部分三部分组成,比例部分直接由比例系数KP构成,积分部分直接由积分系数KI与积分模块∫组成,微分部分直接由微分系数KD与微分模块d/dt组成,三个部分通过求和运算∑得到最终输出。图1所示为本发明构造的X轴方向的模糊自适应PID控制器,其由模糊推理系统、比例部分、积分部分与微分部分构成,其在图2所示的现有常用PID控制器的基础上加以改进,在保留了图2中PID控制器的比例部分、积分部分与微分部分之外,增加了一个模糊推理系统。以X轴方向的模糊自适应PID控制器为例:X轴方向位移误差e
x以及其一阶微分
作为模糊推理系统的输入,模糊推理系统对位移误差e
x和一阶微分
进行计算输出比例修正系数CP、积分修正系数CI以及微分修正系数CD。将比例修正系数CP、积分修正系数CI以及微分修正系数CD分别于相应的比例系数KP、积分系数KI、微分系数KD系数相乘,得到修正后的的修正比例系数、修正积分系数与修正微分系数,其表达为:
对修正后的比例部分、积分部分与微分部分三部分通过求和运算∑得到最终输出,即位移误差e
x通过修正后的比例部分、积分部分与微分部分,即可准确地控制其输出的X轴方向的初始控制电流I
x0。
根据调节参数对系统输出性能的影响情况,制定修正系数CP、CI、CD的调节原则如下:当e
x较大时,应通过修正系数提高
减小
以及使
保持适中来提高系统的响应速度,同时防止过大的超调量;当e
x为中等大小时,通过修正系数使
保持较小值,以及使
适中来减小超调量,同时保持系统有较快的响应速度;当e
x较小时,应通过修正系数提高
以及使
保持适中来保证系统良好的稳定性,同时免系统出现振荡现象,增强系统的抗干扰性。
同理,Y轴方向的模糊自适应PID控制器的构造方向与X轴方向的模糊自适应PID控制器的构造方向雷同。Y轴方向的位移误差e
y及其一阶微分
作为对应的Y轴方向的模糊推理系统的输入,模糊推理系统输出比例修正系数CP、积分修正系数CI以及微分修正系数CD,将比例修正系数CP、积分修正系数CI以及微分修正系数CD各自分别与相应的比例系数KP、积分系数KI、微分系数KD相乘,得到相应的修正后的比例部分、积分部分与微分部分,位移误差e
y各自分别通过修正后的比例部分、积分部分与微分部分,对修正后的比例部分、积分部分与微分部分的输出分别求和运算得到Y轴方向的初始控制电流I
y0。
构造图3所示的主动磁轴承控制器,该主动磁轴承控制器由X轴、Y轴方向的两个模糊自适应PID控制器、放大器模块、查表模块、测量模块构成,连接于主动磁轴承的输入端,实现对主动磁轴承的控制。其中,X轴方向的模糊自适应PID控制器、放大器模块、查表模块串联后与主动磁轴承的输入端相连接,Y轴方向的模糊自适应PID控制器、放大器模块、查表模块串联后与主动磁轴承的输入端相连接,X、Y轴方向的两个测量模块通过位移传感器分别测得主动磁轴承X轴、Y轴方向的实际位移偏心
X轴方向的实际位移偏心
输入X轴方向的查表模块中,Y轴方向的实际位移偏心
输入Y轴方向的查表模块中。X轴方向的参考位移x
*与实际位移偏心
相减得到位移误差e
x,位移误差e
x通过X轴方向的模糊自适应PID控制器得到初始控制电流I
x0,并通过X轴方向的放大器 模块得到实际控制电流
该实际控制电流
输入X轴方向的查表模块中,X轴方向的查表模块根据模型状态表1中的数据获得此时的实际悬浮力
同理,Y轴方向的参考位移y
*与实际位移偏心
相减得到位移误差e
y,位移误差e
y通过Y轴方向的模糊自适应PID控制器得到初始控制电流I
y0,并通过Y轴方向的放大器模块得到实际控制电流
该实际控制电流
输入Y轴方向的查表模块中,Y轴方向的查表模块根据模型状态表2中的数据获得此时的实际悬浮力
并输出给主动磁轴承。即X轴、Y轴方向的查表模块分别输出对应的实际悬浮力
至至主动磁轴承,即可实现对主动磁轴承X、Y轴方向的控制。
Claims (6)
- 一种基于查表法的主动磁轴承控制器的构造方法,其特征是具有以下步骤:步骤(3):由X、Y轴方向的两个模糊自适应PID控制器、两个放大器模块、两个查表模块、两个测量模块构成主动磁轴承控制器,由X轴方向的模糊自适应PID控制器、放大器模块、查表模块串联后与主动磁轴承输入端相接,由Y轴方向的模糊自适应PID控制器、放大器模块、查表模块串联后与主动磁轴承输入端相接,X、Y轴方向的两个测量模块分别测得主动磁轴承X、Y轴方向的实际位移偏心 将实际位移偏心 各自分别输入对应的两个查表模块中,X、Y轴方向的参考位移x *、y *分别与对应的实际位移偏心 相减得到的位移误差e x、e y各自分别通过对应的模糊自适应PID控制器得到初始控制电流I x0、I y0,初始控制电流I x0、I y0各自分别通过对应的放大器模块得到实际控制电流 将实际控制电流 输入对应的查表模块中,两个查表模块输出对应的实际悬浮力 至主动磁轴承。
- 根据权利要求3所述的基于查表法的主动磁轴承控制器的构造方法,其特征是:对于实际位移偏心、实际控制电流不在采样点上的数据,采用插值法计算其实际悬浮力。
- 根据权利要求1所述的基于查表法的主动磁轴承控制器的构造方法,其特征是:步骤(3)中的模糊自适应PID控制器由模糊推理系统、比例部分、积分部分与微分部分构成,位移误差e x、e y及其一阶微分 作为对应的模糊推理系统的输入,模糊推理系统输出比例修正系数CP、积分修正系数CI以及微分修正系数CD,将比例修正系数CP、积分修正系数CI以及微分修正系数CD各自分别与相应的比例系数KP、积分系数KI、微分系数KD相乘,得到相应的修正后的比例部分、积分部分与微分部分,位移误差e x、e y各自分别通过修正后的比例部分、积分部分与微分部分,对修正后的比例部分、积分部分与微分部分的输出分别求和运算得到初始控制电流I x0、I y0。
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CN114355772B (zh) * | 2021-12-16 | 2023-07-11 | 中车株洲电力机车有限公司 | 磁浮列车静浮平衡控制参数整定方法、系统、设备及介质 |
CN115199645A (zh) * | 2022-07-11 | 2022-10-18 | 江苏大学 | 基于车辆工况因素的高稳定低功耗飞轮电池磁悬浮支承控制系统 |
CN115199645B (zh) * | 2022-07-11 | 2024-02-13 | 江苏大学 | 基于车辆工况因素的高稳定低功耗飞轮电池磁悬浮支承控制系统 |
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