CN104793645B - Magnetic Levitation ball position control method - Google Patents

Magnetic Levitation ball position control method Download PDF

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CN104793645B
CN104793645B CN 201510180614 CN201510180614A CN104793645B CN 104793645 B CN104793645 B CN 104793645B CN 201510180614 CN201510180614 CN 201510180614 CN 201510180614 A CN201510180614 A CN 201510180614A CN 104793645 B CN104793645 B CN 104793645B
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CN104793645A (en )
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彭辉
覃业梅
阮文杰
高家成
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中南大学
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Abstract

本发明公开了一种磁悬浮球位置控制方法,针对磁悬浮球系统难以建立精确物理模型的缺点,采用系统辨识方法建立带函数权系数型自回归模型来描述电磁绕组输入电压与钢球位置间的非线性动态特性。 The present invention discloses a method for controlling the position of the magnetic levitation suspension, it is difficult to establish a precise physical model disadvantage for magnetic levitation suspension system, the system identification method for establishing a non-function weighting coefficients belt between the input voltage and the electromagnetic winding position of the ball will be described autoregressive model linear dynamic characteristics. 该模型用钢球位置的一次线性函数作为高斯RBF网络的权系数,并用该RBF网络作为非线性自回归模型的函数型系数,使该模型能较好地刻画磁悬浮球系统的动态特性。 The model with a linear function of the position of the ball as a Gaussian RBF network weights, and by the RBF network as a nonlinear function of the type coefficients from the regression model, so the model can characterize the dynamic properties of Magnetic Levitation System. 该模型在某一时刻回归系数为常数,类似于一个线性ARX模型。 This model is the regression coefficient at a time constant, similar to a linear ARX model. 基于此,本发明设计一个时变的、局部线性的预测控制器,通过在各时刻在线求解二次规划来快速实现钢球的最优位置控制,满足磁悬浮球系统稳定、快速的要求。 Based on this, the present invention is the design of a time-varying, local linear predictive controller, each time by solving the quadratic programming line to quickly achieve the optimum position of the ball control, to meet the magnetic levitation suspension system stable, fast requirements.

Description

_种磁悬浮球位置控制方法 _ The ball levitation position control method Species

技术领域 FIELD

[0001] 本发明涉及自动控制技术领域,特别是一种磁悬浮球位置控制方法。 [0001] The present invention relates to technical field of automatic control, in particular a magnetic levitation position control method ball.

背景技术 Background technique

[0002] 磁悬浮技术是集电磁学、电子技术、控制工程、信号处理、机械学、动力学为一体的、典型的机电一体化技术。 [0002] is a set of electromagnetic levitation technology, electronic technology, control engineering, signal processing, mechanics, one of the kinetics, the typical mechatronics. 磁悬浮技术因其无接触、无摩擦、低噪声等特点已广泛应用于磁悬浮列车、磁悬浮轴承、磁悬浮电机等工程领域。 Maglev technology because of its non-contact, no friction, low noise characteristics have been widely used in maglev trains, magnetic bearings, magnetic levitation motors and other projects. 磁悬浮球系统主要是通过对电磁绕组通以一定的电流产生电磁力,使其与钢球重力相平衡,使钢球悬浮在空中而处于平衡状态,达到系统稳定运行的目的。 Magnetic Levitation System mainly through an electromagnetic force generated at a constant current through the electromagnetic coil, so that the ball equilibrium with gravity, steel balls suspended in the air is in a state of equilibrium, the purpose of stable operation of the system. 具有单一方向的磁悬浮球系统具有本质的非线性、开环不稳定、快速响应的特点,易受电源及外界环境的影响,某些参数具有较强的不确定性,无法精确测量。 Magnetic Levitation System has a single direction with a non-linear nature of open-loop unstable, the characteristics of fast response, vulnerability to power supply and the external environment, some parameters have strong uncertainty can not be accurately measured. 而且电磁场磁饱和现象使得电磁场中输入电流与磁感应强度、电磁绕组的磁通链之间不成正比关系,增大了系统的非线性并导致系统的电磁力模型无法用简单的数学方程表达;同时,处于电磁场中的钢球产生电涡流,将反过来影响电磁绕组的电感,使得电磁绕组的电感不为常数,而是关于钢球到电磁铁磁极表面的气隙g的函数,而且与其成非线性关系。 And an electromagnetic field so that magnetic saturation field is not proportional to input current and flux linkage between the magnetic flux density, the relationship between an electromagnetic coil, and increases the nonlinear system model of the system results in an electromagnetic force can not be expressed in simple mathematical equations; the same time, electromagnetic field is generated in a steel ball eddy current, in turn, will affect the inductance of the electromagnetic coil, the electromagnetic coil such that the inductance is not constant but a function of the surface of the ball to the electromagnet pole gap g, and nonlinearity therewith relationship. 因此,建立磁悬浮球系统的精确物理模型是非常困难的,这是磁悬浮球系统实现稳定控制的难点所在。 Therefore, accurate physics model Magnetic Levitation System is very difficult, this is a difficult system to achieve stable levitation ball control lies.

[0003] PID控制结构简单,可以调节输入电流/电压使钢球悬浮,不需建立磁悬浮系统的物理模型,但控制参数需要人工整定,自适应性较差,对非线性磁悬浮系统的有效控制范围较小,尤其当钢球位置变化快速时超调较大,钢球抖动较大。 [0003] PID control structure is simple and can adjust the input current / voltage causes ball suspension, without having to create a physical model of the suspension system, the control parameter requires manual tuning, poor adaptability, effective control of the nonlinear magnetic levitation system small, especially when the ball changes position quickly when the overshoot is large, larger jitter ball. 用模糊推理自动调节PID的控制参数,可以提高参数随钢球与电磁铁间气隙变化而变化的能力。 Automatically adjusting the control parameters of PID fuzzy reasoning, one can improve the ability parameter electromagnet with an air gap between the ball and variations varies. 但该方法依赖于模糊规则库,它的建立受制于设计者的经验。 However, the method relies on fuzzy rule base, which is subject to the establishment of the designer's experience. 另一方面,通过分析磁悬浮系统工作原理,在一些假设条件的基础上,建立物理模型,然后可对钢球实施自适应控制、滑膜控制、预测控制等。 On the other hand, by analyzing the principle of magnetic suspension system, based on some assumptions on the physical model, and adaptive control may be implemented, synovial control, predictive control of the ball. 这些方法实现的最大难点在于较难获得能准确描述磁悬浮系统动态特性的精确物理模型,因为,某些假设条件难以在工程应用中得到满足。 These methods are the most difficult to achieve is that the more difficult to obtain accurate physical models that accurately describe the dynamic characteristics of the suspension system, since it is difficult to certain assumptions are met in engineering applications. 此外,利用线性化技术对物理模型进行线性化处理,然后设计线性控制策略,能加快在线控制优化速度,但损失了系统非线性特性,弱化了模型对磁悬浮系统的描述能力,从而降低了控制效果。 Further, with the technique of linear physical model linear processing, a linear control strategy and then design, optimized speed control to speed up the line, but the loss characteristics of the nonlinear system, weakening the ability of the model description of the magnetic levitation system, thereby reducing control effect .

发明内容 SUMMARY

[0004] 本发明所要解决的技术问题是,针对现有技术不足,提供一种磁悬浮球位置控制方法。 [0004] The present invention solves the technical problem, for the deficiencies of the prior art, there is provided a magnetic levitation position control method ball.

[0005] 为解决上述技术问题,本发明所采用的技术方案是:一种磁悬浮球位置控制方法, 适用于上下移动的单自由度磁悬浮球系统,所述单自由度磁悬浮球系统包括产生电磁场的线圈绕组和检测钢球位置的光电传感器;所述电磁绕组输入电压由控制器控制驱动电路给出;所述光电传感器采集的钢球位置信号通过数据采集卡传送给控制计算机。 [0005] To solve the above technical problem, the technical solution employed in the present invention is: A method of controlling the position of the magnetic levitation suspension, the degree of freedom for a single magnetic levitation suspension system moves up and down, the magnetic levitation suspension system comprises a single degree of freedom of generating an electromagnetic field and a detection coil winding photosensor ball position; said electromagnetic winding input voltage is given by a controller controls the driving circuit; a signal to the control computer the position of the photosensor balls collected by the data acquisition card transfer. 对磁悬浮球系统建立自回归模型: Since the establishment of regression model Magnetic Levitation System:

Figure CN104793645BD00051

[0007] 其中,g(t)为磁悬浮球的位置;u (t)为电磁绕组输入电压;ξ (t)为白噪声; [0007] wherein, g (t) is the position of the magnetic levitation suspension; u (t) is the input voltage of the electromagnetic coil; ξ (t) is white noise;

Figure CN104793645BD00052

和Vju为RBF网络的权系数,是钢球位置的一次线性函类 And Vju as the RBF network weights, is a linear function of the position of the ball type

Figure CN104793645BD00053

为常数系数,通过SNPOM优化方法辨识,在获得非线性参数的基础上用最小二乘法计算获得。 Is a constant coefficient, by identifying methods to optimize SNPOM, obtained by calculation based on the least squares method to obtain the nonlinear parameters.

[0008] 然后基于所述自回归模型设计预测控制器,优化下列二次规划函数J获得最优控制量,控制磁悬浮球的位置g(t): [0008] Then, based on the autoregressive model predictive controller design, the following quadratic programming optimization function J to obtain optimal control, controlling the position of the ball maglev g (t):

Figure CN104793645BD00054

[0010] 其中 [0010] in which

Figure CN104793645BD00055

为t时刻1步向前钢球位置预测变量,根据t时刻所述自回归模型获得1步预测的表达式,即 Time t 1 is the position predictors paces ball, according to the time t obtained from the regression model prediction expression step 1, i.e.

Figure CN104793645BD00056

^为系统预测系数矩阵,由t时刻所述自回归模型及多步预测变量获獨 ^ Prediction coefficient matrix for the system, the time t and the multi-step autoregressive model independent predictors eligible

Figure CN104793645BD00057

为t时刻给定的1步向前参考位置 T is the time given a step forward reference position

Figure CN104793645BD00058

2,3为t 时刻要优化的电磁绕组输入电压,仅取第一项u (t)作用于被控磁悬浮球; 3 is a time t to be optimized electromagnetic winding input voltage, taking only the first term u (t) acting on the charged magnetic levitation suspension;

Figure CN104793645BD00059

为输入电压增量; Input voltage increment;

Figure CN104793645BD000510

Figure CN104793645BD00061

^和巾/为自回归模型的回归函数系数,φ'=0;1为单位矩阵。 ^ Towel and / autoregressive model regression function coefficients, φ '= 0; 1 is the identity matrix.

[0011] 与现有技术相比,本发明所具有的有益效果为:本发明采用系统辨识建模的思想, 利用系统实际运行的输入/输出数据包含系统动态特性的相关信息建立磁悬浮球系统的动态模型,可以最大可能地描述出系统的动态特性,而不用考虑磁饱和现象及涡流效应对模型的影响(这些影响均已包含在辨识数据中)。 [0011] Compared with the prior art, the present invention has beneficial effects: the present invention uses thought identification modeling system using the actual operating system information input / output data including dynamic characteristics of the system to establish Magnetic Levitation System dynamic models can describe the maximum possible dynamic characteristics of the system, without regard to the effect of magnetic saturation and eddy current effect of the model (these effects have been included in the identification data). 该方法适用于这类强非线性、强不确定性的复杂系统,可推广至其他类似系统;本发明建立的带函数权RBF-ARX模型的RBF网络系数依存于钢球在电磁场中的位置,提高了RBF网络的函数逼近能力,使获得的一组伪线性ARX模型能更好地描述非线性磁悬浮球系统的动态特性。 The method is applicable to such strongly nonlinear and uncertain complex system, may be extended to other similar systems; on RBF network RBF-ARX model coefficients with weight function of the present invention depends on establishing the position of the ball in the electromagnetic field, improve the RBF network function approximation capabilities, so that a set of pseudo-linear ARX model obtained better describe the dynamic behavior of nonlinear Magnetic levitation system. 系统的一步预测输出建模误差在± 0.4%以内;本发明基于带函数权RBF-ARX模型设计时变的、局部线性的预测控制器,能快速优化计算最优控制量,减少在线优化时间,有利于在磁悬浮球系统采样周期(5毫秒)内完成优化计算,实现对钢球位置的快速、稳定控制。 Step predictive model error within ± 0.4%; weight function with RBF-ARX model based design variant of the present invention, the local linear predictive controller calculates the optimal control can quickly optimize the amount of time to reduce the online optimization, facilitate optimization is done in the magnetic levitation suspension system sampling period (5 ms) is calculated, fast, stable position control of the ball.

附图说明 BRIEF DESCRIPTION

[0012] 图1为本发明磁悬浮球系统结构图。 [0012] FIG configuration diagram of a magnetic levitation suspension system of the present invention.

具体实施方式 detailed description

[0013] 本发明磁悬浮球系统的系统结构如图1所示,是一个仅能控制钢球上下方向移动的单自由度系统。 [0013] Magnetic Levitation System architecture of the present invention as shown, is only a single degree of freedom system to control vertical movement of the ball 1. PC机9通过控制器输出控制电压,经D/A转换器8传输给电磁绕组驱动电路6,电磁绕组2在通以相应电流的情况下产生电磁感应,在绕组下方形成电磁场,对处于场中的钢球1施加电磁感应力F,使钢球上/下移动,调整电磁铁与钢球间的气隙g (即钢球位置), 直至电磁力F与钢球重力G平衡;同时,LED光源3与光电板4构成的光电传感器用来检测钢球位置,相应的电压信号经处理电路5及A/D转换器7传回PC机输出。 PC, the output voltage controlled by the controller 9, the D / A converter 8 is transmitted to the electromagnetic coil driving circuit 6, an electromagnetic coil 2 through electromagnetic induction in a corresponding current flow, an electromagnetic field is formed below the winding, in the field of the ball 1 is applied a magnetic force F, so that the ball moves up / down, adjusting the air gap G (i.e., the position of the ball) between the electromagnet and the ball, and the ball until the electromagnetic force F G balance gravity; Meanwhile, LED the light source 3 and the plate 4 photovoltaic photosensor for detecting the position of the balls, a corresponding voltage signal processing circuit 5 and a / D converter 7 outputs the PC returned. 图1所示系统中,钢球1的半径为12.5毫米、质量为22克,电磁绕组2的匝数为2450、等效电阻为13.8欧姆。 The system shown in Figure 1, ball 1 radius of 12.5 mm, mass of 22 g, the number of turns of the electromagnetic coil 2 of 2450, an equivalent resistance of 13.8 ohms.

[0014] 本发明所述磁悬浮球系统受到磁饱和及涡流效应影响,还受到电源及外界干扰的影响。 [0014] The magnetic levitation suspension system of the present invention and the influence of the magnetic saturation by the eddy current effect is also influenced by the power supply and external disturbances. 为此,采用基于带函数权RBF-ARX模型的建模方法,构建电磁绕组输入电压与电磁场中钢球位置间关系的动态模型。 For this reason, the method using the RBF-ARX model modeling with weight function based on the dynamic model constructing an electromagnetic winding voltage input positional relationship between the ball and the electromagnetic field. 在本发明中,利用数据辨识技术,采用钢球位置的线性函数作权系数的、高斯核的RBF网络作为非线性ARX模型中的函数系数。 In the present invention, the use of data identification techniques using linear weight coefficients as a function of the position of the ball, Gaussian RBF kernel nonlinear coefficient as a function of network ARX model. 该模型是一种具有线性ARX模型结构的非线性时变模型,它的自变量是电磁绕组输入电压、钢球位置的回归量,钢球位置为表征系统状态的信号量,采用与钢球位置线性相关的函数逼近RBF神经网络的常数权,然后用该RBF结构对模型参数进行实时在线调整。 The model is a nonlinear model with varying linearly the ARX model structure, its argument is an input voltage of the electromagnetic coil, the amount of the return ball position, ball position signal indicative of an amount of the system state, and the ball position using Related constant linear function approximation RBF neural network weights, and then the structure parameters of the model RBF real time adjustments. 带函数权RBF-ARX模型在局部的线性区间内与线性ARX模型非常近似,另外它的参数能随着系统非线性状态而自动更新、自动调整,具有良好的全局适应特性。 With weight function RBF-ARX model in the linear interval local linear ARX model is very similar, additional parameters that can be automatically updated with the state of nonlinear systems, automatic adjustment, having a better global adaptability.

[0015] 构建钢球位置与电磁绕组输入电压间动态特性模型的函数权系数型RBF-ARX模型,采用列维布格马奎尔特方法(Levenberg-Marquardt Method,LMM)和线性最小二乘法(Least Square Method,LSM)相结合的SNPOM优化方法(详见:Peng H,0zaki T,Haggan-Ozaki VjToyoda Y.2003?A parameter optimization method for the radial basis function type models)辨识该模型参数,获得如下结构: [0015] Construction of the ball between the position of the electromagnetic coil type weight coefficient function of input voltage RBF-ARX model of the dynamic characteristic model, using the method of Stewart 列维布格马奎 (Levenberg-Marquardt Method, LMM), and a linear least squares ( Least Square method, LSM) SNPOM combined optimization method (see:? Peng H, 0zaki T, Haggan-Ozaki VjToyoda Y.2003 a parameter optimization method for the radial basis function type models) identifying the model parameters, the following structure is obtained :

Figure CN104793645BD00071

[0019] g (t)为钢球的位置,也是钢球与电磁铁间的气隙;u (t)为电磁绕组的输入电压;Φο、φ,和Cf分别为自回归模型的回归函数系数;W (t-ι)为系统工作点状态, 用钢球位置g (ti)来表征系统工作点状态;ν'if和G为钢球位置的一次线性函数,作为RBF神经网络的函数权系数;II · II为2范数;ξ (t)为白噪声; Regression function coefficients Φο, φ, and Cf are autoregressive model; [0019] g (t) is the position of the ball, the ball is an air gap between the electromagnet; u (t) is the input voltage of the electromagnetic coil ; W (t-ι) operating point for the system state, the position of the ball with g (ti) to characterize the status of the operating point of the system; ν'if a linear function of the position of the ball and G, as a function of the RBF neural network weights ; II · II for the 2-norm; ξ (t) is white noise;

Figure CN104793645BD00072

为线性常数系数,通过SNPOM优化方法辨识,在获得非线性参数的基础上用LSM计算获得。 Linear constant coefficient, by optimizing SNPOM identification method, to obtain LSM used calculated on the basis of the obtained nonlinear parameters. make

Figure CN104793645BD00073

Θ# = {0.03,1.33,11,74,-3.82},式⑴改写为 Θ # = {0.03,1.33,11,74, -3.82}, the formula is rewritten as ⑴

Figure CN104793645BD00074

Figure CN104793645BD00075

[0021] 其中,5V)为钢球位置的观测数据,SNPOM进行模型辨识时共使用4000个观测数据。 4000 observations were used [0021] wherein, 5V) is observed ball position data, SNPOM for model identification.

[0022] 利用磁悬浮球系统局部线性的特性设计时变、线性的预测控制器。 [0022] Magnetic Levitation System using local linear time-varying characteristics of the design, the linear predictive controller. 将式⑴改写为多项式 The formula ⑴ rewritten as a polynomial

Figure CN104793645BD00076

[0025] 定义系统的状态变量: [0025] The definition of the system state variables:

Figure CN104793645BD00081

[0027]则式⑴的状态空间模型为: [0027] ⑴ state space model is the formula:

Figure CN104793645BD00082

[0031]上式中Φ 〇、Φ f和Φ /1不是常数,而是随着钢球位置g (t)而变化。 [0031] [Phi] billion above formula, Φ f and Φ / 1 is not constant, but the position of the ball with g (t) is changed. 定义相关的预测变量: Define the relevant predictor variables:

Figure CN104793645BD00083

[0033] 其中,吩)是多步向前预测状态向量,紛)是钢球位置多步向前预测向量,ύ(〇是绕组输入电压多步向前预测向量。假设u (t+j) =U (t+3) (j彡4),从(5)〜(7),可以得到: [0033] wherein, thiophene) is a multi-step ahead predicted state vector, numerous) position of the ball is a multi-step ahead prediction vector, ύ (square input voltage winding is a multi-step ahead prediction vector. Suppose u (t + j) = U (t + 3) (j San 4), from (5) to (7) can be obtained:

Figure CN104793645BD00084

[0035] 这里: [0035] here:

Figure CN104793645BD00085

勺系统预测系数矩阵,可由式(5)〜⑶获得,依赖于t时刻电磁场中钢球的位置,均为随钢球位置g (t)变化的值。 Spoon prediction coefficient matrix system, ~⑶ obtained by equation (5), dependent on the position of the ball in the field at time t, both the position of the ball with the change in the value of g (t).

Figure CN104793645BD00086

Figure CN104793645BD00091

[0038] 故而可针对磁悬浮球系统在t时刻的带函数权RBF-ARX模型的局部线性特性设计随t而变化的线性预测控制器。 [0038] and therefore may be directed Magnetic Levitation System Design of Linear Predictive Controller t varies with local linear characteristic with RBF-ARX model function of time t weight.

[0039] 定义控制增量MU)及期望输出变量i.(i) [0039] defined incremental control MU) and the desired output variable i. (I)

Figure CN104793645BD00092

[0041]则有局部线性预测控制的二次规划优化函数 [0041] There is a Local Linear Predictive Control quadratic programming optimization function

Figure CN104793645BD00093

[0044] 对磁悬浮球系统,式(13)为一个二次规划的优化问题,通过在线优化即可获得最优控制量。 [0044] The magnetic levitation ball system, formula (13) is a quadratic programming optimization problem, you can obtain optimal control through online optimization. 从而将非线性磁悬浮球系统的预测控制简化为随钢球位置状态变化的、线性的预测控制,能大大节约最优控制量的在线优化时间,使钢球快速地达到稳定状态。 Thereby simplifying nonlinear predictive control for Magnetic Suspension System with a change in position of the ball, the linear predictive control, optimal control can greatly reduce the amount of time online optimization, allow the balls to quickly reach a steady state.

Claims (2)

  1. 1. 一种磁悬浮球位置控制方法,其特征在于,包括以下步骤: 1) 对磁悬浮球系统建立自回归模型: A magnetic levitation ball position control method, characterized by comprising the following steps: 1) Magnetic Levitation System established autoregressive model:
    Figure CN104793645BC00021
    其中,g⑴为t时刻磁悬浮球的位置;U⑴为电磁绕组输入电压;ξ⑴为白噪声; Wherein, g⑴ is a magnetic levitation position of the ball at time t; U⑴ input voltage to the electromagnetic coil; ξ⑴ white noise;
    Figure CN104793645BC00022
    ;
    Figure CN104793645BC00023
    为RBF网络的权系数, 是钢球位置的一次线性函数; Weights for the RBF network, is a linear function of the position of the ball;
    Figure CN104793645BC00024
    为常数系数,通过SNPOM优化方法辨识;g (t-Ι)为t-Ι时刻磁悬浮球的位置; 2) 基于所述自回归模型设计预测控制器,优化下列二次规划函数J获得最优控制量,控制磁悬浮球的位置g(t): Is a constant coefficient, identification by SNPOM optimization; g (t-Ι) of t-Ι time levitation position of the ball; 2) based on the autoregressive model predictive controller design, the following quadratic programming optimization function J to obtain optimal control amount, controlling the position of the ball maglev g (t):
    Figure CN104793645BC00025
    其中: among them:
    Figure CN104793645BC00026
    ,gi· (t + i)为t时刻给定的1步向前参考位置,1 = 1,2,…,12; , Gi · (t + i) is given at time t 1 the reference step forward position, 1 = 1,2, ..., 12;
    Figure CN104793645BC00027
    ,.u (t+p)为t时刻要优化的电磁绕组输入电压,仅取第一项u (t)作用于被控磁悬浮球,p = 0,1,2,3 ; , .u (t + p) is the time t to optimize electromagnetic winding input voltage, taking only the first term u (t) acting on the charged magnetic levitation suspension, p = 0,1,2,3;
    Figure CN104793645BC00028
    ,Au(t) = u(t)-u(tl)为输入电压增量; , Au (t) = u (t) -u (tl) is the input voltage increment;
    Figure CN104793645BC00029
    为系统预测系数矩阵; System prediction coefficient matrix;
    Figure CN104793645BC000210
    为状态向量; State vector;
    Figure CN104793645BC000211
    Figure CN104793645BC000212
    为自回归模型的回归函数系数,为单位矩阵;112为12阶单位矩阵;I4为4 阶单位矩阵。 Autoregressive coefficients of the model regression function, a unit matrix; 112 is a unit matrix of order 12; I4 fourth-order matrix.
    Figure CN104793645BC000213
  2. 2. 根据权利要求1所述的磁悬浮球位置控制方法,其特征在于, The magnetic levitation ball position control method according to claim 1, characterized in that,
    Figure CN104793645BC00031
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CN1599228A (en) * 2004-09-10 2005-03-23 宁波天明电子股份有限公司 Magnetic suspension device of float capable of random two-way automatic rotation and its control system
JP4348428B2 (en) * 2003-05-27 2009-10-21 独立行政法人 宇宙航空研究開発機構 Inter-axis interference mitigation method and apparatus for controlling magnetic suspension Model

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JP4348428B2 (en) * 2003-05-27 2009-10-21 独立行政法人 宇宙航空研究開発機構 Inter-axis interference mitigation method and apparatus for controlling magnetic suspension Model
CN1599228A (en) * 2004-09-10 2005-03-23 宁波天明电子股份有限公司 Magnetic suspension device of float capable of random two-way automatic rotation and its control system

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