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CN116191963A - Estimation Method of Motor Rotor Position and Speed Based on Accelerated Nesterov Algorithm - Google Patents

Estimation Method of Motor Rotor Position and Speed Based on Accelerated Nesterov Algorithm Download PDF

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CN116191963A
CN116191963A CN202310257207.6A CN202310257207A CN116191963A CN 116191963 A CN116191963 A CN 116191963A CN 202310257207 A CN202310257207 A CN 202310257207A CN 116191963 A CN116191963 A CN 116191963A
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speed
rotor
formula
rotor position
cost function
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张彦平
苏明
尹忠刚
安宁
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Xian University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters with pulse width modulation
    • H02P27/12—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters with pulse width modulation pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2203/00—Indexing scheme relating to controlling arrangements characterised by the means for detecting the position of the rotor
    • H02P2203/03—Determination of the rotor position, e.g. initial rotor position, during standstill or low speed operation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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  • Power Engineering (AREA)
  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses a motor rotor position and speed estimation method based on an acceleration Fresnel-off algorithm, which specifically comprises the following steps: step 1, establishing a discrete mathematical model of a high-speed permanent magnet synchronous motor, and constructing a cost function of the speed and the position of a full-speed domain rotor of the high-speed permanent magnet synchronous motor; step 2, adopting an acceleration Fresnel to solve the minimum value of the speed and position cost function of the full-speed domain rotor constructed in the step 1; and 3, estimating the rotor position and the rotating speed of the high-speed permanent magnet synchronous motor through the phase-locked loop by the minimum value obtained in the step 2. The invention solves the problems of low estimation precision of the rotor position in a high-speed area and easy oscillation of the rotor position and the rotating speed in a composite area of the existing high-speed permanent magnet synchronous motor rotor position and rotating speed estimation method by constructing a high-convexity full-speed domain rotor speed and position cost function and adopting an acceleration Fresnel method to solve the minimum value of the rotor speed and position cost function.

Description

基于加速涅斯特洛夫算法的电机转子位置与速度估算方法Motor rotor position and speed estimation method based on accelerated Nesterov algorithm

技术领域Technical Field

本发明涉及高速永磁同步电机控制技术领域，具体为基于加速涅斯特洛夫算法的电机转子位置与速度估算方法。The invention relates to the technical field of high-speed permanent magnet synchronous motor control, and in particular to a method for estimating the position and speed of a motor rotor based on an accelerated Nesterov algorithm.

背景技术Background Art

转速超过10000r/mi n的永磁同步电机称为高速永磁同步电机，高速永磁同步电机因其功率密度高、转速高、体积小等优点，广泛应用在军工、航空航天、工业等领域。通常通过在转子上安装机械编码器获得高速永磁同步电机转子位置和转速，然而，高速永磁同步电机要求转子尽量短以保证转子具有足够的机械强度和刚度，因此难以在转子上安装机械编码器，并且通常的机械编码器难以检测高速永磁同步电机转速超过10000r/mi n时的转子位置和转速。因此，研究一种可应用于高速永磁同步电机的转子位置和转速估计方法尤为重要。Permanent magnet synchronous motors with speeds exceeding 10000r/min are called high-speed permanent magnet synchronous motors. High-speed permanent magnet synchronous motors are widely used in military, aerospace, and industrial fields due to their high power density, high speed, and small size. Usually, the rotor position and speed of a high-speed permanent magnet synchronous motor are obtained by installing a mechanical encoder on the rotor. However, a high-speed permanent magnet synchronous motor requires the rotor to be as short as possible to ensure that the rotor has sufficient mechanical strength and stiffness. Therefore, it is difficult to install a mechanical encoder on the rotor, and it is difficult for a common mechanical encoder to detect the rotor position and speed of a high-speed permanent magnet synchronous motor when the speed exceeds 10000r/min. Therefore, it is particularly important to study a rotor position and speed estimation method that can be applied to high-speed permanent magnet synchronous motors.

目前，高速永磁同步电机的转子位置和转速估计方法主要包括：滑模观测器、卡尔曼滤波、模型参考自适应等。由于这些方法具有低通滤波特性，当高速永磁同步电机在高速运行时，估计的转子位置严重滞后实际转子位置，导致电流环不能完全解耦，甚至导致系统发散。并且，目前单一的转子位置和转速估计方法难以估计高速永磁同步电机全速域的转速位置和转速，通常通过复合适合低速的估计方法和适合中高速的估计方法估计高速永磁同步电机全速域转子位置和转速。然而，高速永磁同步电机转动惯量小，快速启动时两种转子位置和转速估计方法复合区转子位置和转速易发生振荡，甚至启动失败。At present, the rotor position and speed estimation methods of high-speed permanent magnet synchronous motors mainly include: sliding mode observer, Kalman filter, model reference adaptation, etc. Since these methods have low-pass filtering characteristics, when the high-speed permanent magnet synchronous motor is running at high speed, the estimated rotor position seriously lags behind the actual rotor position, resulting in the inability to completely decouple the current loop and even causing system divergence. In addition, the current single rotor position and speed estimation method is difficult to estimate the speed position and speed of the high-speed permanent magnet synchronous motor in the full speed range. Usually, the rotor position and speed of the high-speed permanent magnet synchronous motor in the full speed range are estimated by combining an estimation method suitable for low speed and an estimation method suitable for medium and high speed. However, the high-speed permanent magnet synchronous motor has a small moment of inertia. During rapid startup, the rotor position and speed of the two rotor position and speed estimation methods are prone to oscillation in the compound area, and even startup failure.

发明内容Summary of the invention

本发明的目的是提供一种基于加速涅斯特洛夫的高速永磁同步电机转子位置和转速估计方法，解决了现有高速永磁同步电机转子位置和转速估计方法在高速区转子位置估计精度低以及复合区转子位置和转速易发生振荡的问题。The purpose of the present invention is to provide a method for estimating the rotor position and speed of a high-speed permanent magnet synchronous motor based on the accelerated Nesterov, which solves the problems of low rotor position estimation accuracy in the high-speed zone and easy oscillation of the rotor position and speed in the composite zone in the existing high-speed permanent magnet synchronous motor rotor position and speed estimation methods.

为实现上述目的，本发明采用的技术方案是：基于加速涅斯特洛夫算法的电机转子位置与速度估算方法，具体包括以下步骤：To achieve the above object, the technical solution adopted by the present invention is: a method for estimating the position and speed of a motor rotor based on the accelerated Nesterov algorithm, which specifically includes the following steps:

步骤1，建立高速永磁同步电机的离散数学模型，构建高速永磁同步电机全速域转子速度与位置的代价函数；Step 1, establish a discrete mathematical model of a high-speed permanent magnet synchronous motor, and construct a cost function of the rotor speed and position of the high-speed permanent magnet synchronous motor in the full speed range;

步骤2，采用加速涅斯特洛夫算法求解步骤1构建的全速域转子速度和位置代价函数的最小值；Step 2, using the accelerated Nesterov algorithm to solve the minimum value of the full-speed domain rotor speed and position cost function constructed in step 1;

步骤3，由步骤2中得到的最小值通过锁相环估计高速永磁同步电机的转子位置和转速。Step 3: Estimate the rotor position and speed of the high-speed permanent magnet synchronous motor through a phase-locked loop using the minimum value obtained in step 2.

优选的，所述步骤1的具体步骤为：Preferably, the specific steps of step 1 are:

步骤1.1，建立高速永磁同步电机的离散数学模型；Step 1.1, establish a discrete mathematical model of the high-speed permanent magnet synchronous motor;

静止坐标系下的高速永磁同步电机电压方程如下式(1)所示：The voltage equation of the high-speed permanent magnet synchronous motor in the stationary coordinate system is shown in the following equation (1):

Figure BDA0004130084110000021
Figure BDA0004130084110000021

式(1)中，vα是定子电压在α轴的分量；vβ是定子电压在β轴的分量，iα是α轴的分量，iβ是定子电流在β轴的分量，R是定子电阻，p是微分算子，φm是转子磁链，ωe是转子电角速度，θe是转子位置；Lα是α轴的电感，Lαβ是α轴的互感，Lβ是β轴的电感，Lα、Lβ、Lαβ分别表示为：In formula (1), vα is the component of the stator voltage on the α-axis; vβ is the component of the stator voltage on the β-axis, iα is the component of the α-axis, iβ is the component of the stator current on the β-axis, R is the stator resistance, p is the differential operator, φm is the rotor flux, ωe is the rotor electrical angular velocity, θe is the rotor position; Lα is the inductance of the α-axis, Lαβ is the mutual inductance of the α-axis, Lβ is the inductance of the β-axis, and Lα , Lβ , and Lαβ are respectively expressed as:

Figure BDA0004130084110000022
Figure BDA0004130084110000022

式(2)中，Ld是d轴电感，Lq是q轴电感；In formula (2), Ld is the d-axis inductance, and Lq is the q-axis inductance;

对公式(1)进行离散化如下公式(3)所示：Formula (1) is discretized as shown in the following formula (3):

Figure BDA0004130084110000031
Figure BDA0004130084110000031

式(3)中，

Figure BDA0004130084110000032
Δθre是本拍转子位置和上一拍转子位置的差值，k是当前拍采样时刻，k-1是上一拍采样时刻，Ts是采样周期；In formula (3),
Figure BDA0004130084110000032
Δθ re is the difference between the rotor position of the current beat and the rotor position of the previous beat, k is the sampling time of the current beat, k-1 is the sampling time of the previous beat, and T s is the sampling period;

步骤1.2，构建高速永磁同步电机全速域转子速度与位置代价函数；Step 1.2, construct the rotor speed and position cost function of the high-speed permanent magnet synchronous motor in the full speed range;

对公式(3)的左半部分进行范数平方，转子速度ωe与转子位置θe作为未知数，构建的转子速度ωe与转子位置θe的代价函数可以写为公式(4)所示：The norm of the left half of formula (3) is squared, and the rotor speed ω e and the rotor position θ e are taken as unknowns. The cost function of the rotor speed ω e and the rotor position θ e can be written as shown in formula (4):

Figure BDA0004130084110000033
Figure BDA0004130084110000033

式(4)中，H(θe(k),ωe(k))是转子速度ωe与转子位置θe的代价函数；In formula (4), H(θ e (k), ω e (k)) is the cost function of rotor speed ω e and rotor position θ e ;

代价函数公式(4)的凸度随速度的降低凸度越小，在零速、低速时代价函数凸度很小，几乎是平坦的曲线，代价函数的凸度越小求解最小值的收敛越慢；为了增加零速、低速时代价函数凸度，在10％额定转速以下在d轴注入高频方波电压信号，注入的高频方波电压信号如下公式(5)所示：The convexity of the cost function formula (4) decreases as the speed decreases. At zero speed and low speed, the convexity of the cost function is very small, almost a flat curve. The smaller the convexity of the cost function, the slower the convergence of the minimum value. In order to increase the convexity of the cost function at zero speed and low speed, a high-frequency square wave voltage signal is injected into the d-axis below 10% of the rated speed. The injected high-frequency square wave voltage signal is shown in the following formula (5):

Figure BDA0004130084110000034
Figure BDA0004130084110000034

式(5)中，udh(k)、uqh(k)分别高频方波电压信号在d、q轴的分量，Vh是高频方波电压的幅值；In formula (5), u dh (k) and u qh (k) are the components of the high-frequency square wave voltage signal on the d and q axes respectively, and V h is the amplitude of the high-frequency square wave voltage;

注入的高频方波电压信号产生的α、β轴的高频电流响应如公式(6)所示：The high-frequency current response of the α and β axes generated by the injected high-frequency square wave voltage signal is shown in formula (6):

Figure BDA0004130084110000041
Figure BDA0004130084110000041

式(6)中，iαh(k)是第k拍采样的高频电流响应在α轴的分量，iβh(k)是第k拍采样的高频电流响应在β轴的分量；In formula (6), i αh (k) is the component of the high-frequency current response sampled at the kth beat on the α-axis, and i βh (k) is the component of the high-frequency current response sampled at the kth beat on the β-axis;

注入高频方波电压后转子速度ωe与转子位置θe代价函数如公式(7)所示：After injecting high-frequency square wave voltage, the cost function of rotor speed ωe and rotor position θe is shown in formula (7):

Figure BDA0004130084110000042
Figure BDA0004130084110000042

式(7)中，iαh(k-1)是第k-1拍采样的高频电流在α轴分量，iβh(k-1)是第k-1拍采样的高频电流在β轴分量，iα(k-1)、iβ(k-1)是第k-1拍采样的定子电流在α、β轴分量，iβ(k-1)是第k-1拍采样的定子电流在β轴分量；In formula (7), i αh (k-1) is the α-axis component of the high-frequency current sampled at the k-1th beat, i βh (k-1) is the β-axis component of the high-frequency current sampled at the k-1th beat, i α (k-1), i β (k-1) are the α-axis and β-axis components of the stator current sampled at the k-1th beat, and i β (k-1) is the β-axis component of the stator current sampled at the k-1th beat;

在额定速度10％以下时，转子速度ωe与转子位置θe代价函数如公式(7)所示，在额定速度10％以上转子速度和位置代价函数如公式(4)所示，全速域转子速度ωe与转子位置θe代价函数如下公式(8)所示：When the rated speed is below 10%, the rotor speed ωe and rotor position θe cost functions are shown in formula (7). When the rated speed is above 10%, the rotor speed and position cost functions are shown in formula (4). The full-speed range rotor speed ωe and rotor position θe cost functions are shown in formula (8):

式(8)中，ωrate是额定转速；In formula (8), ω rate is the rated speed;

公式(8)为局部凸函数，当估算的速度和位置等于实际转子速度和位置时，公式(8)达到最小值；Formula (8) is a local convex function. When the estimated speed and position are equal to the actual rotor speed and position, formula (8) reaches the minimum value;

Figure BDA0004130084110000051
Figure BDA0004130084110000051

估算转子速度和位置等效为求解公式(8)的最小值，如下公式(9)所示：Estimating the rotor speed and position is equivalent to solving the minimum value of formula (8), as shown in the following formula (9):

Figure BDA0004130084110000052
Figure BDA0004130084110000052

式(9)中，D为搜索域，

Figure BDA0004130084110000053
为估算位置，
Figure BDA0004130084110000054
为估算速度，最小值在局部范围D内求取。In formula (9), D is the search domain,
Figure BDA0004130084110000053
To estimate the position,
Figure BDA0004130084110000054
To estimate the velocity, the minimum is found in the local range D.

优选的，所述步骤2的具体过程为：Preferably, the specific process of step 2 is:

加速涅斯特洛夫算法如下公式(10)所示：The accelerated Nesterov algorithm is shown in the following formula (10):

Figure BDA0004130084110000055
Figure BDA0004130084110000055

式(10)中，n为迭代次数，

Figure BDA0004130084110000056
是第n-1次迭代转子速度ωe与转子位置θe代价函数对转子位置的偏导数，
Figure BDA0004130084110000061
是第n-1次迭代转子速度ωe与转子位置θe代价函数对转速的偏导数，y1 (n)是n次迭代转子位置的动量项，y1 (n)是n次迭代速度的动量项,y1 (k-1)是n-1次迭代转子位置的动量项，y2 (k-1)是n-1次迭代转子速度的动量项，δ是学习率，γ为动量参数；In formula (10), n is the number of iterations,
Figure BDA0004130084110000056
is the partial derivative of the cost function of the rotor speed ωe and rotor position θe at the n-1th iteration with respect to the rotor position,
Figure BDA0004130084110000061
is the partial derivative of the cost function of the rotor speed ω e and the rotor position θ e at the n-1th iteration with respect to the speed, y 1 (n) is the momentum term of the rotor position at the nth iteration, y 1 (n) is the momentum term of the speed at the nth iteration, y 1 (k-1) is the momentum term of the rotor position at the n-1th iteration, y 2 (k-1) is the momentum term of the rotor speed at the n-1th iteration, δ is the learning rate, and γ is the momentum parameter;

动量参数γ的大小会影响收敛速度的快慢，根据代价函数随着转速的增大凸度越大的特性自适应调节动量参数γ，如下公式(11)所示；The size of the momentum parameter γ will affect the speed of convergence. According to the characteristic of the cost function that the convexity increases with the increase of the rotation speed, the momentum parameter γ is adaptively adjusted, as shown in the following formula (11);

Figure BDA0004130084110000062
Figure BDA0004130084110000062

式(11)中，

Figure BDA0004130084110000063
为第n次迭代的梯度，
Figure BDA0004130084110000064
T为矩阵的转置，i为常数，指1和2；In formula (11),
Figure BDA0004130084110000063
is the gradient of the nth iteration,
Figure BDA0004130084110000064
T is the transpose of the matrix, i is a constant, which refers to 1 and 2;

当转速小于1046rpm且

Figure BDA0004130084110000065
时，动量参数设置0，防止迭代震荡，当转速小于1046rpm且
Figure BDA0004130084110000066
时，初始值点距离最优值接近，动量参数γ设置为0.25，随着转速上升，令动量参数γ随着转速的升高而增大；When the speed is less than 1046rpm and
Figure BDA0004130084110000065
When the speed is less than 1046 rpm and
Figure BDA0004130084110000066
When , the initial value point is close to the optimal value, and the momentum parameter γ is set to 0.25. As the speed increases, the momentum parameter γ increases with the increase of the speed;

采用加速涅斯特洛夫算法估计转子位置与速度的迭代过程如下：The iterative process of estimating rotor position and speed using the accelerated Nesterov algorithm is as follows:

步骤1)给定迭代初始值θe (0)＝θe(k-1)、ωe (0)＝ωe(k-1)，设置最大迭代次数nmax≥1，收敛精度ε＝1×10-5；Step 1) Given the initial iteration values θ e (0) =θ e (k-1), ω e (0) =ω e (k-1), set the maximum number of iterations n max ≥ 1, and the convergence accuracy ε = 1×10 -5 ;

步骤2)根据公式(8)计算全速域转子速度ωe与转子位置θe代价函数；Step 2) Calculate the full-speed range rotor speed ωe and rotor position θe cost function according to formula (8);

步骤3)根据公式(11)计算动量参数γ；Step 3) Calculate the momentum parameter γ according to formula (11);

步骤4)根据公式(10)计算本次迭代的转子速度ωe与转子位置θe；Step 4) Calculate the rotor speed ω e and rotor position θ e of this iteration according to formula (10);

步骤5)根据

Figure BDA0004130084110000071
判断是否收敛，若满足
Figure BDA0004130084110000072
则结束本次寻优并输出本拍的转子位置θe(k)＝θe (n)和速度ωe(k)＝ωe (n)；若不满足
Figure BDA0004130084110000073
则判断本次迭代次数n是否大于最大迭代次数nmax，若n≥nmax则结束本次寻优并输出本拍的转子位置θe(k)＝θe(k-1)+ωe(k-1)Ts和速度ωe(k)＝ωe(k-1)，否则设置n＝n+1，返回步骤2)。Step 5) According to
Figure BDA0004130084110000071
Determine whether it converges. If it satisfies
Figure BDA0004130084110000072
Then the optimization is terminated and the rotor position θ e (k) = θ e (n) and speed ω e (k) = ω e (n) of this beat are output; if it is not satisfied
Figure BDA0004130084110000073
Then determine whether the number of iterations n is greater than the maximum number of iterations n max . If n ≥ n max , end the optimization and output the rotor position θ e (k) = θ e (k-1) + ω e (k-1) T s and speed ω e (k) = ω e (k-1) of this beat . Otherwise , set n = n + 1 and return to step 2 ).

优选的，所述步骤3具体过程为：Preferably, the specific process of step 3 is:

由步骤2中得到的第k拍的转子位置θe(k)与锁相环上一拍输出的转子位置θe_PLL(k-1)做差，经过PI之后得到估计的转速如下公式(12)所示：The rotor position θe (k) of the kth beat obtained in step 2 is subtracted from the rotor position θe_PLL (k-1) output by the previous beat of the phase-locked loop, and the estimated speed is obtained after PI as shown in the following formula (12):

Figure BDA0004130084110000074
Figure BDA0004130084110000074

式(12)中，转速环与电流环都有PI控制器，PI是比例积分控制器；Kp是比例系数，Ki是积分系数，ωe_PLL(k)是第k拍锁相环输出的速度，θe_PLL(k-1)是第k-1拍锁相环输出的转子位置；In formula (12), both the speed loop and the current loop have PI controllers, PI is a proportional integral controller; Kp is the proportional coefficient, Ki is the integral coefficient, ωe_PLL (k) is the speed output by the k-th phase-locked loop, θe_PLL (k-1) is the rotor position output by the k-1th phase-locked loop;

由公式(12)估计的速度ωe_PLL(k)通过积分得到估计转子位置如下公式(13)所示：The speed ω e_PLL (k) estimated by formula (12) is integrated to obtain the estimated rotor position as shown in the following formula (13):

θe_PLL(k)＝θe_PLL(k-1)+ωe_PLL(k)Ts (13)θ e_PLL (k)＝θ e_PLL (k-1)+ω e_PLL (k)T s (13)

式(13)中，θe_PLL(k)是第k拍锁相环输出的转子位置。In formula (13), θ e_PLL (k) is the rotor position output by the k-th phase-locked loop.

本发明的有益效果：本发明提供的基于加速涅斯特洛夫算法的电机转子位置与速度估算方法，通过构建高凸度全速域转子速度和位置代价函数，采用加速涅斯特洛夫算法求解转子速度和位置代价函数的最小值，从而提高了高速区转子位置估计精度，全速域采用单一的方法估计转子位置与转速，从根本上解决了全速域复合区转子位置和转速易发生振荡的问题。Beneficial effects of the present invention: The motor rotor position and speed estimation method based on the accelerated Nesterov algorithm provided by the present invention constructs a high-convex full-speed domain rotor speed and position cost function, and adopts the accelerated Nesterov algorithm to solve the minimum value of the rotor speed and position cost function, thereby improving the rotor position estimation accuracy in the high-speed zone. A single method is used in the full-speed domain to estimate the rotor position and speed, fundamentally solving the problem that the rotor position and speed are prone to oscillation in the composite zone of the full-speed domain.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1是本发明基于加速涅斯特洛夫算法的电机转子位置与速度估算方法的控制系统框图；FIG1 is a control system block diagram of a method for estimating the position and speed of a motor rotor based on an accelerated Nesterov algorithm according to the present invention;

图2是零速、低速不注入高频方波电压时在不同转速下转子速度与位置代价函数的仿真结果；FIG2 is the simulation result of the rotor speed and position cost function at different speeds when the high-frequency square wave voltage is not injected at zero speed and low speed;

图3是低速50rpm时注入和不注入高频方波电压的转子速度与位置代价函数的对比仿真结果；FIG3 is a simulation result comparing the rotor speed and position cost functions with and without high-frequency square wave voltage injection at a low speed of 50 rpm;

图4是本发明基于加速涅斯特洛夫算法的电机转子位置与速度估算方法所采用锁相环框图；4 is a block diagram of a phase-locked loop used in the motor rotor position and speed estimation method based on the accelerated Nesterov algorithm of the present invention;

图5是本发明的基于加速涅斯特洛夫算法的电机转子位置与速度估算方法所采用的加速涅斯特洛夫方法估计转子位置与速度的迭代过程流程图。5 is a flowchart of an iterative process of estimating rotor position and speed using the accelerated Nesterov algorithm used in the motor rotor position and speed estimation method based on the accelerated Nesterov algorithm of the present invention.

具体实施方式DETAILED DESCRIPTION

下面将结合附图对本发明中的技术方案进行清楚、完整地描述。The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings.

如图1-5所示所示；As shown in Figure 1-5;

通过两相静止坐标系下的uα(k)、uβ(k)、iα(k)、iβ(k)和上一拍的ωe(k-1)和θe(k-1)作为如图5所示加速涅斯特洛夫估计转子位置与速度模块的输入，加速涅斯特洛夫估计转子位置与速度模块的输出是转子位置θe(k)和转速ωe(k)；转子位置θe(k)作为如图4所示锁相环的输入，锁相环的输出为估计的转子位置θe_PLL(k)和转速ωe_PLL(k)；给定值转速

Figure BDA0004130084110000081
与转速ωe_PLL(k)做差作为速度环PI的输入，速度环P I的输出为给定q轴定子电流
Figure BDA0004130084110000082
通过电流霍尔传感器检测三相静止坐标系定子电流ia(k)、ib(k)、ic(k)；检测的三相定子电流ia(k)、ib(k)、ic(k)通过abc/αβ变换得到两相静止坐标系下电流值iα(k)、iβ(k)；iα(k)、iβ(k)通过αβ/dq变换得到两相同步旋转坐标系下电流值id(k)、iq(k)；给定q轴定子电流
Figure BDA0004130084110000091
与电流值iq(k)做差作为q轴电流环P I的输入，q轴电流环P I的输出为q轴电压指令uq(k)；给定d轴定子电流
Figure BDA0004130084110000092
与电流值id(k)做差作为d轴电流环PI的输入，d轴电流环PI的输出为d轴电压指令ud(k)；若转速ωe_PLL(k)小于等于10％的额定转速，d轴电压指令ud(k)与高频电压udh(k)的和与q轴电压指令uq(k)通过dq/αβ变换得到两相静止坐标系下电压指令uα(k)、uβ(k)；若转速ωe_PLL(k)大于10％的额定转速，d轴电压指令ud(k)与q轴电压指令uq(k)通过dq/αβ变换得到两相静止坐标系下电压指令uα(k)、uβ(k)；uα(k)、uβ(k)作为空间矢量调制的输入，经过空间矢量调制控制三相逆变器驱动高速永磁同步电机工作。u α (k), u β (k), i α (k), i β (k) in the two-phase stationary coordinate system and ω e (k-1) and θ e (k-1) of the previous beat are used as the input of the accelerated Nesterov estimation module of the rotor position and speed as shown in FIG5 , and the output of the accelerated Nesterov estimation module of the rotor position and speed is the rotor position θ e (k) and the speed ω e (k); the rotor position θ e (k) is used as the input of the phase-locked loop as shown in FIG4 , and the output of the phase-locked loop is the estimated rotor position θ e_PLL (k) and the speed ω e_PLL (k); the given value speed
Figure BDA0004130084110000081
The difference between the speed and the speed ω e_PLL (k) is used as the input of the speed loop PI. The output of the speed loop PI is the given q-axis stator current.
Figure BDA0004130084110000082
The three-phase stationary coordinate system stator currents i a (k), i b (k), and i c (k) are detected by the current Hall sensor; the detected three-phase stator currents i a (k), i b (k), and i c (k) are transformed by abc/αβ to obtain the current values i α (k) and i β (k) in the two-phase stationary coordinate system; i α (k) and i β (k) are transformed by αβ/dq to obtain the current values i d (k) and i q (k) in the two-phase synchronous rotating coordinate system; the q-axis stator current is given
Figure BDA0004130084110000091
The difference between the current value iq (k) and the current value iq (k) is used as the input of the q-axis current loop PI. The output of the q-axis current loop PI is the q-axis voltage command uq(k); Given the d-axis stator current
Figure BDA0004130084110000092
The difference between the current value i d (k) and the current value i d (k) is used as the input of the d-axis current loop PI, and the output of the d-axis current loop PI is the d-axis voltage command u d (k); if the speed ω e _ PLL (k) is less than or equal to 10% of the rated speed, the sum of the d-axis voltage command u d (k) and the high-frequency voltage u dh (k) and the q-axis voltage command u q (k) are transformed through dq/αβ to obtain the voltage commands u α (k) and u β (k) in the two-phase stationary coordinate system; if the speed ω e _ PLL (k) is greater than 10% of the rated speed, the d-axis voltage command u d (k) and the q-axis voltage command u q (k) are transformed through dq/αβ to obtain the voltage commands u α (k) and u β (k) in the two-phase stationary coordinate system; u α (k) and u β (k) are used as the input of space vector modulation, and the three-phase inverter is controlled to drive the high-speed permanent magnet synchronous motor through space vector modulation.

最后应说明的是：以上所述仅为本发明的优选实施例而已，并不用于限制本发明，尽管参照前述实施例对本发明进行了详细的说明，对于本领域的技术人员来说，其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分技术特征进行等同替换，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims (4)

1. The motor rotor position and speed estimation method based on the acceleration Fresnel algorithm is characterized by comprising the following steps of:
step 1, establishing a discrete mathematical model of a high-speed permanent magnet synchronous motor, and constructing a cost function of the speed and the position of a full-speed domain rotor of the high-speed permanent magnet synchronous motor;
step 2, solving the minimum value of the speed and position cost function of the full-speed domain rotor constructed in the step 1 by adopting an acceleration Fresnel algorithm;
and 3, estimating the rotor position and the rotating speed of the high-speed permanent magnet synchronous motor through the phase-locked loop by the minimum value obtained in the step 2.
2. The method for estimating the position and the speed of the motor rotor based on the accelerated fresnel algorithm according to claim 1, wherein the specific steps of step 1 are as follows:
step 1.1, establishing a discrete mathematical model of a high-speed permanent magnet synchronous motor;
the voltage equation of the high-speed permanent magnet synchronous motor under the static coordinate system is shown in the following formula (1):
Figure FDA0004130084090000011
in the formula (1), v α Is the component of the stator voltage on the alpha axis; v β Is the component of the stator voltage on the beta axis, i α Is the component of the alpha-axis, i β Is the component of the stator current in the beta axis, R is the stator resistance, p is the differential operator, phi m Is the rotor flux linkage omega e Is the rotor electric angular velocity, theta e Is the rotor position; l (L) α Is the inductance of the alpha axis, L αβ Is the mutual inductance of the alpha axis, L β Is the inductance of the beta axis, L α 、L β 、L αβ Expressed as:
Figure FDA0004130084090000012
in the formula (2), L d Is d-axis inductance, L q Is the q-axis inductance;
discretizing the formula (1) is shown in the following formula (3):
Figure FDA0004130084090000021
in the formula (3), the amino acid sequence of the compound,
Figure FDA0004130084090000022
Δθ re is the difference between the rotor position of the current beat and the rotor position of the last beat, k is the current beat sampling time, k-1 is the last beat sampling time, T s Is the sampling period;
step 1.2, constructing a full-speed domain rotor speed and position cost function of the high-speed permanent magnet synchronous motor;
the left half of equation (3) is subjected to norm square, rotor speed ω e And rotor position theta e As an unknown, the rotor speed ω is built e And rotor position theta e Can be written as shown in equation (4):
Figure FDA0004130084090000023
in the formula (4), H (θ) e (k),ω e (k) Is rotor speed omega e And rotor position theta e Is a cost function of (2);
the convexity of the cost function formula (4) is smaller along with the speed, the convexity of the cost function is very small at zero speed and low speed and is a nearly flat curve, and the smaller the convexity of the cost function is, the slower the convergence of the minimum value is solved; in order to increase the convexity of the price function in the zero-speed and low-speed time, a high-frequency square wave voltage signal is injected into the d-axis below 10% of rated rotation speed, and the injected high-frequency square wave voltage signal is shown in the following formula (5):
Figure FDA0004130084090000024
in the formula (5), u dh (k)、u qh (k) Components of the high-frequency square wave voltage signal on d and q axes respectively, V h Is the amplitude of the high frequency square wave voltage;
the high-frequency current response of the alpha and beta axes generated by the injected high-frequency square wave voltage signal is shown in the formula (6):
Figure FDA0004130084090000031
in the formula (6), i αh (k) Is the component of the high frequency current response sampled at the kth beat in the alpha axis, i βh (k) Is the component of the high frequency current response sampled at the kth beat in the beta axis;
rotor speed omega after injection of high frequency square wave voltage e And rotor position theta e The cost function is shown in equation (7):
Figure FDA0004130084090000032
in the formula (7), i αh (k-1) is that the high frequency current sampled at the kth-1 beat has an alpha-axis component, i βh (k-1) is the beta-axis component, i, of the high frequency current sampled at the kth-1 beat α (k-1)、i β (k-1) is the component of the stator current sampled at the k-1 th beat in the alpha and beta axes, i β (k-1) is the β axis component of the stator current sampled at beat k-1;
at a rated speed of 10% or less, the rotor speed ω e And rotor position theta e The cost function is shown in formula (7);
the rotor speed and position cost function above 10% of rated speed is shown in formula (4);
full speed domain rotor speed omega e And rotor position theta e The cost function is shown in the following equation (8): in the formula (8), ω rate Is the rated rotation speed; equation (8) is a local convex function, and equation (8) reaches a minimum when the estimated speed and position are equal to the actual rotor speed and position;
Figure FDA0004130084090000041
estimating the rotor speed and position equivalent to the minimum value of the solution formula (8), as shown in the following formula (9):
Figure FDA0004130084090000042
in the formula (9), D is a search domain,
Figure FDA0004130084090000043
for estimating the position +.>
Figure FDA0004130084090000044
For estimating the speed, the minimum value is found within the local range D.
3. The method for estimating the position and the speed of the motor rotor based on the accelerated fresnel algorithm according to claim 1, wherein the specific process of the step 2 is as follows:
the accelerating fresnel algorithm is shown in the following formula (10):
Figure FDA0004130084090000045
in the formula (10), n is the iteration number,
Figure FDA0004130084090000051
is the n-1 th iteration rotor speed omega e And rotor position theta e Partial derivative of the cost function with respect to the rotor position, +.>
Figure FDA0004130084090000052
Is the n-1 th iteration rotor speed omega e And rotor position theta e Partial derivative of the cost function with respect to the rotational speed, y 1 (n) Is the momentum term of the rotor position for n iterations, y 1 (n) Momentum term, y, which is the velocity of n iterations 1 (k-1) Momentum term, y, being the rotor position of n-1 iterations 2 (k-1) Momentum items of the rotor speed of n-1 times of iteration are obtained, delta is a learning rate, and gamma is a momentum parameter;
the magnitude of the momentum parameter gamma can influence the speed of convergence, and the momentum parameter gamma is adaptively adjusted according to the characteristic that the convexity of the cost function is larger along with the increase of the rotating speed, as shown in the following formula (11);
Figure FDA0004130084090000053
in the formula (11), the amino acid sequence of the compound,
Figure FDA0004130084090000054
gradient for the nth iteration, +.>
Figure FDA0004130084090000055
T isTranspose of matrix, i is a constant, referring to 1 and 2;
when the rotating speed is less than 1046rpm
Figure FDA0004130084090000056
When the rotation speed is less than 1046rpm and +.>
Figure FDA0004130084090000057
When the initial value point is close to the optimal value, the momentum parameter gamma is set to 0.25, and the momentum parameter gamma is increased along with the increase of the rotating speed;
the iterative process of estimating rotor position and speed using the accelerated fresnel algorithm is as follows:
step 1) giving an iteration initial value θ e (0) ＝θ e (k-1)、ω e (0) ＝ω e (k-1) setting a maximum number of iterations n max Not less than 1, convergence accuracy ε=1×10 -5 ；
Step 2) calculating the full-speed-domain rotor speed ω according to equation (8) e And rotor position theta e A cost function;
step 3) calculating a momentum parameter gamma according to a formula (11);
step 4) calculating the rotor speed omega of the current iteration according to the formula (10) e And rotor position theta e ；
Step 5) according to
Figure FDA0004130084090000061
Judging whether to converge, if yes>
Figure FDA0004130084090000062
Then the current optimizing is ended and the rotor position theta of the current beat is output e (k)＝θ e (n) And velocity omega e (k)＝ω e (n) The method comprises the steps of carrying out a first treatment on the surface of the If it does not meet
Figure FDA0004130084090000063
Then judge the bookWhether the number of iterations n is greater than the maximum number of iterations n max If n is greater than or equal to n max Then the current optimizing is ended and the rotor position theta of the current beat is output e (k)＝θ e (k-1)+ω e (k-1)T s And velocity omega e (k)＝ω e (k-1), otherwise, setting n=n+1, and returning to step 2).
4. The method for estimating the position and the speed of the motor rotor based on the accelerated fresnel algorithm according to claim 1, wherein the specific process of the step 3 is as follows:
rotor position θ from the kth beat obtained in step 2 e (k) With rotor position theta output by one beat on the phase-locked loop e_PLL (k-1) taking the difference, and obtaining the estimated rotation speed after PI as shown in the following formula (12):
Figure FDA0004130084090000064
in the formula (12), the rotating speed ring and the current ring are provided with PI controllers, and PI is a proportional integral controller; k (K) p Is a proportionality coefficient, K i Is the integral coefficient omega e_PLL (k) Is the speed of the output of the kth beat phase locked loop, θ e_PLL (k-1) is the rotor position of the output of the kth-1 beat phase locked loop;
the velocity ω estimated by equation (12) e_PLL (k) The estimated rotor position obtained by integration is shown in the following equation (13):
θ e_PLL (k)＝θ e_PLL (k-1)+ω e_PLL (k)T s (13)
in the formula (13), θ e_PLL (k) Is the rotor position of the kth beat phase locked loop output.
CN202310257207.6A 2023-03-16 2023-03-16 Estimation Method of Motor Rotor Position and Speed Based on Accelerated Nesterov Algorithm Pending CN116191963A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP4475426A1 (en) * 2023-06-06 2024-12-11 Siemens Gamesa Renewable Energy A/S Position observer for synchronous machines
CN119171791A (en) * 2024-11-21 2024-12-20 浙江大学 Position sensorless control method and device for synchronous motor

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP4475426A1 (en) * 2023-06-06 2024-12-11 Siemens Gamesa Renewable Energy A/S Position observer for synchronous machines
WO2024251491A1 (en) * 2023-06-06 2024-12-12 Siemens Gamesa Renewable Energy A/S Position observer for synchronous machines
CN119171791A (en) * 2024-11-21 2024-12-20 浙江大学 Position sensorless control method and device for synchronous motor
CN119171791B (en) * 2024-11-21 2025-03-25 浙江大学 Synchronous motor position sensorless control method and device

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