CN103701386B - Based on the acquisition methods of the full rank flux observer of the Speed Sensorless Induction Motor of observation magnetic linkage error - Google Patents
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Abstract
基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器的获取方法,属于无速度传感器矢量控制全阶磁链观测器领域。解决了现有无速度传感器矢量控制系统在电机低速运行时,由于电机参数误差较大,造成全阶磁链观测器的观测准确度低,最终导致系统运行稳定性差的问题。根据以下准则获得全阶磁链观测器误差反馈矩阵系数:观测器极点实部小于异步电机极点实部,且都为负数,估计转速传递函数的零极点实部都为负数,利用估计磁链与真实磁链的误差,保证系统在电机低速运行时,等效为电流模型,系统电机高速运行时,等效为电压模型。利用转子磁链相位误差系数iλ和引入转子磁链幅值误差系数k来增加估计转速精度。具体用在无速度传感器矢量控制领域。
The invention discloses a method for obtaining a full-order flux observer without a speed sensor of an asynchronous motor based on observing flux error, and belongs to the field of full-order flux observers for speed sensorless vector control. It solves the problem that in the existing speed sensorless vector control system, when the motor is running at low speed, due to the large error of the motor parameters, the observation accuracy of the full-order flux observer is low, which eventually leads to poor system operation stability. According to the following criteria, the error feedback matrix coefficients of the full-order flux linkage observer are obtained: the real part of the pole of the observer is smaller than the real part of the pole of the asynchronous motor, and both are negative numbers, and the real parts of the zero and pole points of the estimated speed transfer function are all negative numbers, using the estimated flux linkage and The error of the real flux linkage ensures that the system is equivalent to a current model when the motor is running at low speed, and is equivalent to a voltage model when the system motor is running at high speed. Using the rotor flux phase error coefficient i λ and introducing the rotor flux magnitude error coefficient k to increase the accuracy of the estimated speed. It is specifically used in the field of speed sensorless vector control.
Description
技术领域technical field
本发明属于无速度传感器矢量控制全阶磁链观测器领域。The invention belongs to the field of a speed sensorless vector control full-order flux linkage observer.
背景技术Background technique
异步电机矢量控制技术能够实现转矩和磁链的解耦,并且具有良好的动态特性和稳态特性,所以在工业系统中得到了非常广泛的应用。在很多工业场合中要求电机能够稳定运行在低转速区域,如提升机,卷扬机,挖掘机等,但是由于控制所需的转速传感器价格昂贵且极易损坏,所以降低了调速系统的可靠性,增加了维护成本。而无速度传感器矢量控制系统在低速运行时,由于电机参数误差较大,很容易导致系统运行不稳定。综上,为了避免使用转速传感器,增强系统的使用寿命,有必要进行无速度传感器矢量控制低速稳定运行方案研究。Asynchronous motor vector control technology can realize the decoupling of torque and flux linkage, and has good dynamic characteristics and steady-state characteristics, so it has been widely used in industrial systems. In many industrial occasions, motors are required to run stably in low-speed areas, such as hoists, winches, excavators, etc., but because the speed sensors required for control are expensive and easily damaged, the reliability of the speed control system is reduced. Increased maintenance costs. However, when the speed sensorless vector control system is running at low speed, due to the large error of the motor parameters, it is easy to cause the system to run unstable. To sum up, in order to avoid the use of speed sensors and enhance the service life of the system, it is necessary to study the low-speed stable operation scheme of the speed sensorless vector control.
无速度传感器矢量控制根据观测器原理,利用异步电机动态模型构成的状态方程组估计定子和转子磁链,并引入误差反馈来提高状态变量的观测精度。由于观测器中包含转子转速变量信息,因此可以根据观测器原理设计转速自适应律观测转子转速。但是磁链观测准确度和转速观测准确度与电机参数密切相关,当电机参数不准确时,会对电机稳定运行,尤其是电机在低速运行时造成非常大的影响。当电机运行在中高速时,电机反电动势很大,所以参数对控制系统的影响相对较小,无速度传感器矢量控制系统能够保持稳定运行。但当电机运行在低速时(30rpm以下),电机反电动势较小,电机参数的影响变大,若参数不准确,会导致磁链和转子转速估计不准确,造成控制失效。异步电机参数在实际工作中不可能准确获得,而且当电机长时间运行后,电机参数也会发生较大变化,所以控制电机在低速和极低速(15rpm以下)运行时能够实现良好的转速精度和稳定性具有一定难度。According to the observer principle, the speed sensorless vector control uses the state equations composed of the dynamic model of the asynchronous motor to estimate the flux linkage of the stator and the rotor, and introduces error feedback to improve the observation accuracy of the state variables. Since the observer contains rotor speed variable information, the speed adaptive law can be designed according to the observer principle to observe the rotor speed. However, the accuracy of flux linkage observation and speed observation accuracy are closely related to the motor parameters. When the motor parameters are inaccurate, it will have a great impact on the stable operation of the motor, especially when the motor is running at low speed. When the motor is running at medium and high speeds, the back electromotive force of the motor is very large, so the influence of the parameters on the control system is relatively small, and the sensorless vector control system can maintain stable operation. But when the motor is running at low speed (below 30rpm), the back electromotive force of the motor is small, and the influence of the motor parameters becomes greater. If the parameters are inaccurate, the estimation of the flux linkage and rotor speed will be inaccurate, resulting in control failure. It is impossible to obtain the parameters of asynchronous motor accurately in actual work, and when the motor runs for a long time, the motor parameters will also change greatly, so when the motor is controlled at low speed and very low speed (below 15rpm), it can achieve good speed accuracy and Stability is somewhat difficult.
从目前现有的无速度传感器矢量控制技术来看,磁链的观测方法主要分为以下两种:1)开环磁链观测。开环磁链观测是以电机动态方程为基础的磁链计算方法,可以分为电压模型法,电流模型法以及开环全阶磁链观测器,电压模型法由于包含定子电阻参数,所以不适用与电机低速运行时,同样地,电流模型不适用与电机高速运行时。而开环全阶磁链观测器由于没有误差反馈补偿项,所以系统鲁棒性较差。2)闭环磁链观测。闭环磁链观测相比较于开环磁链观测系统引入了误差反馈项,提高了系统的鲁棒性。可以分为模型参考自适应,闭环全阶磁链观测器,闭环降阶磁链观测器和卡尔曼滤波器法。目前应用较多的为闭环全阶磁链观测器。对于该方法来说,主要解决的问题为磁链观测准确度和系统稳定性问题,这需要通过合理设计误差反馈矩阵和转速自适应律来满足要求。但现有技术中,仅仅通过设计误差反馈矩阵来单一的满足观测磁链准确度要求,或系统稳定性要求。能够同时满足两种要求的设计方法未见报道。Judging from the existing speed sensorless vector control technology, the observation methods of flux linkage are mainly divided into the following two types: 1) Open-loop flux linkage observation. Open-loop flux linkage observation is a flux linkage calculation method based on the motor dynamic equation, which can be divided into voltage model method, current model method and open-loop full-order flux linkage observer. The voltage model method is not applicable because it includes stator resistance parameters. Same as when the motor is running at low speed, the current model is not applicable when the motor is running at high speed. However, the open-loop full-order flux observer has poor system robustness because it has no error feedback compensation term. 2) Closed-loop flux linkage observation. Compared with the open-loop flux observation system, the closed-loop flux observation system introduces an error feedback item, which improves the robustness of the system. It can be divided into model reference adaptive, closed-loop full-order flux observer, closed-loop reduced-order flux observer and Kalman filter method. At present, the closed-loop full-order flux observer is widely used. For this method, the main problems to be solved are the accuracy of flux linkage observation and the stability of the system, which need to be satisfied by designing the error feedback matrix and the speed adaptive law reasonably. However, in the prior art, only the error feedback matrix is designed to meet the accuracy requirements of the observed flux linkage or the system stability requirements. A design method that can satisfy both requirements has not been reported yet.
发明内容Contents of the invention
本发明是为了解决现有无速度传感器矢量控制系统在电机低速运行时,由于电机参数误差较大,造成全阶磁链观测器的观测准确度低,最终导致系统运行稳定性差的问题,本发明提供了一种基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器的获取方法。The present invention aims to solve the problem that in the existing speed sensorless vector control system when the motor is running at low speed, the observation accuracy of the full-order flux observer is low due to the large error of the motor parameters, which ultimately leads to poor system operation stability. A method for obtaining a full-order flux observer without a speed sensor of an asynchronous motor based on observing the flux error is provided.
基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器的获取方法,该方法是基于现有的全阶磁链观测器实现的,其特征在于,该方法包括如下步骤,A method for obtaining a full-order flux observer without a speed sensor for an asynchronous motor based on observing flux linkage errors, the method is realized based on an existing full-order flux observer, and it is characterized in that the method includes the following steps,
步骤一、在满足以下3个条件时,获取4个误差反馈系数,且该4个误差反馈系数分别为g1、g2、g3和g4,将获取的4个误差反馈系数代入Step 1. When the following three conditions are met, obtain 4 error feedback coefficients, and the 4 error feedback coefficients are g 1 , g 2 , g 3 and g 4 respectively, and substitute the obtained 4 error feedback coefficients into
中,获得G,In, get G,
其中,G表示观测器的误差反馈矩阵,Among them, G represents the error feedback matrix of the observer,
3个条件分别为,The three conditions are,
条件一:观测器极点实部小于异步电机极点实部,且都为负数,Condition 1: The real part of the pole of the observer is smaller than the real part of the pole of the asynchronous motor, and both are negative numbers,
条件二:估计转速传递函数的零极点实部都为负数,Condition 2: The real parts of the poles and zeros of the estimated speed transfer function are all negative numbers,
条件三:利用估计磁链与真实磁链的误差,保证系统在电机低速运行时,等效为电流模型,系统在电机高速运行时,等效为电压模型;Condition 3: Use the error between the estimated flux linkage and the real flux linkage to ensure that the system is equivalent to a current model when the motor is running at low speed, and the system is equivalent to a voltage model when the motor is running at high speed;
步骤二、根据已知转速自适应律方程:Step 2. According to the known rotational speed adaptive law equation:
获得变形后转速自适应律方程Obtain the adaptive law equation of the rotational speed after deformation
其中,表示估计的电机转速,in, represents the estimated motor speed,
k1表示定子电流误差增益,k 1 represents the stator current error gain,
eiα表示估计定子电流与实际定子电流相比在静止坐标系下横轴的误差分量,e iα represents the error component of the horizontal axis in the stationary coordinate system between the estimated stator current and the actual stator current,
表示估计转子磁链在静止坐标系下的纵轴分量, Indicates the vertical axis component of the estimated rotor flux linkage in the stationary coordinate system,
eiβ表示估计定子电流与实际定子电流相比在静止坐标系下纵轴的误差分量,e iβ represents the error component of the vertical axis in the stationary coordinate system between the estimated stator current and the actual stator current,
表述估计转子磁链在静止坐标系下的横轴分量, Express the horizontal axis component of the estimated rotor flux linkage in the stationary coordinate system,
k2表示转子磁链误差增益,k 2 represents the rotor flux linkage error gain,
eλα表示估计转子磁链与实际转子磁链相比在静止坐标系下横轴的误差分量,e λα represents the error component of the horizontal axis in the stationary coordinate system between the estimated rotor flux linkage and the actual rotor flux linkage,
表示估计转子磁链在静止坐标系下的纵轴分量, Indicates the vertical axis component of the estimated rotor flux linkage in the stationary coordinate system,
eλβ表示估计转子磁链与实际转子磁链相比在静止坐标系下纵轴的误差分量,e λβ represents the error component of the vertical axis in the stationary coordinate system between the estimated rotor flux linkage and the actual rotor flux linkage,
表示估计转子磁链在静止坐标系下的横轴分量, Indicates the horizontal axis component of the estimated rotor flux linkage in the stationary coordinate system,
kp表示比例积分控制器的比例增益,k p represents the proportional gain of the proportional-integral controller,
ki表示比例积分控制器的积分增益,k i represents the integral gain of the proportional-integral controller,
isq表示实际定子电流在旋转坐标系下的纵轴分量,i sq represents the vertical axis component of the actual stator current in the rotating coordinate system,
表示估计转子电流在旋转坐标系下的纵轴分量, Indicates the vertical axis component of the estimated rotor current in the rotating coordinate system,
表示估计转子磁链在旋转坐标系下的横轴分量, Indicates the horizontal axis component of the estimated rotor flux linkage in the rotating coordinate system,
k表示转子磁链幅值误差系数,k represents the rotor flux amplitude error coefficient,
isd表示实际定子电流在旋转坐标系下的横轴分量,i sd represents the horizontal axis component of the actual stator current in the rotating coordinate system,
表示估计定子电流在旋转坐标系下的横轴分量, Indicates the horizontal axis component of the estimated stator current in the rotating coordinate system,
iλ表示转子磁链相位误差系数,i λ is the rotor flux phase error coefficient,
步骤三、将步骤一中获取的观测器的误差反馈矩阵G替换现有全阶磁链观测器中的误差反馈矩阵,将步骤二中获取的变形后转速自适应律方程Step 3. Replace the error feedback matrix G of the observer obtained in step 1 with the error feedback matrix in the existing full-order flux observer, and replace the transformed rotational speed adaptive law equation obtained in step 2 with
替换现有全阶磁链观测器中的转速自适应律,即成功获取基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器。To replace the speed adaptive law in the existing full-order flux observer, that is, to successfully obtain a full-order flux observer based on the observed flux error of the asynchronous motor without a speed sensor.
所述的步骤二中,根据已知转速自适应律方程:In the second step, according to the known rotational speed adaptive law equation:
获得变形后转速自适应律方程Obtain the adaptive law equation of the rotational speed after deformation
的具体过程为,The specific process is,
(公式2)中,(Equation 2),
其中,isα表示静止坐标下的横轴定子电流分量实际值,Among them, i sα represents the actual value of the stator current component on the horizontal axis in the static coordinates,
表示静止坐标下的横轴定子电流分量的估计值, represents the estimated value of the stator current component on the transverse axis in stationary coordinates,
isβ表示静止坐标下的纵轴定子电流分量实际值,表示静止坐标下的纵轴定子电流分量的估计值,i sβ represents the actual value of the stator current component on the vertical axis under the static coordinates, represents the estimated value of the stator current component on the longitudinal axis in stationary coordinates,
λrα表示静止坐标下的横轴转子磁链分量实际值,表示静止坐标下的横轴转子磁链分量估计值,λ rα represents the actual value of the flux linkage component of the horizontal axis rotor in the static coordinates, Indicates the estimated value of the flux linkage component of the horizontal axis rotor in stationary coordinates,
λrβ表示静止坐标下的纵轴转子磁链分量实际值,λ rβ represents the actual value of the flux linkage component of the longitudinal axis rotor in the static coordinates,
表示静止坐标下的纵轴转子磁链分量估计值, Indicates the estimated value of the rotor flux component on the longitudinal axis in stationary coordinates,
将(公式4)至(公式7)代入(公式2)的中,进行化简后得到:
假设在静止坐标系下,实际转子磁链矢量和估计转子磁链矢量与α坐标轴的夹角分别为θ和且θ和之差为△θ,因此,根据转子磁链矢量旋转速度等于定子电流矢量旋转速度,(公式8)经变形后得到:Assuming that in the stationary coordinate system, the actual rotor flux vector and the estimated rotor flux vector The included angles with the α coordinate axis are θ and and θ and The difference is △θ, therefore, according to the rotation speed of the rotor flux vector is equal to the rotation speed of the stator current vector, (Formula 8) can be obtained after deformation:
其中,为估计的转子磁链幅值,为实际的转子磁链幅值,△λ为实际转子磁链与估计转子磁链的幅值误差,且△λ为0,in, is the estimated rotor flux amplitude, is the actual rotor flux amplitude, △λ is the magnitude error between the actual rotor flux and the estimated rotor flux, and △λ is 0,
令make
其中,k为转子磁链幅值误差系数,Among them, k is the rotor flux amplitude error coefficient,
在异步电机中,转子磁链矢量、定子磁链矢量和定子电流矢量的空间旋转速度是一致的,在观测器中,这三者的空间旋转速度也是一致的,因此,令实际转子磁链旋转角度与估计的转子磁链旋转角度的误差,等于实际定子电流矢量旋转角度与观测的定子电流旋转角度的误差,利用余弦定理得到,In an asynchronous motor, the spatial rotation speeds of the rotor flux vector, the stator flux vector and the stator current vector are consistent, and in the observer, the spatial rotation speeds of the three are also consistent. Therefore, the actual rotor flux rotation The error between the angle and the estimated rotor flux rotation angle is equal to the error between the actual stator current vector rotation angle and the observed stator current rotation angle, which is obtained by using the cosine law,
其中,表示实际定子电流矢量,表示估计定子电流矢量幅值,in, represents the actual stator current vector, represents the estimated stator current vector magnitude,
将(公式10)和(公式11)代入到(公式9)中,获得Substituting (Equation 10) and (Equation 11) into (Equation 9) yields
将代入到(公式12)中,Will Substituting into (Equation 12),
利用PI调节器(kp+ki∫dt)替换(公式2)中的k1和k2,并将(公式13)代入到(公式2)中,即获得
所述的现有的全阶磁链观测器包括Α、B、C、G、1/s、转速自适应率、角度计算模块、一个加法器和两个减法器,所述的Α表示全阶磁链观测矩阵,B表示电压输入矩阵,C表示电流输出矩阵,1/s表示积分运算,Described existing full-order flux observer comprises A, B, C, G, 1/s, speed adaptive rate, angle calculation module, an adder and two subtractors, and described A represents full-order Flux linkage observation matrix, B represents the voltage input matrix, C represents the current output matrix, 1/s represents the integral operation,
加法器用于对B输出电压信号、Α输出的观测信号和G输出的误差补偿信号进行求和,获得转子磁链微分信号,The adder is used to sum the output voltage signal of B, the observation signal of A output and the error compensation signal of G output to obtain the rotor flux linkage differential signal,
1/s用于对加法器输出的转子磁链微分信号进行积分运算,获得转子磁链信号,并将转子磁链信号分别发送至C、Α、角度计算模块、转速自适应率,1/s is used to perform an integral operation on the differential signal of the rotor flux linkage output by the adder to obtain the rotor flux linkage signal, and send the rotor flux linkage signal to C, Α, the angle calculation module, and the speed adaptive rate, respectively.
C用于输出估计定子电流在旋转坐标系下横轴分量和估计定子电流在旋转坐标系下纵轴分量 C is used to output the horizontal axis component of the estimated stator current in the rotating coordinate system and estimate the vertical axis component of the stator current in the rotating coordinate system
其中,一个减法器用于对输入的实际定子电流旋转坐标系下横轴分量isd与估计定子电流旋转坐标系下横轴分量作差,获得的定子电流在旋转坐标系下横轴分量的误差信号,并将该定子电流在旋转坐标系下横轴分量的误差信号发送至转速自适应率和G,Among them, a subtractor is used to compare the horizontal axis component i sd of the input actual stator current rotating coordinate system and the horizontal axis component of the estimated stator current rotating coordinate system As a difference, the error signal of the horizontal axis component of the stator current in the rotating coordinate system is obtained, and the error signal of the horizontal axis component of the stator current in the rotating coordinate system is sent to the speed adaptive rate and G,
另一个减法器用于对输入的实际定子电流旋转坐标系下纵轴分量isq与估计定子电流旋转坐标系下纵轴分量作差,获得的定子电流在旋转坐标系下纵轴分量的误差信号,并将该定子电流在旋转坐标系下纵轴分量的误差信号同时发送至转速自适应率和G,Another subtractor is used to compare the vertical axis component i sq of the input actual stator current rotating coordinate system and the vertical axis component of the estimated stator current rotating coordinate system As a difference, the error signal of the stator current in the vertical axis component of the rotating coordinate system is obtained, and the error signal of the stator current in the rotating coordinate system of the vertical axis component is sent to the speed adaptive rate and G at the same time,
角度计算模块用与对转子磁链信号进行角度计算,Α用于输出观测信号,转速自适应率用于输出转速反馈信号,并将该转速反馈信号发送至Α。The angle calculation module is used to calculate the angle of the rotor flux signal, A is used to output the observation signal, and the speed adaptation rate is used to output the speed feedback signal, and the speed feedback signal is sent to A.
本发明获取的基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器具体应用在通用变频器无速度传感器矢量控制系统中,该通用变频器无速度传感器矢量控制系统的逻辑机构示意图具体参见图3。The full-order flux observer of the asynchronous motor without speed sensor based on the observation of flux linkage error obtained by the present invention is specifically applied in the general-purpose frequency converter speed sensorless vector control system, and the logic mechanism schematic diagram of the general-purpose frequency converter speed sensorless vector control system See Figure 3 for details.
本发明所述的方法是基于两相旋转坐标系下的转子磁链定向进行的,旋转dq坐标系与转子磁链矢量旋转速度一致,令d轴与转子磁链矢量重合,并计算出转子磁链矢量的旋转角度,利用该角度进行定子电流三相静止坐标系与两相旋转坐标系之间的变换,变换公式如下所示:The method of the present invention is based on the orientation of the rotor flux linkage in the two-phase rotating coordinate system. The rotating dq coordinate system is consistent with the rotation speed of the rotor flux vector, so that the d-axis coincides with the rotor flux vector, and the rotor flux vector is calculated. The rotation angle of the chain vector, which is used to transform the stator current three-phase stationary coordinate system and the two-phase rotating coordinate system, the transformation formula is as follows:
其中,θ为利用估计转子磁链计算出的转子磁场旋转角度,其计算公式为:Among them, θ is the rotation angle of the rotor magnetic field calculated by using the estimated rotor flux linkage, and its calculation formula is:
其中,isα表示实际定子电流静止坐标系下横轴分量,isβ表示实际定子电流静止坐标系下纵轴分量,iU表示三相定子电流第一相,iV表示三相定子电流第二相,iW表示三相定子电流第三相,Among them, i sα represents the horizontal axis component of the actual stator current static coordinate system, is β represents the vertical axis component of the actual stator current static coordinate system, i U represents the first phase of the three-phase stator current, and i V represents the second phase of the three-phase stator current phase, i W represents the third phase of the three-phase stator current,
最后利用电流指令和采样分解的dq轴电流构成矢量控制系统的电流内环,并输出指令电压,经过SVPWM调制后产生开关信号控制开关管的开通和关断,最终达到变频调速的目的。Finally, the current inner loop of the vector control system is formed by using the current command and the sampled and decomposed dq axis current, and the command voltage is output. After SVPWM modulation, a switching signal is generated to control the opening and closing of the switching tube, and finally achieve the purpose of frequency conversion speed regulation.
利用通用变频器无速度传感器矢量控制系统驱动和控制感应电机,该感应电机的参数如下:额定电压:380V,额定电流15.4A,额定功率为7.5Kw,额定转速为1440r/min,额定频率为50Hz,转速检测编码器线数为5000P/R,经过1028次细分后,总线数为5×106;The induction motor is driven and controlled by a general frequency converter speed sensorless vector control system. The parameters of the induction motor are as follows: rated voltage: 380V, rated current 15.4A, rated power 7.5Kw, rated speed 1440r/min, rated frequency 50Hz , the speed detection encoder line number is 5000P/R, after 1028 subdivisions, the total number is 5×10 6 ;
图4为有速度传感器矢量控制时的转子转速波形图,图4中采用的速度传感器线数为1000P/R,从图4可以看出,由于负载存在6%额定转矩的波动以及高精度编码器检测设备的应用,所以即使在有速度传感器控制时,转速仍然存在3rpm的波动,因此可以得出结论,无速度传感矢量控制的电机低速性能与有速度传感器矢量控制的电机低速性能相似,由此可知本发明提出的方法的有效性。图5为无速度传感器矢量控制时的转速波形图,图4中有速度传感器矢量控制与图5中无速度传感器矢量控制相比,转速波动没有发生很大变化,Figure 4 is the waveform diagram of the rotor speed under vector control with a speed sensor. The number of lines of the speed sensor used in Figure 4 is 1000P/R. The application of sensor detection equipment, so even when there is speed sensor control, the rotation speed still has 3rpm fluctuations, so it can be concluded that the low-speed performance of the motor without speed sensor vector control is similar to the low-speed performance of the motor with speed sensor vector control, This shows the effectiveness of the method proposed by the present invention. Fig. 5 is the rotational speed waveform diagram during the speed sensorless vector control. Compared with the speed sensor vector control in Fig. 4 and the speed sensorless vector control in Fig. 5, the rotational speed fluctuation does not change greatly.
图6为在无速度传感器矢量控制条件下,当负载波动为34%的额定转矩时,转子转速波形图,利用当负载波动为34%的额定转矩时,对本发明获得的基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器,进行抗扰动实验,系统仍然可以在极低速运行状态保持稳定,具体参见图7至图10,图7中有速度传感器矢量控制时,1.5rpm转速指令100%额定负载,负载波动为6%,图8中有速度传感器矢量控制时,1.5rpm转速指令100%额定负载,负载波动为6%,图9中无速度传感器矢量控制,1.5rpm转速指令100%额定负载,负载波动为6%,图10中无速度传感器矢量控制,1.5rpm转速指令100%额定负载,负载波动为6%,无速度传感器矢量控制和有速度传感器矢量控制相比,在电机极低速运行时的效果相似,能够保持系统稳定运行,没有出现恶劣的变化。Fig. 6 is under the speed sensorless vector control condition, when the load fluctuation is 34% of the rated torque, the rotor speed waveform diagram, using when the load fluctuation is 34% of the rated torque, based on the observed flux linkage obtained by the present invention The error-free asynchronous motor has a full-order flux observer without a speed sensor, and the anti-disturbance experiment is carried out. The system can still maintain stability at a very low speed. See Figures 7 to 10 for details. The rpm speed command is 100% of the rated load, and the load fluctuation is 6%. When there is a speed sensor vector control in Figure 8, the 1.5rpm speed command is 100% of the rated load, and the load fluctuation is 6%. In Figure 9, there is no speed sensor vector control, 1.5rpm The speed command is 100% of the rated load, and the load fluctuation is 6%. In Figure 10, the speed sensorless vector control, the 1.5rpm speed command is 100% of the rated load, and the load fluctuation is 6%. Compared with the speed sensor vector control and the speed sensor vector control , the effect is similar when the motor is running at a very low speed, and it can keep the system running stably without bad changes.
本发明为了同时保证观测器的观测准确度和系统稳定性,根据以下准则来设计全阶磁链观测器误差反馈矩阵系数:(1)观测器极点实部小于异步电机极点实部,且都为负数,使之能够保证观测磁链的收敛速度大于真实磁链的收敛速度;(2)估计转速的传递函数零极点实部都为负数,保证估计转速在任何系统增益下都能收敛;(3)利用估计磁链与真实磁链的误差,保证系统在电机低速运行时,等效为电流模型,系统在电机高速运行时,等效为电压模型,来缩小观测磁链幅值误差和相位误差;并且根据估计磁链与实际磁链的相角误差设计转速自适应律中的转子磁链相位误差系数iλ,引入转子磁链幅值误差系数k增加估计转速精度。In order to ensure the observation accuracy and system stability of the observer at the same time, the present invention designs the error feedback matrix coefficients of the full-order flux observer according to the following criteria: (1) The real part of the pole of the observer is smaller than the real part of the pole of the asynchronous motor, and both are Negative numbers, so that it can ensure that the convergence speed of the observed flux linkage is greater than that of the real flux linkage; (2) The real parts of the zero and pole points of the transfer function of the estimated rotational speed are all negative numbers, ensuring that the estimated rotational speed can converge under any system gain; ( 3) Use the error between the estimated flux linkage and the real flux linkage to ensure that the system is equivalent to a current model when the motor is running at low speed, and the system is equivalent to a voltage model when the motor is running at high speed, so as to reduce the magnitude error and phase of the observed flux linkage error; and according to the phase angle error between the estimated flux linkage and the actual flux linkage, the rotor flux linkage phase error coefficient i λ in the rotational speed adaptive law is designed, and the rotor flux linkage amplitude error coefficient k is introduced to increase the accuracy of the estimated rotational speed.
本发明带来的有益效果是,由于分别利用转速自适应律和全阶磁链误差反馈矩阵解决系统磁链估计准确度和稳定性的问题,所以能够保证电机在无速度传感器的条件下,在非常低的转速下(1.5rpm)长时间稳定运行。并且由于引入的参数较少,使得本发明具有较强的通用性。当电机运行在极低速时,本发明所述的基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器的准确度提高了30%以上,使调速系统能够稳定运行。The beneficial effect brought by the present invention is that since the problem of the accuracy and stability of the system flux linkage estimation is solved by using the rotational speed adaptive law and the full-order flux linkage error feedback matrix respectively, it can ensure that the motor can operate under the condition of no speed sensor. Stable operation for a long time at very low speed (1.5rpm). And because fewer parameters are introduced, the present invention has stronger versatility. When the motor runs at a very low speed, the accuracy of the sensorless full-order flux observer of the asynchronous motor based on the observed flux error of the present invention is increased by more than 30%, so that the speed regulating system can run stably.
附图说明Description of drawings
图1为具体实施方式三所述的现有的全阶磁链观测器的逻辑结构示意图;Fig. 1 is a schematic diagram of the logical structure of the existing full-order flux linkage observer described in the third embodiment;
图2为具体实施方式一中变形后转速自适应律方程的逻辑结构示意图;其中,PI为比例积分控制器,“”表示减法器,“”表示加法器,Fig. 2 is a schematic diagram of the logic structure of the adaptive law equation of the rotational speed after deformation in the first embodiment; wherein, PI is a proportional-integral controller, " "Denotes a subtractor," "Denotes an adder,
图3为发明内容中通用变频器无速度传感器矢量控制系统的逻辑结构示意图;其中,为转速指令信号,为磁链指令信号,为定子电流指令静止坐标系下横轴分量,为定子电流指令静止坐标系下纵轴分量,为定子电压矢量,表示定子电压矢量指令,SVPWM为空间矢量脉宽调制,dq\αβ表示旋转坐标变换,αβ\abc表示静止坐标变换;Fig. 3 is a schematic diagram of the logical structure of the general frequency converter speed sensorless vector control system in the content of the invention; wherein, is the speed command signal, is the flux linkage instruction signal, is the lower horizontal axis component of the stator current command static coordinate system, is the vertical axis component of the stator current command in the stationary coordinate system, is the stator voltage vector, Indicates stator voltage vector command, SVPWM is space vector pulse width modulation, dq\αβ indicates rotating coordinate transformation, αβ\abc indicates stationary coordinate transformation;
图4为有速度传感器矢量控制时的转子转速波形图;Fig. 4 is the waveform diagram of the rotor speed when there is speed sensor vector control;
图5为无速度传感器矢量控制时的转子转速波形图;Fig. 5 is the waveform diagram of the rotor speed during the speed sensorless vector control;
图6为在无速度传感器矢量控制条件下,当负载波动为34%的额定转矩时,转子转速波形图;Figure 6 is a waveform diagram of the rotor speed when the load fluctuation is 34% of the rated torque under the condition of speed sensorless vector control;
图7为有速度传感器矢量控制时,感应电机运行在1.5rpm时的转子转速波形图;Figure 7 is a waveform diagram of the rotor speed when the induction motor runs at 1.5rpm when there is a speed sensor vector control;
图8为有速度传感器矢量控制时,感应电机运行在1.5rpm时的定子电流、转矩电流和磁链电流的波形图;Figure 8 is a waveform diagram of the stator current, torque current and flux linkage current when the induction motor runs at 1.5rpm when there is a speed sensor vector control;
图9为无速度传感器矢量控制时,感应电机运行在1.5rpm时的转子转速波形图;Figure 9 is a waveform diagram of the rotor speed when the induction motor runs at 1.5rpm during the speed sensorless vector control;
图10为无速度传感器矢量控制时,感应电机运行在1.5rpm时的定子电流、转矩电流和磁链电流波形图。Figure 10 is the waveform diagram of stator current, torque current and flux linkage current when the induction motor is running at 1.5rpm under speed sensorless vector control.
具体实施方式detailed description
具体实施方式一:参见图2说明本实施方式,本实施方式所述的基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器的获取方法,该方法是基于现有的全阶磁链观测器实现的,该方法包括如下步骤,Specific Embodiment 1: Refer to Fig. 2 to illustrate this embodiment. The acquisition method of a full-order flux observer for an asynchronous motor without a speed sensor based on the observation of flux linkage error described in this embodiment is based on the existing full-order Flux linkage observer, the method includes the following steps,
步骤一、在满足以下3个条件时,获取4个误差反馈系数,且该4个误差反馈系数分别为g1、g2、g3和g4,将获取的4个误差反馈系数代入Step 1. When the following three conditions are met, obtain 4 error feedback coefficients, and the 4 error feedback coefficients are g 1 , g 2 , g 3 and g 4 respectively, and substitute the obtained 4 error feedback coefficients into
中,获得G,In, get G,
其中,G表示观测器的误差反馈矩阵,Among them, G represents the error feedback matrix of the observer,
3个条件分别为,The three conditions are,
条件一:观测器极点实部小于异步电机极点实部,且都为负数,Condition 1: The real part of the pole of the observer is smaller than the real part of the pole of the asynchronous motor, and both are negative numbers,
条件二:估计转速传递函数的零极点实部都为负数,Condition 2: The real parts of the poles and zeros of the estimated speed transfer function are all negative numbers,
条件三:利用估计磁链与真实磁链的误差,保证系统在电机低速运行时,等效为电流模型,系统在电机高速运行时,等效为电压模型;Condition 3: Use the error between the estimated flux linkage and the real flux linkage to ensure that the system is equivalent to a current model when the motor is running at low speed, and the system is equivalent to a voltage model when the motor is running at high speed;
步骤二、根据已知转速自适应律方程:Step 2. According to the known rotational speed adaptive law equation:
获得变形后转速自适应律方程Obtain the adaptive law equation of the rotational speed after deformation
其中,表示估计的电机转速,in, represents the estimated motor speed,
k1表示定子电流误差增益,k 1 represents the stator current error gain,
eiα表示估计定子电流与实际定子电流相比在静止坐标系下横轴的误差分量,e iα represents the error component of the horizontal axis in the stationary coordinate system between the estimated stator current and the actual stator current,
表示估计转子磁链在静止坐标系下的纵轴分量, Indicates the vertical axis component of the estimated rotor flux linkage in the stationary coordinate system,
eiβ表示估计定子电流与实际定子电流相比在静止坐标系下纵轴的误差分量,e iβ represents the error component of the vertical axis in the stationary coordinate system between the estimated stator current and the actual stator current,
表述估计转子磁链在静止坐标系下的横轴分量, Express the horizontal axis component of the estimated rotor flux linkage in the stationary coordinate system,
k2表示转子磁链误差增益,k 2 represents the rotor flux linkage error gain,
eλα表示估计转子磁链与实际转子磁链相比在静止坐标系下横轴的误差分量,e λα represents the error component of the horizontal axis in the stationary coordinate system between the estimated rotor flux linkage and the actual rotor flux linkage,
表示估计转子磁链在静止坐标系下的纵轴分量, Indicates the vertical axis component of the estimated rotor flux linkage in the stationary coordinate system,
eλβ表示估计转子磁链与实际转子磁链相比在静止坐标系下纵轴的误差分量,e λβ represents the error component of the vertical axis in the stationary coordinate system between the estimated rotor flux linkage and the actual rotor flux linkage,
表示估计转子磁链在静止坐标系下的横轴分量, Indicates the horizontal axis component of the estimated rotor flux linkage in the stationary coordinate system,
kp表示比例积分控制器的比例增益,k p represents the proportional gain of the proportional-integral controller,
ki表示比例积分控制器的积分增益,k i represents the integral gain of the proportional-integral controller,
isq表示实际定子电流在旋转坐标系下的纵轴分量,i sq represents the vertical axis component of the actual stator current in the rotating coordinate system,
表示估计转子电流在旋转坐标系下的纵轴分量, Indicates the vertical axis component of the estimated rotor current in the rotating coordinate system,
表示估计转子磁链在旋转坐标系下的横轴分量, Indicates the horizontal axis component of the estimated rotor flux linkage in the rotating coordinate system,
k表示转子磁链幅值误差系数,k represents the rotor flux amplitude error coefficient,
isd表示实际定子电流在旋转坐标系下的横轴分量,i sd represents the horizontal axis component of the actual stator current in the rotating coordinate system,
表示估计定子电流在旋转坐标系下的横轴分量, Indicates the horizontal axis component of the estimated stator current in the rotating coordinate system,
iλ表示转子磁链相位误差系数,i λ is the rotor flux phase error coefficient,
步骤三、将步骤一中获取的观测器的误差反馈矩阵G替换现有全阶磁链观测器中的误差反馈矩阵,将步骤二中获取的变形后转速自适应律方程Step 3. Replace the error feedback matrix G of the observer obtained in step 1 with the error feedback matrix in the existing full-order flux observer, and replace the transformed rotational speed adaptive law equation obtained in step 2 with
替换现有全阶磁链观测器中的转速自适应律,即成功获取基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器。To replace the speed adaptive law in the existing full-order flux observer, that is, to successfully obtain a full-order flux observer based on the observed flux error of the asynchronous motor without a speed sensor.
具体实施方式二:参见图1说明本实施方式,本实施方式与具体实施方式一所述的基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器的获取方法的区别在于,所述的步骤二中,根据已知转速自适应律方程:Specific embodiment 2: Referring to Fig. 1 to illustrate this embodiment, the difference between this embodiment and the acquisition method of a full-order flux observer without a speed sensor for an asynchronous motor based on the observation of flux linkage error described in Embodiment 1 is that the In the second step mentioned above, according to the known rotational speed adaptive law equation:
获得变形后转速自适应律方程Obtain the adaptive law equation of the rotational speed after deformation
的具体过程为,The specific process is,
(公式2)中,(Equation 2),
其中,isα表示静止坐标下的横轴定子电流分量实际值,Among them, i sα represents the actual value of the stator current component on the horizontal axis in the static coordinates,
表示静止坐标下的横轴定子电流分量的估计值, represents the estimated value of the stator current component on the transverse axis in stationary coordinates,
isβ表示静止坐标下的纵轴定子电流分量实际值,表示静止坐标下的纵轴定子电流分量的估计值,i sβ represents the actual value of the stator current component on the vertical axis under the static coordinates, represents the estimated value of the stator current component on the longitudinal axis in stationary coordinates,
λrα表示静止坐标下的横轴转子磁链分量实际值,表示静止坐标下的横轴转子磁链分量估计值,λ rα represents the actual value of the flux linkage component of the horizontal axis rotor in the static coordinates, Indicates the estimated value of the flux linkage component of the horizontal axis rotor in stationary coordinates,
λrβ表示静止坐标下的纵轴转子磁链分量实际值,λ rβ represents the actual value of the flux linkage component of the longitudinal axis rotor in the static coordinates,
表示静止坐标下的纵轴转子磁链分量估计值, Indicates the estimated value of the rotor flux component on the longitudinal axis in stationary coordinates,
将(公式4)至(公式7)代入(公式2)的中,进行化简后得到:
假设在静止坐标系下,实际转子磁链矢量和估计转子磁链矢量与α坐标轴的夹角分别为θ和且θ和之差为△θ,因此,根据转子磁链矢量旋转速度等于定子电流矢量旋转速度,(公式8)经变形后得到:
其中,为估计的转子磁链幅值,为实际的转子磁链幅值,△λ为实际转子磁链与估计转子磁链的幅值误差,且△λ为0,in, is the estimated rotor flux amplitude, is the actual rotor flux amplitude, △λ is the magnitude error between the actual rotor flux and the estimated rotor flux, and △λ is 0,
令make
其中,k为转子磁链幅值误差系数,Among them, k is the rotor flux amplitude error coefficient,
在异步电机中,转子磁链矢量、定子磁链矢量和定子电流矢量的空间旋转速度是一致的,在观测器中,这三者的空间旋转速度也是一致的,因此,令实际转子磁链旋转角度与估计的转子磁链旋转角度的误差,等于实际定子电流矢量旋转角度与观测的定子电流旋转角度的误差,利用余弦定理得到,In an asynchronous motor, the spatial rotation speeds of the rotor flux vector, the stator flux vector and the stator current vector are consistent, and in the observer, the spatial rotation speeds of the three are also consistent. Therefore, the actual rotor flux rotation The error between the angle and the estimated rotor flux rotation angle is equal to the error between the actual stator current vector rotation angle and the observed stator current rotation angle, which is obtained by using the cosine law,
其中,表示实际定子电流矢量,表示估计定子电流矢量幅值,in, represents the actual stator current vector, represents the estimated stator current vector magnitude,
将(公式10)和(公式11)代入到(公式9)中,获得Substituting (Equation 10) and (Equation 11) into (Equation 9) yields
将代入到(公式12)中,Will Substituting into (Equation 12),
利用PI调节器(kp+ki∫dt)替换(公式2)中的k1和k2,并将(公式13)代入到(公式2)中,即获得
具体实施方式三:参见图3说明本实施方式,本实施方式与具体实施方式一所述的基于观测磁链误差的异步电机无速度传感器的全阶磁链观测器的获取方法的区别在于,所述的现有的全阶磁链观测器包括Α、B、C、G、1/s、转速自适应率、角度计算模块、一个加法器和两个减法器,所述的Α表示全阶磁链观测矩阵,B表示电压输入矩阵,C表示电流输出矩阵,1/s表示积分运算,Specific embodiment three: Referring to FIG. 3 to illustrate this embodiment, the difference between this embodiment and the acquisition method of a full-order flux observer without a speed sensor for an asynchronous motor based on observing flux linkage errors described in the first embodiment is that the The existing full-order flux observer described includes A, B, C, G, 1/s, speed adaptation rate, angle calculation module, an adder and two subtractors, and the described A represents the full-order flux Chain observation matrix, B represents the voltage input matrix, C represents the current output matrix, 1/s represents the integral operation,
加法器用于对B输出电压信号、Α输出的观测信号和G输出的误差补偿信号进行求和,获得转子磁链微分信号,The adder is used to sum the output voltage signal of B, the observation signal of A output and the error compensation signal of G output to obtain the rotor flux linkage differential signal,
1/s用于对加法器输出的转子磁链微分信号进行积分运算,获得转子磁链信号,并将转子磁链信号分别发送至C、Α、角度计算模块、转速自适应率,1/s is used to perform an integral operation on the differential signal of the rotor flux linkage output by the adder to obtain the rotor flux linkage signal, and send the rotor flux linkage signal to C, Α, the angle calculation module, and the speed adaptive rate, respectively.
C用于输出估计定子电流在旋转坐标系下横轴分量和估计定子电流在旋转坐标系下纵轴分量 C is used to output the horizontal axis component of the estimated stator current in the rotating coordinate system and estimate the vertical axis component of the stator current in the rotating coordinate system
其中,一个减法器用于对输入的实际定子电流旋转坐标系下横轴分量isd与估计定子电流旋转坐标系下横轴分量作差,获得的定子电流在旋转坐标系下横轴分量的误差信号,并将该定子电流在旋转坐标系下横轴分量的误差信号发送至转速自适应率和G,Among them, a subtractor is used to compare the horizontal axis component i sd of the input actual stator current rotating coordinate system and the horizontal axis component of the estimated stator current rotating coordinate system As a difference, the error signal of the horizontal axis component of the stator current in the rotating coordinate system is obtained, and the error signal of the horizontal axis component of the stator current in the rotating coordinate system is sent to the speed adaptive rate and G,
另一个减法器用于对输入的实际定子电流旋转坐标系下纵轴分量isq与估计定子电流旋转坐标系下纵轴分量作差,获得的定子电流在旋转坐标系下纵轴分量的误差信号,并将该定子电流在旋转坐标系下纵轴分量的误差信号同时发送至转速自适应率和G,Another subtractor is used to compare the vertical axis component i sq of the input actual stator current rotating coordinate system and the vertical axis component of the estimated stator current rotating coordinate system As a difference, the error signal of the stator current in the vertical axis component of the rotating coordinate system is obtained, and the error signal of the stator current in the rotating coordinate system of the vertical axis component is sent to the speed adaptive rate and G at the same time,
角度计算模块用与对转子磁链信号进行角度计算,Α用于输出观测信号,转速自适应率用于输出转速反馈信号,并将该转速反馈信号发送至Α。The angle calculation module is used to calculate the angle of the rotor flux signal, A is used to output the observation signal, and the speed adaptation rate is used to output the speed feedback signal, and the speed feedback signal is sent to A.
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