CN109167547A - Based on the PMSM method for controlling position-less sensor for improving sliding mode observer - Google Patents

Based on the PMSM method for controlling position-less sensor for improving sliding mode observer Download PDF

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CN109167547A
CN109167547A CN201810936075.9A CN201810936075A CN109167547A CN 109167547 A CN109167547 A CN 109167547A CN 201810936075 A CN201810936075 A CN 201810936075A CN 109167547 A CN109167547 A CN 109167547A
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observer
phase
sliding mode
torque
stator
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周长攀
唐伟
孙向东
周兆吉
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Xian University of Technology
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/24Vector control not involving the use of rotor position or rotor speed sensors
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13Observer control, e.g. using Luenberger observers or Kalman filters
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02Arrangements 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
    • H02P25/022Synchronous motors
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02Arrangements 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
    • H02P25/022Synchronous motors
    • H02P25/024Synchronous motors controlled by supply frequency
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05Synchronous machines, e.g. with permanent magnets or DC excitation

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

Abstract

本发明公开了一种基于改进滑模观测器的PMSM无位置传感器控制方法,采用可变边界层厚度的sigmoid函数代替符号函数,并且构建反电动势观测器用于分离反电动势信号,消除了低通滤波器以及相位补偿环节,同时可以使观测器增益随速度大小动态调整,有效抑制了滑模观测器的抖振现象并获得宽调速范围内的理想观测精度。在改进滑模观测器中加入定子电阻在线辨识和转矩观测环节,提高了系统对内部和外部参数变化的鲁棒性。

The invention discloses a PMSM sensorless control method based on an improved sliding mode observer. The sigmoid function with variable boundary layer thickness is used to replace the sign function, and a back electromotive force observer is constructed to separate back electromotive force signals, eliminating low-pass filtering. At the same time, the gain of the observer can be dynamically adjusted with the speed, which effectively suppresses the chattering phenomenon of the sliding mode observer and obtains the ideal observation accuracy in a wide speed regulation range. The online identification of stator resistance and torque observation are added to the improved sliding mode observer, which improves the robustness of the system to changes in internal and external parameters.

Description

基于改进滑模观测器的PMSM无位置传感器控制方法Position Sensorless Control Method for PMSM Based on Improved Sliding Mode Observer

技术领域technical field

本发明属于电机无位置传感器控制技术领域,具体涉及一种基于 改进滑模观测器的PMSM无位置传感器控制方法。The invention belongs to the technical field of motor position sensorless control, and in particular relates to a PMSM position sensorless control method based on an improved sliding mode observer.

背景技术Background technique

永磁同步电机(permanent magnet synchronous machines,PMSM) 具有高功率密度、高效率、结构简单的优点,因而在工业领域得到了 广泛的应用。Permanent magnet synchronous machines (PMSM) have the advantages of high power density, high efficiency and simple structure, so they have been widely used in the industrial field.

为了对永磁同步电机进行精确地控制,需要转子的位置信息和转 速信息,因此需要在电机轴上安装位置传感器。但会增加系统的成本 和复杂性,降低系统的可靠性。因此永磁同步电机无位置传感器控制 成为了研究热点。In order to accurately control the permanent magnet synchronous motor, the position information and speed information of the rotor are required, so it is necessary to install a position sensor on the motor shaft. But it will increase the cost and complexity of the system and reduce the reliability of the system. Therefore, the sensorless control of permanent magnet synchronous motor has become a research hotspot.

目前永磁同步电机的无位置传感器控制策略主要可以分为两类: 一类为基于观测器的估计策略;另一类是利用电机凸极特性的高频信 号注入法。基于观测器的估计策略主要有模型参考自适应法和扩展卡 尔曼滤波法。这类方法依赖于电机模型的精度,影响了估计性能。高 频信号注入法不依赖电机模型,但会带来噪声,并且要求电机转子具 有一定的凸极性,适用范围受到限制。鉴于上述问题,由于滑模观测 器(Sliding Mode Observer,SMO)结构简单并且具有较强的鲁棒性, 在一定程度上弥补了观测器对电机数学模型的依赖性,因而广泛应用 于交流电机控制系统。At present, the sensorless control strategies of PMSM can be mainly divided into two categories: one is the estimation strategy based on the observer; the other is the high-frequency signal injection method using the salient pole characteristics of the motor. The estimation strategies based on the observer mainly include the model reference adaptive method and the extended Kalman filter method. Such methods rely on the accuracy of the motor model, which affects the estimation performance. The high-frequency signal injection method does not depend on the motor model, but it will bring noise and require the motor rotor to have a certain saliency, so the scope of application is limited. In view of the above problems, the Sliding Mode Observer (SMO) is widely used in AC motor control because of its simple structure and strong robustness, making up for the dependence of the observer on the mathematical model of the motor to a certain extent. system.

滑模观测器中采用的是不连续的开关控制,因此抖振现象是滑模 变结构系统的固有特征。为了减小抖振,需要对观测结果进行低通滤 波和转子角度补偿,角度补偿又依赖转子转速,因此增加了系统的复 杂性并且不能满足高性能应用的控制需求。The discontinuous switching control is used in the sliding mode observer, so chattering is an inherent feature of the sliding mode variable structure system. In order to reduce buffeting, low-pass filtering and rotor angle compensation are required for the observation results, which in turn depends on the rotor speed, which increases the complexity of the system and cannot meet the control requirements of high-performance applications.

采用sigmoid函数作为控制函数可以减弱抖振现象,但是会降低滑模 观测器的鲁棒性。Using the sigmoid function as the control function can reduce the chattering phenomenon, but it will reduce the robustness of the sliding mode observer.

发明内容SUMMARY OF THE INVENTION

本发明的目的是提供一种基于改进滑模观测器的PMSM无位置 传感器控制方法,基于改进滑模观测器,同时对外界转矩扰动和内部 电阻参数变化进行辨识,解决了现有滑模观测器中观测信号抖振现象 较大,需要进行低通滤波和转子角度补偿并且系统鲁棒性不高的问题。The purpose of the present invention is to provide a PMSM sensorless control method based on an improved sliding mode observer. Based on the improved sliding mode observer, the external torque disturbance and the change of internal resistance parameters are simultaneously identified, which solves the problem of the existing sliding mode observation method. The observed signal chattering phenomenon in the device is large, which requires low-pass filtering and rotor angle compensation, and the system is not robust.

本发明所采用的技术方案,一种基于改进滑模观测器的PMSM 无位置传感器控制方法,包括以下步骤:The technical solution adopted by the present invention, a PMSM sensorless control method based on an improved sliding mode observer, includes the following steps:

步骤1,计算永磁同步电机在两相静止坐标系下定子电流的观测 值以及反电动势的观测值再以定子电流的观测误差 作为滑模面,构建改进滑模电流观测器方程,同时根据转速改变 sigmoid函数的反馈增益k;Step 1. Calculate the observed value of the stator current of the permanent magnet synchronous motor in the two-phase stationary coordinate system and the observed value of the back EMF Then, the observation error of the stator current is used as the sliding mode surface, and the improved sliding mode current observer equation is constructed, and the feedback gain k of the sigmoid function is changed according to the rotation speed;

步骤2,利用步骤1中得到的反电动势观测值构建反电动 势观测器数学模型,计算转速估计值再经过锁相环估算转子位 置;Step 2, use the back EMF observations obtained in step 1 Build the mathematical model of the back EMF observer and calculate the speed estimate Then estimate the rotor position through the phase-locked loop;

步骤3,利用定子电流的观测值和实际值iα、iβ构建Lyapunov 函数,对步骤2的反电动势观测器进行稳定性分析;Step 3, using the observed value of the stator current Construct the Lyapunov function with the actual values i α and i β , and analyze the stability of the back EMF observer in step 2;

步骤4,对改进滑模观测器进行稳定性分析,计算定子电阻观测 值;Step 4, carry out stability analysis on the improved sliding mode observer, and calculate the observed value of stator resistance;

步骤5,利用改进滑模观测器观测出的转速永磁体磁链Ψf以及永磁同步电机在两相旋转坐标系下的转矩电流分量iq构建转矩 观测器方程,将观测出的转矩变化量与转矩电流给定iq *相加,作为 新的q轴电流给定,即完成对永磁同步电机无位置传感器的控制。Step 5, the rotational speed observed by the improved sliding mode observer The permanent magnet flux linkage Ψ f and the torque current component i q of the permanent magnet synchronous motor in the two-phase rotating coordinate system construct the torque observer equation, and the observed torque change and the torque current given i q * phase Add, as a new q-axis current given, that is, to complete the sensorless control of the permanent magnet synchronous motor.

本发明的技术特征还在于,The technical feature of the present invention is also that,

其中,所述步骤1包括以下步骤:Wherein, the step 1 includes the following steps:

步骤1.1,采用sigmoid函数,分别以永磁同步电机在两相静止 坐标系下的相电流iα、iβ作为输入值,计算出两相静止坐标系下定子 电流的观测值sigmoid函数式如下:Step 1.1, using the sigmoid function, the phase currents i α and i β of the permanent magnet synchronous motor in the two-phase static coordinate system are used as input values to calculate the observed value of the stator current in the two-phase static coordinate system. and The sigmoid function formula is as follows:

其中,a为可调参数;Among them, a is an adjustable parameter;

步骤1.2,采用sigmoid函数,分别以永磁同步电机在两相静止 坐标系下定子电流的观测误差值作为输入值,计 算出两相静止坐标系下反电动势的观测值 Step 1.2, using the sigmoid function, respectively use the observation error value of the stator current of the permanent magnet synchronous motor in the two-phase stationary coordinate system As the input value, the observed value of the back EMF in the two-phase stationary coordinate system is calculated and

步骤1.3,构建基于sigmoid函数作为控制函数的滑模电流观测 器方程,表达式如下:Step 1.3, construct the sliding mode current observer equation based on the sigmoid function as the control function, the expression is as follows:

其中,Rs为定子相电阻,Ls为定子相电感,uα、uβ分别为两相静 止坐标系下的相电压分量,k为观测器的反馈增益。Among them, R s is the stator phase resistance, L s is the stator phase inductance, u α and u β are the phase voltage components in the two-phase stationary coordinate system, respectively, and k is the feedback gain of the observer.

所述步骤1.3中,更优选的方案是利用kva=k·ωref代替原观测器 中的反馈增益k,ωref表示转子角速度。In the step 1.3, a more preferred solution is to use k va =k·ω ref to replace the feedback gain k in the original observer, where ω ref represents the rotor angular velocity.

所述步骤2中的反电动势观测器方程的表达式如下:The expression of the back EMF observer equation in the step 2 is as follows:

其中,l是观测器增益,l>0,eα、eβ分别为两相静止坐标系 下的反电动势分量和电角速度观测值,通过锁相环获取转子的角度信 息,转速估计值表达式如下:where l is the observer gain, l>0, e α , e β , are the back-EMF component and the observed value of the electrical angular velocity in the two-phase stationary coordinate system, respectively. The angle information of the rotor is obtained through the phase-locked loop. The estimated value of the rotational speed is expressed as follows:

所述步骤3中构建的Lyapunov函数如下:The Lyapunov function constructed in the step 3 is as follows:

其中, in,

Rs为定子电阻的实际值和观测值;R s , are the actual and observed values of the stator resistance;

定子电阻的变化用估计,根据Lyapunov稳定性定理, 当时,系统是渐进稳定的,满足 的条件为:For the change of stator resistance Estimate, according to Lyapunov stability theorem, when , the system is asymptotically stable, satisfying The conditions are:

其中,分别为定子电流和定子 电阻的观测误差; in, are the observation errors of stator current and stator resistance, respectively;

根据系统渐进稳定的条件,可得所述步骤4中定子电阻观测值为:According to the condition of the asymptotic stability of the system, the observed value of the stator resistance in the step 4 can be obtained:

反馈增益k的取值范围为:The value range of the feedback gain k is:

k>max(|eα|,|eβ|)。k>max(|e α |, |e β |).

所述步骤5中的转矩观测器方程为:The torque observer equation in step 5 is:

其中,k1,k2为转矩观测器增益系数;为滑模观测器估算转速; 为转矩观测器估算转速;Ψf为永磁体磁链;为估算转矩;J为 转动惯量。Among them, k 1 , k 2 are torque observer gain coefficients; Estimate the rotational speed for the sliding mode observer; Estimate the rotational speed for the torque observer; Ψ f is the permanent magnet flux linkage; is the estimated torque; J is the moment of inertia.

本发明的有益效果如下:The beneficial effects of the present invention are as follows:

1、本发明采用可变边界层厚度的sigmoid函数代替符号函数, 并且构建反电动势观测器用于分离反电动势信号,消除了低通滤波器 以及相位补偿环节,有效抑制了滑模观测器的抖振现象并获得宽调速 范围内的理想观测精度。1. The present invention uses the sigmoid function of variable boundary layer thickness to replace the sign function, and constructs a back-EMF observer for separating back-EMF signals, eliminating the low-pass filter and phase compensation links, and effectively suppressing the chattering of the sliding mode observer. phenomenon and obtain ideal observation accuracy over a wide speed range.

2、本发明采用定子电阻在线辨识环节,并且利用Lyapunov函数 设计了电阻参数在线辨识算法。通过对电阻的在线辨识,实时调整滑 模观测器的辨识模型,提高了系统对内部参数变化的鲁棒性。2. The present invention adopts the stator resistance online identification link, and uses the Lyapunov function to design the resistance parameter online identification algorithm. Through the online identification of the resistance, the identification model of the sliding mode observer is adjusted in real time, which improves the robustness of the system to changes in internal parameters.

3、本发明加入转矩观测器进行转矩前馈控制,减小了转矩扰动 对永磁同步电机控制系统的影响,提高了系统对外部参数变化的鲁棒 性。3. The present invention adds a torque observer to perform torque feedforward control, reduces the influence of torque disturbance on the control system of the permanent magnet synchronous motor, and improves the robustness of the system to changes in external parameters.

附图说明Description of drawings

图1是本发明基于改进滑模观测器的永磁同步电机无位置传感 器矢量控制系统框图;1 is a block diagram of a position sensorless vector control system of a permanent magnet synchronous motor based on an improved sliding mode observer of the present invention;

图2是本发明中边界层厚度可变的sigmoid函数原理框图;Fig. 2 is the principle block diagram of the sigmoid function with variable boundary layer thickness in the present invention;

图3是本发明基于反电动势的锁相环结构图;Fig. 3 is the phase-locked loop structure diagram based on back electromotive force of the present invention;

图4是本发明中改进滑模观测器的原理框图;Fig. 4 is the principle block diagram of the improved sliding mode observer in the present invention;

图5是本发明中负载转矩观测器的原理框图;Fig. 5 is the principle block diagram of the load torque observer in the present invention;

图6是电机转速在0.05s时由500r/min阶跃至1000r/min时,本 发明观测器估算出的转速与采用sigmoid函数估算出的转速波形;Fig. 6 is when the motor speed is stepped from 500r/min to 1000r/min in 0.05s, the speed estimated by the observer of the present invention and the speed waveform estimated by the sigmoid function;

图7是电机转速为1000r/min,电机转矩在0.03s时由5N·m变为 10N·m时,采用转矩前馈控制与不采用转矩前馈控制观测出的转速误 差波形。Figure 7 is the rotation speed error waveform observed when the motor speed is 1000r/min and the motor torque changes from 5N m to 10N m in 0.03s, using torque feedforward control and not using torque feedforward control.

具体实施方式Detailed ways

下面结合附图和具体实施方式对本发明做进一步的详细说明,但 本发明并不局限于该具体实施方式。The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, but the present invention is not limited to the specific embodiments.

本发明基于改进滑模观测器的PMSM无位置传感器控制方法, 包括基于sigmoid函数的改进滑模观测器、定子电阻辨识环节、反电 动势观测器以及转矩观测器。The PMSM position sensorless control method based on the improved sliding mode observer of the present invention includes the improved sliding mode observer based on the sigmoid function, a stator resistance identification link, a back electromotive force observer and a torque observer.

参照图1,本发明的改进滑模观测器应用在永磁同步电机的矢量 控制中。控制方法采用id=0控制,永磁同步电机的三相电流和电压经 过Clarke变换以后得到两相静止坐标系下的分量iα、iβ和uα、uβ作为 改进滑模观测器的输入,改进滑模观测器观测出的转速以及电机电流 的转矩分量iq作为负载转矩观测器的输入,其输出与转矩电流给定相 加,作为新的q轴电流给定,用于永磁同步电机的矢量控制中。具体 包括以下步骤:Referring to FIG. 1 , the improved sliding mode observer of the present invention is applied in the vector control of a permanent magnet synchronous motor. The control method adopts id = 0 control. After the three-phase current and voltage of the permanent magnet synchronous motor are transformed by Clarke, the components i α , i β and u α , u β in the two - phase stationary coordinate system are obtained as the components of the improved sliding mode observer. Input, the rotational speed observed by the improved sliding mode observer and the torque component i q of the motor current are used as the input of the load torque observer, and its output is added to the torque current given as a new q-axis current given, with In the vector control of permanent magnet synchronous motor. Specifically include the following steps:

步骤1,将永磁同步电机在两相静止坐标系下的相电压uα、uβ和 相电流iα、iβ作为基于sigmoid函数的滑模观测器的输入,输出为定 子电流的观测值将iα、iβ作差,作为sigmoid函数的 输入,其输出为两相静止坐标系下反电动势的观测值同时根 据转速改变sigmoid函数的边界层宽度,即sigmoid函数的反馈增益。Step 1, take the phase voltage u α , u β and phase current i α , i β of the permanent magnet synchronous motor in the two-phase stationary coordinate system as the input of the sliding mode observer based on the sigmoid function, and the output is the observed value of the stator current and Put i α , i β with The difference is used as the input of the sigmoid function, and its output is the observed value of the back EMF in the two-phase stationary coordinate system At the same time, the width of the boundary layer of the sigmoid function is changed according to the rotational speed, that is, the feedback gain of the sigmoid function.

步骤1中构建的基于sigmoid函数的滑模观测器方程表达式如下:The expression of the sliding mode observer equation based on the sigmoid function constructed in step 1 is as follows:

其中,Rs为定子相电阻,Ls为定子相电感,iα、iβ、uα、uβ分别为 两相静止坐标系下的相电流、相电压分量,为相电流的观测值。 为sigmoid函数,a为可调参数,k为观测器的反 馈增益。Among them, R s is the stator phase resistance, L s is the stator phase inductance, i α , i β , u α , u β are the phase current and phase voltage components in the two-phase stationary coordinate system, respectively, is the observed value of the phase current. is the sigmoid function, a is an adjustable parameter, and k is the feedback gain of the observer.

参照图2,利用kva=k·ωref代替原观测器中的反馈增益k,根据转 速改变边界层的宽度,从而减弱抖振现象。Referring to FIG. 2 , the feedback gain k in the original observer is replaced by k va =k·ω ref , and the width of the boundary layer is changed according to the rotation speed, thereby reducing the chattering phenomenon.

步骤2,利用步骤1中得到的反电动势观测值和电机实际 的反电动势分量eα、eβ构建反电动势观测器,得到转速估计值再 经过图3的锁相环得到转子位置,构建的反电动势观测器数学模型如 下式所示:Step 2, use the back EMF observations obtained in step 1 and the actual back-EMF components e α and e β of the motor to construct a back-EMF observer to obtain the estimated speed Then, the rotor position is obtained through the phase-locked loop in Figure 3, and the mathematical model of the back EMF observer is constructed as follows:

其中l是观测器增益,l>0,分别为两相静止坐标系下 的反电动势观测值和电角速度观测值,通过锁相环获取转子的角度信 息,转速估计值表达式如下:where l is the observer gain, l > 0, are the observed value of back electromotive force and the observed value of electrical angular velocity in the two-phase stationary coordinate system, respectively. The angle information of the rotor is obtained through the phase-locked loop, and the estimated value of the rotational speed is expressed as follows:

步骤3,选取Lyapunov函数对步骤2中构建的反电动势观测器 进行稳定性分析,反电动势观测器的误差方程为:Step 3, select the Lyapunov function to analyze the stability of the back-EMF observer constructed in step 2. The error equation of the back-EMF observer is:

其中分别为反电动势和转 速的观测误差;in are the observation errors of back EMF and rotational speed, respectively;

选取Lyapunov函数为:The Lyapunov function is selected as:

要保证系统稳定,必须满足:To ensure system stability, it must meet:

根据反电动势的误差方程对上式进行化简,可以得到:Simplify the above equation according to the error equation of the back EMF, we can get:

由于l>0,因此所以反电动势观测器始终是渐进稳定的。Since l>0, so So the back EMF observer is always asymptotically stable.

步骤4,定义Lyapunov函数,对改进滑模观测器进行稳定性分 析,并且设计电阻参数在线辨识算法,计算定子电阻观测值 Step 4, define the Lyapunov function, analyze the stability of the improved sliding mode observer, and design the online identification algorithm of resistance parameters to calculate the observed value of stator resistance

定义Lyapunov函数为:Define the Lyapunov function as:

式中定子电阻的变化 用估计;in the formula For the change of stator resistance estimate;

表贴式永磁同步电机在两相静止坐标系下的数学模型为:The mathematical model of the surface-mounted permanent magnet synchronous motor in the two-phase stationary coordinate system is:

式中,iα、iβ、uα、uβ以及eα、eβ分别为两相静止坐标系下的相电 流、相电压以及反电动势分量,Rs为定子相电阻,Ls为定子相电感, Ψf为永磁体磁链,ωr为转子电角速度,θ为转子位置;In the formula, i α , i β , u α , u β and e α , e β are the phase current, phase voltage and back EMF component in the two-phase stationary coordinate system, R s is the stator phase resistance, L s is the stator Phase inductance, Ψ f is the permanent magnet flux linkage, ω r is the rotor electrical angular velocity, θ is the rotor position;

根据表贴式永磁同步电机在两相静止坐标系下的数学模型以及 构建的基于sigmoid函数的滑模电流观测器方程可以得到:According to the mathematical model of the surface-mounted permanent magnet synchronous motor in the two-phase stationary coordinate system and the constructed sliding mode current observer equation based on the sigmoid function, it can be obtained:

其中: in:

根据Lyapunov稳定性定理,要保证系统稳定,必须满足:According to Lyapunov stability theorem, to ensure the stability of the system, it must satisfy:

进一步推导,可以得到滑动模态的稳定性条件为:Further derivation, the stability condition of the sliding mode can be obtained as:

其中分别为定子电流和定子 电阻的观测误差。in are the observation errors of stator current and stator resistance, respectively.

从而步骤4中所述的定子电阻观测值为:Thus the observed value of the stator resistance described in step 4 is:

反馈增益k的取值范围为:The value range of the feedback gain k is:

k>max(|eα|,|eβ|)k>max(|e α |,|e β |)

最终得到的改进滑模观测器的框图(如图4)。The resulting block diagram of the improved sliding mode observer (see Figure 4).

步骤5,参照图5,利用改进滑模观测器观测出的转速永磁 体磁链Ψf以及永磁同步电机在两相旋转坐标系下的转矩电流分量iq构建转矩观测器方程,表达式如下:Step 5, referring to Fig. 5, the rotational speed observed by the improved sliding mode observer The permanent magnet flux linkage Ψ f and the torque current component i q of the permanent magnet synchronous motor in the two-phase rotating coordinate system construct the torque observer equation, and the expression is as follows:

其中,k1,k2为转矩观测器增益系数;为滑模观测器估算转速; 为转矩观测器估算转速;为估算转矩,J为转动惯量。Among them, k 1 , k 2 are torque observer gain coefficients; Estimate the rotational speed for the sliding mode observer; Estimate the speed for the torque observer; To estimate the torque, J is the moment of inertia.

将观测出的转矩变化量与转矩电流给定iq *相加,作为新的q轴 电流给定,即完成对永磁同步电机无位置传感器的控制。Add the observed torque change to the torque current given i q * as a new q-axis current given, that is, to complete the sensorless control of the permanent magnet synchronous motor.

下面结合图6至图7的仿真波形验证本发明的可行性。The feasibility of the present invention is verified below with reference to the simulation waveforms in FIGS. 6 to 7 .

图6为本发明的改进滑模观测器与基于sigmoid函数的滑模观测 器的对比仿真图。仿真时间为0~0.1s,空载,电机初始转速设定为 500r/min,在0.05s时给定电机转速为1000r/min。从图6中可以看出, 采用sigmoid函数可以减小抖振但是随着转速的升高,估计误差会变 大,而本发明的改进滑模观测器在转速较高时仍然有较小的估计误差。Fig. 6 is the comparative simulation diagram of the improved sliding mode observer of the present invention and the sliding mode observer based on the sigmoid function. The simulation time is 0~0.1s, no load, the initial speed of the motor is set to 500r/min, and the given motor speed is 1000r/min at 0.05s. It can be seen from Fig. 6 that the chattering can be reduced by using the sigmoid function, but as the rotation speed increases, the estimation error will become larger, while the improved sliding mode observer of the present invention still has a smaller estimation when the rotation speed is higher error.

图7为传统不加转矩前馈观测的滑模观测器与本发明的改进滑 模观测器在转速为1000r/min,负载转矩在0.03s时由5N·m突变至 10N·m时观测的转速误差波形对比,由图7中可以看出,当永磁同步 电机受到转矩扰动时,转矩前馈观测器可以将负载转矩的变化信息实 时反馈到q轴电流环的前向通道,通过迅速增大q轴电流给定的方式 加快电流环的调节速度,因此转速估计误差具有更小的超调和更快的 收敛速度。Fig. 7 shows the observation of the traditional sliding mode observer without torque feedforward observation and the improved sliding mode observer of the present invention when the rotation speed is 1000r/min, and the load torque changes suddenly from 5N·m to 10N·m at 0.03s As can be seen from Figure 7, when the permanent magnet synchronous motor is subjected to torque disturbance, the torque feedforward observer can feed back the change information of the load torque to the forward channel of the q-axis current loop in real time. , by rapidly increasing the q-axis current given way to speed up the adjustment speed of the current loop, so the speed estimation error has less overshoot and faster convergence speed.

本发明采用可变边界层厚度的sigmoid函数代替符号函数,并且 构建反电动势观测器用于分离反电动势信号,消除了低通滤波器以及 相位补偿环节,同时可以使观测器增益随速度大小动态调整,有效抑 制了滑模观测器的抖振现象并获得宽调速范围内的理想观测精度。在 改进滑模观测器中加入定子电阻在线辨识和转矩观测环节,提高了系 统对内部和外部参数变化的鲁棒性。The invention adopts the sigmoid function of the variable boundary layer thickness to replace the sign function, and constructs a back electromotive force observer for separating the back electromotive force signal, eliminating the low-pass filter and the phase compensation link, and at the same time, the observer gain can be dynamically adjusted with the speed. The chattering phenomenon of the sliding mode observer is effectively suppressed and the ideal observation accuracy in a wide speed regulation range is obtained. The stator resistance online identification and torque observation links are added to the improved sliding mode observer, which improves the robustness of the system to changes in internal and external parameters.

Claims (7)

1. A PMSM (permanent magnet synchronous motor) position sensorless control method based on an improved sliding-mode observer is characterized by comprising the following steps:
step 1, calculating an observed value of stator current of a permanent magnet synchronous motor under a two-phase static coordinate systemAnd observed value of back electromotive forceThen, taking the observation error of the stator current as a sliding mode surface, constructing an improved sliding mode current observer equation, and simultaneously changing the feedback gain k of the sigmoid function according to the rotating speed;
step 2, utilizing the observed value of the back electromotive force obtained in the step 1Constructing a mathematical model of a counter electromotive force observer and calculating a rotating speed estimation valueEstimating the position of the rotor through a phase-locked loop;
step 3, utilizing the observed value of the stator currentAnd the actual value iα、iβConstructing a Lyapunov function, and performing stability analysis on the back electromotive force observer in the step 2;
step 4, carrying out stability analysis on the improved sliding mode observer, and calculating a stator resistance observation value;
step 5, utilizing the observed rotating speed of the improved sliding mode observerPermanent magnet flux linkage ΨfAnd the torque current component i of the permanent magnet synchronous motor under the two-phase rotating coordinate systemqConstructing a torque observer equation, and giving i to the observed torque variation and the torque currentq *And adding, and finishing the control of the permanent magnet synchronous motor without the position sensor as new q-axis current setting.
2. The improved sliding-mode observer based PMSM position sensorless control method according to claim 1, wherein the step 1 comprises the steps of:
step 1.1, adopting sigmoid function, and respectively using phase current i of the permanent magnet synchronous motor in a two-phase static coordinate systemα、iβAs an input value, an observed value of the stator current in a two-phase stationary coordinate system is calculatedAndthe sigmoid function is as follows:
wherein a is an adjustable parameter;
step 1.2, adopting sigmoid function, and respectively using the observation error values of the stator current of the permanent magnet synchronous motor under the two-phase static coordinate systemAs an input value, an observed value of back electromotive force in a two-phase stationary coordinate system is calculatedAnd
step 1.3, constructing a sliding mode current observer equation based on a sigmoid function as a control function, wherein the expression is as follows:
wherein R issIs stator phase resistance, LsIs a stator phase inductance uα、uβThe phase voltage components are respectively under a two-phase static coordinate system, and k is the feedback gain of the observer.
3. The improved sliding-mode observer based PMSM position sensorless control method according to claim 2, characterized in thatIn the step 1.3, it is more preferable to use kva=k·ωrefReplacing the feedback gain k, ω in the original observerrefRepresenting the rotor angular velocity.
4. The improved sliding-mode observer-based PMSM position sensorless control method according to claim 1, characterized in that the expression of the back electromotive force observer mathematical model constructed in step 2 is as follows:
where l is the observer gain, l>0,eα、eβThe method comprises the following steps of respectively obtaining back electromotive force components and electric angular velocity observed values under a two-phase static coordinate system through a phase-locked loop, wherein the rotation speed estimated value expression is as follows:
5. the improved sliding-mode observer-based PMSM position-sensorless control method according to claim 1, characterized in that the Lyapunov function constructed in step 3 is as follows:
wherein,
Rsrespectively representing an actual value and an observed value of the stator resistance;
for variation of stator resistanceEstimation, according to the Lyapunov theorem of stability whenThe system is gradually stable and meets the requirementsThe conditions of (a) are as follows:
wherein,the observation errors of the stator current and the stator resistance are respectively;
6. the improved sliding-mode observer-based PMSM position sensorless control method according to claim 5, characterized in that according to the condition of system asymptotic stability, the stator resistance observed value in the step 4 can be obtained as follows:
the value range of the feedback gain k is as follows:
k>max(|eα|,|eβ|)。
7. the improved sliding-mode observer based PMSM position sensorless control method according to claim 6, wherein the torque observer equation in step 5 is:
wherein k is1,k2Is a torque observer gain factor;estimating a rotation speed for the sliding mode observer;estimating a rotational speed for the torque observer;to estimate the torque, J is the moment of inertia.
CN201810936075.9A 2018-08-16 2018-08-16 Based on the PMSM method for controlling position-less sensor for improving sliding mode observer Pending CN109167547A (en)

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CN111726048A (en) * 2020-07-28 2020-09-29 南通大学 Rotor position and speed estimation method for permanent magnet synchronous motor based on sliding mode observer
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CN112003526A (en) * 2020-08-20 2020-11-27 苏州崧崧智能控制技术有限公司 High-speed permanent magnet synchronous motor non-inductive control system and method based on low-buffeting sliding-mode observer
CN112882053B (en) * 2021-01-21 2023-07-18 清华大学深圳国际研究生院 Method for actively calibrating external parameters of laser radar and encoder
CN112882053A (en) * 2021-01-21 2021-06-01 清华大学深圳国际研究生院 Method for actively calibrating external parameters of laser radar and encoder
CN113364375A (en) * 2021-06-18 2021-09-07 湖南科技大学 Sensorless control method for PMSM (permanent magnet synchronous motor) driving system of variable-structure current regulator
CN114172426A (en) * 2021-10-27 2022-03-11 北京自动化控制设备研究所 A kind of permanent magnet synchronous motor coefficient self-tuning speed compensation control method
CN114172426B (en) * 2021-10-27 2024-06-11 北京自动化控制设备研究所 Permanent magnet synchronous motor coefficient self-tuning speed compensation control method
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