CN102931906B

CN102931906B - Method for asynchronous motor rotor flux linkage observation and rotation speed identification

Info

Publication number: CN102931906B
Application number: CN201210486855.0A
Authority: CN
Inventors: 黄进; 赵力航; 李炳楠; 孔武斌; 卢彬芳; 何航
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2012-10-26
Filing date: 2012-11-23
Publication date: 2014-11-12
Anticipated expiration: 2032-11-23
Also published as: CN102931906A

Abstract

本发明公开了一种异步电机转子磁链观测与转速辨识的方法。根据实时测得的定子电压、电流信号，通过基于极致扭曲（Super-Twisting）理论的滑模观测器，观测得到转子磁链并作为参考值，由转子磁链电流模型求得的转子磁链作为可调值，构成基于转子磁链的模型参考自适应系统（MRAS），通过自适应律来辨识异步电机转速。本发明提供的转速辨识方法对定子电阻的变化有较强的鲁棒性，能提供准确的转子磁链和转速值，尤其适用于异步电机矢量控制系统。The invention discloses a method for observing and identifying the rotor flux of an asynchronous motor. According to the stator voltage measured in real time , current signal , through the sliding mode observer based on the super-twisting (Super-Twisting) theory, the rotor flux linkage is observed And as a reference value, the rotor flux obtained by the rotor flux current model As an adjustable value, a model reference adaptive system (MRAS) based on the rotor flux linkage is formed to identify the speed of the asynchronous motor through the adaptive law . The rotation speed identification method provided by the invention has strong robustness to the change of stator resistance, can provide accurate rotor flux linkage and rotation speed value, and is especially suitable for asynchronous motor vector control system.

Description

A Method for Observation of Rotor Flux Linkage and Speed Identification of Asynchronous Motor

技术领域technical field

本发明公开一种电机参数的辨识方法，特别涉及一种鲁棒性很强的转子磁链观测器，和基于该观测器的无速度传感器异步电机矢量控制方案。The invention discloses a motor parameter identification method, in particular to a rotor flux observer with strong robustness, and a speed sensorless asynchronous motor vector control scheme based on the observer.

背景技术Background technique

目前，三相异步电机的控制方式已趋成熟，矢量控制和直接转矩控制能满足大部分工况需求。无论哪种控制方式，转速都是一个非常重要的控制量。但速度传感器在某些情况下安装困难，或是有时为了节省这部分成本，人们希望只根据变频器上易测得的相电流、相电压数据，实时辨识转速，实现无速度传感器控制。At present, the control methods of three-phase asynchronous motors have matured, and vector control and direct torque control can meet the requirements of most working conditions. Regardless of the control method, the speed is a very important control quantity. However, the speed sensor is difficult to install in some cases, or sometimes in order to save this part of the cost, people hope to identify the speed in real time only based on the easily measured phase current and phase voltage data on the inverter, and realize speed sensorless control.

异步电机无速度传感器原理可以分为两种类型：一类要求转子具有不对称性，如转子槽谐波法、高频注入法，这类方法需要对信号的频谱进行分析，程序费时费力，高速时对硬件要求很严苛；另一类方法是基于异步电机的数学模型，用某种数学方法辨识其中的转速，如基于状态观测器的方法，涉及人工智能的方法，以及基于模型参考自适应原理（MRAS）的方法。The principle of asynchronous motor without speed sensor can be divided into two types: one type requires the rotor to have asymmetry, such as rotor slot harmonic method and high frequency injection method. The hardware requirements are very strict; the other method is based on the mathematical model of the asynchronous motor, using a certain mathematical method to identify the rotational speed, such as the method based on the state observer, the method involving artificial intelligence, and the model-based reference adaptive principle (MRAS) method.

如今，科研工作者已经研发出很多基于异步电机数学模型的无速度传感器算法。属于状态观测器范畴的有：全阶状态观测器与降阶状态观测器，扩展卡尔曼滤波器（EKF)，以及滑模观测器（SMO)。状态观测器法对电机参数变化敏感，为了满足全局稳定使得算法复杂；EKF计算复杂，大量随机参数要调试得到；SMO鲁棒性较强，但固有的抖动对电机低速运行有害。涉及人工智能的方法一直是本行业的研究热点之一，只是受限于硬件，离实用化还有一定距离。传统MRAS的物理意义明确，算法较简单，稳态精度比较好，但易受电机参数变化影响，比如定子电阻R_s。随着对MRAS算法的深入研究，人们发现选择不同的参考模型和可调模型，可以演化出不同结构的MRAS辨识算法，如基于转子磁链、基于反电势、基于瞬时无功功率等。此外，在MRAS结构下应用滑模原理、模糊控制原理等，可以演化出很多不同的结构，研究改进的余地很大。Nowadays, researchers have developed many speed sensorless algorithms based on the mathematical model of asynchronous motors. Belonging to the category of state observers are: full-order state observers and reduced-order state observers, extended Kalman filter (EKF), and sliding mode observer (SMO). The state observer method is sensitive to changes in motor parameters, and the algorithm is complicated to meet global stability; the EKF calculation is complex, and a large number of random parameters need to be debugged; the SMO is robust, but the inherent jitter is harmful to the low-speed operation of the motor. Methods involving artificial intelligence have always been one of the research hotspots in this industry, but limited by hardware, there is still a certain distance from practicality. The physical meaning of traditional MRAS is clear, the algorithm is relatively simple, and the steady-state accuracy is relatively good, but it is easily affected by changes in motor parameters, such as the stator resistance R _s . With the in-depth research on the MRAS algorithm, it is found that choosing different reference models and adjustable models can evolve MRAS identification algorithms with different structures, such as based on rotor flux linkage, based on back EMF, based on instantaneous reactive power, etc. In addition, many different structures can be evolved by applying the principle of sliding mode and fuzzy control under the MRAS structure, and there is a lot of room for research and improvement.

判断一种转速辨识算法的好坏，主要是看这种算法能否在一个较宽的调速范围内保持辨识精度。电机的数学模型总是不够精确，而且一些参数还会随着电机运行而变化，从而大大影响辨识的精确性。低速下，定子电阻R_s的变化对转子磁链ψ_r观测的影响最大，进而影响基于磁链观测器的无速度传感器的辨识精度。针对R_s的影响，有学者在观测器中加入R_s的自适应辨识来改善低速性能，但此法对观测器的稳定性设计要求较高，通用性不强。Judging the quality of a speed identification algorithm mainly depends on whether the algorithm can maintain the identification accuracy in a wide speed range. The mathematical model of the motor is always not accurate enough, and some parameters will change with the operation of the motor, which greatly affects the accuracy of identification. At low speed, the change of stator resistance R _s has the greatest impact on the observation of rotor flux ψ _r , which in turn affects the identification accuracy of the sensorless speed sensor based on flux observer. Aiming at the influence of R _s , some scholars add R _s adaptive identification to the observer to improve the low-speed performance, but this method has high requirements on the stability design of the observer, and its versatility is not strong.

发明内容Contents of the invention

为了解决上述技术问题，本发明提出一种与定子电阻无关的转子磁链观测方法，能够在线观测异步电机的转子磁链，辨识转速。该方法对定子电阻变化不敏感，而对干扰有较强的鲁棒性。In order to solve the above technical problems, the present invention proposes a rotor flux linkage observation method independent of stator resistance, which can observe the rotor flux linkage of an asynchronous motor online and identify the rotational speed. This method is not sensitive to the change of stator resistance, but has strong robustness to disturbance.

这种异步电机转子磁链观测与转速辨识的方法，根据实时测得的定子电压u_s、定子电流i_s，通过基于极致扭曲（Super-Twisting）理论的滑模观测器，观测得到转子磁链ψ_r并作为参考值，由转子磁链电流模型求得的转子磁链并作为可调值，构成基于转子磁链的模型参考自适应系统（Model Reference AdaptiveSystem，MRAS），通过自适应律来辨识异步电机转速 This method of rotor flux observation and speed identification of asynchronous motors, based on the real-time measured stator voltage u _s and stator current i _s , through the sliding mode observer based on the Super-Twisting theory, obtains the rotor flux ψ _r and as a reference value, the rotor flux obtained from the rotor flux current model And as an adjustable value, a model reference adaptive system (Model Reference Adaptive System, MRAS) based on the rotor flux linkage is formed to identify the speed of the asynchronous motor through the adaptive law

由所述的极致扭曲（Super-Twisting）理论的滑模观测器，观测得到转子磁链ψ_r的过程如下：According to the sliding mode observer of the Super-Twisting theory, the process of observing the rotor flux ψ _r is as follows:

首先，将三相异步电机在静止坐标系下的数学模型写作如下形式：First, the mathematical model of the three-phase asynchronous motor in the stationary coordinate system is written as follows:

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{i i}}_{sα sα} = = - - {k k}_{11} \cdot \cdot {i i}_{sα sα} + + {k k}_{22} \cdot \cdot ((b b \cdot &Center Dot; {ψ ψ}_{rα rα} + + {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rβ rβ})) + + {k k}_{33} \cdot \cdot {u u}_{sα sα} \\ {\overset{\cdot \cdot}{i i}}_{sβ sβ} = = - - {k k}_{11} \cdot &Center Dot; {i i}_{sβ sβ} + + {k k}_{22} \cdot &Center Dot; ((b b \cdot &Center Dot; {ψ ψ}_{rβ rβ} - - {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rα rα})) + + {k k}_{33} \cdot &Center Dot; {u u}_{sβ sβ} \\ {\overset{\cdot &Center Dot;}{ψ ψ}}_{rα rα} = = a a \cdot &Center Dot; {i i}_{sα sα} - - b b \cdot &Center Dot; {ψ ψ}_{rα rα} - - {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rβ rβ} \\ {\overset{\cdot \cdot}{ψ ψ}}_{rβ rβ} = = a a \cdot &Center Dot; {i i}_{sβ sβ} - - b b \cdot \cdot {ψ ψ}_{rβ rβ} + + {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rα rα} \end{matrix}$

上式中，i_sα和i_sβ为定子电流i_s的分量，u_sα和u_sβ为定子电压u_s的分量，ψ_rα和ψ_rβ为转子磁链ψ_r分量；In the above formula, i _sα and is _β are the components of the stator current _is , u _sα and u _sβ are the components of the stator voltage u _s , ψ _rα and ψ _rβ are the components of the rotor flux linkage ψ _r ;

R_s为定子电阻，L_m为励磁电感的稳态值，L_s和L_r分别为定子、转子电感，T_r为转子时间常数，ω_r为转子转速，则上式中出现的其他量表示为：R _s is the stator resistance, L _m is the steady-state value of the excitation inductance, L _s and L _r are the stator and rotor inductances respectively, T _r is the rotor time constant, ω _r is the rotor speed, and other quantities appearing in the above formula represent for:

$σ σ = = 11 - - {L L}_{m m}^{22} / / {L L}_{s the s} {L L}_{r r}$

${k k}_{11} = = {R R}_{s the s} / / {σL σ L}_{s the s} + + {L L}_{m m}^{22} / / {σL σ L}_{s the s} {L L}_{r r} {T T}_{r r}$

k₂＝L_m/σL_sL_r k ₂ ＝L _m /σL _s L _r

k₃＝1/σL_s k ₃ =1/σL _s

a＝L_m/T_r a=L _m /T _r

b＝1/T_r b=1/ _Tr

其次，对上述模型作基于极致扭曲理论的变换如下：Secondly, the transformation of the above model based on the extreme distortion theory is as follows:

$\{\begin{matrix} {z z}_{11} = = {i i}_{sα sα} \\ {z z}_{22} = = {i i}_{sβ sβ} \\ {z z}_{33} = = b b \cdot \cdot {ψ ψ}_{rα rα} + + {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rβ rβ} \\ {z z}_{44} = = b b \cdot &Center Dot; {ψ ψ}_{rβ rβ} - - {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rα rα} \end{matrix}$

其中z₁~z₄为数学中间变量；Among them, z ₁ ~ z ₄ are mathematical intermediate variables;

变换后，三相异步电机静止坐标系下的数学模型写为：After transformation, the mathematical model of the three-phase asynchronous motor in the static coordinate system is written as:

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{z z}}_{11} = = - - {k k}_{11} \cdot &Center Dot; {z z}_{11} + + {k k}_{22} \cdot &Center Dot; {z z}_{33} + + {k k}_{33} \cdot &Center Dot; {u u}_{sα sα} \\ {\overset{\cdot \cdot}{z z}}_{22} = = - - {k k}_{11} \cdot &Center Dot; {z z}_{22} + + {k k}_{22} \cdot &Center Dot; {z z}_{44} + + {k k}_{33} \cdot &Center Dot; {u u}_{sβ sβ} \end{matrix}$

于是，根据极致扭曲理论的形式构建转子磁链观测器如下：Therefore, the rotor flux observer is constructed according to the form of extreme twist theory as follows:

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{\overset{^^}{z z}}}_{11} = = - - {k k}_{11} \cdot &Center Dot; {z z}_{11} + + {k k}_{22} \cdot &Center Dot; {\overset{~ ~}{z z}}_{33} + + {k k}_{33} \cdot &Center Dot; {u u}_{sα sα} + + {λ λ}_{11} \cdot &Center Dot; {| | {e e}_{11} | |}^{0.5 0.5} \cdot &Center Dot; sgn sgn (({e e}_{11})) \\ {\overset{\cdot \cdot}{\overset{~ ~}{z z}}}_{33} = = {δ δ}_{11} \cdot \cdot sgn sgn (({e e}_{11})) \\ {\overset{\cdot \cdot}{\overset{^^}{z z}}}_{22} = = - - {k k}_{11} \cdot &Center Dot; {z z}_{22} + + {k k}_{22} \cdot &Center Dot; {\overset{~ ~}{z z}}_{44} + + {k k}_{33} \cdot &Center Dot; {u u}_{sβ sβ} + + {λ λ}_{22} \cdot &Center Dot; {| | {e e}_{22} | |}^{0.5 0.5} \cdot &Center Dot; sgn sgn (({e e}_{22})) \\ {\overset{\cdot &Center Dot;}{\overset{~ ~}{z z}}}_{44} = = {δ δ}_{22} \cdot \cdot sgn sgn (({e e}_{22})) \end{matrix}$

其中，e₁和e₂为误差值，有 sgn()是符号函数，λ₁、λ₂和δ₁、δ₂为预先设定的滑模增益；Among them, e ₁ and e ₂ are error values, there are sgn() is a sign function, λ ₁ , λ ₂ and δ ₁ , δ ₂ are preset sliding mode gains;

最后，从上式得到的观测值和它们与转子磁链有如下关系：Finally, the observations obtained from the above formula and They have the following relationship with the rotor flux linkage:

${ψ ψ}_{rα rα} = = {&Integral; &Integral;}_{00}^{t t} ((- - {\overset{~ ~}{z z}}_{33} + + \frac{{L L}_{m m}}{{T T}_{r r}} \cdot &Center Dot; {\overset{^^}{z z}}_{11})) \cdot &Center Dot; dt dt$

${ψ ψ}_{rβ rβ} = = {&Integral; &Integral;}_{00}^{t t} ((- - {\overset{~ ~}{z z}}_{44} + + \frac{{L L}_{m m}}{{T T}_{r r}} \cdot \cdot {\overset{^^}{z z}}_{22})) \cdot \cdot dt dt$

上式中，L_m为励磁电感，T_r为转子时间常数。In the above formula, L _m is the excitation inductance, T _r is the rotor time constant.

由上述观测器得到的转子磁链，在静止坐标系下表示为[ψ_rαψ_rβ]^T，作为模型参考自适应法的参考值。The rotor flux linkage obtained by the above-mentioned observer is expressed as [ψ _rα ψ _rβ ] ^T in the stationary coordinate system, which is used as the reference value of the model reference adaptive method.

所述的转子磁链电流模型作为可调模型，通过自适应律来辨识异步电机转速的过程如下：The rotor flux current model is used as an adjustable model to identify the speed of the asynchronous motor through the adaptive law The process is as follows:

首先，构建基于转子磁链电流模型的观测器，First, construct an observer based on the rotor flux current model,

${\overset{^^}{ψ ψ}}_{rα rα} = = \frac{11}{11 + + {T T}_{r r} \cdot &Center Dot; p p} \cdot &Center Dot; (({L L}_{m m} \cdot &Center Dot; {i i}_{sα sα} - - {\overset{^^}{ω ω}}_{r r} \cdot &Center Dot; {T T}_{r r} \cdot &Center Dot; {\overset{^^}{ψ ψ}}_{rβ rβ}))$

${\overset{^^}{ψ ψ}}_{rβ rβ} = = \frac{11}{11 + + {T T}_{r r} \cdot \cdot p p} \cdot &Center Dot; (({L L}_{m m} \cdot &Center Dot; {i i}_{sβ sβ} + + {\overset{^^}{ω ω}}_{r r} \cdot &Center Dot; {T T}_{r r} \cdot &Center Dot; {\overset{^^}{ψ ψ}}_{rα rα}))$

上式中， ${[\begin{matrix} {\hat{ψ}}_{rα} & {\hat{ψ}}_{rβ} \end{matrix}]}^{T}$ 是估计的转子磁链值，p为微分算子，是辨识得到的异步电机转速，T_r为转子时间常数；In the above formula, ${[\begin{matrix} {\hat{ψ}}_{rα} & {\hat{ψ}}_{rβ} \end{matrix}]}^{T}$ is the estimated rotor flux linkage value, p is the differential operator, is the identified asynchronous motor speed, T _r is the rotor time constant;

其次，将基于极致扭曲（Super-Twisting）理论的滑模观测器的输出值[ψ_rαψ_rβ]^T作为参考值， ${[\begin{matrix} {\hat{ψ}}_{rα} & {\hat{ψ}}_{rβ} \end{matrix}]}^{T}$ 作为可调值，根据模型参考自适应（MRAS）原理，自适应误差值按下式求得：Secondly, the output value [ψ _rα ψ _rβ ] ^T of the sliding mode observer based on the Super-Twisting theory is used as a reference value, ${[\begin{matrix} {\hat{ψ}}_{rα} & {\hat{ψ}}_{rβ} \end{matrix}]}^{T}$ As an adjustable value, according to the model reference adaptive (MRAS) principle, the adaptive error value is obtained as follows:

$ϵ ϵ = = {\overset{^^}{ψ ψ}}_{rα rα} \cdot \cdot {ψ ψ}_{rβ rβ} - - {\overset{^^}{ψ ψ}}_{rβ rβ} \cdot &Center Dot; {ψ ψ}_{rα rα}$

最后，根据稳定性原理设计转速的自适应律，用PI控制器等效，因此PI控制器的输出值即为异步电机转速辨识结果 Finally, the adaptive law of the speed is designed according to the principle of stability, which is equivalent to the PI controller, so the output value of the PI controller is the result of the identification of the speed of the asynchronous motor

本发明的有益效果在于，采用了基于极致扭曲理论的滑模观测器，该观测器不需要定子电阻R_s的值，能在全速范围内保证转子磁链ψ_r的观测精度。以它的输出值作为参考值，构建基于转子磁链的MRAS无速度传感器，能有效改善低速情况下电机转速的辨识精度。The beneficial effect of the present invention is that a sliding mode observer based on the extreme twist theory is adopted, the observer does not need the value of the stator resistance R _s , and can ensure the observation accuracy of the rotor flux linkage ψ _r in the full speed range. Taking its output value as a reference value, constructing a MRAS speed sensor based on the rotor flux linkage can effectively improve the identification accuracy of the motor speed at low speed.

附图说明Description of drawings

图1异步电机矢量控制系统示意图；Figure 1 Schematic diagram of asynchronous motor vector control system;

图2异步电机转子磁链观测和转速辨识方法的结构示意图；Fig. 2 Schematic diagram of the structure of the rotor flux observation and speed identification method of the asynchronous motor;

图3基于极致扭曲理论的转子磁链滑模观测器的结构示意图；Fig. 3 Schematic diagram of the structure of the rotor flux sliding mode observer based on the extreme twist theory;

图4磁链观测和转速辨识结果图-转速对比；Fig. 4 Flux linkage observation and rotational speed identification results diagram - rotational speed comparison;

图5磁链观测和转速辨识结果图-磁链对比。Fig. 5 Flux linkage observation and rotational speed identification results diagram - flux linkage comparison.

具体实施方式Detailed ways

下面结合附图和实施例对本发明作进一步的阐述。The present invention will be further elaborated below in conjunction with the accompanying drawings and embodiments.

参见图1，强电部分，三相交流电源经过不控整流得到直流母线电压U_dc，供给电压源型逆变器，再得到供给异步电机的三相电源。Refer to Fig. 1, the part of high power, the three-phase AC power supply is uncontrolled rectified to obtain the DC bus voltage U _dc , which is supplied to the voltage source inverter, and then the three-phase power supply to the asynchronous motor is obtained.

弱电部分，采用矢量控制方式，包含电压、电流传感器，3相/2相静止坐标变换模块，2相静止/2相同步速坐标变换模块，新型观测器模块，转子磁链幅值判断模块，速度环PI控制器模块，电流环PI控制器模块，2相同步速/2相静止坐标变换模块，电压空间矢量脉宽调制模块。The weak current part adopts vector control mode, including voltage and current sensors, 3-phase/2-phase static coordinate transformation module, 2-phase static/2-phase synchronous speed coordinate transformation module, new observer module, rotor flux amplitude judgment module, speed Loop PI controller module, current loop PI controller module, 2-phase synchronous speed/2-phase static coordinate transformation module, voltage space vector pulse width modulation module.

本发明主要涉及新型观测器模块，其他模块为异步电机矢量控制所需的功能性模块，为本领域公知常识。The present invention mainly relates to a novel observer module, and other modules are functional modules required for vector control of asynchronous motors, which are common knowledge in the field.

下面描述整个系统的工作流程，以介绍各模块的连接关系。The workflow of the whole system is described below to introduce the connection relationship of each module.

1.由传感器测得三相异步电机的各相电流与电压，输入“3相/2相静止坐标变换模块”，得到定子电流i_s的分量i_sα和i_sβ，定子电压u_s的分量u_sα和u_sβ。1. The current and voltage of each phase of the three-phase asynchronous motor are measured by the sensor, and input into the "3-phase/2-phase static coordinate transformation module" to obtain the components i _sα and _isβ of the stator current i _s and the component u of the stator voltage u _s _sα and u _sβ .

2.利用定子电压、电流信号，通过本发明的新型观测器，得到实时转速和同步速角度。新型观测器包含：(a)基于极致扭曲理论的滑模观测器模块，(b)转子磁链空间位置角计算模块，(c)转子磁链电流模型模块，(d)误差值计算模块，(e)转速自适应模块。具体的细节如图2所示。2. Using the stator voltage and current signals, the real-time rotational speed and synchronous speed angle are obtained through the novel observer of the present invention. The new observer includes: (a) sliding mode observer module based on extreme twist theory, (b) rotor flux space position angle calculation module, (c) rotor flux current model module, (d) error value calculation module, ( e) Speed adaptive module. The specific details are shown in Figure 2.

(a)首先，将三相异步电机静止坐标系下的数学模型写作如下形式：(a) First, write the mathematical model of the three-phase asynchronous motor in the static coordinate system as follows:

$\{\begin{matrix} {\overset{\cdot \cdot}{i i}}_{sα sα} = = - - {k k}_{11} \cdot \cdot {i i}_{sα sα} + + {k k}_{22} \cdot &Center Dot; ((b b \cdot \cdot {ψ ψ}_{rα rα} + + {ω ω}_{r r} \cdot \cdot {ψ ψ}_{rβ rβ})) + + {k k}_{33} \cdot &Center Dot; {u u}_{sα sα} \\ {\overset{\cdot \cdot}{i i}}_{sβ sβ} = = - - {k k}_{11} \cdot \cdot {i i}_{sβ sβ} + + {k k}_{22} \cdot &Center Dot; ((b b \cdot \cdot {ψ ψ}_{rβ rβ} - - {ω ω}_{r r} \cdot \cdot {ψ ψ}_{rα rα})) + + {k k}_{33} \cdot &Center Dot; {u u}_{sβ sβ} \\ {\overset{\cdot \cdot}{ψ ψ}}_{rα rα} = = a a \cdot &Center Dot; {i i}_{sα sα} - - b b \cdot &Center Dot; {ψ ψ}_{rα rα} - - {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rβ rβ} \\ {\overset{\cdot &Center Dot;}{ψ ψ}}_{rβ rβ} = = a a \cdot &Center Dot; {i i}_{sβ sβ} - - b b \cdot &Center Dot; {ψ ψ}_{rβ rβ} + + {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rα rα} \end{matrix}$

上式中，静止坐标系下，i_sα和i_sβ为定子电流i_s的分量，u_sα和u_sβ为定子电压u_s的分量，ψ_rα和ψ_rβ为转子磁链ψ_r分量；In the above formula, in the static coordinate system, i _sα and is _β are the components of the stator current i _s , u _sα and u _sβ are the components of the stator voltage u _s , and ψ _rα and ψ _rβ are the components of the rotor flux linkage ψ _r ;

$σ σ = = 11 - - {L L}_{m m}^{22} / / {L L}_{s the s} {L L}_{r r}$

k₂＝L_m/σL_sL_r k ₂ ＝L _m /σL _s L _r

k₃＝1/σL_s k ₃ =1/σL _s

a＝L_m/T_r a=L _m /T _r

b＝1/T_r b=1/ _Tr

其次，对上述模型作基于极致扭曲（Super-Twisting）理论的变换如下：Secondly, the transformation of the above model based on the Super-Twisting theory is as follows:

$\{\begin{matrix} {z z}_{11} = = {i i}_{sα sα} \\ {z z}_{22} = = {i i}_{sβ sβ} \\ {z z}_{33} = = b b \cdot &Center Dot; {ψ ψ}_{rα rα} + + {ω ω}_{r r} \cdot &Center Dot; {ψ ψ}_{rβ rβ} \\ {z z}_{44} = = b b \cdot \cdot {ψ ψ}_{rβ rβ} - - {ω ω}_{r r} \cdot \cdot {ψ ψ}_{rα rα} \end{matrix}$

$\{\begin{matrix} {\overset{\cdot \cdot}{z z}}_{11} = = - - {k k}_{11} \cdot \cdot {z z}_{11} + + {k k}_{22} \cdot &Center Dot; {z z}_{33} + + {k k}_{33} \cdot &Center Dot; {u u}_{sα sα} \\ {\overset{\cdot &Center Dot;}{z z}}_{22} = = - - {k k}_{11} \cdot &Center Dot; {z z}_{22} + + {k k}_{22} \cdot &Center Dot; {z z}_{44} + + {k k}_{33} \cdot &Center Dot; {u u}_{sβ sβ} \end{matrix}$

于是，根据极致扭曲（Super-Twisting）理论的形式构建转子磁链观测器：Therefore, the rotor flux observer is constructed according to the form of the Super-Twisting theory:

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{\overset{^^}{z z}}}_{11} = = - - {k k}_{11} \cdot &Center Dot; {z z}_{11} + + {k k}_{22} \cdot \cdot {\overset{~ ~}{z z}}_{33} + + {k k}_{33} \cdot &Center Dot; {u u}_{sα sα} + + {λ λ}_{11} \cdot &Center Dot; {| | {e e}_{11} | |}^{0.5 0.5} \cdot &Center Dot; sgn sgn (({e e}_{11})) \\ {\overset{\cdot \cdot}{\overset{~ ~}{z z}}}_{33} = = {δ δ}_{11} \cdot &Center Dot; sgn sgn (({e e}_{11})) \\ {\overset{\cdot \cdot}{\overset{^^}{z z}}}_{22} = = - - {k k}_{11} \cdot \cdot {z z}_{22} + + {k k}_{22} \cdot \cdot {\overset{~ ~}{z z}}_{44} + + {k k}_{33} \cdot &Center Dot; {u u}_{sβ sβ} + + {λ λ}_{22} \cdot &Center Dot; {| | {e e}_{22} | |}^{0.5 0.5} \cdot &Center Dot; sgn sgn (({e e}_{22})) \\ {\overset{\cdot &Center Dot;}{\overset{~ ~}{z z}}}_{44} = = {δ δ}_{22} \cdot &Center Dot; sgn sgn (({e e}_{22})) \end{matrix}$

其中，e₁和e₂为误差值，有 sgn()是符号函数，λ₁、λ₂和δ₁、δ₂为预先设定的滑模增益。Among them, e ₁ and e ₂ are error values, there are sgn() is a sign function, and λ ₁ , λ ₂ and δ ₁ , δ ₂ are preset sliding mode gains.

将上式离散化，得到下式表述：The above formula is discretized, and the following formula is obtained:

$\{\begin{matrix} {\overset{^^}{z z}}_{11} ((k k)) = = {\overset{^^}{z z}}_{11} ((k k - - 11)) + + T T \cdot &Center Dot; [[- - {k k}_{11} \cdot &Center Dot; {z z}_{11} ((k k - - 11)) + + {k k}_{22} \cdot \cdot {\overset{~ ~}{z z}}_{33} ((k k - - 11)) \\ + + {k k}_{33} \cdot &Center Dot; {u u}_{sα sα} ((k k - - 11)) + + {λ λ}_{11} \cdot \cdot {| | {e e}_{11} ((k k - - 11)) | |}^{0.5 0.5} \cdot &Center Dot; sgn sgn (({e e}_{11} ((k k - - 11))))]] \\ {\overset{~ ~}{z z}}_{33} ((k k)) = = {\overset{~ ~}{z z}}_{33} ((k k - - 11)) + + T T \cdot \cdot {δ δ}_{11} \cdot &Center Dot; sgn sgn (({e e}_{11} ((k k - - 11)))) \\ {\overset{^^}{z z}}_{22} ((k k)) = = {\overset{^^}{z z}}_{22} ((k k - - 11)) + + T T \cdot \cdot [[- - {k k}_{11} \cdot \cdot {z z}_{22} ((k k - - 11)) + + {k k}_{22} \cdot \cdot {\overset{~ ~}{z z}}_{44} ((k k - - 11)) \\ + + {k k}_{33} \cdot \cdot {u u}_{sβ sβ} ((k k - - 11)) + + {λ λ}_{22} \cdot \cdot {| | | | {e e}_{22} ((k k - - 11)) | | | |}^{0.5 0.5} \cdot &Center Dot; sgn sgn (({e e}_{22} ((k k - - 11))))]] \\ {\overset{~ ~}{z z}}_{44} ((k k)) = = {\overset{~ ~}{z z}}_{44} ((k k - - 11)) + + T T \cdot &Center Dot; {δ δ}_{22} \cdot &Center Dot; sgn sgn (({e e}_{22} ((k k - - 11)))) \end{matrix}$

其中T表示系统处理周期，k表示某一次运算。Among them, T represents the system processing cycle, and k represents a certain operation.

最后，上式跟踪定子电流分量i_sα和i_sβ，输出观测结果和它们与转子磁链有如下关系：Finally, the above formula tracks the stator current components i _sα and i _sβ , and outputs the observed results and They have the following relationship with the rotor flux linkage:

${ψ ψ}_{rβ rβ} = = {&Integral; &Integral;}_{00}^{t t} ((- - {\overset{~ ~}{z z}}_{44} + + \frac{{L L}_{m m}}{{T T}_{r r}} \cdot &Center Dot; {\overset{^^}{z z}}_{22})) \cdot &Center Dot; dt dt$

其中，L_m为励磁电感，T_r为转子时间常数；Among them, L _m is the excitation inductance, T _r is the rotor time constant;

上式的实现过程中有两点值得说明。There are two points worth explaining in the implementation of the above formula.

第一，上式中包含纯积分环节。纯积分环节受积分初值和零漂影响，存在直流偏置和初始相位问题。为解决这一问题，用一阶低通滤波器来代替纯积分环节，并加以适当的幅值和相位补偿。此外，根据极致扭曲（Super-Twisting）理论的形式构建的转子磁链观测器虽然也含有纯积分环节，但是它同时应用了滑模，所以直流偏置的影响会被滑模作用纠正。First, the above formula contains a pure integral link. The pure integration link is affected by the initial value of the integration and zero drift, and there are DC bias and initial phase problems. To solve this problem, a first-order low-pass filter is used to replace the pure integral link, and appropriate amplitude and phase compensation are added. In addition, although the rotor flux observer constructed in the form of Super-Twisting theory also contains a pure integral link, it also applies a sliding mode, so the influence of the DC bias will be corrected by the sliding mode effect.

第二，上式中含有转子时间常数T_r。当电机运行时，T_r的值会因为温升和转差变化导致的集肤效应异动，而产生变化。但是，实际系统中比大两个数量级，因此T_r的变化对转子磁链的观测结果影响不大。Second, the above formula contains the rotor time constant T _r . When the motor is running, the value of _Tr will change due to skin effect changes caused by temperature rise and slip changes. However, in real systems Compare is two orders of magnitude larger, so changes in _Tr have little effect on the observed results of rotor flux linkage.

具体实施时，用带有幅值和相位补偿的一阶低通滤波器，代替纯积分环节，其流程图如图3所示。假设当前定子频率为ω_e，一阶低通滤波器的截止频率ω_c，则补偿增益系数K应为K＝ω_c/ω_e。实际使用时可保持K为常值3，而截止频率ω_c根据电机运行状况给定。整套系统刚开始运行时，将截止频率ω_c设为一个合适的固定值（如30rad/s）；待下述空间位置角θ₁稳定后，ω_c由θ₁经过微分换算得到的定子角频率ω_e决定。During specific implementation, a first-order low-pass filter with amplitude and phase compensation is used to replace the pure integral link, and its flow chart is shown in Figure 3. Assuming that the current stator frequency is ω _e and the cut-off frequency ω _c of the first-order low-pass filter, the compensation gain coefficient K should be K=ω _c /ω _e . In actual use, K can be kept at a constant value of 3, and the cut-off frequency ω _c is given according to the operating conditions of the motor. When the whole system starts to run, set the cut-off frequency ω _c to an appropriate fixed value (such as 30rad/s); after the following spatial position angle θ ₁ is stabilized, ω _c is the angular frequency of the stator obtained by differential conversion from θ ₁ ω _e decides.

(b)由上述观测的转子磁链值[ψ_rαψ_rβ]^T，计算其空间位置角θ₁。(b) From the rotor flux value [ψ _rα ψ _rβ ] ^T observed above, calculate its spatial position angle θ ₁ .

${θ θ}_{11} = = a a tan the tan ((\frac{{ψ ψ}_{rα rα}}{{ψ ψ}_{rβ rβ}}))$

该空间位置角为转子磁链定向的依据，即同步速坐标系的空间位置角。The spatial position angle is the basis for the orientation of the rotor flux linkage, that is, the spatial position angle of the synchronous speed coordinate system.

(c)将转子磁链电流模型作为可调模型，通过自适应律来辨识异步电机转速的过程如下。(c) Using the rotor flux current model as an adjustable model, the process of identifying the speed of the asynchronous motor through the adaptive law is as follows.

首先，构建基于转子磁链电流模型的观测器：First, construct an observer based on the rotor flux current model:

${\overset{^^}{ψ ψ}}_{rα rα} = = \frac{11}{11 + + {T T}_{r r} \cdot &Center Dot; p p} \cdot \cdot (({L L}_{m m} \cdot \cdot {i i}_{sα sα} - - {\overset{^^}{ω ω}}_{r r} \cdot &Center Dot; {T T}_{r r} \cdot &Center Dot; {\overset{^^}{ψ ψ}}_{rβ rβ}))$

${\overset{^^}{ψ ψ}}_{rβ rβ} = = \frac{11}{11 + + {T T}_{r r} \cdot &Center Dot; p p} \cdot &Center Dot; (({L L}_{m m} \cdot &Center Dot; {i i}_{sβ sβ} + + {\overset{^^}{ω ω}}_{r r} \cdot &Center Dot; {T T}_{r r} \cdot &Center Dot; {\overset{^^}{ψ ψ}}_{rα rα}))$

上式中， ${[\begin{matrix} {\hat{ψ}}_{rα} & {\hat{ψ}}_{rβ} \end{matrix}]}^{T}$ 是估计的转子磁链值，p为微分算子，是辨识得到的异步电机转速，L_m为励磁电感，T_r为转子时间常数。In the above formula, ${[\begin{matrix} {\hat{ψ}}_{rα} & {\hat{ψ}}_{rβ} \end{matrix}]}^{T}$ is the estimated rotor flux linkage value, p is the differential operator, is the identified asynchronous motor speed, L _m is the excitation inductance, T _r is the rotor time constant.

其次，将基于极致扭曲（Super-Twisting）理论的滑模观测器的输出值[ψ_rαψ_rβ]^T作为参考值， ${[\begin{matrix} {\hat{ψ}}_{rα} & {\hat{ψ}}_{rβ} \end{matrix}]}^{T}$ 作为可调值，根据模型参考自适应（MRAS）原理，静止坐标系下，自适应误差值按下式求得：Secondly, the output value [ψ _rα ψ _rβ ] ^T of the sliding mode observer based on the Super-Twisting theory is used as a reference value, ${[\begin{matrix} {\hat{ψ}}_{rα} & {\hat{ψ}}_{rβ} \end{matrix}]}^{T}$ As an adjustable value, according to the model reference adaptive (MRAS) principle, in the stationary coordinate system, the adaptive error value is obtained by the following formula:

$ϵ ϵ = = {\overset{^^}{ψ ψ}}_{rα rα} \cdot &Center Dot; {ψ ψ}_{rβ rβ} - - {\overset{^^}{ψ ψ}}_{rβ rβ} \cdot &Center Dot; {ψ ψ}_{rα rα}$

最后，根据稳定性原理设计转速的自适应律，用PI控制器等效，因此“转速自适应模块”PI控制器的输出值即为异步电机转速辨识结果 Finally, according to the principle of stability, the adaptive law of the speed is designed, which is equivalent to the PI controller, so the output value of the PI controller of the "speed adaptive module" is the speed identification result of the asynchronous motor

3.将静止坐标系下的量，以及由观测器得到的转子磁链空间位置角θ₁，输入“2相静止/2相同步速坐标变换模块”，得到同步速坐标系下的定子电流i_s的分量i_sd和i_sq。3. Input the quantity in the static coordinate system and the rotor flux linkage spatial position angle θ ₁ obtained by the observer into the "2-phase stationary/2-phase synchronous speed coordinate transformation module" to obtain the stator current i in the synchronous speed coordinate system The components i _sd and i _sq of _s .

4.转子磁链幅值控制：输入转速给定值由“转子磁链幅值判断模块”判断电机是否运行在弱磁状态下。若电机在恒磁通运行状态，则输出定子电流d轴分量给定值为常值。若电机弱磁运行，则根据查表法得到将作为给定值，i_sd作为反馈值，通过“电流环PI控制器模块”，输出定子电压d轴分量的给定值 4. Rotor flux amplitude control: input speed given value The "rotor flux amplitude judging module" judges whether the motor is running in a field-weakening state. If the motor is in the state of constant magnetic flux operation, the given value of the d-axis component of the stator current will be output is a constant value. If the motor is running with weak field, it can be obtained according to the look-up table method Will As a given value, i _sd is used as a feedback value, through the "current loop PI controller module", the given value of the d-axis component of the stator voltage is output

5.速度与转矩控制：外部指定作为转速给定值，将辨识结果作为反馈值，通过“速度环PI控制器模块”，输出定子电流q轴分量给定值将作为给定值，i_sq作为反馈值，通过“电流环PI控制器模块”，输出定子电压q轴分量的给定值 5. Speed and torque control: external designation As the speed given value, the identification result As a feedback value, through the "speed loop PI controller module", the given value of the stator current q-axis component is output Will As a given value, i _sq is used as a feedback value, through the "current loop PI controller module", the given value of the q-axis component of the stator voltage is output

6.逆变器控制信号产生：将上述求得的定子电压给定值和以及转子磁链空间位置角θ₁，输入“2相同步速/2相静止坐标变换模块”，得到定子电压在静止坐标系下的分量和上述分量经由电压空间矢量脉宽调制模块计算得到逆变器触发脉冲，输给逆变器，即可控制供给三相异步电机的各相电压。6. Inverter control signal generation: the stator voltage given value obtained above and And rotor flux space position angle θ ₁ , input "2-phase synchronous speed/2-phase static coordinate transformation module" to get the component of stator voltage in the static coordinate system and The above components are calculated by the voltage space vector pulse width modulation module to obtain the trigger pulse of the inverter, and then input to the inverter to control the voltage of each phase supplied to the three-phase asynchronous motor.

实施例1Example 1

下面给出一个具体实施例，一台三相异步电机的出厂参数如下表：A specific embodiment is provided below, and the factory parameters of a three-phase asynchronous motor are as follows:

电机参数表Motor parameter table

应用本发明异步电机转子磁链观测与转速辨识的方法，控制电机运行状况为启动-40r/min-500r/min-1000r/min-500r/min-40r/min-停止，共运行约40秒，各运行状况的持续时间和结果如图4、图5所示，两张图为同一结果的不同排版。Apply the method of the present invention for rotor flux observation and speed identification of asynchronous motors, and control the motor operating conditions to start-40r/min-500r/min-1000r/min-500r/min-40r/min-stop, and run for about 40 seconds in total. The duration and results of each operating status are shown in Figure 4 and Figure 5, and the two figures are different layouts of the same result.

图4中：A为本发明算法辨识的转速、B为光电码盘读取的转速、C为两种方法获得转速的差、D是作为参考模型和可调模型的磁链观测结果（几近重合），E为图中黑框处放大的波形。Among Fig. 4: A is the rotating speed identified by the algorithm of the present invention, B is the rotating speed read by the photoelectric code disc, C is the difference between the two methods of obtaining the rotating speed, and D is the flux linkage observation result as a reference model and an adjustable model (almost Coincidence), E is the enlarged waveform at the black box in the figure.

图5中：A为辨识转速与码盘转速（几近重合）、B为参考模型和可调模型的磁链观测之差、C是作为可调模型磁链观测结果、D是作为参考模型磁链观测结果，E为图中黑框处放大的波形。In Figure 5: A is the identification speed and code wheel speed (almost coincident), B is the difference between the flux linkage observations of the reference model and the adjustable model, C is the flux observation result of the adjustable model, and D is the magnetic flux of the reference model. Chain observation results, E is the enlarged waveform at the black box in the figure.

上述图4、图5是由控制系统数模转换输出，用YOKOGAWA公司DL750示波器记录得到的。The above Figure 4 and Figure 5 are obtained by the digital-to-analog conversion output of the control system and recorded with the DL750 oscilloscope of YOKOGAWA Company.

40r/min运行状况下，基于极致扭曲理论的转子磁链观测器，其观测结果比传统技术更加准确，能够作为参考模型，所以本发明在低速下的转速辨识结较为准确。Under the operating condition of 40r/min, the observation result of the rotor flux observer based on the extreme twist theory is more accurate than the traditional technology, and can be used as a reference model, so the speed identification knot of the present invention at low speed is more accurate.

Claims

1. a method for asynchronous machine rotor flux observation and Speed Identification, is characterized in that, according to the stator voltage u of the asynchronous machine recording in real time _s, stator current i _s, by the sliding mode observer based on ultimate attainment distortion theory, observation obtains rotor flux ψ _rand as reference value, the rotor flux of being tried to achieve by rotor flux current model as adjustable value, form the model reference adaptive system based on rotor flux, by adaptive law, carry out identification Rotational Speed of Asynchronous Motor

By the described sliding mode observer based on ultimate attainment distortion theory, observation obtains rotor flux ψ _rprocess as follows:

First, threephase asynchronous machine is write to following form in the Mathematical Modeling under rest frame:

\{\begin{matrix} {\overset{\cdot}{i}}_{sα} = - k_{1} \cdot i_{sα} + k_{2} \cdot (b \cdot ψ_{rα} + ω_{r} \cdot ψ_{rβ}) + k_{3} \cdot u_{sα} \\ {\overset{\cdot}{i}}_{sβ} = - k_{1} \cdot i_{sβ} + k_{2} \cdot (b \cdot ψ_{rβ} - ω_{r} \cdot ψ_{rα}) + k_{3} \cdot u_{sβ} \\ {\overset{\cdot}{ψ}}_{rα} = a \cdot i_{sα} - b \cdot ψ_{rα} - ω_{r} \cdot ψ_{rβ} \\ {\overset{\cdot}{ψ}}_{rβ} = a \cdot i_{sβ} - b \cdot ψ_{rβ} + ω_{r} \cdot Ψ_{rα} \end{matrix}

In above formula, i _{s α}and i _{s β}for stator current i _scomponent, u _{s α}and u _{s β}for stator voltage u _scomponent, ψ _{r α}and ψ _{r β}for rotor flux ψ _rcomponent;

R _sfor stator resistance, L _mfor the steady-state value of magnetizing inductance, L _sand L _rbe respectively stator, inductor rotor, T _rfor rotor time constant, ω _rfor rotor speed, other scales that occur in above formula are shown:

σ = 1 - L_{m}^{2} / L_{s} L_{r}

k_{1} = R_{s} / {σL}_{s} + L_{m}^{2} / {σL}_{s} L_{r} T_{r}

k ₂＝L _m/σL _sL _r

k ₃＝1/σL _s

a＝L _m/T _r

b＝1/T _r

Secondly, the conversion of above-mentioned model being done based on ultimate attainment distortion theory is as follows:

\{\begin{matrix} z_{1} = i_{sα} \\ z_{2} = i_{sβ} \\ z_{3} = b \cdot ψ_{rα} + ω_{r} \cdot ψ_{rβ} \\ z_{4} = b \cdot ψ_{rβ} - ω_{r} \cdot ψ_{rα} \end{matrix}

Z wherein ₁～z ₄for mathematics intermediate variable;

After conversion, the Mathematical Modeling under threephase asynchronous machine rest frame is written as:

\{\begin{matrix} {\overset{\cdot}{z}}_{1} = - k_{1} \cdot z_{1} + k_{2} \cdot z_{3} + k_{3} \cdot u_{sα} \\ {\overset{\cdot}{z}}_{2} = - k_{1} \cdot z_{2} + k_{2} \cdot z_{4} + k_{3} \cdot u_{sβ} \end{matrix}

So, according to the form of ultimate attainment distortion theory, build rotor flux observer:

\{\begin{matrix} {\overset{\overset{\cdot}{^}}{z}}_{1} = - k_{1} \cdot z_{1} + k_{2} \cdot {\tilde{z}}_{3} + k_{3} \cdot u_{sα} + λ_{1} \cdot {| e_{1} |}^{0.5} \cdot sgn (e_{1}) \\ {\overset{\overset{\cdot}{~}}{z}}_{3} = δ_{1} \cdot sgn (e_{1}) \\ {\overset{\overset{\cdot}{^}}{z}}_{2} = - k_{1} \cdot z_{2} + k_{2} \cdot {\tilde{z}}_{4} + k_{3} \cdot u_{sβ} + λ_{2} \cdot {| e_{2} |}^{0.5} \cdot sgn (e_{2}) \\ {\overset{\overset{\cdot}{~}}{z}}_{4} = δ_{2} \cdot sgn (e_{2}) \end{matrix}

Wherein, e ₁and e ₂for error amount, have sgn () is-symbol function, λ ₁, λ ₂and δ ₁, δ ₂for predefined sliding formwork gain;

Finally, the measured value obtaining from above formula with they and rotor flux have following relation:

ψ_{rα} = {&Integral;}_{0}^{t} (- {\tilde{z}}_{3} + \frac{L_{m}}{T_{r}} \cdot {\hat{z}}_{1}) \cdot dt

ψ_{rβ} = {&Integral;}_{0}^{t} (- {\tilde{z}}_{4} + \frac{L_{m}}{T_{r}} \cdot {\hat{z}}_{2}) \cdot dt

In above formula, L _mfor magnetizing inductance, T _rfor rotor time constant;

The rotor flux being obtained by above-mentioned observer is expressed as [ψ under rest frame _{r α}ψ _{r β}] ^t, as the reference value of model reference adaptive method.

2. the method for rotor flux observation according to claim 1 and Speed Identification, is characterized in that, described rotor flux current model is as adjustable model, by adaptive law identification Rotational Speed of Asynchronous Motor process as follows:

First, build the observer based on rotor flux current model,

{\hat{ψ}}_{rα} = \frac{1}{1 + T_{r} \cdot p} \cdot (L_{m} \cdot i_{sα} - {\hat{ω}}_{r} \cdot T_{r} \cdot {\hat{ψ}}_{rβ})

{\hat{ψ}}_{rβ} = \frac{1}{1 + T_{r} \cdot p} \cdot (L_{m} \cdot i_{sβ} + {\hat{ω}}_{r} \cdot T_{r} \cdot {\hat{ψ}}_{rα})

In above formula, be the rotor flux value of observation, p is differential operator, the Rotational Speed of Asynchronous Motor that identification obtains, T _rfor rotor time constant;

Secondly, by the output valve [ψ of the sliding mode observer based on ultimate attainment distortion theory _{r α}ψ _{r β}] ^tas reference value, as adjustable value, according to model reference adaptive method, adaptive error value is tried to achieve by following formula:

ϵ = {\hat{ψ}}_{rα} \cdot ψ_{rβ} - {\hat{ψ}}_{rβ} \cdot ψ_{rα}

Finally, according to the adaptive law of stability principle design speed, with the equivalence of PI controller, so the output valve of PI controller is Identification of Rotational Speed of Asynchronous Motor result