CN115208251A - Self-adaptive quasi-proportional resonance sensorless control method with parameter identification - Google Patents

Abstract

The invention provides a self-adaptive quasi-proportional resonance sensorless control method with parameter identification, which aims at solving the problem that the output buffeting of a system is obvious due to the fact that a large amount of higher harmonics generated by a sign function are introduced when the traditional sliding mode control (SMO) utilizes the sign function and a Low Pass Filter (LPF) to realize sensorless control of a Permanent Magnet Synchronous Motor (PMSM). Meanwhile, the PMSM parameters of the system are identified on line and fed back to the control model, and the robustness and the control precision of the system parameters are improved. And respectively adopting a Bode diagram, a Popov theory and a root locus to carry out stability analysis on the AQPR, the parameter identification and the system controller model. Finally, experimental results show that the method has higher tracking precision and stronger parameter robustness under different carrier ratios and working conditions.

Description

Self-adaptive quasi-proportional resonance sensorless control method with parameter identification

Technical Field

The invention belongs to the technical field of permanent magnet synchronous motor control, and particularly relates to a self-adaptive quasi-proportional resonant sensorless control method with parameter identification.

Background

The permanent magnet synchronous motor is widely applied to daily life due to the advantages of simple structure, small volume, low manufacturing cost and the like. In order to realize excellent control performance of a Permanent Magnet Synchronous Motor (PMSM), it is necessary to accurately acquire the rotational speed and position information of the motor. The traditional position detection method adopts mechanical sensors such as electronic type or electromechanical type to directly measure, such as Hall effect devices, rotary transformers, optical encoders and the like.

However, the installation of these mechanical sensors increases the size, volume, weight, etc. of the system, which severely limits the development of miniaturization of the motor. Meanwhile, some sensors have strict requirements on working environment, the measurement precision is greatly influenced by the environment, the number of the connected electric elements is increased, and the anti-interference performance is reduced. Therefore, the research on sensorless control of PMSM has received much attention, and many control methods have been proposed, such as an extended back electromotive force (EMF) method, a flux linkage observation method, an extended kalman filter method, and a high-frequency signal injection method. The EMF method is simple and reliable, and is widely applied to medium-high speed occasions, and the EMF-based control method mainly comprises methods such as sliding mode control, a state observer, model reference adaptive control and the like. The sliding mode control has low requirement on the precision of a system model, is insensitive to parameter change and external interference, and is a special nonlinear control system with a variable structure, so that the sliding mode control can be used for estimating EMF and extracting the rotating speed and position information in the EMF. In the prior art, the phenomenon that resonance is caused due to the fact that the low switching frequency period is close to an LC resonance point under medium and high rotating speeds is analyzed, so that the rotating speed and position estimation performance of a motor is poor. In the prior art, aiming at nonlinearity, uncertainty and disturbance of a PMSM mathematical model, the PMSM mathematical model is linearized by using Jacobian linearization, an integral state feedback controller is designed, and a Sliding Mode Observer (SMO) and a disturbance Observer are used in a cascade Mode. Experimental results show that the method improves the sensorless control performance in a wide speed range. In addition, the prior art analyzes the estimation error of the rotor position, and harmonic waves in an estimation signal are difficult to eliminate, so that an adaptive notch filter is provided, the fundamental wave of the position estimation signal is extracted from the output of the SMO system and is applied to a phase-locked loop (PLL), and EMF harmonic wave error can be effectively compensated in an adaptive manner. The method aims at the problems of non-linearity of an inverter and flux linkage space harmonic waves, so that EMF estimation is inaccurate, and harmonic fluctuation of a rotor position is caused.

However, the sign function introduced by the SMO-based sensorless control method may deteriorate the system output and aggravate the high-frequency buffeting phenomenon, and the LPF may generate a phase shift while filtering the high-frequency signal, which may cause an increase in the system output error and a decrease in the control accuracy. In order to solve the above problems and improve PMSM control performance, the prior art combines an SMO and a Phase Locked Loop (PLL), and on the basis of the conventional SMO principle, in order to reduce high-frequency buffeting, a switching function with a double boundary layer structure is adopted to replace a conventional sign function, and a PLL is used to extract position information, and experimental results show that the method has good tracking performance. In the prior art, a self-adaptive frequency second-order disturbance observer is established to estimate the flux linkage and the EMF, so that the requirement that the phase delay compensation is required for estimating the EMF by the traditional SMO is eliminated, and the position estimation error is reduced. Experimental results prove that the method can provide excellent sensorless control performance. Because of the presence of low-order harmonic components, magnetic field saturation, dc offset, etc., the EMF information extracted by conventional low-pass filters (LPFs) is not accurate, resulting in low position estimation accuracy and significant phase delay. In order to solve the problem, the prior art also provides sliding mode control of a bi-quad generalized integrator phase-locked loop, eliminates harmonic components in EMF estimated values, performs delay compensation, and improves dynamic response speed and control accuracy. Aiming at the high-frequency buffeting of the traditional SMO and the lack of limited time convergence, a high-order sliding mode control law is provided in the prior art to restrain the high-frequency buffeting, and a terminal sliding mode surface is designed to realize the limited time convergence. Experiments prove that the method has higher estimation precision under the condition of ensuring robustness. However, although the methods have better control accuracy, the methods still have the problems that when the permanent magnet synchronous motor runs at zero speed or extremely low speed, the signal-to-noise ratio of effective signals is low, extraction is difficult, and the control performance of the motor cannot be guaranteed under different carrier ratios, so that the method extracts the speed and position information of the rotor inaccurately and reduces the control accuracy of the motor when the motor runs at zero speed or extremely low speed.

Disclosure of Invention

In view of the above problems, the present invention provides a method for controlling a self-adaptive quasi-proportional resonant sensorless system with parameter identification.

The technical solution for realizing the purpose of the invention is as follows:

an adaptive quasi-proportional resonant sensorless control method with parameter identification is characterized by comprising the following steps:

step 1: establishing a current state equation of the permanent magnet synchronous motor on a static coordinate system:

wherein，R ₀ Represents the stator resistance, [ i ] _α ,i _β ] ^T Represents the current in the alpha-beta axis, [ E ] _α ,E _β ] ^T Represents the extended back emf;

step 2: establishing an AQPR _ PI control model according to the formula (3);

and step 3: acquiring an extended back electromotive force estimation value by using an AQPR _ PI control model;

and 4, step 4: and obtaining the rotating speed estimated value and the rotor angle of the permanent magnet synchronous motor according to the expanded back electromotive force estimated value.

Further, the step of establishing an AQPR _ PI control model in step 2 includes:

step 21: establishing a sliding mode observation function shown in the formula (10) according to the formula (3), and acquiring a current observation value:

wherein the content of the first and second substances,

and

represents an observed value of the stator current,

the identification value of the stator resistance is represented,

representing an inductance identification value;

step 22: subtracting the current detection value from the current observation value to obtain a stator current error:

wherein:

step 23: according to the Popov hyperstability theory, equation (17) is obtained:

wherein, gamma 1 ² Represents any finite positive number;

step 24: solving equation (17) in reverse to obtain equation (18):

wherein:

step 25: substituting equation (19) into equation (18) yields the values for the stator resistance and inductance parameter, respectively:

identification value of stator resistance:

identification value of inductance parameter:

wherein k is _p ，k _i Is a gain parameter.

Further, the specific operation steps of step 3 include:

step 31: converting the time domain state equation of equation (10) into the S domain state equation of equation (11):

step 32: calculating an estimate of the extended back emf using a transfer function, the transfer function being:

wherein k is _p 、k _r Representing the gain parameter, ω _c Representing bandwidth, ω ₀ Represents the resonance frequency;

step 33: substituting equation (12) into equation (11) yields an extended bemf estimate calculation equation:

step 34: and (5) substituting the identification value of the stator resistance and the identification value of the inductance parameter obtained in the step (25) into a formula (13), and finally calculating the estimation value of the expanded back electromotive force.

Compared with the prior art, the invention has the following beneficial effects:

firstly, the model of the invention has simple structure, less control parameters and convenient adjustment; meanwhile, the online calculation speed is high, the model running time is short, and the stability is high; the method can reduce the output error of the system, weaken the buffeting phenomenon and improve the robustness and the control precision of system parameters.

Secondly, the invention provides a self-adaptive quasi-proportional resonance sensorless control method with parameter identification, which utilizes the frequency domain selection characteristic and the self-adaptive filtering performance of self-adaptive quasi-proportional resonance control to replace a sign function and an LPF model, reduces the output error of a system and improves the control precision; meanwhile, parameters in the controller are identified on line and fed back to the controller, and the robustness and the anti-interference capability of system parameters are enhanced. Finally, experimental results show that the method has higher tracking precision and stronger parameter robustness under different carrier ratios and working conditions.

Drawings

FIG. 1 is a diagram of a sensor-less control architecture for SMO based PLL;

FIG. 2 is a diagram of an AQPR _ PI control model;

3 a-3 c are Bode plot analyses of the effect of changes in three parameters, kp, kr, and ω c, on the controller;

FIGS. 4 a-4 b are simulation results of parameter identification;

FIGS. 5 a-5 c are root trajectories of the control system in a discrete state;

FIG. 6 is a PMSM experimental platform;

FIG. 7 is a control model structure proposed in the present invention;

FIGS. 8 a-8 b are experimental results of the SMO method at a high carrier ratio;

FIGS. 9 a-9 b are experimental results of SMO method at low carrier ratio;

FIGS. 10 a-10 b are experimental results of the AQPR _ PI method under the condition of high carrier ratio; FIG. 10a is an experimental result of estimating current and measuring current; FIG. 10b is an experimental result of EMF estimation, rotational speed error and position error;

11 a-11 b are experimental results of AQPR _ PI method under low carrier ratio condition; FIG. 11a is an experimental result of estimating current and measuring current; FIG. 11b is an experimental result of EMF estimation, rotational speed error, and position error;

FIG. 12 shows the results of a parameter identification experiment of resistance and inductance under dynamic conditions;

FIGS. 13 a-13 d are comparative results of control performance before and after identification; fig. 13a is an experimental result of measuring the rotation speed, the estimated rotation speed and the rotation speed error before identification, fig. 13b is an experimental result of measuring the position, the estimated position and the position error before identification, fig. 13c is an experimental result of measuring the rotation speed, the estimated rotation and the rotation speed error after identification, and fig. 13d is an experimental result of measuring the position, the estimated position and the position error after identification.

Detailed Description

In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.

1. Against the background of conventional SMO sensorless control

The PMSM mathematical model in the stationary coordinate system can be expressed as:

wherein [ u ] _α ,u _β ] ^T Denotes the voltage at the alpha-beta axis of the stationary coordinate system, [ i ] _α ,i _β ] ^T Denotes the current in the alpha-beta axis, R ₀ Representing stator resistance, ω _e Representing electrical angular velocity, theta _e Indicating rotor position angle, L _d And L _q Representing stator inductance, for surface-mounted PMSM, L _d ＝L _q ＝L ₀ . p represents a differential operator, Ψ _f Denotes a permanent magnet flux linkage, [ E ] _α ,E _β ] ^T Represents extended back-electromotive force (EMF).

As can be seen from equation (2), since the EMF includes information on the rotational speed and the rotor position, the rotational speed and the rotor position can be calculated by accurately observing the EMF. Therefore, the EMF is obtained by using the SMO method, and in order to establish the SMO model, equation (2) is converted into a current state equation shown in equation (3) for obtaining the current detection value:

the [ i ] in the formula (3) _α ,i _β ] ^T As a variable of the equation of state, [ u ] _α ,u _β ] ^T As a system outputEstablishing a sliding mode observation function shown as a formula (4) to obtain a current observation value:

wherein the content of the first and second substances,

and

represents the observed value of stator current, [ Z ] _α ,Z _β ] ^T An observed value representing the EMF;

subtracting the formula (3) from the formula (4) to obtain a stator current error equation formula (5), which is:

wherein, [ Delta i [ ] _α ,Δi _β ] ^T Represents a current error;

designing a sliding mode control rate as shown in equation (6):

wherein k represents a sliding mode controller gain parameter, sgn (·) represents a sign function. In order to make the current error converge finally, the function condition is reached according to the sliding mode surface

Namely:

therefore, the gain k needs to satisfy:

k＞max{-R ₀ |Δi _α |+E _α sgn(Δi _α )，-R ₀ |Δi _β |+E _β sgn(Δi _β )} (8)

fig. 1 shows a sensorless structure of a PLL-based SMO, and a sign function is adopted as a sliding mode surface switching function in a conventional SMO model, which will result in outputting a large amount of higher harmonics and causing buffeting. In order to reduce the phenomenon of buffeting, a low-pass filter is connected after the symbol function. When the state variable converges to the slip-form face, i.e. Δ i _α ＝0,Δi _β =0, equation (9) can be obtained:

wherein, the first and the second end of the pipe are connected with each other,

representing an estimate of EMF, ω _p Is the cut-off frequency of the LPF.

2. The invention provides a sensorless control method of adaptive quasi-proportional resonance with parameter identification

In the traditional SMO method, a sign function is adopted in order to enable the system to rapidly converge to a sliding mode surface, but the introduction of the sign function can cause a large amount of higher harmonics, so that the system output buffeting is obvious. Meanwhile, the LPF added in the traditional SMO can generate control delay and phase shift, and when the fundamental frequency is close to the switching frequency, the filtering effect is reduced, and the control precision of the system is influenced. Therefore, the method adopts the AQPR (adaptive quasi-proportional resonance) to replace a sign function and the LPF, and simultaneously carries out online identification (PI) on stator resistance and inductance parameters and feeds the parameters back to the AQPR to establish an AQPR _ PI control model, thereby finally improving the robustness of system parameters, reducing the output buffeting of the system and improving the tracking precision. Fig. 2 is a diagram of an AQPR _ PI control model, in which the upper half represents AQPR and the lower half represents PI (parameter identification). The specific process comprises the following steps:

from equation (3), equation (10) can be derived:

wherein the content of the first and second substances,

the identification value of the stator resistance is represented,

representing an inductance identification value;

converting the time domain state equation of equation (10) into the S domain state equation of equation (11):

wherein k is _p 、k _r Representing the gain parameter, ω _c Representing bandwidth, ω ₀ Represents the resonant frequency;

substituting equation (12) into equation (11) yields an estimate of EMF:

subtracting the formula (10) from the formula (3) to obtain the current error equation shown in the formula (14), and the variable expressions related to the formulas (15), (16) and the formula (14).

According to the Popov hyperstability theory, equation (17) is obtained:

wherein, gamma is ₁ ² Representing any finite positive number, the parameter identification model is stable as shown in equation (17).

Solving equation (17) inversely to obtain equation (18), where equation (19) is the variable R in equation (18) ₁ And (5) expressing.

Substituting the formula (19) into the formula (18) to obtain the identification value of the stator electric group, as shown in the formula (20):

similarly, the identification value of the inductance parameter can be obtained, as shown in formula (21):

wherein k is _p ，k _i Is a gain parameter;

because the stator resistance and inductance parameters in the formula (13) are fixed values generally determined when a manufacturer produces a motor, but in the use process of the motor, the resistance and the inductance can be changed along with factors such as temperature rise and magnetic field saturation, actual values of the two parameters are measured through the formulas (20) and (21), and estimated values of the stator resistance and inductance parameters identified by the formulas (20) and (21) are fed back to the formula (13), so that the parameter robustness of the system is improved.

3. AQPR controller and parameter identification analysis

The control model provided by the invention comprises an AQPR controller and a parameter identification part, and the AQPR comprises three parameters as shown in a formula (12): k is a radical of formula _p 、k _r And ω _c . FIG. 3 shows a Bode plot analysis of the effect of these three parameter changes on the controller. Wherein FIG. 3a shows the resonance frequency ω ₀ 251rad/s, bandwidth ω _c Is 2.51rad/s, k _r Is 10,k _p Bode plots for the sequence 1.5,1,0.5 changes. When k is _p The amplitude outside the middle frequency range is increased, but the amplitude at the resonance frequency is almost the same, which shows that k _p The effect on resonance is small. Usually for harmonic suppression, k _p Should be less than 1. FIG. 3b shows the resonance frequency ω ₀ 251rad/s, bandwidth ω _c Is 2.51rad/s, k _p Is 0.5,k _r In turn, bode plots for 20, 10,5 changes. When k is _r Increase, amplitude increase at resonant frequency, indicating k _r Is the effect of reducing steady state error, but k _r The increase of the frequency band makes the frequency band range larger, increases the resonance influence, enlarges the useless signals and is not beneficial to the system stability. FIG. 3c shows the resonance frequency ω ₀ Is 251rad/s, k _p Is 0.5,k _r Is 10, bandwidth ω _c Bode plots were sequentially varied at 2.51rad/s, 5.02rad/s, and 7.53 rad/s. When ω is _c The amplitude value is almost unchanged at the resonance frequency, the bandwidth is reduced in sequence, the frequency domain selectivity is good, but the dynamic response speed of the system is reduced. Therefore, k is adjusted in order to have good control effect of AQPR _r Reduce steady state error and regulate omega _c The influence of frequency fluctuation is suppressed.

FIG. 4 shows simulation results of parameter identification. In the simulation, the PMSM rotation speed is set to 1000rpm, and the initial time resistor R is set ₀ 2.84 omega, inductance L ₀ It was 8.5mH. In order to verify the convergence rate and tracking accuracy of the parameter identification method, the resistance and the inductance are respectively expanded by two times at 0.1s, and are respectively expanded by two times at 0.3sAnd the value of the initial moment is restored. As can be seen from FIGS. 4a and 4b, in the steady-state process, the parameter identification tracking precision is higher, and the given value can be stably tracked. In the dynamic process of parameter change, the parameter identification can quickly track the change and converge to an actual value, and the dynamic response speed is higher.

4. Stability analysis of AQPR-PI model

According to equation (13), the closed loop transfer function of the EMF is found as:

and (2) combining the formula (12) and the formula (22), and according to the control principle, obtaining an EMF open-loop transfer function as follows:

wherein the content of the first and second substances,

denotes the gain parameter, T _e Representing the electrical time constant, T, of the PMSM _r Representing the equivalent time constant.

Considering the one-beat delay of the control system, and using bilinear transformation, the transfer function of the continuous time domain is converted into a discrete time system, and the S plane is mapped to the unit circle of the Z plane, resulting in formula (24):

where z represents a discrete operator.

Fig. 5 shows the root trajectory in a discrete state of the control system. FIG. 5a uses T _e ＝T _r =15ms, gain parameter k with increasing rotational speed _a And gradually increased, and the appropriate gain parameters are selected so that the characteristic root of the controller is inside the unit circle, and the system is stable. FIG. 5b is a graph showing the change in the inductance and resistanceDifferent electrical time constants are obtained. The change in the electrical constant has little effect on the gain parameter. FIG. 5c at 1000rpm with T _r Increase of (2), gain parameter k _a Gradually decreases. The critical gain parameter is obtained according to the root locus and the unit circle focus of fig. 5, and a proper gain parameter is selected so that the root locus is in the unit circle, and at this time, the system is in a stable state.

Examples

To further illustrate the effectiveness of the control method provided by the present invention, an experiment is performed on the PMSM experimental platform shown in fig. 6, and fig. 7 is a structure of an AQPR _ PI control model. The experimental platform is designed based on MATLAB/Simulink servo system algorithm model, when the control algorithm is built, an object code is compiled and generated, the object code is downloaded to an object machine through developed software, the object machine controls a servo PMSM through a special control card, a load PMSM is controlled through a motion control card, and PMSM parameters are represented in table 1.

TABLE 1 parameters of the PMSM model

1. Control performance comparison test under different carrier ratios

In order to verify the control performance of the AQPR-PI method under the condition of low carrier ratio, the method provided by the invention is compared with the SMO method based on PLL. Setting the PMSM rotation speed at 500rpm and the switching frequency at 10kHz and 1kHz, respectively, the corresponding carrier ratios are 300 and 30. Fig. 8 and 9 show the results of the SMO method in the high carrier ratio and the low carrier ratio, respectively. Fig. 10 and 11 show experimental results of the AQPR _ PI method at a high carrier ratio and a low carrier ratio, respectively.

Under high carrier ratio conditions, fig. 8a shows measured and estimated values of the SMO process α - β current, and fig. 8b shows the EMF estimate, the rotational speed error, and the position error of the SMO process. Fig. 7 shows that the estimated current can stably track the sampled current, the estimated EMF is not distorted, the standard deviations of the rotation speed error and the position error are 7.1483 and 0.1802 respectively, and the error fluctuation is small, which shows that the estimated values of the rotation speed and the position are relatively close to the measured values.

Under low carrier ratio conditions, fig. 9a shows measured and estimated values of the SMO process α - β current, and fig. 9b shows the EMF estimate, the rotational speed error, and the position error of the SMO process. As can be seen from fig. 9a, the estimated current has been distorted significantly and the measured current cannot be stably tracked. EMF estimates exhibit a large number of harmonics, creating severe distortion and buffeting. The standard deviation of the rotation speed error and the position error is 12.9091 and 0.205 respectively, and the error fluctuation is large, so that the smooth control of the PMSM is not facilitated.

Fig. 10 shows the experimental results of the AQPR _ PI method under high carrier ratio conditions. As can be seen from FIG. 10, under a high carrier ratio, the current estimated by the method can stably track the measured current, the EMF estimation is stable, the buffeting phenomenon is not obvious, the standard deviations of the rotating speed error and the position error are 5.8579 and 0.1316 respectively, the error fluctuation is small, and the tracking accuracy is high.

Fig. 11 shows the experimental results of the AQPR _ PI method under low carrier ratio conditions. As can be seen from fig. 11, the estimated current fluctuation is large, but the measured current can still be stably tracked, the EMF chattering is intensified, the standard deviation of the rotating speed error and the position error is 6.3405 and 0.1539 respectively, and the fluctuation is increased but still stable compared with the AQPR _ PI method under the high carrier ratio. Compared with the SMO method, the method provided by the invention has the advantages that the fluctuation of the estimated current and EMF is small under different carrier ratios, the measured value can be stably tracked, although the performance of the AQPI _ PI method is reduced to some extent under a low carrier ratio, no serious distortion and buffeting occur, and the estimation accuracy of the rotating speed and the position is still high.

2. Parameter robustness verification of AQPR _ PI method under dynamic condition

In order to verify the parameter robustness of the method provided by the invention, whether the parameter identification can be converged to an actual value is observed under the complex dynamic conditions of variable rotating speed and variable load. Fig. 12 shows the results of the parameter identification experiment of the resistance and the inductance under the dynamic condition, wherein when t =1s and load 6n.m is added, t =2s, the rotation speed is suddenly changed, and when 600rpm is changed to 1000rpm and t =3s, the load is removed. As can be seen from fig. 12, in the motor starting phase, since the parameters are in the alternating state, the recognition result has a convergence process, but can quickly return to the stable state. After the parameter identification method provided by the invention is adopted, the average value of the resistance identification is 1.8511, the standard deviation is about 0.0195 and the resistance can be effectively identified in a stable state. In steady state, the average value of inductance identification is 6.6721, and the standard deviation is about 0.0275. When a load is added, the current increases, causing the magnetic field saturation to increase, resulting in a decrease in inductance, and the opposite occurs when the load is removed. The identification result shows that the method can effectively identify the parameters under the dynamic condition, and the identification error is less than 1%.

Fig. 13 compares the control performance before and after recognition. As can be seen from fig. 13a and 13b, the rotation speed pulsation is large before identification, the rotation speed error fluctuation is obvious, and the standard deviation is 20.8062. Meanwhile, the position error is enlarged, the buffeting is intensified, the standard deviation is 0.1523, and the position error tends to rise along with the increase of the rotating speed. As can be seen from fig. 13c and 13d, when the parameter identification result is fed back to the control model, the rotation speed error and the position error become small, the fluctuation is reduced, and the standard deviation is 13.2467 and 0.0791, respectively. The result shows that the method can enhance the robustness of parameters, reduce the errors of the rotating speed and the position and improve the estimation precision.

Those not described in detail in this specification are within the skill of the art. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes in the embodiments and modifications of the invention can be made, and equivalents of some features of the invention can be substituted, and any changes, equivalents, improvements and the like, which fall within the spirit and principle of the invention, are intended to be included within the scope of the invention.

Claims (3)

1. An adaptive quasi-proportional resonant sensorless control method with parameter identification is characterized by comprising the following steps:

step 1: establishing a current state equation of the permanent magnet synchronous motor on a static coordinate system:

wherein R is ₀ Represents the stator resistance, [ i ] _α, i _β ] ^T Represents the current in the alpha-beta axis, [ E ] _α ,E _β ] ^T Represents the extended back emf;

and 2, step: establishing an AQPR _ PI control model according to the formula (3);

and 3, step 3: acquiring an extended back electromotive force estimation value by using an AQPR _ PI control model;

and 4, step 4: and obtaining the estimated value of the rotating speed of the permanent magnet synchronous motor and the rotor angle according to the estimated value of the expanded back electromotive force.

2. The adaptive quasi-proportional resonant sensorless control method with parameter identification as claimed in claim 1, wherein the step of establishing AQPR _ PI control model in step 2 comprises:

step 21: establishing a sliding mode observation function shown in the formula (10) according to the formula (3) to obtain a current observation value:

wherein the content of the first and second substances,

and

represents an observed value of the stator current,

the identification value of the stator resistance is represented,

representing an inductance identification value;

step 22: subtracting the current detection value from the current observation value to obtain a stator current error:

wherein:

step 23: according to the Popov hyperstability theory, equation (17) is obtained:

wherein γ 12 represents any finite positive number;

step 24: solving equation (17) in reverse to obtain equation (18):

wherein:

step 25: substituting equation (19) into equation (18) can obtain the stator resistance identification value and the inductance parameter identification value as follows:

identification value of stator resistance:

identification value of inductance parameter:

wherein k is _p ，k _i Is a gain parameter.

3. The adaptive quasi-proportional resonant sensorless control method with parameter identification as claimed in claim 2, wherein the specific operation of step 3 includes:

step 31: converting the time domain state equation of equation (10) into the S domain state equation of equation (11):

step 32: calculating an estimate of the extended back emf using a transfer function, the transfer function being:

wherein k is _p 、k _r Representing the gain parameter, ω _c Representing bandwidth, ω ₀ Represents the resonance frequency;

step 33: substituting equation (12) into equation (11) yields an extended bemf estimate calculation equation:

step 34: substituting the identification value of the stator resistance and the identification value of the inductance parameter obtained in the step 25 into the formula (13), and finally calculating the estimation value of the extended back electromotive force.

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