CN112422002A - Robust permanent magnet synchronous motor single current sensor prediction control method - Google Patents

Abstract

A robust single-current sensor predictive control method for permanent magnet synchronous motors. In this method, the α-axis expansion state quantity can follow the voltage disturbance caused by the parameter disturbance in real time. Combined with the derived α-axis expansion state quantity and β-axis The relationship between the expansion state quantities enables the β-axis expansion state quantities to follow the β-axis voltage disturbance synchronously when the motor model parameters are inaccurate, thereby realizing the robustness of the parameters and effectively overcoming the restriction of the inaccurate motor model parameters on the accuracy of current reconstruction. . During the execution of the algorithm of the extended state observer, in addition to the rotor electrical angular velocity, rotor position, stator voltage and motor a-phase current, no additional parameters are required to reconstruct the complete information of the motor's three-phase current. The difficulty of obtaining the parameters of the expanded observer and the computational complexity of the reconstruction process are significantly reduced.

Description

A Robust Single Current Sensor Predictive Control Method for Permanent Magnet Synchronous Motors

technical field

The invention relates to the technical field of permanent magnet synchronous motor control, in particular to a single-phase current sensor predictive control technology with improved robustness.

Background technique

At present, some existing technologies for controlling permanent magnet synchronous motors use a single current sensor. Compared with the control of permanent magnet synchronous motors without position sensors, this technical method can not only achieve the purpose of reducing the number of physical sensors , it can also achieve a good motor speed control effect under the condition of low motor speed.

Most of the existing single current sensor control implementations use a single DC bus current sensor to reconstruct the three-phase current of the motor according to the relationship between the bus current and the phase current. However, this method will first introduce noise errors that cannot be eliminated. Secondly, there is a current reconstruction dead zone, and the methods for compensating for the current reconstruction dead zone are complicated. A few existing technologies that have appeared recently have begun to consider phase current reconstruction based on a single phase current sensor, but since most of the current reconstruction methods using a single phase current sensor are based on the motor model method, there is a reconstruction effect that affects the accuracy of the motor model parameters. The disadvantage of high dependence on sex.

SUMMARY OF THE INVENTION

In view of this,

In order to solve the problem that the phase current reconstruction depends too much on the accuracy of the motor model parameters in the prediction control of the single phase current sensor of the existing permanent magnet synchronous motor, the present invention provides a robust single current sensor prediction control method of the permanent magnet synchronous motor. , the method specifically includes the following steps:

Step 1: Collect the phase a current, rotational speed and rotor position angle of the permanent magnet synchronous motor in real time online;

Step 2: In the α-β coordinate system, the phase a current, rotational speed, and rotor position angle collected in step 1 are used as input, and the relationship between the α-axis and β-axis voltage disturbances is deduced:

f _α = -ΔR _s ×i _α +ω _e ×Δψ _f ×sinθ

where f _α , f _β are the voltage disturbances caused by inaccurate motor model parameters; i _α is the measured α-axis stator current; Δψ _f is the motor flux linkage estimation error; ΔR _s is the stator resistance estimation error; ω _e is the electrical angular velocity of the rotor; θ is the rotor position angle;

Establish a phase current reconstruction equation based on the extended state observer algorithm, update and calculate the α-axis and β-axis currents in the α-β coordinate system in real time and output them to realize the reconstruction of abc three-phase currents. The axis current is transformed by Park to obtain the d and q axis currents in the d-q coordinate system;

Step 3: Establish a deadbeat current predictive control model, and calculate the reference voltage at the next moment in real time by using the motor speed, rotor position angle and the current parameters obtained in the step 2 collected in the step 1; The reference voltage is controlled by SVPWM.

Further, in the second step, the phase current reconstruction equation based on the extended state observer algorithm specifically adopts the following formula:

分别为α轴、β轴电流的观测值；u_α,u_β为α-β坐标系下定子电压；ψ_{r_change}为估计的转子磁链；R_{s_change}为估计的定子电阻；L_s为定子电感；ε为α轴观测电流

与测量电流的i_α差值，

为f_α的导数，α1，α2，δ为fal函数的可调节参数，用于实现所需的非光滑反馈，β₀₁、β₀₂均为可调节的参数，根据不同的电机参数选取控制效果最优值；t为时间；in,

are the observed values of the α-axis and β-axis currents, respectively; u _α , u _β are the stator voltages in the α-β coordinate system; ψ _{r_change} is the estimated rotor flux linkage; R _{s_change} is the estimated stator resistance; L _s is the stator inductance; ε is the α-axis observation current

The difference between i _α and the measured current,

is the derivative of f _α , α1, α2, δ are the adjustable parameters of the fal function, which are used to achieve the required non-smooth feedback, β ₀₁ and β ₀₂ are adjustable parameters, and the control effect is selected according to different motor parameters. figure of merit; t is time;

取电流观测值

作为扩张状态观测器的输出电流值；Through the above formula, the observed current value in the α-β coordinate system can be obtained

Take current observations

As the output current value of the expansion state observer;

The fal function in the extended state observer equation is:

Among them, α and δ are adjustable parameters, which are adjusted according to the control requirements. When α<1, the fal function has the characteristics of: small error, large gain; large error, small gain.

Because, the transformation of the three-phase coordinate system current to the α-β coordinate system current is:

Since i _a +i _b + _ic =0, replace _ic with -(i _a +i _b ), the above formula can be expressed as:

It can be seen that the α-axis current i _α = i _a in the α-β stationary coordinate system, then the α-axis current i _α in the α-β coordinate system is the collected a-phase current, which only needs to be in the α-β coordinate system. After estimating the β-axis current i _β , the complete three-phase current information can be obtained. Therefore, the _iβ current is obtained using the above-described expansion observer. That is, the reconstruction of abc three-phase current is completed.

Further, in the step 3, the deadbeat current predictive control model is used to obtain the reference voltage at the next moment, which specifically includes:

In the formula, u _d (k) and u _q (k) are the stator voltages at the current moment; _ud (k+1) and u _q (k+1) are the reference voltages at the next moment; T _s is the control period; i _qref is the q-axis reference current; ψ _r is the rotor flux linkage of the motor.

In the above-mentioned method provided by the present invention, the α-axis expansion state quantity can change in real time with the voltage disturbance caused by the parameter disturbance. Combined with the derived relationship between the α-axis expansion state quantity and the β-axis expansion state quantity, the motor model When the parameters are inaccurate, the β-axis expansion state quantity can synchronously follow the β-axis voltage disturbance, which realizes the robustness of the parameters and effectively overcomes the restriction of the inaccurate parameters of the motor model on the accuracy of the current reconstruction. During the execution of the algorithm of the extended state observer, in addition to the rotor electrical angular velocity, rotor position, stator voltage and motor a-phase current, no additional parameters are required to reconstruct the complete information of the motor's three-phase current. The difficulty of obtaining the parameters of the extended observer and the computational complexity of the reconstruction process are significantly reduced.

Description of drawings

Fig. 1 is the block diagram of the permanent magnet synchronous motor control model of the method provided by the present invention;

FIG. 2 is an operation curve of a permanent magnet synchronous motor that implements predictive control in a preferred embodiment of the present invention.

Detailed ways

The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

A robust single-current sensor predictive control method for a permanent magnet synchronous motor provided by the present invention, as shown in FIG. 1 , specifically includes the following steps:

Step 1: Collect the phase a current, rotational speed and rotor position angle of the permanent magnet synchronous motor in real time online;

Step 2: In the α-β coordinate system, the phase a current, rotational speed, and rotor position angle collected in step 1 are used as input, and the relationship between the α-axis and β-axis voltage disturbances is deduced:

f _α = -ΔR _s ×i _α +ω _e ×Δψ _f ×sinθ

where f _α , f _β are the voltage disturbances caused by inaccurate motor model parameters; i _α is the measured α-axis stator current; Δψ _f is the motor flux linkage estimation error; ΔR _s is the stator resistance estimation error; ω _e is the electrical angular velocity of the rotor; θ is the rotor position angle;

Establish a phase current reconstruction equation based on the extended state observer algorithm, update and calculate the α-axis and β-axis currents in the α-β coordinate system in real time and output them to realize the reconstruction of abc three-phase currents. The axis current is transformed by Park to obtain the d and q axis currents in the d-q coordinate system;

Step 3: Establish a deadbeat current predictive control model, and calculate the reference voltage at the next moment in real time by using the motor speed, rotor position angle and the current parameters obtained in the step 2 collected in the step 1; The reference voltage is controlled by SVPWM.

In step 1, the phase a current of the permanent magnet synchronous motor is collected online in real time, because the transformation from the current in the abc three-phase coordinate system to the current in the α-β coordinate system is:

Since i _a +i _b + _ic =0, replace _ic with -(i _a +i _b ), the above formula can be expressed as:

It can be seen that the α-axis current i _α = i _a in the α-β stationary coordinate system, then the α-axis current i _α in the α-β coordinate system is the collected a-phase current, and only in the α-β coordinate system By estimating the β-axis current i _β , the complete three-phase current information can be obtained. Therefore, the _iβ current is obtained using the above-described expansion observer. That is, the reconstruction of abc three-phase current is completed.

In step 2, the voltage equation of the permanent magnet synchronous motor in the α-β coordinate system is first established:

In the formula, u _α , u _β are the stator voltages in the α-β coordinate system; i _α , i _β are the stator currents in the α-β coordinate system; ψ _r is the actual rotor flux linkage; R _s is the actual stator resistance; L _s is the stator inductance; ω _e is the electrical angular velocity of the rotor; θ is the rotor position angle.

According to the voltage equation of the above formula, when the estimated motor parameters are inaccurate, the voltage equation of the permanent magnet synchronous motor model in the α-β coordinate system can be obtained:

分别为电机模型中α,β轴的定子电流；ψ_{f_change}为估计的电机转子磁链；R_{s_change}为估计的定子电阻；f_α,f_β分别为电机模型参数不准确引起的α，β轴电压的未知扰动量；其余参数同上式。In the formula,

are the stator currents of the α and β axes in the motor model, respectively; ψ _{f_change} is the estimated rotor flux linkage of the motor; R _{s_change} is the estimated stator resistance; f _α , f _β are the α and β axis voltages caused by inaccurate motor model parameters, respectively The unknown disturbance amount of ; the other parameters are the same as above.

Subtract the two equations to get:

分别等于实际电流i_α,i_β，则需满足：If you want to realize the observed current of the motor model

are equal to the actual currents i _α , i _β respectively, then it is necessary to satisfy:

(R _{s_change} -R _s )×i _α -ω _e ×(ψ _{f_change -ψ f} )×sinθ+f _α =0

(R _{s_change} -R _s )×i _β +ω _e ×(ψ _{f_change -ψ f} )×cosθ+f _β =0

f _α = -ΔR _s ×i _α +ω _e ×Δψ _f ×sinθ

f _β = -ΔR _s ×i _β -ω _e ×Δψ _f ×cosθ

Among them: ΔR _s =(R _{s_change} -R _s ), represents the motor model resistance estimation error, and Δψ _f =(ψ _{f_change -ψ f} ) represents the motor model flux linkage estimation error.

则可以近似得到：Transformation formula from α-β coordinate system to dq coordinate system: i _d =i _α ×cosθ+i _β ×sinθ and reference current

can be approximated by:

Substitute it into the relationship between the observed current and the actual current to get:

f _α = -ΔR _s ×i _α +ω _e ×Δψ _f ×sinθ

It can be seen from the above formula: in the α-β coordinate system, the voltage caused by the inaccurate parameters of the motor model

The disturbance magnitude satisfies:

Therefore, combined with the theory of the extended state observer, taking f _α and f _β as the extended state variables, the phase current reconstruction equation based on the extended state observer algorithm can be obtained:

分别为α轴、β轴电流的观测值；u_α,u_β为α-β坐标系下定子电压；f_α,f_β分别为α轴、β轴电压的未知扰动量；ψ_{r_change}为估计的转子磁链；R_{s_change}为估计的定子电阻；L_s为定子电感；ω_e为转子的电角速度；θ为转子位置角；ε为α轴观测电流

与测量电流的i_α差值；

为f_α的导数；α1，α2，δ为fal函数的可调节参数，用于实现所需的非光滑反馈；β₀₁、β₀₂均为可调节的参数，根据不同的电机参数选取控制效果最优值；Among them, i _α is the measured α-axis stator current;

are the observed values of the α-axis and β-axis currents, respectively; u _α , u _β are the stator voltages in the α-β coordinate system; f _α , f _β are the unknown disturbances of the α-axis and β-axis voltages, respectively; ψ _{r_change} is the estimated Rotor flux linkage; R _{s_change} is the estimated stator resistance; L _s is the stator inductance; ω _e is the electrical angular velocity of the rotor; θ is the rotor position angle; ε is the α-axis observation current

The difference between i _α and the measured current;

is the derivative of f _α ; α1, α2, δ are adjustable parameters of the fal function, which are used to achieve the required non-smooth feedback; β ₀₁ and β ₀₂ are adjustable parameters, and the best control effect is selected according to different motor parameters. figure of merit;

取电流观测值

为扩张状态观测器的输出电流值；Through the above formula, the observed current value in the α-β coordinate system can be obtained

Take current observations

is the output current value of the expansion state observer;

趋于无限大，引起瞬时电流脉冲，应该对其进行限幅，在本发明的一个实例中采用：

Preferably, in order to prevent

tends to be infinite, causing instantaneous current pulses, which should be limited, in an example of the present invention:

The fal function in the extended state observer equation is:

When α<1, the fal function has the characteristics of: small error, large gain; large error, small gain.

In the third step, the deadbeat current predictive control model is used to obtain the reference voltage at the next moment, which specifically includes:

In the formula, u _d (k) and u _q (k) are the stator voltages at the current moment; _ud (k+1) and u _q (k+1) are the reference voltages at the next moment; T _s is the control period; i _qref is the q-axis reference current; ψ _r is the rotor flux linkage of the motor.

Preferably, when the calculated reference voltage exceeds the maximum output voltage limit of SVPWM, the output reference voltage needs to be adjusted to obtain the reference voltage within the output range of SVPWM:

为d-q坐标系下修正后的SVPWM输出电压范围内的参考电压；U_dc为直流母线电压。In the formula,

is the reference voltage within the corrected SVPWM output voltage range under the dq coordinate system; U _dc is the DC bus voltage.

Fig. 2 shows a preferred example based on the present invention, when ψ _{r_change} = 1.5*ψ _r , using a single current sensor to perform predictive control using the current information reconstructed by the extended state observer to perform predictive control of the motor speed, torque, and weight Constructed three-phase current curve. It can be seen from Figure 2 that when the estimated flux linkage is 1.5 times the actual flux linkage, the three-phase current reconstructed by the expanded state observer has only a small current fluctuation, and the current waveform is very close to a perfect sine wave; It can be seen from the change of rotational speed that the three-phase current reconstructed by the expanded state observer is used to perform predictive control of the motor, and the rotational speed can follow the control requirements in a timely and accurate manner; it can be seen from the torque change of the motor that the expanded state observer is used The reconstructed three-phase current is used for predictive control of the motor, and the motor has only a small torque ripple (less than 10% of the maximum torque). The simulation results show that the proposed robust single-current sensor predictive control method can reconstruct the three-phase current information well when the motor model parameters are inaccurate, and the reconstructed three-phase current can completely replace the The actual three-phase current is used as the closed-loop feedback to control the motor.

It should be understood that the size of the sequence numbers of the steps in the embodiments of the present invention does not imply the sequence of execution, and the execution sequence of each process should be determined by its functions and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention .

Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, and substitutions can be made in these embodiments without departing from the principle and spirit of the invention and modifications, the scope of the present invention is defined by the appended claims and their equivalents.

Claims (3)

1. a robust permanent magnet synchronous motor single current sensor predictive control method, is characterized in that: the method specifically comprises the following steps: Step 1: Collect the phase a current, rotational speed and rotor position angle of the permanent magnet synchronous motor in real time online; Step 2: In the α-β coordinate system, the phase a current, rotational speed, and rotor position angle collected in step 1 are used as input, and the relationship between the α-axis and β-axis voltage disturbances is deduced: f _α = -ΔR _s ×i _α +ω _e ×Δψ _f ×sinθ

where f _α , f _β are the voltage disturbances caused by inaccurate motor model parameters; i _α is the measured α-axis stator current; Δψ _f is the motor flux linkage estimation error; ΔR _s is the stator resistance estimation error; ω _e is the electrical angular velocity of the rotor; θ is the rotor position angle; Establish a phase current reconstruction equation based on the extended state observer algorithm, update and calculate the α-axis and β-axis currents in the α-β coordinate system in real time and output them to realize the reconstruction of abc three-phase currents. The axis current is transformed by Park to obtain the d and q axis currents in the d-q coordinate system; Step 3: Establish a deadbeat current predictive control model, and calculate the reference voltage at the next moment in real time by using the motor speed, rotor position angle and the current parameters obtained in the step 2 collected in the step 1; The reference voltage is controlled by SVPWM. 2. The method according to claim 1, characterized in that: in the step 2, the phase current reconstruction equation based on the extended state observer algorithm specifically adopts the following formula:

in,

are the observed values of the α-axis and β-axis currents, respectively; u _α , u _β are the stator voltages in the α-β coordinate system; ψ _{r_change} is the estimated rotor flux linkage; R _{s_change} is the estimated stator resistance; L _s is the stator inductance; ε is the α-axis observation current

The difference from the measured current i _α ,

is the derivative of f _α , α1, α2, δ are adjustable parameters of fal function; β ₀₁ and β ₀₂ are adjustable parameters; t is time; The fal function in the extended state observer equation is:

Among them, α and δ are adjustable parameters. 3. The method according to claim 2, wherein: in the step 3, the deadbeat current predictive control model is used to obtain the reference voltage at the next moment, specifically comprising:

In the formula, u _d (k) and u _q (k) are the stator voltages at the current moment; _ud (k+1) and u _q (k+1) are the reference voltages at the next moment; T _s is the control period; i _qref is the q-axis reference current; ψ _r is the rotor flux linkage of the motor.

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