WO2020186656A1

WO2020186656A1 - Method for estimating position of linear time-variant rotor of low-speed permanent magnet synchronous motor

Info

Publication number: WO2020186656A1
Application number: PCT/CN2019/094791
Authority: WO
Inventors: 张卫东; 衣博文; 奥特加罗密欧; 乌克塞维克斯洛博丹∙N; 斯坦科维奇亚历山大
Original assignee: 上海交通大学
Priority date: 2019-03-21
Filing date: 2019-07-05
Publication date: 2020-09-24
Also published as: CN109889118A

Abstract

A method for estimating the position of a linear time-variant rotor of a low-speed permanent magnet synchronous motor, comprising: first, injecting a high-frequency sinusoidal signal from a voltage end of a stator, thereby causing stator current output to contain rotor position information; then, passing the detected stator current signal through a first-order time- lag high-pass filter obtained from the difference between pure time lag and an average zero-order holder, and then passing the obtained signal through a class gradient descent time-variant low-pass filter, thereby obtaining a virtual output signal; finally, performing analytical operation on the virtual signal to obtain an estimated value for the rotor position. The described method has the advantages of being high-precision, being simple and effective, each filtering link being linear, having high calculation efficiency, and having downward compatibility.

Description

A linear time-varying rotor position estimation method for low-speed permanent magnet synchronous motors

Technical field

The invention relates to the field of motor driving and control, and in particular to a linear time-varying rotor position estimation method of a low-speed permanent magnet synchronous motor based on high-frequency signal injection under the condition of no position sensor.

Background technique

Permanent magnet synchronous motors are widely used in industrial production and precision manufacturing, and their advantages are small size, light weight, simple structure, reliable operation and high power density. According to the permanent magnet structure, permanent magnet synchronous motors can be divided into surface mount type and built-in type. The air gap between the rotor and the stator of the latter will change periodically, that is, the salient pole effect. Therefore, the generated torque has a reluctance torque component, and its efficiency is high. This patent relates to the control of a built-in permanent magnet synchronous motor field.

The high-precision servo control of the motor relies on reliable rotor position information. In some application scenarios, the installation of position sensors at the tail of the motor is limited. This is due to restrictions on the overall size of the equipment in these scenarios, which makes it impossible to install position sensors and increases the probability of system failure. In addition, mechanical position sensors are fragile, difficult to package, and are easily affected by electromagnetic interference and signal distortion. Therefore, the use of column position sensors should be minimized. The sensorless control and rotor position estimation methods of permanent magnet synchronous motors have therefore become a hot spot in motor control technology.

In the low-speed operating conditions of permanent magnet synchronous motors, the disadvantages of the back EMF method are reflected in:

1) The signal-to-noise ratio is too low, and it is difficult to extract a reliable back-EMF signal from the measurement signal;

2) The system is not uniformly differentially observable, especially in the zero-speed condition, the system is unmeasurable.

The above two points lead to a significant decrease in the estimation performance at low speeds. At this time, the salient pole characteristics of the motor need to be used to estimate the rotor position. This method injects a high-frequency signal into the stator voltage terminal of the motor, whereby operating the stator current terminal will contain rotor position information. Therefore, the core problem in the high-frequency signal injection method is the subsequent high-frequency signal processing, that is, the rotor position filtering technology. The traditional estimation method is based on the framework of high-pass filtering and low-pass filtering. The measured current signal is processed by two linear time invariant (LTI) systems. The disadvantage of this method is that the steady-state accuracy is difficult to qualitatively analyze, and the dynamic process is difficult to control.

Summary of the invention

The purpose of the present invention is to provide a linear time-varying rotor position estimation method for a low-speed permanent magnet synchronous motor in order to overcome the above-mentioned defects in the prior art.

The purpose of the present invention can be achieved through the following technical solutions:

A linear time-varying rotor position estimation method for a low-speed permanent magnet synchronous motor is used to obtain an accurate rotor position without a position sensor, including the following steps:

1) Inject a sinusoidal signal with an angular frequency of ω _h into the stator α-axis voltage of the built-in permanent magnet synchronous motor, so that the output stator current signal contains rotor position information;

2) Pass the detected stator current signal through a first-order time-delay high-pass filter and a gradient descent-like time-varying low-pass filter in sequence to obtain a virtual output signal;

3) Analyze the virtual signal to obtain the rotor position estimate.

The step 1) specifically includes the following steps:

11) To construct a dynamic model of the built-in permanent magnet synchronous motor in the stator coordinate system, there are:

L(θ):=L ₀ I+L ₁ Q(θ)

Among them, v _αβ is the stator voltage, i _αβ is the stator current, R _s is the stator resistance, I is the identity matrix, L(θ) and Q(θ) are maps, s is the differential operator, and n _p is the number of pole pairs , Ω is the angular velocity, θ is the electrical angle of the rotor, Φ[·] is the magnetic flux, L ₀ is the average inductance, L ₁ is the difference inductance, and L _d and L _q are the self-inductances of the d and q axes, respectively;

12) In the existing nominal control signal

On the basis of, superimpose and inject high-frequency sinusoidal signals on the stator α-axis voltage, then:

Among them, V _h is the amplitude of the injected sinusoidal signal, and ω _h is the angular frequency of the injected signal.

The step 2) specifically includes the following steps:

21) Filter the stator current signal i _αβ through a first-order time-delay high-pass filter to obtain the output Y _f (s);

22) After low-pass filtering the output Y _f (s) through a gradient-like time-varying low-pass filter to obtain a virtual output

In the step 21), the first-order time-delay high-pass filter consists of a pure time-delay link and a weighted zero-order holder, and its expression is:

Y _f (s)=G _d (s)i _αβ (s)

Among them, Y _f (s) is the output of the first-order time-delay high-pass filter, G _d (s) is the transfer function, and s is the Laplace transform constant. The symbols here are no longer distinguished between the Laplace transform symbol and Differential operator, d is the transfer parameter.

In the step 22), the gradient descent-like time-varying low-pass filter is expressed as:

among them,

Is the output of the gradient-descent time-varying low-pass filter, Y _f (t) is the first-order time-delay high-pass filter output Y _f (s) in the time domain, G _grad is the filter operator, x( t) is the dynamic state of the operator, γ is the performance adjustment parameter, S(t) is the original function of the injected periodic signal, ε is the injected signal period, and u(t) is the operator input.

In the step 3), the rotor position estimate

The calculation formula is:

among them,

They are the virtual outputs corresponding to each dimension of the filtered two-dimensional stator current i _αβ .

The performance adjustment parameter γ is used to represent the compromise state between the steady state and the transient state. When the convergence speed is slow, the parameter γ is increased, and when the noise influence is large, the parameter γ is decreased.

The angular frequency ω _h of the injected sinusoidal signal is in the range of 100-1000 Hz.

Said step 2) also includes the following steps:

23) For virtual output

Perform compensation to prevent additional phase shifts, and estimate the rotor position based on the compensated virtual output, then:

Among them, l ₁ , l ₂ , l ₃ , and l ₄ are compensation parameters,

Is the compensated virtual output,

The value of the compensation parameter l _i satisfies the following conditions:

Make

with

The amplitude of

Mean

Compared with the prior art, the present invention has the following advantages:

1. In the linear time-varying rotor estimation method proposed by the present invention, the steady-state error converges to a small neighborhood with a zero radius of Ο(ε). Compared with the traditional method, the steady-state estimation accuracy is improved.

Raise to O(e).

2. The transient and steady-state performance of the traditional linear time-invariant method is difficult to quantitatively analyze. The method proposed by the present invention overcomes the above problems because of the mathematically complete second-order average analysis used in the design process, and provides Tuning methods of three design parameters.

3. All links in the present invention are linear and have high efficiency. The computational complexity added by the traditional method is negligible, and it also meets the framework of high-pass and low-pass filtering. The physical concept is clear, and it is backward compatible with traditional methods. specialty.

Fourth, the high-frequency signal in the present invention is injected from the stator voltage terminal, and the estimation algorithm does not use any rotating coordinate system variables, which is simple and convenient to implement.

Description of the drawings

Fig. 1 is the frequency domain characteristic diagram of the designed high-pass filter, the parameters are ω _h =500, n=2 as an example.

Fig. 2 is a structural decomposition diagram of the neutron part of the low-pass filter designed in the present invention. The parameters are V _h =1 and γ=1 as an example.

Figure 3 is a schematic diagram of signal processing from stator current to virtual output.

Figure 4 is a schematic diagram of the signal flow of step 3 in the design of the invention.

Figure 5 shows the stator current under the injection of high-frequency signals and the voltage at the injection end in the test experiment in the embodiment, where Figure (5a) is the stator current under the injection of high-frequency signals, and Figure (5b) is the voltage at the injection end.

Figure 6 shows the estimated and measured values of the rotor in the test experiment of the embodiment.

Figure 7 is the test experiment control group 1 in the embodiment, where Figure (7a) is the estimated value and measured value of the rotor when the injection frequency is 200Hz, and Figure (7b) is the estimated value and the measured value of the rotor when the injection frequency is 100Hz.

Figure 8 is the test experimental control group 2 in the embodiment. Figure (8a) is the estimated value and measured value of the rotor when the injection angular frequency is 60rad/s, and Figure (8b) is the estimated value of the rotor when the injection angular frequency is 40rad/s. Compared with the measured value, Figure (8c) shows the estimated value and measured value of the rotor during acceleration.

Figure 9 is an inventive flow chart of the present invention.

detailed description

The present invention will be described in detail below with reference to the drawings and specific embodiments.

The present invention provides a specific example of a permanent magnet synchronous motor to introduce related content, but the present invention is not limited to this example, and can be applied to a general built-in permanent magnet synchronous motor through simple adjustment. The following design considerations have been Park transformation to obtain the model under the two-phase current (voltage) coordinate system from the three-phase current (voltage).

In order to solve the problem of high-frequency signal processing in rotor position estimation of low-speed permanent magnet synchronous motors, the present invention provides a rotor position estimation algorithm with higher accuracy than existing methods, and the estimation accuracy of the method is close to such high-frequency injection technology The theoretical limit of Ο(ε), where ε is the injection signal period.

The method includes the following steps:

Step 1. Consider the dynamic model of the built-in permanent magnet synchronous motor in the stator coordinate system, and inject a sinusoidal signal with a frequency of ω _h into the stator α axis voltage.

Step 1.1 Consider the following motor dynamics model, where the mechanical state variable part is ignored. The model is suitable for each frequency band of the motor (not limited to high frequency).

Mapping:

Define as follows:

L(θ):=L ₀ I+L ₁ Q(θ)

Is the average inductance,

Is the difference inductance.

Step 1.2 Consider the existing nominal control signal

Based on this, the following high-frequency sinusoidal signals are superimposed and injected into the stator α-axis voltage.

Where V _h is the amplitude of the injected sinusoidal signal in volts, and ω _h is the angular frequency of the signal.

Step 2. Perform linear time-varying (LTV) high-pass + low-pass filtering on the stator current signal i _αβ after inverse Park transformation to obtain a virtual output signal.

Step 2.1 The stator current signal i _αβ first passes through the following first-order time-delay high-pass filter. The transfer function of this link is as follows

The above parameter d is selected as d=ε, and the symbol s represents the Laplace transform symbol. The high-pass filter G _d (s) is essentially composed of a pure time-delay link and a weighted zero-order holder, and its frequency characteristics can be seen in Figure 1. The output of this link is denoted as Y _f , namely:

Y _f (s)=G _d (s)i _αβ (s)

Step 2.2 Perform low-pass filtering on the obtained Y _f through the following linear time-varying system (LTV), which is constructed as follows:

The signal obtained in this link is called the virtual output, denoted as

which is:

The G _grad operator conforms to the input u _p (t):=S(t)u(t) has low-pass characteristics because the neutron part of the operator

It can be decomposed as shown in Figure 2, and the transfer function of the middle term obviously shows low-pass characteristics.

A schematic diagram of the entire signal processing process in step 2 is shown in FIG. 3.

Step 3. From the acquired virtual output, calculate the rotor position through the following function.

Refer to Figure 4 for the signal processing process of this step. The linear time-varying algorithm provided in the present invention has high calculation efficiency and high reliability because all the constructed dynamic systems are linear. In addition, the calculation accuracy of the invention is Ο(ε), that is, the steady-state error converges to a small neighborhood with a zero radius of Ο(ε), denoted as

This accuracy is higher than that of the traditional linear time-invariant filtering scheme Ο(ε).

Step 4. Design algorithm performance adjustment, parameter adjustment and loss compensation for this invention.

Step 4.1 by observing the virtual output signal

The performance adjustment parameter γ of, if the convergence speed is slow, this parameter can be increased, and if the noise is large, the parameter should be decreased. This parameter characterizes the compromise between steady state and transient state.

Step 4.2 During the debugging process, if the measurement error is large, the injection frequency ω _h should be increased or the injection signal voltage amplitude V _{h should} be reduced, but it will reduce the signal-to-noise ratio of the system. The recommended range of this parameter is 100-1000 Hz.

Step 4.3 Due to the defects of the inverter (such as lock time), the excitation frequency eddy current in the magnetic circuit, etc., it will have a hysteresis effect on the stator current i _αβ . Ideally, the model assumes that the coil has zero resistance, and the phase difference between the injected signal and the high frequency response of the current is 90 degrees. This condition cannot be met in the actual system, so the phase shift should be less than 90 degrees. The iron loss acts as a short-circuit of the secondary winding in an electromagnetic device similar to a transformer, which also produces an additional phase shift. Therefore, corresponding compensation is usually required. Use the following compensation virtual output

And use the following formula to calculate the rotor position estimation

The parameter l _i (i=1,...,4) is adjusted based on such

The amplitude of

Mean

Examples:

In this embodiment, the selected test platform is the built-in permanent magnet synchronous motor FAST PMSM. The test platform has a line-to-line peak value of 72 volts at 1000 rpm. The DC bus voltage used is 521 volts, and the driving PWM frequency is 5 kHz. The platform is equipped with two PMSMs, one running in the control mode to drag and test FAST PMSM, and they are linked by a toothed belt, including inertial wheels.

The experimental device is equipped with two mechanically coupled, inverter-powered brushless DC motors:

1) The main power supply unit includes a line rectifier and two 3-phase PWM inverters with control circuits;

2) DC bus support with dynamic disconnection;

3) Speed control motor;

4) Torque control motor;

5) There is an inertial coupling between the two motors.

The test motor is built as follows:

The industry standard FAST motor is adopted and changes are introduced into the rotor magnetic circuit to obtain the difference between the d-axis and q-axis inductance (2:3). The motor operates in torque control mode, and the speed and position are installed on the shaft The sampling time is Ts=300ns, the acquisition time is set to cover at least two electrical cycles, and the three-phase current and voltage are measured from the drive measurement system-"Sincoder" axis sensor And rotor position.

The parameters of the experimental motor are as follows: pole pair number 3, magnetic normal number 0.39Wb, d-direction inductance L _d =3.38mH, q-direction inductance L _q =5.07mH, stator resistance R _s =0.47 ohm.

In the test, we injected a sine signal with a frequency of 400 Hz and an amplitude of 2V at the α-axis voltage terminal. The specific parameter configuration in the present invention is as follows: γ=[1.25×10 ⁴ , 2.5×10 ⁴ ], the compensation parameter is

The experimental results of the embodiment can be seen in Figs. 5 and 6. Figure 7 shows the first set of control experiments. Different injection frequencies were selected under the same test conditions, namely 100 Hz and 200 Hz. The three injection frequencies show that relatively good experimental results have been achieved at high frequencies. Of course, the upper limit of reliable injection frequency is restricted by factors such as PWM frequency and signal-to-noise ratio. Figure 8 is the second set of control experiments. In the experiment, considering that the permanent magnet synchronous motor is operating in different working conditions, that is, different speeds and acceleration conditions, the rotor position estimation is relatively ideal.

After obtaining the accurate rotor position estimation value, the signal can obtain the rotor angular velocity at the same time through the phase-locked loop, and feed them back to the motor stator voltage terminal at the same time. Using methods such as magnetic field quantitative control, the motor can realize the non-inductive speed control and torque. Control, this control method does not use any detection device of the rotating coordinate system.

Claims

A linear time-varying rotor position estimation method for a low-speed permanent magnet synchronous motor is used to obtain an accurate rotor position without a position sensor, and is characterized in that it includes the following steps:

1) Inject a sinusoidal signal with an angular frequency of ω h into the stator α-axis voltage of the built-in permanent magnet synchronous motor, so that the output stator current signal contains rotor position information;

2) Pass the detected stator current signal through a first-order time-delay high-pass filter and a gradient descent-like time-varying low-pass filter in sequence to obtain a virtual output signal;

3) Analyze the virtual signal to obtain the rotor position estimate.
The linear time-varying rotor position estimation method of a low-speed permanent magnet synchronous motor according to claim 1, wherein said step 1) specifically includes the following steps:

11) To construct a dynamic model of the built-in permanent magnet synchronous motor in the stator coordinate system, there are:

L(θ):=L 0 I+L 1 Q(θ)

Among them, v αβ is the stator voltage, i αβ is the stator current, R s is the stator resistance, I is the identity matrix, L(θ) and Q(θ) are maps, s is the differential operator, and n p is the number of pole pairs , Ω is the angular velocity, θ is the electrical angle of the rotor, Φ[·] is the magnetic flux, L 0 is the average inductance, L 1 is the difference inductance, and L d and L q are the self-inductances of the d and q axes, respectively;

12) In the existing nominal control signal
On the basis of, superimpose and inject high-frequency sinusoidal signals on the stator α-axis voltage, then:

Among them, V h is the amplitude of the injected sinusoidal signal, and ω h is the angular frequency of the injected signal.
The linear time-varying rotor position estimation method of a low-speed permanent magnet synchronous motor according to claim 1, wherein said step 2) specifically includes the following steps:

21) Filter the stator current signal i αβ through a first-order time-delay high-pass filter to obtain the output Y f (s);

22) After low-pass filtering the output Y f (s) through a gradient-like time-varying low-pass filter to obtain a virtual output
The linear time-varying rotor position estimation method of a low-speed permanent magnet synchronous motor according to claim 3, wherein in said step 21), the first-order time-delay high-pass filter consists of a pure time-delay element and a weighted zero The composition of order retainer, its expression is:

Y f (s)=G d (s)i αβ (s)

Among them, Y f (s) is the output of the first-order time-delay high-pass filter, G d (s) is the transfer function, s is the Laplace transform constant, and d is the transfer parameter.
A linear time-varying rotor position estimation method for a low-speed permanent magnet synchronous motor according to claim 4, wherein in said step 22), the gradient descent-like time-varying low-pass filter is expressed as:

among them,
Is the output of the gradient-descent time-varying low-pass filter, Y f (t) is the first-order time-delay high-pass filter output Y f (s) in the time domain, G grad is the filter operator, x( t) is the dynamic state of the operator, γ is the performance adjustment parameter, S(t) is the original function of the injected periodic signal, ε is the injected signal period, and u(t) is the operator input.
A linear time-varying rotor position estimation method for a low-speed permanent magnet synchronous motor according to claim 5, wherein in said step 3), the rotor position estimation value
The calculation formula is:

among them,
They are the virtual outputs corresponding to each dimension of the filtered two-dimensional stator current i αβ .
The linear time-varying rotor position estimation method of a low-speed permanent magnet synchronous motor according to claim 5, wherein the performance adjustment parameter γ is used to represent a compromise state between steady state and transient state, and when the convergence speed is slow When the influence of noise is large, increase the parameter γ, and decrease the parameter γ when the influence of noise is large.
The linear time-varying rotor position estimation method of a low-speed permanent magnet synchronous motor according to claim 1, wherein the angular frequency ω h of the injected sinusoidal signal is in the range of 100-1000 Hz.
A linear time-varying rotor position estimation method of a low-speed permanent magnet synchronous motor according to claim 6, wherein said step 2) further comprises the following steps:

23) For virtual output
Perform compensation to prevent additional phase shifts, and estimate the rotor position based on the compensated virtual output, then:

Among them, l 1 , l 2 , l 3 , and l 4 are compensation parameters,
Is the compensated virtual output,
The linear time-varying rotor position estimation method of a low-speed permanent magnet synchronous motor according to claim 9, wherein the value of the compensation parameter l i satisfies the following conditions:

Make
with
The amplitude of
Mean