CN104158456B - A kind of position sensorless control method for driving motor for electric automobile - Google Patents

Abstract

The invention discloses a kind of position sensorless control method for driving motor for electric automobile, use pulse voltage injection method to driving original position of electric motor's rotator to carry out detection formula before electric automobile starts；After electric automobile starts, in order to detect accurately, the rotary high frequency signal injection method adopted at low speed segment detects driving motor rotor position in real time, and in order to avoid the impact of the multiple saliency of motor, the structure of high frequency signal injection method adds dual salient pole decoupling observer, use mode that high-frequency signal injection and counter electromotive force method combine during middling speed and process detection through nerve network controller and drive motor rotor position, counter electromotive force is used to detect driving motor rotor position during high speed, simultaneously for solving to cause observer to converge to the state of rotor magnetic pole opposite location at high speeds due to external interference, add rotor-position Robust Observers.The present invention can be accurate and effective detection driving motor for electric automobile rotor position information.

Description

A position sensorless control method for electric vehicle drive motor

technical field

The invention relates to a position-sensing control method for driving motors of electric vehicles, which combines pulse voltage injection method, rotating high-frequency voltage injection method, back electromotive force method, neural network controller, double salient pole decoupling observer and rotor Position Robust Observer Combined with Position Sensor Technology.

Background technique

The development of electric vehicles is the inevitable product of the oil crisis and people's environmental requirements. Compared with internal combustion engine vehicles, electric vehicles are powered by on-board power supplies, drive wheels with electric motors, and meet the requirements of road safety regulations for vehicles. . Due to the high power density and fast, precise and high control performance of permanent magnet synchronous motors, it is the first choice for electric vehicles. Permanent magnet synchronous motor (PMSM) is widely used in electric vehicles due to its high operating efficiency and high power density. In the current high-performance permanent magnet synchronous motor speed control system, the most mature is the vector control technology, but usually a position sensor is installed on the side of the motor shaft to detect the real-time position and speed information of the rotor. But the existence of the position sensor not only increases the cost of the whole system, but also reduces the reliability of the system, so the position sensorless control technology has become an important research direction today.

The core of the sensor is that the control system can accurately estimate the real-time position and speed of the rotor. The commonly used sensorless control methods can be divided into three categories:

(1) The open-loop calculation method of the ideal model of the motor is adopted, such as the direct calculation method, the back electromotive force integration method, etc.; the calculation method based on the open-loop is simple and direct, and the dynamic performance is good; but the calculation depends on the motor parameters, and the parameters of the motor during operation It is always changing, which will inevitably affect the accuracy of rotor position estimation; and when the motor speed is very low, the back electromotive force is very small, and it is easy to be mixed with various interference signals, and the signal-to-noise ratio becomes low, making the back electromotive force Difficult to detect. So this method is not suitable for sensorless position estimation when the motor is stationary or at low speed.

(2) Rotor position identification schemes based on external high-frequency signal injection, such as rotating high-frequency voltage injection method, rotating high-frequency voltage injection method and rotating high-frequency current injection method. The high-frequency signal injection method is to inject a high-frequency signal (voltage or current signal) into the three-phase winding of the motor, relying on the saliency of the motor rotor itself or the saliency effect caused by saturation, so that the magnetic field generated by the high-frequency signal is affected by the saliency of the rotor. Therefore, the high-frequency signal will contain rotor position information, and then the high-frequency signal can be demodulated from the stator current or voltage to extract the position information of the motor rotor. This method relies on an external excitation signal and does not depend on the rotational speed, but it takes a long time to estimate the rotor position, and the update frequency of the position value is not high, so the high-frequency signal injection method has a better estimation effect when the motor is stationary and at low speed .

(3) Closed-loop algorithms based on state observers, such as sliding mode observer method (SMO), model reference adaptive system method (MRAS), extended Kalman filter method (EKF), etc. The essence of the observer is system state reconstruction, that is, to reconstruct a system, use the output vector and input vector that can be directly measured in the original system as its input signal, and make the output signal of the reconstructed system equal to Based on the state of the original system, this reconstructed system is called an observer.

The above methods all have their own scope of application, and there is no method that can make all kinds of permanent magnet synchronous motors run perfectly and stably at full speed.

Contents of the invention

Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a position-sensing control method for electric vehicle drive motors, which divides the full speed cycle into initial position detection, low-speed position detection, and middle-speed position detection. Detection and high-speed section position detection, so as to realize the sensorless control of the electric vehicle drive motor in the full speed range, the detection method can be selected for different speed sections and pulse voltage injection method, rotating high-frequency voltage injection method, back electromotive force method, The combination of neural network controller, double salient decoupling observer and robust rotor position observer can accurately and effectively detect the rotor position information of electric vehicle drive motor.

Technical scheme: in order to achieve the above object, the technical scheme adopted in the present invention is:

A position sensorless control method for a drive motor of an electric vehicle, comprising initial position detection, low-speed position detection, medium-speed position detection and high-speed position detection, specifically comprising the following steps:

(1) Initial position detection: use the pulse voltage injection method to detect the rotor position, apply the space voltage vector to the armature winding of the motor, use the difference in the time constant of the equivalent circuit, and determine the initial position of the rotor by comparing the decay time of the response current, the shortest The voltage vector angle corresponding to the decay time is the initial angle of the rotor; finally, it is guaranteed that the electric vehicle can achieve no reverse rotation and start with the maximum torque;

(2) Low-speed section position detection: use the rotary high-frequency voltage injection method to detect the rotor position in real time, and realize the phase tracking of the negative sequence high-frequency current through the software phase-locked loop, so as to obtain the vector angle error, and use the PI regulator to adjust at the same time The error of the vector angle makes it tend to zero, so that the estimated value of the rotor position angle converges to the true value θ _r , for Differentiate over time to obtain the angular velocity of the rotor In order to avoid the influence of the multiple salient pole effect of the motor, a double salient pole decoupling observer is added to the structure of the high frequency voltage injection method;

(3) The position detection of the medium speed section adopts the method of combining the high frequency injection method and the back electromotive force method and processes the real-time detection of the rotor position through the neural network controller, the detection results of the high frequency injection method, the back electromotive force method and the detection results of the two The error signal processed by the neural network controller is adjusted by the PI regulator, and its output is used as the rotor position information;

(4) Position detection in the high-speed section, the counter electromotive force is used to detect the rotor position in real time, and the synovial film observer is used to obtain the rotor position information; in order to weaken the chattering phenomenon of the synovial film observer, the saturation function is used instead of the traditional switching function z, and the obtained Equivalent electromotive force, so as to obtain the rotor position detection value; in order to solve the situation that the synovial film observer may converge to the opposite position of the rotor magnetic pole due to external interference at high speed, a rotor position robust observer is added.

Beneficial effects: The position-sensing control method for electric vehicle drive motors provided by the present invention combines pulse voltage injection method, rotating high-frequency voltage injection method, back electromotive force method, neural network controller, and double salient pole decoupling observer Combined with the rotor position robust observer, it has the following advantages: 1. The initial position detection adopts the method of pulse voltage injection, and the space voltage vector is applied to the armature winding of the electric vehicle drive motor, which can detect the driving force of the electric vehicle very accurately. The initial position of the rotor of the motor realizes the smooth start of the electric vehicle; 2. The detection method can be selected for different speed sections, which improves the stability and accuracy of the electric vehicle drive system; 3. In the low-speed section, the high-frequency injection method is used , and cooperate with the double salient decoupling observer, which effectively solves the problems of performance degradation and low control accuracy in the low speed section; The rotor position robust observer solves the problem of magnetic pole convergence, and effectively solves the problem of rotor position detection and magnetic pole convergence at high speed; 5. Saves hardware costs and maintenance costs, and improves the anti-interference and robustness of the system at the same time sex.

Description of drawings

Figure 1 is a schematic diagram of two sets of d and q windings in different positions;

Figure 2 is a space voltage vector diagram;

Fig. 3 is an initial position detection flowchart and an operation diagram;

Figure 4 is a schematic diagram of the rotary high-frequency voltage injection method;

Fig. 5 is a model diagram of a double salient pole decoupling observer used in the high-frequency voltage injection method;

Fig. 6 is a schematic diagram of the back electromotive force detection method with a sliding mode observer;

Figure 7 is a schematic diagram of the rotor position robust observer used in the back EMF method

Fig. 8 is a schematic diagram of the detection principle of the rotor position of the drive motor in the medium speed range.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings.

A position sensorless control method for a drive motor of an electric vehicle, comprising initial position detection, low-speed position detection, medium-speed position detection and high-speed position detection, specifically comprising the following steps:

(1) Initial position detection: use the pulse voltage injection method to detect the rotor position, apply the space voltage vector to the armature winding of the motor, use the difference in the time constant of the equivalent circuit, and determine the initial position of the rotor by comparing the decay time of the response current, the shortest The voltage vector angle corresponding to the decay time is the initial angle of the rotor; finally, it is guaranteed that the electric vehicle can achieve no reverse rotation and start with the maximum torque;

(2) Low-speed section position detection: use the rotary high-frequency voltage injection method to detect the rotor position in real time, and realize the phase tracking of the negative sequence high-frequency current through the software phase-locked loop, so as to obtain the vector angle error, and use the PI regulator to adjust at the same time The error of the vector angle makes it tend to zero, so that the estimated value of the rotor position angle converges to the true value θ _r , for Differentiate over time to obtain the angular velocity of the rotor In order to avoid the influence of the multiple salient pole effect of the motor, a double salient pole decoupling observer is added to the structure of the high frequency voltage injection method;

(3) The position detection of the medium speed section adopts the method of combining the high frequency injection method and the back electromotive force method and processes the real-time detection of the rotor position through the neural network controller, the detection results of the high frequency injection method, the back electromotive force method and the detection results of the two The error signal processed by the neural network controller is adjusted by the PI regulator, and its output is used as the rotor position information;

(4) Position detection in the high-speed section, the counter electromotive force is used to detect the rotor position in real time, and the synovial film observer is used to obtain the rotor position information; in order to weaken the chattering phenomenon of the synovial film observer, the saturation function is used instead of the traditional switching function z, and the obtained Equivalent electromotive force, so as to obtain the rotor position detection value; in order to solve the situation that the synovial film observer may converge to the opposite position of the rotor magnetic pole due to external interference at high speed, a rotor position robust observer is added.

The specific implementation thought and process of the present invention will be described below.

initial position detection

The detection principle of the rotor position is based on the nonlinear magnetization characteristics of the stator core. As shown in Figure 1, suppose the flux linkage generated by the permanent magnet of the rotor is ψ _f , and the direction coincides with the d ¹ axis, then the component in the direction of the d ² axis is ψ _f cos△θ; the d axis flux linkage of the motor under the d and q axes The equation is:

ψ _d =L _d i _d +ψ _f (1)

Among them, θ is the rotor position angle, L _d is the d-axis inductance, and i _d is the d-axis current.

According to formula (1):

ψ _d1 =L _d1 i _d1 +ψ _f

(2)

ψ _d2 ＝ L _d2 i _d2 + ψ _f cosΔθ

Comparing formula (1) and formula (2) has:

ψ _d1 >ψ _d2 (3)

As shown in Figure 1, because the direction of the magnetic flux of the L _d1 winding is consistent with the direction of the permanent magnet pole, when the currents in the L _d1 and L _d2 windings increase at the same time, the magnetic circuit in the direction of the d ¹ axis tends to be more saturated. According to the inductance saturation effect, it can be concluded that L _d1 <L _d2 . According to the zero state response current formula:

i(t)=U[1-e- ^(R/L)t ]/R (4)

Among them, U is the applied voltage amplitude, L, R are the self-inductance and resistance of the stator winding.

Then there are:

i _d1 >i _d2 (5)

From the above analysis, the following conclusions can be drawn: when the synthetic flux linkage generated by two groups of the same windings is equal, the equivalent inductance saturation of the winding whose flux direction is closest to the rotor magnetic pole is the highest, the inductance value is the smallest, and the current is the largest, so it can be The initial position of the rotor is determined by detecting the amplitude of the current response generated by the voltage pulse, but this method needs to detect the peak value of the current, which requires high sampling circuits, and the sampling frequency will also affect the accuracy of its judgment. The patent of the present invention On top of this, by using the characteristics of different time constants of the d-axis equivalent circuit under different voltage vectors, the initial position of the rotor can be judged by detecting the different time for the response current to decay to 0, and there is no need to detect the current peak value, which reduces the need for sampling circuits. Dependency, the specific principles are as follows:

When the electric vehicle drive motor PMSM is at rest, when the direction of the incoming voltage pulse is equal to the direction of d ¹ , L=L _d1 , then the time constant of the circuit is τ _d1 ; when the direction of the passing voltage pulse is the same as d ² , L= L _d2 , then the time constant of the circuit is τ _d2 . According to the inductance saturation effect, we know that τ _d1 <τ _d2 , then t _d1 <t _d2 . The time required for the response current generated by the two voltage pulses to decay to 0 is t _d1 and t _d2 respectively. By comparing the time between the two, it can be seen that the initial position of the rotor is closer to d ¹ . According to this principle, as shown in Figure 2, 12 voltage vectors in different directions are sequentially fed in, and the voltage vector in the same direction as the rotor magnetic pole N (that is, when the angle of the voltage vector fed in is the actual angle of the rotor), the corresponding circuit time The constant τ is the smallest, then t is the smallest.

Therefore, the initial position of the rotor can be determined by comparing the time when the d-axis current decays to 0 under the action of a constant voltage vector, and the angle of the voltage vector corresponding to the measured time minimum value t _{d_min} is the initial angle of the rotor.

According to the original question above, the specific operation process is shown in Figure 3, specifically:

The entire detection process can be divided into two steps. Figure 3 is a flow chart of the detection process, where n represents one of the space voltage vectors in Figure 2, and θ _n is the angle of the space voltage vector n.

In the first step, 12 different voltage vectors are applied to the motor according to the sequence (1→2→3→...→12) in Figure 2(a), and the time t when the d-axis current decays from the steady-state value to 0 is detected. As the voltage vector gradually approaches the rotor N pole, the decay time t will gradually decrease due to the magnetic saturation phenomenon. Finally, the angle range of the voltage vector corresponding to t _{d_min} is the initial angle range of the rotor.

In the second step, firstly, θ _M2 is used as the median value of the angle range of the voltage vector preliminarily judged. On the basis of the first step, the angles of θ _M2 - △ θ, θ _M2 and θ _M2 + △ θ are applied to the motor respectively. The initial value of △θ is 7.5°, so the voltage vector applied to the motor in the second step is shown in Figure 2(b). Finally, the voltage vector angle range corresponding to _{t'd_min} is the rotor initial angle range with higher precision.

Then, in order to obtain the rotor position more accurately, take θ' _M2 as the median value of the voltage vector angle range with higher precision, repeat the second step, the voltage vector applied to the motor is shown in Figure 2(c), and follow the same direction Detect the new rotor position angle θ″ _M2 , and finally get the initial rotor angle whose accuracy meets the requirements.

Low speed segment position detection

After the electric vehicle is started, as shown in Figure 4, if the angular frequency of the rotating high-frequency voltage signal is ω _i and the amplitude is v _si , then the rotating high-frequency voltage signal Expressed as:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; qdsi</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; qsi</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\\ {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; dsi</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; the\; si</span>}}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; the\; si</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

in: is the q-axis component of the high-frequency voltage; is the d-axis component of the high-frequency voltage.

The DC response of the motor at the output end of the three-phase inverter under the excitation of the rotating high-frequency voltage signal is Will After being filtered by the band-pass filter BPF, the high-frequency current of the dq axis is obtained for:

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; qdi</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; dqs</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; ip</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; dqs</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; in</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ip</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

in: $i_{\mathrm{dqs}\_\mathrm{ip}}^{\mathrm{the\; s}}=i_{\mathrm{ip}}{e}^{j({\mathrm{\&theta;}}_t\left(t\right)-\mathrm{\&pi;}/2)}$ is the positive phase sequence current component; $i_{\mathrm{dqs}\_\mathrm{in}}^{\mathrm{the\; s}}=i_{\mathrm{in}}{e}^{j({2\mathrm{\&theta;}}_{r1}-{\mathrm{\&theta;}}_t\left(t\right)+\mathrm{\&pi;}/2)}$ is the negative phase sequence current component; i _ip is the positive phase sequence current DC component; i _in is the negative phase sequence current DC component; _{θ t} (t) is the moving element speed; Angle, that is, the position angle of the mover at the position of the low speed section; since only the negative phase sequence current component Contains the position angle information θ _r1 of the mover, so the positive phase sequence current component is first passed through the high-pass filter SFF filter out, and then let the negative phase sequence current component multiply by get After that, multiply by After that, the vector angle error ε can be obtained as:

in: is the q-axis component of the negative phase sequence current; is the d-axis component of the negative phase sequence current; is the estimated value of the mover position at the low-speed position, θ _r1 is the real value of the mover at the low-speed position; at the same time, the PI regulator is used to adjust the error of the vector angle to make it tend to zero, so that converges to the true value θ _r1 , for Differentiate over time to obtain the angular velocity of the mover

In formula (7), the mathematical model of electric vehicle drive motor only considers the spatial salient poles that depend on the rotor structure. However, in reality, the motor has multiple salient poles, including the multiple salient poles produced by the nonlinearity of the rotor, stator and inverter, and the salient poles caused by saturation.

The multiple salient poles of the electric vehicle drive motor under the good injection of the rotating high-frequency voltage signal can be expressed by the complex vector sum of the current, that is, the formula (7) can be written as:

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; qdi</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; dqs</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; ip</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; dqs</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; in</span>}}^{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ip</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Among them: i _{ip_1} ≈i _ip ; i _{in_2} ≈i _in .

The salient pole when k=0 is the DC offset in the negative-sequence carrier coordinate system caused by the asymmetric structure of the motor and the asymmetry of the current measurement; when k=1, the spatial salient pole component is caused by the difference in inductance between the d-axis and the q-axis. The magnetic saturation effect of other salient poles (k=±1, ±2, ±3, ±4) under hand load conditions is called the salient pole caused by saturation. The resulting complex vector sum of the currents is approximately:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; qdi</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; ip</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}<span\; class="notranslate">\; \_</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}<span\; class="notranslate">\; \_</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; twenty\; four</span>}<span\; class="notranslate">\; )</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

The first item of formula (10) is the positive sequence component of the high-frequency current, the second item is the static salient pole of the motor when k=0, and the third item is when k=1, by the d-axis and q-axis The negative sequence component of the current caused by the difference in inductance. Items from item 4 to item 8 are affected by magnetic saturation under load conditions when k=-1, k=±2, k=3 and k=4, the salient poles introduced by saturation, and the remaining salient poles due to amplitude The value is very small, and its influence can be ignored, and the decoupling method can be adopted for other salient poles caused by saturation in the driving motor. Figure 5 decouples the sixth item in equation (10) in the stationary coordinate system Schematic of the tracking observer. In the same way, other items can also be decoupled in the same way.

High-speed segment position detection

When in the high-speed section of the electric vehicle, the sliding mode observer is used to obtain the position information of the drive motor rotor, and the voltage equation of the drive motor in the d-q rotating coordinate system is:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; DL</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}& {<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\\ {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}& \mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; DL</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Among them, [u _d u _q ] ^T is the voltage in the rotating coordinate system; [i _d i _q ] ^T is the current in the rotating coordinate system; R is the stator resistance; D is the differential operator; w _r is the rotor angular velocity (electrical angle) ; K _E is the back EMF constant; L _d is the d-axis inductance; L _q is the q-axis inductance.

Transform equation (11) into the α-β static coordinate system, and get:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; DL</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}& {<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;\&beta;</span>}}\\ {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;\&beta;</span>}}& \mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; DL</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}\left[\begin{array}{c}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

Among them, [u _α u _β ] ^T is the voltage in the rotating coordinate system; [i _α i _β ] ^T is the current in the rotating coordinate system; L _α ＝L _o +L ₁ cos2θ _r2 ; L _αβ ＝L ₁ sin2θ _r2 ; L _β ＝L _o -L ₁ cos2θ; L _o ＝(L _d +L _q )/2; L ₁ ＝(L _d -L _q )/2; θ _r2 is the PMSM position angle of the electric vehicle at high speed.

Equation (11) contains θ and 2θ items, among which 2θ will bring great difficulty to the later calculation, therefore, it can be eliminated through appropriate transformation, as can be seen from Equation (12): the inductance matrix Asymmetry is the main reason for the appearance of 2θ. Therefore, the voltage equation (11) of the driving motor under the d-q axis is rewritten as:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; DL</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}& {<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\\ {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}& \mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; DL</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Equation (13) is transformed into the α-β stationary coordinate system, and we get:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; DL</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}& {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>\\ {<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; DL</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\left[\begin{array}{c}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

In order to observe the back electromotive force with a synovial film observer, the voltage equation (11) is rewritten into the state equation of the current:

$\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; \&CenterDot;</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

in,

$\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}\left[\begin{array}{cc}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}& {<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

in, ${\left[\begin{array}{cc}{\hat{i}}_{\mathrm{\&alpha;}}& {\hat{i}}_{\mathrm{\&beta;}}\end{array}\right]}^T$ is the observed value of stator α and β axis current; Z _αβ =[k/L _d sinθ _r2 ,-k/L _d cosθ _r2 ], k is the sliding mode gain.

Equation (16) minus Equation (15), the state equation of the current observation error is obtained as:

$\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

When the following conditions are met, the sliding mode observer enters the sliding mode state:

$<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; ]</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

If the sliding mode gain k is large enough, inequality (18) holds true, and the system enters the sliding film state, as follows:

$\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

Put formula (19) into formula (17), get:

Z = E (20)

Among them, Z contains discontinuous high-frequency signals, so in order to remove discontinuous high-frequency signals, the equivalent control amount is obtained after passing them through a low-pass filter, namely:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\left[\begin{array}{c}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}<span\; class="notranslate">\; )</span>$

From formula (21), the rotor position angle θ _r of the driving motor at high speed can be obtained:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; )</span>$

In order to reduce the observation error, the error caused by the phase lag of the low-pass filter is compensated, and the compensation value is:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; re</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; cut\; off</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; three</span>}<span\; class="notranslate">\; )</span>$

Among them, w _cutoff =1/τ ₀ is the cutoff frequency of the low-pass filter, and τ ₀ is the time constant of the low-pass filter.

In order to prevent the observation value of the rotor position from converging due to wind speed resistance when the electric vehicle is running at high speed, in order to solve this problem, the patent of the present invention adds a rotor position robust observer, and its specific working principle is as follows:

Detecting θ _r2 is the position angle detected at time _T1 , is the position angle detected at T ₂ time, and T ₂ -T ₁ = 20ms, set the position error signal Taking ξ as input and adding matrix feedforward input, according to the mechanical motion model of the driving motor, the equivalent structure diagram of the rotor position robust observer shown in Figure 7 can be constructed. The position error signal constructs the state observation through the linear feedback, so as to realize the observation of the rotor position. The Second Order Differential Term of Electromagnetic Torque As the equivalent input of the observer, it can take into account the wind speed disturbance with different rate of change under different wind speeds, so that the observer has sufficient crater disturbance capability.

The mechanical state equation in the upper part of Figure 7 can be expressed as:

$\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; AX</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Bu</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; four</span>}<span\; class="notranslate">\; )</span>$

y=CX (25)

in: $\stackrel{\&CenterDot;}{x}={\left[\begin{array}{cccc}{\stackrel{\&Center\; Dot;}{T}}_e& T_e& w_r& {\mathrm{\&theta;}}_r\end{array}\right]}^T;u={\stackrel{\&Center\; Dot;\&Center\; Dot;}{T}}_e;$ y = θ _r ; $A=\left[\begin{array}{cccc}0& 0& 0& 0\\ 1& 0& 0& 0\\ 0& \frac{1}{J}& 0& 0\\ 0& 0& P_{\mathrm{no}}& 0\end{array}\begin{array}{}\end{array}\right];B=\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right];C=\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right];$ P _n pole logarithm; J is moment of inertia.

The state equation of the rotor position observer can be expressed as:

$\stackrel{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{<span\; class="notranslate">\; ^</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; J</span>}}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\begin{array}{}\end{array}\right]\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \frac{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; J</span>}}}\\ \frac{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; J</span>}}}\end{array}\right]<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 26</span>}<span\; class="notranslate">\; )</span>$

In the definition formula (26) $\left[\begin{array}{cccc}{l}_1& l_2& \frac{l_3}{\hat{J}}& \frac{l_4}{\hat{J}}\end{array}\right]$ is the feedback matrix.

According to the structure of the position observer shown in Figure 7, the transfer function relationship between the position observation error and the disturbance torque can be established:

${\mathrm{<span\; class="notranslate">\; \&Delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\frac{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; J</span>}}}{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 27</span>}<span\; class="notranslate">\; )</span>$

In the formula, T _d (s) is the disturbance torque caused by the wind speed.

It can be seen from formula (27) that when the wind speed torque changes continuously due to the wind speed, the disturbance steady-state error of the observer is 0, and the load disturbance capacity of the observer pit can be effectively improved, avoiding the electric vehicle running at high speed. When the wind speed is too high, the torque disturbance will increase the error of the observer and lead to the problem that the observed value converges to the S pole.

Middle-speed position detection

When the electric vehicle is in the medium speed range, the high frequency injection method and the back electromotive force method are used to detect the rotor position of the drive motor through the processing of the neural network controller. The neural network speed controller is required to respond to the detection results of the high frequency injection method The test result of back electromotive force method And the effect of the error of the two detection results on the controller; the above signal is used as the input terminal ε _r of the neural network controller, and after being processed by the neural network controller, its output terminal is the position information of the electric vehicle drive motor The block diagram of the entire system is shown in Figure 8, and its neural network controller works as follows.

The neural network controller design uses a 3-layer network: input layer, hidden layer and output layer. The input layer has 3 inputs ε _r ; the hidden layer has 6 neurons; the output layer is

Input layer: consists of 3 neurons

$\begin{array}{cc}{\mathrm{\&sigma;}}_1={\widehat{\mathrm{\&theta;}}}_{r1}& {\mathrm{\&sigma;}}_2={\widehat{\mathrm{\&theta;}}}_{r2}\end{array}$ σ ₃ =ε _r

o _i (t) = σ _i i = 1,2,3

${\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; ji</span>}}{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2,3</span>}$

Hidden layer: consists of 6 neurons

o _2j (t)=f ₁ [n _2j (t)] j=1,2,...,6

${\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 6</span>}$

Output layer: consists of 1 neuron

o ₃ (t) = f ₂ [n ₃ (t)]

Choosing different output functions can enhance the mapping function of the network and improve the convergence speed of the network. The output function of the hidden layer is the logsigmoid function, and the output function of the output layer is the trnsig moid function.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; log</span>}\mathrm{<span\; class="notranslate">\; sig</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}}}$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; sig</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}$

After the above process processing, the position information of the electric vehicle drive motor rotor in the middle speed section is finally checked

The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.

Claims (2)

1. A position-sensorless control method for a driving motor of an electric automobile is characterized by comprising the following steps: the method comprises the following steps of initial position detection, low-speed section position detection, medium-speed section position detection and high-speed section position detection:

(1) initial position detection: detecting the position of a rotor by adopting a pulse voltage injection method, applying a space voltage vector to an armature winding of the motor, determining the initial position of the rotor by comparing the decay time of response current according to the difference of equivalent circuit time constants, wherein the voltage vector angle corresponding to the shortest decay time is the initial angle of the rotor; finally, the electric automobile is enabled to be started without reverse rotation and with the maximum torque;

(2) and (3) low-speed section position detection: the rotor position is detected in real time by adopting a rotary high-frequency voltage injection method, the tracking of the phase of negative sequence high-frequency current is realized by a software phase-locked loop, so that the vector angle error is obtained, and meanwhile, the PI regulator is adopted to regulate the vector angle error to be zero, so that the estimated value of the rotor position angle is enabled to be zeroConvergence to true value theta_rTo, forObtaining the angular speed of the rotor by time differentiationIn order to avoid the influence of the multiple salient pole effect of the motor, a double salient pole decoupling observer is added to the structure of the high-frequency voltage injection method;

(3) detecting the position of the middle speed section, namely detecting the position of the rotor in real time by adopting a mode of combining a high-frequency injection method and a back electromotive force method and processing the position by a neural network controller, adjusting signals of a detection result of the high-frequency injection method, a detection result of the back electromotive force method and an error of the detection results of the high-frequency injection method and the back electromotive force method after the detection results are processed by the neural network controller by adopting a PI (proportional integral) regulator, and taking the output quantity of the signals as;

(4) detecting the position of the high-speed section, detecting the position of the rotor in real time by adopting back electromotive force, and acquiring the position information of the rotor by adopting a synovial membrane observer; in order to weaken the buffeting phenomenon of the sliding-film observer, a saturation function is adopted to replace a traditional switching function z to obtain equivalent electromotive force, so that a rotor position detection value is obtained; in order to solve the problem that the synovium observer can converge to the state of the opposite position of the rotor magnetic pole due to external interference at high speed, a rotor position robust observer is added.

2. Position sensorless control for electric vehicle drive motors according to claim 1The manufacturing method is characterized in that: in the step (1), the specific implementation process of the initial position detection is as follows: (11) firstly, applying a space voltage vector to an armature winding of the motor every 30 degrees, and applying 12 different voltage vectors in total; (12) then, for each voltage vector, a time t when the d-axis current decays from a steady-state value to 0 is detected, and the minimum time t is recorded as t_{d_min}，t_{d_min}The corresponding voltage vector angle range is the initial angle range of the rotor; (13) n equal division is carried out on the obtained initial angle range of the rotor, a space voltage vector is applied to an armature winding of the motor every other equal division value, and n +1 different voltage vectors are applied in total; and (5) repeating the step (12) until the initial rotor angle within the precision range is obtained.