CN116247988A - Method for estimating rotor position and rotating speed of ultra-high-speed permanent magnet synchronous motor - Google Patents

Abstract

The invention discloses a method for estimating the position and the rotating speed of a rotor of an ultra-high-speed permanent magnet synchronous motor, which comprises the following steps: step 1, establishing a full-speed domain rotor position cost function of a super-speed permanent magnet synchronous motor considering iron loss resistance; step 2, estimating a preliminary rotor position by accelerating the self-adaptive convex optimization by the full-speed domain rotor position cost function obtained in the step 1; and 3, estimating the rotor position and the rotating speed of the ultra-high-speed permanent magnet synchronous motor through a phase-locked loop from the estimated preliminary rotor position obtained in the step 2. The method solves the problems that the rotor position and the rotating speed of the transition zone are easy to oscillate when the existing composite observer estimation method is started quickly, the rotor position and the rotating speed are difficult to estimate accurately when the motor operates at an ultra-high speed, and even the system diverges.

Description

Rotor position and speed estimation method for ultra-high-speed permanent magnet synchronous motor

Technical Field

The invention belongs to the technical field of ultra-high-speed permanent magnet synchronous motor control, and relates to a method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor.

Background Art

Ultra-high-speed permanent magnet synchronous motors have high speed, small size, high power density, and the rotor is directly connected to the high-speed load, which gets rid of the traditional "low-speed motor + speed changer" mechanical structure, improves system integration and reliability, and has wide application value in military, industrial and other fields. Ultra-high-speed permanent magnet synchronous motors usually refer to permanent magnet synchronous motors with speeds higher than 100,000 r/min, and their control performance is heavily dependent on the accurate acquisition of the rotor position. However, the maximum detection speed of conventional mechanical sensors does not exceed 40,000 r/min, and cannot detect the rotor position in the high-speed zone of ultra-high-speed permanent magnet synchronous motors. In addition, ultra-high-speed permanent magnet synchronous motors require the rotor to be as short as possible, so it is difficult to install mechanical sensors on the rotor. In addition, installing mechanical sensors will not only increase the size and cost of the system, but also reduce the reliability of the system. Therefore, ultra-high-speed permanent magnet synchronous motor position sensorless control technology is crucial.

At present, a composite observer is usually used to estimate the rotor position and speed of ultra-high-speed permanent magnet synchronous motors in the full speed range. The composite observer uses two observers suitable for low speed and medium and high speed for composite control to achieve full-speed rotor position estimation. However, ultra-high-speed permanent magnet synchronous motors have small rotational inertia and fast dynamic response. When the composite observer estimation method is used for rapid startup, the rotor position and speed in the transition zone are prone to oscillation, and even cause startup failure. In addition, the rated speed of ultra-high-speed permanent magnet synchronous motors exceeds 100,000 r/min, requiring the drive system to have a high switching frequency, and thus requiring the rotor position estimation algorithm to have a short execution time, which makes it difficult for the composite observer estimation method to accurately discretize. When the motor is running at ultra-high speed, the carrier ratio is low, which makes it difficult for the composite observer estimation method to accurately estimate the rotor position and speed, and even causes the system to diverge.

Summary of the invention

The purpose of the present invention is to provide a method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor, which solves the problem that the rotor position and speed in the transition zone of the existing composite observer estimation method are prone to oscillation during rapid startup, and it is difficult to accurately estimate the rotor position and speed when the motor is running at ultra-high speed, resulting in system divergence.

The technical solution adopted by the present invention is a method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor, which specifically includes the following steps:

Step 1, establishing a full-speed domain rotor position cost function of an ultra-high-speed permanent magnet synchronous motor taking into account iron loss resistance;

Step 2, the full-speed domain rotor position cost function obtained in step 1 is used to estimate the preliminary rotor position through accelerated adaptive convex optimization;

Step 3, using the estimated preliminary rotor position obtained in step 2 to estimate the rotor position and speed of the ultra-high-speed permanent magnet synchronous motor through a phase-locked loop.

The present invention is also characterized in that:

The specific process of step 1 is:

The voltage equation of the ultra-high-speed permanent magnet synchronous motor considering iron loss in the two-phase stationary coordinate system is shown in the following formula (1):

Wherein, _Ri =( _ωr (k)) ^2LdLq / _ri is _{the iron} loss, _ωr (k) is the rotor electrical angular frequency of the kth cycle, _Ld is the d-axis inductance, _Lq is the q-axis inductance, _ri is the iron loss resistance, _uα (k) and _uβ (k) are the components of the kth cycle stator voltage on the α-axis and β-axis, _iα (k) and _iβ (k) are the components of the kth cycle stator current on the α-axis and β-axis, and _Rs is the stator resistance;

θ _r (k) is the actual rotor position at the kth beat, L ₁ =0.5(L _d +L _q ), L ₂ =0.5(L _d -L _q ), T _s is the switching period, Δi _α (k) =i _α (k)-i _α (k-1), Δi _β (k) =i _β (k)-i _β (k-1), ψ _f is the permanent magnet flux;

In order to separate the terms that are independent of the rotor position, the intermediate variables are defined as shown in the following formula (2):

Among them, e _α (k) and e _β (k) are the components of the intermediate variable that does not contain the rotor position information in the kth beat on the α-axis and β-axis respectively;

From formula (1) and formula (2), the rotor position related function can be obtained as shown in the following formula (3):

Wherein, F _α (θ _e (k)) and F _β (θ _e (k)) are the components of the k-th rotor position correlation function on the α-axis and the β-axis, respectively, F(θ _e (k)) = [F _α (θ _e (k)) F _β (θ _e (k))] ^T ;

The rotor position cost function is constructed from formula (3) as shown in formula (4):

Where h(θ _e (k)) is the rotor position cost function;

In order to ensure the solvability of the rotor position, the rotor position cost function (4) is at least a local convex function. The rotor position cost function in the stationary and low-speed areas and the medium-high-speed areas is simplified to the following formula (5):

In order to increase the convexity of the rotor position cost function at rest and low speed, a high-frequency square wave voltage is injected below 10% of the rated speed as shown in the following formula (6):

Wherein, u _dh and u _qh are the high-frequency square wave voltages injected into the d-axis and q-axis respectively, and V _h is the amplitude of the injected high-frequency square wave voltage.

The specific process of step 2 is:

Step 2.1, calculate the accelerated iteration step size of the accelerated adaptive convex optimization;

Step 2.2, estimate the preliminary rotor position by accelerated adaptive convex optimization.

The specific process of step 2.1 is:

如下公式(7)所示：Calculate the adaptive factor according to formula (3):

As shown in the following formula (7):

是自适应因子，λ_i是自适应系数，i表示第i次迭代；in,

is the adaptive factor, λ _i is the adaptive coefficient, i represents the i-th iteration;

According to formula (3) and formula (7), the iterative step length of adaptive accelerated convex optimization is calculated as shown in the following formula (8):

I是单位矩阵；Where l _i is the iteration step size of adaptive accelerated convex optimization, R(θ _e (i)) is the Jacobian matrix of the current step or the Jacobian matrix used in the previous iteration, and the Jacobian matrix of the current step is

I is the identity matrix;

According to formula (3), formula (7) and formula (8), the approximate iterative step size of adaptive accelerated convex optimization is calculated as shown in the following formula (9):

Where, _gi is the approximate iteration step size of adaptive accelerated convex optimization;

According to formula (8) and formula (9), the acceleration iteration step size of the adaptive accelerated convex optimization is calculated as shown in the following formula (10):

_ci = l _i + σ _i g _i (10);

Among them, _ci is the acceleration iteration step size of adaptive accelerated convex optimization, and _σi is an adjustable parameter.

The specific process of step 2.2 is:

In order to verify the effectiveness of the current iteration step, the adaptive evaluation index is used as shown in the following formula (11):

Among them, e _i is the adaptive evaluation index;

According to the result calculated by formula (11), whether to accept the accelerated iteration step of this iterative calculation is as shown in the following formula (12):

Where, d ₀ is the acceleration iteration step size cut-off index, θ _e (i+1) is the rotor position obtained at the i+1th iteration;

According to the result of formula (11), the adjustable parameter σ _i+1 is calculated as shown in the following formula (13):

According to the result calculated by formula (11), whether to choose to update the Jacobian matrix R(θ _e (i+1)) is as shown in the following formula (14):

Among them, d ₁ is the lower limit threshold of the adaptive evaluation index e _i for updating the Jacobian matrix, x is the number of times the current Jacobian matrix is used, and x _max is the maximum number of times the same Jacobian matrix is used;

According to the result calculated by formula (11), whether to choose to update the adaptive coefficient λ _i+1 is as shown in the following formula (15):

Among them, λ _min is the minimum value of the adaptive coefficient, d ₂ is the lower limit threshold of the adaptive evaluation index e _i when the adaptive factor is , and d ₃ is the upper limit threshold of the adaptive evaluation index e _i when the adaptive factor is ;

如下公式(16)所示：According to the result calculated by formula (11), whether to select the adaptive factor

As shown in the following formula (16):

The specific process of step 3 is:

The rotor position error is calculated by subtracting the preliminary rotor position _θe (k) estimated by the accelerated adaptive convex optimization from the estimated rotor position _θer (k-1) output by the previous phase-locked loop, as shown in the following formula (17):

Δθ(k)=θ _e (k)-θ _er (k-1) (17);

Wherein, θ _e (k) is the preliminary rotor position of the kth beat estimated by the accelerated adaptive convex optimization, θ _er (k-1) is the estimated rotor position output by the phase-locked loop at the k-1th beat, and Δθ(k) is the rotor position error of the kth beat;

The k-th rotor position error Δθ(k) is adjusted by the PI regulator to obtain the estimated speed as shown in the following formula (18):

Where, _ωer (k) is the estimated rotor speed at the kth beat, _Kp is the proportional gain of PI, and _Ki is the integral gain of PI;

The rotor speed _ωer (k) of the kth cycle is integrated to obtain the rotor position of the kth cycle as shown in the following formula (19):

θ _er (k)=θ _er (k-1)+ω _er (k)T _s (19);

where _θer (k) is the estimated rotor position at the kth beat.

The beneficial effect of the present invention is that the present invention adopts an accelerated adaptive convex optimization method to estimate the rotor position and speed of the ultra-high-speed permanent magnet synchronous motor in the full-speed domain, and a single method is used to realize the rotor position estimation in the full-speed domain without a transition zone, which fundamentally solves the problem that the ultra-high-speed permanent magnet synchronous motor has a small moment of inertia and a fast dynamic response, and the rotor position and speed estimated in the transition zone are prone to oscillation, and even lead to startup failure. At the same time, for the ultra-high-speed permanent magnet synchronous motor drive system, the switching frequency is high, and the algorithm execution time is required to be short. The adopted accelerated adaptive convex optimization method improves the algorithm convergence speed through adaptive factors and accelerated iteration step length, and reduces the average amount of calculation per iteration through adaptive updating of the Jacobian matrix, thereby ensuring that the rotor position and speed of the ultra-high-speed permanent magnet synchronous motor in the full-speed domain are accurately estimated under the constraint of short algorithm execution time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a block diagram of a vector control system used in a method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor according to the present invention;

2 is a flowchart of the accelerated adaptive convex optimization used in the method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor of the present invention;

3 is a block diagram of a phase-locked loop structure used in the method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor according to the present invention;

FIG4 is a diagram showing simulation results of rotor speed estimated using a conventional composite observer;

FIG. 5 is a diagram showing the simulation results of the rotor speed estimated by the accelerated adaptive convex optimization method proposed in the present invention.

DETAILED DESCRIPTION

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

The method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor of the present invention, wherein the vector control system block diagram adopted is shown in FIG1 , is specifically implemented according to the following steps:

Step 1: Establish the full-speed domain rotor position cost function of the ultra-high-speed permanent magnet synchronous motor considering the iron loss resistance, specifically:

The iron loss resistance is proportional to the angular frequency. If the iron loss resistance is ignored in the high-speed region, the voltage equation of the ultra-high-speed permanent magnet synchronous motor cannot accurately represent the actual operating state of the motor, resulting in the cost function constructed by the voltage equation being difficult to accurately estimate the rotor position. The voltage equation of the ultra-high-speed permanent magnet synchronous motor considering iron loss in the two-phase stationary coordinate system is shown in the following formula (1):

Wherein, _Ri =( _ωr (k)) ^2LdLq / _ri is _{the iron} loss, _ωr (k) is the rotor electrical angular frequency of the kth cycle, _Ld is the d-axis inductance, _Lq is the q-axis inductance, _ri is the iron loss resistance, _uα (k) and _uβ (k) are the components of the kth cycle stator voltage on the α-axis and β-axis, _iα (k) and _iβ (k) are the components of the kth cycle stator current on the α-axis and β-axis, and _Rs is the stator resistance;

θ _r (k) is the actual rotor position at the kth beat, L ₁ =0.5(L _d +L _q ), L ₂ =0.5(L _d -L _q ), T _s is the switching period, Δi _α (k) =i _α (k)-i _α (k-1), Δi _β (k) =i _β (k)-i _β (k-1), and ψ _f is the permanent magnet flux.

The first two terms on the right side of formula (1) do not contain rotor position information, while the last three terms do. In order to separate the terms irrelevant to the rotor position, the intermediate variables are defined as shown in the following formula (2):

Among them, e _α (k) and e _β (k) are the components of the intermediate variable that does not contain the rotor position information in the kth beat on the α-axis and β-axis respectively.

From formula (1) and formula (2), the rotor position related function can be obtained as shown in the following formula (3):

Wherein, F _α (θ _e (k)) and F _β (θ _e (k)) are the components of the k-th rotor position correlation function on the α-axis and β-axis, respectively, and F(θ _e (k)) = [F _α (θ _e (k)) F _β (θ _e (k))] ^T .

The rotor position cost function is constructed from formula (3) as shown in formula (4):

where h(θ _e (k)) is the rotor position cost function.

In order to ensure the solvability of the rotor position, the rotor position cost function (4) is at least a local convex function. In the stationary and low-speed areas and the medium-high-speed areas, the rotor position cost function can be simplified as shown in formula (5):

When _ωe is less than 10% of the rated speed, it is a low speed. When _ωe is greater than or equal to 10% of the rated speed, it is a medium-high speed. It can be seen from formula (5) that at medium-high speed, the rotor position cost function is a periodic function with a period of 360°, and is a locally convex function in the interval [-180°, 180°]. When the motor is running at zero speed or low speed, if Δi _αβ (k)＝0, the rotor position cost function is a constant, and the estimated rotor position cannot converge to the actual rotor position. If Δi _αβ (k)≠0, the rotor position cost function is a periodic function with a period of 180°, and is a locally convex function in the interval [-90°, 90°]. Minimizing the rotor position cost function can make the estimated rotor position converge to the actual rotor position. However, the rotor position cost function is a weak convexity function. The weak convexity not only slows down the convergence speed of the rotor position, but also increases the error of the estimated rotor position. Therefore, in order to increase the convexity of the rotor position cost function at rest and low speed, a high-frequency square wave voltage is injected below 10% of the rated speed as shown in the following formula (6):

Wherein, u _dh and u _qh are the high-frequency square wave voltages injected into the d-axis and q-axis respectively, and V _h is the amplitude of the injected high-frequency square wave voltage.

Step 2, the full-speed domain rotor position cost function obtained in step 1 is used to estimate the preliminary rotor position through the accelerated adaptive convex optimization as shown in FIG2 ;

Step 2.1, calculate the accelerated iteration step size of the accelerated adaptive convex optimization;

如下公式(7)所示：Calculate the adaptive factor according to formula (3):

As shown in the following formula (7):

是自适应因子，λ_i是自适应系数，i表示第i次迭代。in,

is the adaptive factor, λ _i is the adaptive coefficient, and i represents the i-th iteration.

According to formula (3) and formula (7), the iterative step length of adaptive accelerated convex optimization is calculated as shown in the following formula (8):

I是单位矩阵。Where, l _i is the iteration step size of adaptive accelerated convex optimization, R(θ _e (i)) is the Jacobian matrix of the current step or the Jacobian matrix used in the previous iteration, and its value depends on the update quality of the previous step.

I is the identity matrix.

According to formula (3), formula (7) and formula (8), the approximate iterative step size of adaptive accelerated convex optimization is calculated as shown in the following formula (9):

where _gi is the approximate iteration step size of the adaptive accelerated convex optimization.

According to formula (8) and formula (9), the acceleration iteration step size of the adaptive accelerated convex optimization is calculated as shown in the following formula (10):

_ci = l _i + σ _i g _i (10);

Among them, _ci is the acceleration iteration step size of adaptive accelerated convex optimization, and _σi is an adjustable parameter.

Step 2.2, estimate the preliminary rotor position by accelerated adaptive convex optimization.

In order to verify the effectiveness of the current iteration step, the adaptive evaluation index is used as shown in the following formula (11):

Among them, e _i is an adaptive evaluation index.

According to the result calculated by formula (11), whether to accept the accelerated iteration step of this iterative calculation is as shown in the following formula (12):

Wherein, d ₀ is the acceleration iteration step size cut-off indicator, and θ _e (i+1) is the rotor position obtained at the i+1th iteration.

According to the result of formula (11), the adjustable parameter σ _i+1 is calculated as shown in the following formula (13):

According to the result calculated by formula (11), whether to choose to update the Jacobian matrix R(θ _e (i+1)) is as shown in the following formula (14):

Among them, d ₁ is the lower limit threshold of the adaptive evaluation index e _i for updating the Jacobian matrix, x is the number of times the current Jacobian matrix is used, and x _max is the maximum number of times the same Jacobian matrix is used.

According to the result calculated by formula (11), whether to choose to update the adaptive coefficient λ _i+1 is as shown in the following formula (15):

Among them, λ _min is the minimum value of the adaptive coefficient, d ₂ is the lower limit threshold of the adaptive evaluation index e _i when the adaptive factor is , and d ₃ is the upper limit threshold of the adaptive evaluation index e _i when the adaptive factor is .

如下公式(16)所示：According to the result calculated by formula (11), whether to select the adaptive factor

As shown in the following formula (16):

The process of estimating the preliminary rotor position using the accelerated adaptive convex optimization method is as follows:

1) Given the initial value of the iteration θ _er (1), set the maximum number of iterations i _max ≥ 1, set the maximum number of times the same Jacobian matrix is used x _max ≥ 1, given the constants 0 < d ₀ < d ₂ < d ₁ < d ₃ < 1 and the convergence accuracy ε, set R(θ _e (1)) = J(θ _e (1)), i = 1, x = 1,

2) Calculate the adaptive factor according to formula (7)

3) Calculate the accelerated iteration step size c _i according to formulas (8) to (10);

4) Calculate the adaptive evaluation index e _i according to formula (11);

5) Calculate the rotor position of this iteration according to formula (12), and use the criterion ||R( _θe (i)) ^T F( _θe (i))|| ₂ ＜ε to determine whether it has converged. If it has converged, exit the optimization search and output the preliminary rotor position _θe (k) estimated for this beat. Otherwise, determine whether the iteration number i has reached the maximum iteration number _imax . If it has reached the maximum iteration number _imax , exit the optimization search and output the preliminary rotor position _θe (k)= _θe (k-1)+ _ωer (k-1) _Ts estimated for this beat, _{where ωer} (k-1) is the rotor electrical angular frequency estimated for the (k-1)th beat. Otherwise, set i=i+1 and continue to execute step 6);

6) Calculate the adjustable parameter σ _i+1 according to formula (13);

7) Update the Jacobian matrix R(θ _e (i+1)) according to formula (14);

8) Update the adaptive coefficient λ _i+1 according to formula (15);

返回步骤3)。9) Update the adaptive factor according to formula (16)

Return to step 3).

Step 3, the rotor position and speed of the ultra-high-speed permanent magnet synchronous motor are estimated by using the estimated preliminary rotor position obtained in step 2 through a phase-locked loop as shown in FIG. 3, specifically:

The rotor position error is calculated by subtracting the preliminary rotor position _θe (k) estimated by the accelerated adaptive convex optimization from the estimated rotor position _θer (k-1) output by the previous phase-locked loop, as shown in the following formula (17):

Δθ(k)=θ _e (k)-θ _er (k-1) (17);

Wherein, _θe (k) is the preliminary rotor position of the kth beat estimated by the accelerated adaptive convex optimization, _θer (k-1) is the estimated rotor position output by the phase-locked loop at the k-1th beat, and Δθ(k) is the rotor position error of the kth beat.

The k-th rotor position error Δθ(k) is adjusted by the PI regulator to obtain the estimated speed as shown in the following formula (18):

Where _ωer (k) is the estimated rotor speed at the kth beat, _Kp is the proportional gain of PI, and _Ki is the integral gain of PI.

The rotor speed _ωer (k) of the kth cycle is integrated to obtain the rotor position of the kth cycle as shown in the following formula (19):

θ _er (k)=θ _er (k-1)+ω _er (k)T _s (19);

where _θer (k) is the estimated rotor position at the kth beat.

作为电流环PI调节器的输入，电流调节器的输出控制电力电子变换器。The block diagram of the vector control system used in the method for estimating the rotor position and speed of the ultra-high-speed permanent magnet synchronous motor of the present invention is shown in FIG1. The system consists of three PI regulators to form a dual-loop control of the speed loop and the current loop. The output of the speed loop PI regulator is used as the input of the maximum torque current ratio control (MTPA). The current command output by the MTPA is

As the input of the current loop PI regulator, the output of the current regulator controls the power electronic converter.

再由最大转矩电流比(MTPA)得到给定励磁电流

和给定转矩电流

给定励磁电流

与反馈电流i_d[k]作差，经过电流环PI控制器输出d轴电压

给定励磁电流

与反馈电流i_q[k]作差，经过电流环PI控制器输出q轴电压

若转速ω_er(k)小于10％的电机额定转速，d轴电压

与注入高频方波电压u_dh的和与q轴电压

经过dq/αβ变换得到两相静止坐标系下的电压u_α[k]、u_β[k]；若转速ω_er(k)大于等于10％的电机额定转速，d轴电压

与q轴电压

经过dq/αβ变换得到两相静止坐标系下的电压u_α[k]、u_β[k]；然后u_α[k]、u_β[k]经过SVPWM调制控制三相逆变器，最后驱动超高速永磁同步电机工作。The k-th beat stator current i _a [k], i _b [k], i _c [k] of the ultra-high-speed permanent magnet synchronous motor in the three-phase stationary coordinate system is detected by the current Hall sensor; the detected three-phase stator current i _a [k], i _b [k], i _c [k] is converted to the two-phase stationary coordinate system through abc/αβ transformation to obtain the k-th beat current value i _α [k], i _β [k]; i _α [k], i _β [k] is converted to the two-phase synchronous rotating coordinate system through αβ/dq transformation to obtain the k-th beat current value i _d [k], i _q [k]; the two-phase voltage u _α [k], u _β [k] and the two-phase current i _α [k], i _β [k] in the two-phase stationary coordinate system of the k-th beat and the estimated speed ω _er (k-1) and the estimated rotor position θ _er of the phase-locked loop output as shown in FIG. (k-1) is used as the input of the accelerated adaptive convex optimization as shown in FIG2 , and the output of the accelerated adaptive convex optimization is the preliminary rotor position θ _e (k) estimated at the kth beat; the preliminary rotor position θ _e (k) estimated at the kth beat is passed through the phase-locked loop as shown in FIG3 to obtain the speed ω _er (k) and rotor position θ _er (k) estimated at the kth beat; the given speed ω ^* of the speed loop is subtracted from the speed ω _er (k) estimated by the phase-locked loop, and the electromagnetic torque given value is output after passing through the speed loop PI controller

Then the given excitation current is obtained from the maximum torque current ratio (MTPA)

and given torque current

Given excitation current

Subtract the feedback current i _d [k] and output the d-axis voltage through the current loop PI controller

Given excitation current

Subtract the feedback current _iq [k] and output the q-axis voltage through the current loop PI controller

If the speed _ωer (k) is less than 10% of the rated speed of the motor, the d-axis voltage

The sum of the injected high frequency square wave voltage u _dh and the q axis voltage

After dq/αβ transformation, the voltages u _α [k] and u _β [k] in the two-phase stationary coordinate system are obtained; if the speed ω _er (k) is greater than or equal to 10% of the rated speed of the motor, the d-axis voltage

and q-axis voltage

After dq/αβ transformation, the voltages u _α [k] and u _β [k] in the two-phase stationary coordinate system are obtained; then u _α [k] and u _β [k] are modulated by SVPWM to control the three-phase inverter, and finally drive the ultra-high-speed permanent magnet synchronous motor to work.

FIG. 4 is a simulation result of rotor speed estimated by a conventional composite observer, where two observers are composited at 11000 rpm; FIG. 5 is a simulation result of speed estimated by the method for estimating rotor position and speed of an ultra-high-speed permanent magnet synchronous motor of the present invention.

The parameters of the ultra-high-speed permanent magnet synchronous motor used in the simulation are shown in Table 1. The speed settings in the simulation results of Figures 4 and 5 are as follows: 0s-1s motor accelerates from 0rpm to 50000rpm; 1s-2s motor runs at 50000rpm; 2s-3s motor accelerates from 50000rpm to 110000rpm; 3s-4s motor runs at 110000rpm.

By comparing Figure 4 and Figure 5, it can be found that: when the motor accelerates from 0rpm to 50000rpm, the speed estimated by the traditional composite observer in the transition area of 11000rpm has serious jitter, while the speed estimated by the present invention is smooth and has no oscillation; when the motor accelerates from 50000rpm to 110000rpm, the rotor speed estimated by the traditional composite observer oscillates severely with the increase of speed, causing the system to diverge, while the rotor speed estimated by the present invention can accurately track the set speed. The above simulation results show that the ultra-high-speed permanent magnet synchronous motor rotor position and speed estimation method of the present invention can effectively solve the problem that the rotor speed in the transition area is prone to oscillation when the existing composite observer estimation method is quickly started, and it is difficult to accurately estimate the rotor speed when the motor is running at ultra-high speed, and even causes the system to diverge.

Table 1 Parameters of ultra-high-speed permanent magnet synchronous motor

parameter Numeric parameter Numeric Rated Power 15kW Rated torque 1.6N.m Pole pairs 1 Rated current 35A Maximum speed 110000rpm Maximum frequency 1833.33Hz

Claims (6)

1. A method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor, characterized in that it specifically comprises the following steps: Step 1, establishing a full-speed domain rotor position cost function of an ultra-high-speed permanent magnet synchronous motor taking into account iron loss resistance; Step 2, the full-speed domain rotor position cost function obtained in step 1 is used to estimate the preliminary rotor position through accelerated adaptive convex optimization; Step 3, using the estimated preliminary rotor position obtained in step 2 to estimate the rotor position and speed of the ultra-high-speed permanent magnet synchronous motor through a phase-locked loop. 2. The method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor according to claim 1, wherein the specific process of step 1 is as follows: The voltage equation of the ultra-high-speed permanent magnet synchronous motor considering iron loss in the two-phase stationary coordinate system is shown in the following formula (1):

Wherein, _Ri =( _ωr (k)) ^2LdLq / _ri is _{the iron} loss, _ωr (k) is the rotor electrical angular frequency of the kth cycle, _Ld is the d-axis inductance, _Lq is the q-axis inductance, _ri is the iron loss resistance, _uα (k) and _uβ (k) are the components of the kth cycle stator voltage on the α-axis and β-axis, _iα (k) and _iβ (k) are the components of the kth cycle stator current on the α-axis and β-axis, and _Rs is the stator resistance;

θ _r (k) is the actual rotor position at the kth beat, L ₁ =0.5(L _d +L _q ), L ₂ =0.5(L _d -L _q ), T _s is the switching period, Δi _α (k) =i _α (k)-i _α (k-1), Δi _β (k) =i _β (k)-i _β (k-1), ψ _f is the permanent magnet flux; In order to separate the terms that are independent of the rotor position, the intermediate variables are defined as shown in the following formula (2):

Among them, e _α (k) and e _β (k) are the components of the intermediate variable that does not contain the rotor position information in the kth beat on the α-axis and β-axis respectively; From formula (1) and formula (2), the rotor position related function can be obtained as shown in the following formula (3):

Wherein, F _α (θ _e (k)) and F _β (θ _e (k)) are the components of the k-th rotor position correlation function on the α-axis and the β-axis, respectively, F(θ _e (k)) = [F _α (θ _e (k)) F _β (θ _e (k))] ^T ; The rotor position cost function is constructed from formula (3) as shown in formula (4):

Where h(θ _e (k)) is the rotor position cost function; In order to ensure the solvability of the rotor position, the rotor position cost function (4) is at least a local convex function. The rotor position cost function in the stationary and low-speed areas and the medium-high-speed areas is simplified to the following formula (5):

In order to increase the convexity of the rotor position cost function at rest and low speed, a high-frequency square wave voltage is injected below 10% of the rated speed as shown in the following formula (6):

Wherein, u _dh and u _qh are the high-frequency square wave voltages injected into the d-axis and q-axis respectively, and V _h is the amplitude of the injected high-frequency square wave voltage. 3. The method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor according to claim 2, characterized in that the specific process of step 2 is as follows: Step 2.1, calculate the accelerated iteration step size of the accelerated adaptive convex optimization; Step 2.2, estimate the preliminary rotor position by accelerated adaptive convex optimization. 4. The method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor according to claim 3, characterized in that the specific process of step 2.1 is as follows: Calculate the adaptive factor according to formula (3):

As shown in the following formula (7):

in,

is the adaptive factor, λ _i is the adaptive coefficient, i represents the i-th iteration; According to formula (3) and formula (7), the iterative step length of adaptive accelerated convex optimization is calculated as shown in the following formula (8):

Where l _i is the iteration step size of adaptive accelerated convex optimization, R(θ _e (i)) is the Jacobian matrix of the current step or the Jacobian matrix used in the previous iteration, and the Jacobian matrix of the current step is

I is the identity matrix; According to formula (3), formula (7) and formula (8), the approximate iterative step size of adaptive accelerated convex optimization is calculated as shown in the following formula (9):

Where, _gi is the approximate iteration step size of adaptive accelerated convex optimization; According to formula (8) and formula (9), the acceleration iteration step size of the adaptive accelerated convex optimization is calculated as shown in the following formula (10): _ci = l _i + σ _i g _i (10); Among them, _ci is the acceleration iteration step size of adaptive accelerated convex optimization, and _σi is an adjustable parameter. 5. The method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor according to claim 4, characterized in that the specific process of step 2.2 is as follows: In order to verify the effectiveness of the current iteration step, the adaptive evaluation index is used as shown in the following formula (11):

Among them, e _i is the adaptive evaluation index; According to the result calculated by formula (11), whether to accept the accelerated iteration step of this iterative calculation is as shown in the following formula (12):

Where, d ₀ is the acceleration iteration step size cut-off index, θ _e (i+1) is the rotor position obtained at the i+1th iteration; According to the result of formula (11), the adjustable parameter σ _i+1 is calculated as shown in the following formula (13):

According to the result calculated by formula (11), whether to choose to update the Jacobian matrix R(θ _e (i+1)) is as shown in the following formula (14):

Among them, d ₁ is the lower limit threshold of the adaptive evaluation index e _i for updating the Jacobian matrix, x is the number of times the current Jacobian matrix is used, and x _max is the maximum number of times the same Jacobian matrix is used; According to the result calculated by formula (11), whether to choose to update the adaptive coefficient λ _i+1 is as shown in the following formula (15):

Among them, λ _min is the minimum value of the adaptive coefficient, d ₂ is the lower limit threshold of the adaptive evaluation index e _i when the adaptive factor is , and d ₃ is the upper limit threshold of the adaptive evaluation index e _i when the adaptive factor is ; According to the result calculated by formula (11), whether to select the adaptive factor

As shown in the following formula (16):

6. The method for estimating the rotor position and speed of an ultra-high-speed permanent magnet synchronous motor according to claim 5, characterized in that the specific process of step 3 is as follows: The rotor position error is calculated by subtracting the preliminary rotor position _θe (k) estimated by the accelerated adaptive convex optimization from the estimated rotor position _θer (k-1) output by the previous phase-locked loop, as shown in the following formula (17): Δθ(k)=θ _e (k)-θ _er (k-1) (17); Wherein, θ _e (k) is the preliminary rotor position of the kth beat estimated by the accelerated adaptive convex optimization, θ _er (k-1) is the estimated rotor position output by the phase-locked loop at the k-1th beat, and Δθ(k) is the rotor position error of the kth beat; The k-th rotor position error Δθ(k) is adjusted by the PI regulator to obtain the estimated speed as shown in the following formula (18):

Where, _ωer (k) is the estimated rotor speed at the kth beat, _Kp is the proportional gain of PI, and _Ki is the integral gain of PI; The k-th rotor speed _ωer (k) is integrated to obtain the k-th rotor position as shown in the following formula (19): θ _er (k)=θ _er (k-1)+ω _er (k)T _s (19); where _θer (k) is the estimated rotor position at the kth beat.

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