CN111835252A - Flexible load vibration and PMSM torque ripple comprehensive suppression method under stator current vector orientation considering electrical loss - Google Patents

Abstract

The control method comprises the steps of firstly deducing a stator current constraint condition under the condition of minimum loss based on a PMSM minimum loss mathematical model. And then combining a dynamic mathematical model of the PMSM under the current vector orientation with a vibration model of the permanent magnet synchronous motor to establish an integral mathematical model of the permanent magnet synchronous motor driven by the permanent magnet synchronous motor considering the electrical loss of the motor. And deducing constraint conditions of the STS vibration, the electrical loss and the torque ripple comprehensive control of the permanent magnet synchronous motor. Then, based on a reverse control principle, a comprehensive suppression method (a closed loop I/f comprehensive control method for short) for flexible load vibration and PMSM torque ripple under stator current vector orientation considering electrical loss is provided under an I/f control framework. In order to accurately acquire a speed signal, the invention simultaneously designs a PMSM speed identification algorithm based on a least square method. Simulation and experiments prove that the provided closed-loop I/f comprehensive control method can enable the state variables to quickly and accurately track respective reference values, effectively inhibit torque pulsation and load vibration and improve the operating efficiency of the system.

Description

Flexible load vibration and PMSM torque ripple comprehensive suppression method under stator current vector orientation considering electrical loss

Technical Field

The invention relates to a control method of a permanent magnet synchronous motor, and belongs to the technical field of motors.

Background

For modern power systems, access to the grid by a large number of new renewable energy sources has become a common trend. The intermittency and the uncontrollable property of new renewable energy sources can generate adverse effects on the basic operation rule of the existing power network, and the development of energy storage technology is urgent. A spiral spring (STS) has the characteristics of large energy storage, high power density, long service life and the like, and the STS is widely concerned and researched when applied to the field of energy storage. A Permanent Magnet Synchronous Motor (PMSM) has the advantages of simple structure, large torque inertia ratio, small loss and the like, and is selected as a driving motor during energy storage. When the flexible load STS is driven by the PMSM to store energy, the scroll spring is subjected to external force and winds around the main shaft to cause a series of mechanical resonances with lower frequency and considerable amplitude; meanwhile, due to the reasons of nonideal structural design of the motor, distortion of an air gap magnetic field, nonlinearity of an inverter and the like, the torque of the permanent magnet synchronous motor has large pulsation. Both of which will adversely affect the stable operation of the unit. On the other hand, when the problem of energy shortage is highlighted, the operation efficiency of the motor mainly depends on the control condition of motor loss, and when the damping winding is ignored, the loss of the PMSM comprises iron loss, copper loss and mechanical loss. Therefore, the PMSM running loss is reduced, and the method has important significance for improving the control performance of the motor and saving energy. Most of the existing researches on the three problems are single, but the three problems are actually coupled and mutually influenced. Therefore, the three problems are brought into a unified framework for research, and the method has important significance for strengthening the operation stability of the unit and improving the operation efficiency.

Disclosure of Invention

In view of the above problems, the present invention aims to make two innovations against the drawbacks of the prior art: firstly, a comprehensive suppression method (a closed loop I/f comprehensive control method for short) of flexible load vibration and PMSM torque ripple under stator current vector orientation considering electrical loss is provided to realize comprehensive control of the flexible load vibration, the PMSM torque ripple and the PMSM electrical loss. Secondly, a PMSM speed identification method based on a least square method is designed to realize the tracking of the PMSM rotating speed.

The problem of the invention is realized by the following technical scheme:

the method for comprehensively inhibiting the flexible load vibration and the PMSM torque ripple under stator current vector orientation considering the electrical loss comprises the following steps:

firstly, deriving a stator current constraint condition under a minimum loss condition based on a PMSM minimum loss mathematical model:

then, a dynamic mathematical model of the PMSM under the current vector orientation is combined with a vibration model of the permanent magnet synchronous motor, and an overall mathematical model of the permanent magnet synchronous motor driven by the permanent magnet synchronous motor considering the electrical loss of the motor is established:

wherein: u. of_sd*And u_sq*Are respectively d^*Axis and q^*A stator voltage of the shaft; n is_pIs the number of pole pairs of the rotor; psi_rExciting space vectors for permanent magnets; omega_rIs the rotor angular velocity; theta_LIs q^*The included angle between the axis and the d axis; theta_rThe angle of rotation of the rotor; omega_iAs stator current vector i_sThe rotational mechanical angular velocity of (a); eta₁Is the first order mode of STS; r_sIs a stator resistor; l is_q*Is q^*A stator inductance of the shaft; i.e. i_sIs the stator current; e is the modulus of elasticity of STS;

i is a cross section of STSMoment of inertia, I ═ bh³6; ρ, b, and h are the density, width, and thickness, respectively, of the STS; phi (x) is the mode equation of STS; t is_spFor load torque, T_eIs an electromagnetic torque.

Based on a reverse control principle, obtaining parameters of the PMSM and a voltage control equation as follows:

then, based on an electromagnetic torque equation under a PMSM magnetic common energy model, an optimal stator harmonic current when torque ripple is ensured to be minimized is established

The constraint of (2):

wherein:

i_s0is the fundamental current amplitude; lambda [ alpha ]₀Is d-axis average flux linkage; lambda [ alpha ]_dkAnd λ_qkThe k-th magnetic linkage harmonic component of d and q axes; i is_skOptimizing the amplitude of the front k harmonic current; k is the harmonic number; t is_ckThe amplitude of the kth harmonic of the cogging torque.

Based on the reverse control principle, the harmonic control equation is as follows:

wherein: u. of_sqk*Is q^*A stator k harmonic voltage component of the shaft; r_sIs a stator resistor; i.e. i_skAmplitude psi of k-th harmonic current of stator current_rExciting space vectors for permanent magnets; omega_rIs the rotor angular velocity; l is_q*Is q^*A stator inductance of the shaft; theta_LIs q^*The included angle between the axis and the d axis; n is_pBeing pole pairs of rotorsCounting;

finally, the controller for achieving PMSM torque ripple suppression considering electrical losses is obtained as follows:

the accurate acquisition of the speed signal is the basis for realizing the PMSM control algorithm, and for the PMSM wide-range speed identification method based on the least square algorithm, the control method comprises the following steps: based on a least square algorithm structure with forgetting factors, discretizing a stator voltage equation under stator current vector orientation to obtain:

wherein:

is an estimated value of the rotation speed, is a parameter vector to be identified, L (n) is a gain vector at n time, P (n) is a covariance matrix at n time,

is the information vector at n moments, y (n) is the output vector of the system, T_sN is the sampling period.

And on the basis of the previous estimation result, correcting the previous estimation result according to a recurrence rule for new data to obtain a new parameter estimation value.

The controller is designed to realize the comprehensive control of flexible load vibration, PMSM torque ripple and electrical loss, and the rotation speed of the PMSM is identified to obtain the stability of the speed signal enhanced controller. The test result shows that: under the action of the proposed closed-loop I/f comprehensive control method, all parameters of the motor operate, vibration of the flexible load and torque pulsation in the PMSM are effectively inhibited, and meanwhile, electrical loss is obviously reduced. The rotation speed under the conditions of low, medium and high can be accurately tracked and identified, and the full-speed tracking of the PMSM is realized.

Drawings

FIG. 1 is a d-axis equivalent circuit of a PMSM;

FIG. 2 is a q-axis equivalent circuit of a PMSM;

FIG. 3 is a schematic structural diagram of a PMSM direct drive volute spring;

FIG. 4 is a PMSM spatial vector diagram;

FIG. 5 is an overall control block diagram of a closed loop I/f controller;

FIG. 6 shows a vector angle θ under the PMSM closed-loop I/f integrated control method_LA waveform;

FIG. 7 shows the rotation speed ω under the PMSM closed-loop I/f integrated control method_rA waveform;

FIG. 8 shows the fundamental current amplitude I under the PMSM closed-loop I/f integrated control method_s0A waveform;

FIG. 9 shows torque ripple T waveforms before and after PMSM adds a closed-loop I/f integrated control method;

FIG. 10 shows the total loss P under the action of a PMSM respectively being a closed loop I/f integrated controller and a reverse-thrust controller without considering the optimal loss condition_lossThe comparison waveform of (1);

FIG. 11 shows a vector angle θ of rotation speed mutation under the PMSM closed-loop I/f integrated control method_LA waveform;

FIG. 12 shows the rotation speed ω of the rotation speed jump under the PMSM closed-loop I/f integrated control method_rA waveform;

FIG. 13 shows the fundamental current amplitude I with sudden rotation speed change under the PMSM closed-loop I/f integrated control method_s0A waveform;

FIG. 14 is a torque ripple T waveform of abrupt change of rotation speed under the PMSM closed-loop I/f integrated control method;

FIG. 15 shows the total loss P under the action of a closed-loop I/f integrated controller and a back-thrust controller without considering the optimal loss condition when the rotation speed and the torque of the PMSM are suddenly changed_lossThe comparison waveform of (1);

FIG. 16 is an identification waveform of a PMSM starting from a stationary state to a rated speed.

The symbols in the text are: e is the modulus of elasticity of STS; i is SMoment of inertia in cross section of TS, I ═ bh³6; rho, b, h and L are the lengths of the scroll springs, and are the density, width, thickness and length of the STS respectively; phi (x) is the mode equation of STS; η (t) is the modal coordinate; s_pThe cross section area of the unit length of the volute spring is shown, and f (x, t) is the distribution force acting on the volute spring; s (x, T) is the bending moment T of the volute spring_LDisplacement change in a dynamic coordinate system xoy after deformation is generated; t is kinetic energy generated when the vortex spring is screwed down by external force; v is the elastic energy generated by the elastic deformation of the volute spring; q_iIs an external force; q. q.s₁For PMSM over angle theta_r，q_i(i 2.., N +1) is the ith order vibration mode coordinate eta of the vortex spring_i；R_sIs a stator resistor; i.e. i_wdAnd i_wqIs the active component of the stator current on the dq axis; i.e. i_sdAnd i_sqIs the component of the stator current in the dq axis; i.e. i_cdAnd i_cqIs the iron loss component of the stator current on the dq axis; l is_d、L_qEquivalent inductance of the stator winding on the dq axis; u. of_sd、u_sqIs the component of the stator voltage on the dq axis; r_cEquivalent iron loss resistance; i.e. i_sd*And i_sq*Are respectively d^*Axis and q^*Stator current of the shaft; u. of_sd*And u_sq*Are respectively d^*Axis and q^*A stator voltage of the shaft; psi_sd*And psi_sq*Are respectively d^*Axis and q^*A stator flux linkage of the shaft; psi_rd*And psi_rq*Are respectively d^*Axis and q^*A rotor flux linkage of the shaft; psi_rIs a permanent magnet flux linkage; l is_d*And L_q*Are respectively d^*Axis and q^*A stator inductance of the shaft; omega_rIs the rotor angular velocity; omega_iAs stator current vector i_sThe rotational mechanical angular velocity of (a); n is_pIs the number of pole pairs of the rotor; theta is the angle of the rotor; psi_rExciting space vectors for permanent magnets; j is moment of inertia; b is a viscosity coefficient; t is_LIs a bending moment, T₀Is the effective torque; t is_cogIs the cogging torque; t is_spFor self-torque of the volute spring, T_sp＝k_sp·θ_r，k_spIs the elastic coefficient of the volute spring; i.e. i_s0Is the fundamental current amplitude; i.e. i_skIs the kth harmonic current amplitude; i is_skOptimizing the current amplitude of the k-th harmonic wave; lambda [ alpha ]_dAnd λ_qThe d-axis and q-axis magnetic linkage under a dq0 coordinate system; lambda [ alpha ]₀Is d-axis average flux linkage; phi is a_skIs the phase angle of the kth harmonic current; lambda [ alpha ]₀Is d-axis average flux linkage; lambda [ alpha ]_dkAnd λ_qkThe k-th magnetic linkage harmonic component of d and q axes; phi is a_λkIs the k harmonic flux linkage phase angle; t is_cj、φ_ckAmplitude and phase angle for the kth harmonic of cogging torque; k is the harmonic number; p_LossThe total loss is; p_cuCopper loss; p_FeIs the iron loss; e.g. of the type_ω、e_iAnd e_θTracking errors of the motor speed, the current and the rotation angle are respectively; theta^*、

And

reference values of a motor rotation angle, a motor speed, a fundamental current amplitude and a k-th harmonic current amplitude are respectively set; k is a radical of_θ、k_ω、k_iAnd k_ikTo control the gain; t is_sIs a sampling period; n is a sampling point; b ═ B₁B₂...B_n]Is a parameter vector to be identified; xi is a forgetting factor, and xi is more than 0 and less than 1;

the estimated value of the rotating speed is a parameter vector to be identified; l (n) is a gain vector at time n; p (n) is a covariance matrix at time n;

an information vector at n moments; y (n) is the output vector of the system.

Detailed Description

The invention is realized by the following technical scheme:

1. derivation of minimum loss constraints

The PMSM loss mainly comprises iron loss, copper loss and mechanical loss, wherein the mechanical loss is mainly caused by bearing friction, the loss size is not easy to be described quantitatively, and the proportion of the loss in the total loss is not high, so that only controllable iron loss and copper loss are considered herein, and the mechanical loss is ignored, and a PMSM dq shaft equivalent circuit shown in attached figures 1-2 is established.

The electromagnetic torque equation can be written as:

total loss P of PMSM system_LossComprises the following steps:

when the PMSM system is in a steady state, the electromagnetic torque T_eWith the speed of rotation omega_rAre all constants, i_wqIs also a constant; at this time, the total loss P of the PMSM system_LossOnly with i_wdIt is related. Therefore, the optimal stator current with the minimum loss is solved only by solving

Active component i of time d-axis current_wdref。

At this time, the d-axis current is represented as:

2. mathematical model of volute spring

Points o and o' respectively represent the connection point of the PMSM output shaft and the start end of the scroll spring and the circle center of the cross section of the connection point, and a schematic structural diagram of the PMSM direct drive scroll spring is drawn and shown in attached figure 3, which isIn the specification, a coordinate system xoy is a dynamic coordinate system rotating along with a rotor, a coordinate system x ' o ' y ' is a static coordinate system, and s (x, T) is a bending moment T of a volute spring after passing through the volute spring_LThe change of displacement in the dynamic coordinate system xoy after deformation is generated under action, namely the deflection of the volute spring at the position of x, theta_rFor the angle of rotation of the PMSM rotor

Assuming that the scroll spring is formed by bending a slender rod with the length of l into a spiral shape, the initial end of the scroll spring is directly connected with the output shaft of the PMSM, the tail end of the scroll spring is fixed, the length of the scroll spring is far larger than the section size of the scroll spring, only the transverse vibration of the scroll spring is considered in research, the longitudinal vibration is ignored, and the scroll spring is regarded as an Euler-Bernouli beam, so that the vibration equation of the scroll spring can be expressed as follows:

the boundary conditions of the volute spring are as follows:

from vibration theory, the displacement s (x, t) can be described as:

in order to solve the vortex spring vibration mode phi (x), f (x, t) is ignored, formula (9) is substituted into formula (7), and the formula can be obtained by using a separation variable method:

if the left side of equation (10) is only associated with time t and the right side is only associated with coordinate x, the result can only be a constant, assuming that-a²Therefore, the mode function and the mode coordinate can be solved as follows:

wherein the eigen equation of (11) is:

γ⁴-χ⁴＝0 (12)

the mode function phi (x) and the mode coordinate eta (t) can be solved by the formula (11) and the formula (12):

according to the boundary condition in (8), coefficient a₁，a₂，a₃And a₄Can be expressed as:

{a₁＝-a₃，a₂＝-a₄，cos(γl)cosh(γl)＝1} (14)

the angular velocity of the vibration of the scroll spring obtained from equation (11) is:

ignoring the modes after the N-th order, considering only the N-th order and the previous modes, there are:

during energy storage, the coordinate (X) of any point P on the vortex spring_P，Y_P) Can be written as:

the kinetic energy T generated when the vortex spring is screwed down by external force is as follows:

simplifying and collating formula (18) to obtain:

if the volute spring is tightly coiled in the horizontal plane under the action of external force, the potential energy V is the elastic energy generated by the elastic deformation of the volute spring, namely

The lagrange equation at this point is as follows:

for q₁：

For q_iOrder:

the flexible volute spring kinetic equation can be described as:

3. PMSM dynamic modeling under stator current vector orientation

In order to study the stator current vector i in PMSM_sBy introducing a new synchronous rotating coordinate system d^*q^*o is as shown in FIG. 4, wherein d^*And q is^*Respectively, a real axis and an imaginary axis, and the dq axis is the real axis and the imaginary axis of the original rotor rotation coordinate system. q. q.s^*Axial direction and stator current vector i_sThe direction of (a) is kept consistent. q. q.s^*The included angle between the axis and the d axis is theta_L，ω_rIs a permanent magnet excitation space vector.

At d^*q^*In the o coordinate system, the stator voltage equation can be expressed as:

due to q^*Axial direction and current vector i_sThe directions of (a) and (b) are kept consistent, one can obtain: i.e. i_sd*＝0，i_sq*＝i_sTherefore, the stator voltage equation expression can be simplified as:

u_sd*＝-n_pψ_rω_rcos θ_L-n_pω_iL_q*i_s(26)

additionally, the PMSM rotor equations of motion can be written as:

and, theta_L、ω_iAnd ω_rThe relationship between can be expressed as:

PMSM Torque ripple modeling

The PMSM electromagnetic torque equation based on the magnetic common energy model can be written as:

wherein:

and the following steps:

substitution of (31) into (30) due to λ_dk、λ_qkAnd I_skRelatively small, two product terms in the formula are omitted, and the method is obtained by appropriate simplification:

wherein: t is₀Is effective torque, phi_kAnd

for introducing two auxiliary angles simultaneously

If the harmonics in (32) are eliminated, it is necessary to satisfy:

i.e. for each harmonic:

then:

first, the conversion angle phi can be obtained by combining the expressions (33) and (36)_k、

And optimum phase angle of k harmonic current

Then, suppose C_k+D_kPositive, then:

c in (33)_k，D_kWhen (37) is substituted, then:

to make it possible to

And minimum, introducing a Lagrange multiplier gamma, and establishing an auxiliary function:

solving the formula (39) to obtain the optimal harmonic current under the condition of torque ripple inhibition

The expression is as follows:

5. closed loop I/f integrated controller design

e_θ，e_ω，e_iAnd e and_ikare each theta_L，ω_r，i_s0And i_skThe control error of (2) is determined,

and

are each theta_L，ω_r，i_s0And i_skTo the reference value of (c).

Designing a first virtual control quantity

To satisfy the minimum loss condition:

based on a reverse control, e_θ＝θ_L-θ_L ^*Then e_θAnd can be represented as:

the second virtual control quantity

Can be expressed as:

wherein: k is a radical of_θTo control the gain. Substituting (43) into (42):

the expression for the electromagnetic torque can again be written as follows from fig. 3 and equation (2):

because of the fact that

E is then_ωAnd can be represented as:

the third virtual control quantity

Can be expressed as:

wherein: k is a radical of_ωTo control the gain. Substituting (30) into (29):

in this case (41) can again be expressed as:

because of the fact that

E is then_iAnd can be represented as:

voltage u_sq0*The governing equation of (c) can be expressed as:

wherein: k is a radical of_iTo control the gain. Substituting (51) into (50):

d^*q^*in the o coordinate system, the k-th harmonic voltage equation can be expressed as:

u_sd*k＝-kn_pψ_rkω_rcos θ_L-kn_pω_iL_q*i_sk(53)

because of the fact that

E is then_ikAnd can be represented as:

voltage u_sqk*The governing equation of (c) can be expressed as:

wherein: k is a radical of_ikTo control the gain. Substituting (56) into (55):

in summary, the voltage control equation for a closed loop I/f controller can be expressed as:

6. PMSM speed identification based on recursive least squares

Accurate acquisition of speed signals is the basis for implementing a PMSM control algorithm, and a least square method based on a forgetting factor is a commonly used identification method in the industry:

wherein: n is the sampling point, B ═ B₁B₂... B_n]For the parameter vector to be identified, L (n) is the gain vector at n time, and P (n) is the covariance matrix at k time;

an information vector at n moments; y (n) is the output vector of the system; xi is a forgetting factor, and xi is more than 0 and less than 1.

Based on the method, a PMSM speed identification algorithm based on least square identification under an I/f framework is provided.

Discretization of equations (26) and (27) yields:

wherein:

wherein: t is_sIs the sampling period.

Substituting the formula (62) into the formula (60) can identify the iteration formula of the PMSM rotating speed

The overall control block diagram of the closed-loop I/f controller proposed by the above design is shown in FIG. 5.

7. Algorithm implementation

Based on the above description, the control algorithm is implemented and verified. The selected PMSM parameters are as follows: stator resistance R_S2.875 Ω, iron loss resistance R _c300 Ω, stator inductance L_s0.033H, 50 pole pair number P, permanent magnetic linkage psi_r0.3 Wb. The genetic factor xi in the least square algorithm is 0.98. The values of the parameters of the controller are as follows: k is a radical of_θ＝50，k_ω＝75，k_i＝240，k_i6320. The results are shown in fig. 6 to 16.

FIGS. 6-9 show the vector angle θ under the control of the method for comprehensive suppression of flexible load vibration and PMSM torque ripple under stator current vector orientation considering electrical loss at a steady state rotation speed of 60r/min_LRotational speed omega_rCurrent vector i_s0And suppressing the waveform of the front and rear torque ripple T. FIG. 10 shows the total loss P of the PMSM under the control of the inverse model and the proposed algorithm, respectively, without considering the optimal loss_lossA comparative graph of (a). Therefore, under the control of the control method provided by the patent, all parameters can be rapidly converged and reach stable values, vibration caused by flexible load and torque pulsation of PMSM are effectively inhibited, and the operation efficiency of PMSM is obviousAnd (5) lifting. In the experiments of FIGS. 11-15, the steady state speed was abruptly changed from 60r/min to 100r/min at the 10 th second and then returned to 60r/min at the 30 th second. FIGS. 11-14 show the vector angle θ under the control of the proposed control method, respectively_LRotational speed omega_rCurrent vector i_s0And the waveform of the torque ripple T. FIG. 15 shows the total loss P of the PMSM under the control of the inverse model and the proposed algorithm, respectively, without considering the optimal loss_lossA comparative graph of (a). Therefore, each parameter only has small fluctuation at a load abrupt change point and can quickly return to a steady state value, and the comprehensive suppression method for the flexible load vibration and the PMSM torque ripple under stator current vector orientation considering the electrical loss has good dynamic performance. FIG. 16 shows the identification curves of the PMSM speed identification algorithm based on the least squares method for different speeds at steady-state speeds of 20r/min and 150r/min, respectively. Therefore, the algorithm can accurately track and identify the high, medium and low rotating speeds in a considerable range, and realize the wide-range speed tracking of the PMSM. Therefore, the comprehensive suppression method for the flexible load vibration and the PMSM torque ripple under the stator current vector orientation considering the electrical loss and the wide-range speed identification have good practical significance.

Claims (2)

1. For a comprehensive suppression method of flexible load vibration and PMSM torque ripple under stator current vector orientation considering electrical loss, the control method comprises the following steps:

firstly, deriving a stator current constraint condition under a minimum loss condition based on a PMSM minimum loss mathematical model:

then, a dynamic mathematical model of the PMSM under the current vector orientation is combined with a vibration model of the permanent magnet synchronous motor, and an overall mathematical model of the permanent magnet synchronous motor driven by the permanent magnet synchronous motor considering the electrical loss of the motor is established:

wherein:

and

are respectively d^*Axis and q^*A stator voltage of the shaft; n is_pIs the number of pole pairs of the rotor; psi_rExciting space vectors for permanent magnets; omega_rIs the rotor angular velocity; theta_LIs q^*The included angle between the axis and the d axis; theta_rThe angle of rotation of the rotor; omega_iAs stator current vector i_sThe rotational mechanical angular velocity of (a); eta₁Is the first order mode of STS; r_sIs a stator resistor;

is q^*A stator inductance of the shaft; i.e. i_sIs the stator current; e is the modulus of elasticity of STS;

i is the second moment of area of STS, I ═ bh³6; ρ, b, and h are the density, width, and thickness, respectively, of the STS; phi (x) is the mode equation of STS; t is_spFor load torque, T_eIs an electromagnetic torque;

based on a reverse control principle, obtaining parameters of the PMSM and a voltage control equation as follows:

then, based on an electromagnetic torque equation under a PMSM magnetic common energy model, an optimal stator harmonic current when torque ripple is ensured to be minimized is established

The constraint of (2):

wherein:

i_s0is the fundamental current amplitude; lambda [ alpha ]₀Is d-axis average flux linkage; lambda [ alpha ]_dkAnd λ_qkThe k-th magnetic linkage harmonic component of d and q axes; i is_skOptimizing the amplitude of the front k harmonic current; k is the harmonic number; t is_ckThe amplitude of the kth harmonic of the cogging torque.

Based on the reverse control principle, the harmonic control equation is as follows:

wherein:

is q^*A stator k harmonic voltage component of the shaft; r_sIs a stator resistor; i.e. i_skAmplitude psi of k-th harmonic current of stator current_rExciting space vectors for permanent magnets; omega_rIs the rotor angular velocity;

is q^*A stator inductance of the shaft; theta_LIs q^*The included angle between the axis and the d axis; n is_pIs the number of pole pairs of the rotor;

finally, the controller for achieving PMSM torque ripple suppression considering electrical losses is obtained as follows:

2. the accurate acquisition of the speed signal is the basis for realizing the PMSM control algorithm, and for the PMSM wide-range speed identification method based on the least square algorithm, the control method comprises the following steps: based on a least square algorithm structure with forgetting factors, discretizing a stator voltage equation under stator current vector orientation to obtain:

wherein:

is an estimated value of the rotation speed, is a parameter vector to be identified, L (n) is a gain vector at n time, P (n) is a covariance matrix at n time,

is the information vector at n moments, y (n) is the output vector of the system, T_sN is the sampling period.

And on the basis of the previous estimation result, correcting the previous estimation result according to a recurrence rule for new data to obtain a new parameter estimation value.

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