Dead-zone harmonic suppression method for permanent magnet synchronous motor based on improved Gauss-Newton method

Abstract

The present invention discloses a method for suppressing dead-zone harmonics in a permanent magnet synchronous motor based on an improved Gauss-Newton method, which specifically includes the following steps: Step 1, constructing a current, speed, and torque harmonic transfer function caused by the dead-zone effect; Step 2, constructing a target function for suppressing harmonics based on the current, speed, and torque harmonic transfer function of Step 1; Step 3, using the improved Gauss-Newton method to find the minimum value of the target function obtained in Step 2 to obtain the optimal PI parameters. The present invention solves the problem of current and torque harmonics caused by the dead-zone effect when a high-speed motor is running, as well as the problem of large computational complexity and slow convergence speed when optimizing the harmonic target function. Using the optimal PI parameters to reduce the harmonics caused by the dead-zone effect can simultaneously maintain good dynamic response performance of the drive system and maintain the stability of the control system. In addition, the improved optimization algorithm can solve the optimal value of the harmonic suppression target function more quickly and easily, ultimately achieving the effect of suppressing harmonics.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed permanent magnet synchronous motor control, and in particular to a method for suppressing dead-zone harmonics of a permanent magnet synchronous motor based on an improved Gauss-Newton method. Background Art

[0002] High-speed permanent magnet synchronous motors (PMSMs) generally operate at speeds exceeding 10,000 r / min. They are widely used in military, aerospace, and other fields due to their compact size, high efficiency, high power factor, and minimal rotor losses. However, due to their low inductance, current harmonics caused by inverter nonlinearity cannot be effectively filtered out, resulting in severe heating and reduced control performance.

[0003] Currently, current harmonic suppression in high-speed permanent magnet synchronous motors typically involves adding hardware filters or optimizing controller parameters. Installing hardware filters not only increases system cost and size, but also increases the system order, further increasing the complexity of system design. Current harmonic suppression using control parameter optimization requires no additional hardware and offers advantages such as low cost and high versatility. Genetic algorithms are typically used to optimize control parameters and suppress current harmonics. High-speed permanent magnet synchronous motor systems require high switching frequencies, requiring fast algorithm execution times. However, genetic algorithms have long execution times and a strong dependence on initial values, making them ineffective in suppressing current harmonics in high-speed permanent magnet synchronous motors. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for suppressing dead-zone harmonics of a high-speed permanent magnet synchronous motor based on an improved Gauss-Newton method, which solves the problems of complex calculation process and slow parameter optimization speed in the method of suppressing current harmonics by optimizing control parameters in the control system of a high-speed permanent magnet synchronous motor.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a method for suppressing dead-zone harmonics of a permanent magnet synchronous motor based on an improved Gauss-Newton method, which specifically includes the following steps:

[0006] Step 1: Construct the harmonic transfer functions of current, speed and torque caused by the dead zone effect;

[0007] Step 2: constructing a harmonic suppression objective function based on the current, speed, and torque harmonic transfer functions of step 1;

[0008] Step 3: Use the improved Gauss-Newton method to find the minimum value of the objective function obtained in step 2 to obtain the optimal PI parameters.

[0009] Preferably, the specific process of step 1 is:

[0010] Step 1.1, establish a mathematical model of the permanent magnet synchronous motor in a rotating coordinate system;

[0011] The mathematical model formula (1) is shown as follows:

[0012]

[0013] In formula (1), u d is the voltage component on the d-axis, u q is the component of voltage on the q axis; i d is the component of the current on the d-axis, i q is the component of the current in the q axis; R is the stator resistance; ψ f is the rotor flux; ω e is the rotor speed; d / dt is the derivative, L d is the d-axis inductance, L q is the q-axis inductance;

[0014] The electromagnetic torque is shown in formula (2):

[0015] T e =1.5pi q [(L d -L q )i d +ψ f ]=1.5pψ f i q (2)

[0016] Among them, T e is the electromagnetic torque, L in the surface-mount motor d =L q ; p is the number of pole pairs; ψ f is the rotor flux;

[0017] The equation of motion is shown in formula (3):

[0018] T e -T L =Jdω m / dt+Bω m (3)

[0019] In formula (3), T L is the load torque, T e is the electromagnetic torque, J is the moment of inertia, ω m =ω e / p, B is the damping coefficient, ω is the mechanical angular velocity;

[0020] m

[0021] Step 1.2, build from u d and u q to i d and i q ,i q to Te and Te to ωm The transfer function of

[0022] From formula (1), we can get u d 、u q to i d 、i q The transfer function is shown in formula (4):

[0023]

[0024] In formula (4), L s is the stator inductance, H uidq (s) is u d 、u q to i d 、i q The transfer function of

[0025] From formula (2), we can get i q to T e The transfer function is shown in formula (5):

[0026] H Te (s) = T e / i q =1.5pψ f (5)

[0027] In formula (5), H Te (s) is i q to T e The transfer function of

[0028] From formula (3), we can get the no-load condition, that is, T L = 0 when T e to ω m The transfer function is shown in formula (6):

[0029]

[0030] In formula (6), T e to ω m The transfer function of ; s is the Laplace transform;

[0031] According to formula (5) and (6), we can get formula (7), i q to ω m The transfer function is shown in the following formula (7):

[0032]

[0033] In formula (7), H iq_ω (s) is i q to ω m The transfer function of

[0034] The transfer function of the switching delay in the d and q axes is shown in the following formula (8):

[0035]

[0036] Where τ is the total delay time including inverter switching delay and calculation delay, H τ (s) is the transfer function of the switching delay, e is the exponential, and τs is the Laplace transform of the delay time;

[0037] The transfer function of the speed loop PI control is:

[0038] H piω (s) = k pω +k iω / s (9)

[0039] Among them, H piω (s) is the transfer function of the speed loop PI control, k pω is the speed loop proportional coefficient, k iω is the integral coefficient of the speed loop; both the speed loop and the current loop have PI controllers, and PI is a proportional integral controller;

[0040] The current loop PI control transfer function is:

[0041]

[0042] Among them, H pi_id (s) is the d-axis component of the PI control transfer function of the current loop, H pi_iq (s) is the q-axis component of the PI control transfer function of the current loop, k p_id is the proportional coefficient of the current loop on the d-axis, k p_iq is the proportional coefficient of the current loop on the q axis, k i_id is the integral coefficient of the current loop on the d-axis, k p_iq is the integral coefficient of the current loop on the q-axis. Formulas (10) and (11) are simplified to formula (12):

[0043]

[0044] In formula (12), H pi_idq (s) is the PI control transfer function of the current loop;

[0045] Step 1.3: Analyze the harmonics related to the dead zone and derive the transfer function from the voltage error caused by the dead zone effect to the d-axis and q-axis currents.

[0046] The time domain expression of voltage error is shown in the following formula (13):

[0047]

[0048] In formula (13), E d (t) is the component of voltage error on the d-axis, E q (t) is the component of voltage error on the q axis, τ d is the dead time, F c is the inverter switching frequency, U DC is the DC voltage, V d is the voltage drop, k is a natural number, k=1,2...n, θ i is the initial phase of the fundamental frequency of the stator current, π is pi, ∑ is the summation sign, t is time, +∞ is positive infinity, sin is for sine, and cos is for cosine;

[0049] The feedback transfer function of voltage error to stator current is:

[0050]

[0051] Among them, H FE (s) is the feedback transfer function of voltage error to stator current, H FEiq (s) is the q-axis component of the feedback transfer function of the voltage error to the stator current, H FEid (s) is the d-axis component of the feedback transfer function of the voltage error to the stator current;

[0052] H FEiq (s)=-H pi_iq (s)[H Te (s)H Teω (s)H piω (s)], H FEid (s)=-H pi_id (s);

[0053] The d and q axis voltage errors E can be obtained by using formulas (4), (13) and (14): d (s), E q (s) to i d 、i q The closed-loop transfer function is shown in the following formula (15):

[0054]

[0055] In formula (15), H Ei (s) is the closed-loop transfer function of the d-axis and q-axis voltage errors to , and I is the unit matrix;

[0056] The complex amplitude expression of the 6kth harmonic of the dead zone effect is obtained from formula (13) as shown in the following formula (16):

[0057]

[0058] In formula (16), E d 6k is the d-axis component of the complex amplitude of the 6kth harmonic of the dead zone effect, E q 6k is the component of the complex amplitude of the 6kth harmonic of the dead zone effect on the q axis, and j is an imaginary number;

[0059] The 6kth harmonic expression of the d-axis and q-axis currents is shown in the following formula (17):

[0060]

[0061] In formula (17), i d 6k is the 6kth harmonic of the d-axis current, i q 6k is the 6kth harmonic of the q-axis current;

[0062] According to formulas (5), (7) and (18), the 6kth harmonic expressions of torque and speed can be obtained respectively as shown in formula (18):

[0063]

[0064] In formula (18), is the 6kth harmonic of the torque, It is the 6kth harmonic of the speed.

[0065] Preferably, the specific process of step 2 is:

[0066] Step 2.1, construct the objective function for suppressing harmonics;

[0067] Construct the objective function including d-axis current, q-axis current, torque, and speed 6th and 12th harmonics:

[0068] H(x)=f(x)f(x) T (19);

[0069] In formula (19), H(x) is the harmonic objective function, T is the transpose of the matrix, f(x) is the total harmonic expression, and x is the unknown quantity of the objective function. f(x) can be expressed as shown in the following formula (20):

[0070]

[0071] According to the relationship between the harmonics of current, speed and torque and the PI control parameters of the current loop and speed loop derived in step 1, when the PI parameters in the objective function are optimal, the value of the harmonics will be minimized. The unknowns of the objective function are the PI control parameters of the speed loop and the current loop:

[0072] xi =(x1,x2,x3,x4,x5,x6)

[0073] =(k pω ,k iω ,k p_id ,k i_id ,k p_iq ,k i_iq ) (twenty one);

[0074] In formula (21), k pω is the speed loop proportional coefficient, k iω is the speed loop integral coefficient, k p_id is the d-axis current loop proportional coefficient, k i_id is the d-axis current loop integral coefficient, k p_iq is the q-axis current loop proportional coefficient, k i_iq is the q-axis current loop integral coefficient;

[0075] Step 2.2: derive the relationship between PI parameters, open-loop cutoff frequency, and phase margin, and find the constraint range of PI parameters during optimization.

[0076] According to the current transfer relationship in step 1, the relationship between the d-axis and q-axis currents in the current loop and the d-axis and q-axis currents of the motor feedback can be obtained. According to formulas (4), (8), and (12), the open-loop transfer function from the d-axis given current in the current loop to the d-axis current of the feedback can be obtained as shown in the following formula (22):

[0077]

[0078] According to formulas (4), (8), and (12), the open-loop transfer function from the q-axis given current in the current loop to the feedback q-axis current can be obtained as shown in the following formula (23):

[0079]

[0080] In formulas (22) and (23), H id_OP (s) is the open-loop transfer function from the d-axis reference current to the feedback d-axis current, H iq_OP (s) is the open-loop transfer function from the q-axis reference current to the feedback q-axis current;

[0081] The current loop response is generally faster than the speed loop, so when analyzing the open-loop cutoff frequency and phase margin of the speed loop, the current loop transfer function is expressed as shown in the following formula (24):

[0082]

[0083] In formula (24), H iq_K (s) is the current loop transfer function, F qis the q-axis current open-loop cut-off frequency;

[0084] Given speed To feedback speed ω m The open-loop transfer function is shown in the following formula (25):

[0085] H ω_OP (s)=H pi_ω (s)H iq_K (s)H iq_ω (s) (25)

[0086] In formula (25), H ω_OP (s) is the open-loop transfer function from the given speed to the feedback speed;

[0087] According to formula (23), formula (24) and formula (25), the open-loop cutoff frequency and phase margin of the speed loop and current loop are shown in the following formulas (26), (27) and (28):

[0088]

[0089]

[0090]

[0091] Formula (26) defines the open-loop cutoff frequency and phase margin of the d-axis current loop, Formula (27) defines the open-loop cutoff frequency and phase margin of the q-axis current loop, and Formula (28) defines the open-loop cutoff frequency and phase margin of the speed loop. d is the open-loop cutoff frequency of the d-axis current loop, F q is the open-loop cutoff frequency of the q-axis current loop, F ω is the open-loop cutoff frequency of the speed loop, is the phase margin of the d-axis current loop, is the phase margin of the q-axis current loop, is the phase margin of the speed loop, where || is the absolute value and ∠ is the angle;

[0092] According to the requirements of the field working conditions for the dynamic performance and anti-interference performance of the permanent magnet synchronous motor, the constraint range of the open-loop cutoff frequency and phase margin is set as shown in formula (30):

[0093]

[0094] In formula (30), y i are the six open-loop cutoff frequencies and phase margin parameters, F d_min The minimum cut-off frequency of the d-axis current loop is set. q_min is the minimum value of the q-axis current loop open-loop cutoff frequency, Fω_min It is the minimum value of the speed loop open loop cut-off frequency. is the minimum value of the d-axis current loop phase margin. is the minimum value of the q-axis current loop phase margin, is the minimum value of the speed loop phase margin, F d_max is the maximum value of the d-axis current loop open-loop cutoff frequency, F q_max is the maximum value of the q-axis current loop open-loop cutoff frequency, F ω_max It is the maximum value of the speed loop open loop cut-off frequency. is the maximum value of the d-axis current loop phase margin. is the maximum value of the q-axis current loop phase margin. It is the maximum value of the speed loop phase margin.

[0095] Substituting the maximum and minimum values of the loop cutoff frequency and phase margin set by formula (30) into formulas (26), (27), and (28) yields the constraint ranges of the speed loop PI parameters and the current loop PI parameters as shown in the following formula (31):

[0096]

[0097] In formula (31), x i There are six unknowns in the cost function, k pω_min is the minimum value of the proportional parameter range of the speed loop, k iω_min is the minimum value of the integral parameter range of the speed loop, k p_id_min is the minimum value of the proportional parameter range of the d-axis current loop, k i_id_min is the minimum value of the integral parameter range of the d-axis current loop, k p_iq_min is the minimum value of the proportional parameter range of the q-axis current loop, k i_iq_min is the minimum value of the integral parameter range of the q-axis current loop, k pω_max is the maximum value of the proportional parameter range of the speed loop, k iω_max is the maximum value of the integral parameter range of the speed loop, k p_id_max is the maximum value of the proportional parameter range of the d-axis current loop, k i_id_max is the maximum value of the integral parameter range of the d-axis current loop, k p_iq_max is the maximum value of the proportional parameter range of the q-axis current loop, k i_iq_max It is the maximum value of the integral parameter range of the q-axis current loop.

[0098] Preferably, the specific process of step 3 is:

[0099] The iterative formula of the Gauss-Newton method is shown in the following formula (32):

[0100] x n+1 =x n -2J(x n ) T J(x n ) -1 J(x n )-μ(x n -x n-1 ) (32)

[0101] In formula (32), n is the number of iterations, -1 is the inverse matrix, T is the transposed matrix, μ is the momentum parameter, J(x n ) is the first-order Jacobian matrix; x n is the unknown number of the nth iteration, x n+1 is the unknown number of the n+1th iteration;

[0102] The first-order Jacobian matrix is:

[0103]

[0104] In formula (33), It is to find the partial derivative of the i-th unknown number of the cost function;

[0105] The adaptive adjustment formula of momentum parameter μ is shown in the following formula (34):

[0106] μ=0.5+e r / 6 (34)

[0107] In formula (34), e r The iterative reference error is calculated as shown in the following formula (35):

[0108]

[0109] In formula (35), is the value of the i-th unknown at the n-th iteration, is the value of the i-th unknown number at the n-1th iteration, x i_max is the maximum value of the i-th unknown number, x i_min is the minimum value of the i-th unknown number;

[0110] The iterative process of harmonic suppression using the improved Gauss-Newton method is as follows:

[0111] Given the initial value x of the iteration i (0) =0, set the maximum number of iterations n max ≥1, convergence accuracy ε=1×10 -5 ;

[0112] According to formula (33), J(x n )T and J(x n ) -1 ;

[0113] Where J(x n ) T is the transpose of Jacobian, J(x n ) -1 It is the inverse matrix of the Jacobian matrix;

[0114] Calculate the reference error e according to formulas (34) and (35): r and momentum parameter μ;

[0115] Calculate the PI parameters of this iteration according to formula (32);

[0116] according to Determine whether it converges. If it satisfies Judge x i (n) Is it out of the limit? If x i (n) If x exceeds the upper limit, the maximum value of the range is taken. i (n) If the value exceeds the lower limit, the minimum value of the range is taken, the optimization is terminated and the PI value x of this shot is output. i (k) = x i (n) , k is the sampling time; if it does not meet Then determine whether the number of iterations n is greater than the maximum number of iterations n max , if n≥n max Then end this optimization and output the PI value of the previous shot; otherwise, set n=n+1 and return to step 2).

[0117] Beneficial effects of the present invention: The present invention provides a high-speed permanent magnet synchronous motor rotor position and speed estimation method based on the improved Gauss-Newton method. The method uses the optimal PI parameters to reduce the harmonics caused by the dead zone effect while maintaining good dynamic response performance of the drive system. The method does not require modification of the motor control algorithm and the motor structure, has strong versatility and economy, and can maintain the stability of the control system. In addition, the improved optimization algorithm can solve the optimal value of the harmonic suppression objective function more quickly and easily, reduce the amount of calculation, and ultimately achieve the effect of suppressing harmonics. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 This is a vector control block diagram used in the method for suppressing dead-zone harmonics in a permanent magnet synchronous motor based on the improved Gauss-Newton method of the present invention;

[0119] Figure 2It is a harmonic suppression iterative process of the improved Gauss-Newton method adopted in the permanent magnet synchronous motor dead zone harmonic suppression method based on the improved Gauss-Newton method of the present invention. DETAILED DESCRIPTION

[0120] The technical solutions of the present invention will be described clearly and completely below with reference to the accompanying drawings.

[0121] like Figure 1-2 As shown, Figure 1 This is a block diagram of harmonic suppression of a high-speed permanent magnet synchronous motor in the present invention, specifically:

[0122] 1. By deriving the transfer function of the dead zone effect to the d- and q-axis current harmonics, the current and torque harmonic target functions related to the dead zone effect are established. The improved Newton method is used to optimize the target function and obtain the optimal PI parameters.

[0123] 2. The input of the optimization module is the 6kth harmonic of current, speed and torque, and the output is the speed converted to PI parameter k pω 、k iω , d, q axis current loop controller PI parameter k p_id 、k i_id 、k p_iq 、k i_iq ;Set value speed and the actual speed ω e The difference is used as the input of the speed loop PI, and the PI parameter is k pω 、k iω , the output of the speed loop PI is the given q-axis stator current

[0124] 3. Detect the three-phase stationary coordinate system stator current i through the current Hall sensor a 、i b 、i c ; Detected three-phase stator current i a 、i b 、i c The current value i in the two-phase stationary coordinate system is obtained by abc / αβ transformation α 、i β ;i α 、i β The current value i in the two-phase synchronous rotating coordinate system is obtained by αβ / dq transformation d 、i q ; Given q-axis stator current With the current value i q The difference is used as the input of the q-axis current loop PI, and the output of the q-axis current loop PI is the q-axis voltage command u q ; Given d-axis stator current With the current value i dThe difference is used as the input of the d-axis current loop PI, and the output of the d-axis current loop PI is the d-axis voltage command u d ; d-axis voltage command u d and q-axis voltage command u q The voltage command u in the two-phase stationary coordinate system is obtained by dq / αβ transformation α 、u β ;u α 、u β As the input of space vector modulation, the three-phase inverter is controlled by space vector modulation to drive the high-speed permanent magnet synchronous motor.

[0125] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for suppressing dead-zone harmonics in a permanent magnet synchronous motor based on an improved Gauss-Newton method, characterized by: The specific steps include: Step 1: Construct the harmonic transfer functions of current, speed and torque caused by the dead zone effect; Step 2: constructing a harmonic suppression objective function based on the current, speed, and torque harmonic transfer functions of step 1; Step 3: Use the improved Gauss-Newton method to find the minimum value of the objective function obtained in step 2 to obtain the optimal PI parameters; The specific process of step 3 is: The iterative formula of the Gauss-Newton method is shown in the following formula (32): x n+1 =x n -2J(x n ) T J(x n ) -1 J(x n )-μ(x n -x n-1 ) (32) In formula (32), n is the number of iterations, -1 is the inverse matrix, T is the transposed matrix, μ is the momentum parameter, J(x n ) is the first-order Jacobian matrix; x n is the unknown number of the nth iteration, x n+1 is the unknown number of the n+1th iteration; The first-order Jacobian matrix is: In formula (33), It is to find the partial derivative of the i-th unknown number of the cost function; The adaptive adjustment formula of momentum parameter μ is shown in the following formula (34): μ=0.5+e r / 6 (34) In formula (34), e r The iterative reference error is calculated as shown in the following formula (35): In formula (35), is the value of the i-th unknown at the n-th iteration, is the value of the i-th unknown number at the n-1th iteration, x i_max is the maximum value of the i-th unknown number, x i_min is the minimum value of the i-th unknown number; The iterative process of harmonic suppression using the improved Gauss-Newton method is as follows: Given the initial value x of the iteration i (0) =0, set the maximum number of iterations n max ≥1, convergence accuracy ε=1×10 -5 ; According to formula (33), J(x n ) T and J(x n ) -1 ; Where J(x n ) T is the transpose of Jacobian, J(x n ) -1 It is the inverse matrix of the Jacobian matrix; Calculate the reference error e according to formulas (34) and (35): r and momentum parameter μ; Calculate the PI parameters of this iteration according to formula (32); according to Determine whether it converges. If it satisfies Judge x i (n) Is it out of the limit? If x i (n) If x exceeds the upper limit, the maximum value of the range is taken. i (n) If the value exceeds the lower limit, the minimum value of the range is taken, the optimization is terminated and the PI value x of this shot is output. i (k) = x i (n) , k is the sampling time; if it does not meet Then determine whether the number of iterations n is greater than the maximum number of iterations n max , if n≥n max Then end this optimization and output the PI value of the previous shot; otherwise, set n=n+1 and return to step 2.

2. The method for suppressing dead zone harmonics of a permanent magnet synchronous motor based on the improved Gauss-Newton method according to claim 1, characterized in that: The specific process of step 1 is: Step 1.1, establish a mathematical model of the permanent magnet synchronous motor in a rotating coordinate system; The mathematical model formula (1) is shown as follows: In formula (1), u d is the voltage component on the d-axis, u q is the component of voltage on the q axis; i d is the component of the current on the d-axis, i q is the component of the current in the q axis; R is the stator resistance; ψ f is the rotor flux; ω e is the rotor speed; d / dt is the derivative, L d is the d-axis inductance, L q is the q-axis inductance; The electromagnetic torque is shown in formula (2): T e =1.5pi q [(L d -L q )i d +ψ f ]=1.5pψ f i q (2) Among them, T e is the electromagnetic torque, L in the surface-mount motor d =L q ; p is the number of pole pairs; ψ f is the rotor flux; The equation of motion is shown in formula (3): T e -T L =Jdω m / dt+Bω m (3) In formula (3), T L is the load torque, T e is the electromagnetic torque, J is the moment of inertia, ω m =ω e / p, B is the damping coefficient, ω m is the mechanical angular velocity; Step 1.2, build from u d and u q to i d and i q ,i q to Te and Te to ω m The transfer function of From formula (1), we can get u d 、u q to i d 、i q The transfer function is shown in formula (4): In formula (4), L s is the stator inductance, H uidq (s) is u d 、u q to i d 、i q The transfer function of From formula (2), we can get i q to T e The transfer function is shown in formula (5): H Te (s)=T e / i q =1.5pψ f (5) In formula (5), H Te (s) is i q to T e The transfer function of From formula (3), we can get the no-load condition, that is, T L = 0 when T e to ω m The transfer function is shown in formula (6): H Teω (s)=ω m / T e =1 / (Js+B) (6) In formula (6), H Teω (s) is T e to ω m The transfer function of ; s is the Laplace transform; According to formula (5) and (6), we can get formula (7), i q to ω m The transfer function is shown in the following formula (7): In formula (7), H iq_ω (s) is i q to ω m The transfer function of The transfer function of the switching delay in the d and q axes is shown in the following formula (8): Where τ is the total delay time including inverter switching delay and calculation delay, H τ (s) is the transfer function of the switching delay, e is the exponential, and τs is the Laplace transform of the delay time; The transfer function of the speed loop PI control is: H piω (s)=k pω +k iω / s (9) Among them, H piω (s) is the transfer function of the speed loop PI control, k pω is the speed loop proportional coefficient, k iω is the speed loop integral coefficient; The current loop PI control transfer function is: H pi_id (s)=k p_id +k i_id / s (10) H pi_iq (s)=k p_iq +k i_iq / s (11) Among them, H pi_id (s) is the d-axis component of the PI control transfer function of the current loop, H pi_iq (s) is the q-axis component of the PI control transfer function of the current loop, k p_id is the proportional coefficient of the current loop on the d-axis, k p_iq is the proportional coefficient of the current loop on the q axis, k i_id is the integral coefficient of the current loop on the d-axis, k p_iq is the integral coefficient of the current loop on the q-axis. Formulas (10) and (11) are simplified to formula (12): In formula (12), H pi_idq (s) is the PI control transfer function of the current loop; Step 1.3: Analyze the harmonics related to the dead zone and derive the transfer function from the voltage error caused by the dead zone effect to the d-axis and q-axis currents. The time domain expression of voltage error is shown in the following formula (13): In formula (13), E d (t) is the component of voltage error on the d-axis, E q (t) is the component of voltage error on the q axis, τ d is the dead time, F c is the inverter switching frequency, U DC is the DC voltage, V d is the voltage drop, k is a natural number, k=1,2...n, θ i is the initial phase of the fundamental frequency of the stator current, π is pi, ∑ is the summation sign, t is time, +∞ is positive infinity, sin is for sine, and cos is for cosine; The feedback transfer function of voltage error to stator current is: Among them, H FE (s) is the feedback transfer function of voltage error to stator current, H FEiq (s) is the q-axis component of the feedback transfer function of the voltage error to the stator current, H FEid (s) is the d-axis component of the feedback transfer function of the voltage error to the stator current; H FEiq (s)=-H pi_iq (s)[H Te (s)H Teω (s)H piω (s)],H FEid (s)=-H pi_id (s); The d and q axis voltage errors E can be obtained by using formulas (4), (13) and (14): d (s), E q (s) to i d 、i q The closed-loop transfer function is shown in the following formula (15): In formula (15), H Ei (s) is the closed-loop transfer function of the d-axis and q-axis voltage errors to , and I is the unit matrix; The complex amplitude expression of the 6kth harmonic of the dead zone effect is obtained from formula (13) as shown in the following formula (16): In formula (16), E d 6k is the d-axis component of the complex amplitude of the 6kth harmonic of the dead zone effect, E q 6k is the component of the complex amplitude of the 6kth harmonic of the dead zone effect on the q axis, and j is an imaginary number; The 6kth harmonic expression of the d-axis and q-axis currents is shown in the following formula (17): [i d 6k and q 6k ]=[E d 6k E q 6k ]×H Ei (s),k=1,2,3... (17) In formula (17), i d 6k is the 6kth harmonic of the d-axis current, i q 6k is the 6kth harmonic of the q-axis current; According to formulas (5), (7) and (18), the 6kth harmonic expressions of torque and speed can be obtained respectively as shown in formula (18): In formula (18), T e 6k is the 6kth harmonic of the torque, It is the 6k harmonic of the speed.

3. The method for suppressing dead zone harmonics of a permanent magnet synchronous motor based on the improved Gauss-Newton method according to claim 1, characterized in that: The specific process of step 2 is: Step 2.1, construct the objective function for suppressing harmonics; Construct the objective function including d-axis current, q-axis current, torque, and speed 6th and 12th harmonics: H(x)=f(x)f(x) T (19); In formula (19), H(x) is the harmonic objective function, T is the transpose of the matrix, f(x) is the total harmonic expression, x is the unknown quantity of the objective function, and f(x) is expressed as shown in the following formula (20): According to the relationship between the harmonics of current, speed and torque and the PI control parameters of the current loop and speed loop derived in step 1, when the PI parameters in the objective function are optimal, the value of the harmonics will be minimized. The unknowns of the objective function are the PI control parameters of the speed loop and the current loop: In formula (21), k pω is the speed loop proportional coefficient, k iω is the speed loop integral coefficient, k p_id is the d-axis current loop proportional coefficient, k i_id is the d-axis current loop integral coefficient, k p_iq is the q-axis current loop proportional coefficient, k i_iq is the q-axis current loop integral coefficient, x i is the i-th unknown number, i = 1, 2, 3, 4, 5, 6; Step 2.2: derive the relationship between PI parameters, open-loop cutoff frequency, and phase margin, and find the constraint range of PI parameters during optimization. According to the current transfer relationship in step 1, the relationship between the d-axis and q-axis currents in the current loop and the d-axis and q-axis currents of the motor feedback can be obtained. According to formulas (4), (8), and (12), the open-loop transfer function from the d-axis given current in the current loop to the d-axis current of the feedback can be obtained as shown in the following formula (22): According to formulas (4), (8), and (12), the open-loop transfer function from the q-axis given current in the current loop to the feedback q-axis current can be obtained as shown in the following formula (23): In formulas (22) and (23), H id_OP (s) is the open-loop transfer function from the d-axis reference current to the feedback d-axis current, H iq_OP (s) is the open-loop transfer function from the q-axis reference current to the feedback q-axis current; The current loop response is generally faster than the speed loop, so when analyzing the open-loop cutoff frequency and phase margin of the speed loop, the current loop transfer function is expressed as shown in the following formula (24): In formula (24), H iq_K (s) is the current loop transfer function, F q is the q-axis current open-loop cut-off frequency; Given speed To feedback speed ω m The open-loop transfer function is shown in the following formula (25): H ω_OP (s)=H pi_ω (s)H iq_K (s)H iq_ω (s) (25) In formula (25), H ω_OP (s) is the open-loop transfer function from the given speed to the feedback speed; According to formula (23), formula (24) and formula (25), the open-loop cutoff frequency and phase margin of the speed loop and current loop are shown in the following formulas (26), (27) and (28): Formula (26) defines the open-loop cutoff frequency and phase margin of the d-axis current loop, Formula (27) defines the open-loop cutoff frequency and phase margin of the q-axis current loop, and Formula (28) defines the open-loop cutoff frequency and phase margin of the speed loop. d is the open-loop cutoff frequency of the d-axis current loop, F q is the open-loop cutoff frequency of the q-axis current loop, F ω is the open-loop cutoff frequency of the speed loop, is the phase margin of the d-axis current loop, is the phase margin of the q-axis current loop, is the phase margin of the speed loop, where || is the absolute value and ∠ is the angle; According to the requirements of the field working conditions for the dynamic performance and anti-interference performance of the permanent magnet synchronous motor, the constraint range of the open-loop cutoff frequency and phase margin is set as shown in formula (30): In formula (30), y i are the six open-loop cutoff frequencies and phase margin parameters, F d_min The minimum cut-off frequency of the d-axis current loop is set. q_min is the minimum value of the q-axis current loop open-loop cutoff frequency, F ω_min It is the minimum value of the speed loop open loop cut-off frequency. is the minimum value of the d-axis current loop phase margin. is the minimum value of the q-axis current loop phase margin, is the minimum value of the speed loop phase margin, F d_max is the maximum value of the d-axis current loop open-loop cutoff frequency, F q_max is the maximum value of the q-axis current loop open-loop cutoff frequency, F ω_max It is the maximum value of the speed loop open loop cut-off frequency. is the maximum value of the d-axis current loop phase margin. is the maximum value of the q-axis current loop phase margin. It is the maximum value of the speed loop phase margin. Substituting the maximum and minimum values of the loop cutoff frequency and phase margin set by formula (30) into formulas (26), (27), and (28) yields the constraint ranges of the speed loop PI parameters and the current loop PI parameters as shown in the following formula (31): In formula (31), x i There are six unknowns in the cost function, k pω_min is the minimum value of the proportional parameter range of the speed loop, k iω_min is the minimum value of the integral parameter range of the speed loop, k p_id_min is the minimum value of the proportional parameter range of the d-axis current loop, k i_id_min is the minimum value of the integral parameter range of the d-axis current loop, k p_iq_min is the minimum value of the proportional parameter range of the q-axis current loop, k i_iq_min is the minimum value of the integral parameter range of the q-axis current loop, k pω_max is the maximum value of the proportional parameter range of the speed loop, k iω_max is the maximum value of the integral parameter range of the speed loop, k p_id_max is the maximum value of the proportional parameter range of the d-axis current loop, k i_id_max is the maximum value of the integral parameter range of the d-axis current loop, k p_iq_max is the maximum value of the proportional parameter range of the q-axis current loop, k i_iq_max It is the maximum value of the integral parameter range of the q-axis current loop.

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