A harmonic compensation control method for suppressing torque ripple of a synRM

Abstract

This invention discloses a harmonic compensation control method for suppressing torque ripple in SynRM motors, specifically implemented according to the following steps: Step 1, establishing the relationship between torque harmonics and speed harmonics of the synchronous reluctance motor, and designing a speed harmonic extraction module; Step 2, designing an outer-loop torque ripple minimization controller for the synchronous reluctance motor; Step 3, extracting the current harmonics of the synchronous reluctance motor; Step 4, designing an improved inner-loop resonant current controller for the synchronous reluctance motor to obtain the output compensation voltage, thereby suppressing torque ripple. This invention solves the problem of excessive torque harmonics caused by uneven reluctance variation in SynRM motors.

Description

Technical Field

[0001] This invention belongs to the field of synchronous reluctance motor control technology, specifically relating to a harmonic compensation control method for suppressing SynRM torque pulsation. Background Technology

[0002] Synchronous reluctance motors (SynRMs) have no permanent magnets or excitation windings on their rotors, thus they do not rely on rare-earth materials and have advantages such as high efficiency, high reliability, and low cost. However, compared with permanent magnet synchronous motors (PMSMs), SynRM rotors have highly salient poles, and the electronic current contains abundant harmonics. In addition to the DC component, the electromagnetic torque generated by SynRMs also contains a large harmonic component.

[0003] Currently, torque harmonics are typically suppressed using feedforward control. Feedforward methods require a comprehensive torque model and accurate machine parameters to provide precise torque ripple predictions for optimal harmonic current design. These methods can be implemented using analytical methods, finite element analysis, and winding function methods. However, machine parameters can change significantly during operation. Therefore, the performance of feedforward control methods depends on the accuracy of torque ripple prediction for harmonic current design, which in turn depends on the accuracy of motor or inverter modeling. Summary of the Invention

[0004] The purpose of this invention is to provide a harmonic compensation control method for suppressing torque ripple in SynRM, which solves the problem of excessive torque ripple caused by the salient pole structure of the rotor in SynRM.

[0005] The technical solution adopted in this invention is:

[0006] A resonant compensation control method for suppressing SynRM torque ripple includes the following steps:

[0007] Step 1: Establish the relationship between torque harmonics and speed harmonics of the synchronous reluctance motor, and design a module for extracting speed harmonics;

[0008] Step 2: Design a controller to minimize the outer loop torque ripple of the synchronous reluctance motor;

[0009] Step 3: Extract the current harmonics of the synchronous reluctance motor;

[0010] Step 4: Design an improved inner-loop resonant current controller for the synchronous reluctance motor, obtain the output compensation voltage, and superimpose the compensation voltage onto... d , q On the shaft voltage output, the total output voltage generates torque pulsation that is opposite to that in the motor system, thus suppressing torque pulsation.

[0011] Furthermore, the specific implementation of step 1 is as follows:

[0012] SynRM in dq The velocity equations under the rotating coordinate axes are shown in equation (1):

[0013] (1)

[0014] in, For mechanical angular velocity, Let the moment of inertia of SynRM be... It is electromagnetic torque. For load torque, The coefficient of friction;

[0015] To minimize torque harmonics, the electromagnetic torque of the synchronous reluctance motor is expressed in the form of a Fourier series as shown in equation (2):

[0016] (2)

[0017] in, This is the total torque output by the SynRM, including the DC component. Harmonic components , and They are The amplitude and phase, The electrical angle representing the rotor, Represents the harmonic order;

[0018] The velocity is expressed in the form of a Fourier series as shown in formula (3):

[0019] (3)

[0020] in, The average speed of the motor. For the speed harmonics of the motor, and They are respectively The amplitude and phase angle;

[0021] Substituting formulas (2) and (3) into formula (1) yields:

[0022] (4)

[0023] The magnitude of torque harmonics decreases as the harmonic order decreases. Considering only the major harmonic orders, and taking the 6th speed pulsation as an example, the controller obtains the 6th harmonic current, and the results are as follows:

[0024] (5)

[0025] in, Represents load torque The first in k Secondary torque harmonic components, assuming There is no interference from pulsating components. Negligible; due to much smaller ,therefore If it can be ignored, then formula (5) can be simplified to:

[0026] (6)

[0027] Under the influence of electromagnetic torque pulsation, the SynRM generates speed pulsation of the same order, and the torque of the first order... k Sub-pulse amplitude With the rotational speed of the first k Sub-pulse amplitude They are directly proportional, with a phase difference of The relationship between the amplitude and magnitude of torque pulsation is shown in the following formula (7):

[0028] (7)

[0029] To extract the amplitude and phase of the 6th rotational harmonic, the following steps were taken: Multiply by a sine wave of 6 times the frequency. and cosine quantity And expand to obtain:

[0030] (8)

[0031] In addition to the 6th and 12th harmonic components, formula (8) also contains a DC component. and By filtering it, the corresponding speed pulsation information can be obtained:

[0032] (9)

[0033] The amplitude and phase angle of the rotational speed pulsation are obtained as shown in formulas (10) and (11) below:

[0034] (10)

[0035] (11)

[0036] The low-pass filter used is a second-order LPF, and its transfer function is shown in the following formula (12):

[0037] (12)

[0038] Where s is the Laplace operator, For the natural frequency, The damping ratio is typically taken as 0.707. This is the transfer function of the LPF.

[0039] Furthermore, the specific implementation of step 2 is as follows:

[0040] d , q The shaft current is expressed in the form of the following formula (13):

[0041] (13)

[0042] in, and They are and DC component; and They are respectively The amplitude and phase angle; and They are respectively The amplitude and phase angle;

[0043] when d , q Axis No. k Subharmonic current and When formula (14) is satisfied, the first k Secondary torque harmonics Minimize:

[0044] (14)

[0045] in, , , yes d The average magnetic flux of the axis, , They are respectively d shaft and q Shaft stator inductance;

[0046] Substituting formula (14) into formula (13) yields the harmonic current. and As shown in formula (15):

[0047] (15)

[0048] From the first in formula (15) k The first harmonic current caused by the first harmonic current k Secondary torque harmonics As shown in formula (16):

[0049] (16)

[0050] in, , , It is the extreme logarithm;

[0051] Total k Secondary torque harmonics It is the sum of formulas (2) and (16), that is:

[0052] (17)

[0053] In order to To minimize the torque harmonics caused by the added harmonic current. It should be in harmony with the inherent torque harmonics of the motor. They cancel each other out, therefore formula (18) must be satisfied:

[0054] (18)

[0055] The required optimal harmonic current can be directly calculated from the motor parameters using the above formula. However, when the motor is saturated, the parameters are not constant, so there will be errors in the calculation of the optimal harmonic current. Moreover, torque measurement is not available in industrial drives. Therefore, speed harmonics are used as feedback signals.

[0056] Substituting formula (7) into formula (18) yields the first... k Second best q The shaft current is shown in formula (19):

[0057] (19)

[0058] As can be seen from formula (19), the harmonic current for minimizing torque harmonics can be directly calculated from the speed harmonics. Therefore, the input of the controller for minimizing torque harmonics is... amplitude and phase angle The output is q Shaft Optimal Reference Current amplitude and phase angle , d Shaft Optimal Reference Current amplitude and phase angle ,because Size and Proportional to speed, therefore, a PI controller can be selected for control. For amplitude control, the goal is to minimize speed harmonics to zero; therefore, the reference value for speed harmonics is... Set to zero, that is:

[0059] (20)

[0060] PI controller output As shown in formula (21):

[0061] (twenty one)

[0062] in, and These are the proportional and integral gains of the PI controller;

[0063] For phase angle control The result can be obtained using formula (19) as shown in formula (22):

[0064] (twenty two)

[0065] The amplitude and phase angle can be obtained from formula (14) as shown in formula (23):

[0066] (twenty three) .

[0067] Furthermore, step 3 is specifically performed as follows:

[0068] Step 3.1, extract the synchronous reluctance motor d Shaft current harmonics;

[0069] Extraction 6 times d , q The amplitude and phase of the shaft current harmonics, for Multiply by a sine wave of 6 times the frequency. and cosine quantity And expanded, it yields the result shown in formula (24):

[0070] (twenty four)

[0071] The LPF obtained by applying formula (24) to formula (12) is:

[0072] (25)

[0073] Thus obtain d The amplitude and phase angle of the shaft current harmonics are shown in formulas (26) and (27):

[0074] (26)

[0075] (27)

[0076] Step 3.2, extract the synchronous reluctance motor data. q Shaft current harmonics;

[0077] right Multiply by a sine wave of 6 times the frequency. and cosine quantity And expanded, it yields the result shown in formula (28):

[0078] (28)

[0079] The LPF obtained by applying formula (28) to formula (12) is:

[0080] (29)

[0081] Thus obtain q The amplitude and phase angle of the shaft current harmonics are shown in formulas (30) and (31):

[0082] (30)

[0083] (31).

[0084] Furthermore, step 4 is specifically implemented as follows:

[0085] Based on step 2, combining the amplitude and phase of the optimal harmonic current output in step 2 yields the optimal output harmonic current. and The expression for is shown in the following formula (32):

[0086] (32)

[0087] Combining the amplitude and phase of the actual harmonic current obtained in step 3 yields the actual harmonic current. and As shown in the following formula (33):

[0088] (33)

[0089] The task of the current controller is to control the actual current. and To follow the optimal harmonic current from step 2, an improved resonant controller is used to follow the optimal harmonic current of the output. and Then, the output voltage is added to the voltage output by the PI controller in the main circuit to obtain the required voltage. d , q Shaft reference voltage;

[0090] A quasi-resonant controller is used, and the transfer function of the quasi-resonant controller is... As shown in the following formula (34):

[0091] (34)

[0092] in, The cutoff frequency of the quasi-resonant controller. To suppress the 6th current harmonic at the resonant frequency, the resonant disturbance estimator should be used. for , For integral gain;

[0093] As the resonant frequency and sampling period increase, frequency and phase shifts will occur in digital implementation. The phase and amplitude compensation methods are adopted by aligning the resonant controller. First, the phase lag of the system is compensated, and its transfer function is obtained as shown in the following formula (35):

[0094] (35)

[0095] in, This is the expected phase lead angle;

[0096] The specific steps for determining this are as follows:

[0097] by d Taking the axis as an example, let's assume the mathematical model of SynRM in a rotating coordinate system. As shown in formula (36):

[0098] (36)

[0099] Considering the zero-order hold function of the voltage source inverter and the delay caused by algorithm execution, the mathematical model of SynRM is obtained. As shown in formula (37):

[0100] (37)

[0101] in, The sampling period is As a delay element of the algorithm, after phase compensation using formula (35), the mathematical model of SynRM is obtained as shown in formula (38) below:

[0102] (38)

[0103] Therefore, we obtain The phase frequency characteristic is shown in the following formula (39):

[0104] (39)

[0105] The magnitude of this value depends on the resistance and inductance of the motor, and increases with the increase of motor speed. Therefore, it is proposed that... The simple linear equation is shown in the following formula (40):

[0106] (40)

[0107] in, The rotational speed of SynRM, Let be the slope of the linear equation. The intercept of the linear equation and the slope of the phase frequency curve are given. As shown in the following formula (41):

[0108] (41)

[0109] Pick Therefore, the slope of the linear equation is shown in formula (42):

[0110] (42)

[0111] intercept b We can take an intermediate value, let's say... ,therefore, The simple linear equation is shown in the following formula (43):

[0112] (43)

[0113] Secondly, an improved bilinear transform is used to ensure that the amplitude-frequency characteristics are the same at the resonant frequency. The transform is shown in the following formula (44):

[0114] (44)

[0115] Discretize equation (35) and use the improved bilinear transform of equation (44) to obtain equation (45):

[0116] (45)

[0117] in, , , , , ,

[0118] Rearranging formula (45) yields the following formula (46):

[0119] (46)

[0120] The transformation relationship is shown in the following formula (47):

[0121] (47)

[0122] The difference equation for the output obtained from formulas (46) and (47) is shown in formula (48) below:

[0123] (48)

[0124] The input to the difference equation in the system is and As shown in the following formula (49):

[0125] (49)

[0126] Therefore, formula (48) can be rewritten as:

[0127] (50)

[0128] in, , for d shaft and q The output compensation voltage of the shaft resonant current controller;

[0129] The output compensation voltage of the resonant current controller , Superimposed on each d , q Shaft voltage output , This achieves the suppression of SynRM torque ripple.

[0130] The beneficial effects of this invention are:

[0131] This invention is a resonant compensation control method for suppressing torque ripple in SynRM circuits. To suppress torque ripple in SynRM circuits, it proposes adding appropriate current harmonics to the sinusoidal current to cancel out torque harmonics. The optimal current can be obtained through velocity harmonics. Since the magnitude of the velocity harmonics is proportional to the magnitude of the torque harmonics, information about the torque harmonics can be indirectly obtained through the velocity harmonics. Furthermore, since the magnitude of the optimal current harmonic is proportional to the velocity harmonic, the magnitude of the optimal current harmonic can be output by a PI controller. The phase of the optimal current harmonic can be calculated from the phase of the velocity harmonic. Additionally, it is necessary to control the actual current harmonic to follow the given current harmonic, which can be achieved through an improved resonant controller. The output of the resonant controller is superimposed on the d-axis and q-axis voltage outputs, thereby suppressing torque ripple. Attached Figure Description

[0132] Figure 1 This is a vector control block diagram used in a harmonic compensation control method for suppressing SynRM torque ripple in this invention.

[0133] Figure 2 This is a block diagram of the speed harmonic extraction structure used in the harmonic compensation control method for suppressing SynRM torque pulsation in this invention.

[0134] Figure 3 This is the harmonic compensation control method for suppressing SynRM torque ripple in this invention. d Block diagram of shaft current harmonic extraction structure;

[0135] Figure 4 This is the harmonic compensation control method for suppressing SynRM torque ripple in this invention. q Block diagram of shaft current harmonic extraction structure;

[0136] Figure 5 This is a block diagram of the resonant torque ripple minimization controller used in the harmonic compensation control method for suppressing SynRM torque ripple in this invention. Detailed Implementation

[0137] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0138] This invention relates to a resonant compensation control method for suppressing SynRM torque ripple, wherein the block diagram of the SynRM torque ripple suppression system based on a current controller under speed harmonics is shown below. Figure 1 As shown, the vector control system using a synchronous reluctance motor is as follows:

[0139] The system comprises a main signal circuit, a detection circuit, and a control circuit. The main circuit includes a three-phase inverter and a synchronous reluctance motor. The detection circuit consists of a current detection circuit and a sensor module. The current detection circuit detects the current signal of the synchronous reluctance motor, while the sensor module uses a position sensor to acquire the position and speed of the synchronous reluctance motor rotor. The control circuit includes a Clark converter module, a Park converter module, a current controller module, a maximum torque-to-current ratio (MTPA) module, a Park inverse converter module, and an SVPWM modulation module. It primarily processes the signals obtained from the signal detection circuit to generate the control signals for the main control circuit.

[0140] The work process is as follows:

[0141] The current signal detection circuit detects the three-phase input current of the synchronous reluctance motor in the three-phase stationary coordinate system using a Hall sensor. , , The three-phase input current is transformed by Clark converter (3 s / 2 s ), converted to current in a stationary two-phase coordinate system , The position sensor can obtain the rotor position angle of the synchronous reluctance motor. and electric angular velocity The current controller based on speed harmonics first utilizes the motor's speed signal. The speed amplitude and phase are extracted by the speed detection module, and then the reference harmonic current is output by the outer loop torque ripple minimization controller. Next, the motor current signal is used... , The amplitude and phase of the actual current are extracted by the current detection module. The harmonics of the actual current follow the reference harmonic current through an improved resonant controller, and the output voltage is superimposed on the main circuit. , This allows for the compensation of optimal harmonic currents within the sinusoidal current, thereby suppressing the torque pulsation of the SynRM.

[0142] Furthermore, after the inverse Park transformation (2r / 2s), it is converted into a two-phase voltage in a stationary two-phase coordinate system. , Two-phase voltage , The PWM wave is generated by the SVPWM generator module and then drives the synchronous reluctance motor (SynRM) after passing through the three-phase inverter.

[0143] The specific steps are as follows:

[0144] Step 1: Establish the relationship between torque harmonics and speed harmonics of the synchronous reluctance motor, and design a speed harmonic extraction module, specifically:

[0145] SynRM in dq The velocity equations under the rotating coordinate axes are shown in the following formula (1):

[0146] (1)

[0147] in, For mechanical angular velocity, Let the moment of inertia of SynRM be... It is electromagnetic torque. For load torque, is the coefficient of friction.

[0148] To minimize torque harmonics, the electromagnetic torque of the synchronous reluctance motor is expressed in Fourier series form as shown in formula (2) below:

[0149] (2)

[0150] in, This is the total torque output by the SynRM, including the DC component. Harmonic components , and They are The amplitude and phase, The electrical angle representing the rotor, It represents the harmonic order.

[0151] The velocity can be expressed in the form of a Fourier series as shown in formula (3):

[0152] (3)

[0153] in, The average speed of the motor. For the speed harmonics of the motor, and They are respectively The amplitude and phase angle. Substituting formulas (2) and (3) into formula (1) yields:

[0154] (4)

[0155] In fact, the magnitude of torque harmonics decreases as the harmonic order decreases. Therefore, this paper only considers the major harmonic orders. This paper considers the 6th harmonic current obtained through a controller based on the 6th speed pulsation. Considering the 6th harmonic, the results are as follows:

[0156] (5)

[0157] in, Represents load torque The first in k Secondary torque harmonic components. Assume... There is no interference from pulsating components. Negligible. Because... much smaller ,therefore It can be ignored. Therefore, formula (5) can be simplified to:

[0158] (6)

[0159] It is evident that under the influence of electromagnetic torque pulsation, the SynRM generates speed pulsation of the same order, and the torque of the first order... k Sub-pulse amplitude With the rotational speed of the first k Sub-pulse amplitude They are directly proportional, with a phase difference of The relationship between its amplitude and magnitude is shown in the following formula (7):

[0160] (7)

[0161] Figure 2 This is a block diagram of the speed harmonic extraction module. To extract the amplitude and phase of the 6th speed harmonic, the following steps are performed: Multiply by a sine wave of 6 times the frequency. and cosine quantity And expand to obtain:

[0162] (8)

[0163] It can be seen that, in addition to the 6th and 12th harmonic components, formula (8) also contains a DC component. and If filtered, the corresponding speed pulsation information can be obtained.

[0164] (9)

[0165] The amplitude and phase angle of the rotational speed pulsation are obtained as shown in formulas (10) and (11) below:

[0166] (10)

[0167] (11)

[0168] The low-pass filter used is a second-order LPF, and its transfer function is shown in the following formula (12):

[0169] (12)

[0170] Where s is the Laplace operator, For the natural frequency, The damping ratio is typically taken as 0.707. The transfer function of the LPF is given. This harmonic extraction and detection module does not involve complex calculations, only multiplication, calculation of the square root, and low-pass filter, making it simpler and more convenient.

[0171] Step 2: Design an outer-loop torque ripple minimization controller for the synchronous reluctance motor, specifically as follows:

[0172] d , q The shaft current is expressed in the form of the following formula (13):

[0173] (13)

[0174] in, and They are and DC component; and They are respectively The amplitude and phase angle; and They are respectively The amplitude and phase angle.

[0175] when d , q Axis No. k Subharmonic current and When formula (14) is satisfied, the first k Secondary torque harmonics Minimize:

[0176] (14)

[0177] in, , , yes d The average magnetic flux of the axis, , They are respectively d shaft and q Shaft stator inductance.

[0178] Substituting formula (14) into formula (13) yields the harmonic current. and As shown in the following formula (15):

[0179] (15)

[0180] From the first in formula (15) k The first harmonic current caused by the first harmonic current k Secondary torque harmonics As shown in the following formula (16):

[0181] (16)

[0182] in, , , It is an extreme logarithm.

[0183] Therefore, the total number k Secondary torque harmonics It is the sum of formulas (2) and (16), that is:

[0184] (17)

[0185] In order to To minimize the torque harmonics caused by the added harmonic current. It should be in harmony with the inherent torque harmonics of the motor. They cancel each other out, therefore formula (18) must be satisfied:

[0186] (18)

[0187] The optimal harmonic current can be directly calculated from the motor parameters using the above formula. However, when the motor is saturated, the parameters are not constant, so there will be errors in the calculation of the optimal harmonic current. Moreover, torque measurement is not available in industrial drives. Therefore, speed harmonics are generally used as the feedback signal.

[0188] Substituting formula (7) into formula (18) yields the first... k Second best q The shaft current is shown in the following formula (19):

[0189] (19)

[0190] As can be seen from formula (19), the harmonic current for minimizing torque harmonics can be directly calculated from the speed harmonics. Therefore, the input of the controller for minimizing torque harmonics is... amplitude and phase angle The output is q Shaft Optimal Reference Current amplitude and phase angle , d Shaft Optimal Reference Current amplitude and phase angle .because Size and Proportional to speed, therefore, a PI controller can be selected for control. For amplitude control, the goal is to minimize speed harmonics to zero; therefore, the reference value for speed harmonics is... Set to zero, that is:

[0191] (20)

[0192] PI controller output As shown in the following formula (21):

[0193] (twenty one)

[0194] in, and These are the proportional and integral gains of the PI controller.

[0195] For phase angle control The following formula (22) can be obtained by using formula (19):

[0196] (twenty two)

[0197] The amplitude and phase angle can be obtained from formula (14) as shown in formula (23):

[0198] (twenty three)

[0199] Step 3: Extract the current harmonics of the synchronous reluctance motor, specifically:

[0200] Step 3.1, extract the synchronous reluctance motor d Shaft current harmonics;

[0201] Extraction 6 times d , q The amplitude and phase of the shaft current harmonics, such as Figure 3 As shown, for Multiply by a sine wave of 6 times the frequency. and cosine quantity And expanded, we get the following formula (24):

[0202] (twenty four)

[0203] The LPF obtained by applying formula (24) to formula (12) is:

[0204] (25)

[0205] Thus obtain d The amplitude and phase angle of the shaft current harmonics are shown in formulas (26) and (27) below:

[0206] (26)

[0207] (27)

[0208] Step 3.2, extract the synchronous reluctance motor data. q Shaft current harmonics;

[0209] like Figure 3 As shown, for Multiply by a sine wave of 6 times the frequency. and cosine quantity And expanded, we get the following formula (28):

[0210] (28)

[0211] The LPF obtained by applying formula (28) to formula (12) is:

[0212] (29)

[0213] Thus obtain q The amplitude and phase angle of the shaft current harmonics are shown in formulas (30) and (31) below:

[0214] (30)

[0215] (31)

[0216] Step 4: Design an improved inner-loop resonant current controller for the synchronous reluctance motor to obtain the output compensation voltage, specifically:

[0217] like Figure 5 As shown, based on step 2, the reference harmonic current can be obtained by combining the amplitude and phase of the reference harmonic current. and The expression for is shown in the following formula (32):

[0218] (32)

[0219] Similarly, by combining the amplitude and phase of the actual harmonic current obtained in step 3, the actual harmonic current can be obtained. and As shown in the following formula (33):

[0220] (33)

[0221] The task of the current controller is to control the actual current. and To follow the optimal harmonic current from step 2, the present invention uses an improved resonant controller to follow the optimal harmonic current of the output. and Then, the output voltage is added to the voltage output by the PI controller in the main circuit to obtain the required voltage. d , q Shaft reference voltage.

[0222] Resonant controllers utilize the infinite gain characteristic at the resonant frequency to suppress current harmonics under periodic disturbances. Compared to ideal resonant controllers, quasi-resonant controllers increase the bandwidth at the resonant frequency, reducing the system's frequency sensitivity and improving stability, resulting in better harmonic suppression and making them more suitable for motor systems with torque ripple. The transfer function of a quasi-resonant controller... As shown in the following formula (34):

[0223] (34)

[0224] in, The cutoff frequency of the quasi-resonant controller. To suppress the 6th current harmonic at the resonant frequency, this paper uses the resonant disturbance estimator... for , The integral gain is given. However, with the increase of resonant frequency and sampling period, frequency and phase shifts occur in digital implementation. To solve this problem, a method for phase and amplitude compensation of the quasi-resonant controller is proposed. First, the phase lag of the system is compensated, and its transfer function is obtained as shown in the following formula (35):

[0225] (35)

[0226] in, This is the expected phase lead angle. The following will introduce... The steps to determine, in order to d Taking the axis as an example. Assume the mathematical model of SynRM in a rotating coordinate system. As shown in the following formula (36):

[0227] (36)

[0228] Considering the zero-order hold function of the voltage source inverter and the delay caused by algorithm execution, the mathematical model of SynRM is obtained. As shown in the following formula (37):

[0229] (37)

[0230] in, The sampling period is This is the delay stage of the algorithm. After phase compensation using formula (35), the mathematical model of SynRM is obtained as shown in formula (38):

[0231] (38)

[0232] Therefore, we obtain The phase frequency characteristic is shown in the following formula (39):

[0233] (39)

[0234] The magnitude of this value depends on the resistance and inductance of the motor, and increases with the increase of motor speed. Therefore, it is proposed that... The simple linear equation is shown in the following formula (40):

[0235] (40)

[0236] in, The rotational speed of SynRM, Let be the slope of the linear equation. The intercept of the linear equation. The slope of the phase frequency curve. As shown in the following formula (41):

[0237] (41)

[0238] Pick Therefore, the slope of the linear equation is shown in formula (42):

[0239] (42)

[0240] Additionally, the intercept b can take an intermediate value, assuming... .therefore, The simple linear equation is shown in the following formula (43):

[0241] (43)

[0242] Secondly, bilinear transformation is generally used to discretize the controller, but at high frequencies the deviation is large. An improved bilinear transformation can be used to ensure that the amplitude-frequency characteristics are the same at the resonant frequency. The transformation is shown in the following formula (44):

[0243] (44)

[0244] Discretize equation (35) and use the improved bilinear transform of equation (44) to obtain equation (45):

[0245] (45)

[0246] in, , , , , , .

[0247] Rearranging formula (45) yields the following formula (46):

[0248] (46)

[0249] The transformation relationship is shown in the following formula (47):

[0250] (47)

[0251] The difference equation for the output obtained from formulas (46) and (47) is shown in formula (48) below:

[0252] (48)

[0253] The input to the difference equation in the system is and As shown in the following formula (49):

[0254] (49)

[0255] Therefore, formula (48) can be rewritten as:

[0256] (50)

[0257] in, , for d shaft and q The output compensation voltage of the shaft resonant current controller.

[0258] The output compensation voltage of the resonant current controller , Superimposed on each d , q Shaft voltage output , This achieves the suppression of SynRM torque ripple.

[0259] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A resonant compensation control method for suppressing SynRM torque ripple, characterized in that, Includes the following steps: Step 1: Establish the relationship between torque harmonics and speed harmonics of the synchronous reluctance motor, and design a module for extracting speed harmonics; The specific steps are as follows: SynRM in dq The velocity equations under the rotating coordinate axes are shown in equation (1): (1) in, For mechanical angular velocity, Let the moment of inertia of SynRM be... It is electromagnetic torque. For load torque, The coefficient of friction; To minimize torque harmonics, the electromagnetic torque of the synchronous reluctance motor is expressed in the form of a Fourier series as shown in equation (2): (2) in, This is the total torque output by the SynRM, including the DC component. Harmonic components , and They are The amplitude and phase, The electrical angle representing the rotor, Represents the harmonic order; The velocity is expressed in the form of a Fourier series as shown in formula (3): (3) in, The average speed of the motor. For the speed harmonics of the motor, and They are respectively The amplitude and phase angle; Substituting formulas (2) and (3) into formula (1) yields: (4) in, This represents the number of pole pairs of the motor. The magnitude of torque harmonics decreases as the harmonic order decreases. Considering the 6th speed pulsation, the controller obtains the 6th harmonic current, and the result is: (5) in, Represents load torque The first in k Secondary torque harmonic components, assuming There is no interference from pulsating components. Negligible; due to much smaller ,therefore If we ignore the null terminology, then formula (5) simplifies to: (6) Under the influence of electromagnetic torque pulsation, the SynRM generates speed pulsation of the same order, and the torque of the first order... k Sub-pulse amplitude With the rotational speed of the first k Sub-pulse amplitude They are directly proportional, with a phase difference of The relationship between the amplitude and magnitude of torque pulsation is shown in the following formula (7): (7) To extract the amplitude and phase of the 6th rotational harmonic, the following steps were taken: Multiply by a sine wave of 6 times the frequency. and cosine quantity And expand to obtain: (8) In addition to the 6th and 12th harmonic components, formula (8) also contains a DC component. and Filtering this information yields the corresponding speed fluctuation information: (9) The amplitude and phase angle of the rotational speed pulsation are obtained as shown in formulas (10) and (11) below: (10) (11) The low-pass filter used is a second-order LPF, and its transfer function is shown in the following formula (12): (12) Where s is the Laplace operator, For the natural frequency, For the damping ratio, The transfer function of the LPF; Step 2: Design an outer loop torque ripple minimization controller for the synchronous reluctance motor; The specific steps are as follows: d , q The shaft current is expressed in the form of the following formula (13): (13) in, and They are and DC component; and They are respectively The amplitude and phase angle; and They are respectively The amplitude and phase angle; when d , q Axis No. k Subharmonic current and When formula (14) is satisfied, the first k Secondary torque harmonics Minimize: (14) in, , , yes d The average magnetic flux of the axis, , They are respectively d shaft and q Shaft stator inductance; Substituting formula (14) into formula (13) yields the harmonic current. and As shown in formula (15): (15) From the first in formula (15) k The first harmonic current caused by the second harmonic current k Secondary torque harmonics As shown in formula (16): (16) in, , , It is the extreme logarithm; Total k Secondary torque harmonics It is the sum of formulas (2) and (16), that is: (17) In order to To minimize the torque harmonics caused by the added harmonic current. It should be in harmony with the inherent torque harmonics of the motor. They cancel each other out, therefore formula (18) must be satisfied: (18) The required optimal harmonic current can be directly calculated from the motor parameters using the above formula. However, when the motor is saturated, the parameters are not constant, so there will be errors in the calculation of the optimal harmonic current. Moreover, torque measurement is not available in industrial drives. Therefore, speed harmonics are used as feedback signals. Substituting formula (7) into formula (18) yields the first... k Second best q The shaft current is shown in formula (19): (19) As can be seen from formula (19), the harmonic current for minimizing torque harmonics is directly calculated from the speed harmonics. Therefore, the input of the controller for minimizing torque harmonics is... amplitude and phase angle The output is q Shaft Optimal Reference Current amplitude and phase angle , d Shaft Optimal Reference Current amplitude and phase angle ,because Size and Proportional to speed, therefore, a PI controller is chosen for control. For amplitude control, the goal is to minimize speed harmonics to zero; therefore, the reference value for speed harmonics is... It is set to zero, that is: (20) PI controller output As shown in formula (21): (21) in, and These are the proportional and integral gains of the PI controller; For phase angle control The result obtained by formula (19) is shown in formula (22): (22) The amplitude and phase angle are obtained through formula (14) as shown in formula (23): (23) ； Step 3: Extract the current harmonics of the synchronous reluctance motor; Step 4: Design the inner-loop resonant current controller for the synchronous reluctance motor, obtain the output compensation voltage, and superimpose the compensation voltage onto... d , q On the shaft voltage output, the total output voltage suppresses torque pulsation.

2. The resonant compensation control method for suppressing SynRM torque ripple according to claim 1, characterized in that, The specific steps of step 3 are as follows: Step 3.1, extract the synchronous reluctance motor d Shaft current harmonics; Extract 6 times d , q The amplitude and phase of the shaft current harmonics, for Multiply by a sine wave of 6 times the frequency. and cosine quantity And expanded, it yields the result shown in formula (24): (24) The LPF of formula (24) obtained by applying formula (12) is: (25) Thus obtain d The amplitude and phase angle of the shaft current harmonics are shown in formulas (26) and (27): (26) (27) Step 3.2, extract the synchronous reluctance motor q Shaft current harmonics; right Multiply by a sine wave of 6 times the frequency. and cosine quantity And expanded, it yields the result shown in formula (28): (28) The LPF of formula (28) obtained by applying formula (12) is: (29) Thus obtain q The amplitude and phase angle of the shaft current harmonics are shown in formulas (30) and (31): (30) (31)。 3. The resonant compensation control method for suppressing SynRM torque ripple according to claim 2, characterized in that, The specific steps of step 4 are as follows: Based on step 2, the amplitude and phase of the optimal harmonic current output in step 2 are combined to obtain the optimal harmonic current output. and The expression for is shown in the following formula (32): (32) The amplitude and phase of the actual harmonic current obtained in step 3 are combined to obtain the actual harmonic current. and As shown in the following formula (33): (33) The task of the current controller is to control the actual current. and To follow the optimal harmonic current from step 2, an improved resonant controller is used to follow the optimal harmonic current of the output. and Then, the output voltage is added to the voltage output by the PI controller in the main circuit to obtain the required voltage. d , q Shaft reference voltage; A quasi-resonant controller is used, and the transfer function of the quasi-resonant controller is... As shown in the following formula (34): (34) in, The cutoff frequency of the quasi-resonant controller. The resonant frequency, For integral gain; As the resonant frequency and sampling period increase, frequency and phase shifts will occur in digital implementation. The phase and amplitude compensation methods are adopted by aligning the resonant controller. First, the phase lag of the system is compensated, and its transfer function is obtained as shown in the following formula (35): (35) in, This is the expected phase lead angle; The specific steps for determining this are as follows: for d Axis, mathematical model of SynRM in rotating coordinate system As shown in formula (36): (36) Considering the zero-order hold function of the voltage source inverter and the delay caused by algorithm execution, the mathematical model of SynRM is obtained. As shown in formula (37): (37) in, The sampling period is As a delay element of the algorithm, after phase compensation using formula (35), the mathematical model of SynRM is obtained as shown in formula (38) below: (38) Therefore, we obtain The phase frequency characteristic is shown in the following formula (39): (39) The magnitude of this value depends on the motor's resistance and inductance, and increases with increasing motor speed. Therefore, it is proposed that... The simple linear equation is shown in the following formula (40): (40) in, The rotational speed of SynRM, The slope of the linear equation. The intercept of the linear equation and the slope of the phase frequency curve are given. As shown in the following formula (41): (41) Pick Therefore, the slope of the linear equation is shown in formula (42): (42) intercept ,therefore, The simple linear equation is shown in the following formula (43): (43) Secondly, an improved bilinear transform is used to ensure that the amplitude-frequency characteristics are the same at the resonant frequency. The transform is shown in the following formula (44): (44) Discretize equation (35) and use the improved bilinear transform of equation (44) to obtain equation (45): (45) in, , , , , , Rearranging formula (45) yields the following formula (46): (46) The transformation relationship is shown in the following formula (47): (47) The difference equation for the output obtained from formulas (46) and (47) is shown in formula (48) below: (48) The input to the difference equation in the system is and As shown in the following formula (49): (49) Therefore, formula (48) can be rewritten as: (50) in, , for d shaft and q The output compensation voltage of the shaft resonant current controller; The output compensation voltage of the resonant current controller , Superimposed on each d , q Shaft voltage output , This achieves the suppression of SynRM torque ripple.

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