CN113346811B - Method for inhibiting motor torque pulsation and vibration based on back electromotive force observer - Google Patents
Method for inhibiting motor torque pulsation and vibration based on back electromotive force observer Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/10—Arrangements for controlling torque ripple, e.g. providing reduced torque ripple
Abstract
The invention discloses a method for inhibiting motor torque pulsation and vibration based on a back electromotive force observer, which relates to the field of motor vibration noise control, and the torque pulsation of a motor is reduced by utilizing a mode of offsetting cogging torque by ripple torque in an opposite phase manner; fitting the cogging torque and the motor rotating speed to obtain a fitting formula, fitting the cogging torque amplitude of a specific order of different rotating speed working points with the rotating speed of the working points, and acquiring torque pulsation of the motor at different rotating speeds by using a balanced measurement method based on a torque sensor; and obtaining the phase of the cogging torque according to the electrical angle, finally calculating the harmonic voltage to be introduced, and injecting the harmonic voltage into a control system. Harmonic current and harmonic counter electromotive force are introduced into the motor to generate ripple torque with the same amplitude and opposite phase with the cogging torque so as to inhibit torque pulsation, so that the problem of vibration noise of the motor is solved.
Description
Technical Field
The invention belongs to the field of motor vibration noise control, and particularly relates to a motor vibration noise suppression method based on torque ripple control of a harmonic back electromotive force observer, in particular to a method for suppressing torque ripple of a 4-pole 12-slot Permanent Magnet Synchronous Motor (PMSM).
Background
The permanent magnet synchronous motor can generate torque pulsation due to the defects of a self control system and the intrinsic parameters of the motor body, the stability of the output torque of the motor can be influenced, and the motor base can generate vibration with a certain amplitude. The torque ripple of the permanent magnet synchronous motor can be mainly classified into two types: one is ripple torque, caused by current harmonics generated by the motor control system; the other is cogging torque, which is generated by the interaction between the permanent magnets of the motor and the stator cogging.
In a motor control system, the harmonic action of harmonic current and back electromotive force in the motor can generate ripple torque with the frequency 6 times of the angular frequency of fundamental wave, and further torque pulsation is caused. The frequency of the cogging torque depends on the number of poles and slots in the motor, and for a 4-pole 12-slot machine, the cogging frequency is 6 times the fundamental angular frequency.
The torque generated when the permanent magnet synchronous motor is driven by the sine wave power source can be divided into the basic torque and the above-described ripple torque. The basic torque is a constant torque component independent of the rotation angle, and the pulsating torque is a torque that varies periodically with the rotation angle, these torque components are not negligible, and the pulsating torque affects the accuracy of the output torque of the motor. Therefore, reducing the output torque ripple of the permanent magnet synchronous motor is an important method for improving the service performance of the motor.
Disclosure of Invention
The invention aims to solve the problem of torque output pulsation caused by harmonic current of a permanent magnet synchronous motor and cogging torque of the motor, and provides a method for inhibiting the torque pulsation and vibration of the motor based on a back electromotive force observer.
The present invention achieves the above-described object by the following technical means.
A method for inhibiting motor torque pulsation and vibration based on a back electromotive force observer comprises a back electromotive force observation module, a harmonic current calculation module, a harmonic voltage calculation module and a torque measurement module; the torque measurement module is used for acquiring relevant data; firstly, a counter electromotive force observation module is used for observing current components i on d-q coordinate axes of the permanent magnet synchronous motor d And i q Observing to obtain 6-th harmonic counter electromotive force, and inputting the counter electromotive force into a harmonic current calculation module to participate in calculation; the harmonic current calculation module is preset with a fitting polynomial between the cogging torque amplitude and the motor rotating speed, and the rotating speed is obtained through a slip film observer
Calculating a cogging torque amplitude according to the fitting polynomial; regarding the acquisition of a fitting polynomial of a cogging torque amplitude and a motor rotating speed, a balanced measurement method based on a torque sensor is utilized to directly obtain the fitting polynomialMeasuring the amplitude of the specific-order cogging torque ripple at different rotating speed working points, and fitting the amplitude into a polynomial; electric angle of motor rotor obtained according to sliding film observer
Calculating the phase position of the cogging torque, and obtaining the amplitude and the phase position of the cogging torque of a specific order; the amplitude and the phase of the harmonic current to be input are calculated in the harmonic current calculation module, then the corresponding harmonic voltage is calculated by the harmonic voltage calculation module and injected into the control system to generate specific order ripple torque to counteract the cogging torque, and therefore the purpose of reducing torque pulsation is achieved.
The processing error of the motor body and the defect of the permanent magnet of the motor rotor can cause the distortion of the air gap field of the motor, and the harmonic flux linkage is brought to the permanent magnet flux linkage, when the counter electromotive force caused by the harmonic flux linkage acts in a three-phase circuit, and due to the Y-connection characteristic of the circuit, the even-order counter electromotive force and the integral multiple of 3 can be counteracted. Since the amplitude of the harmonic electromotive force decreases with the increase of the order, only the harmonic electromotive forces caused by the 5 th and 7 th harmonic flux linkages are considered, while in the stationary coordinate system, the rotation directions of the 5 th and 7 th harmonic flux linkages are opposite, so that the permanent magnet flux linkage equation considered by us is expressed by the following formula:
ψ fA (θ)＝ψ f1 sin(θ)+ψ f5 sin(-5θ)+ψ f7 sin(7θ)
in the formula, # fn The (n-5, 7) is the amplitude of the harmonic flux linkage of each phase winding 5, 7.
The harmonic flux linkage brings a series of harmonics to the back electromotive force of the motor stator winding, the difference of the primary phase of the back electromotive force harmonics is not considered temporarily, and the expression of the back electromotive force is as follows:
E a (t)＝e 1 sin(ωt)+e 5 sin(-5ωt)+e 7 sin(7ωt)
in the formula, e n The amplitudes of the fundamental wave of back electromotive force of each phase and the 5 th and 7 th harmonics are (n is 1, 5, and 7), respectively.
Meanwhile, if the above operation of introducing the harmonic current of opposite phase is not performed, harmonic current exists in the phase current, only the harmonic current of 5 th and 7 th orders is discussed here, and the initial phase difference of the harmonic current is not considered, so the phase current can be expressed by the following formula:
I a (t)＝i 1 sin(ωt)+i 5 sin(-5ωt)+i 7 sin(7ωt)
in the formula i n The amplitudes of the fundamental wave and the 5 th and 7 th harmonics of the phase winding current are (n is 1, 5, 7).
The expression of the back emf harmonic and the current harmonic resulting in ripple torque is as follows:
in the formula, omega r The mechanical rotating speed of the motor is obtained by unfolding the above formula:
it can be found that the torque ripple caused by the harmonic counter electromotive force of 5, 7 and the harmonic current is mainly 6 and 12.
Meanwhile, due to the existence of the stator tooth grooves, even under the condition that the motor is not electrified, the interaction between the permanent magnet and the tooth grooves generates periodic torque pulsation along with the rotation of the motor.
The cogging torque is generally analyzed by an energy method, and the expression of the magnetic field energy is as follows:
in the formula, B r Is the distribution of the remanence of the permanent magnet along the circumferential direction, g (theta, alpha) is the distribution of the air gap length along the circumferential direction, h m Is the length of the permanent magnet in the magnetizing direction.
Will be provided with
And
performing Fourier decomposition, and respectively expressing the expansion forms as follows:
finally, the cogging torque can be expressed by the expression:
wherein z is the number of slots of the PMSM, l ef Is the armature core length, mu 0 Is the magnetic permeability in vacuum, R 1 Is the outer radius of the armature, R 2 Is the outer radius of the rotor, p is the number of pole pairs of the machine, where n is such that
Is a positive integer of an integer; in a 4-pole, 12-slot machine, p is equal to 2 and z is equal to 12, so n can be equal to 1, 2, 3, etc., with corresponding cogging torque orders of 12, 24, 48, etc., respectively. Since the 12-order cogging torque has the largest amplitude among the cogging torques of the respective orders, and the influence of the brought torque ripple is also the largest, we only consider the 12-order cogging torque here.
In summary, the torque ripple can be suppressed in the 4-pole 12-slot permanent magnet synchronous motor by the method of the ripple torque and the cogging torque of the same order of opposite phase cancellation.
First, 5 th and 7 th harmonic counter electromotive forces in a three-phase stationary coordinate system need to be acquired.
The method adopts two extended state observers to observe harmonic counter electromotive force under a d-q coordinate system respectively.
And the harmonic counter electromotive force observation module adopts two extended state observers to respectively observe 6-th harmonic counter electromotive force on the d axis and the q axis.
For 6 th harmonic back emf on the d-axis, the observation is as follows.
The equation of state of the d-axis of the permanent magnet synchronous motor can be expressed as:
in the formula (I), the compound is shown in the specification,
is the differential of the d-axis current, L d Is d-axis inductance, u d Is d-axis voltage, E dn Is the harmonic back electromotive force, k, on the d-axis d Is a d-axis known disturbance, expressed as:
in the formula, R s Is stator resistance, ω is electrical angular velocity, L q Is the q-axis inductance.
The expression of the extended state observer for observing the d-axis harmonic counter electromotive force is as follows:
Δ d1 ＝z d1 -i d
in the formula, z d1 Is d-axis current i d An observed value of z d2 Is composed of
The observed value of (1) is a d-axis third observed variable, a d-axis fourth observed variable and a d-axis fifth observed variable,
is z d1 The differential of (a) is determined,
is z d2 The differential of (a) is determined,
is z d3 The differential of (a) is obtained by differentiating,
is z d4 The differential of (a) is determined,
is z d5 Differential of, Δ d1 Is z d1 And d-axis current i d Error of (1), beta d1 Is a d-axis first gain factor, beta d2 Is a d-axis second gain factor, beta d3 Is the d-axis third gain factor, beta d4 Is a d-axis fourth gain factor, β d5 Is the d-axis fifth gain factor.
The d-axis 6 th harmonic back electromotive force observed by the extended state observer can be expressed as:
E d6 ＝L d z d2
the state equation of the q-axis of the permanent magnet synchronous motor can be expressed as:
in the formula (I), the compound is shown in the specification,
is the differential of the q-axis current, L q Is the q-axis inductance, u q Is the q-axis voltage, E qn Is the harmonic back electromotive force, k, on the q-axis q Is a q-axis known disturbance, the expression:
in the formula, λ d Is the flux linkage dc component.
The expression of the extended state observer for observing the q-axis harmonic counter electromotive force is as follows:
Δ q1 ＝z q1 -i q
in the formula, z q1 Is q-axis current i q An observed value of z q2 Is composed of
The observed value of (a) is a q-axis third observed variable, is a q-axis fourth observed variable, is a q-axis fifth observed variable,
is z q1 The differential of (a) is determined,
is z q2 The differential of (a) is obtained by differentiating,
is z q3 The differential of (a) is obtained by differentiating,
is z q4 The differential of (a) is obtained by differentiating,
is z q5 Differential of, Δ q1 Is z q1 And q-axis current i q Error of (1), beta q1 Is a first gain coefficient of q-axis, beta q2 Is a q-axis second gain factor, beta q3 Is the q-axis third gain factor, beta q4 Is the q-axis fourth gain factor, beta q5 The q-axis fifth gain factor.
The q-axis 6 th harmonic back electromotive force observed by the extended state observer can be expressed as:
E q6 ＝L q z q2
in order to obtain the amplitude of 12-order cogging torque of the permanent magnet synchronous motor, a balanced measurement method based on a torque sensor is adopted to measure the amplitude of corresponding cogging torque at different rotating speeds, and a polynomial is fitted.
The tested permanent magnet synchronous motor is respectively connected with a small-range torque sensor and a large-range torque sensor through couplers, the small-range torque sensor is connected with a large inertia flywheel through a coupler, the large-range torque sensor is connected with a speed reducing mechanism through a coupler, and the speed reducing mechanism is connected with a magnetic powder brake to serve as a load.
In the measuring process, the average torque of the motor is balanced with the braking torque, only the torque fluctuation part acts on the flywheel through the small-range torque sensor, and therefore the torque fluctuation of the motor can be measured through the small-range torque sensor.
And (3) carrying out coordinate transformation on harmonic counter electromotive force observed by the extended counter electromotive force observer, transforming the harmonic counter electromotive force into a three-phase static coordinate system, wherein the transformed harmonic counter electromotive force takes the initial phase of each order of counter electromotive force into consideration and then has the following expression:
in the formula (I), the compound is shown in the specification,
and
the initial phases of the harmonic back emf of 5 th and 7 th order for each phase, respectively.
The expressions for the respective phase currents introduced are as follows:
in the formula (I), the compound is shown in the specification,
and
the initial phases of the 5 th and 7 th harmonic currents, respectively.
From the expression of the ripple torque, we can find that we can adjust the harmonic current i 5 And i 7 So that the 12 th order torque amplitude of the ripple torque is equal to the cogging torque and the phase is opposite to the cogging torque. But at the same time, the harmonic current i is introduced 5 And i 7 The ripple torque of order 6 may be increased, so that the harmonic current i is required 5 And i 7 Respectively generated 6-order ripple torque are mutually counteracted, and introduced harmonic current i 5 And i 7 The following two equations need to be satisfied:
i.e. the introduced harmonic current i 5 And i 7 The ripple torque generated needs to satisfy the following two sets of equations:
from the first set of equations i 5 And i 7 And the relationship between the initial phases of the harmonic currents of the respective orders is as follows:
in the second set of equations, the initial phase parameters of the back emf of each phase order are too many to make the equations difficult to solve, so we make the following estimation calculations:
will be provided with
And
as initial phases of the 5 th order back electromotive force and the 7 th order back electromotive force of each phase,
and with
I is obtained by combining the first set of equations as the initial phase of the 5 and 7 order currents of each phase to simplify calculation 5 And i 7 And the relationship between the initial phases of the harmonic currents of each order, the simplified equation is as follows:
if it is desired that the generated ripple torque be cancelled out by the cogging torque rather than gain from each other, it is desired that the phase of the 7 th order current harmonic satisfy the following condition:
if it is
If true, the inequality is not solved.
Only when
Then, the corresponding solution can be obtained.
Thus, can obtain i 5 And i 7 The expression for the initial phase of the order harmonic current is as follows:
i 5 and i 7 The expression for the order harmonic current magnitude is as follows:
in summary, the expression of the harmonic current to be input is:
converting the three-phase harmonic current obtained by calculation into 5 th and 7 th harmonic currents i on a d-q axis coordinate system after coordinate transformation d5 And i q5 And i d7 And i q7 。
And then inputting the harmonic current after coordinate transformation into a harmonic voltage calculation module, wherein the calculation formula of 5 th and 7 th harmonic voltages obtained according to a stator voltage formula is as follows:
in the formula u d5 、u q5 、u d7 、u q7 Synthesizing the generated 5 th and 7 th harmonic voltages into d-axis compensation voltage u for the 5 th and 7 th harmonic voltages on the d-q axis d-c And q-axis compensation voltage u q-c And inputting the signals into a control link, thereby completing the process of restraining the cogging torque through the ripple torque.
Has the beneficial effects that:
1. the invention reduces the torque ripple of the motor by using a mode of offsetting the cogging torque by the ripple torque in an opposite phase manner, and specifically comprises the following steps: the method comprises the steps of obtaining 6-order harmonic counter electromotive force in a motor through an extended state observer, obtaining a cogging torque amplitude by combining the current rotating speed and a fitting relation between preset cogging torque and the rotating speed, obtaining the fitting relation between the current rotating speed and the rotating speed of the motor by fitting the cogging torque amplitude of a specific order of different rotating speed working points with the rotating speed of the working points, obtaining torque pulsation of the permanent magnet synchronous motor at different rotating speeds by using a balanced measurement method based on a torque sensor, obtaining the phase of the cogging torque through an electrical angle, calculating harmonic current to be introduced, calculating the harmonic voltage to be injected, and injecting the harmonic voltage into a control system. Harmonic current is introduced into the motor, and then the harmonic counter electromotive force and the harmonic counter electromotive force generate ripple torque with the same amplitude and opposite phase as the cogging torque, and torque pulsation is effectively inhibited.
2. Aiming at the problem of torque output pulsation caused by harmonic current of a permanent magnet synchronous motor and motor cogging torque, the invention provides a permanent magnet synchronous motor torque pulsation suppression method based on harmonic injection and a torque sensor.
Drawings
Fig. 1 is a motor control block diagram for suppressing motor torque ripple in the present invention;
FIG. 2 is a detailed analysis diagram of the back EMF observation module;
FIG. 3 is a schematic diagram of a balanced cogging torque measurement based torque sensor;
fig. 4 is a detailed analysis diagram of the harmonic current calculation module.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
FIG. 1 is a motor control block diagram of a motor torque ripple suppression scheme in accordance with the present invention, which is based on SMO-based zero
On a position sensor motor control system, a rotor angle required by motor control is calculated through a sliding mode observer
And the rotational speed
The calculated rotor angle and the calculated rotating speed are used for participating in the control of a rotating speed loop and a current loop of the motor and are also input into a harmonic current calculation module to participate in calculation;
the back electromotive force observation module in fig. 1 can extract main 5 and 7 harmonic back electromotive forces, input the extracted back electromotive forces into the harmonic current calculation module, and calculate the harmonic current required for generating the ripple torque for canceling the cogging torque, and then calculate and inject the corresponding harmonic voltage through the harmonic voltage calculation module.
First, 6 th harmonic counter electromotive force needs to be observed to obtain input powerAfter three-phase current of the machine is converted into two current components i on d-q axis d And i q Then input into a harmonic back electromotive force observation module as shown in FIG. 2;
the harmonic counter electromotive force observation module adopts two extended state observers to respectively observe 6 harmonic counter electromotive forces on the d axis and the q axis;
the equation of state of the d-axis of the permanent magnet synchronous motor can be expressed as:
in the formula (I), the compound is shown in the specification,
is the differential of the d-axis current, L d Is d-axis inductance, u d Is d-axis voltage, E dn Is the harmonic voltage on the d-axis, k d Is the d-axis known disturbance, and the expression is:
in the formula, R s Is stator resistance, ω is electrical angular velocity, L q Is a q-axis inductance;
the harmonic counter electromotive force observation module adopts two extended state observers to respectively observe 6 harmonic counter electromotive forces on the d axis and the q axis;
the expression of the extended state observer ESO-d shown in the figure is:
Δ d1 ＝z d1 -i d
in the formula, z d1 Is d-axis current i d Observed value of (a), z d2 Is composed of
The observed value of (2) is a d-axis third observed variable, is a d-axis fourth observed variable, is a d-axis fifth observed variable,
is z d1 The differential of (a) is determined,
is z d2 The differential of (a) is determined,
is z d3 The differential of (a) is determined,
is z d4 The differential of (a) is determined,
is z d5 Differential of, Δ d1 Is z d1 And d-axis current i d Error of (1), beta d1 Is a d-axis first gain factor, beta d2 Is a d-axis second gain factor, beta d3 Is the d-axis third gain factor, beta d4 Is a d-axis fourth gain factor, β d5 A fifth gain factor for the d-axis;
the d-axis 6 harmonic back electromotive force observed by an ESO-d extended state observer can be expressed as:
E d6 ＝L d z d2
the equation of state for the q-axis of a permanent magnet synchronous motor can be expressed as:
in the formula (I), the compound is shown in the specification,
is the differential of the q-axis current, L q Is the q-axis inductance, u q Is the q-axis voltage, E qn Is the harmonic voltage on the q-axis, k q Is a known perturbation of the q axis, the expression:
in the formula, λ d Is the flux linkage dc component.
The expression of the extended state observer ESO-q shown in the figure is:
Δ q1 ＝z q1 -i q
in the formula, z q1 Is q-axis current i q An observed value of z q2 Is composed of
The observed value of (a) is a q-axis third observed variable, is a q-axis fourth observed variable, is a q-axis fifth observed variable,
is z q1 The differential of (a) is determined,
is z q2 The differential of (a) is determined,
is z q3 The differential of (a) is determined,
is z q4 The differential of (a) is obtained by differentiating,
is z q5 Differential of, Δ q1 Is z q1 And q-axis current i q Error of (1), beta q1 Is a first gain coefficient of q-axis, beta q2 Is the q-axis second gain factor, beta q3 Is the q-axis third gain factor, beta q4 Is the q-axis fourth gain factor, beta q5 The q-axis fifth gain factor.
The q-axis 6 harmonic back electromotive force observed by an ESO-q extended state observer can be expressed as:
E q6 ＝L q z q2
after 6 harmonic counter electromotive force on a d-q axis is obtained, coordinate transformation is carried out on the counter electromotive force, and the counter electromotive force is converted into 5 harmonic counter electromotive force E on a three-phase static coordinate system a5 ,E b5 ,E c5 Counter electromotive force E of harmonic 7 a7 ,E b7 ,E c7 Harmonic of 5, 7 th orderThe back electromotive force is input into a harmonic current calculation module to participate in calculation.
In order to obtain the cogging torque to be offset, on the premise of ensuring that the current output by the inverter is close to the ideal current, the invention uses the balanced cogging torque measurement method based on the torque sensor shown in fig. 3 to obtain the amplitude of 12-order cogging torque at different rotating speeds, fits the amplitude into a polynomial and presets the polynomial in a harmonic current calculation module.
In the attached figure 3, the tested permanent magnet synchronous motor is respectively connected with a small-range torque sensor and a large-range torque sensor through couplers, the small-range torque sensor is connected with a large-inertia flywheel through a coupler, the large-range torque sensor is connected with a speed reducing mechanism through a coupler, the speed reducing mechanism is responsible for adjusting the rotating speed to adapt to the measuring condition of the load, and the speed reducing mechanism is connected with the load through a coupler.
In the measuring process, the average torque of the motor is balanced with the braking torque, only the torque fluctuation part acts on the flywheel through the small-range torque sensor, and therefore the rated torque fluctuation of the motor can be measured through the small-range torque sensor.
The load adopts a magnetic powder brake. The magnetic powder brake is characterized in that magnetic powder is filled in an air gap between a stator and a rotor, when a stator coil passes through current, the magnetic powder in the air gap is magnetized under the action of a magnetic field, when torque is transmitted, braking torque is generated due to distortion of the magnetic field, the torque can be realized by adjusting exciting current, and the exciting current and the transmitting torque are basically in a linear relation. The magnetic powder brake can avoid the measurement error caused by the overlarge torque ripple of the load, and improve the measurement precision.
The braking torque and the rotating speed required to be provided by the magnetic powder brake are calculated according to the following formula:
T B ≥T E ×i
n B ≥n E /i
in the formula, T B 、n B Braking torque and speed, T, respectively, required for the magnetic powder brake E 、n E The rated torque and the rated rotating speed of the motor are respectively, and i is the reduction ratio of the reduction mechanism.
The sensor system is required to have a high sampling rate and to enable dynamic torque measurements.
The torque sensor adopts a strain type torque sensor, the torque sensor measures the torque of the motor by measuring the stress and strain parameter change of an internal elastic element of the torque sensor, and a strain mathematical model of the torque sensor can be represented by the following formula:
in the formula, epsilon 45° And ε 135° The strain values T are respectively 45 degrees and 135 degrees between the cylindrical torsion shaft surface spiral line of the strain type torque sensor and the bus r And d is the torsion shaft diameter, and G is the torsion shaft material shear elastic modulus.
A4-pole motor is adopted, and the power frequency is 50Hz, so the maximum rotating speed is 1500 rpm. The torque pulsation of each rotating speed working point between 50rpm and 1500rpm is measured by taking 50rpm as a rotating speed adjusting interval. And Fourier transform is carried out on the torque ripple measured at each rotating speed working point, and the torque ripple amplitude of 12 orders is extracted and is used as the amplitude of the cogging torque studied by people.
And then fitting the rotating speed of each working point and the cogging torque amplitude into a polynomial, wherein the polynomial is in the form of:
the period of the motor cogging torque is closely related to the relative position change between the stator and the rotor, so that the phase of the cogging torque can be determined by knowing the position of the rotor.
The position estimation method based on a synovial observer (SMO) is adopted, and the estimated position of the rotor obtained by the SMO is in an alpha-beta coordinate system
For an alpha-beta coordinate system, an alpha axis coincides with A in the three-phase coordinate system, and a beta axis is perpendicular to the alpha axis and rotates 90 degrees counterclockwise. For a 4-pole 12-slot motor, when the symmetric center line of a permanent magnet is superposed with the center line of a certain stator tooth, the cogging torque is 0; when the symmetric center line of the permanent magnet moves to the center line of the adjacent slot, the cogging torque is 0 again, and the cogging torque goes through a half wave; the cogging torque ripple goes through one cycle as the permanent magnet centerline moves to the next tooth centerline.
For a 4-pole 12-slot motor, 12 periods of cogging torque ripple occur per rotation of the rotor, and each period corresponds to a mechanical rotation angle of the rotor of 30 degrees, as shown in the following table:
| period of time | T 1 | T 2 | T 3 | T 4 | T 5 | T 6 |
| Range of rotation angle | 0°-30° | 30°-60° | 60°-90° | 90°-120° | 120°-150° | 150°-180° |
| Period of time | T 7 | T 8 | T 9 | T 10 | T 11 | T 12 |
| Range of rotation | 180°-210° | 210°-240° | 240°-270° | 270°-300° | 300°-330° | 330°-360° |
Thus, the phase of the cogging torque can be determined according to the position angle of the rotor
Can be calculated from the following formula:
then, the expression of the cogging torque is:
after obtaining the amplitude and phase of the 12 th order cogging torque, we will calculate the amplitude and phase of the desired input current so that it is in phase opposition to the ripple torque generated by the back emf and the same amplitude as the cogging torque.
In the testing process of each working point, the rotating speed of the motor is set through the permanent magnet synchronous motor controller, and the corresponding load is set.
Starting a motor, slowly loading the motor to the set load, and measuring torque fluctuation through a small-range torque sensor after the rotating speed of the motor tends to be stable; the measurement is repeated for 30 operating points.
And carrying out Fourier transform on the torque ripple measured at each rotating speed working point, extracting the torque ripple amplitude of 12 orders, and taking the torque ripple amplitude as the amplitude of the cogging torque studied by the user.
Then the rotating speed omega of each working point is calculated ri Torque amplitude T of tooth socket cog12 Fitting a polynomial of the form:
the polynomial fit is preset in the harmonic current calculation module.
FIG. 4 is a harmonic current calculation module, a motor rotor position and speed signal obtained by a synovial observer
Respectively, for calculating the magnitude and phase of the cogging torque.
Will be provided with
Substituting into the fitting polynomial to calculate the amplitude of the cogging torque.
According to the position angle of the rotor
Determining the phase of the cogging torque
Can be calculated from the following formula：
Then, the expression of the cogging torque is:
and calculating corresponding harmonic current according to the calculated cogging torque and the harmonic counter electromotive force observed by the extended state observer, and using the harmonic current to generate ripple torque to counteract the 12-order cogging torque of the motor.
And under the condition that harmonic counter electromotive force acquired by the extended counter electromotive force observer is subjected to coordinate transformation to a three-phase stationary coordinate system, each counter electromotive force expression after the initial phase of each order of harmonic counter electromotive force is considered is as follows:
in the formula (I), the compound is shown in the specification,
and
the initial phases of the 5 th and 7 th harmonic back emf of each phase, respectively.
Assume that the harmonic current expressions of the phases introduced are as follows:
in the formula (I), the compound is shown in the specification,
and
the initial phases of the 5 th and 7 th harmonic currents, respectively.
The expression for the 6 th and 12 th ripple torques generated by the harmonic current in combination with the harmonic back emf is as follows:
in the formula (I), the compound is shown in the specification,
and
the initial phases of the ripple torque are 6 th and 12 th, respectively, and are determined by the initial phases of the harmonic current and the harmonic voltage.
We adjust the harmonic current i 5 And i 7 The amplitude and the phase of the ripple torque are equal to the cogging torque in 12 orders, and the phase is opposite to the cogging torque, so that the purpose of reducing the cogging torque pulsation is achieved. While avoiding the introduction of harmonic currents i 5 And i 7 Increase ripple torque of 6 orders, and
part of the 6 th ripple torque is an inherent value generated by harmonic back electromotive force and primary current and cannot be adjusted by adjusting i 5 And i 7 Cancellation is performed so that it is not taken into account, only the harmonic current i 5 And i 7 The ripple torques of the 6 th order generated respectively can be cancelled out. In summary, the induced harmonic current i is required 5 And i 7 The following two equations need to be satisfied:
so the harmonic current i is introduced 5 And i 7 The ripple torque generated needs to satisfy the following two sets of equations:
from the first set of equations i can be derived 5 And i 7 And the relationship between the initial phases of the harmonic currents of the respective orders is as follows:
in the second set of equations, the initial phase parameters of each phase of each order of back electromotive force are too much to make the equations difficult to solve, so we simplify the initial phase parameters and make the following estimation calculation:
will be provided with
And with
As initial phases of the 5 th order back electromotive force and the 7 th order back electromotive force of each phase,
and
i is obtained by combining the first set of equations as the initial phase of the 5 and 7 order currents of each phase to simplify calculation 5 And i 7 And the relationship between the initial phases of the harmonic currents of each order, the simplified equation is as follows:
in order to make the ripple torque generated by the input harmonic current and harmonic counter electromotive force cancel out the cogging torque rather than the phase gain, the phase of the 7 th order current harmonic should satisfy the following condition:
when in use
Then, a corresponding solution can be obtained.
Available i 5 And i 7 The expression for the initial phase of the order harmonic current is as follows:
i 5 and i 7 The expression for the order harmonic current magnitude is as follows:
in summary, the expression of the harmonic current to be input is calculated as follows:
converting the three-phase harmonic current obtained by calculation into 5 and 7 harmonic currents i on a d-q axis coordinate system after coordinate transformation d5 And i q5 And i d7 And i q7 。
And then inputting the harmonic current after coordinate transformation into a harmonic voltage calculation module, wherein the calculation formula of 5 th and 7 th harmonic voltages obtained according to a stator voltage formula is as follows:
in the formula u d5 、u q5 、u d7 、u q7 And inputting the harmonic voltage generated by calculation into a control link for 5 and 7 harmonic voltages on the d-q axis, thereby finishing the process of restraining the cogging torque by the ripple torque.
In the description of the specification, reference to the description of "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" or the like means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.
Claims (8)
1. A permanent magnet synchronous motor torque ripple suppression method based on harmonic injection and a torque sensor is characterized by comprising a back electromotive force observation module, a harmonic current calculation module, a harmonic voltage calculation module and a torque measurement module; wherein the torque measurement module is used for acquiring relevant data; the counter electromotive force observation module is used for observing the 5 th and 7 th harmonic counter electromotive force e of the permanent magnet synchronous motor 5 、e 7 Observing, inputting the harmonic current into a harmonic current calculation module to participate in calculation; a fitting polynomial between a tooth space torque amplitude and the motor rotating speed is preset in the harmonic current calculation module; calculating the amplitude and the phase of the input harmonic current in a harmonic current calculation module, and calculating by a harmonic voltage calculation module to obtain corresponding harmonic voltage;
the amplitude and phase of the harmonic current are specifically:
i 5 and i 7 The expression for the order harmonic current magnitude is as follows:
i 5 and i 7 The expression for the initial phase of the order harmonic current is as follows:
in the formula i 5 、i 7 Are respectively provided withAre the calculated amplitudes of the 5 th and 7 th compensation harmonic currents,
respectively, the calculated 5 th and 7 th compensation harmonic current phases, omega r Is the mechanical angular velocity, T, of the rotor of the motor cog12 、
Amplitude and phase of the cogging torque, e, 12 times respectively 5 、e 7 Respectively the harmonic counter electromotive force amplitudes of 5 th order and 7 th order observed by the counter electromotive force observation module,
the harmonic counter electromotive force phases of 5 th and 7 th order are respectively observed by a counter electromotive force observation module;
specifically, obtaining a fitting polynomial of the cogging torque amplitude and the motor rotating speed: directly measuring the amplitude of the specific-order cogging torque ripple at different rotating speed working points by using a balanced measurement method based on a torque sensor, and fitting the amplitude into a polynomial; electric angle of motor rotor obtained according to sliding film observer
The calculated cogging torque phase is obtained, and the amplitude and the phase of the cogging torque of a specific order are obtained.
2. The harmonic injection and torque sensor based permanent magnet synchronous motor torque ripple suppression method according to claim 1, characterized in that the rotor angle of a 4-pole 12-slot permanent magnet synchronous motor is calculated by a slip film observer on top of the SMO based position sensorless motor control system
And the rotational speed
Rotational speed
Obtaining a tooth space torque amplitude value and a rotor angle by combining a 12-time tooth space torque amplitude value fitting polynomial
A phase for calculating a cogging torque; and observing 6-order harmonic counter electromotive force by adopting an extended state observer, inputting the observed result into a harmonic current calculation module for calculating the harmonic current required for generating the ripple torque for offsetting the cogging torque, and calculating and injecting corresponding harmonic voltage by using a harmonic voltage calculation module.
3. The harmonic injection and torque sensor based permanent magnet synchronous motor torque ripple suppression method according to claim 1, characterized in that two extended state observers are used to observe 6 th harmonic back electromotive force on d-axis and q-axis respectively;
the equation of state of the d-axis of the permanent magnet synchronous motor can be expressed as:
in the formula (I), the compound is shown in the specification,
is the differential of the d-axis current, L d Is d-axis inductance, u d Is d-axis voltage, E dn Is the harmonic voltage on the d-axis, k d Is the d-axis known disturbance, and the expression is:
in the formula (I), the compound is shown in the specification,R s is stator resistance, ω is electrical angular velocity, L q Is a q-axis inductance;
the expression of the extended state observer ESO-d for the d-axis is:
Δ d1 ＝z d1 -i d
in the formula, z d1 Is d-axis current i d Observed value of (a), z d2 Is composed of
Observed value of (a), z d3 Is a d-axis third observed variable, z d4 Is the fourth observed variable of the d-axis, z d5 For the fifth observed variable of the d-axis,
is z d1 The differential of (a) is determined,
is z d2 The differential of (a) is determined,
is z d3 The differential of (a) is determined,
is z d4 The differential of (a) is determined,
is z d5 Differential of, Δ d1 Is z d1 And d-axis current i d Error of (1), beta d1 Is the d-axis first gain factor, beta d2 Is a d-axis second gain factor, beta d3 Is a d-axis third gain factor, beta d4 Is a d-axis fourth gain factor, β d5 A fifth gain factor for the d-axis;
the d-axis 6 harmonic back electromotive force observed by an ESO-d extended state observer can be expressed as:
E d6 ＝L d z d2
the state equation of the q-axis of the permanent magnet synchronous motor can be expressed as:
in the formula (I), the compound is shown in the specification,
is the differential of the q-axis current, L q Is the q-axis inductance, u q Is the q-axis voltage, E qn Is the harmonic voltage on the q-axis, k q Is a q-axis known disturbance, the expression:
in the formula, λ d Is the flux linkage dc component;
the expression of the extended state observer ESO-q for the q-axis is:
Δ q1 ＝z q1 -i q
in the formula, z q1 Is q-axis current i q Observed value of (a), z q2 Is composed of
The observed value of (a) is a q-axis third observed variable, is a q-axis fourth observed variable, is a q-axis fifth observed variable,
is z q1 The differential of (a) is determined,
is z q2 The differential of (a) is determined,
is z q3 The differential of (a) is determined,
is z q4 The differential of (a) is obtained by differentiating,
is z q5 Differential of, Δ q1 Is z q1 And q-axis current i q Error of (1), beta q1 Is the first gain factor of q-axis, beta q2 Is a q-axis second gain factor, beta q3 Is the q-axis third gain factor, beta q4 Is the q-axis fourth gain factor, beta q5 A q-axis fifth gain factor;
the q-axis 6 harmonic back electromotive force observed by an ESO-q extended state observer can be expressed as:
E q6 ＝L q z q2
after 6 harmonic counter electromotive force on the d-q axis is obtained, coordinate transformation is carried out on the counter electromotive force, and the counter electromotive force is converted into 5 harmonic counter electromotive force E on a three-phase static coordinate system a5 ,E b5 ,E c5 Counter electromotive force E of harmonic 7 a7 ,E b7 ,E c7 And 5, 7 harmonic counter electromotive forces are input into the harmonic current calculation module to participate in calculation.
4. The harmonic injection and torque sensor based torque ripple suppression method of the PMSM of claim 1, wherein the motor rotor speed
And 12 times of cogging torque amplitude T cog12 And fitting a polynomial, namely obtaining the amplitude of 12-order cogging torque at different rotating speeds by using a torque sensor-based balanced cogging torque measurement method, fitting the polynomial into the polynomial, and presetting the polynomial in a harmonic current calculation module.
5. The harmonic injection and torque sensor based PMSM torque ripple suppression method of claim 4, wherein rotor speed
And 12 times of cogging torque amplitude T cog12 The polynomial form is as follows:
in the formula, D i Constant values representing the fitted terms of a plurality of terms, the terms being represented by D i Respectively corresponding to the rotor speed
The products of the powers of the two are added; constant value of polynomial is determined by rotor speed
And 12 times of cogging torque amplitude T cog12 And fitting to obtain.
6. The harmonic injection and torque sensor based permanent magnet synchronous motor torque ripple suppression method of claim 1, wherein the motor rotor position and speed signals obtained by a synovial observer
Respectively used for calculating the amplitude and phase of the cogging torque
Substituting the fitting polynomial into the fitting polynomial to calculate the amplitude of the cogging torque;
according to the position angle of the rotor
Determining the phase of the cogging torque
Can be calculated from the following formula:
then, the expression of the cogging torque is:
7. the method for suppressing torque ripple of a permanent magnet synchronous motor based on harmonic injection and a torque sensor according to claim 1, wherein the calculated cogging torque is combined with the harmonic back electromotive force observed by an extended state observer to calculate the corresponding harmonic current for generating 12-order ripple torque to counteract the 12-order cogging torque of the motor, and the harmonic back electromotive force obtained by the extended back electromotive force observer is coordinate-transformed into a three-phase stationary coordinate system, and each back electromotive force expression after considering the initial phase of each order of harmonic back electromotive force is as follows:
in the formula, e 1 、e 5 、e 7 The magnitudes of the fundamental back emf and the 5 th and 7 th harmonic back emf respectively,
and
the initial phase, omega, of the counter electromotive force of the 5 th and 7 th harmonics of each phase, respectively e Is the electrical angular velocity of the motor;
assume that the harmonic current expressions of the phases introduced are as follows:
in the formula i 1 、i 5 、i 7 The magnitudes of the fundamental current and the 5 th and 7 th harmonic currents respectively,
and
initial phases of 5 th and 7 th harmonic currents, respectively;
the expression for the 6 th and 12 th ripple torques generated by the harmonic current in combination with the harmonic back emf is as follows:
in the formula, ω r Is the mechanical rotating speed of the motor,
and
the initial phases of the ripple torque of 6 times and 12 times are respectively determined by the initial phases of the harmonic current and the harmonic voltage;
by regulating harmonic current i 5 And i 7 The amplitude and the phase of the ripple torque are equal to the cogging torque in the 12 th order, and the phase is opposite to the cogging torque; while avoiding the introduction of harmonic currents i 5 And i 7 Increase ripple torque of 6 orders, and
part of the 6 th ripple torque is an inherent value generated by harmonic back electromotive force and primary current and cannot be adjusted by adjusting i 5 And i 7 Cancellation is performed so that only the harmonic current i is disregarded 5 And i 7 Respectively generating 6-order ripple torque to counteract each other; in summary, the introduced harmonic current i 5 And i 7 The following two equations need to be satisfied:
wherein, T cog12 12 cogging torque amplitudes;
so the harmonic current i is introduced 5 And i 7 The ripple torque generated needs to satisfy the following two sets of equations:
from the first set of equations i can be derived 5 And i 7 And the relationship between the initial phases of the harmonic currents of the respective orders is as follows:
in the second set of equations, the initial phase parameters are simplified to make the following estimation calculation because the initial phase parameters of each order back electromotive force of each phase are too much to make the equations difficult to solve:
in the formula (I), the compound is shown in the specification,
and
initial phases of 5 th and 7 th harmonic back electromotive force of each phase respectively
Will be provided with
And
as initial phases of the 5 th order back electromotive force and the 7 th order back electromotive force of each phase,
and with
I is obtained by combining the first set of equations as the initial phase of the 5 and 7 order currents of each phase to simplify calculation 5 And i 7 And the relationship between the initial phases of the harmonic currents of each order, the simplified equation is as follows:
in order to make the ripple torque generated by the input harmonic current and harmonic counter electromotive force cancel out the cogging torque rather than the phase gain, the phase of the 7 th order current harmonic should satisfy the following condition:
when in use
Then, a corresponding solution can be obtained;
available i 5 And i 7 The expression for the initial phase of the order harmonic current is as follows:
i 5 and i 7 The expression for the order harmonic current magnitude is as follows:
in summary, the expression of the harmonic current to be input is calculated as follows:
converting the three-phase harmonic current obtained by calculation into 5 and 7 harmonic currents i on a d-q axis coordinate system after coordinate transformation d5 And i q5 And i d7 And i q7 。
8. The method for suppressing the torque ripple of the permanent magnet synchronous motor based on the harmonic injection and the torque sensor as claimed in claim 7, wherein the harmonic current after the coordinate transformation is input into a harmonic voltage calculation module, and the calculation formula of the harmonic voltage of 5 th order and the harmonic voltage of 7 th order obtained according to the stator voltage formula is as follows:
in the formula, R s Is the resistance, L, of each phase winding d 、L q D-axis inductance and q-axis inductance, omega, of the motor respectively e Is the electrical angular velocity of the motor, u d5 、u q5 、u d7 、u q7 Synthesizing the generated 5 th and 7 th harmonic voltages into d-axis compensation voltage u for the 5 th and 7 th harmonic voltages on the d-q axis d-c And q-axis compensation voltage u q-c And inputting the signals into a control link so as to finish the process of restraining the cogging torque through the ripple torque.
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