CN116032169B - Torque ripple suppression method for self-adaptive anti-interference control high-speed permanent magnet synchronous motor - Google Patents
Torque ripple suppression method for self-adaptive anti-interference control high-speed permanent magnet synchronous motor Download PDFInfo
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Abstract
The invention discloses a torque ripple suppression method of a self-adaptive anti-interference control high-speed permanent magnet synchronous motor, which specifically comprises the following steps: step 1, establishing a torque ripple model caused by non-ideal factors of a high-speed permanent magnet synchronous motor driving system; step 2, constructing a state equation of a high-speed permanent magnet synchronous motor driving system through the torque ripple model obtained in the step 1; and 3, establishing an adaptive disturbance rejection controller to suppress torque ripple by the state equation obtained in the step 2. The problem that the conventional extended state observer is difficult to inhibit periodic torque ripple in torque ripple of the high-speed permanent magnet synchronous motor driving system is solved.
Description
Technical Field
The invention belongs to the technical field of high-speed permanent magnet synchronous motor control, and relates to a torque ripple suppression method of a self-adaptive anti-interference control high-speed permanent magnet synchronous motor.
Background
The high-speed permanent magnet synchronous motor has high rotating speed, small volume and high power density, and the rotor is directly connected with a high-speed load, so that the complexity and redundancy of the system structure are reduced, the integration level and reliability of the system are improved, and the high-speed permanent magnet synchronous motor has important research prospect and wide application value in the fields of military, aerospace, industry, medical treatment, civil use and the like. The torque ripple is generated by the high-speed permanent magnet synchronous motor driving system due to the factors of magnetic saturation characteristics, assembly errors, current deviation in control, harmonic waves and the like of the high-speed permanent magnet synchronous motor. Torque ripple of the high-speed permanent magnet synchronous motor can reduce the service performance and service life of equipment, for example, torque ripple can reduce the machining precision of a numerical control machine tool, the running stability of an electric automobile, the positioning precision of a robot and the like. Therefore, the key to improving the service performance and prolonging the service life of equipment containing the high-speed permanent magnet synchronous motor driving system is to restrain torque ripple of the high-speed permanent magnet synchronous motor driving system and improve the torque quality of the driving system.
At present, in the torque ripple suppression method of the high-speed permanent magnet synchronous motor driving system, the extended state observer observes the system total disturbance as an extended state variable of the system by regarding the nonlinear dynamics, parameter uncertainty and external disturbance in the system as the system total disturbance, and does not depend on an accurate mathematical model of a controlled object, so that the disturbance rejection capability is high, and the method has wide research and application. However, the extended state observer has a low-pass filter characteristic, and the torque ripple includes a non-periodic low-frequency torque ripple and a periodic torque ripple, the frequency of which increases with an increase in the frequency at which the motor operates, resulting in difficulty in suppressing the periodic torque ripple by the extended state observer.
Disclosure of Invention
The invention aims to provide a torque ripple suppression method for a self-adaptive anti-interference control high-speed permanent magnet synchronous motor, which solves the problem that the conventional extended state observer is difficult to suppress periodic torque ripples in torque ripples of a high-speed permanent magnet synchronous motor driving system.
The technical scheme adopted by the invention is that the torque ripple suppression method of the high-speed permanent magnet synchronous motor for self-adaptive anti-interference control specifically comprises the following steps:
step 1, establishing a torque ripple model caused by non-ideal factors of a high-speed permanent magnet synchronous motor driving system;
step 2, constructing a state equation of a high-speed permanent magnet synchronous motor driving system through the torque ripple model obtained in the step 1;
and 3, establishing an adaptive disturbance rejection controller to suppress torque ripple by the state equation obtained in the step 2.
The invention is also characterized in that:
the specific process of the step 1 is as follows:
assuming that only a-phase and b-phase currents are sampled in the current sampling process, torque ripple caused by a current sampling direct current bias error is shown in the following formula (1):
wherein ,ΔT1 Is the torque ripple caused by the current sampling DC offset error, K is the torque coefficient, Δi a 、Δi a Direct current bias error, omega, is sampled for a phase and b phase currents respectively r Is the operating angular frequency of the motor,is the initial phase angle;
the torque ripple caused by the current sample scaling error is shown in equation (2) below:
wherein ,ΔTs Is the torque ripple caused by current sampling scaling error, I is the amplitude of the phase current, K a 、K b The a-phase and b-phase current samples scale errors respectively,
torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics is shown in the following formula (3):
wherein ,ΔTq Is torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics,6 th and 12 th torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics, respectively, < >>Respectively are provided withIs the initial phase angle of 6 th and 12 th torque ripple caused by cogging torque, flux linkage harmonic wave and voltage harmonic wave, T 6 、T 12 The amplitudes of 6 and 12 torque ripples caused by cogging torque, flux linkage harmonics, voltage harmonics, respectively.
The specific process of the step 2 is as follows:
the dynamics equation of the high-speed permanent magnet synchronous motor is shown in the following formula (4):
where p is the differential operator, ω m Is the mechanical angular frequency, B is the viscous coefficient of friction, c= (3/2J) n p ψ f sin beta, J is moment of inertia, n p Is the polar logarithm, ψ f Is the permanent magnet flux linkage, beta is the included angle between the stator flux linkage and the permanent magnet flux linkage, delta T e ＝(3/2J)n p (L d -L q )I 2 sinβcosβ，L d Is d-axis inductance, L q Is the q-axis inductance;
considering the torque ripple of formulas (1) to (3), the dynamic formula (4) is expressed as the following formula (5):
wherein Δc=c-c 0 ，c 0 C is calculated by taking nominal motor parameters, and d is unknown aperiodic disturbance;
the frequency characteristic equation (5) according to the disturbance can be expressed as the following equation (6):
pω m ＝c 0 I+d a +d 1 +d 2 +d 6 +d 12 (6)；
wherein ,non-periodic disturbance, +.>Is 1-cycle ripple,/o>Is a 2-cycle ripple,/->Is 6-cycle ripple->Is 12 cycles of ripple;
the total disturbance d in the formula (6) t ＝d a +d 1 +d 2 +d 6 +d 12 As an extended state variable, the kinetic equation (6) with the total disturbance can be expressed as an extended state equation form as shown in the following equation (7):
where z is the total disturbance d t Is a derivative of (a).
The specific process of the step 3 is as follows:
step 3.1, establishing an adaptive disturbance rejection controller to inhibit torque ripple through the state equation obtained in the step 2;
step 3.2, designing a nonlinear function f in the adaptive immunity controller in step 3.1;
step 3.3, designing a period disturbance estimator g in the adaptive immunity controller 1 、g 2 、g 6 、g 12 。
The specific process of the step 3.1 is as follows:
the adaptive immunity controller is constructed through the formula (7) as shown in the following formula (8):
wherein ,is the estimated mechanical angular frequency, Δω m Is the difference between the estimated mechanical angular frequency and the actual angular frequency,/or->Is the estimated total disturbance, beta 1 、β 2 Is an adjustable parameter, f is a nonlinear function, g 1 、g 2 、g 6 、g 12 The periodic disturbance estimators respectively estimate 1 time, 2 times, 6 times and 12 times of torque ripple.
The specific process of the step 3.2 is as follows:
the nonlinear function f in the designed adaptive disturbance rejection controller is shown in the following formula (9):
wherein χ is an adjustable parameter, the greater χ, the same Δω m Under the input, the larger the value of the nonlinear function f is, the better the rapidity of disturbance estimation is, however, the larger χ is easy to cause system instability; lambda is an adjustable parameter.
The specific process of the step 3.3 is as follows:
designed period disturbance estimator g 1 、g 2 、g 6 、g 12 The following formula (10) shows:
wherein k is an adjustable parameter; η is the parameter to be adjusted,is the width of the center frequency, +.>The adjusting method is shown in the following formula (11):
compared with the torque ripple suppression method of the traditional extended state observer, the adaptive anti-interference controller adopted by the invention can suppress not only non-periodic torque ripple but also periodic torque ripple, and can effectively suppress the periodic torque ripple which changes rapidly even if the high-speed permanent magnet synchronous motor runs at high speed, and the designed periodic disturbance estimator can adjust adjustable parameters through self adaptionStability and rapidity of estimating periodic torque ripple are improved. Meanwhile, the designed nonlinear function f has a robust effect on large errors, torque ripple waves can be effectively restrained, and meanwhile the risk of system instability is not increased. The problem that the conventional extended state observer is difficult to inhibit periodic torque ripple in torque ripple of the high-speed permanent magnet synchronous motor driving system is solved.
Drawings
FIG. 1 is a block diagram of a vector control system employed in the torque ripple suppression method of a high-speed permanent magnet synchronous motor for adaptive immunity control of the present invention;
FIG. 2 is a block diagram of an adaptive immunity controller employed in the torque ripple suppression method of the high-speed permanent magnet synchronous motor of the adaptive immunity control of the present invention;
FIG. 3 is a simulation of a feedback velocity waveform without employing the method of the present invention;
FIG. 4 is a simulation of electromagnetic torque waveforms without employing the method of the present invention;
FIG. 5 is a simulation diagram of a feedback speed waveform of a torque ripple suppression method of a high-speed permanent magnet synchronous motor employing adaptive immunity control of the present invention;
fig. 6 is a simulation diagram of electromagnetic torque waveforms of a torque ripple suppression method of a high-speed permanent magnet synchronous motor employing adaptive immunity control according to the present invention.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention discloses a torque ripple suppression method of a self-adaptive anti-interference control high-speed permanent magnet synchronous motor, wherein a block diagram of a vector control system adopted by the method is shown in figure 1, and the method is implemented specifically according to the following steps:
step 1, a torque ripple model caused by non-ideal factors of a high-speed permanent magnet synchronous motor driving system is established, and the torque ripple model specifically comprises the following steps:
assuming that only a-phase and b-phase currents are sampled in the current sampling process, torque ripple caused by a current sampling direct current bias error is shown in the following formula (1):
wherein ,ΔT1 Is the torque ripple caused by the current sampling DC offset error, K is the torque coefficient, Δi a 、Δi a Direct current bias error, omega, is sampled for a phase and b phase currents respectively r Is the operating angular frequency of the motor,is the initial phase angle.
The torque ripple caused by the current sample scaling error is shown in equation (2) below:
wherein ,ΔTs Is the torque ripple caused by current sampling scaling error, I is the amplitude of the phase current, K a 、K b The a-phase and b-phase current samples scale errors respectively,
torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics is shown in the following formula (3):
wherein ,ΔTq Is torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics,6 th and 12 th torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics, respectively, < >>The initial phase angles of 6 times and 12 times of torque ripple waves caused by cogging torque, flux linkage harmonic waves and voltage harmonic waves are respectively T 6 、T 12 The amplitudes of 6 and 12 torque ripples caused by cogging torque, flux linkage harmonics, voltage harmonics, respectively.
Step 2, constructing a state equation of a high-speed permanent magnet synchronous motor driving system through the torque ripple model obtained in the step 1, wherein the state equation is specifically as follows:
the dynamics equation of the high-speed permanent magnet synchronous motor is shown in the following formula (4):
where p is the differential operator, ω m Is the mechanical angular frequency, B is the viscous coefficient of friction, c= (3/2J) n p ψ f sin beta, J is moment of inertia, n p Is the polar logarithm, ψ f Is the permanent magnet flux linkage, beta is the included angle between the stator flux linkage and the permanent magnet flux linkage, delta T e ＝(3/2J)n p (L d -L q )I 2 sinβcosβ，L d Is d-axis inductance, L q Is the q-axis inductance.
Considering the torque ripple of formulas (1) to (3), the dynamic formula (4) is expressed as the following formula (5):
wherein Δc=c-c 0 ，c 0 C is calculated taking nominal motor parameters and d is an unknown aperiodic disturbance.
Since the torque ripple amplitude value exceeding 12 times is small, it can be ignored, and the frequency characteristic equation (5) according to the disturbance can be expressed as the following equation (6):
pω m ＝c 0 I+d a +d 1 +d 2 +d 6 +d 12 (6)；
wherein ,non-periodic disturbance, +.>Is 1-cycle ripple,/o>Is a 2-cycle ripple,/->Is 6-cycle ripple->Is 12 cycles ripple.
The total disturbance d in the formula (6) t ＝d a +d 1 +d 2 +d 6 +d 12 As an extended state variable, the kinetic equation (6) with the total disturbance can be expressed as an extended state equation form as shown in the following equation (7):
where z is the total disturbance d t Is a derivative of (a).
Step 3, the adaptive disturbance rejection controller shown in fig. 2 is built according to the state equation obtained in the step 2 to suppress torque ripple, specifically:
step 3.1, establishing an adaptive disturbance rejection controller shown in figure 2 to inhibit torque ripple through the state equation obtained in the step 2;
the adaptive immunity controller is constructed through the formula (7) as shown in the following formula (8):
wherein ,is the estimated mechanical angular frequency, Δω m Is the difference between the estimated mechanical angular frequency and the actual angular frequency,/or->Is the estimated total disturbance, beta 1 、β 2 Is an adjustable parameter, f is a nonlinear function, g 1 、g 2 、g 6 、g 12 The periodic disturbance estimators respectively estimate 1 time, 2 times, 6 times and 12 times of torque ripple.
Step 3.2, designing a nonlinear function f in the adaptive immunity controller in step 3.1;
the nature of the nonlinear function f in the adaptive immunity controller determines the adaptive immunity controller estimate the aperiodic disturbance d a The nonlinear function f should have the characteristic of small error and large gain, and the nonlinear function f in the designed adaptive disturbance rejection controller is shown in the following formula (9):
wherein χ is an adjustable parameter, the greater χ, the same Δω m The larger the value of the nonlinear function f, the better the rapidity of disturbance estimation, however, too large χ is liable to cause system instability, taking χ=0.1. λ is an adjustable parameter, and the smaller λ value has faster dynamic response, but too small λ value causes system oscillation, conversely, the larger λ value has smaller overshoot, but the slower dynamic performance, taking λ=0.2+0.02|Δω m If λ is greater than 0.7, λ=0.7.
Step 3.3, designing a period disturbance estimator g in the adaptive immunity controller 1 、g 2 、g 6 、g 12 ；
Designed period disturbance estimator g 1 、g 2 、g 6 、g 12 The following formula (10) shows:
wherein k is an adjustable parameter, the value of k mainly affects the amplitude at the center frequency, taking k=60; η is an adjustable parameter, the larger η is, the better the system stability is, but the η makes the center frequency shift the disturbance frequency, so that the estimation performance of the period disturbance estimator is reduced, and η=0.2 is taken;is the width of the center frequency, +.>The larger the amplitude and phase variation around the center frequency is smaller, the stronger the robustness to the center frequency is, but the frequency selecting performance is lowered, the noise suppressing ability is lowered, and the motor should be enlarged when it is dynamic +.>Increasing the robustness to the center frequency increases the stability, and the motor should be turned down +.>Enhancing the noise suppression capacity, +.>The adjusting method is shown in the following formula (11):
the vector control system block diagram adopted by the high-speed permanent magnet synchronous motor torque ripple suppression method for the adaptive disturbance rejection control is shown in figure 1, and the system is formed by double-loop control of a rotating speed loop and a current loop through 3 PI regulators. The output of the rotating speed ring PI regulator is I pi . Mechanical angular frequency ω detected by encoder m And given the stator current I as an input to an adaptive immunity controller as shown in fig. 2, the output of the adaptive immunity controller is an estimate of the total disturbanceEstimating total disturbance->Divided by c 0 With a given stator current I output by a speed loop PI controller pi The addition results in a given stator current I. The given stator current I gives the given excitation current +.>And a given torque current>Given exciting current +.>And a given torque current>As an input to the current loop PI regulator, the output of the current regulator controls the power electronic converter.
Detecting the mechanical angular frequency omega of a rotor by mounting an encoder on the rotor shaft of a high-speed permanent magnet synchronous motor m And a mechanical position theta m Given mechanical angular frequency of rotating speed ringMechanical angular frequency omega detected by encoder m The difference is made and the difference is made,after passing through the rotating speed loop PI controller, a given stator current I is output pi The method comprises the steps of carrying out a first treatment on the surface of the Given the stator current I and the mechanical angular frequency ω detected by the encoder m As input to the adaptive immunity controller as shown in fig. 2, the output of the adaptive immunity controller is the estimated total disturbance +.>Estimating total disturbance->Divided by c 0 With a given stator current I output by a speed loop PI controller pi Adding to obtain a given stator current I; the given stator current I gives the given excitation current +.>And a given torque current>Stator current i of permanent magnet synchronous motor in three-phase static coordinate system is detected through current Hall sensor a 、i b 、i c The method comprises the steps of carrying out a first treatment on the surface of the Detected three-phase stator current i a 、i b 、i c Conversion to a current value i in a two-phase stationary coordinate system by abc/αβ transformation α 、i β ；i α 、i β Conversion to a current value i in a two-phase synchronous rotating coordinate system by alpha beta/dq conversion d 、i q The method comprises the steps of carrying out a first treatment on the surface of the Given exciting current +.>And feedback current i d Difference is made, d-axis voltage is output through a current loop PI controller>Given exciting current +.>And feedback current i q Difference making through current loop PI controlThe output q-axis voltage +.> Obtaining two-phase voltage u under two-phase static coordinate system through dq/alpha beta transformation α 、u β And then, a three-phase inverter is controlled through SVPWM modulation, and finally, a permanent magnet synchronous motor is driven to work.
FIG. 3 is a feedback velocity waveform without employing the method of the present invention; FIG. 4 is an electromagnetic torque waveform without employing the method of the present invention; FIG. 5 is a feedback velocity waveform employing the method of the present invention; fig. 6 is an electromagnetic torque waveform employing the method of the present invention.
Parameters of the high-speed permanent magnet synchronous motor used in the simulations of fig. 3 to 6 are shown in table 1. In the simulation results of fig. 3 to 6, the motor was set to a rated rotational speed of 15000rpm, and the load drawn by the motor was set to a rated load of 1.75n.m.
As can be seen by comparing fig. 3 and fig. 5, the method proposed by the present invention can significantly reduce the rotational speed ripple. As can be seen from comparing fig. 4 and fig. 6, the method proposed by the present invention can significantly reduce torque ripple. The simulation result shows that the torque ripple suppression method for the self-adaptive anti-interference control high-speed permanent magnet synchronous motor can effectively suppress rotational speed ripple and torque ripple.
Table 1 parameters of high speed permanent magnet synchronous motor
| Parameters (parameters) | Numerical value | Parameters (parameters) | Numerical value |
| Rated power | 2.2kW | Rated torque | 1.75N.m |
| Polar logarithm | 2 | Rated current | 11.3A |
| Rated rotational speed | 15000rpm | Rated frequency | 500Hz |
Claims (1)
1. The torque ripple suppression method of the self-adaptive anti-interference control high-speed permanent magnet synchronous motor is characterized by comprising the following steps of: the method specifically comprises the following steps:
step 1, establishing a torque ripple model caused by non-ideal factors of a high-speed permanent magnet synchronous motor driving system;
the specific process of the step 1 is as follows:
assuming that only a-phase and b-phase currents are sampled in the current sampling process, torque ripple caused by a current sampling direct current bias error is shown in the following formula (1):
wherein ,ΔT1 Is the torque ripple caused by the current sampling DC offset error, K is the torque coefficient, Δi a 、Δi a Direct current bias error, omega, is sampled for a phase and b phase currents respectively r Is the operating angular frequency of the motor,is the initial phase angle;
the torque ripple caused by the current sample scaling error is shown in equation (2) below:
wherein ,ΔTs Is the torque ripple caused by current sampling scaling error, I is the amplitude of the phase current, K a 、K b The a-phase and b-phase current samples scale errors respectively,
torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics is shown in the following formula (3):
wherein ,ΔTq Is torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics,6 th and 12 th torque ripple caused by cogging torque, flux linkage harmonics, voltage harmonics, respectively, < >>The initial phase angles of 6 times and 12 times of torque ripple waves caused by cogging torque, flux linkage harmonic waves and voltage harmonic waves are respectively T 6 、T 12 The amplitudes of 6 and 12 torque ripples caused by cogging torque, flux linkage harmonics, and voltage harmonics, respectively;
step 2, constructing a state equation of a high-speed permanent magnet synchronous motor driving system through the torque ripple model obtained in the step 1;
the specific process of the step 2 is as follows:
the dynamics equation of the high-speed permanent magnet synchronous motor is shown in the following formula (4):
where p is the differential operator, ω m Is the mechanical angular frequency, B is the viscous coefficient of friction, c= (3/2J) n p ψ f sin beta, J is moment of inertia, n p Is the polar logarithm, ψ f Is the permanent magnet flux linkage, beta is the included angle between the stator flux linkage and the permanent magnet flux linkage, delta T e ＝(3/2J)n p (L d -L q )I 2 sinβcosβ，L d Is d-axis inductance, L q Is the q-axis inductance;
considering the torque ripple of formulas (1) to (3), the dynamic formula (4) is expressed as the following formula (5):
wherein Δc=c-c 0 ，c 0 C is calculated by taking nominal motor parameters, and d is unknown aperiodic disturbance;
the frequency characteristic equation (5) according to the disturbance can be expressed as the following equation (6):
pω m ＝c 0 I+d a +d 1 +d 2 +d 6 +d 12 (6)；
wherein ,non-periodic disturbance, +.>Is 1-cycle ripple,/o>Is a 2-cycle ripple,/->Is 6-cycle ripple->Is 12 cycles of ripple;
the total disturbance d in the formula (6) t ＝d a +d 1 +d 2 +d 6 +d 12 As an extended state variable, the kinetic equation (6) with the total disturbance can be expressed as an extended state equation form as shown in the following equation (7):
where z is the total disturbance d t Is a derivative of (2);
step 3, the adaptive disturbance rejection controller is established to inhibit torque ripple according to the state equation obtained in the step 2;
the specific process of the step 3 is as follows:
step 3.1, establishing an adaptive disturbance rejection controller to inhibit torque ripple through the state equation obtained in the step 2;
the specific process of the step 3.1 is as follows:
the adaptive immunity controller is constructed through the formula (7) as shown in the following formula (8):
wherein ,is the estimated mechanical angular frequency, Δω m Is the difference between the estimated mechanical angular frequency and the actual angular frequency,/or->Is the estimated total disturbance, beta 1 、β 2 Is an adjustable parameter, f is a nonlinear function, g 1 、g 2 、g 6 、g 12 The periodic disturbance estimators are used for estimating torque ripple waves 1 time, 2 times, 6 times and 12 times respectively;
step 3.2, designing a nonlinear function f in the adaptive immunity controller in step 3.1;
the specific process of the step 3.2 is as follows:
the nonlinear function f in the designed adaptive disturbance rejection controller is shown in the following formula (9):
wherein χ is an adjustable parameter, the greater χ, the same Δω m Under the input, the larger the value of the nonlinear function f is, the better the rapidity of disturbance estimation is, however, the larger χ is easy to cause system instability; λ is an adjustable parameter;
step 3.3, designing a period disturbance estimator g in the adaptive immunity controller 1 、g 2 、g 6 、g 12 ；
The specific process of the step 3.3 is as follows:
designed period disturbance estimator g 1 、g 2 、g 6 、g 12 The following formula (10) shows:
wherein k is an adjustable parameter; η is the parameter to be adjusted,is the width of the center frequency, +.>The adjusting method is shown in the following formula (11):
and->
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| CN116032169A (en) | 2023-04-28 |
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