A Method for Estimating the Resonance Frequency of a Permanent Magnet Synchronous Motor Drive System

Abstract

The present invention discloses a method for estimating the resonance frequency of a permanent magnet synchronous motor drive system, specifically as follows: Establish a vector control model of the permanent magnet synchronous motor, transform the three-phase stator current into the d-q coordinate system, and based on the current under the d-q axis and the measured actual speed including the resonance component, build a second-order extended state observer according to the dynamic equation of the permanent magnet synchronous motor to obtain the observation error, that is, the resonance harmonic component; Build a single-phase enhanced phase-locked loop, input the resonance harmonic component into the single-phase enhanced phase-locked loop to obtain the estimated resonance angular frequency; Divide the estimated resonance angular frequency by 2π, that is, realize the estimation of the resonance frequency of the permanent magnet synchronous motor drive system. The present invention can be implemented in off-line simulation, on-line real-time simulation, and hardware-in-the-loop simulation systems, which can effectively reduce the computational burden of traditional resonance frequency estimation schemes; and the present invention can also maintain good estimation performance under dynamic conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of AC drive for electric traction, and particularly relates to a method for estimating the resonance frequency of a permanent magnet synchronous motor drive system. Background Art

[0002] In a permanent magnet synchronous motor drive system, mechanical resonance not only reduces the system performance but also causes mechanical structure fatigue and generates noise. This problem can be solved by changing the mechanical structure of the system, but this will greatly increase the cost. Another solution is to change the control means, such as feedforward compensation for torque ripple and using notch filters. It should be noted that this solution usually requires the resonance frequency. Resonance information can be obtained by adding additional sensors, such as acceleration sensors. However, in practice, due to the compact structure of the permanent magnet synchronous motor drive system, it is difficult to install acceleration sensors.

[0003] Some scholars have studied methods without acceleration sensors. Among them, the resonance frequency estimation method based on fast Fourier transform (FFT) has attracted the most attention. However, this method has a long time period, heavy computational burden, and is mostly used under steady-state conditions, which limits the application of this type of method. Summary of the Invention

[0004] In view of the deficiencies of the existing resonance frequency estimation methods, the purpose of the present invention is to provide a method for estimating the resonance frequency of a permanent magnet synchronous motor drive system applicable to offline simulation, online real-time simulation, and hardware-in-the-loop simulation systems, with small computational load and applicable to the resonance frequency estimation of permanent magnet synchronous motor drive systems under various working conditions.

[0005] To achieve the above-mentioned invention purpose, the present invention provides a method for estimating the resonance frequency of a permanent magnet synchronous motor drive system.

[0006] A method for estimating the resonance frequency of a permanent magnet synchronous motor drive system according to the present invention uses a second-order extended state observer to estimate the resonance harmonic components, and completes the estimation of the resonance frequency of the permanent magnet synchronous motor drive system through a single-phase enhanced phase-locked loop, specifically including the following steps:

[0007] Step 1: Establish a vector control model of the permanent magnet synchronous motor and calculate the resonance harmonic components.

[0008] Establish a vector control model of the permanent magnet synchronous motor, transform the three-phase stator current into the d-q coordinate system, and based on the dynamic equation of the permanent magnet synchronous motor, build a second-order extended state observer for the current under the d-q axis and the measured actual speed including resonance components, and obtain the observation error, that is, the resonance harmonic components.

[0009] Step 2: Build a single-phase enhanced phase-locked loop, input the resonant harmonic components into the single-phase enhanced phase-locked loop, and obtain the estimated resonant angular frequency.

[0010] Step 3: Divide the estimated resonant angular frequency by 2π, that is, the estimation of the resonant frequency of the permanent magnet synchronous motor drive system is realized.

[0011] Specifically, Step 1 is as follows:

[0012] The electromagnetic torque of the permanent magnet synchronous motor in the dq-axis synchronous rotating reference frame is expressed as:

[0013]

[0014] where: T e is the electromagnetic torque, n p is the number of pole pairs, ψ f is the magnetic flux linkage, L d , L q are the d-axis inductance and q-axis inductance respectively, i d , i q are the d-axis current component and q-axis current component respectively.

[0015] Subsequently, the mechanical dynamics of the permanent magnet synchronous motor is expressed as:

[0016]

[0017] where: a = 3n p ψ f / 2J, b = 3n p (L d -L q ) / 2J, c = B / J, d = n p / J; among them, ω r is the electrical angular velocity, J is the moment of inertia, T L is the load torque, and B is the friction coefficient;

[0018] After considering the disturbance of parameter changes, Equation (2) is rewritten as

[0019]

[0020] where Δa, Δb, Δc, and Δd are the disturbances caused by parameter changes;

[0021] Furthermore, it can be obtained that:

[0022]

[0023] where: z is the overall disturbance of the system, and further it can be obtained that:

[0024] z = Δai q +Δbid i q -(c + Δc)ω r -(d + Δd)T L (5)

[0025] Based on Equation (4), the disturbance observation scheme for the permanent magnet synchronous motor drive system based on the second-order extended state observer is designed as follows:

[0026]

[0027] where: β1, β2 are the gains of the second-order extended observer, e f is the observation error, and the gains of the second-order extended observer are configured as:

[0028]

[0029] where: ω o is the bandwidth of the second-order extended observer.

[0030] According to Equations (6) and (7), the transfer function of the second-order extended observer is obtained as:

[0031]

[0032] where: the superscript “^” represents the estimated value.

[0033] Thus, the resonant harmonic component is provided by the observation error of the second-order extended observer:

[0034]

[0035] where: ε h represents the resonant harmonic component.

[0036] Step 2 is specifically as follows:

[0037] Let:

[0038]

[0039] where U, ω, are the amplitude, angular frequency, and initial phase of the resonant harmonic component, respectively.

[0040] Subsequently,

[0041]

[0042] where: θ is the phase, ε h-est represents the single-phase enhanced phase-locked loop estimated value;

[0043] Furthermore, it can be obtained that:

[0044]

[0045] Step 3 is specifically as follows:

[0046] The resonance angular frequency estimated in Step 2 is calculated as shown in Equation (13) to obtain the resonance frequency of the permanent magnet synchronous motor drive system:

[0047]

[0048] where: is the estimated resonance frequency of the permanent magnet synchronous motor drive system.

[0049] The beneficial technical effects of the present invention are as follows:

[0050] 1. The present invention uses a second-order extended state observer to estimate the resonance harmonic components of the permanent magnet synchronous motor drive system, with a simple structure and small computational load.

[0051] 2. The present invention uses a second-order extended state observer to estimate the resonance harmonic components, which can maintain the estimation performance under the dynamic state of the motor. In addition, this method has good generality and can also be transplanted to other AC motor drive systems.

[0052] 3. The present invention uses a single-phase enhanced phase-locked loop to accurately estimate the resonance frequency and effectively reduce the influence of harmonics on the estimation performance. Description of the Drawings

[0053] Figure 1 is the schematic diagram of the resonance frequency estimation method for the permanent magnet synchronous motor drive system based on the second-order extended state observer implemented by the present invention.

[0054] Figure 2 is the block diagram of the second-order extended state observer structure implemented by the present invention.

[0055] Figure 3 is the block diagram of the structure of the single-phase enhanced phase-locked loop implemented by the present invention.

[0056] Figure 4 is the waveform diagram of the actual speed and the estimated speed of the second-order extended state observer under the condition that the permanent magnet synchronous motor drive system in the embodiment of the present invention simulates the mechanical resonance of the permanent magnet synchronous motor drive system by introducing a resonance harmonic with an amplitude of 1 and a frequency of 15 Hz in the Matlab / Simulink environment. The set speed is 800 r / min and the load is 400 N·m.

[0057] Figure 5In the embodiment of the present invention, for the permanent magnet synchronous motor drive system in the Matlab / Simulink environment, mechanical resonance of the permanent magnet synchronous motor drive system is simulated by introducing a resonance harmonic with an amplitude of 1 and a frequency of 15 Hz. The waveform diagram of the observation error, that is, the estimated resonance harmonic component, under the condition that the speed is set to 800 r / min and the load is 400 N·m.

[0058] Figure 6 In the embodiment of the present invention, for the permanent magnet synchronous motor drive system in the Matlab / Simulink environment, mechanical resonance of the permanent magnet synchronous motor drive system is simulated by introducing a resonance harmonic with an amplitude of 1 and a frequency of 15 Hz. The waveform diagram of the estimated resonance frequency under the condition that the speed is set to 800 r / min and the load is 400 N·m.

[0059] Figure 7 In the embodiment of the present invention, for the permanent magnet synchronous motor drive system in the Matlab / Simulink environment, mechanical resonance of the permanent magnet synchronous motor drive system is simulated by introducing a resonance harmonic with an amplitude of 1 and a frequency of 15 Hz. The waveform diagram of the actual speed and the estimated speed of the second-order extended state observer under the condition that the speed is increased and the load is 400 N·m.

[0060] Figure 8 In the embodiment of the present invention, for the permanent magnet synchronous motor drive system in the Matlab / Simulink environment, mechanical resonance of the permanent magnet synchronous motor drive system is simulated by introducing a resonance harmonic with an amplitude of 1 and a frequency of 15 Hz. The waveform diagram of the observation error, that is, the estimated resonance harmonic component, under the condition that the speed is increased and the load is 400 N·m.

[0061] Figure 9 In the embodiment of the present invention, for the permanent magnet synchronous motor drive system in the Matlab / Simulink environment, mechanical resonance of the permanent magnet synchronous motor drive system is simulated by introducing a resonance harmonic with an amplitude of 1 and a frequency of 15 Hz. The waveform diagram of the estimated resonance frequency under the condition that the speed is increased and the load is 400 N·m. Detailed implementation method

[0062] The following further elaborates on the present invention in detail in conjunction with the attached drawings and specific implementation methods.

[0063] The schematic diagram of the resonance frequency estimation method for a permanent magnet synchronous motor drive system of the present invention is as Figure 1 shown. That is, according to the dynamic equation model of the permanent magnet synchronous motor, a second-order extended state observer is established to obtain the estimated resonance harmonic component; on this basis, the estimated resonance harmonic component is input into a single-phase enhanced phase-locked loop, and finally the estimated resonance frequency is obtained by using the single-phase enhanced phase-locked loop. The structural diagram of the second-order extended state observer in the resonance frequency estimation method implemented by the present invention is asFigure 2 As shown, it is used to provide an estimated resonant harmonic component as the input signal of a single-phase enhanced phase-locked loop, so as to obtain the estimated resonant frequency.

[0064] A method for estimating the resonant frequency of a permanent magnet synchronous motor drive system according to the present invention specifically includes the following steps:

[0065] Step 1: Establish a vector control model of the permanent magnet synchronous motor and calculate the resonant harmonic component.

[0066] Establish a vector control model of the permanent magnet synchronous motor, transform the three-phase stator current into the d-q coordinate system, and build a second-order extended state observer based on the current in the d-q axis and the measured actual speed including the resonant component to obtain the observation error, that is, the resonant harmonic component.

[0067] The electromagnetic torque of the permanent magnet synchronous motor in the dq-axis synchronous rotating reference frame is expressed as:

[0068]

[0069] In the formula: T e is the electromagnetic torque, n p is the number of pole pairs, ψ f is the magnetic flux, L d , L q are the d-axis inductance and q-axis inductance respectively, i d , i q are the d-axis current component and q-axis current component respectively.

[0070] Subsequently, the mechanical dynamics of the permanent magnet synchronous motor is expressed as:

[0071]

[0072] In the formula: a = 3n p ψ f / 2J, b = 3n p (L d -L q ) / 2J, c = B / J, d = n p / J; where, ω r is the electrical angular velocity, J is the moment of inertia, T L is the load torque, and B is the friction coefficient;

[0073] After considering the disturbance of parameter variation, Equation (2) is rewritten as

[0074]

[0075] In the formula, Δa, Δb, Δc and Δd are the disturbances caused by parameter variation;

[0076] Furthermore, it can be obtained that:

[0077]

[0078] In the formula: z is the overall disturbance of the system, and further obtained:

[0079] z = Δai q +Δbi d i q -(c + Δc)ω r -(d + Δd)T L (5)

[0080] Based on Equation (4), the disturbance observation scheme of the permanent magnet synchronous motor drive system based on the second-order extended state observer is designed as:

[0081]

[0082] In the formula: β1, β2 are the gains of the second-order extended observer, e f is the observation error, and the gains of the second-order extended observer are configured as:

[0083]

[0084] In the formula: ω o is the bandwidth of the second-order extended observer.

[0085] According to Equation (6) and Equation (7), the transfer function of the second-order extended observer is obtained as:

[0086]

[0087] In the formula: the superscript "^" represents the estimated value.

[0088] It can be found that the second-order extended observer has a low-pass filtering characteristic, and the amplitude attenuation degree can be adjusted by ω o . Therefore, the observed speed may not include the high-frequency components of the actual speed, such as the resonance components of the permanent magnet synchronous motor drive system. In this way, the resonance harmonic components are provided by the observation error of the second-order extended observer:

[0089]

[0090] In the formula: ε h represents the resonance harmonic components.

[0091] Step 2: Build a single-phase enhanced phase-locked loop. The single-phase enhanced phase-locked loop of the present invention is as Figure 3 shown. Input the resonance harmonic components into the single-phase enhanced phase-locked loop to obtain the estimated resonance angular frequency.

[0092] Let:

[0093]

[0094] Wherein, U, ω, are respectively the amplitude, angular frequency and initial phase of the resonant harmonic component.

[0095] Subsequently,

[0096]

[0097] Wherein: θ is the phase, ε h-est represents the estimated value of the single-phase enhanced phase-locked loop;

[0098] Furthermore, it can be obtained that:

[0099]

[0100] Step 3: Divide the estimated resonant angular frequency by 2π, that is, the estimation of the resonant frequency of the permanent magnet synchronous motor drive system is realized.

[0101] The resonant angular frequency estimated in Step 2 is calculated as shown in Equation (13) to obtain the resonant frequency of the permanent magnet synchronous motor drive system:

[0102]

[0103] Wherein: is the estimated resonant frequency of the permanent magnet synchronous motor drive system.

[0104] By adopting the present invention, off-line simulation, on-line real-time simulation and hardware-in-the-loop simulation systems can realize the simulation of the permanent magnet synchronous motor drive system under steady-state conditions and dynamic conditions, and this resonant frequency estimation method has the characteristics of being easy to implement and having a small computational burden. More importantly, this scheme can effectively ensure the resonant frequency estimation performance under the dynamic conditions of the motor, making up for the problem of poor dynamic performance of the existing resonant frequency estimation methods. The established resonant frequency estimation method can be applied to all simulations and physical experimental studies of the permanent magnet synchronous motor drive system based on computer implementation, and can further be extended to other AC motor drive systems.

[0105] Based on the above model for simulation testing, the parameters of the permanent magnet synchronous motor are: stator resistance R s = 0.0459 Ω, d-axis inductance L d = 1.58 mH, q-axis inductance L q = 3.96 mH, permanent magnet flux linkage is ψ f= 0.6838 Wb, the introduced resonance harmonic amplitude is 1, and the frequency is 15 Hz. The estimated simulation results of the speed resonance frequency of the permanent magnet synchronous motor drive system under different working conditions are as Figures 4 - 9 shown ( Figure 4 is the test result of the actual speed and the estimated speed of the second-order extended state observer when the speed of the permanent magnet synchronous motor is 800 r / min and the load is 400 N·m; Figure 5 is the test result of the observation error, that is, the estimated resonance harmonic component, when the speed of the permanent magnet synchronous motor is 800 r / min and the load is 400 N·m; Figure 6 is the test result of the estimated resonance frequency when the speed of the permanent magnet synchronous motor is 800 r / min and the load is 400 N·m; Figure 7 is the test result of the actual speed and the estimated speed of the second-order extended state observer when the speed of the permanent magnet synchronous motor increases and the load is 400 N·m; Figure 8 is the test result of the observation error, that is, the estimated resonance harmonic component, when the speed of the permanent magnet synchronous motor increases and the load is 400 N·m; Figure 9 is the test result of the estimated resonance frequency when the speed of the permanent magnet synchronous motor increases and the load is 400 N·m).

[0106] Based on this implementation method, the test of the resonance frequency estimation of the permanent magnet synchronous motor drive system can be carried out in the Matlab / Simulink environment. Based on this implementation method, the simulation of the permanent magnet synchronous motor operating under different working conditions can also be carried out in a real-time simulator such as RT-LAB.

[0107] The resonance frequency estimation method of the permanent magnet synchronous motor drive system provided by the present invention is based on a second-order extended state observer, has a simple structure, small calculation amount, and is applicable to various operating conditions of the permanent magnet synchronous motor drive system.

Claims

1. A method for estimating the resonance frequency of a permanent magnet synchronous motor drive system, characterized in that, The estimation of the resonant harmonic components is achieved by using a second-order extended state observer, and the resonant frequency of the permanent magnet synchronous motor drive system is estimated by a single-phase enhanced phase-locked loop, which specifically includes the following steps: Step 1: Establish a vector control model of the permanent magnet synchronous motor and calculate the resonant harmonic components; Establish a vector control model of the permanent magnet synchronous motor, transform the three-phase stator currents into the d-q coordinate system, and based on the dynamic equations of the permanent magnet synchronous motor, build a second-order extended state observer for the currents on the d-q axes and the measured actual speed containing the resonant components, so as to obtain the observation error, i.e., the resonant harmonic components; The electromagnetic torque of the permanent magnet synchronous motor in the dq-axis synchronous rotating reference frame is expressed as: Where: T e is the electromagnetic torque, n p is the number of pole pairs, ψ f is the magnetic flux linkage, L d , L q are the d-axis inductance and q-axis inductance respectively, i d , i q are the d-axis current component and q-axis current component respectively; Subsequently, the mechanical dynamics of the permanent magnet synchronous motor is expressed as: where: a = 3n p ψ f / 2J, b = 3n p (L d -L q ) / 2J, c = B / J, d = n p / J; where, ω r is the electrical angular velocity, J is the moment of inertia, T L is the load torque, and B is the friction coefficient; After considering the disturbances caused by parameter variations, Equation (2) is rewritten as: where Δa, Δb, Δc, and Δd are the disturbances caused by parameter variations; Furthermore, it can be obtained that: where z is the overall disturbance of the system, and further: z = Δai q + Δbi d i q -(c + Δc)ω r -(d + Δd)T L (5) Based on Equation (4), the disturbance observation scheme of the permanent magnet synchronous motor drive system based on the second-order extended state observer is designed as: where: β1 and β2 are the gains of the second-order extended observer, and e f is the observation error, and the gains of the second-order extended observer are configured as: where: ω o is the bandwidth of the second-order extended observer; According to Equations (6) and (7), the transfer function of the second-order extended observer is obtained as: where the superscript "^" represents the estimated value; In this way, the resonant harmonic components are provided by the observation error of the second-order extended observer: where: ε h represents the resonant harmonic component; Step 2: Build a single-phase enhanced phase-locked loop, input the resonant harmonic components into the single-phase enhanced phase-locked loop, and obtain the estimated resonant angular frequency; Let: where U, ω, are the amplitude, angular frequency and initial phase of the resonant harmonic component, respectively; Subsequently, where: θ is the phase, ε h-est represents the estimated value of the single-phase enhanced phase-locked loop; Furthermore, it can be obtained that: Step 3: Divide the estimated resonant angular frequency by 2π, that is, the estimation of the resonant frequency of the permanent magnet synchronous motor drive system is realized.

2. A method for estimating the resonance frequency of a permanent magnet synchronous motor drive system according to claim 1, characterized in that, The specific content of Step 3 is: Perform the calculation as shown in Equation (13) on the resonant angular frequency estimated in Step 2 to obtain the resonant frequency of the permanent magnet synchronous motor drive system: Wherein: is the estimated resonance frequency of the permanent magnet synchronous motor drive system.

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