A Permanent Magnet Synchronous Motor Estimation Method Based on a Third-Order Switched Extended State Observer

Abstract

This invention discloses a method for estimating the speed and position of a permanent magnet synchronous motor (PMSM) based on a third-order switched extended state observer. Specifically, based on the mathematical model of the PMSM, a back-EMF observer based on a sliding mode observer is constructed to obtain the estimated back-EMF. Further, the estimated back-EMF signal is processed using a low-pass filter and amplitude normalization. The processed back-EMF is then used as the input signal to a position estimation scheme based on the third-order switched extended state observer, achieving accurate estimation of the PMSM's speed and position under different operating conditions. This invention is simple in principle and easy to implement. It combines the advantages of both third-order linear and third-order nonlinear extended state observers, improving estimation accuracy and dynamic performance while reducing the adverse effects of noise on the estimation scheme. This solves the technical problems of low estimation accuracy, high noise sensitivity, and difficulty in parameter tuning in existing estimation schemes.

Description

Technical Field

[0001] This invention belongs to the field of sensorless control technology for permanent magnet synchronous motors, and particularly relates to an estimation method for permanent magnet synchronous motors based on a third-order switching extended state observer. Background Technology

[0002] As a key component for energy conversion, the interior permanent magnet synchronous motor (IPMSM) is widely used in industrial / agricultural production, transportation, and household appliances due to its advantages such as simple structure, high reliability, convenient maintenance, high operating efficiency, and good speed regulation performance. In IMSM drive systems, position sensors provide position information for high-performance closed-loop control. However, due to the complex operating environment and variable operating conditions, coupled with the long-term effects of strong electrothermal and mechanical stresses, the failure rate of position sensors remains high. When a position sensor fails, the control performance of the AC motor deteriorates significantly, and may even cause the control system to collapse and the motor to be damaged, seriously threatening the reliable operation of the AC motor drive system.

[0003] In response, an important development trend to ensure the reliable operation of built-in permanent magnet synchronous motor drive systems is to adopt high-performance position sensor control technology. This involves replacing position sensors with high failure rates with position estimation schemes to achieve position information detection, thereby improving the reliability of built-in permanent magnet synchronous motor drive systems.

[0004] Among numerous position estimation schemes, those based on extended state observers are widely popular due to their simple structure and ease of implementation. Generally, position estimation schemes based on extended state observers can be broadly categorized into those based on linear extended state observers and those based on nonlinear extended state observers. While linear extended state observer-based schemes offer good dynamic performance, they increase noise sensitivity. Conversely, nonlinear extended state observer-based schemes, while boasting high accuracy in noise estimation, face challenges in parameter tuning, and their estimation performance can significantly degrade under certain operating conditions. Summary of the Invention

[0005] To address the shortcomings of existing position estimation schemes based on extended state observers, this invention provides a permanent magnet synchronous motor estimation method based on a third-order switched extended state observer.

[0006] The present invention provides a method for estimating permanent magnet synchronous motors based on a third-order switched extended state observer, comprising the following steps:

[0007] Step 1: The electromagnetic torque of the interior permanent magnet synchronous motor (IPMSM) is expressed as follows:

[0008]

[0009] In the formula: T e n p ψ f i d i q L d and L q These are the motor electromagnetic torque, number of pole pairs, permanent magnet flux linkage, d-axis component of stator current, q-axis component of stator current, d-axis inductance, and q-axis inductance, respectively.

[0010] Furthermore, the equation of motion for the permanent magnet synchronous motor is:

[0011]

[0012] In the formula: ω r J, T L a, b, c, and d represent the motor speed, moment of inertia, load torque, and gain, respectively, and we have:

[0013]

[0014] After considering the disturbance of parameter changes, equation (2) can be rewritten as:

[0015]

[0016] In the formula: Δa, Δb, Δc, and Δd are disturbances caused by parameter mismatch.

[0017] Based on the relationship between the speed and position of the permanent magnet synchronous motor, we get:

[0018]

[0019] In the formula: θ r Let z be the motor rotor position and z be the total system disturbance, respectively, and we have:

[0020]

[0021] Step 2: The idea behind the extended state observer (ESO) is to treat the total disturbance as an extended state variable; according to equation (5), the third-order linear extended state observer is designed as follows:

[0022]

[0023] In the formula: For the estimated rotor position and motor speed, β1, β2, and β3 are the gains of the third-order linear extended state observer, and we have:

[0024]

[0025] In the formula: ω o This represents the bandwidth of the third-order linear extended state observer.

[0026] The error equation for the third-order linear extended state observer is:

[0027]

[0028] In the formula: e1, e2, and e3 are estimation errors, and we have:

[0029]

[0030] In the formula: h is the bounded gain.

[0031] Once the third-order linear extended state observer is running in steady state, then:

[0032]

[0033] Substituting equation (11) into equation (9), we get:

[0034]

[0035] Based on equation (4), the third-order nonlinear extended state observer is further designed as follows:

[0036]

[0037] In the formula: β′1, β′2, and β′3 are the gains of the third-order nonlinear extended state observer, fal(·) is a nonlinear function, and we have:

[0038]

[0039] In the formula: ε, α, δ are the error and the nonlinear function gain.

[0040] The error equation for the third-order nonlinear extended state observer is written as:

[0041]

[0042] Step 3: Third-order linear extended state observers and third-order nonlinear extended state observers each have their own advantages and disadvantages. Therefore, a position estimation scheme based on a third-order switched extended state observer is designed, expressed as:

[0043]

[0044] In the formula: and Let be the switching function, and we have:

[0045]

[0046] In the formula: fal1(·) and fal2(·) are nonlinear functions, and we have:

[0047]

[0048] Step 4: Finally, the estimated back EMF is obtained using a sliding mode observer-based back EMF observer, and the estimated back EMF is processed using a low-pass filter and amplitude normalization; further, the processed back EMF is used as the input signal of the position estimation scheme based on a third-order switched extended state observer to achieve accurate estimation of rotational speed and position under different operating conditions.

[0049] The beneficial technical effects of this invention compared to the prior art are as follows:

[0050] I. This invention employs a low-pass filter and amplitude normalization to reduce the adverse effects of external disturbances on back EMF estimation, effectively ensuring the performance of speed and position estimation.

[0051] Second, this invention employs a third-order switched extended state observer to adaptively adjust the system bandwidth by estimating the error, thereby ensuring the dynamic performance of the system while reducing the adverse effects of noise on the system.

[0052] Third, this invention uses a third-order switched extended state observer to estimate the total system disturbance by utilizing the estimation error, which significantly improves the disturbance estimation accuracy and thus ensures the position estimation performance.

[0053] Fourth, the method proposed in this invention has excellent adaptability to changes in operating conditions and provides high-precision estimation, meeting the reliability requirements of built-in permanent magnet synchronous motor drive systems. Furthermore, this method has good versatility and can be adapted to position estimation schemes for other AC motor drive systems. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of an estimation method based on a third-order switched extended state observer.

[0055] Figure 2 This is a specific implementation of the estimation method based on the third-order switched extended state observer.

[0056] Figure 3 This describes the speed estimation performance of different estimation methods under varying load conditions.

[0057] Figure 4It is the speed estimation performance of different estimation methods under the condition of changing speed command.

[0058] Figure 5 It is the disturbance estimation performance of different estimation methods under load variation conditions.

[0059] Figure 6 The speed estimation performance of different methods under steady-state conditions.

[0060] Figure 7 This is the position estimation performance of the estimation method based on the third-order switched extended state observer under the condition of changing velocity command.

[0061] Figure 8 This is the position estimation performance of the estimation method based on the third-order switched extended state observer under load variation conditions. Detailed Implementation

[0062] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0063] The principle of the permanent magnet synchronous motor estimation method based on a third-order switched extended state observer of the present invention is as follows: Figure 1 As shown, based on the mathematical model of the permanent magnet synchronous motor, a back EMF observer based on a sliding mode observer is constructed to obtain the estimated back EMF. Furthermore, the estimated back EMF signal is processed using a low-pass filter and amplitude normalization. The processed back EMF is used as the input signal of the position estimation scheme based on a third-order switched extended state observer to achieve accurate estimation of the speed and position of the permanent magnet synchronous motor under different operating conditions.

[0064] The permanent magnet synchronous motor (PMSM) estimation method based on a third-order switched extended state observer of this invention is applied to a sensorless control system for an embedded PMSM. It utilizes a third-order switched extended state observer to achieve accurate estimation of the PMSM position under different operating conditions. The specific implementation process is as follows: Figure 2 As shown, the specific steps are as follows:

[0065] Step 1: The electromagnetic torque of the interior permanent magnet synchronous motor (IPMSM) is expressed as follows:

[0066]

[0067] In the formula: T e n p ψ f i d i q L d and L qThese are the motor electromagnetic torque, number of pole pairs, permanent magnet flux linkage, d-axis component of stator current, q-axis component of stator current, d-axis inductance, and q-axis inductance, respectively.

[0068] Furthermore, the equation of motion for the permanent magnet synchronous motor is:

[0069]

[0070] In the formula: ω r J, T L a, b, c, and d represent the motor speed, moment of inertia, load torque, and gain, respectively, and we have:

[0071]

[0072] After considering the disturbance of parameter changes, equation (2) can be rewritten as:

[0073]

[0074] In the formula: Δa, Δb, Δc, and Δd are disturbances caused by parameter mismatch.

[0075] Based on the relationship between the speed and position of the permanent magnet synchronous motor, we get:

[0076]

[0077] In the formula: θ r Let z be the motor rotor position and z be the total system disturbance, respectively, and we have:

[0078]

[0079] Step 2: The idea behind the extended state observer (ESO) is to treat the total disturbance as an extended state variable; according to equation (5), the third-order linear extended state observer is designed as follows:

[0080]

[0081] In the formula: For the estimated rotor position and motor speed, β1, β2, and β3 are the gains of the third-order linear extended state observer, and we have:

[0082]

[0083] In the formula: ω o This represents the bandwidth of the third-order linear extended state observer.

[0084] The error equation for the third-order linear extended state observer is:

[0085]

[0086] In the formula: e1, e2, and e3 are estimation errors, and we have:

[0087]

[0088] In the formula: h is the bounded gain.

[0089] Once the third-order linear extended state observer is running in steady state, then:

[0090]

[0091] Substituting equation (11) into equation (9), we get:

[0092]

[0093] Based on equation (4), the third-order nonlinear extended state observer is further designed as follows:

[0094]

[0095] In the formula: β′1, β′2, and β′3 are the gains of the third-order nonlinear extended state observer, fal(·) is a nonlinear function, and we have:

[0096]

[0097] In the formula: ε, α, δ are the error and the nonlinear function gain.

[0098] The error equation for the third-order nonlinear extended state observer is written as:

[0099]

[0100] Step 3: Third-order linear extended state observers and third-order nonlinear extended state observers each have their own advantages and disadvantages. Therefore, a position estimation scheme based on a third-order switched extended state observer is designed, expressed as:

[0101]

[0102] In the formula: and Let be the switching function, and we have:

[0103]

[0104]

[0105] In the formula: fal1(·) and fal2(·) are nonlinear functions, and we have:

[0106]

[0107] Step 4: Finally, the estimated back EMF is obtained using a sliding mode observer-based back EMF observer, and the estimated back EMF is processed using a low-pass filter and amplitude normalization; further, the processed back EMF is used as the input signal of the position estimation scheme based on a third-order switched extended state observer to achieve accurate estimation of rotational speed and position under different operating conditions.

[0108] Figure 3 A comparison of the speed estimation performance of different schemes under varying load conditions is presented. As shown in the figure, when the load increases from 0.5 N·m to 8 N·m, the estimation scheme based on the third-order linear extended state observer has a larger speed estimation error than the scheme based on the third-order nonlinear extended state observer, but its convergence speed is faster. Conversely, the estimation scheme based on the third-order nonlinear extended state observer has a smaller estimation error, but its convergence speed is slower. It is worth noting that the estimation scheme based on the third-order switched extended state observer achieves faster tracking and has a smaller estimation error than the scheme based on the third-order nonlinear extended state observer.

[0109] Figure 4 A comparison of the speed estimation performance of different schemes under varying speed command conditions is presented. As shown in the figure, when the speed command increases from 300 r / min to 500 r / min, the estimation scheme based on the third-order linear extended state observer has a larger speed estimation error than the scheme based on the third-order nonlinear extended state observer, but its convergence speed is faster. Conversely, the estimation scheme based on the third-order nonlinear extended state observer has a smaller estimation error, but its convergence speed is slower. It is worth noting that the estimation scheme based on the third-order switched extended state observer achieves faster tracking and has a smaller estimation error than the scheme based on the third-order nonlinear extended state observer.

[0110] Figure 5 A comparison of the total disturbance estimation performance of different schemes is presented. As can be seen from the figure, the estimation scheme based on the third-order switched extended state observer combines the advantages of the estimation schemes based on the third-order nonlinear extended state observer and the estimation scheme based on the third-order linear extended state observer, achieving accurate and fast estimation of the total disturbance.

[0111] Figure 6 The estimation performance of different schemes under steady state is presented. It can be found that the steady-state performance of the estimation scheme based on the third-order switched extended state observer is comparable to that of the estimation scheme based on the third-order nonlinear extended state observer, and is better than that of the estimation scheme based on the third-order linear extended state observer.

[0112] Figure 7The position estimation performance of the proposed scheme under varying load conditions is presented. Under these conditions, the load increases from 0.5 N·m to 8 N·m. It can be observed that the estimation scheme based on the third-order switched extended state observer can achieve accurate position estimation under varying load conditions.

[0113] Figure 8 The position estimation performance of the proposed scheme under the condition of changing speed command is presented. It can be seen that under this condition, the speed command increases from 300 r / min to 500 r / min. It can also be seen that the estimation scheme based on the third-order switched extended state observer can achieve accurate position estimation under the condition of changing speed command.

[0114] The method of this invention is simple in principle and easy to implement. It combines the advantages of third-order linear extended state observer and third-order nonlinear extended state observer to improve estimation accuracy and dynamic performance, while reducing the adverse effects of noise on the estimation scheme. It solves the technical problems of low estimation accuracy, high noise sensitivity and difficulty in parameter tuning of estimation schemes based on third-order linear extended state observer and third-order nonlinear extended state observer.

[0115] The position estimation method implemented in this invention fully considers the impact of harmonics and amplitude variations on the position estimation scheme. It employs a low-pass filter and amplitude normalization to reduce the adverse effects of harmonics and amplitude variations. To address the problems of low estimation accuracy, high noise sensitivity, and difficult parameter tuning in estimation schemes based on third-order linear extended state observers and third-order nonlinear extended state observers, a third-order switched extended state observer is designed, which combines the advantages of third-order linear extended state observers and third-order nonlinear extended state observers while avoiding their disadvantages.

[0116] This invention enables accurate estimation of the speed and position of a permanent magnet synchronous motor under various operating conditions. More importantly, compared to estimation schemes based on third-order linear extended state observers and third-order nonlinear extended state observers, the proposed method significantly improves speed and position estimation performance, solving technical problems such as low estimation accuracy, high noise sensitivity, and difficulty in parameter tuning associated with these methods. Furthermore, the proposed position estimation method can be further extended to AC motor drive systems (e.g., induction motor drive systems and switched reluctance motor drive systems).

Claims

1. A method for estimating permanent magnet synchronous motors based on a third-order switched extended state observer, characterized in that, Includes the following steps: Step 1: The electromagnetic torque of the built-in permanent magnet synchronous motor is expressed as: wherein: T e , n p , ψ f , i d , i q , L d and L q are the motor electromagnetic torque, the number of pole pairs, the permanent magnet flux linkage, the stator current d-axis component, the stator current q-axis component, the d-axis inductance and the q-axis inductance, respectively; Furthermore, the equation of motion for the permanent magnet synchronous motor is: where ω r , J, T L , a, b, c and d are motor speed, moment of inertia, load torque and gain, respectively, and have: After considering the disturbance of parameter changes, equation (2) can be rewritten as: In the formula: Δa, Δb, Δc, and Δd are disturbances caused by parameter mismatch; Based on the relationship between the speed and position of the permanent magnet synchronous motor, we get: where θ r and z are the motor rotor position and the total system disturbance, respectively, and have: Step 2: The idea behind the extended state observer is to treat the total disturbance as an extended state variable; according to equation (5), the third-order linear extended state observer is designed as follows: In the formula: For the estimated rotor position and motor speed, β1, β2, and β3 are the gains of the third-order linear extended state observer, and we have: wherein ω o is the bandwidth of the third order linear extended state observer; The error equation for the third-order linear extended state observer is: In the formula: e1, e2, and e3 are estimation errors, and we have: In the formula: h is the bounded gain; Once the third-order linear extended state observer is running in steady state, then: Substituting equation (11) into equation (9), we get: Based on equation (4), the third-order nonlinear extended state observer is further designed as follows: In the formula: β′1, β′2, and β′3 are the gains of the third-order nonlinear extended state observer, fal(·) is a nonlinear function, and we have: In the formula: ε, α, δ are the error and the gain of the nonlinear function; The error equation for the third-order nonlinear extended state observer is written as: Step 3: Design a position estimation scheme based on a third-order switched extended state observer, expressed as: In the formula: and Let be the switching function, and we have: In the formula: fal1(·) and fal2(·) are nonlinear functions, and we have: Step 4: Finally, the estimated back EMF is obtained using a sliding mode observer-based back EMF observer, and the estimated back EMF is processed using a low-pass filter and amplitude normalization; further, the processed back EMF is used as the input signal of the position estimation scheme based on a third-order switched extended state observer to achieve accurate estimation of rotational speed and position under different operating conditions.

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