Permanent magnet synchronous motor estimation method based on third-order switching extended state observer

Abstract

The invention discloses a permanent magnet synchronous motor estimation method based on a third-order switching extended state observer, and the method specifically comprises the steps: constructing a back electromotive force observer based on a sliding-mode observer according to a mathematical model of a permanent magnet synchronous motor, and obtaining the estimated back electromotive force; further, the estimated counter electromotive force signal is processed by using a low-pass filter and amplitude normalization; and the processed back electromotive force is used as an input signal of a position estimation scheme based on a third-order switching extended state observer, and accurate estimation of the rotating speed and the position of the permanent magnet synchronous motor under different working conditions is realized. The method is simple in principle and easy to implement, combines the advantages of a third-order linear extension state observer and a third-order nonlinear extension state observer, improves the estimation precision and dynamic performance, reduces the adverse effect of noise on an estimation scheme, and improves the estimation accuracy. The technical problems of low estimation precision, high noise sensitivity, difficulty in parameter tuning and the like of an estimation scheme in the prior art are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of position sensorless control of permanent magnet synchronous motors, and in particular relates to a permanent magnet synchronous motor estimation method based on a third-order switching extended state observer. Background Art

[0002] As a key component of energy conversion, interior permanent magnet synchronous motor (IPMSM) has been widely used in industrial / agricultural production, transportation, household appliances and other fields due to its simple structure, high reliability, easy maintenance, high operating efficiency and good speed regulation performance. In the drive system of interior permanent magnet synchronous motor, position sensor provides position information for high-performance closed-loop control. However, affected by the complex operating environment and variable operating conditions, and under the long-term action of strong electrothermal stress and mechanical stress, the failure rate of position sensor has remained high. When the position sensor fails, the control performance of the AC motor will be significantly reduced, and it may even cause the control system to crash and the motor to be damaged, which seriously threatens the reliable operation of the AC motor drive system.

[0003] In this regard, an important development trend to ensure the reliable operation of the built-in permanent magnet synchronous motor drive system is to adopt high-performance position sensor control technology, that is, to replace the position sensor with a high failure rate through a position estimation scheme to realize position information detection, thereby improving the reliability of the built-in permanent magnet synchronous motor drive system.

[0004] Among the numerous position estimation schemes, the position estimation scheme based on the extended state observer is widely popular due to its simple structure and easy implementation. Generally, the position estimation scheme based on the extended state observer can be roughly divided into the estimation scheme based on the linear extended state observer and the estimation scheme based on the nonlinear extended state observer. Although the estimation scheme based on the linear extended state observer has good dynamic performance, it will increase the noise sensitivity. While the estimation scheme based on the nonlinear extended state observer has the advantage of high interference estimation accuracy, it also faces the problem of difficult parameter tuning, and under certain working conditions, the estimation performance of the estimation scheme based on the nonlinear extended state observer will be significantly reduced. Summary of the invention

[0005] In view of the shortcomings of the existing position estimation scheme based on the extended state observer, the present invention provides a permanent magnet synchronous motor estimation method based on the third-order switching extended state observer.

[0006] A permanent magnet synchronous motor estimation method based on a third-order switching extended state observer of the present invention comprises the following steps:

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

[0008]

[0009] Where: T e 、n p , f 、i d 、i q , L d and L q They are the motor electromagnetic torque, pole pair number, permanent magnet flux, stator current d-axis component, stator current q-axis component, d-axis inductance and q-axis inductance respectively.

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

[0011]

[0012] Where: r , J, T L , a, b, c and d are the motor speed, moment of inertia, load torque and gain respectively, and:

[0013]

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

[0015]

[0016] Where: Δa, Δb, Δc, Δd are disturbances caused by parameter mismatch.

[0017] According to the speed and position relationship of the permanent magnet synchronous motor, we can get:

[0018]

[0019] Where: θ r and z are the motor rotor position and the total system disturbance respectively, and:

[0020]

[0021] Step 2: The idea of ​​the extended state observer (ESO) is to regard the total disturbance as an extended state variable. According to equation (5), the third-order linear extended state observer is designed as:

[0022]

[0023] Where: is the estimated rotor position and motor speed, β1, β2, β3 are the gains of the third-order linear extended state observer, and:

[0024]

[0025] Where: o is the bandwidth of the third-order linear extended state observer.

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

[0027]

[0028] Where: e1, e2, e3 are estimation errors, and:

[0029]

[0030] Where: h is the bounded gain.

[0031] When the third-order linear extended state observer operates in a steady state, we have:

[0032]

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

[0034]

[0035] According to formula (4), the third-order nonlinear extended state observer is further designed as:

[0036]

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

[0038]

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

[0040] The error equation of the third-order nonlinear extended state observer can be written as:

[0041]

[0042] Step 3: The third-order linear extended state observer and the third-order nonlinear extended state observer have their own advantages and disadvantages. To this end, a position estimation scheme based on a third-order switching extended state observer is designed, which is expressed as:

[0043]

[0044] Where: and is a switching function, and:

[0045]

[0046] Where: fal1(·) and fal2(·) are nonlinear functions, and:

[0047]

[0048] Step 4: Finally, the estimated back EMF is obtained using the back EMF observer based on the sliding mode 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 the third-order switching extended state observer to achieve accurate estimation of the speed and position under different working conditions.

[0049] The beneficial technical effects of the present invention compared with the prior art are:

[0050] 1. The present invention adopts a low-pass filter and amplitude normalization to reduce the adverse effect of external disturbance on back electromotive force estimation, effectively ensuring the speed and position estimation performance.

[0051] 2. The present invention adopts a third-order switching 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] 3. The present invention adopts a third-order switching extended state observer to use the estimation error to estimate the total disturbance of the system, which significantly improves the disturbance estimation accuracy and thus ensures the position estimation performance.

[0053] Fourth, the method proposed in the present invention has good adaptability to changes in working conditions, and the estimation is relatively high, which can meet the reliability requirements of the built-in permanent magnet synchronous motor drive system. In addition, the method has good versatility and can also be transplanted to other AC motor drive system position estimation solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of the estimation method based on the third-order switching extended state observer.

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

[0056] Figure 3 It is the speed estimation performance of different estimation methods under load variation conditions.

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

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

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

[0060] Figure 7 It is the position estimation performance of the estimation method based on the third-order switching extended state observer under the condition of speed command variation.

[0061] Figure 8 It is the position estimation performance of the estimation method based on the third-order switching extended state observer under load variation conditions. DETAILED DESCRIPTION

[0062] The present invention is 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 the third-order switching extended state observer of the present invention is as follows: Figure 1 As shown, according to the mathematical model of the permanent magnet synchronous motor, a back-EMF observer based on the sliding mode observer is constructed to obtain the estimated back-EMF; further, the estimated back-EMF signal is processed by 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 the third-order switching extended state observer to achieve accurate estimation of the speed and position of the permanent magnet synchronous motor under different working conditions.

[0064] The permanent magnet synchronous motor estimation method based on the third-order switching extended state observer of the present invention is used for the position sensorless control system of the built-in permanent magnet synchronous motor, and the third-order switching extended state observer is used to realize the accurate estimation of the position of the permanent magnet synchronous motor under different working conditions. The specific implementation process is as follows Figure 2 As shown, the specific steps are:

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

[0066]

[0067] Where: T e 、n p , f 、i d 、i q , L d and L qThey are the motor electromagnetic torque, pole pair number, permanent magnet flux, stator current d-axis component, stator current q-axis component, d-axis inductance and q-axis inductance respectively.

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

[0069]

[0070] Where: r , J, T L , a, b, c and d are the motor speed, moment of inertia, load torque and gain respectively, and:

[0071]

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

[0073]

[0074] Where: Δa, Δb, Δc, Δd are disturbances caused by parameter mismatch.

[0075] According to the speed and position relationship of the permanent magnet synchronous motor, we can get:

[0076]

[0077] Where: θ r and z are the motor rotor position and the total system disturbance respectively, and:

[0078]

[0079] Step 2: The idea of ​​the extended state observer (ESO) is to regard the total disturbance as an extended state variable. According to equation (5), the third-order linear extended state observer is designed as:

[0080]

[0081] Where: is the estimated rotor position and motor speed, β1, β2, β3 are the gains of the third-order linear extended state observer, and:

[0082]

[0083] Where: o is the bandwidth of the third-order linear extended state observer.

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

[0085]

[0086] Where: e1, e2, e3 are estimation errors, and:

[0087]

[0088] Where: h is the bounded gain.

[0089] When the third-order linear extended state observer operates in a steady state, we have:

[0090]

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

[0092]

[0093] According to formula (4), the third-order nonlinear extended state observer is further designed as:

[0094]

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

[0096]

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

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

[0099]

[0100] Step 3: The third-order linear extended state observer and the third-order nonlinear extended state observer have their own advantages and disadvantages. To this end, a position estimation scheme based on a third-order switching extended state observer is designed, which is expressed as:

[0101]

[0102] Where: and is a switching function, and:

[0103]

[0104]

[0105] Where: fal1(·) and fal2(·) are nonlinear functions, and:

[0106]

[0107] Step 4: Finally, the estimated back EMF is obtained using the back EMF observer based on the sliding mode 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 the third-order switching extended state observer to achieve accurate estimation of the speed and position under different working conditions.

[0108] Figure 3 The speed estimation performance comparison of different schemes under load variation conditions is given. As can be seen from the figure, when the load increases from 0.5N·m to 8N·m, the speed estimation error of the estimation scheme based on the third-order linear extended state observer is larger than that of the estimation scheme based on the third-order nonlinear extended state observer, but its convergence speed is faster. On the contrary, the estimation error of the estimation scheme based on the third-order nonlinear extended state observer is smaller, but the convergence speed is slower. It is worth noting that the estimation scheme based on the third-order switching extended state observer achieves faster tracking than the estimation scheme based on the third-order nonlinear extended state observer, and the estimation error is smaller than that of the estimation scheme based on the third-order linear extended state observer.

[0109] Figure 4 The speed estimation performance comparison of different schemes under the condition of speed command change is given. It can be seen from the figure that when the speed command increases from 300r / min to 500r / min, the speed estimation error of the estimation scheme based on the third-order linear extended state observer is greater than that of the estimation scheme based on the third-order nonlinear extended state observer, but its convergence speed is faster. On the contrary, the estimation error of the estimation scheme based on the third-order nonlinear extended state observer is smaller, but the convergence speed is slower. It is worth noting that the estimation scheme based on the third-order switching extended state observer achieves faster tracking than the estimation scheme based on the third-order nonlinear extended state observer, and the estimation error is smaller than that of the estimation scheme based on the third-order linear extended state observer.

[0110] Figure 5 The total disturbance estimation performance comparison of different schemes is given. As can be seen from the figure, the estimation scheme based on the third-order switching extended state observer combines the advantages of the estimation scheme 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 in steady state is given. It can be found that the steady-state performance of speed estimation of the estimation scheme based on the third-order switching 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 load variation is given. Under this condition, the load increases from 0.5N·m to 8N·m. It can be found that the estimation scheme based on the third-order switching extended state observer can achieve accurate position estimation under load variation conditions.

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

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

[0115] The position estimation method implemented by the present invention fully considers the influence of harmonics and amplitude changes on the position estimation scheme, adopts a low-pass filter and amplitude normalization to reduce the adverse influence of harmonics and amplitude changes; in view of the problems of low estimation accuracy, high noise sensitivity, and difficulty in parameter tuning of estimation schemes based on a third-order linear extended state observer and a third-order nonlinear extended state observer, a third-order switching extended state observer is designed, which combines the advantages of the third-order linear extended state observer and the third-order nonlinear extended state observer, and avoids the disadvantages of the third-order linear extended state observer and the third-order nonlinear extended state observer.

[0116] By adopting the present invention, accurate estimation of the speed and position of the permanent magnet synchronous motor under different working conditions can be achieved. More importantly, compared with the estimation scheme based on the third-order linear extended state observer and the third-order nonlinear extended state observer, the studied method can significantly improve the speed and position estimation performance, and solve the technical problems of low estimation accuracy, high noise sensitivity, and difficult parameter tuning of the estimation scheme based on the third-order linear extended state observer and the third-order nonlinear extended state observer. In addition, the adopted position estimation method can also be further promoted and applied to AC motor drive systems (such as: induction motor drive systems and switched reluctance motor drive systems).

Claims

1. A permanent magnet synchronous motor estimation method based on a third-order switching extended state observer, characterized in that: The following steps are involved: Step 1: The electromagnetic torque of the interior permanent magnet synchronous motor is expressed as: Where: T e 、n p , f 、i d 、i q , L d and L q They are the motor electromagnetic torque, pole pair number, permanent magnet flux, stator current d-axis component, stator current q-axis component, d-axis inductance and q-axis inductance respectively; Furthermore, the motion equation of the permanent magnet synchronous motor is: Where: r , J, T L , a, b, c and d are the motor speed, moment of inertia, load torque and gain respectively, and: After considering the disturbance of parameter changes, equation (2) can be rewritten as: Where: Δa, Δb, Δc, Δd are disturbances caused by parameter mismatch; According to the speed and position relationship of the permanent magnet synchronous motor, we can get: Where: θ r and z are the motor rotor position and the total system disturbance respectively, and: Step 2: The idea of ​​the extended state observer is to regard the total disturbance as an extended state variable; according to equation (5), the third-order linear extended state observer is designed as: Where: is the estimated rotor position and motor speed, β1, β2, β3 are the gains of the third-order linear extended state observer, and: Where: o is the bandwidth of the third-order linear extended state observer; The error equation of the third-order linear extended state observer is: Where: e1, e2, e3 are estimation errors, and: Where: h is the bounded gain; When the third-order linear extended state observer operates in a steady state, we have: Substituting formula (11) into formula (9), we get: According to formula (4), the third-order nonlinear extended state observer is further designed as: Where: β′1, β′2, β′3 are the gains of the third-order nonlinear extended state observer, fal(·) is a nonlinear function, and: Where: ε, α, δ are the error and nonlinear function gain; The error equation of the third-order nonlinear extended state observer is written as: Step 3: Design a position estimation scheme based on a third-order switching extended state observer, expressed as: Where: and is a switching function, and: Where: fal1(·) and fal2(·) are nonlinear functions, and: Step 4: Finally, the estimated back EMF is obtained using the back EMF observer based on the sliding mode 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 the third-order switching extended state observer to achieve accurate estimation of the speed and position under different working conditions.

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