阅读说明：本技术 Pmsm驱动系统失磁故障控制方法、永磁同步电机 (PMSM drive system field loss fault control method and permanent magnet synchronous motor ) 是由 黄刚 李佳俊 于惠钧 何静 张昌凡 胡家喜 刘建华 马振宇 南永辉 黄伟 于 2021-04-22 设计创作，主要内容包括：本发明提供一种PMSM驱动系统失磁故障控制方法,具体步骤为：首先,建立了dq轴坐标系下PMSM失磁故障数学模型,其次,将失磁模型转化为等价输入干扰系统,采用积分滑模观测器对EID系统状态变量及等价输入失磁故障进行估计,并将等价输入失磁故障的估计值以前馈的方式补偿,得到最终的控制律,实现对PMSM失磁的容错性、鲁棒性。最后,给出了积分滑模观测器及整个EID系统的稳定性证明。所提方法有效提高了PMSM失磁驱动系统的容错控制性能。本发明还提供了一种基于上述PMSM驱动系统失磁故障控制方法的永磁同步电机。(The invention provides a method for controlling a loss of excitation fault of a PMSM (permanent magnet synchronous motor) driving system, which comprises the following specific steps of: firstly, a PMSM magnetic loss fault mathematical model under a dq axis coordinate system is established, secondly, the magnetic loss model is converted into an equivalent input disturbance system, an integral sliding-mode observer is adopted to estimate EID system state variables and equivalent input magnetic loss faults, the estimated values of the equivalent input magnetic loss faults are compensated in a feedforward mode, a final control law is obtained, and fault tolerance and robustness of PMSM magnetic loss are achieved. Finally, the stability testifies of the integral sliding mode observer and the whole EID system are provided. The method effectively improves the fault-tolerant control performance of the PMSM field loss driving system. The invention also provides a permanent magnet synchronous motor based on the PMSM drive system field loss fault control method.)

The method for controlling the loss of excitation fault of the PMSM drive system is characterized by comprising the following steps:

s1, establishing a PMSM model under a loss of field fault;

s2, estimating a loss of excitation fault by using equivalent input interference estimation;

obtaining an equivalent input loss-of-magnetization fault estimation value by using an integral sliding mode observer and a low-pass filter, wherein the integral sliding mode observer has the equation:

in the formulaAre estimates of x (y), respectively; u. of_fIs an input; l and L_IIs the observer gain to be designed(ii) a v is a sliding mode control function; the above-mentionedWherein Is to be designed and has k₁> 0 and k₂＞0；L_I1> 0 and L_I2＞0；

S3, compensating the loss of excitation fault by adopting an equivalent input interference estimation value;

the loss-of-magnetization fault suppression control rate based on the integral sliding mode observer is as follows:where u is the system input, u_fFor system input under the influence of a loss of field fault,is an equivalent input estimate for a loss of field fault.

2. The method for controlling the loss of excitation fault of the PMSM drive system according to claim 1, wherein the PMSM model under the loss of excitation fault is:

3. the method for controlling the field loss fault of the PMSM drive system of claim 2, wherein a mechanical equation of the PMSM under a d and q coordinate system is as follows:

in the formula, T_eIs the electromagnetic torque of the PMSM; t is_LIs the load torque; j is moment of inertia; b is a damping coefficient; omega_mIs the mechanical angular speed of the rotor.

4. The PMSM drive system field loss fault control method of claims 2 and 3, wherein the current equation under the field loss fault in d and q coordinate systems is as follows:

wherein x, u, d and y are respectively state variables, system input, loss of field fault and system output, and x is defined as [ i ═ i%_d i_q]^T；u＝[u_d u_q]^T；d＝[Δλ_rd Δλ_rq]^T。

5. The PMSM drive system field loss fault control method of claim 4, wherein the current equations apply an equivalent disturbance d_e＝[d_ed d_eq]^TThe system described is:wherein d is_eIs the equivalent input fault to the loss of field fault d.

6. The method of claim 1, wherein the sliding mode surface is selected to be a sliding mode surface

7. The method of claim 6 wherein the error state equation is

8. The PMSM drive system field loss fault control method of claim 7, wherein the estimate is an estimateSatisfy the requirement ofΔ d is a variable and satisfies

9. The method for controlling the loss of excitation fault of the PMSM drive system of claim 8, wherein the filtered equivalent input loss of excitation fault is obtained by designing a low pass filter H(s)

10. A permanent magnet synchronous motor, characterized in that a method for suppressing a loss of field fault of a PMSM drive system according to any one of claims 1 to 9 is employed.

Technical Field

The invention relates to an Equivalent Input Disturbance (EID) fault-tolerant control method of a permanent magnet synchronous motor driving system, in particular to an equivalent input disturbance fault-tolerant control method based on an integral sliding-mode observer.

Background

The permanent magnet synchronous motor is widely applied to various high-performance industrial practices due to the advantages of high efficiency, high power density, high dynamic performance and the like, such as the fields of electric automobiles, industrial robots, aviation and navigation, rail transit and the like. Particularly, in high-precision and high-performance engineering applications, the fast dynamic response speed and the high-precision torque response performance of the permanent magnet synchronous motor driving system are very important. However, under complicated working conditions, the excitation performance of the Permanent Magnet (PM) of the PMSM rotor is reduced due to the influence of high temperature, high load, electromagnetism, machinery and other factors, so that the loss of excitation fault is easy to occur. This results in a mismatch of the rotor flux linkage of the controller with the actual flux linkage, which necessarily results in a degradation of the performance of the PMSM drive system. Therefore, the good control performance of the controller is maintained, and the realization of fault-tolerant control on the loss of excitation fault is a necessary condition for ensuring the stable operation of the PMSM driving system.

The problem of detecting and inhibiting the loss of excitation fault of the permanent magnet gradually draws attention, a great deal of relevant research is published, and particularly, a model-based method becomes a main method for research of numerous scholars. The methods such as robust control, adaptive control, predictive control, sliding mode control and the like are widely applied to disturbance detection and suppression in an electromechanical system. Among them, the Sliding Mode Observer (SMO) has the advantages of robustness to disturbance, low sensitivity to system parameter change, fast response, easy implementation, and the like, and receives more and more attention.

However, the above method uses a feedback strategy to design the system, and the designed control system usually has only one degree of freedom. This results in a system that needs to make trade-offs between control performance, such as robustness and fault tolerance. When the external disturbance of the system is large, a high gain is usually employed to reduce the influence of the disturbance. The high gain effectively reduces the disturbance influence and brings the reduction of the robust performance and the nominal performance of the system. Compared to these single degree of freedom methods, active disturbance suppression methods with two degrees of freedom are gaining wide attention. One for disturbance rejection and the other for feedback compensation, which effectively solves the trade-off problem of system performance in a single degree of freedom system. Common active disturbance suppression methods mainly include a Disturbance Observer (DOB) based method and an Active Disturbance Rejection Control (ADRC) based method, and are widely applied to disturbance and fault suppression of a PMSM drive system. The two active disturbance suppression methods realize fault-tolerant control on disturbance and faults by reconstructing the controller, so that the structure of the original controller is changed, and the risk of the system is greatly increased. The invention patent application with publication number CN107482976A discloses a failure-tolerant predictive control method for a loss-of-field fault of a permanent magnet synchronous motor, which obtains a control law by using a sliding-mode observer, but the control is the control of current and rotating speed, the loss-of-field fault is not predicted and eliminated from the system input as a whole, and the influence of the loss-of-field fault on the system cannot be eliminated.

Disclosure of Invention

Aiming at the problem of fault-tolerant control of the loss-of-magnetization fault of the permanent magnet, the equivalent input disturbance method based on the integral sliding-mode observer is provided by combining the advantages of the SMO and the PIO and adopting the equivalent input disturbance method and introducing a decoupling coefficient and an integral term.

The technical scheme adopted by the method is as follows:

the PMSM drive system field loss fault suppression method based on the integral sliding mode observer is characterized in that an equation of the integral sliding mode observer is as follows:

in the formulaAre estimates of x (y), respectively; u. of_fIs an input; l and L_IIs the observer gain to be designed; v is a sliding mode control function; the above-mentionedWherein Is to be designed and has k₁> 0 and k₂＞0；L_I1> 0 and L_I2＞0；

Further, the loss-of-magnetization fault suppression control rate based on the integral sliding mode observer is as follows:where u is the system input, u_fFor system input under the influence of a loss of field fault,is an equivalent input estimate for a loss of field fault.

And (3) performing equivalent estimation on the loss-of-magnetization fault by using an integral sliding mode observer and an equivalent input interference estimator, and compensating the loss-of-magnetization fault.

Further, the PMSM model under the loss of field fault is:

further, the mechanical equation of the PMSM in the d and q coordinate systems is:

in the formula, T_eIs the electromagnetic torque of the PMSM; t is_LIs the load torque; j is moment of inertia; b is a damping coefficient; omega_mIs the mechanical angular speed of the rotor.

Further, the current equation under d and q coordinate systems under the loss of excitation fault is as follows:

wherein x, u, d and y are respectively state variables, system input, loss of field fault and system output, and x is defined as [ i ═ i%_d i_q]^T；u＝[u_d u_q]^T；d＝[Δλ_rd Δλ_rq]^T。

Further, the current equation applies an equivalent disturbance d_e＝[d_ed d_eq]^TThe system described is:wherein d is_eIs the equivalent input fault to the loss of field fault d.

Further, the selected slip form surface is

Further, the error state equation is:

further, the estimated valueSatisfy the requirement ofΔ d is a variable and satisfies

Further, by designing a low-pass filter H(s), the filtered equivalent input loss-of-magnetization fault is obtained

The integral sliding mode observer introduces a decoupling coefficient and an integral term, the influence of the speed of a motor on the error of the observer is eliminated by introducing the decoupling coefficient, and the accuracy of equivalent magnetic loss fault estimation and the robustness of a system are effectively enhanced; the introduction of the integral term helps to introduce a slack variable in the system design, which increases the flexibility of the system.

Drawings

FIG. 1 is a variation of the flux linkage of a PMSM permanent magnet;

FIG. 2 is an equivalent input disturbance system based on an integral sliding mode observer;

FIG. 3 is an equivalent input disturbance PMSM drive system structure based on an integral sliding mode observer.

Detailed Description

The invention is further illustrated by the following specific examples. The starting materials and methods employed in the examples of the present invention are those conventionally available in the market and conventionally used in the art, unless otherwise specified.

Example 1

A PMSM drive system of a permanent magnet synchronous motor adopts the following technical scheme to control the PMSM drive system.

S1, firstly, establishing an ideal mathematical model of a PMSM (permanent magnet synchronous motor) driving system

An ideal mathematical model under a nominal parameter is adopted in a PMSM (permanent magnet synchronous motor) driving system based on the model, namely, the saturation and the loss of an iron core of the PMSM are neglected, and when the perturbation of the parameter is not considered, a voltage equation of the PMSM under a d coordinate system and a q coordinate system is obtained as

Wherein, the permanent magnet synchronous motor stator flux linkage equation is

In the formula R_sA stator winding resistor; u. of_d(u_q)，i_d(i_q)，L_d(L_q),λ_d(λ_q) Voltage component, current component, inductance component and flux linkage component of the d (q) axis of the stator winding respectively; omega_eIs the rotor electrical angular velocity; lambda [ alpha ]_r0Is a rotor permanent magnet flux linkage.

In actual engineering, due to the influence of temperature and other factors, a rotor permanent magnet is prone to have a loss of field fault, when the permanent magnet synchronous motor has the loss of field fault, the size and the direction of a permanent magnet flux linkage are changed as shown in figure 1, and then the flux linkage equation corresponding to the formula (2) is changed into

Wherein

Wherein, Δ λ_rd(Δλ_rq) The flux linkage perturbation components of the d (q) axis, γ ∈ [0 °,90 °), respectively.

According to the formulas (1), (3), (4) and (5), the PMSM model under the loss of field fault can be obtained as

The electromagnetic torque equation of the PMSM under the d and q coordinate systems is changed from equation (7) to equation (8), namely

In the formula, n_pIs the number of pole pairs.

The mechanical equation of PMSM under d and q coordinate systems is

In the formula, T_eIs the electromagnetic torque of the PMSM; t is_LIs the load torque; j is moment of inertia; b is a damping coefficient; omega_mIs the mechanical angular speed of the rotor.

Considering that the electromagnetic time constant is much smaller than the mechanical time constant in the actual drive system, it can be considered that

Thus, the formula (6) can be rewritten as

From this, the current equation under d, q coordinate system under the loss of field fault can be obtained as

Order to

The system (12) can be described as

In the formula, x, u, d and y are respectively state variables, system input, loss of field fault and system output. Definition x ═ i_d i_q]^T；u＝[u_d u_q]^T；d＝[Δλ_rd Δλ_rq]^T。

S2, restraining the loss of excitation fault by using equivalent input interference of an integral sliding mode observer

Considering the loss of field fault as a disturbance, according to the EID theory, using the equivalent disturbance d_e＝[d_ed d_eq]^TTo describe the system (13) to obtain

Wherein d is_eIs the equivalent input fault to the loss of field fault d.

An equivalent input disturbance PMSM control system based on an integral sliding mode observer is designed for the system (14), as shown in FIG. 2. The system mainly comprises a state equation, an integral sliding-mode observer and an equivalent input disturbance estimator. The integral sliding mode observer and the equivalent input interference estimator realize equivalent estimation on the loss of excitation fault and compensate the loss of excitation fault.

S21, designing an integral sliding mode observer

The traditional PMSM sliding mode observer is designed as follows:

by introducing a decoupling factor omega_eAnd integral termAn integral sliding-mode observer is constructed, i.e.

In the formulaAre estimates of x (y), respectively; u. of_fIs an input; l and L_IIs the observer gain to be designed; v is a sliding mode control function.

WhereinIs to be designed and has k₁> 0 and k₂＞0；L_I1> 0 and L_I2＞0。

The surface of the sliding form is selected as

Substituting equations of state (14) and (16) into equation (18) yields an error equation of state of

Substituting equation (16) into equation (19) yields

According to (20), obtaining

Suppose there is a variable Δ d that satisfies

Suppose d_eIs estimated value ofSatisfy the requirement of

Substituting the formulas (22) and (23) into (21) to obtain

The comparative formula (16) and the formula (24) have

Thereby obtaining

Wherein

B⁺＝(B^TB)^-1B^T (27)

S22, designing a reasonable low-pass filter H(s) to obtain the equivalent input loss-of-magnetization fault after filtering

Wherein the content of the first and second substances,andare respectively asAndis performed by the laplace transform.

The designed low-pass filter satisfies

Wherein the content of the first and second substances,for rejection of angular bands, omega_rThe highest angular frequency required by the EID estimator. Reasonably designed observer ensuresConverge onSelecting the time constant of the low-pass filter H(s)So thatFor allIs satisfactory.

Therefore, an improved loss of excitation fault suppression control rate of

u is the system input, u_fFor system input under the influence of a loss of field fault,is an equivalent input estimate for a loss of field fault. The improved control rate improves the disturbance suppression performance, and the influence of the magnetic loss interference on the system tends to be zero.

S3, testing the stability and the gain design of the integral sliding mode observer

The equation of state of error and the equation of dynamics of the integral sliding mode observer can be obtained by combining the equations (14), (16), (18) and (30) as

In the formula

A₁+A₂ω_e＝A (32)

Wherein

Order to

A₂-LC＝0 (33)

Can obtain

L＝A₂C⁺ (34)

Wherein C is⁺＝(C^TC)^-1C^T。

Thereby, can obtain

The above equation can also be derived from an equivalent input interference system through conventional SMO, i.e.

Comparing equation (35) and equation (36), it can be seen that, compared to the conventional SMO, the error state equation coefficient matrix of the integral sliding mode observerWithout electrical angular velocity omega of the motor_eCoefficient of decoupling ω_eThe introduction of the method eliminates the influence of the angular speed of the motor on an error system of the integral observer, and simultaneously notices the integral sliding-mode observer which comprises an integral term x_IThe introduction of the integral term increases the order of the state observer and the output of the system. The high-order observer can realize the quick dynamic estimation of the state variable, and the gain L is_IThe additional degree of freedom of (a) enhances the robustness of the observer.

The stability analysis of the integral sliding-mode observer is as follows:

assume that 1: for d_eAndthere is a small positive constant η₁Satisfy the requirement of

Theorem 1: there is a small normal number η₁，η₂And gamma satisfies

Where I is an identity matrix, selecting an appropriate gain L_IAnd K, the designed integral sliding mode observer (16) is gradually converged and finally stable.

And (3) proving that: selecting the Lyapunov function as

V₁＝e^Te (39)

Derived therefrom to obtain

According to the Yang inequality, a small normal number eta exists₂Satisfy the requirement of

Thus, can obtain

Therefore, as known from the Lyapunov stability theory, the designed integral sliding mode observer (16) is progressively convergent and finally bounded.

System stability analysis was as follows:

to analyze the stability of the entire EID system, consider an augmented system that includes a designed integral sliding mode observer, a low pass filter h(s), and a system (14).

The state space equation of the low-pass filter is

The combinations (26), (30) and (43) can be obtained

By substituting formulae (30) and (43) for formula (14)

According to formulae (19), (30) and (43) have

Combining the formulae (44), (45) and (46) to obtain an augmentation system of

Wherein

Theorem 2: there is a small normal number η₃，η₄，η₅And Λ satisfy

Then X will converge to the neighborhood Ω near the origin

Where τ is a small positive constant, so the augmentation system (47) is globally coherent and ultimately bounded.

And (3) proving that: selecting the Lyapunov function as

V₂＝X^TX (50)

Derived from formula (50)

According to the Yang inequality has eta₃，η₄，η₅Satisfy the requirement of

Then there is

When X is outside the region Ω, there are

Thus can be obtained inAt a time there is

This completes the system stability certification.

The designed magnetic loss fault tolerance control method is verified through an application example of a PMSM drive system, and the whole system framework diagram is shown in figure 3.

It should be understood that the above examples are only for clearly illustrating the technical solutions of the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.