阅读说明：本技术 一种表贴式永磁同步电机调速系统的饱和控制方法 (saturation control method of surface-mounted permanent magnet synchronous motor speed regulation system ) 是由 何友国 田肖肖 袁朝春 蔡英凤 郭柯屹 于 2019-08-26 设计创作，主要内容包括：本发明公开了一种表贴式永磁同步电机调速系统的饱和控制方法,属于电机控制领域,本发明的表贴式永磁同步电机控制方法采用电流环和速度环双闭环控制方法,电流环采用传统PI控制方法,速度环采用基于低增益Lyapunov函数饱和控制方法。本发明能够有效地避免电流积分饱和,在快速响应的同时有效地抑制了过大电流,能够保证表贴式永磁同步电机在弱磁升速工况时电流出现饱和的情况下使得表贴式永磁同步电机工作在安全电流范围内,提高了表贴式永磁同步电机的可靠性,解决了表贴式永磁同步电机快速响应与启动或变负载运行时大电流之间的矛盾。(the invention discloses a saturation control method of a surface-mounted permanent magnet synchronous motor speed regulation system, which belongs to the field of motor control. The invention can effectively avoid current integral saturation, effectively inhibit overlarge current while realizing quick response, ensure that the surface-mounted permanent magnet synchronous motor works in a safe current range under the condition that the current is saturated when the surface-mounted permanent magnet synchronous motor is under the weak magnetic speed-up working condition, improve the reliability of the surface-mounted permanent magnet synchronous motor and solve the contradiction between quick response and large current when the surface-mounted permanent magnet synchronous motor is started or has variable load.)

1. A saturation control method of a surface-mounted permanent magnet synchronous motor speed regulation system is composed of a speed loop and current loop double-closed-loop control vector control method; the method is characterized in that the speed ring adopts a low-gain saturation control method based on a Lyapunov function.

2. The saturation control method of the surface-mounted permanent magnet synchronous motor speed regulating system according to claim 1, wherein the speed ring adopts a Lyapunov function-based low-gain saturation control method to act on a surface-mounted permanent magnet synchronous motor current saturation control model.

3. The saturation control method of the surface-mounted permanent magnet synchronous motor speed regulating system according to claim 2, wherein the design method of the current saturation control model is as follows:

The mathematical model of the surface-mounted permanent magnet synchronous motor under the synchronous rotating coordinate system d-q is obtained through coordinate transformation and is as follows:

Wherein: u. of_d、u_qD-q axis components of the stator voltage, respectively; i.e. i_d、i_qAre the d-q axis components of the stator current, respectively; r is the stator resistance; p is a radical of_nThe number of pole pairs of the motor rotor is; psi_fIs a permanent magnet flux linkage; j is the rotational inertia of the motor; t is_LIs the load torque; l is_sIs a stator inductance; omega is the actual rotating speed;

By using i_dThe rotor magnetic field orientation control method which is 0 carries out control, and the mathematical model is as follows:

Defining the state variables of the surface-mounted permanent magnet synchronous motor system as follows:

wherein x is₁Is given a reference speed of rotation omega^*The rotation speed omega measured by the photoelectric encoder is subjected to velocity deviation by a subtracter;

From equations (2) and (3), the following equation of state is obtained:

Definition x ═ x₁ x₂]^T，The equation of state is

4. The saturation control method of the surface-mounted permanent magnet synchronous motor speed regulating system according to claim 3, characterized in that a saturation function sat () is introduced to perform saturation processing on the q-axis current of the motor, and the state equation of the saturation control model of the surface-mounted permanent magnet synchronous motor is designed as follows:

5. the saturation control method of the surface-mounted permanent magnet synchronous motor speed regulating system according to claim 4, wherein the Lyapunov function-based low-gain saturation control method comprises the following steps: the low-gain Lyapunov function is designed as follows:

V(x(t))＝x^T(t)P(γ)x(t) (7)

And gamma in the positive definite matrix P (gamma) is very small, so that the requirement of a low-gain Lyapunov function is met.

6. the saturation control method of the surface-mounted permanent magnet synchronous motor speed regulating system according to claim 5, wherein the Lyapunov function-based low-gain saturation control method further comprises the following steps: the saturation controller is designed as follows: u (t) ═ R^{- 1}B^TP(γ)x(t)；

where R is a reversible parameter-tunable matrix with a unique positive solution to make P (γ) satisfy the Riccati equation.

7. The saturation control method of the surface-mounted permanent magnet synchronous motor speed regulating system according to claim 6, wherein the Lyapunov function-based low-gain saturation control method comprises the following specific steps:

Establishing Riccati equation A^TP+PA-PBR^-1B^T＝-γP；

Solving the Riccati equation to obtain P (γ):

the saturation controller is designed as follows:

u(t)＝-R^-1B^TP(γ)x(t)

Wherein R is a reversible parameter-adjustable matrix having a unique positive solution for P (gamma) satisfying the Riccati equation; namely:

8. The saturation control method for the speed regulating system of the surface-mounted permanent magnet synchronous motor according to any one of claims 1 to 7, wherein the current loop adopts a PI control method.

Technical Field

The invention relates to the field of motor control, in particular to a saturation control method of a surface-mounted permanent magnet synchronous motor speed regulating system.

Background

The surface-mounted permanent magnet synchronous motor has the advantages of small volume, high efficiency, simple structure, small rotational inertia and the like, is widely applied in the fields of spaceflight, numerical control machines, electric automobiles and the like, most of the surface-mounted permanent magnet synchronous motor speed controllers at the present stage adopt PI regulators, the algorithm is simple, the reliability is high, the regulation is convenient, and the control requirement in a certain range can be met, however, the surface-mounted permanent magnet synchronous motor is a complex system with nonlinearity, multivariable, strong coupling and variable parameters, the performance of the PI regulators is easily influenced by system parameter change, external disturbance and the like, and the requirement of the system on high performance control cannot be met. In addition, in the PI regulator control strategy, the static error of the control system is eliminated by using an error integral term, and at the moment, the current integral saturation phenomenon is caused. Meanwhile, the surface-mounted permanent magnet synchronous motor also has the problem of current regulator saturation in the weak magnetic speed-up operation, which leads to the loss of control of the stator current. Therefore, the PI controller cannot meet the smaller overshoot while achieving the system response rapidity under the current saturation. The sliding mode variable structure control is a nonlinear control method, has good robustness and dynamic performance on internal parameters and external disturbance, and has high steady-state control precision, so the sliding mode variable structure control becomes a research hotspot in the field of motor control. However, due to the fact that discontinuous switch control exists in sliding mode variable structure control, the application of a sliding mode control technology in actual engineering is severely limited by the existence of buffeting and integral saturation problems, and the performance of a control system is affected. Through the analysis, the stable control of the surface-mounted permanent magnet synchronous motor can be realized only by carrying out saturation control on the stator current. Therefore, in order to improve the robustness and the rapidity of the speed regulating system of the surface-mounted permanent magnet synchronous motor and avoid the problem of regulator saturation caused by overlarge current when the motor is started and operates with variable load, the invention provides a saturation control strategy of the speed regulating system of the surface-mounted permanent magnet synchronous motor.

disclosure of Invention

The invention aims to provide a saturation control strategy of a surface-mounted permanent magnet synchronous motor speed regulating system, which solves the contradiction between quick response and large current during starting or variable load operation of the surface-mounted permanent magnet synchronous motor. The control method of the surface-mounted permanent magnet synchronous motor adopts a current loop and speed loop double-closed-loop control method, the current loop adopts a traditional PI control method, and the speed loop adopts a saturation control method based on a low-gain Lyapunov function. The invention can effectively avoid current integral saturation, effectively inhibit overlarge current while realizing quick response, ensure that the surface-mounted permanent magnet synchronous motor works in a safe current range under the condition that the current is saturated when the surface-mounted permanent magnet synchronous motor is under the weak magnetic speed-up working condition, and improve the reliability of the surface-mounted permanent magnet synchronous motor.

The technical scheme of the invention is as follows: a saturation control method of a surface-mounted permanent magnet synchronous motor speed regulation system is composed of a double closed-loop control vector control method consisting of a current loop and a speed loop. The current loop adopts a traditional PI control method, and the speed loop adopts a saturation control method based on a low-gain Lyapunov function, as shown in FIG. 3.

The surface-mounted permanent magnet synchronous motor saturation control model is modeled as follows:

as shown in fig. 1, in order to simplify the mathematical model of the three-phase surface-mounted permanent magnet synchronous motor in the natural coordinate system, the present invention adopts stationary coordinate transformation (Clark transformation) and synchronous rotating coordinate transformation (Park transformation), as shown in fig. 2, the mathematical model of the surface-mounted permanent magnet synchronous motor in the synchronous rotating coordinate system d-q is obtained as follows:

Wherein: u. of_d、u_qd-q axis components of the stator voltage, respectively; i.e. i_d、i_qare the d-q axis components of the stator current, respectively; r is the stator resistance; p is a radical of_nthe number of pole pairs of the motor rotor is; psi_fIs a permanent magnet flux linkage; j is the rotational inertia of the motor; t is_LIs the load torque; l is_sIs a stator inductance; ω is the actual rotational speed.

for a surface-mounted permanent magnet synchronous motor, i is adopted_dthe rotor magnetic field orientation control method which is 0 carries out control, and the mathematical model is as follows:

taking the state variable of the surface-mounted permanent magnet synchronous motor system as follows:

wherein x is₁is given a reference speed of rotation omega^*And the speed deviation is obtained through a subtracter together with the rotating speed omega measured by the photoelectric encoder.

From equations (2) and (3), the following equation of state is obtained:

definition ofThe state equation can be rewritten as

in the control of the surface-mounted permanent magnet synchronous motor, the current and the rotating speed of the motor cannot exceed a certain range, and when the current and the rotating speed exceed the range, the current and the rotating speed are saturated. During speed loop control, the speed loop outputs a q-axis current value, which is integrated, and current saturation occurs when the current exceeds the range of current that can be supplied by the motor. Therefore, the saturation function sat (-) is introduced to perform saturation processing on the q-axis current of the motor, and the state equation of the saturation control model of the surface-mounted permanent magnet synchronous motor is as follows:

the speed loop saturation control algorithm of the invention is as follows:

The low gain Lyapunov function was chosen as:

V(x(t))＝x^T(t)P(γ)x(t) (7)

and gamma in the positive definite matrix P (gamma) is very small, so that the requirement of a low-gain Lyapunov function is met.

setting adjustable parameter gamma^*> 0, and satisfies the following equation

Wherein: xi (P (gamma), 1) is ellipsoid { x: x^TPx≤1}。

The saturation state feedback controller is designed as follows:

u(t)＝-R^-1B^TP(γ)x(t) (9)

Such that the derivative of the low-gain Lyapunov function V (x (t)) along the trajectory of the closed-loop system (6) satisfies

the closed loop system (6) is rewritten to

Then if and only iffor any given γ ∈ (0, γ) when bounded by Φ^*]The system (11) will not saturate, so for any γ ∈ (0, γ ∈)^*]The closed loop system (11) is progressively stable in saturation conditions.

In order to enable P (gamma) to meet the requirements, the invention adopts a parametric Riccati equation method to solve P (gamma).

The parametric Riccati equation from equation of state (5) is:

A^TP+PA-PBR^-1B^T＝-Q (12)

Wherein Q is a positive definite matrix and R is a reversible parameter adjustable matrix.

Let Q be γ P, where γ > 0, P being the only symmetric positive solution of the parametric Riccati equation shown in equation (13).

A^TP+PA-PBR^-1B^T＝-γP (13)

To solve the Riccati equation to obtain P (γ) > 0, let P (γ) be W^-1(γ), then equation (13) becomes:

Solving formula (14) to obtain W (gamma), and further obtaining P (gamma), wherein W_(γ)Is an invertible matrix of a matrix P (γ), P (γ) being an effective parameter of the controller, obtained by solving the lyapunov equation:

i.e. when u (t) ═ R^-1B^TP (γ) x (t), the closed loop system (11) becomes progressively stable under saturation conditions.

Wherein the content of the first and second substances,

The invention has the beneficial effects that:

in order to solve the problem that the current of a q axis is overlarge and fluctuates due to the fact that an existing surface-mounted permanent magnet synchronous motor speed regulating system dynamically and quickly tracks a given speed, the invention provides a saturation control method of the surface-mounted permanent magnet synchronous motor speed regulating system. The low-gain saturation controller designed by the invention can ensure that the surface-mounted permanent magnet synchronous motor works in a safe current range under the condition that the current is saturated when the surface-mounted permanent magnet synchronous motor is under a weak magnetic speed-up working condition, thereby avoiding the occurrence of an overcurrent phenomenon and improving the reliability of the surface-mounted permanent magnet synchronous motor.

drawings

Fig. 1 is a physical model of a surface-mounted permanent magnet synchronous motor controlled by the present invention.

Fig. 2 is a schematic diagram of coordinate transformation.

Fig. 3 is a schematic block diagram of a surface-mounted permanent magnet synchronous motor speed control system of the present invention.

FIG. 4 is a flow chart of the controller design according to the present invention.

Detailed Description

The invention will be further explained with reference to the drawings.

The parameters in FIGS. 1-4 are first explained:

A. B, C is natural coordinate system, alpha-beta is stationary coordinate system, d-q is synchronous rotating coordinate system, omega_eis the angular velocity, θ, of the motor_eThe conversion angle of a natural coordinate system and a synchronous rotation coordinate system is obtained; omega^*For a given reference speed, ω is the actual speed, θ is the motor rotation angle, i_d ^*、i_q ^*For d-q axis input current, U_d、U_qAre the d-q axis components of the stator voltage, U, respectively_α、U_βAre the alpha-beta axis component, U, of the stator voltage, respectively_dcIs the bus voltage i_d、i_qAre the d-q axis components, i, of the stator current, respectively_a、i_bThe motor phase current is, the PI is a proportional integral controller, the SVPWM is space vector pulse width modulation, and the PMSM is a surface-mounted permanent magnet synchronous motor.

referring to fig. 3, a saturation control method of a surface-mounted permanent magnet synchronous motor speed regulation system is composed of a double closed-loop control vector control method composed of a speed loop and a current loop. The current loop adopts a traditional PI control method, and the speed loop adopts a low-gain saturation control method based on a Lyapunov function.

As shown in fig. 4, the implementation steps of the control method of the present invention include: firstly, establishing a current saturation control model according to a surface-mounted permanent magnet synchronous motor; secondly, a low-gain saturation control method is designed based on the Lyapunov function.