阅读说明：本技术 一种基于滑模变结构的多电机系统高性能协同控制方法 (Sliding mode variable structure-based multi-motor system high-performance cooperative control method ) 是由 何静 张昌凡 *** 丁进 于 2020-05-27 设计创作，主要内容包括：本发明提供一种基于滑模变结构的多电机系统高性能协同控制方法,包括以下步骤：S1.设计多电机系统协同控制结构框架图；S2.建立以多永磁同步电机为执行器的数学模型及其状态方程；S3.设计多电机系统的转速环控制器和转矩控制器；S4.对S3中所设计的转速环控制器和转矩控制器进行稳定性证明。本发明能够解决轧机传动系统各电机的转矩均衡与转速同步控制的问题,使系统能够实现开卷与卷取张力实时处于动态平衡的控制状态。(The invention provides a sliding mode variable structure-based high-performance cooperative control method for a multi-motor system, which comprises the following steps of: s1, designing a multi-motor system cooperative control structure frame diagram; s2, establishing a mathematical model and a state equation thereof by taking a plurality of permanent magnet synchronous motors as actuators; s3, designing a rotating speed loop controller and a torque controller of the multi-motor system; and S4, carrying out stability verification on the rotating speed ring controller and the torque controller designed in the S3. The invention can solve the problems of torque balance and synchronous control of the rotating speed of each motor of the transmission system of the rolling mill, so that the system can realize the control state of dynamic balance of uncoiling and coiling tension in real time.)

1. A high-performance cooperative control method for a multi-motor system based on a sliding mode variable structure is characterized by comprising the following steps:

s1, designing a multi-motor system cooperative control structure frame diagram;

s2, establishing a mathematical model and a state equation thereof by taking a plurality of permanent magnet synchronous motors as actuators;

s3, designing a rotating speed loop controller and a torque controller of the multi-motor system;

s4, carrying out stability certification on the rotating speed ring controller and the torque controller designed in the S3;

the specific steps in step S1 include:

s11: tracking error e of j (1, 2,3, …, n) th motor in system_jComprises the following steps:

e_j＝ω_d-ω_j

wherein, ω is_dAnd ω_jInput rotation speed and output rotation speed of jth motor, when j equals n, omega_j+1＝ω₁；

S12: according to the designed multi-motor system cooperative control structure frame diagram, the tracking error E of the system after the jth motor compensation can be known_jComprises the following steps:

E_j＝e_j-γ_j(ω_j-ω_j+1)

wherein, γ_jRepresenting the feedback gain of the jth motor of the system;

s13: defining the synchronous error between the jth motor and the adjacent (j +1) th motor of the system as_jThen, there are:

_j＝ω_j-ω_j+1

s14: according to the tracking error e_jAnd synchronization error_jThe general expression of the tracking error of the jth motor of the system after coupling compensation can be obtained as follows:

E_j＝e_j-γ_{j j}

s15: the feedback gain of each motor of the system is designed to meet the following inequality, so that the rationality of a frame diagram of the designed multi-motor system cooperative control structure is ensured, and the synchronism of the rotating speed of each motor of the system is ensured; the feedback gain of each motor of the system is as follows:

(1+γ₁)(1+γ₂)(1+γ₃)…(1+γ_n)-γ₁γ₂γ₃…γ_n≠0。

2. the high-performance cooperative control method for the multi-motor system based on the sliding mode variable structure is characterized in that in step S2, the mathematical model of the permanent magnet synchronous motor is as follows:

wherein u is_dj、u_qjRespectively, the voltage component in the direction of the dq axis, i_dj、i_qjRespectively a direct-axis component and a quadrature-axis component of the stator current; r_sjAs stator winding resistance, omega_jIs the rotor electrical angular velocity; l is_dj、L_qjSynchronous inductances, psi, of direct and quadrature axes, respectively_fjIs the rotor flux linkage.

3. The method for the high-performance cooperative control over the multi-motor system based on the sliding mode variable structure according to claim 2 is characterized in that a torque equation and a mechanical motion equation of the permanent magnet synchronous motor are as follows:

wherein T is_ejFor electromagnetic torque, T_LjIs the load torque on the shaft, n_pjIs the number of pole pairs, R, of the motor_ΩjIs the coefficient of rotation resistance of the motor, omega_jIs the mechanical angular velocity of the rotor, J_jIs the moment of inertia.

4. The high-performance cooperative control method for the multi-motor system based on the sliding mode variable structure according to claim 1, wherein in step S3, the rotating speed loop controller is:

5. the high-performance cooperative control method for the multi-motor system based on the sliding mode variable structure according to claim 1, wherein in step S3, the torque controller is:

6. the high-performance cooperative control method for the multi-motor system based on the sliding mode variable structure is characterized in that sgn(s)_j) Can use continuous functions

7. The high-performance cooperative control method for the multi-motor system based on the sliding mode variable structure is characterized in that the stability of the rotating speed loop controller and the torque controller in S3 is proved through a Lyapunov function in the step S4.

8. The high-performance cooperative control method for the multiple motor system based on the sliding mode variable structure according to claim 1, wherein in step S2, the type of the permanent magnet synchronous motor is a non-salient pole type permanent magnet synchronous motor.

Technical Field

The invention relates to the field of multi-axis synchronous control equipment, in particular to a sliding mode variable structure-based multi-motor system high-performance cooperative control method.

Background

The transmission system of the rolling mill is a particularly key process link in the production process of the metallurgical industry, and has a great significance in the metallurgical industry.

The essence of the rolling mill transmission system belongs to the technical field of multi-motor synchronous control, the multi-motor synchronous control system belongs to a complex model with strong coupling, nonlinearity and multivariable, and the rolling mill transmission system is provided with rigorous control requirements on the torque and the rotating speed of each motor of the system, so that the system puts higher requirements on the cooperative control performance of the multi-motor.

In the existing rolling mill transmission system, the cooperative control performance of multiple motors still has certain defects, for example, the problem of double synchronous control of torque and rotating speed cannot be considered, which leads to the incapability of powerfully guaranteeing the cooperative performance of each motor of the rolling mill transmission control system; the cooperative performance is the key for the effective application of the multi-motor synchronous control technology in the transmission system of the rolling mill, because the cooperative performance directly influences the reliability of the production of machine equipment and the quality of products.

Disclosure of Invention

The invention aims at the problem that the existing multi-motor system control technology can not ensure that all motors can keep synchronous rotating speed while ensuring the torque balance, so that the uncoiling and coiling tension of the system can realize dynamic balance; the high-performance cooperative control method for the multi-motor system based on the sliding mode variable structure is provided.

In order to achieve the purpose, the invention adopts the following technical scheme:

a sliding mode variable structure-based multi-motor system high-performance cooperative control method comprises the following steps:

s1, designing a multi-motor system cooperative control structure frame diagram;

s2, establishing a mathematical model and a state equation thereof by taking a plurality of permanent magnet synchronous motors as actuators;

s3, designing a rotating speed loop controller and a torque controller of the multi-motor system;

s4, the stability of the rotating speed ring controller and the torque controller designed in the S3 is proved.

Further, the specific steps in step S1 include:

s11: tracking error e of j (1, 2,3, …, n) th motor in system_jComprises the following steps:

e_j＝ω_d-ω_j

wherein, ω is_dAnd ω_jInput rotation speed and output rotation speed of jth motor, when j equals n, omega_j+1＝ω₁；

S12: according to the designed multi-motor system cooperative control structure frame diagram, the tracking error E of the system after the jth motor compensation can be known_jComprises the following steps:

E_j＝e_j-γ_j(ω_j-ω_j+1)

wherein, γ_jRepresenting the feedback gain of the jth motor of the system;

s13: defining the synchronous error between the jth motor and the adjacent (j +1) th motor of the system as_jThen, there are:

_j＝ω_j-ω_j+1

s14: according to the tracking error e_jAnd synchronization error_jThe general expression of the tracking error of the jth motor of the system after coupling compensation can be obtained as follows:

E_j＝e_j-γ_{j j}

s15: the feedback gain of each motor of the system is designed to meet the following inequality, so that the rationality of a frame diagram of the designed multi-motor system cooperative control structure is ensured, and the synchronism of the rotating speed of each motor of the system is ensured; the feedback gain of each motor of the system is as follows:

(1+γ₁)(1+γ₂)(1+γ₃)···(1+γ_n)-γ₁γ₂γ₃···γ_n≠0

further, in step S2, the mathematical model of the permanent magnet synchronous motor is:

wherein u is_dj、u_qjRespectively in the dq axis directionA voltage component of_dj、i_qjRespectively a direct-axis component and a quadrature-axis component of the stator current; r_sjAs stator winding resistance, omega_jIs the rotor electrical angular velocity; l is_dj、L_qjSynchronous inductances, psi, of direct and quadrature axes, respectively_fjIs the rotor flux linkage.

Further, the torque equation and the mechanical motion equation of the permanent magnet synchronous motor are as follows:

wherein, T_ejFor electromagnetic torque, T_LjIs the load torque on the shaft, n_pjIs the number of pole pairs, R, of the motor_ΩjIs the coefficient of rotation resistance of the motor, omega_jIs the mechanical angular velocity of the rotor, J_jIs the moment of inertia.

Further, in step S3, the speed loop controller is:

further, in step S3, the torque controller is:

further, sgn(s)_j) Can use continuous functionsInstead, the value is a smaller normal number.

Further, the stability of the speed loop controller and the torque controller in S3 is verified by the Lyapunov function in step S4.

Further, in step S2, the permanent magnet synchronous motor is a non-salient pole type permanent magnet synchronous motor.

The invention has the beneficial effects that: the problems of multivariable, strong coupling, time-varying physical parameters and the like of a multi-motor synchronous control system are effectively overcome, so that the system has the advantages of high dynamic response characteristic, high reliability and high synergistic capability, the motors of the system can well meet the complex working condition requirement of full time domain synchronization of torque and rotating speed, and the system has certain help for practical engineering application of a rolling mill transmission control system.

Drawings

FIG. 1 is a framework diagram of a multi-motor system high-performance cooperative control structure based on a sliding mode variable structure.

Detailed Description

The present invention will be further described with reference to the following embodiments.

A sliding mode variable structure-based multi-motor system high-performance cooperative control method comprises the following steps:

s1, designing a multi-motor cooperative control structure block diagram aiming at the working characteristics of a transmission system of the rolling mill;

s11: tracking error e of j (1, 2,3, …, n) th motor in system_jComprises the following steps:

e_j＝ω_d-ω_j(1)

in the formula (1), ω is_dAnd ω_jThe input rotation speed and the output rotation speed of the jth motor are respectively, wherein when j equals n, omega_j+1＝ω₁。

S12: according to the designed multi-motor cooperative control structure block diagram, the tracking error E of the system after the compensation of the jth motor can be known_jComprises the following steps:

E_j＝e_j-γ_j(ω_j-ω_j+1) (2)

in the formula (2), gamma_jRepresenting the feedback gain of the jth motor of the system.

S13: defining the synchronous error between the jth motor and the adjacent (j +1) th motor of the system as_jThen, there are:

_j＝ω_j-ω_j+1(3)

s14: by substituting equations (1) and (3) into equation (2), the general expression of the tracking error of the jth motor of the system after coupling compensation can be obtained as follows:

E_j＝e_j-γ_{j j}(4)

s15: e can be substituted by the formula (2)_jThe transformation is performed as follows:

the above equation (5) is formulated in matrix form as:

Y＝AX (6)

wherein Y ═ E₁,E₂,…,E_n]^T；

X＝[e₁,e₂,…,e_n]^TIf the matrix equation (6) has only a unique zero solution, the determinant of the matrix a is not zero, i.e. there is:

this is obtained by solving the following equation (7):

(1+γ₁)(1+γ₂)(1+γ₃)···(1+γ_n)-γ₁γ₂γ₃···γ_n≠0 (8)

as is clear from formulas (5) and (6), when Y is 0, E is also the same_jWhen 0 is satisfied, only the design parameter γ is required_jIf equation (8) is satisfied, the tracking error X can be made 0, i.e., e_jWhen the system synchronization error is found by the combination formula (4) as 0_jAnd 0, so that the tracking error and the synchronization error of the system can be eliminated, and necessary conditions can be effectively created for the synchronization control of the system.

S2: establishing a mathematical model and a state equation thereof by taking a plurality of permanent magnet synchronous motors as an actuator;

s21: the permanent magnet synchronous motor adopts a non-salient pole type, and a mathematical model based on a j (j ═ 1,2, ·, n) th motor under a d-q coordinate system is as follows:

in the formula (9), u_dj、u_qjRespectively, the voltage component in the direction of the dq axis, i_dj、i_qjRespectively a direct-axis component and a quadrature-axis component of the stator current; r_sjAs stator winding resistance, omega_jIs the electrical angular velocity of the rotor, L_dj、L_qjSynchronous inductances, psi, of direct and quadrature axes, respectively_fjIs the rotor flux linkage.

S22: the torque equation and the mechanical motion equation of the permanent magnet synchronous motor are as follows:

in the formula (10), T_ejFor electromagnetic torque, T_LjIs the load torque on the shaft, n_pjIs the number of pole pairs, R, of the motor_ΩjIs the coefficient of rotation resistance of the motor, omega_jIs the mechanical angular velocity of the rotor, J_jIs the moment of inertia. The conversion formula of the electrical angular velocity and the mechanical angular velocity is as follows:

considering a non-salient pole synchronous motor L_dj＝L_qj＝L_jWhile employing i_djIn the current vector control method of 0, the torque equation in equation (10) may be changed to:

T_ej＝1.5n_pjψ_fji_qj(12)

s23: substituting equations (11) and (12) for the mechanical equation of motion in equation (10) yields the following relationship:

let in the above formula (13)

i_qj＝f_jThen, formula (13) can be converted to:

step S3: a rotating speed ring controller and a torque controller of the system are respectively designed;

s31: design speed loop controller u₀：

According to the theoretical explanation of S1, if E is to be adjusted_jIf 0 holds true, then the Lyapunov function can be constructed

Then

When in useWhen present, then there areThus, at this time E_j→ 0, the system is stable, where k_jThe larger normal number.

The equation can be derived from equation (4):

the formula (14) may be substituted for the formula (15):

the virtual controller can be constructed according to equation (16) as follows:

will be provided with

Substituting formula (16) to obtain:

-k_jE_j＝-k_j(e_j-γ_{j j})＝-[(1+γ_j)a_j-γ_ja_j+1)]e_j+γ_ja_{j+1 j}+u_j(18)

the system virtual controller obtained by solving equation (18) is as follows:

u_j＝[(1+γ_j)a_j-γ_ja_j+1)-k_j]e_j+[γ_j(k_j-a_j+1)]_j(19)

at this time, the system satisfies E_j→ 0, provides the necessary demonstration conditions for the theoretical explanation of S1.

The speed loop controller u can then be obtained from equation (19)₀The following were used:

by designing the controller shown in the formula (20), the system can also meet the requirement E_j→ 0 from the theoretical explanation of equation (6), the tracking error e can be derived_jAnd synchronization error_jCan be eliminated.

S32: design Torque controller u'_j：

Defining the tracking error of the electromagnetic torque of the jth motor of the system as tau_jThen, there are:

τ_j＝T_ej-T_ed(21)

from the formula (12):

let 1.5n in the above formula (22)_pjψ_fj＝b_j，Is the controller u 'to be designed'_jEquation (22) can therefore be simplified to the following form:

selecting a slip form surface as follows:

s_j＝τ_j(24)

s4: the stability of the rotating speed ring controller and the torque controller designed in the S3 is proved;

theorem 1: aiming at the designed multi-motor cooperative control structure block diagram, a sliding mode surface of an equation (24) is selected, and if the controller is designed as follows:

the controller designed by the system can balance and synchronously control the torques of the motors.

Proof 1: the Lyapunov function is defined as follows:

derivation is performed on equation (26):

substituting the controller designed in equation (25) into equation (27) can obtain:

as can be seen from equation (28), the system is formed from the slip surface s_jStarting from any state except 0, the system reaches the sliding mode surface within a limited time, and once the system reaches the sliding mode surface, the system has s_j＝0，d(s_j) Where dt is 0, the torque tracking error τ of each motor in the system can be found from the equations (21) and (24)_j0, the system is therefore progressively stable.

Fig. 1 is a framework diagram of a high-performance cooperative control structure of a multi-motor system based on a sliding mode variable structure, and as shown in the figure, the structural design concept is to use the 1 st permanent magnet synchronous motor as a master motor and use the other n-1 motors as slave motors. Firstly, summing the virtual controllers of n motors, and then obtaining a rotation speed loop controller u by averaging₀And then the electromagnetic torque of the 1 st motor is used as the input of other n-1 motors, and finally, the torque balance and the full-time synchronization of the rotating speed of the system are ensured through a torque closed loop and a rotating speed closed loop.