阅读说明：本技术 一种基于改进型偏差耦合的多电机滑模协同控制方法 (Multi-motor sliding mode cooperative control method based on improved deviation coupling ) 是由 张昌凡 肖明杰 何静 于 2020-03-25 设计创作，主要内容包括：本发明提供一种基于改进型偏差耦合的多电机滑模协同控制方法；包括以下步骤：S1、在多电机系统中,根据永磁同步电机矢量控制策略,得到永磁同步电机的状态方程；S2、在多电机系统中,将灌装电机状态方程设计为切换系统,传送电机系统状态方程保持不变,同时定义各电机的系统误差、跟踪误差和同步误差信号；S3、设计等效滑模控制器；S4、验证系统的稳定性。通过对经典偏差耦合控制策略进行改进,重点在于解决灌装多电机系统在复杂工况下的协同控制问题。其中,设计的滑模变结构控制器可以保证系统的单轴误差收敛,灌装电机的切换子系统可以在停机-启动时刻负载转矩突变的复杂工况下,提高多电机系统的协同性能。(The invention provides a multi-motor sliding mode cooperative control method based on improved deviation coupling; the method comprises the following steps: s1, in the multi-motor system, according to the vector control strategy of the permanent magnet synchronous motor, obtaining a state equation of the permanent magnet synchronous motor; s2, in the multi-motor system, designing the state equation of the filling motor as a switching system, keeping the state equation of the transmission motor system unchanged, and defining the system error, the tracking error and the synchronous error signal of each motor; s3, designing an equivalent sliding mode controller; and S4, verifying the stability of the system. By improving the classical deviation coupling control strategy, the method mainly solves the problem of cooperative control of the filling multi-motor system under the complex working condition. The designed sliding mode variable structure controller can ensure single-axis error convergence of the system, and the switching subsystem of the filling motor can improve the cooperative performance of a multi-motor system under the complex working condition of sudden load torque change at the moment of stopping and starting.)

1. A multi-motor sliding mode cooperative control method based on improved deviation coupling is characterized by comprising the following steps:

s1, in the multi-motor system, according to the vector control strategy of the permanent magnet synchronous motor, obtaining the state equation of the jth motor in the multi-motor system as follows:

in the formula, theta_jAs rotor position, ω_jAs electrical angular velocity, T, of the rotor_LjIs the load torque on the shaft, R_ΩjIs the coefficient of rotation resistance of the motor, J_jIs moment of inertia, n_pjIs the pole pair number of the motor, psi_fjFor rotor flux linkage i_dj、i_qjRespectively a direct-axis component and a quadrature-axis component of the stator current;

order toThe above formula can be expressed as:

wherein: u. of_j＝i_qjA controller to be designed;

s2, the multi-motor system is composed of filling motors and transmission motors, a state equation of the filling motors is designed to be a switching system, the state equation of the transmission motor system is kept unchanged, and system errors, tracking errors and synchronous errors of the motors are defined; the filling motor switching system expression is as follows:

wherein f is₁(ω₁₁T) and ω₁₁Respectively the subsystem and the rotation speed f of the motor 1 in the shutdown state₂(ω₁₂T) and ω₁₂The subsystems and the rotating speed of the motor 1 in the starting state are respectively;

the transmission motor system expression is as follows:

wherein: omega_kTransmitting the rotating speed of the motor in a multi-motor system;

s3, designing an equivalent sliding mode controller; the equivalent sliding mode controller expression is:

j＝1,k.k＝2,…,n.i＝1,2,…,n，i≠j

wherein, K_jFor the sliding form coefficient to be designed, s_jIs a slip form surface to be designed;

and S4, verifying the stability of the system.

2. The method for multi-motor sliding-mode cooperative control based on improved deviation coupling according to claim 1, wherein in step S2, the specific expression of the systematic error is as follows:

3. the multi-motor sliding-mode cooperative control method based on the improved deviation coupling as claimed in claim 1, wherein the tracking error concrete expression in step S2 is as follows:

4. the method for multi-motor sliding-mode cooperative control based on improved deviation coupling according to claim 1, wherein in step S2, the specific expression of the synchronization error is as follows:

5. the improved deviation coupling-based multi-motor sliding mode cooperative control method according to claim 1, wherein a system L yapunov function is selected for proving in step S4.

Technical Field

The invention relates to the technical field of filling production control of thick sauce and viscous food, in particular to a multi-motor sliding mode cooperative control method based on improved deviation coupling.

Background

From the dietary structure of the people, thick sauce such as seasoning sauce, honey and the like and viscous food are deeply liked by the people in life, and the matched intelligent filling equipment is required to meet the special requirement of high-viscosity filling materials, so that the food industry huge market demand is met. Under the background, aiming at the situation that a large amount of start-stop operations occur in the filling process of thick sauce food production process flows, particularly in the filling process, the filling operation is completed under a static condition, and a multi-motor transmission system is a dynamic process, so that after the material filling is completed, the multi-motor system can be restarted, the change of filling materials can bring sudden changes of load torque of a servo motor driving a filling station, and the process can greatly influence the synchronization performance of the multi-motor system. Therefore, the technical problem of multi-machine cooperative control under complex filling conditions needs to be solved, and the synchronous control of the rotating speed of a multi-motor system is realized mainly by researching the special condition that the motor load torque of a filling station is suddenly changed in the starting-stopping and starting-stopping transition states, particularly in the stopping-starting process.

Disclosure of Invention

The invention provides an improved deviation coupling-based multi-motor sliding mode cooperative control method, aiming at the problem that in the prior art, the synchronous performance of a multi-motor system is greatly influenced due to sudden change of motor torque caused by material filling of the multi-motor system.

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

a multi-motor sliding mode cooperative control method based on improved deviation coupling comprises the following steps:

s1, in the multi-motor system, according to the vector control strategy of the permanent magnet synchronous motor, obtaining the state equation of the jth motor in the multi-motor system as follows:

in the formula, theta_jAs rotor position, ω_jAs electrical angular velocity, T, of the rotor_LjIs the load torque on the shaft, R_ΩjIs the coefficient of rotation resistance of the motor, J_jIs moment of inertia, n_pjIs the pole pair number of the motor, psi_fjFor rotor flux linkage i_dj、i_qjRespectively a direct-axis component and a quadrature-axis component of the stator current;

order toThe above can be expressed as:

wherein: u. of_j＝i_qjAnd is the controller to be designed.

And S2, the multi-motor system is composed of a filling motor and a transmission motor, the state equation of the filling motor is designed into a switching system, the transmission motor system is kept unchanged, and the system error, the tracking error and the synchronization error of each motor are defined. The filling motor switching system expression is as follows:

wherein f is₁(ω₁₁T) and ω₁₁Respectively the subsystem and the rotation speed f of the motor 1 in the shutdown state₂(ω₁₂T) and ω₁₂Which are the subsystem and the rotation speed, respectively, of the electric machine 1 in the starting state.

The transmission motor system expression is as follows:

wherein: omega_kThe rotating speed of the motor is transmitted in a multi-motor system.

S3, designing an equivalent sliding mode controller; the equivalent sliding mode controller expression is:

j＝1,k.k＝2,…,n.i＝1,2,…,n，i≠j

wherein, K_jFor the sliding form coefficient to be designed, s_jIs a slip form surface to be designed;

and S4, verifying the stability of the system.

Further, in step S2, the specific expression of the system error is:

further, the tracking error concrete expression in step S2 is:

further, in step S2, the synchronization error concrete expression is:

further, in step S4, a system L yapunov function is selected for the proof.

The invention has the advantages that the smooth characteristic of the switching system is utilized to solve the synchronization problem of the filling multi-motor system under the complex working condition, and the problems of poor tracking precision and untimely synchronous response of the control system caused by the sudden change of the motor load torque in the stopping-starting process, further generation of a large amount of unqualified products and resource waste are prevented; meanwhile, an equivalent sliding mode controller is used for eliminating tracking errors and synchronization errors among all servo in the operation process of the multi-motor system, and further synchronous control of the filling multi-motor transmission system is achieved.

Drawings

FIG. 1 is a block diagram of the structure;

fig. 2 is a rotation speed following graph of the motor 1;

fig. 3 is a graph of the rotational speed following the motor 2;

fig. 4 is a rotation speed following graph of the motor 3;

fig. 5 is a comparison graph of the rotational speed tracking error of the motor 1;

fig. 6 is a comparison graph of the rotational speed tracking error of the motor 2;

fig. 7 is a comparison graph of the rotational speed tracking error of the motor 3;

FIG. 8 is a comparison graph of the rotational speed synchronization error between the motor 1 and the motor 2;

FIG. 9 is a comparison graph of the rotational speed synchronization error between the motor 1 and the motor 3;

fig. 10 is a comparison graph of the rotational speed synchronization error between the motors 2 and 3.

Detailed Description

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

A multi-motor sliding mode cooperative control method based on improved deviation coupling; the method comprises the following steps:

s1, in the multi-motor system, according to the vector control strategy of the permanent magnet synchronous motor, obtaining a state equation of the permanent magnet synchronous motor; the state equation of the permanent magnet synchronous motor is as follows:

in the formula, theta_jAs rotor position, ω_jAs electrical angular velocity, T, of the rotor_LjIs the load torque on the shaft, R_ΩjIs the coefficient of rotation resistance of the motor, J_jIs moment of inertia, n_pjIs the pole pair number of the motor, psi_fjFor rotor flux linkage i_dj、i_qjRespectively a direct-axis component and a quadrature-axis component of the stator current;

order toThe above can be expressed as:

in the formula: u. of_i＝i_qjAnd is the controller to be designed.

And S2, in the multi-motor system, the multi-motor system mainly comprises a filling motor and a transmission motor. The filling motor state equation is designed into a switching system, a conveying motor system is kept unchanged, and the system error, the tracking error and the synchronization error of each motor are defined. The filling motor switching system expression is as follows:

in the formula (f)₁(ω₁₁T) and ω₁₁Respectively the subsystem and the rotation speed f of the motor 1 in the shutdown state₂(ω₁₂T) and ω₁₂Which are the subsystem and the rotation speed, respectively, of the electric machine 1 in the starting state.

The transmission motor system expression is as follows:

in the formula: omega_kThe rotating speed of the motor is transmitted in a multi-motor system.

Further, the definition of the single-axis tracking error of the multi-motor system is given and specifically expressed as follows:

in the formula:ω_jrespectively, the given rotating speed and the actual output rotating speed of the jth motor of the system.

Further, a single axis synchronization error is given, which is expressed as:

τ_ji＝ω_j-ω_i,j＝1,k.k＝2,…,n.i＝1,2,…,n，i≠j. (6)

in the formula: tau is_jiIndicating the synchronization error between the jth motor and the ith motor.

In the deviation coupling control strategy, a speed compensator is often adopted for feedback adjustment aiming at synchronous errors, in order to eliminate the influence on the synchronous performance caused by different rotational inertia of each motor, a speed compensator module adopts a fixed gain compensator, and synchronous error compensation signals are as follows:

in the formula:

will track errorAnd a synchronization error compensation signal Δ ω_jCoupling to obtain the single-shaft system error of the multi-motor system, which is specifically expressed as follows:

s3, designing an equivalent sliding mode controller; the equivalent sliding mode controller expression is:

wherein, K_jFor the sliding form coefficient to be designed, s_jIs a slip form surface to be designed;

controller u_jThe design process specifically comprises the following steps:

defining the slip form surface as:

s_j＝c_je_j，j＝1,k.k＝2,…,n. (11)

in the formula: design of slip form parameter c_j> 0, the derivation of the above formula yields:

order toObtain the equivalent control term u_jeqThe concrete expression is as follows:

the sliding mode control law consists of an equivalent control item and a switching control item, and is specifically expressed as follows:

u_j＝u_jeq+u_jsw(14)

and S4, verifying the stability of the system.

Selecting a multi-motor system L yapunov function which can also be used as a common L yapunov function of a switching system, and finally proving that the switching system can trend to a common sliding mode surface from any initial state so as to ensure the gradual stability of the whole system.

The conveyor motor system stability was first analyzed and the system L yapunov function was chosen:

the derivation is carried out on the formula, which is specifically expressed as:

the designed controller u_kSubstituting the formula into the formula, specifically expressing as:

in the formula:

designing proper sliding mode coefficient K_k＞p_k+η_k，η_jIs any one ofSmall normality, one can get:

from the Barbalt theorem, when t → ∞, s_k→ 0, and the uniaxial error e of each transmission motor can be obtained from the equation (11)_k→0.

Then, the stability of the filling motor system is analyzed, and a common sliding mode surface s of the switching system is selected₁And a common L yapunov function V₁：

For the handover subsystem f₁(x₁₁T), deriving the above formula to obtain:

by substituting and simplifying formula (10) for formula (20):

in the formula:

designing proper sliding mode coefficient K₁＞η₁，η₁At any small normal number, one can obtain:

at this time, a handover subsystem f is available₁(x₁₁Uniaxial error e) of t)₁Asymptotically converging to 0.

Further, for the handover subsystem f₂(x₁₂T), only designing a proper sliding mode coefficient K₁＞p₁+η₁The same applies to the equation (22), i.e. the switching subsystem f₂(x₁₂Uniaxial error e) of t)₁Asymptotically converging to 0. As known from the common L yapunov function, there is a convergence to 0 regardless of which subsystem is activatedCorresponding to a sliding mode function s₁Not equal to 0 is attenuated. In summary, when t → ∞, e_j→0，j＝1,k.k＝2,…,n.

Further, the single-axis tracking error and synchronization error convergence are proved, and the specific expression is as follows:

from formulas (5), (7) and (9):

rewriting equation (23) into a matrix form can obtain:

the coefficient matrix of the known systematic error matrix equation is a non-singular matrix, since e has been demonstrated above_j→ 0, can be obtainedThere is only one zero solution, so the tracking error of each axis can be converged to 0, and there is also synchronous compensation signal delta omega_jConverging to 0.

Fig. 1 is a structural diagram of an improved deviation coupling-based multi-motor sliding mode cooperative control, as shown in the figure, the multi-motor system is composed of n permanent magnet synchronous motors, a deviation coupling control strategy with a switching structure is adopted, and a sliding mode controller is combined to couple tracking error and synchronous error signals into a system error, the controller actually enables the system error, and finally, tracking control and synchronous control of the multi-motor system are achieved. The control system mainly comprises: the speed compensator, the sliding mode controller and the filling motor with the switching structure. The synchronization of the rotating speed of each motor and other motors during the operation of the system is mainly realized through the speed compensator, so that the feedback adjustment of the sliding mode controller is facilitated, the robustness is improved through subsystem switching under the special working condition of sudden motor load change at the stop-start time, and finally the system has good cooperative performance

Fig. 2, fig. 3 and fig. 4 are graphs of the following rotation speed of the motor 1, the motor 2 and the motor 3 provided by the invention respectively. A designed system rotating speed given curve simulates a stop-start process of filling production, and the specific expression is as follows: within 0-0.1 s, the rotation speed is 0 (rad.min)^-1) Within 0.1-0.2 s, the rotation speed is 300 (rad.min)^-1) And the 0.1s moment is the rotating speed jumping moment. Wherein the designed subsystems of the electrical machine 1 are switched over at 0.1s, given a subsystem f₂(x₁₂T) a load torque of 1 N.m; the load torque of the motor 2 is given to be 0.1 N.m, and the process of conveying empty bottles to a filling station in filling production is simulated; the load torque of the motor 3 is given to be 1 N.m, and the process of conveying finished products to the next station in filling production is simulated. The analysis and simulation results show that the rotating speed of the motor 1 can ensure good tracking effect at the starting moment and the switching moment, the rotating speeds of the motors 2 and 3 can also track the given value, particularly, the adjusting time of the controller at the switching moment only needs about 0.01s, and the rotating speed is not obviously overshot.

Fig. 5, fig. 6 and fig. 7 are comparison diagrams of tracking errors of the rotating speeds of the motor 1, the motor 2 and the motor 3, respectively, which are provided by the present invention, and are mainly used to better supplement the description of fig. 2, fig. 3 and fig. 4, and compare with a simulation result of the action of the PI controller under the classical deviation coupling control strategy. Analysis results show that compared with a traditional deviation coupling control structure, each motor can realize rapid convergence of tracking errors within 0.01s under an improved control method, particularly at the stop-start time of 0.1s, the motor 1 has a good control effect on the influence of sudden changes of load torque, but at the initial stage within 0-0.1 s, the tracking error jitter of the motor 3 is larger than that of other motors, mainly because the load torque is larger.

FIG. 8, FIG. 9 and FIG. 10 are graphs comparing the error of the synchronous rotation speed between the motors according to the present invention, which are electrically connectedSynchronization error tau between machine 1 and motor 2₁₂Synchronous error tau between motor 1 and motor 3₁₃And the synchronization error tau between the motor 2 and the motor 3₂₃And meanwhile, the simulation result is compared with the simulation result of the PI controller under the classical deviation coupling control strategy. The analysis result shows that, compared with the conventional deviation coupling control structure, the improved control method can achieve fast convergence of the synchronous errors of the motors within 0.01s, and particularly has more obvious error jitter suppression effect and faster convergence time, wherein the synchronous errors of the motors 1 and 2 in the initial stage within 0-0.1 s are smaller, mainly due to the difference of the load torques of the motors.

The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention.