CN111431440A - Multi-motor sliding mode cooperative control method based on improved deviation coupling - Google Patents

Multi-motor sliding mode cooperative control method based on improved deviation coupling Download PDF

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CN111431440A
CN111431440A CN202010219477.4A CN202010219477A CN111431440A CN 111431440 A CN111431440 A CN 111431440A CN 202010219477 A CN202010219477 A CN 202010219477A CN 111431440 A CN111431440 A CN 111431440A
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motor
sliding mode
filling
error
cooperative control
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CN111431440B (en
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张昌凡
肖明杰
何静
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Hunan University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/04—Arrangements for controlling or regulating the speed or torque of more than one motor
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control

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Abstract

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.

Description

Multi-motor sliding mode cooperative control method based on improved deviation coupling
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:
Figure BDA0002425570040000011
in the formula, thetajAs rotor position, ωjAs electrical angular velocity, T, of the rotorLjIs the load torque on the shaft, RΩjIs the coefficient of rotation resistance of the motor, JjIs moment of inertia, npjIs the pole pair number of the motor, psifjFor rotor flux linkage idj、iqjRespectively a direct-axis component and a quadrature-axis component of the stator current;
order to
Figure BDA0002425570040000021
The above can be expressed as:
Figure BDA0002425570040000022
wherein: u. ofj＝iqjAnd 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:
Figure BDA0002425570040000023
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:
Figure BDA0002425570040000024
wherein: omegakThe 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:
Figure BDA0002425570040000025
j＝1,k.k＝2,…,n.i＝1,2,…,n，i≠j
wherein, KjFor the sliding form coefficient to be designed, sjIs 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:
Figure BDA0002425570040000026
further, the tracking error concrete expression in step S2 is:
Figure BDA0002425570040000031
further, in step S2, the synchronization error concrete expression is:
Figure BDA0002425570040000032
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:
Figure BDA0002425570040000033
in the formula, thetajAs rotor position, ωjAs electrical angular velocity, T, of the rotorLjIs the load torque on the shaft, RΩjIs the coefficient of rotation resistance of the motor, JjIs moment of inertia, npjIs the pole pair number of the motor, psifjFor rotor flux linkage idj、iqjRespectively a direct-axis component and a quadrature-axis component of the stator current;
order to
Figure BDA0002425570040000041
The above can be expressed as:
Figure BDA0002425570040000042
in the formula: u. ofi＝iqjAnd 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:
Figure BDA0002425570040000043
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:
Figure BDA0002425570040000044
in the formula: omegakThe 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:
Figure BDA0002425570040000045
in the formula:
Figure BDA0002425570040000046
ωjrespectively, 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:
τji＝ωj-ωi,j＝1,k.k＝2,…,n.i＝1,2,…,n，i≠j. (6)
in the formula: tau isjiIndicating 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:
Figure BDA0002425570040000051
in the formula:
Figure BDA0002425570040000052
will track error
Figure BDA0002425570040000053
And a synchronization error compensation signal Δ ωjCoupling to obtain the single-shaft system error of the multi-motor system, which is specifically expressed as follows:
Figure BDA0002425570040000054
s3, designing an equivalent sliding mode controller; the equivalent sliding mode controller expression is:
Figure BDA0002425570040000055
wherein, KjFor the sliding form coefficient to be designed, sjIs a slip form surface to be designed;
controller ujThe design process specifically comprises the following steps:
defining the slip form surface as:
sj＝cjej，j＝1,k.k＝2,…,n. (11)
in the formula: design of slip form parameter cj> 0, the derivation of the above formula yields:
Figure BDA0002425570040000056
order to
Figure BDA0002425570040000057
Obtain the equivalent control term ujeqThe concrete expression is as follows:
Figure BDA0002425570040000058
the sliding mode control law consists of an equivalent control item and a switching control item, and is specifically expressed as follows:
uj＝ujeq+ujsw(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:
Figure BDA0002425570040000061
the derivation is carried out on the formula, which is specifically expressed as:
Figure BDA0002425570040000062
the designed controller ukSubstituting the formula into the formula, specifically expressing as:
Figure BDA0002425570040000063
in the formula:
Figure BDA0002425570040000064
designing proper sliding mode coefficient Kk＞pk+ηk，ηjIs any one ofSmall normality, one can get:
Figure BDA0002425570040000065
from the Barbalt theorem, when t → ∞, sk→ 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：
Figure BDA0002425570040000066
For the handover subsystem f1(x11T), deriving the above formula to obtain:
Figure BDA0002425570040000067
by substituting and simplifying formula (10) for formula (20):
Figure BDA0002425570040000068
in the formula:
Figure BDA0002425570040000071
designing proper sliding mode coefficient K1＞η1，η1At any small normal number, one can obtain:
Figure BDA0002425570040000072
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 activated
Figure BDA0002425570040000073
Corresponding to a sliding mode function s1Not equal to 0 is attenuated. In summary, when t → ∞, ej→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):
Figure BDA0002425570040000074
rewriting equation (23) into a matrix form can obtain:
Figure BDA0002425570040000075
the coefficient matrix of the known systematic error matrix equation is a non-singular matrix, since e has been demonstrated abovej→ 0, can be obtained
Figure BDA0002425570040000076
There 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 omegajConverging 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.

Claims (5)

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:
Figure FDA0002425570030000011
in the formula, thetajAs rotor position, ωjAs electrical angular velocity, T, of the rotorLjIs the load torque on the shaft, RΩjIs the coefficient of rotation resistance of the motor, JjIs moment of inertia, npjIs the pole pair number of the motor, psifjFor rotor flux linkage idj、iqjRespectively a direct-axis component and a quadrature-axis component of the stator current;
order to
Figure FDA0002425570030000012
The above formula can be expressed as:
Figure FDA0002425570030000013
wherein: u. ofj＝iqjA 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:
Figure FDA0002425570030000014
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:
Figure FDA0002425570030000015
wherein: omegakTransmitting 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:
Figure FDA0002425570030000021
j＝1,k.k＝2,…,n.i＝1,2,…,n，i≠j
wherein, KjFor the sliding form coefficient to be designed, sjIs 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:
Figure FDA0002425570030000022
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:
Figure FDA0002425570030000023
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:
Figure FDA0002425570030000024
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.
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