CN112865638B - Multi-motor position synchronous control method and system with controllable synchronous time - Google Patents

Multi-motor position synchronous control method and system with controllable synchronous time Download PDF

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CN112865638B
CN112865638B CN202110110381.9A CN202110110381A CN112865638B CN 112865638 B CN112865638 B CN 112865638B CN 202110110381 A CN202110110381 A CN 202110110381A CN 112865638 B CN112865638 B CN 112865638B
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CN112865638A (en
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张晓飞
谢金平
黄凤琴
黄守道
龙卓
谭济珽
梁惟芝
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Hunan University
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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
    • 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
    • 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
    • H02P21/22—Current control, e.g. using a current control loop
    • 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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H02P25/03—Synchronous motors with brushless excitation

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Abstract

The invention discloses a multi-motor position synchronous control method and a system with controllable synchronous time, wherein the method comprises the steps of receiving the synchronous time and giving a mechanical position angle; collecting stator current of a sub-motor, a real-time rotor position angle and a rotating speed; defining a state variable according to the position angle and the rotating speed of the rotor; establishing a nonlinear second-order equation of the sub-motor system according to the state variable and the sub-motor motion equation; defining an error vector, and designing a sliding mode function according to the error vector and the synchronous time; designing a sub-motor position and rotating speed combined control law model to obtain a q-axis output current control given quantity; and controlling the output currents of the d and q axes by a given amount, and generating a control signal of the sub motor through a current loop and the like. The invention can realize controllable synchronous time of a multi-motor system, can specify the position synchronous time of each sub-motor to meet the requirement of special application, has certain disturbance resistance and ensures the stable operation of the system.

Description

Multi-motor position synchronous control method and system with controllable synchronous time
Technical Field
The invention relates to the technical field of multi-motor synchronous control, in particular to a multi-motor position synchronous control method and system with controllable synchronous time.
Background
The motor is the heart of the manufacturing equipment, and the high-end manufacturing equipment has high requirements on the control performance of the motor. The permanent magnet synchronous motor has the advantages of high torque-inertia ratio, high power density, high efficiency, simple structure and the like, and is widely applied to the fields of high-precision numerical control machines, robots and the like. With the rapid increase of scientific and technical and economic levels, it is obvious that the traditional drive control of a single motor cannot meet the requirements of modern automation equipment, and multiple motors are often required to work in cooperation in application occasions such as high-precision numerical control machines and intelligent manufacturing robots, so that people are forced to gradually study the control of multiple motors. In some special places, the position servo performance of the permanent magnet synchronous motor with high precision is required so as to meet the requirement of accurate positioning of multiple motors.
However, the multi-motor synchronous control system is a multivariable, nonlinear complex model, and in research and development, tracking control of a single subsystem is relatively easy to implement, but synchronous control among multiple motors is always a difficult point and a key point of the control system. At present, the control modes of multiple motors mainly comprise a non-coupling cooperative control mode and a coupling cooperative control mode. The non-coupling cooperative control mode comprises master reference control, master-slave control, virtual electronic spindle control and the like. The coupling cooperative control mode comprises cross coupling control and deviation coupling control. At present, a multi-motor cooperative control method is mainly based on a PID algorithm and traditional sliding mode control in application. Sliding mode variable structure control is applicable to nonlinear and model uncertain systems due to the fact that the sliding mode variable structure control is not influenced by control object parameter change, and is widely used for solving a plurality of practical complex industrial problems at present. However, the conventional multi-motor cooperative control mainly aims at the research on multi-motor power balance or torque balance, is easily influenced by motor parameter changes, and is not strong in robustness. However, in some special occasions, such as a multi-degree-of-freedom mechanical arm, the same given position is required to be reached from any different initial position angles within the required specified time, and in the reaching process, the motor is influenced by various external disturbances, when the load suddenly changes, the control performance of the whole control system is reduced, the high-precision positioning and synchronous operation target cannot be reached, and therefore, the multi-motor position synchronous control with controllable synchronous time is provided necessarily.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the invention can realize controllable synchronous time of a multi-motor system, can specify the position synchronous time of each sub-motor to meet the requirement of special application, has certain disturbance resistance and ensures the stable operation of the system.
In order to solve the technical problems, the invention adopts the technical scheme that:
a multi-motor position synchronous control method with controllable synchronous time comprises the following steps:
1) receiving a synchronization time and a given mechanical position angle;
2) collecting stator current of a sub-motor, a real-time rotor position angle and a rotating speed;
3) defining a state variable according to the position angle and the rotating speed of the rotor;
4) establishing a nonlinear second-order equation of the sub-motor system according to the state variable and the sub-motor motion equation;
5) defining an error vector, and designing a sliding mode function according to the error vector and the synchronous time;
6) designing a sub-motor position and rotating speed combined control law model according to a nonlinear second order equation, a sliding mode function and a sliding mode approximation law of a sub-motor system to obtain a q-axis output current control given quantity
Figure BDA0002918947920000021
7) Let the d-axis output current control a given amount
Figure BDA0002918947920000022
To zero, the d-axis and q-axis output currents are controlled by given amounts respectively
Figure BDA0002918947920000023
And
Figure BDA0002918947920000024
PI part input to PI current compensation controller generates initial d and q axis voltage control quantity u' id (t) and u' iq (t); and the compensation part of the PI current compensation controller is based on real-time d and q axis currents and real-time rotating speed omega im Controlling quantity u 'of initial d and q axis voltages' id And u' iq Compensating to obtain d and q axis control quantity
Figure BDA0002918947920000025
And
Figure BDA0002918947920000026
and controlling the amount according to d and q axes
Figure BDA0002918947920000027
And
Figure BDA0002918947920000028
and generating a control signal of the sub-motor to control the operation of the sub-motor.
Optionally, the state variables defined in step 3) are as follows:
Figure BDA0002918947920000029
Figure BDA00029189479200000210
in the above formula, x i1 And x i2 Is a first set of state variables that are,
Figure BDA00029189479200000211
is a state variable x i1 Derivative of (a), x 1d And x 2d Is a second set of state variables, θ im Is the mechanical position angle of the ith table motor,
Figure BDA00029189479200000212
is theta im Derivative of, ω im The mechanical angular velocity of the ith sub-motor,
Figure BDA00029189479200000213
for a given angle of the mechanical position,
Figure BDA00029189479200000214
for a given mechanical angular velocity.
Optionally, the sub-motor is a permanent magnet servo motor, and the functional expression of the motion equation of the sub-motor in step 4) is as follows:
Figure BDA00029189479200000215
in the above formula, J is moment of inertia, ω im Mechanical angular velocity, T, of the ith motor ie Is the electromagnetic torque of the ith stage motor, T iL Is the load torque of the ith motor, B is the damping coefficient, P n The number of the pole pairs is the number of the pole pairs,
Figure BDA00029189479200000216
is a permanent magnet flux linkage i iq Is q-axis component of stator current of ith stator motor; the function expression of the nonlinear second-order equation of the sub-motor system established in the step 4) is as follows:
Figure BDA0002918947920000031
in the above formula, x i1 And x i2 As a first set of state variables, the state variables,
Figure BDA0002918947920000032
is a state variable x i1 The derivative of (a) of (b),
Figure BDA0002918947920000033
is a state variable x i2 Derivative of, ω im The mechanical angular velocity of the ith sub-motor,
Figure BDA0002918947920000034
is omega im The derivative of (a) of (b),b is damping coefficient, J is moment of inertia, P n The number of the pole pairs is the number of the pole pairs,
Figure BDA0002918947920000035
is a permanent magnet flux linkage i iq Is q-axis component, T, of stator current of ith stator motor iL Is the load torque of the ith motor.
Optionally, the functional expression defining the error vector in step 5) is:
Figure BDA0002918947920000036
in the above formula, E i Representing the error vector, x i1 And x i2 Is a first set of state variables, x 1d And x 2d Is a second set of state variables, θ im Is the mechanical position angle, ω, of the ith stage motor im The mechanical angular velocity of the ith sub-motor,
Figure BDA0002918947920000037
for a given angle of the mechanical position,
Figure BDA0002918947920000038
for a given mechanical angular velocity,. epsilon i Is a mechanical position angle theta im Given mechanical position angle
Figure BDA0002918947920000039
The difference between the values of the two signals,
Figure BDA00029189479200000310
for mechanical angular velocity, given mechanical angular velocity
Figure BDA00029189479200000311
The difference between them; designing a function expression of the sliding mode function according to the error vector and the synchronous time in the step 5) as follows:
Figure BDA00029189479200000312
in the above formula, s i As a function of sliding modes, B i And Q is an intermediate variable, E i Is an error vector, b i Q (t) is a terminal polynomial function,
Figure BDA00029189479200000314
the derivative of q (t).
Optionally, the function expression of the term polynomial function is:
Figure BDA00029189479200000313
in the above formula, q (t) represents a terminal polynomial function, ε (0) is an error amount at 0 time,
Figure BDA0002918947920000041
is the first derivative of epsilon (0),
Figure BDA0002918947920000042
is the second derivative of ε (0), t is time,
Figure BDA0002918947920000043
is the synchronization time.
Optionally, the function expression of the sliding mode approach law adopted in step 6) is as follows:
Figure BDA0002918947920000044
in the above formula, the first and second carbon atoms are,
Figure BDA0002918947920000045
is s is i Derivative of (a), k i Giving coefficient, s, for ith sub-motor i For the sliding mode function, sgn(s) is the sign function, and the sign function sgn(s) employs the sign saturation function whose functional expression is:
Figure BDA0002918947920000046
in the above formula, sat(s) i ) A boundary layer representing a saturation function, h ═ 1/Δ α, Δ α;
designing a function expression of the sub-motor position and rotating speed joint control law model in the step 6) as follows:
Figure BDA0002918947920000047
in the above formula, the first and second carbon atoms are,
Figure BDA0002918947920000048
represents the given control quantity of the q-axis output current of the ith sub-motor, J is the moment of inertia, P n The number of the pole pairs is the number of the pole pairs,
Figure BDA0002918947920000049
is a permanent magnet flux linkage, b i Is a constant coefficient of a sliding mode function,
Figure BDA00029189479200000410
for mechanical angular velocity, given mechanical angular velocity
Figure BDA00029189479200000411
The difference between the values of the two signals,
Figure BDA00029189479200000412
representing the first derivative of the term polynomial function q (t), B being the damping coefficient, x i2 In order to be a state variable, the state variable,
Figure BDA00029189479200000413
is a state variable x 1d The derivative of (a) of (b),
Figure BDA00029189479200000414
representing the second derivative of the term polynomial function q (t), sat(s) representing the sign saturation function.
Optionally, PI electricity in step 7)The PI portion of the flow compensation controller generates an initial d and q-axis voltage control quantity u' id (t) and u' iq The functional expression of (t) is:
Figure BDA00029189479200000415
in the above formula, k ip And k ii Respectively representing the proportionality constant and the integration constant of the PI part,
Figure BDA00029189479200000416
and
Figure BDA00029189479200000417
controlling given quantity, i, for d-axis and q-axis output currents of ith table motor respectively id (t) and i iq And (t) is the d-axis and q-axis real-time components of the stator current of the ith motor.
The compensation part of the PI current compensation controller is based on real-time d and q axis currents and real-time rotating speed omega im Controlling quantity u 'of initial d and q axis voltages' id (t) and u' iq (t) compensating to obtain d and q axis control quantity
Figure BDA00029189479200000418
And
Figure BDA00029189479200000419
the functional expression of (a) is:
Figure BDA0002918947920000051
in the above formula, the first and second carbon atoms are,
Figure BDA0002918947920000052
and
Figure BDA0002918947920000053
d and q axis control quantities u 'of the ith sub-motor' id (t) and u' iq (t) initial generation of PI moieties respectivelyd. The q-axis voltage control quantity is,
Figure BDA0002918947920000054
is a permanent magnet flux linkage, omega im Mechanical angular velocity, L, of the ith stage motor id And L iq D, q-axis components, i, of stator inductances of the ith motor, respectively id (t) and i iq And (t) is the d-axis and q-axis real-time components of the stator current of the ith motor.
In addition, the invention also provides a multi-motor position synchronous control system with controllable synchronous time, which comprises a microprocessor and a memory which are connected with each other, wherein the microprocessor is programmed or configured to execute the steps of the multi-motor position synchronous control method with controllable synchronous time.
In addition, the invention also provides a multi-motor position synchronous control system with controllable synchronous time, which comprises an upper computer and a plurality of control units corresponding to the sub-motors one by one, wherein each control unit comprises a microprocessor, a memory and a communication module, the memories and the communication modules are respectively connected with the microprocessors, the microprocessors are in communication connection with the upper computer through the communication modules, and the microprocessors are programmed or configured to execute the steps of the multi-motor position synchronous control method with controllable synchronous time.
Furthermore, the present invention also provides a computer-readable storage medium having stored therein a computer program programmed or configured to execute the aforementioned synchronized time controllable multi-motor position synchronization control method.
Compared with the prior art, the invention has the following advantages:
1. the invention adopts the position and rotating speed joint control law, does not need to respectively carry out the design of a control method for the position and the rotating speed, simplifies the control method, simultaneously realizes the position synchronization of the sub-motors in a multi-motor system under the appointed synchronization time, and meets the requirements of special application occasions on the controllability of the position synchronization time.
2. The invention improves the traditional current PI control method, enables the system to stably run under the influence of external disturbance by compensating the feedback of the disturbance term, and has certain disturbance resistance.
Drawings
FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.
Fig. 2 is a schematic control diagram of a method according to an embodiment of the present invention.
Fig. 3 is a schematic structural diagram of a control system in an embodiment of the present invention.
Fig. 4 is a schematic structural diagram of a system according to an embodiment of the present invention.
Fig. 5 is a schematic structural diagram of a three-robot arm manufacturing robot according to an embodiment of the present invention.
Fig. 6 is an effect diagram of assigning the synchronization time to be 1S for the three-robot manufacturing robot according to the embodiment of the present invention.
FIG. 7 is a diagram illustrating the effect of specifying the synchronization time as 2S for the three-robot manufacturing robot according to the embodiment of the present invention.
Detailed Description
The purpose and effect of the present invention will be more apparent from the following further description of the present invention with reference to the accompanying drawings. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
As shown in fig. 1, the multi-motor position synchronization control method with controllable synchronization time of the present embodiment includes:
1) receiving a synchronization time and a given mechanical position angle;
2) collecting stator current of a sub-motor, a real-time rotor position angle and a rotating speed;
3) defining a state variable according to the position angle and the rotating speed of the rotor;
4) establishing a nonlinear second-order equation of the sub-motor system according to the state variable and the sub-motor motion equation;
5) defining an error vector, and designing a sliding mode function according to the error vector and the synchronous time;
6) designing a sub-motor position and rotating speed joint control law according to a nonlinear second order equation, a sliding mode function and a sliding mode approximation law of a sub-motor systemModel to obtain q-axis output current control given quantity
Figure BDA0002918947920000061
7) Let the d-axis output current control a given amount
Figure BDA0002918947920000062
The output currents of the d and q axes are respectively controlled to be zero by given quantities
Figure BDA0002918947920000063
And
Figure BDA0002918947920000064
PI part input to PI current compensation controller generates initial d and q axis voltage control quantity u' id (t) and u' iq (t); and the compensation part of the PI current compensation controller is used for compensating the control signal according to the real-time d and q axis currents and the real-time rotating speed omega im Controlling quantity u 'of initial d and q axis voltages' id And u' iq Compensating to obtain d and q axis control quantity
Figure BDA0002918947920000065
And
Figure BDA0002918947920000066
and controlling the quantity according to the d and q axes
Figure BDA0002918947920000067
And
Figure BDA0002918947920000068
and generating a control signal of the sub-motor to control the operation of the sub-motor.
As shown in fig. 2 and 3, the state variables defined in step 3) of the present embodiment are as follows:
Figure BDA0002918947920000069
Figure BDA00029189479200000610
in the above formula, x i1 And x i2 As a first set of state variables, the state variables,
Figure BDA00029189479200000611
is a state variable x i1 Derivative of (a), x 1d And x 2d Is a second set of state variables, θ im Is the mechanical position angle of the ith table motor,
Figure BDA00029189479200000612
is theta im Derivative of, ω im The mechanical angular velocity of the ith motor,
Figure BDA00029189479200000613
for a given angle of the mechanical position,
Figure BDA00029189479200000614
for a given mechanical angular velocity.
As shown in fig. 2 and fig. 3, the sub-motor in this embodiment is specifically a permanent magnet servo motor, and the functional expression of the motion equation of the sub-motor in step 4) is:
Figure BDA0002918947920000071
in the above formula, J is moment of inertia, ω im Mechanical angular velocity, T, of the ith motor ie Is the electromagnetic torque of the ith stage motor, T iL Is the load torque of the ith motor, B is the damping coefficient, P n The number of the pole pairs is the number of the pole pairs,
Figure BDA0002918947920000072
is a permanent magnet flux linkage i iq Is q-axis component of stator current of ith stator motor; the function expression of the nonlinear second-order equation of the sub-motor system established in the step 4) is as follows:
Figure BDA0002918947920000073
in the above formula, x i1 And x i2 As a first set of state variables, the state variables,
Figure BDA0002918947920000074
is a state variable x i1 The derivative of (a) of (b),
Figure BDA0002918947920000075
is a state variable x i2 Derivative of, ω im The mechanical angular velocity of the ith sub-motor,
Figure BDA0002918947920000076
is omega im B is damping coefficient, J is moment of inertia, P n The number of the pole pairs is the number of the pole pairs,
Figure BDA0002918947920000077
is a permanent magnet flux linkage i iq Is q-axis component, T, of stator current of ith stator motor iL Is the load torque of the ith motor.
As shown in fig. 2 and 3, the function expression defining the error vector in step 5) is:
Figure BDA0002918947920000078
in the above formula, E i Representing the error vector, x i1 And x i2 Is a first set of state variables, x 1d And x 2d Is a second set of state variables, θ im Is the mechanical position angle, ω, of the ith stage motor im The mechanical angular velocity of the ith sub-motor,
Figure BDA0002918947920000079
for a given angle of the mechanical position,
Figure BDA00029189479200000710
for a given mechanical angular velocity,. epsilon i Is a mechanical position angle theta im Given mechanical position angle
Figure BDA00029189479200000711
The difference between the values of the two signals,
Figure BDA00029189479200000712
for mechanical angular velocity, given mechanical angular velocity
Figure BDA00029189479200000713
The difference between them; designing a function expression of the sliding mode function according to the error vector and the synchronous time in the step 5) as follows:
Figure BDA00029189479200000714
in the above formula, s i As a function of sliding modes, B i And Q is an intermediate variable, E i Is an error vector, b i Constant coefficients of a sliding mode function (the concrete size of the constant coefficients can be adjusted in a control system according to experience to realize accuracy), q (t) is a term polynomial function,
Figure BDA00029189479200000715
the derivative of q (t).
As shown in fig. 2 and 3, the function expression of the terminal polynomial function is:
Figure BDA0002918947920000081
in the above formula, q (t) represents a terminal polynomial function, ε (0) is an error amount at 0 time,
Figure BDA0002918947920000082
is the first derivative of epsilon (0),
Figure BDA0002918947920000083
is the second derivative of ε (0), t is time,
Figure BDA0002918947920000084
is the synchronization time.
As shown in fig. 2 and 3, the function expression of the sliding mode approximation law adopted in step 6) is:
Figure BDA0002918947920000085
in the above formula, the first and second carbon atoms are,
Figure BDA0002918947920000086
is s is i Derivative of (a), k i Giving coefficient, s, for ith sub-motor i For the sliding mode function, sgn(s) is the sign function, and the sign function sgn(s) adopts the sign saturation function, and the function expression of the sign saturation function is:
Figure BDA0002918947920000087
in the above formula, sat(s) i ) A boundary layer representing a saturation function, h ═ 1/Δ α, Δ α;
designing a function expression of the sub-motor position and rotating speed joint control law model in the step 6) as follows:
Figure BDA0002918947920000088
in the above formula, the first and second carbon atoms are,
Figure BDA0002918947920000089
represents the given control quantity of the q-axis output current of the ith sub-motor, J is the moment of inertia, P n The number of the pole pairs is the number of the pole pairs,
Figure BDA00029189479200000810
is a permanent magnet flux linkage, b i Is a constant coefficient of a sliding mode function,
Figure BDA00029189479200000811
is mechanical angular velocity, toDetermining mechanical angular velocity
Figure BDA00029189479200000812
The difference between the values of the two signals,
Figure BDA00029189479200000813
representing the first derivative of the term polynomial function q (t), B being the damping coefficient, x i2 In order to be a state variable, the state variable,
Figure BDA00029189479200000814
is a state variable x 1d The derivative of (a) of (b),
Figure BDA00029189479200000815
representing the second derivative of the term polynomial function q (t), sat(s) representing the sign saturation function.
In this embodiment, the current loop of the sub-motor adopts a PI current compensation controller with disturbance rejection, and includes a PI part and a compensation part, respectively. The PI part of the PI current compensation controller in the step 7) generates initial d-axis and q-axis voltage control quantity u' id (t) and u' iq The functional expression of (t) is:
Figure BDA0002918947920000091
in the above formula, k ip And k ii Respectively representing the proportionality constant and the integration constant of the PI part,
Figure BDA0002918947920000092
and
Figure BDA0002918947920000093
controlling given quantity, i, for d-axis and q-axis output currents of ith table motor respectively id (t) and i iq And (t) is the d and q axis real-time components of the stator current of the ith motor, and t is time.
The compensation part of the PI current compensation controller is based on real-time d and q axis currents and real-time rotating speed omega im Controlling quantity u 'of initial d and q axis voltages' id (t) And u' iq (t) compensating to obtain d and q axis control quantity
Figure BDA0002918947920000094
And
Figure BDA0002918947920000095
the functional expression of (a) is:
Figure BDA0002918947920000096
in the above formula, the first and second carbon atoms are,
Figure BDA0002918947920000097
and
Figure BDA0002918947920000098
d and q axis control quantities u 'of the ith sub-motor' id (t) and u' iq (t) initial d-and q-axis voltage control amounts generated by the PI section, respectively,
Figure BDA0002918947920000099
is a permanent magnet flux linkage, omega im Mechanical angular velocity, L, of the ith stage motor id And L iq D, q-axis components, i, of stator inductances of the ith stator motors, respectively id (t) and i iq And (t) is the d-axis and q-axis real-time components of the stator current of the ith motor.
Referring to fig. 3, the system in the present embodiment includes: the upper main monitoring system generates synchronous time and synchronous rotor position angle instructions, and each sub-motor in the multi-motor system is controlled in parallel; collecting stator current of a sub-motor, a real-time rotor position angle and a rotating speed; defining 1 state variable according to the position angle and the rotating speed of the rotor; establishing a nonlinear second-order equation of the sub-motor system according to the state variable and the sub-motor motion equation; defining an error vector, and designing a sliding mode function according to the error vector and the specified synchronous time; designing a sub-motor position and rotating speed combined control law model according to a system equation, a sliding mode function and a sliding mode approximation law; PI compensation with disturbance resistance is adopted in current loop of sub-motorA compensation controller. As shown in fig. 4, the control modules of the sub-motors in this embodiment are respectively connected to the upper main monitoring system, the control modules of the sub-motors respectively include encoders for acquiring the position angle of the rotor, and deriving the position angle to obtain the rotation speed, and the control modules of the sub-motors respectively control the corresponding sub-motors through drivers, for example, the total number 1 to n of sub-motor drivers in the figure, which are respectively used for driving the number 1 to n of sub-motors. Referring to fig. 5, the sub-motor of the embodiment is a motor of a robot arm a/b/c of a three-robot arm manufacturing robot, and three sub-servo permanent magnet synchronous motors a, b, and c are used for controlling the rotation position of the arm, so as to realize the precise position control of the three arms with controllable time at the same time. In the embodiment, the upper main monitoring system is provided with upper main monitoring software written by Labview and used for generating synchronous time of the three-mechanical-arm manufacturing robot
Figure BDA00029189479200000910
And synchronous rotor position angle
Figure BDA00029189479200000911
And the command part monitors the real-time state of the synchronous position angle of each sub-motor. FIG. 6 is a diagram showing the effect of assigning a synchronization time of 1S to the three-robot arm manufacturing robot, and FIG. 7 is a diagram showing the effect of assigning a synchronization time of 2S to the three-robot arm manufacturing robot, wherein the position commands are indicated
Figure BDA0002918947920000101
Is a sinusoidal command where Themeref sinusoidally varies given the synchronous position angle, Theme1 is the real-time position angle of sub-motor 1, Theme2 is the real-time position angle of sub-motor 2, and Theme3 is the real-time position angle of sub-motor 2. As can be seen from fig. 6 and 7, the positions of the three arms of the three-robot arm manufacturing robot adopting the multi-motor position synchronization control method with controllable synchronization time of the present embodiment can be synchronized after convergence of the specified time.
In summary, in the multi-motor position synchronization control method with controllable synchronization time of the embodiment, the stator current of the sub-motor, the real-time rotor position angle and the rotation speed are collected; defining a state variable according to the position angle and the rotating speed of the rotor; establishing a nonlinear second-order equation of the sub-motor system according to the state variable and the sub-motor motion equation; defining an error vector, and designing a sliding mode function according to the error vector and the specified synchronous time; designing a sub-motor position and rotating speed combined control law model according to a system equation, a sliding mode function and a sliding mode approximation law; the current loop of the sub-motors adopts the PI compensation controller with disturbance resistance, the controllable synchronous time is realized, the position synchronous time of each sub-motor can be appointed to meet the requirement of special application, certain disturbance resistance is realized, and the stable operation of the system is ensured.
In addition, the present embodiment also provides a synchronous time controllable multi-motor position synchronous control system, which includes a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to execute the steps of the synchronous time controllable multi-motor position synchronous control method.
In addition, the embodiment further provides a multi-motor position synchronous control system with controllable synchronous time, the system comprises an upper computer and a plurality of control units corresponding to the sub-motors one by one, each control unit comprises a microprocessor, a memory and a communication module, the memories and the communication modules are respectively connected with the microprocessors, the microprocessors are in communication connection with the upper computer through the communication modules, and the microprocessors are programmed or configured to execute the steps of the multi-motor position synchronous control method with controllable synchronous time.
Further, the present embodiment also provides a computer-readable storage medium having stored therein a computer program programmed or configured to execute the aforementioned synchronized time controllable multi-motor position synchronization control method.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The present application is directed to methods, apparatus (systems), and computer program products according to embodiments of the application, wherein the instructions that execute via the flowcharts and/or processors of the computer program product create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.

Claims (9)

1. A multi-motor position synchronous control method with controllable synchronous time is characterized by comprising the following steps:
1) receiving a synchronization time and a given mechanical position angle;
2) collecting stator current of a sub-motor, a real-time rotor position angle and a rotating speed;
3) defining a state variable according to the position angle and the rotating speed of the rotor;
4) establishing a nonlinear second-order equation of the sub-motor system according to the state variable and the sub-motor motion equation;
5) defining an error vector, and designing a sliding mode function according to the error vector and the synchronous time;
6) designing a sub-motor position and rotating speed combined control law model according to a nonlinear second order equation, a sliding mode function and a sliding mode approximation law of a sub-motor system to obtain a q-axis output current control given quantity
Figure FDA0003686041440000011
And the function expression of the adopted sliding mode approximation law is as follows:
Figure FDA0003686041440000012
in the above-mentioned formula, the compound has the following structure,
Figure FDA0003686041440000013
is s is i Derivative of (a), k i Giving coefficient, s, for ith sub-motor i For the sliding mode function, sgn(s) is the sign function, and the sign function sgn(s) employs the sign saturation function whose functional expression is:
Figure FDA0003686041440000014
in the above formula, sat(s) i ) A boundary layer representing a saturation function, h ═ 1/Δ α, Δ α;
designing a function expression of the sub-motor position and rotating speed combined control law model in the step 6) as follows:
Figure FDA0003686041440000015
in the above formula, the first and second carbon atoms are,
Figure FDA0003686041440000016
represents q-axis output of the ith sub-motorCurrent control given quantity, J is moment of inertia, P n The number of the pole pairs is the number of the pole pairs,
Figure FDA0003686041440000017
is a permanent magnet flux linkage, b i Is a constant coefficient of a sliding mode function,
Figure FDA0003686041440000018
for mechanical angular velocity, given mechanical angular velocity
Figure FDA0003686041440000019
The difference between the values of the two signals,
Figure FDA00036860414400000110
representing the first derivative of the term polynomial function q (t), B being the damping coefficient, x i2 In order to be a state variable, the state variable,
Figure FDA00036860414400000111
is a state variable x 1d The derivative of (a) is determined,
Figure FDA00036860414400000112
representing the second derivative of the term polynomial function q (t), sat(s) representing the sign saturation function;
7) let the d-axis output current control a given amount
Figure FDA00036860414400000113
To zero, the d-axis and q-axis output currents are controlled by given amounts respectively
Figure FDA00036860414400000114
And
Figure FDA00036860414400000115
PI part input to PI current compensation controller generates initial d and q axis voltage control quantity u' id (t) and u' iq (t); and the compensation part of the PI current compensation controller is based on real-time d and q axis currents and real-timeSpeed of rotation omega im Controlling quantity u 'of initial d and q axis voltages' id (t) and u' iq (t) compensating to obtain d and q axis control quantity
Figure FDA00036860414400000116
And
Figure FDA00036860414400000117
and controlling the quantity according to the d and q axes
Figure FDA00036860414400000118
And
Figure FDA00036860414400000119
and generating a control signal of the sub-motor to control the operation of the sub-motor.
2. A multi-motor position synchronization control method whose synchronization time is controllable according to claim 1, characterized in that the state variables defined in step 3) are as follows:
Figure FDA0003686041440000021
Figure FDA0003686041440000022
in the above formula, x i1 And x i2 As a first set of state variables, the state variables,
Figure FDA0003686041440000023
is a state variable x i1 Derivative of (a), x 1d And x 2d Is a second set of state variables, θ im Is the mechanical position angle of the ith table motor,
Figure FDA0003686041440000024
is theta im Derivative of, ω im The mechanical angular velocity of the ith sub-motor,
Figure FDA0003686041440000025
for a given angle of the mechanical position,
Figure FDA0003686041440000026
for a given mechanical angular velocity.
3. The multi-motor position synchronous control method with controllable synchronous time according to claim 1, wherein the sub-motors are permanent magnet servo motors, and the functional expression of the motion equation of the sub-motors in the step 4) is as follows:
Figure FDA0003686041440000027
in the above formula, J is moment of inertia, ω im Mechanical angular velocity, T, of the ith motor ie Is the electromagnetic torque of the ith stage motor, T iL Is the load torque of the ith motor, B is the damping coefficient, P n The number of the pole pairs is the number of the pole pairs,
Figure FDA0003686041440000028
is a permanent magnet flux linkage i iq Is q-axis component of stator current of ith stator motor; the function expression of the nonlinear second-order equation of the sub-motor system established in the step 4) is as follows:
Figure FDA0003686041440000029
in the above formula, x i1 And x i2 As a first set of state variables, the state variables,
Figure FDA00036860414400000210
is a state variable x i1 The derivative of (a) of (b),
Figure FDA00036860414400000211
is a state variable x i2 Derivative of, ω im The mechanical angular velocity of the ith sub-motor,
Figure FDA00036860414400000212
is omega im B is damping coefficient, J is moment of inertia, P n The number of the pole pairs is the number of the pole pairs,
Figure FDA00036860414400000213
is a permanent magnet flux linkage i iq Is q-axis component, T, of stator current of ith stator motor iL Is the load torque of the ith motor.
4. The method for synchronously controlling the positions of multiple motors with controllable synchronous time according to claim 1, wherein the function expression of the error vector defined in step 5) is:
Figure FDA0003686041440000031
in the above formula, E i Representing the error vector, x i1 And x i2 Is a first set of state variables, x 1d And x 2d Is a second set of state variables, θ im Is the mechanical position angle, ω, of the ith stage motor im The mechanical angular velocity of the ith sub-motor,
Figure FDA0003686041440000032
for a given angle of the mechanical position,
Figure FDA0003686041440000033
for a given mechanical angular velocity,. epsilon i Is a mechanical position angle theta im Given mechanical position angle
Figure FDA0003686041440000034
The difference between the values of the two signals,
Figure FDA0003686041440000035
for mechanical angular velocity, given mechanical angular velocity
Figure FDA0003686041440000036
The difference between them; designing a function expression of the sliding mode function according to the error vector and the synchronous time in the step 5) as follows:
s i ＝B i (E i -Q)，B i ＝[b i ,1]，
Figure FDA0003686041440000037
in the above formula, s i As a function of sliding modes, B i And Q is an intermediate variable, E i Is an error vector, b i Q (t) is a terminal polynomial function,
Figure FDA0003686041440000038
the derivative of q (t).
5. The method for synchronous control of positions of multiple motors with controllable synchronous time according to claim 4, wherein the function expression of the terminal polynomial function is:
Figure FDA0003686041440000039
in the above formula, q (t) represents a terminal polynomial function, ε (0) is an error amount at 0 time,
Figure FDA00036860414400000310
is the first derivative of epsilon (0),
Figure FDA00036860414400000311
is the second derivative of ε (0), t is time,
Figure FDA00036860414400000312
is the synchronization time.
6. The method for synchronously controlling the positions of multiple motors with controllable synchronous time according to claim 1, wherein the PI part of the PI current compensation controller in step 7) generates an initial d-axis and q-axis voltage control quantity u' id And u' iq The functional expression of (a) is:
Figure FDA00036860414400000313
in the above formula, k ip And k ii Respectively representing the proportionality constant and the integration constant of the PI part,
Figure FDA00036860414400000314
and
Figure FDA00036860414400000315
controlling given quantity, i, for d-axis and q-axis output currents of ith table motor respectively id (t) and i iq (t) is the d and q axis real-time components of the stator current of the ith stator motor, and t is time;
the compensation part of the PI current compensation controller is based on real-time d and q axis currents and real-time rotating speed omega im Controlling quantity u 'of initial d and q axis voltages' id (t) and u' iq (t) compensating to obtain d and q axis control quantity
Figure FDA0003686041440000041
And
Figure FDA0003686041440000042
the functional expression of (a) is:
Figure FDA0003686041440000043
in the above formula, the first and second carbon atoms are,
Figure FDA0003686041440000044
and
Figure FDA0003686041440000045
d and q axis control quantities u 'of the ith sub-motor' id (t) and u' iq (t) initial d-and q-axis voltage control amounts generated by the PI section, respectively,
Figure FDA0003686041440000046
being a permanent magnet flux linkage, omega im Mechanical angular velocity, L, of the ith stage motor id And L iq D, q-axis components, i, of stator inductances of the ith stator motors, respectively id (t) and i iq And (t) is the d-axis and q-axis real-time components of the stator current of the ith motor.
7. A synchronized time controllable multi-motor position synchronous control system comprising a microprocessor and a memory connected to each other, characterized in that said microprocessor is programmed or configured to perform the steps of the synchronized time controllable multi-motor position synchronous control method of any one of claims 1 to 6.
8. A multi-motor position synchronous control system with controllable synchronous time, which comprises an upper computer and a plurality of control units corresponding to sub motors one by one, wherein each control unit comprises a microprocessor, a memory and a communication module, the memories and the communication modules are respectively connected with the microprocessors, and the microprocessors are in communication connection with the upper computer through the communication modules, and is characterized in that the microprocessors are programmed or configured to execute the steps of the multi-motor position synchronous control method with controllable synchronous time according to any one of claims 1 to 6.
9. A computer-readable storage medium having stored therein a computer program programmed or configured to execute the synchronized time controllable multi-motor position synchronization control method of any one of claims 1 to 6.
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