A method and system for controlling backlash in dual-motor servo systems for antenna feed switching

Abstract

This application proposes a backlash control method and system for an antenna feed dual-motor servo system. This method belongs to the field of backlash control and includes establishing a dynamic model of the dual-motor servo system and analyzing it to obtain a dead zone model of the backlash; establishing a state-space equation model of the dual-motor servo system based on the dead zone model; setting a model-predicted position tracking controller based on the state-space equation model of the dual-motor servo system to track and control the position and speed of the load and the dual motors; formulating a backlash control strategy and a dual-motor synchronization control strategy based on the model-predicted position tracking controller; if backlash occurs, the position difference of the dual motors minus the backlash width is used as the synchronization error, and the synchronization error is twice the backlash width, and the backlash is eliminated through position compensation; when no backlash occurs, the dual-motor synchronization error is zero, the dual motors are synchronized, and jointly drive the load to rotate, thereby simultaneously realizing load position tracking, backlash compensation, and dual-motor synchronization control.

Description

Technical Field

[0001] The present application relates to the field of backlash control, and in particular to a backlash control method and system for an antenna feed switching dual-motor servo system. Background Art

[0002] Servo systems are becoming increasingly important in modern industrial and military fields. With technological advancements, the demand for precise control of various electromechanical equipment continues to increase, making servo systems play a key role in these application scenarios.

[0003] Currently, common antenna feed switching mechanisms include rotary, sliding, and swing feed switching. Rotary feed switching has become the mainstream feed switching method for large antennas due to its relatively simple structure and stable and reliable performance. This mechanism places the feed sources for each frequency band on a turntable offset from the antenna's axis of symmetry. A servo system drives the turntable to rotate, allowing each active feed source to reach the antenna's focal point and lock into place, thus enabling switching between feed sources in different frequency bands. Feed source positioning accuracy directly impacts the antenna's electrical performance, so achieving high-precision tracking of the feed source position is a key objective of the servo system.

[0004] Dual-motor control is particularly essential for the drive control of large antenna feed mechanisms. Due to the high inertia and high disturbance characteristics of large antenna feed mechanisms, single-motor servo systems struggle to meet the high-precision position tracking and power output requirements when driving such loads. For example, while a single motor may provide sufficient torque to drive a high-inertia load, it may not guarantee adequate position control accuracy. Conversely, it may not provide sufficient torque to maintain speed control accuracy. Dual-motor control, on the other hand, can provide high torque, meeting the servo system's power requirements and improving the system's overload capacity. Furthermore, through appropriate control methods, it can effectively eliminate backlash and improve positioning accuracy.

[0005] Backlash control is a key technical step in dual-motor servo systems. Backlash refers to the minute gaps between gears in the servo system's gear transmission process, caused by manufacturing precision, assembly errors, and long-term use. This gap significantly affects the synchronous operation of the dual motors. Furthermore, backlash typically occurs when the drive motor is commutating or stopping. During this time, the servo system's driving torque cannot be transmitted to the driven system, causing temporary load uncontrollability and increasing positioning errors. This hinders the precise control and positioning of the antenna feed mechanism. However, in practical applications, backlash control faces numerous challenges. First, backlash itself is a nonlinear factor, and its impact on the servo system is difficult to completely eliminate using simple linear control methods. Second, when the dual motors are operating in tandem, backlash can affect their synchronous operation. Summary of the Invention

[0006] The purpose of the present application is to provide an anti-backlash control method and system for an antenna feed switching dual-motor servo system, which can simultaneously realize load position tracking, anti-backlash compensation and dual-motor synchronous control.

[0007] This application is implemented as follows:

[0008] In a first aspect, the present application provides an anti-backlash control method for an antenna feed switching dual-motor servo system, comprising:

[0009] S1: Establishing a dynamic model of the dual-motor servo system and analyzing the dynamic model of the dual-motor servo system to obtain a dead zone model of the tooth gap, wherein the dead zone model of the tooth gap is used to describe the dynamic situation of the torque transmission between the two gears when the gear transmission passes through the tooth gap;

[0010] S2: Based on the dynamic situation of the torque transmission between the two gears when the gear transmission passes through the tooth gap in the dead zone model, a state space equation model of the dual-motor servo system is established to model the nonlinear effect of the tooth gap as an external disturbance in the state space model;

[0011] S3: Setting a model prediction position tracking controller based on the state space equation model of the dual-motor servo system to track and control the position and speed of the load and the dual motors, the model prediction position tracking controller including position and speed detection of the load and the servo motor, a state prediction model, rolling optimization and feedback correction; inputting the reference position and reference speed of the load into the model prediction position tracking controller, and simultaneously inputting the state values ​​of the load and the servo motor, obtaining the optimal torque value of the dual motors through rolling optimization, so that the motors output the optimal torque value; when the dual motors drive the load to rotate, feedback correction is performed based on the state values ​​of the load and the servo motors to predict the predicted value of the output state of the dual-motor servo system; the load is a feed-forward mechanism;

[0012] S4: Based on the model prediction position tracking controller, an anti-backlash control strategy and a dual-motor synchronization control strategy are formulated; when the dual-motor servo system is commutating or stopping, tooth gap is about to appear, and the position difference of the dual motors minus the tooth gap width is used as the synchronization error. The reference value of the synchronization error is twice the tooth gap width. Through position compensation, when the synchronization error reaches the reference value, the gap between the motor-end gear and the load-end gear just reaches one times the tooth gap width, eliminating the influence of the tooth gap; when there is no tooth gap, the dual-motor synchronization error is zero. When the synchronization error reaches the reference value, the dual motors are synchronized and jointly drive the load to rotate.

[0013] In a second aspect, the present application provides an anti-backlash control system for an antenna feed switching dual-motor servo system, comprising:

[0014] Backlash dead zone model module: used to establish a dynamic model of the dual-motor servo system and analyze the dynamic model of the dual-motor servo system to obtain a backlash dead zone model. The backlash dead zone model is used to describe the dynamic situation of torque transmission between the two gears when the gear transmission passes through the backlash;

[0015] State-space equation model module: This module is used to establish a state-space equation model for the dual-motor servo system based on the dynamic situation of torque transmission between the two gears when the gear transmission passes through the tooth gap in the dead zone model. It is used to model the nonlinear effect of the tooth gap as an external disturbance in the state-space model.

[0016] Model prediction position tracking controller module: used to set a model prediction position tracking controller based on the state space equation model of the dual-motor servo system to track and control the position and speed of the load and the dual motors. The model prediction position tracking controller includes position and speed detection of the load and servo motor, a state prediction model, rolling optimization and feedback correction; the reference position and reference speed of the load are input into the model prediction position tracking controller, and the state values ​​of the load and servo motor are input at the same time. After rolling optimization, the optimal torque value of the dual motor is obtained, so that the motor outputs the optimal torque value; when the dual motor drives the load to rotate, feedback correction is performed based on the state values ​​of the load and servo motor to predict the predicted value of the output state of the dual-motor servo system; the load is a feed-forward mechanism;

[0017] Anti-backlash synchronization strategy module: used to formulate anti-backlash control strategy and dual-motor synchronization control strategy based on model predictive position tracking controller; when the dual-motor servo system is commutating or stopping, tooth backlash is about to appear, and the position difference of the dual motors minus the tooth backlash width is used as the synchronization error. The reference value of the synchronization error is twice the tooth backlash width. Through position compensation, when the synchronization error reaches the reference value, the gap between the motor-end gear and the load-end gear just reaches one times the tooth backlash width, eliminating the influence of the tooth backlash; when there is no tooth backlash, the dual-motor synchronization error is zero. When the synchronization error reaches the reference value, the dual motors are synchronized and jointly drive the load to rotate.

[0018] Compared with the prior art, this application has at least the following advantages or beneficial effects:

[0019] 1. The present invention uses a backlash dead zone model to model a dual-motor servo system. The state variables of the state-space equation model for the dual-motor servo system are the position and velocity of the motor and load. The model input is the transmission torque of the dual-motor servo system, and the model output includes the load, the kinematic state of the motor, and the position difference between the two motors. The dual-motor servo system model simultaneously considers the effects of gear contact stiffness and damping on backlash. Therefore, the model can more accurately reflect the dynamic process of backlash changes between gears, making the established state-space model more realistic.

[0020] 2. Since the present invention is applied to the rotational feed switching of antennas, in order to reduce the influence of the feed source positioning error on the antenna performance and maintain the dynamic response characteristics of the feed switching mechanism, it is hoped that the rotation process of the feed switching mechanism is slower in the termination stage and faster in the start-up and intermediate stages. The prior art PID control is a control method based on position error. When pursuing a fast response of the position of the feed switching mechanism, it is unable to take into account the speed regulation of the feed switching mechanism. Compared with the traditional PID controller, the model prediction position tracking controller proposed in the present invention can simultaneously realize the position tracking and speed tracking control of the load, and because it combines the actual physical quantities inside the servo system, such as the stiffness and damping information during gear meshing, it can more effectively manage the rotation speed of the feed switching mechanism and realize accurate and overshoot-free position tracking and positioning.

[0021] Decomposing the nonlinear dead-zone model of backlash into a linear model and bounded perturbations facilitates the development of a state-space equation model for the dual-motor servo system and the design of a model-predictive position tracking controller based on this state-space model. Based on this model-predictive position tracking controller, using the position difference between the two motors as feedback, anti-backlash control and motor synchronization control can be introduced. When the desired position is about to be reached, anti-backlash control ensures that the load is precisely positioned at the predetermined position and eliminates motor synchronization errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0023] Figure 1 This is a flow chart of an anti-backlash control method for an antenna feed switching dual-motor servo system;

[0024] Figure 2 This is a schematic diagram of the dual-motor drive principle;

[0025] Figure 3 Schematic diagram of a model prediction position tracking controller, an anti-backlash control strategy, and a dual-motor synchronization control strategy in an anti-backlash control method for an antenna feed switching dual-motor servo system in this application;

[0026] Figure 4 This is an illustration of the prediction time domain and control time domain of the model prediction position tracking controller in the anti-backlash control method for the antenna feed switching dual-motor servo system of this application;

[0027] Figure 5This is a schematic diagram of the control performance of an anti-backlash control method for an antenna feed switching dual-motor servo system in this application, which does not introduce an anti-backlash control strategy and a dual-motor synchronous control strategy; an anti-backlash control strategy and a dual-motor synchronous control strategy;

[0028] Figure 6 This is a schematic diagram showing the control performance of a position tracking controller that only introduces synchronization error control in an anti-backlash control method for an antenna feed switching dual-motor servo system in this application;

[0029] Figure 7 This is a schematic diagram of the control performance of a position tracking controller that only introduces an anti-backlash control strategy in an anti-backlash control method for an antenna feed switching dual-motor servo system in this application;

[0030] Figure 8 This is a schematic diagram showing the control performance of an anti-backlash control method for an antenna feed dual-motor servo system according to the present application, which introduces an anti-backlash control strategy and a dual-motor synchronous control strategy;

[0031] Figure 9 This application discloses a flow chart of an anti-backlash control system for an antenna feed switching dual-motor servo system. DETAILED DESCRIPTION

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Generally, the components of the embodiments of the present application described and shown in the drawings herein can be arranged and configured in various different configurations.

[0033] The following describes some embodiments of the present application in detail with reference to the accompanying drawings. In the absence of conflict, the following embodiments and features thereof may be combined with each other.

[0034] Example

[0035] It's important to understand that during antenna feed switching, the feed mechanism exhibits high inertia and high disturbances. A single-motor servo system, when driving such a load, struggles to meet the high-precision position tracking and power output requirements. Therefore, dual-motor control is necessary. This not only provides high torque, meeting the servo system's power requirements and improving the system's overload capacity, but also effectively eliminates backlash through appropriate control methods, thereby enhancing positioning accuracy. Backlash control is a key technical step in dual-motor servo systems. Backlash typically occurs during commutation and stopping of the drive motor. During these times, the servo system's driving torque cannot be transmitted to the driven system, resulting in temporary load uncontrollability and increased positioning error, hindering precise control and positioning of the antenna feed mechanism. In practical applications, backlash control faces numerous challenges. First, backlash itself is a nonlinear factor, and its impact on the servo system is difficult to completely eliminate using simple linear control methods. Second, when the two motors operate in tandem, backlash can affect their synchronous operation.

[0036] In view of this, an embodiment of the present application provides an anti-backlash control method and system for an antenna feed-switch dual-motor servo system, which can simultaneously achieve load (feed-switch mechanism) position tracking, anti-backlash compensation and dual-motor synchronous control.

[0037] Please refer to Figure 1 , Figure 1 Flowchart of an anti-backlash control method for a dual-motor servo system, the method comprising:

[0038] S1: Establish a dynamic model of the dual-motor servo system and analyze the dynamic model of the dual-motor servo system to obtain a dead zone model of the tooth gap. The dead zone model of the tooth gap is used to describe the dynamic situation of the torque transmission between the two gears when the gear transmission passes through the tooth gap;

[0039] Specifically, we first analyze the dual-motor drive principle and establish a dynamic model of the dual-motor servo system. Figure 2 , providing the motor with the optimal input torque command signal, the motor works, the driving gear on its output shaft drives the driven gear at the load end to rotate, there is a tooth gap between the driving gear and the driven gear, Figure 2 In the equation, u1 and u2 represent the input torques of motor 1 and motor 2, J1 and J2 represent the rotational inertia of motor 1 and motor 2, c1 and c2 represent the viscous friction coefficients of motor 1 and motor 2, θ1 and θ2 represent the rotational positions of motor 1 and motor 2, and Represent the rotational angular velocity of motor 1 and motor 2 respectively. b1 is the position difference between the driving gear and the slave gear of motor 1. The slave gear is the gear at the load end (feedback mechanism). The driving gear at the motor end is the small gear, and the slave gear at the load end is the large gear. b2 is the position difference between the driving gear and the slave gear of motor 2. c b is the damping coefficient of the contact between the driving gear and the driven gear, k b is the stiffness coefficient of the contact between the driving gear and the driven gear. T1 is the torque transmitted between the driving gear and the driven gear of motor 1, and T2 is the torque transmitted between the driving gear and the driven gear of motor 2. J m represents the moment of inertia of the load, c m The viscous friction coefficient of the load, θ L is the load position parameter, is the load rotational angular velocity. According to the dual-motor drive characteristics, the dynamic model of the dual-motor servo system is established, as shown in formula (1):

[0040]

[0041] Among them, θ i (i=1,2) represents the rotation position of the servo motor, θ L Indicates the rotational position of the load; and Indicates the load's angular velocity and angular acceleration; and Indicates the angular velocity and angular acceleration of the servo motor; J i Indicates the moment of inertia of the servo motor; c i Indicates the viscous friction coefficient of the servo motor; J m Indicates the moment of inertia of the load; c m Indicates the viscous friction coefficient of the load; u i Represents the input torque of the dual-motor servo system; T i represents the rotational torque generated by the contact force between the small gear at the motor end and the large gear at the load end; i in formula (1) represents motor 1 and motor 2 of the dual-motor servo system.

[0042] Due to the nonlinear effect of the gap between the small gear at the motor end and the large gear at the load end, the torque T transmitted between the large gear and the small gear is i It can be expressed as a dead zone model that varies with tooth backlash:

[0043]

[0044] Among them, k b is the stiffness coefficient of the contact between the gear and the pinion, c b is the damping coefficient of the contact between the large gear and the small gear, α is the tooth gap width, bi (t) is the position difference between the large gear and the small gear, is the speed difference between the gear and the pinion; where:

[0045] b i (t) = θ i (t)-θ L (t) (3)

[0046] Where θ i (t)(i=1,2) represents the rotation position of motor i at time t; θ L (t) represents the load position at time t;

[0047]

[0048] Where, represents the angular velocity of motor i at time t; represents the load rotational angular velocity at time t.

[0049] S2: Based on the dynamic situation of torque transmission between the two gears when the gear transmission passes through the tooth gap in the dead zone model, a state space equation model of the dual-motor servo system is established to model the nonlinear effect of the tooth gap as an external disturbance in the state space model;

[0050] Specifically, in order to consider the influence of backlash in the state space model, formula (2) is transformed into a linear model with perturbation, as shown in formula (5):

[0051]

[0052] Among them, d α (·) is the interference term of formula (5) and is b i Function of (t):

[0053]

[0054] From formula (6), we can see that ‖d α (·)‖≤α, that is, the interference is bounded, then the transfer torque T of formula (2) i It can be expressed as:

[0055] An angle sensor is installed on the driving motor, and an axis angle unit is installed on the rotating feed mechanism of the antenna to obtain the rotation angle θ of the feed mechanism in real time. L and speed And the rotation angle θ1, θ2 and speed of the driving speed motor For the above physical quantities, define the state variable x = [x1 x2 x3 x4 x5 x6] Tand the corresponding differential states of the state variables

[0056]

[0057] Combining formula (1) to formula (7), the state space equation model of the dual-motor servo system can be obtained as follows:

[0058]

[0059] Where d0, d1, and d2 are the nonlinear interferences of the backlash on the servo system, and the interference values ​​can be obtained in real time by the Kalman estimator or the extended observer. According to the definition of formula (7), x1-x6 represent the state quantities of the state space equation, which are the load position parameters θ, L , load rotation angular velocity Motor 1's rotational position θ1, motor rotational angular velocity The rotational position θ2 of motor 2 and the angular velocity of motor 2 It represents the differential state value of the state quantity of the state space equation with respect to time. The physical meaning of the differential value of the state quantity can be known through formula (7). In the subsequent controller calculation process, the differential value of the state quantity is continuously updated through the formula (8); J1 represents the moment of inertia of servo motor 1; c1 represents the viscous friction coefficient of servo motor 1; J2 represents the moment of inertia of servo motor 2; c2 represents the viscous friction coefficient of servo motor 2; J m Indicates the moment of inertia of the load; c m represents the viscous friction coefficient of the load; according to the definition of formula (2), k b Indicates the stiffness coefficient of gear contact; c b represents the viscous friction coefficient of the gear contact;

[0060] Arranging formula (8) we can get:

[0061]

[0062] Where A, B, C, D, and E are all constant coefficients, and X = [x1 x2 x3 x4 x5 x6] T is the state quantity; since formula (8) represents the differential state quantity of the state quantity with time t In formula (9), the differential state quantity To sort out the available And the control inputs u1 and u2 are organized into a vector U = [u1u2] T ; Y = [y1y2y3y4] T is the output quantity, the output of the model is related to position tracking and velocity tracking; d = [d0 d1 d2] Tis external interference; A, B, C, D, E can be expressed as:

[0063]

[0064]

[0065] From formula (9), we can see that the input state of the control model of the dual-motor servo system is the position and speed of the feed-switch mechanism end and the position and speed of the dual motors. The output state is the position and speed of the feed-switch mechanism and the position difference between the two motors. The control quantity of the control model is the driving torque of the two motors. The nonlinear effect of the tooth gap is reflected in the external interference.

[0066] This step uses a backlash dead-zone model to model the dual-motor servo system. The state variables of the state-space equation model for the dual-motor servo system are the position and velocity of the motor and load. The model input is the transmission torque of the dual-motor servo system, and the model output includes the load, the kinematic state of the motor, and the position difference between the two motors. The dual-motor servo system model considers the effects of gear contact stiffness and damping on backlash. Therefore, the model can more accurately reflect the dynamic process of backlash changes between gears, making the established state-space model more realistic.

[0067] S3: A model prediction position tracking controller is set based on the state space equation model of the dual-motor servo system to track and control the position and speed of the load and the dual motors. The model prediction position tracking controller includes position and speed detection of the load and the servo motor, a state prediction model, rolling optimization, and feedback correction. The reference position and reference speed of the load are input into the model prediction position tracking controller, and the state values ​​of the load and the servo motor are also input. After rolling optimization, the optimal torque value of the dual motors is obtained, so that the motors output the optimal torque value. When the dual motors drive the load to rotate, feedback correction is performed based on the state values ​​of the load and the servo motor to predict the output state of the dual-motor servo system. The load is a feed-forward mechanism.

[0068] For details, please refer to Figure 3 , Figure 3 This is a schematic diagram of the model predictive position tracking controller, the backlash elimination control strategy, and the dual-motor synchronization control strategy. The model predictive position tracking controller includes position and speed detection of the load and servo motor, a state prediction model, rolling optimization, and feedback correction.

[0069] The position and speed detection of the load and servo motor includes: using sensors to measure the position information of the feed mechanism and servo motor, establishing a Kalman estimator to obtain more accurate position information to account for noise during the measurement process; processing the position information to obtain the speed signals of the load and servo motor;

[0070] The state prediction model includes: obtaining a sequence of predicted values ​​of the system output from the next control cycle to the control cycle corresponding to the control time domain through a set of control input sequences; specifically, the dynamic model of the dual-motor system shown in formula (9) is discretized to obtain a prediction model of the servo system in discrete time. In the prediction model, N p and N c represent the time steps of the prediction domain and the control domain respectively. Figure 4 The diagram illustrates the prediction time domain and control time domain of the controller proposed in this example. In order to ensure the stable operation of the antenna feed mechanism, before the feed mechanism starts position tracking control, the position and speed of the load (feed mechanism) during the entire control process can be pre-set based on the historical data of the feed mechanism's operation process. In other words, the reference values ​​of the load at each moment k and the rotational position and rotational speed that the drive motor needs to achieve are calculated in advance and can be recorded as y r (k). In the kth control cycle of the control system, the reference value y of the load and motor corresponding to the kth control cycle is given in advance r (k), as the reference value of the system output. At the same time, obtain the output reference value sequence Y for the entire prediction time domain at the kth moment r (k)=[y r (k+1),y r (k+2),…,y r (k+N c )] T The position and speed of the load and motor are measured to obtain real-time measurement values. According to formula (9), the system output Y can be obtained and recorded as y(k).

[0071] The core of the state prediction model is to use a set of control input sequences U * (k) Get the next control period k+1 to the control period k+N corresponding to the control time domain c The predicted value sequence Y of the system output up to p (k), from formula (9), we can see that the system output includes four variables, so the Y of the entire control domain is p (k) can be expressed as:

[0072]

[0073] The control input sequence U*(k) contains N c Control input variable u * (k).u * (k) includes the output torque u1, u2 of the dual motors, that is, u * (k)=[u1(k)u2(k)] T The control input sequence U in the entire control time domain *(k) may be defined as:

[0074] U * (k)=[u * (k+1|k),u * (k+2|k),…,u * (k+N c |k)] T (11)

[0075] Since the system model in formula (9) is a differential equation, the zero-order holder is used to discretize the system model. The state equation of the discrete model can be expressed as:

[0076] x(k+1)=A d x(k)+B d u(k) (12)

[0077] Where A d =e A*T , T is the sampling period, k represents the discrete time. Since the constant coefficient D is a zero matrix, the output equation can be expressed as: y(k) = Cx(k) + Du(k) = Cx(k).

[0078] At the kth moment of the control cycle, assuming that the system state quantity x(k), the system control input quantity sequence U * (k)=[u * (k+1|k),u * (k+2|k),…,u * (k+N c |k)] T ,but:

[0079]

[0080] Since the output equation corresponds to the predicted value sequence Y of the system output p (k) can be expressed as follows:

[0081]

[0082] The purpose of establishing the optimization problem is to ensure the control effect of position tracking and speed tracking of the load (feedback mechanism) while reducing the fluctuation of the motor output drive torque. In the subsequent controller design, it is necessary to introduce an anti-backlash strategy to adjust the position difference of the dual motors to compensate for the tooth gap. Therefore, the cost function of the optimization problem must include multiple cost objectives. The adjustment of multiple cost objectives is reflected in the weight coefficient of the cost function. The cost function can be expressed as the second norm of the error between the output value of the control system and the reference value and the second norm of the increment of the control input, as shown in formula (13):

[0083]

[0084] Where J(ΔU(k)) represents the cost function of the optimization problem, and ΔU(k) ​​is the variable in the cost function, i.e., the sequence of control increments within the entire control time domain starting at time k: ΔU(k) ​​= [Δu*(k+1|k), Δu*(k+2|k), ..., Δu*(k+Nc|k)]T. p (k+1) represents the predicted value of the servo system output at the kth moment of the control system at the kth moment. Correspondingly, yr(k+1) represents the reference value of the servo system output at the next moment at the kth moment. After the antenna feed switching system starts operating, the reference value of the servo system position and speed during the entire control process can be obtained in advance based on the expected position of the feed switching mechanism. That is, the reference value yr(k) of the control system output is given, k = 1, 2, ... Tend. W y1 ,W y2 ,W y3 ,W y4 ,W u is the weight value of each cost function. By adjusting the weight value, the performance of the control system can be different. y1 ~W y4 is the weight value of position tracking error and velocity tracking error, W u is the weight value of the input increment. When the system places more emphasis on tracking performance, increase W y1 ~W y4 It can speed up the tracking response speed of the control system and reduce the tracking error; when the system is more inclined to reduce the energy consumption of the motor output, increase W u It can reduce the fluctuation of driving torque. In the future, intelligent optimization algorithm will be used to optimize W y1 ~W y4 and W u Carry out optimized design.

[0085] The optimal control input sequence u*(k+1) in the control time domain can be obtained through the incremental sequence ΔU(k). The optimal control input sequence is a set of vectors whose length is N in the entire control time domain. c In order to ensure the continuity of the controller input in each control cycle and the previous control cycle, the optimal control input u* in the previous control cycle is prevOn the basis of , the first element Δu(k)(k=1) of the control increment sequence solved by the controller in the current control cycle is superimposed to obtain the first parameter u*(k)(k=1) of the control input sequence in the current cycle. For the parameter u*(k+1) after the first parameter in the control input sequence, the control input increment Δu(k+1) in the corresponding order is superimposed on the previous parameter u*(k). Therefore, each control input in the control input sequence is associated with the previous control input. For the sake of clarity, the control input u*(k+1) obtained by superimposing u*(k) is recorded as u*(k+1|k). For the sake of mathematical consistency, the superimposed control input u*(k) is recorded as u*(i|k), and the control input increment Δu(k+1) is recorded as Δu(i+1|k). Therefore, the corresponding control input sequence can be obtained based on the control input increment sequence through formula (14):

[0086]

[0087] Where u* prev Refers to the true optimal control input variable acting on the controlled system within the optimal control input sequence during the previous control cycle. u*(i|k) refers to the i-th control input variable in the optimal control input sequence solved during the k-th control cycle; Δu(i+1|k) refers to the i+1-th control input increment variable in the optimal control input increment sequence solved during the k-th control cycle; and u*(i+1|k) refers to the i+1-th parameter in the optimal control input sequence obtained by superimposing u*(i|k) and Δu(i+1|k).

[0088] Rolling optimization: at time k-1, the output state y(k-1) of the dual-motor servo system is obtained through the sensor, and the measured value of the output state is used as the initial condition x(k) of the optimization problem established in the k control cycle. The state prediction model is used to re-predict the system state and system output predicted value of the dual-motor servo system in the future prediction time domain, and the optimization problem is established and solved based on the predicted value; specifically, at time k-1, the output state y(k-1) of the servo system is obtained through the sensor system gear, and the measured value of the output state is used as the initial condition x(k) of the optimization problem established in the k control cycle. The state prediction model is used to re-predict the system state x(k+1|k)~x(k+Nc-1|k) and system output predicted value yp(k+1|k)~yp(k+Nc|k) of the servo system in the future prediction time domain, and the optimization problem is established and solved based on the predicted value and reference value of the system output.

[0089] The optimization problem is to find a suitable set of control input increment parameters ΔU(k) ​​to minimize the function value of the cost function J(ΔU(k)) in formula (13). According to the definition of formula (13), when J(ΔU(k)) is minimized, it is equivalent to the servo system's tracking error and energy consumption reaching a comprehensive optimal state. When finding the solution to the optimal problem, the output torque of the servo motor, that is, the control input, has physical constraints, including that the output torque cannot exceed the rated torque of the motor, and the increase and decrease amplitudes of the motor output torque must be within a safe range within a control cycle, otherwise it will cause excessive current inside the motor, leading to equipment damage and danger. Therefore, when solving the optimization problem, the constraints of the servo system control input must be considered. The constraints can be expressed as inequality constraints for the control input u* and the control input increment Δu. Through the inequality constraints, the limit values ​​of the motor output torque during forward and reverse transmission, as well as the extreme values ​​of the increase and decrease amplitudes of the torque increment, are specified. Therefore, before the start of each control cycle, the constrained optimization problem that needs to be solved inside the controller can be expressed as:

[0090]

[0091] Where min J(ΔU(k)) refers to the optimization process of minimizing the cost function J(ΔU(k)) established in formula (13). max Refers to the extreme value constraint of the torque when the dual motors are in the forward rotation state. At this time, the motor torque can be assumed to be positive; u min Refers to the extreme value constraint of the torque when the dual motors are in reverse state. At this time, the torque of the motor can be assumed to be negative. min Refers to the extreme value constraint of the decrease amplitude of the torque increment when the dual motor torque changes. At this time, the torque increment can be assumed to be a negative value; Δu max Refers to the extreme value constraint of the increase in the torque increment when the dual motor rotational torque changes. At this time, the torque increment can be assumed to be a positive value.

[0092] The above optimization problem can be solved by the quadratic programming algorithm. During the optimization process, it is necessary to search for a set of independent variables of the cost function J(ΔU(k)), that is, the control input sequence ΔU(k). The control input sequence is a set of length 2*N c vector, the optimization variables include 2*N c Multiple variable parameters. According to formula (14), a new set of control quantity sequences u*(k+1) is obtained from the incremental sequence ΔU(k+1). The first component u*(k+1|k) of u*(k+1) is applied to the drive motor of the servo system, and then the model predictive control of the k+1 control cycle is started. This step is repeated until the control is completed.

[0093] Feedback correction: The reference value of the feedback system output is obtained through the historical data of the feedback system operation and recorded as y pre (k), k is the kth cycle of the control process; the actual state value y(k) output by the commutation system and the reference value y pre (k) The predicted error e of the reference value of the output of the feed-forward system relative to the actual situation can be obtained by comparison pre (k); using the prediction error e pre (k) Reference value y of the system output at the next moment k+1 pre (k+1) makes a correction so that the predicted value y of the system output state at time k+1 is p (k+1) is more consistent with the actual state of the system output. Specifically, since the operation mode of the antenna feed switching system has a fixed rule, mathematical tools can be used in the historical data of the past feed switching system operation to calculate the possible state value of the load (feed switching mechanism) during the control process in advance. When the dynamic changes of the system are not considered, it can be used as a reference value for the output of the controlled system. Since at the kth moment of the control process, the output state u p (k) and the real-time status of the load y p (k) can be collected in real time. On this basis, the reference value of the system output can be used as the reference value of the system output considering the dynamic changes of the system after feedback correction. Before starting the feedback correction, the reference value of the system output obtained from the historical data is recorded as y pre (k), k is the kth cycle of the control process. The actual state value y(k) output by the system and the reference value y output by the system pre (k) The prediction error e of the reference value of the system output relative to the actual situation can be obtained by comparison pre (k):

[0094] e pre (k) = y(k) - y pre (k) (16)

[0095] Using the prediction error e of the system output pre (k), the reference value y of the system output at the next moment k+1 pre (k+1) makes a correction so that the predicted value y of the system output state at time k+1 is p (k+1) is more consistent with the actual state of the system output, and its correction process is:

[0096] y p (k+1)=y pre (k+1)+H·e pre (k) (17)

[0097] Wherein, H is the feedback correction coefficient, H = [h1, h2, … h3].

[0098] Since the present invention is applied to the rotational feed switching of antennas, in order to reduce the influence of the feed source positioning error on the antenna performance and maintain the dynamic response characteristics of the feed switching mechanism, it is hoped that the rotation process of the feed switching mechanism is slower in the termination stage and faster in the start-up and intermediate stages. The prior art PID control is a control method based on position error. When pursuing a fast response of the position of the feed switching mechanism, it is unable to take into account the speed regulation of the feed switching mechanism. Compared with the traditional PID controller, the model prediction position tracking controller proposed in the present invention can simultaneously realize the position tracking and speed tracking control of the load, and because it combines the actual physical quantities inside the servo system, such as the stiffness and damping information during gear meshing, it can more effectively manage the rotation speed of the feed switching mechanism and realize accurate and overshoot-free position tracking and positioning.

[0099] S4: Formulate anti-backlash control strategy and dual-motor synchronization control strategy based on model prediction position tracking controller; when the dual-motor servo system is commutating or stopping, tooth gap will appear, and the position difference of the dual motors minus the tooth gap width will be used as the synchronization error. The reference value of the synchronization error is twice the tooth gap width. Through position compensation, when the synchronization error reaches the reference value, the gap between the motor-end gear and the load-end gear just reaches one times the tooth gap width, eliminating the influence of the tooth gap; when there is no tooth gap, the dual-motor synchronization error is zero. When the synchronization error reaches the reference value, the dual motors are synchronized and jointly drive the load to rotate.

[0100] Specifically, the position difference between the two motors is used as the feedback value, and the position difference of the dual motors is defined as the synchronization error. The internal mechanism of the position tracking controller is predicted by the model, and the motor synchronization control strategy and the anti-backlash control strategy are introduced respectively to ensure the synchronization state of the dual-motor servo system and compensate for the nonlinear interference of the tooth backlash.

[0101] For dual-motor servo systems, in addition to achieving position tracking of the rotating feed mechanism, synchronization between the two motors is also required. In general, motor synchronization control is to achieve consistent motion states for each motor in a multi-motor system. However, when backlash occurs in the servo system of the antenna feed mechanism, it is necessary to change the states of the two motors and increase the position difference between the motors to eliminate the backlash, which causes the states of the two motors to become asynchronous. To address motor asynchrony and backlash, the traditional approach is to propose corresponding control algorithms separately and form an integrated controller for the control system together with the load position tracking control method. However, in actual applications, the control algorithms for the three different tasks are difficult to be compatible, which can cause instability and performance degradation in the control system.

[0102] To address the complexity and difficulty of generalizing control systems due to multiple control objectives, this paper defines the position difference between the two motors as a generalized synchronization error and sets this generalized synchronization error as the system output in the prediction model of the position tracking controller. During stable servo system operation, since there is no backlash, the position difference between the two motors is used as the synchronization error. When the servo system is reversing or stopped, and backlash is about to occur in the transmission system, the synchronization error is calculated as the position difference between the two motors minus the backlash width. The position difference between the two motors is adjusted by setting different reference values ​​for the system output.

[0103] Since the reference values ​​of synchronization error for the anti-backlash strategy and the synchronization strategy are different, in order to ensure the smooth operation of the control system when the reference value is switched, the position difference between the motor position and the load position is used as the conversion function to realize the switching between the synchronization control strategy and the anti-backlash control strategy of the dual-motor system, thereby ensuring the simultaneous realization of tracking control, synchronization control and anti-backlash control of the dual-motor control system.

[0104] Conversion function w(b i ) can be defined as:

[0105]

[0106] Among them, β is the parameter related to the switching function, β is related to the switching trigger condition, and α is the tooth gap width. i |≤α, w(b i )≈1; when |b i |≥β, w(b i )≈0; and in α≤|b i When |≤β, the switching function realizes the transition. i When |≤α, that is, when backlash occurs, the synchronization error is required to be twice the backlash, and the backlash is eliminated through position compensation; when backlash does not occur, the synchronization error is required to be zero to achieve the synchronization state of the dual motors. According to the switching function value of formula (18), the synchronization error as the reference value of the system output can be obtained as:

[0107] y r =w(b i )*(2α) (19)

[0108] Since the designed synchronization control strategy and anti-backlash control strategy are both based on the proposed position tracking controller, the realization of dual-motor synchronization and anti-backlash control will not affect the position tracking performance of the servo system, that is, the synchronization control of the dual motors, the anti-backlash control and the position tracking control of the load can be achieved simultaneously.

[0109] In summary, this invention facilitates the establishment of a state-space equation model for a dual-motor servo system by decomposing the nonlinear dead-zone model of backlash into a linear model and bounded perturbations. The design of a model-predictive position tracking controller based on the state-space model, based on the model-predictive position tracking controller, uses the position difference of the dual motors as the feedback state, and can introduce anti-backlash control and motor synchronization control. When the desired position is about to be reached, anti-backlash control ensures that the load is precisely positioned at the predetermined position and eliminates motor synchronization errors.

[0110] In some embodiments of the present invention, further comprising:

[0111] The parameters of the model predictive position tracking controller are optimized using a genetic algorithm.

[0112] Specifically, to ensure the accuracy and stability of the antenna feed mechanism's position tracking, a genetic algorithm was used to optimize the controller's parameters. This resulted in a fast response time, minimal position overshoot, and minimal steady-state error. To achieve this tracking performance, the control system must operate smoothly, ensuring that the servo system's output torque can compensate for backlash in a timely manner without exceeding its rated value.

[0113] Assuming that the load position reference signal is a step signal, the optimization objectives set include the rise time t rise =10, adjust time t settle =15s, overshoot y os =5%, positioning accuracy y se =1%. The response speed, stability speed, overshoot and positioning accuracy of the control system are integrated into a multi-objective function F(x) = [f1(x), f2(x), f3(x), f4(x)], x p =[W y1 W y1 W y1 W y1 W y1 β], f1(x)~f4(x) functions are the gap between the actual control performance of the control system and the set optimization target, and the torque u of the servo system is * There is a maximum value constraint. The multi-objective optimization problem of the controller parameters can be expressed as: Find a set of controller parameters x p , so that the multi-objective function F(x) = [f1(x), f2(x), f3(x), f4(x)] is minimized, and u * ≤T max .

[0114] The NSGA-II genetic algorithm is used to optimize the controller parameters of the dual-motor servo system. The specific optimization results are shown in Table 1, and the parameters of the dual-motor servo system are shown in Table 2.

[0115] Table 1 The optimal parameters of the position tracking controller predicted by the dual-motor drive position tracking model

[0116]

[0117] Table 2 Simulation parameters of dual-motor servo system

[0118]

[0119] Using the Matlab / Simulink simulation environment, combined with the above controller parameters and servo system parameters, a physical simulation model of the dual-motor servo system including a backlash dead zone model was established. This model includes the anti-backlash strategy and synchronization strategy to predict the position tracking controller and the reference curve of the load's position and velocity. Since the main task of the servo system is to ensure the positioning accuracy of the antenna feed mechanism, in order to simplify the simulation scenario, the load position signal is set to a step signal. The Simulink simulation is a discrete time simulation with a simulation time step of 0.01 seconds and a simulation time of 20 seconds.

[0120] In order to reflect the effectiveness of the integrated controller proposed by this invention through comparison, four controllers are simulated under the same simulation conditions. Please refer to the simulation results. Figure 5-8 , Figure 5 This is a schematic diagram of control performance without introducing the anti-backlash control strategy and dual-motor synchronous control strategy; Figure 6 This is a schematic diagram showing the control performance of the position tracking controller when only synchronization error control is introduced; Figure 7 This is a schematic diagram of the control performance of the position tracking controller when only the anti-backlash control strategy is introduced; Figure 8 This is a schematic diagram of the control performance when the anti-backlash control strategy and the dual-motor synchronous control strategy are introduced using the method of the present invention.

[0121] from Figure 5 The simulation results show that without the introduction of anti-backlash control and synchronous control strategies, the tracking error of the control system will experience periodic oscillation. The reason is that when the load is about to be positioned at the reference position, due to the lack of anti-backlash control on the gear transmission, the two motors pass through the tooth gap at the same time, resulting in the transmission torque of the driving gear on the motor end to the driven gear on the load end being zero. When the driven gear on the load end contacts the driving gear on one side of the motor but not on the other side, the position and speed of the load end are in a state of repeated change and out of control. In addition, the position of the dual motors is also in a jittery state, indicating that the tooth gap causes instability in the position tracking control system. Figure 6The control performance of the position tracking controller using only synchronous error control was demonstrated. With synchronous error control, the position and output torque of the dual motors remained consistent, allowing the load to quickly reach the reference position, and the tracking error was reduced to zero. However, without anti-backlash control, the dual motors did not reach the reference position, indicating the presence of backlash within the transmission system. The backlash ultimately caused the load position to deviate from the reference position, causing the dual motors to vibrate, and the control variable generated by the control system to oscillate. Figure 7 The control performance of the position tracking controller with only anti-backlash control is demonstrated. It can be seen that the load eventually reaches the reference position, the tracking error is ultimately zero, and there is no tremor or jitter during the position tracking control process. This is because when the servo system is about to enter the tooth gap, the position tracking controller with anti-backlash control outputs different drive torques, causing the position difference between the two motors to reach a tooth gap interval. The driven gear at the load end is clamped by the driving gears on both sides, preventing the driven gear from jittering within the tooth gap and allowing the load to be stably positioned at the reference position. Without synchronous control, the position difference between the two motors remains at the tooth gap width, and motor asynchrony cannot be avoided. Figure 8 Simulation results show that the load tracking process is free of jitter and oscillation. When the system is about to enter backlash, anti-backlash control creates a position difference between the two motors, preventing load jitter. Synchronous control then replaces anti-backlash control, gradually reducing the position difference between the two motors. This demonstrates that the designed integrated position tracking controller can simultaneously ensure position tracking while eliminating the effects of transmission backlash and achieving synchronous control of the two motors. Comparing the energy consumption performance of the various controllers, it is found that the controller with anti-backlash control consumes less energy than the controller without anti-backlash control. This is because anti-backlash control prevents control system oscillation and reduces ineffective energy output. Comparing the third and fourth controllers, it is found that after introducing synchronous control, the fourth controller performs anti-backlash control at a later time and requires less energy to achieve anti-backlash control than the third controller. The trade-off is that the load takes longer to reach the desired position. Overall, the performance of the fourth controller is superior to that of the third controller. This step optimizes the design parameters of the model predictive controller using a genetic algorithm, avoiding blind selection of design parameters.

[0122] In some embodiments of the present invention, the step of eliminating backlash by position compensation includes:

[0123] The rotational torques T1 and T2 required to drive the two motors based on the position difference of the dual motors are obtained through rolling optimization. According to the rotational torques T1 and T2, the gears at the motor end and the gears at the load end provide driving force and resistance, so that a gear gap is maintained between the gears at the motor end and the gears at the load end to eliminate the influence of the tooth gap width.

[0124] Please refer to Figure 9 The present invention also provides an anti-backlash control system for an antenna feed dual-motor servo system, comprising:

[0125] Backlash dead zone model module 1: used to establish a dynamic model of the dual-motor servo system and analyze the dynamic model of the dual-motor servo system to obtain a backlash dead zone model. The backlash dead zone model is used to describe the dynamic situation of torque transmission between the two gears when the gear transmission passes through the backlash;

[0126] State-space equation model module 2: This module is used to establish a state-space equation model for the dual-motor servo system based on the dynamic situation of torque transmission between the two gears when the gear transmission passes through the tooth gap in the dead zone model. It is used to model the nonlinear effect of the tooth gap as an external disturbance in the state-space model.

[0127] Model prediction position tracking controller module 3: used to set a model prediction position tracking controller based on the state space equation model of the dual-motor servo system to track and control the position and speed of the load and the dual motors. The model prediction position tracking controller includes position and speed detection of the load and servo motor, a state prediction model, rolling optimization and feedback correction; the reference position and reference speed of the load are input into the model prediction position tracking controller, and the state values ​​of the load and servo motor are also input. After rolling optimization, the optimal torque value of the dual motor is obtained, so that the motor outputs the optimal torque value; when the dual motor drives the load to rotate, feedback correction is performed based on the state values ​​of the load and servo motor to predict the predicted value of the output state of the dual-motor servo system; the load is a feed-forward mechanism;

[0128] Anti-backlash synchronization strategy module 4: used to formulate anti-backlash control strategy and dual-motor synchronization control strategy based on model prediction position tracking controller; when the dual-motor servo system is commutating or stopping, tooth backlash is about to appear, and the position difference of the dual motors minus the tooth backlash width is used as the synchronization error. The reference value of the synchronization error is twice the tooth backlash width. Through position compensation, when the synchronization error reaches the reference value, the gap between the motor-end gear and the load-end gear just reaches one times the tooth backlash width, eliminating the influence of the tooth backlash; when there is no tooth backlash, the dual-motor synchronization error is zero. When the synchronization error reaches the reference value, the dual motors are synchronized and jointly drive the load to rotate.

[0129] For the specific implementation method of the anti-backlash control system for the antenna feed switching dual-motor servo system, please refer to the implementation method of the anti-backlash control method for the antenna feed switching dual-motor servo system, and the process will not be described here.

[0130] It will be apparent to those skilled in the art that the present application is not limited to the details of the exemplary embodiments described above and that the present application can be implemented in other specific forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the present application is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

Claims

1. A backlash control method for an antenna feed switching dual-motor servo system, characterized in that: include: S1: Establishing a dynamic model of the dual-motor servo system and analyzing the dynamic model of the dual-motor servo system to obtain a dead zone model of the tooth gap, wherein the dead zone model of the tooth gap is used to describe the dynamic situation of the torque transmission between the two gears when the gear transmission passes through the tooth gap; The steps to establish the dynamic model of the dual-motor servo system include: The dynamic model of the dual-motor servo system is established as shown in formula (1): Among them, θ i (i=1,2) represents the rotation position of the servo motor, θ L Indicates the rotational position of the load; and Indicates the load's angular velocity and angular acceleration; and Indicates the angular velocity and angular acceleration of the servo motor; J i Indicates the moment of inertia of the servo motor; c i Indicates the viscous friction coefficient of the servo motor; J m Indicates the moment of inertia of the load; c m Indicates the viscous friction coefficient of the load; u i Represents the input torque of the servo system; T i represents the rotational torque generated by the contact force between the small gear at the motor end and the large gear at the load end; i in formula (1) represents motor 1 and motor 2 of the dual-motor system; The steps of analyzing the dynamic model of the dual-motor servo system to obtain the dead zone model of the tooth gap include: Due to the nonlinear effect of the gap between the small gear at the motor end and the large gear at the load end, the torque T transmitted between the large gear and the small gear is i It can be expressed as a dead zone model that varies with tooth backlash: Among them, k b is the stiffness coefficient of the contact between the gear and the pinion, c b is the damping coefficient of the contact between the large gear and the small gear, α is the tooth gap width, b i (t) is the position difference between the large gear and the small gear, is the speed difference between the gear and the pinion; where: b i (t)=θ i (t)-θ L (t) (3) Where θ i (t)(i=1,2) represents the rotation position of motor i at time t; θ L (t) represents the load position at time t; Where, represents the angular velocity of motor i at time t; represents the load rotational angular velocity at time t; S2: Based on the dynamic situation of the torque transmission between the two gears when the gear transmission passes through the tooth gap in the dead zone model, a state space equation model of the dual-motor servo system is established to model the nonlinear effect of the tooth gap as an external disturbance in the state space model; The steps to build the state space equation model of the dual-motor servo system include: In order to consider the effect of backlash in the state space model, formula (2) is transformed into a linear model with disturbance, as shown in formula (5): Among them, d α (·) is the interference term of formula (5) and is b i Function of (t): From formula (6), we can see that ‖d α (·)‖≤α, that is, the interference is bounded, then the transfer torque T of formula (2) i It can be expressed as: An angle sensor is installed on the driving motor, and an axis angle unit is installed on the rotating feed mechanism of the antenna to obtain the rotation angle θ of the feed mechanism in real time. L and speed And the rotation angle θ1, θ2 and speed of the driving speed motor For the above physical quantities, define the state variable x = [x1x2 x3 x4 x5 x6] T and the corresponding differential states of the state variables Combining formula (1) to formula (7), the state space equation model of the dual-motor servo system can be obtained as follows: Where d0, d1, and d2 are the nonlinear interferences of the backlash on the servo system, and the interference values ​​can be obtained in real time by the Kalman estimator or the extended observer. According to the definition of formula (7), x1-x6 represent the state quantities of the state space equation, which are the load position parameters θ, L , load rotation angular velocity Motor 1's rotational position θ1, motor rotational angular velocity The rotational position θ2 of motor 2 and the angular velocity of motor 2 It represents the differential state value of the state quantity of the state space equation with respect to time. The physical meaning of the differential value of the state quantity can be known through formula (7). In the subsequent controller calculation process, the differential value of the state quantity is continuously updated through the formula (8); J1 represents the moment of inertia of servo motor 1; c1 represents the viscous friction coefficient of servo motor 1; J2 represents the moment of inertia of servo motor 2; c2 represents the viscous friction coefficient of servo motor 2; J m Indicates the moment of inertia of the load; c m represents the viscous friction coefficient of the load; according to the definition of formula (2), k b Indicates the stiffness coefficient of gear contact; c b represents the viscous friction coefficient of the gear contact; Arranging formula (8) we can get: Where A, B, C, D, and E are all constant coefficients, and X = [x1 x2 x3 x4 x5 x6] T is the state quantity; since formula (8) represents the differential state quantity of the state quantity with time t In formula (9), the differential state quantity To sort out the available And the control inputs u1 and u2 are organized into a vector U = [u1 u2] T ; Y = [y1y2y3y4] T is the output quantity, the output of the model is related to the position tracking and velocity tracking of the position tracking system; d = [d0 d1d2] T is external interference; A, B, C, D, E can be expressed as: From formula (9), we can see that the input state of the control model of the dual-motor servo system is the position and speed of the feed-switch mechanism end, as well as the position and speed of the dual motors. The output state is the position and speed of the feed-switch mechanism, as well as the position difference between the two motors. The control quantity of the control model is the driving torque of the two motors. The nonlinear effect of the backlash is reflected in the external interference. S3: Setting a model prediction position tracking controller based on the state space equation model of the dual-motor servo system to track and control the position and speed of the load and the dual motors, the model prediction position tracking controller including position and speed detection of the load and the servo motor, a state prediction model, rolling optimization and feedback correction; inputting the reference position and reference speed of the load into the model prediction position tracking controller, and simultaneously inputting the state values ​​of the load and the servo motor, obtaining the optimal torque value of the dual motors through rolling optimization, so that the motors output the optimal torque value; when the dual motors drive the load to rotate, feedback correction is performed based on the state values ​​of the load and the servo motors to predict the predicted value of the output state of the dual-motor servo system; the load is a feed-forward mechanism; The position and speed detection of the load and servo motor includes: using sensors to measure the position information of the feed mechanism and the servo motor, establishing a Kalman estimator to obtain more accurate position information for noise in the measurement process; processing the position information to obtain speed signals of the load and servo motor; The state prediction model includes: obtaining a sequence of predicted values ​​of the system output from the next control period to the control period corresponding to the control time domain through a set of control input sequences; The rolling optimization method comprises the following steps: at time k-1, the output state y(k-1) of the dual-motor servo system is obtained through a sensor, the measured value of the output state is used as the initial condition x(k) of the optimization problem established in the k control cycle, the state prediction model is used to re-predict the system state and system output predicted value of the dual-motor servo system in the future prediction time domain, and the optimization problem is established and solved based on the predicted value; Feedback correction: The reference value of the output of the feed-forward system is obtained by the historical data of the feed-forward system operation and is recorded as y pre (k), k is the kth cycle of the control process; the actual state value y(k) output by the commutation system and the reference value y pre (k) By comparison, the predicted error e of the reference value of the feed-forward system output relative to the actual situation can be obtained. pre (k); using the prediction error e pre (k) Reference value y of the system output at the next moment k+1 pre (k+1) makes a correction so that the predicted value y of the system output state at time k+1 is p (k+1) is more consistent with the actual state of the system output; S4: Based on the model prediction position tracking controller, an anti-backlash control strategy and a dual-motor synchronization control strategy are formulated; when the dual-motor servo system is commutating or stopping, tooth gap is about to appear, and the position difference of the dual motors minus the tooth gap width is used as the synchronization error. The reference value of the synchronization error is twice the tooth gap width. Through position compensation, when the synchronization error reaches the reference value, the gap between the motor-end gear and the load-end gear just reaches one times the tooth gap width, eliminating the influence of the tooth gap; when there is no tooth gap, the dual-motor synchronization error is zero. When the synchronization error reaches the reference value, the dual motors are synchronized and jointly drive the load to rotate.

2. The anti-backlash control method for an antenna feed switching dual-motor servo system according to claim 1, characterized in that: Also includes: The parameters of the model predictive position tracking controller are optimized using a genetic algorithm.

3. The anti-backlash control method for an antenna feed switching dual-motor servo system according to claim 1, characterized in that: The steps to eliminate backlash through position compensation include: The rotational torques T1 and T2 required to drive the two motors based on the position difference of the dual motors are obtained through rolling optimization. According to the rotational torques T1 and T2, the gears at the motor end and the gears at the load end provide driving force and resistance, so that a gear gap is maintained between the gears at the motor end and the gears at the load end to eliminate the influence of the tooth gap width.

4. The anti-backlash control method for an antenna feed switching dual-motor servo system according to claim 1, characterized in that: The anti-backlash control strategy and dual-motor synchronous control strategy include: The position difference between the motor position and the load position is used as the conversion function, and the conversion function w(b i ) is defined as: Among them, β is the relevant parameter of the switching function, β is related to the switching trigger condition, α is the tooth gap width; when |b i |≤α, w(b i )≈1; when |b i |≥β, w(b i )≈0; and in α≤|b i When |≤β, the switching function realizes the transition; when |b i When |≤α, that is, when backlash occurs, the synchronization error is required to be twice the backlash, and the backlash is eliminated through position compensation; when no backlash occurs, the synchronization error is required to be zero to achieve the synchronization state of the dual motors.

5. The anti-backlash control method for an antenna feed switching dual-motor servo system according to claim 2, characterized in that: The optimization of the parameters of the model predictive position tracking controller using the genetic algorithm includes: The NSGA-II genetic algorithm is used to optimize the parameters of the model predictive position tracking controller.

6. An anti-backlash control system for an antenna feed switching dual-motor servo system based on the method according to any one of claims 1 to 5, characterized in that: include: Backlash dead zone model module: used to establish a dynamic model of the dual-motor servo system and analyze the dynamic model of the dual-motor servo system to obtain a backlash dead zone model. The backlash dead zone model is used to describe the dynamic situation of torque transmission between the two gears when the gear transmission passes through the backlash; State-space equation model module: This module is used to establish a state-space equation model for the dual-motor servo system based on the dynamic situation of torque transmission between the two gears when the gear transmission passes through the tooth gap in the dead zone model. It is used to model the nonlinear effect of the tooth gap as an external disturbance in the state-space model. Model prediction position tracking controller module: used to set a model prediction position tracking controller based on the state space equation model of the dual-motor servo system to track and control the position and speed of the load and the dual motors. The model prediction position tracking controller includes position and speed detection of the load and servo motor, a state prediction model, rolling optimization and feedback correction; the reference position and reference speed of the load are input into the model prediction position tracking controller, and the state values ​​of the load and servo motor are input at the same time. After rolling optimization, the optimal torque value of the dual motor is obtained, so that the motor outputs the optimal torque value; when the dual motor drives the load to rotate, feedback correction is performed based on the state values ​​of the load and servo motor to predict the predicted value of the output state of the dual-motor servo system; the load is a feed-forward mechanism; Anti-backlash synchronization strategy module: used to formulate anti-backlash control strategy and dual-motor synchronization control strategy based on model predictive position tracking controller; when the dual-motor servo system is commutating or stopping, tooth backlash is about to appear, and the position difference of the dual motors minus the tooth backlash width is used as the synchronization error. The reference value of the synchronization error is twice the tooth backlash width. Through position compensation, when the synchronization error reaches the reference value, the gap between the motor-end gear and the load-end gear just reaches one times the tooth backlash width, eliminating the influence of the tooth backlash; when there is no tooth backlash, the dual-motor synchronization error is zero. When the synchronization error reaches the reference value, the dual motors are synchronized and jointly drive the load to rotate.

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