Anti-backlash control method and system for antenna feed switching dual-motor servo system

Abstract

The invention provides an anti-backlash control method and system for an antenna feed switching dual-motor servo system. The method comprises the following steps: establishing a dynamic model of a dual-motor servo system, and analyzing to obtain a dead zone model of a backlash; establishing a state-space equation model of the dual-motor servo system according to the dead zone model; setting a model prediction position tracking controller based on the state-space equation model of the dual-motor servo system so as to track and control the positions and speeds of the load and the dual motors; formulating an anti-backlash control strategy and a dual-motor synchronous control strategy based on a model prediction position tracking controller; if a backlash occurs, the backlash width is subtracted from the position difference of the double motors to serve as a synchronization error, the synchronization error is twice of the backlash width, and the backlash is eliminated through position compensation; when no backlash occurs, the synchronous error of the double motors is zero, the states of the double motors are synchronous, the double motors jointly drive the load to rotate, and load position tracking, backlash compensation and double-motor synchronous control can be achieved at the same time.

Description

Technical Field

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

[0002] In modern industrial and military fields, the importance of servo systems is becoming increasingly prominent. With the development of technology, the demand for precise control of various electromechanical equipment is increasing, which makes servo systems play a key role in these application scenarios.

[0003] At present, the common forms of antenna feed switching mechanisms include rotary feed switching, sliding feed switching and swing feed switching. Rotary feed switching has become the mainstream feed switching form on large antennas due to its relatively simple structure and stable and reliable performance. The rotary feed switching mechanism places the feed sources of each frequency band on a turntable that deviates from the antenna's symmetry axis. The turntable is driven to rotate by the servo system so that each working feed source reaches the focal position of the antenna and is locked, thereby realizing the switching of feed sources of different frequency bands. The positioning accuracy of the feed source directly affects the electrical performance of the antenna. Therefore, achieving high-precision tracking and positioning of the feed source position is a key goal of the servo system.

[0004] The necessity of dual motor control is particularly prominent in the drive control of large antenna feed switching mechanisms. Due to the large inertia and large disturbance characteristics of large antenna feed switching mechanisms, it is difficult for a single motor servo system to meet the high-precision position tracking and power output requirements when driving such loads. For example, when a single motor provides sufficient torque to drive a large inertia load, it may not be able to guarantee sufficient position control accuracy; conversely, if speed control accuracy is to be guaranteed, it cannot provide sufficient torque. The use of dual motor control, on the one hand, can provide high torque to meet the power required by the servo system and improve the overload capacity of the system; on the other hand, through appropriate control methods, it can effectively eliminate tooth gaps and improve positioning accuracy.

[0005] In the dual-motor servo system, backlash control is a key technical link. Backlash refers to the tiny gap between gears caused by manufacturing accuracy, assembly errors and long-term use during the gear transmission process of the servo system. This type of gap has a significant impact on the synchronous operation of the dual motors. In addition, the backlash phenomenon usually occurs when the drive motor is commutated and stopped. At this time, the driving torque of the servo system cannot be transmitted to the driven system, resulting in temporary uncontrollable loads, increasing the positioning error of the load, and is not conducive to the precise control and positioning of the antenna feed mechanism. In actual application, backlash control faces many difficulties. First of all, the backlash itself is a nonlinear factor, and its impact on the servo system is difficult to completely eliminate with a simple linear control method. Secondly, when the dual motors work together, the backlash will affect the synchronous operation of the dual motors. 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-switch 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 a dual-motor servo system, and analyzing the dynamic model of the dual-motor servo system to obtain a dead zone model of tooth clearance, wherein the dead zone model of tooth clearance is used to describe the dynamic situation of torque transmission between two gears when the gear transmission passes through the tooth clearance;

[0010] S2: According to 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 of the state space model;

[0011] S3: Based on the state space equation model of the dual-motor servo system, a model prediction position tracking controller is set 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 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 through the state values ​​of the load and the servo motor to predict the predicted value of the output state of the dual motor servo system; the load is a feed-forward mechanism;

[0012] 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 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, and 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] The dead zone model module of tooth clearance is used to establish the dynamic model of the dual-motor servo system, and analyze the dynamic model of the dual-motor servo system to obtain the dead zone model of tooth clearance. The dead zone model of tooth clearance is used to describe the dynamic situation of torque transmission between two gears when the gear transmission passes through the tooth clearance.

[0015] State space equation model module: used to establish a state space equation model of the dual-motor servo system 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, and used to model the nonlinear effect of the tooth gap as an external disturbance of 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 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 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 through the state values ​​of the load and the 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, when backlash is about to occur, the position difference of the dual motors minus the backlash width is used as the synchronization error, and the reference value of the synchronization error is twice the 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 backlash width, eliminating the influence of the backlash; when there is no backlash, the dual-motor synchronization error is zero, and 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, the present invention has at least the following advantages or beneficial effects:

[0019] 1. The present invention adopts a backlash dead zone model to model the dual-motor servo system. The state quantities of the state space equation model of the dual-motor servo system are the position and speed of the motor and the load. The input of the model is the transmission torque of the dual-motor servo system. The output of the model includes the load, the motion state of the motor and the position difference of the dual motors. In the model of the dual-motor servo system, the influence of the stiffness and damping of the gear contact on the backlash is considered at the same time. Therefore, the model can more accurately reflect the dynamic process of the backlash change between the gears, so that the established state space model is more in line with the actual situation.

[0020] 2. Since the present invention is applied to the rotational feed-switching of antennas, in order to reduce the impact of feed source positioning errors on 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 startup and intermediate stages. The prior art PID control is a control method based on position error, which cannot take into account the speed regulation of the feed-switching mechanism while pursuing a rapid response of the position of the feed-switching mechanism. Compared with the traditional PID controller, the model predictive 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 of the gear meshing, etc., it can more effectively manage the rotation speed of the feed-switching mechanism and realize accurate and overshoot-free position tracking and positioning.

[0021] By decomposing the nonlinear dead zone model of tooth gap into a linear model and bounded disturbance, it is helpful to establish the state space equation model of the dual motor servo system and design the model prediction position tracking controller based on the state space model. On the basis of the model prediction position tracking controller, the position difference of the dual motors is used as the feedback state, and the anti-backlash control and motor synchronization control can be introduced. When the expected position is about to be reached, the anti-backlash control is used to ensure that the load is accurately positioned to the predetermined position and eliminate the synchronization error of the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. 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 related drawings can be obtained based on these drawings without paying creative work.

[0023] Figure 1 A flowchart of an anti-backlash control method for an antenna feed switching dual-motor servo system is provided for this application;

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

[0025] Figure 3 A 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 the present application;

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

[0027] Figure 5A schematic diagram of control performance of an anti-backlash control method for an antenna feed switching dual-motor servo system in this application without introducing 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 of the control performance of a position tracking controller that only introduces synchronization error control in an anti-backlash control method for an antenna switching dual-motor servo system in this application;

[0029] Figure 7 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 switching dual-motor servo system in this application;

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

[0031] Fig. 9 The present invention discloses a flow chart of an anti-backlash control system for an antenna feed switching dual-motor servo system. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and set in various different configurations.

[0033] In conjunction with the accompanying drawings, some embodiments of the present application are described in detail below. In the absence of conflict, the following embodiments and features in the embodiments can be combined with each other.

[0034] Example

[0035] It should be understood that when the antenna is switched, the switching mechanism has the characteristics of large inertia and large disturbance. When driving such loads, it is difficult for a single motor servo system to meet the requirements of high-precision position tracking and power output. Therefore, dual motor control is required. On the one hand, it can provide high torque to meet the power required by the servo system and improve the overload capacity of the system; on the other hand, it can effectively eliminate the backlash through appropriate control methods to improve positioning accuracy. In the dual motor servo system, backlash control is a key technical link. Backlash phenomenon usually occurs when the drive motor is commutated and stopped. At this time, the driving torque of the servo system cannot be transmitted to the driven system, resulting in temporary uncontrollable loads, increasing the positioning error of the load, and is not conducive to the precise control and positioning of the antenna switching mechanism. In practical applications, backlash control faces many difficulties. First of all, the backlash itself is a nonlinear factor, and its influence on the servo system is difficult to completely eliminate with a simple linear control method. Secondly, when the dual motors work together, the backlash will affect the synchronous operation of the dual motors.

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

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

[0038] S1: establishing a dynamic model of a dual-motor servo system, and analyzing the dynamic model of the dual-motor servo system to obtain a dead zone model of tooth clearance, wherein the dead zone model of tooth clearance is used to describe the dynamic situation of torque transmission between two gears when the gear transmission passes through the tooth clearance;

[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 command signal of the optimal input torque. When the motor works, the driving gear on its output shaft drives the driven gear at the load end to rotate. There is a backlash between the driving gear and the driven gear. Figure 2 In the equation, u1 and u2 represent the input torque of motor 1 and motor 2, J1 and J2 represent the moment of inertia of motor 1 and motor 2, c1 and c2 represent the viscous friction coefficient of motor 1 and motor 2, θ1 and θ2 represent the rotation position of motor 1 and motor 2, and Respectively represent the rotational angular velocity of motor 1 and motor 2. 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 represents the viscous friction coefficient of the load, θ L is the load position parameter, is the load rotation 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 angular velocity and angular acceleration of the load; 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 clearance:

[0043]

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

[0045] b i (t) = θ i (t)-θ L (t) (3)

[0046] In the formula, 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] In the formula, 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 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 of 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 disturbance, 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 drive motor, and an axis angle unit is installed on the rotating feed-switch mechanism of the antenna to obtain the rotation angle θ of the feed-switch 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, d2 are the nonlinear interferences of the backlash to 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 rotation position θ1, motor rotation angular velocity The rotational position θ2 of motor 2 and the rotational angular velocity of motor 2 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 in 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] By rearranging formula (8), we can get:

[0061]

[0062] Among them, A, B, C, D, E are all constant coefficients, X = [x1 x2 x3 x4 x5 x6] T is the state quantity; since formula (8) represents the differential state quantity of the state quantity over time t In formula (9), the differential state quantity To sort out And the control input u1 and u2 are arranged into a vector U = [u1u2] T ; Y = [y1y2y3y4] T is the output quantity, the output of the model is related to position tracking and speed 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 know that the input state of the control model of the dual-motor servo system is the position and speed of the feed-switching mechanism end and the position and speed of the dual motors. The output state is the position and speed of the feed-switching 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 backlash is reflected in the external interference.

[0066] This step uses the backlash dead zone model to model the dual-motor servo system. The state quantities of the state space equation model of the dual-motor servo system are the position and speed of the motor and the load. The input of the model is the transmission torque of the dual-motor servo system. The output of the model includes the load, the motion state of the motor and the position difference of the dual motors. In the model of the dual-motor servo system, the influence of the stiffness and damping of the gear contact on the backlash is considered at the same time. Therefore, the model can more accurately reflect the dynamic process of the backlash change between the gears, so that the established state space model is more in line with the actual situation.

[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 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 through the state values ​​of the load and the servo motor to predict the predicted value of 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 It is a schematic diagram of a model prediction position tracking controller, a backlash elimination control strategy and a dual-motor synchronization control strategy. The model prediction position tracking controller includes position and speed detection of a load and a 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-switching mechanism and the servo motor, establishing a Kalman estimator to obtain more accurate position information for the noise in 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 predicted value sequence 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 prediction time domain and control time domain illustration of the controller proposed in this example. In order to ensure the stable operation of the antenna feed switching mechanism, before the feed switching mechanism starts position tracking control, the position and speed of the load (feed switching mechanism) in the entire control process can be pre-set from the historical data of the operation process of the feed switching mechanism. In other words, the reference values ​​of the load and the rotation position and rotation speed that the drive motor needs to achieve at each moment k are calculated in advance, which can be recorded as y r (k). In the kth control cycle of the control system, the reference values ​​y of the load and motor corresponding to the kth control cycle are 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 time domain 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 system model is discretized using a zero-order holder, and 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] In the formula, 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:

[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 backlash. Therefore, the cost function of the optimization problem needs to contain multiple cost targets. The adjustment of multiple cost targets 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] Wherein, J(ΔU(k)) represents the cost function of the optimization problem, ΔU(k) ​​is the variable in the cost function, i.e., the sequence ΔU(k)=[Δu*(k+1|k),Δu*(k+2|k),...,Δu*(k+Nc|k)]T formed by the control amount increment in the entire control time domain starting from the kth moment. p (k+1) represents the predicted value of the system output of the servo system at the kth moment of the control system at the kth moment in the future k+1th moment. Correspondingly, yr(k+1) represents the reference value of the system output of the servo system at the kth moment in the next moment. After the antenna feed switching system starts to operate, the reference value of the position and speed of the servo system in the entire control process can be obtained in advance through the expected position of the feed switching mechanism, that is, the reference value yr(k) output by the control system 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, and the length of the vector 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 unification, 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] In the formula, u* prev Refers to the real optimal control input variable acting on the controlled system in the optimal control input sequence in the control cycle of the previous moment. u*(i|k) refers to the i-th control input variable in the optimal control input sequence solved in the k control cycle; Δu(i+1|k) refers to the i+1-th control input increment variable in the optimal control input increment sequence solved in the k control cycle; u*(i+1|k) refers to the i+1-th parameter of 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 start re-predicting 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 start re-predicting 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 tracking error and energy consumption of the servo system reaching the optimal state. When looking for 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, resulting in equipment damage and danger. Therefore, when solving the optimization problem, the constraints on the control input of the servo system 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 forward and reverse transmission of the motor output torque, 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 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 a negative value. Δu min It refers to the extreme value constraint of the decreasing 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 It 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 According to formula (14), a new set of control quantity sequence u*(k+1) is obtained from the increment sequence ΔU(k+1), and 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. Repeat this step until the control ends.

[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) of the output of the feed-forward system and the reference value y of the system output pre (k) By comparison, the predicted error e of the reference value of the output of the feed-in-place system relative to the actual situation can be obtained. pre (k); Using the prediction error e pre (k) The reference value y of the system output at the next time 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 previous 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) of the system output and the reference value y pre (k) By comparison, the prediction error e of the reference value of the system output relative to the actual situation can be obtained 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 time 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 startup and intermediate stages. The prior art PID control is a control method based on position error, which cannot take into account the speed regulation of the feed-switching mechanism while pursuing the rapid response of the position 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 of the gear meshing, etc., 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 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.

[0100] Specifically, the position difference between the two motors is taken 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 gap.

[0101] For the dual-motor servo system, in addition to achieving position tracking of the rotating feed-switch mechanism, it is also necessary to achieve synchronization between the dual motors. In general, motor synchronization control is to achieve consistent motion states of each motor in a multi-motor system. However, when the servo system of the antenna feed-switch mechanism has a backlash phenomenon, 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 dual motors to be out of sync. In order to solve the motor asynchrony and backlash phenomena, the traditional method is to propose corresponding control algorithms respectively, and form a comprehensive controller of the control system together with the load position tracking control method. However, in actual applications, the control algorithms for the three different tasks will have incompatibility issues, which will cause instability and performance degradation in the control system.

[0102] In order to solve the problem that the control system becomes complicated and difficult to generalize due to multiple control targets, the present invention proposes to define the position difference of the dual motors as a generalized synchronization error, and set the generalized synchronization error as the system output in the prediction model of the position tracking controller. When the servo system is running stably, since there is no tooth gap, the position difference of the two motors is taken as the synchronization error; when the servo system is reversing or stopping, the transmission system is about to have a tooth gap, and the position difference of the two motors minus the tooth gap width is taken as the synchronization error. The position difference of the dual motors is adjusted by setting different reference values ​​of the system output.

[0103] Since the reference values ​​of the 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 relevant parameter of the switching function, β is related to the conditions of switching triggering, and α is the tooth gap width. i |≤α, w(b i )≈1; when |b i |≥β, w(b i )≈0; and when α≤|b i |≤β, the switching function achieves transition. i When |≤α, that is, when backlash occurs, the synchronization error is required to be twice the backlash, and the backlash is eliminated by 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 reference value of the synchronization error as the system output is:

[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 realized simultaneously.

[0109] In summary, the present invention is conducive to establishing a state space equation model of a dual motor servo system by decomposing the nonlinear dead zone model of tooth clearance into a linear model and a bounded disturbance. The design of a model prediction position tracking controller based on the state space model, on the basis of the model prediction position tracking controller, takes the position difference of the dual motors as the feedback state, and can introduce anti-backlash control and motor synchronization control. When the expected position is about to be reached, the anti-backlash control is used to ensure that the load is accurately positioned to the predetermined position and eliminate the synchronization error of the motor.

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

[0111] A genetic algorithm is used to optimize the parameters of the model predictive position tracking controller.

[0112] Specifically, in order to ensure the accuracy and stability of the position tracking of the antenna feed-switch mechanism, the genetic algorithm is used to optimize the controller parameters so that the response speed of the feed-switch mechanism is fast, the position overshoot and steady-state error are small during the position tracking process. In order to achieve the goal of ensuring tracking performance, the control system needs to run smoothly, and the output torque of the servo system can compensate for the tooth gap in time while avoiding exceeding its rated value.

[0113] Assuming that the position reference signal of the load 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 * There is a maximum value constraint. The multi-objective optimization problem for 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 results of the optimization 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 the backlash dead zone model was established, including the model prediction position tracking controller of the anti-backlash strategy and the synchronization strategy and the reference curve of the position and speed of the load. Since the main task of the servo system is to ensure the positioning accuracy of the antenna switching mechanism, in order to simplify the simulation scenario, the position signal of the load is set to a step signal. The Simulink simulation is a discrete time simulation, the simulation time step is 0.01 seconds, and the simulation time is 20 seconds.

[0120] In order to reflect the effectiveness of the integrated controller proposed by the present 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 the introduction of anti-backlash control strategy and dual-motor synchronous control strategy; Figure 6 This is a schematic diagram of the control performance of the position tracking controller when only the synchronization error control is introduced; Figure 7 This is a schematic diagram of the control performance of the position tracking controller that only introduces the anti-backlash control strategy; Figure 8 The schematic diagram of control performance of introducing the anti-backlash control strategy and the dual-motor synchronous control strategy using the method of the present invention.

[0121] from Figure 5 It can be seen from the simulation results that without the introduction of anti-backlash control and synchronous control strategies, the tracking error of the control system will vibrate periodically. 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 at the motor end to the driven gear at the load end being zero. When the driven gear at the load end contacts the driving gear of one side of the motor, but not the driving gear on the other side, the position and speed of the load end are in a repeatedly changing out-of-control state. In addition, the position of the dual motors is also in a jittering state, indicating that the tooth gap causes the instability of the position tracking control system. Figure 6The control performance of the position tracking controller with only synchronous error control is demonstrated. Under the action of synchronous error control, the position and output torque of the dual motors can be kept consistent, so that the load can quickly reach the reference position, and its tracking error once becomes zero. However, the position of the dual motors did not reach the reference position without the introduction of anti-backlash control, that is, there is a tooth gap in the transmission system. The influence of the tooth gap eventually causes the position of the load to deviate from the reference position, the position of the dual motors also jitters, and the control amount generated by the control system oscillates. Figure 7 The control performance of the position tracking controller with only anti-backlash control is shown. It can be found that the load eventually reaches the reference position, the tracking error is eventually 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 driving torques, causing the position difference between the two motors to reach a tooth gap interval. The driven gear at the load end is stuck by the driving gears on both sides, avoiding the driven gear from jittering inside the tooth gap, allowing the load to be stably positioned at the reference position. The lack of synchronous control causes the position difference of the dual motors to remain at the tooth gap width, and the phenomenon of motor asynchronism cannot be avoided. Figure 8 The simulation results show that there is no jitter or tremor in the tracking process of the load. When the system is about to enter the backlash, the anti-backlash control makes the dual motors produce position difference, avoiding the jitter of the load. After that, the synchronous control replaces the anti-backlash control, so that the position difference of the dual motors gradually decreases. It can be seen that the designed comprehensive position tracking controller can ensure position tracking while eliminating the influence of transmission backlash and realize the synchronous control of the dual motors. Comparing the energy consumption performance of each controller, it can be found that the energy consumption level of the controller with anti-backlash control is lower than that of the controller without anti-backlash control. The reason is that the anti-backlash control can avoid the oscillation of the control system and reduce the invalid energy consumption output. Comparing the third controller and the fourth controller, it can be found that after the introduction of synchronous control, the fourth controller performs anti-backlash control at a later time, and the energy consumption required to achieve anti-backlash control is less than that of the third controller. The cost is that it takes longer for the load to be positioned at the predetermined position. In general, the performance of the fourth controller is better than that of the third control. This step optimizes the design parameters of the model predictive controller through genetic algorithm to avoid blind selection of design parameters.

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

[0123] The position difference of the dual motors is obtained through rolling optimization, and the torques T1 and T2 required to drive the two motors are obtained. According to the 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 gear gap width.

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

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

[0126] State space equation model module 2: used to establish a state space equation model of the dual-motor servo system according to 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, and used to model the nonlinear effect of the tooth gap as an external disturbance of 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 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 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 through the state values ​​of the load and the 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 predictive position tracking controller; when the dual-motor servo system is commutating or stopping, when backlash is about to occur, the position difference of the dual motors minus the backlash width is used as the synchronization error, and the reference value of the synchronization error is twice the 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 backlash width, eliminating the influence of the backlash; when there is no backlash, the dual-motor synchronization error is zero, and 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 features of the present application. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the present application is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims be included in the present application. Any reference numeral in a claim should not be considered 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 a dual-motor servo system, and analyzing the dynamic model of the dual-motor servo system to obtain a dead zone model of tooth clearance, wherein the dead zone model of tooth clearance is used to describe the dynamic situation of torque transmission between two gears when the gear transmission passes through the tooth clearance; S2: According to 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 of the state space model; S3: Based on the state space equation model of the dual-motor servo system, a model prediction position tracking controller is set 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 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 through the state values ​​of the load and the servo motor to predict the predicted value of the output state of the dual motor servo system; the load is a feed-forward mechanism; 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 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, and 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 the antenna feed switching dual-motor servo system according to claim 1 is characterized in that: Also includes: A genetic algorithm is used to optimize the parameters of the model predictive position tracking controller.

3. The anti-backlash control method for the antenna feed switching dual-motor servo system according to claim 1 is characterized in that: The steps to eliminate backlash through position compensation include: The position difference of the dual motors is obtained through rolling optimization, and the torques T1 and T2 required to drive the two motors are obtained. According to the 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 gear gap width.

4. The anti-backlash control method for the antenna feed switching dual-motor servo system according to claim 1 is characterized in that: 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 angular velocity and angular acceleration of the load; 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.

5. The anti-backlash control method for the antenna feed switching dual-motor servo system according to claim 4 is characterized in that: 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 clearance: Among them, k b is the stiffness coefficient of the contact between the large gear and the small gear, c b is the damping coefficient of the contact between the large gear and the small gear, α is the gap width, b i (t) is the position difference between the large gear and the small gear, b. i (t) is the speed difference between the large gear and the small gear; where: b i (t)=θ i (t)-θ L (t) (3) In the formula, 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; In the formula, represents the angular velocity of motor i at time t; represents the load rotational angular velocity at time t.

6. The anti-backlash control method for the antenna feed switching dual-motor servo system according to claim 5, characterized in that: Based on the dead zone model of tooth gap, the steps of establishing 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 (·)‖≤Δ, 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 drive motor, and an axis angle unit is installed on the rotating feed-switch mechanism of the antenna to obtain the rotation angle θ of the feed-switch 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, d2 are the nonlinear interferences of the backlash to 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 rotation position θ1, motor rotation angular velocity The rotational position θ2 of motor 2 and the rotational angular velocity of motor 2 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 in 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; By rearranging formula (8), we can get: Among them, A, B, C, D, E are all constant coefficients, X = [x1 x2 x3 x4 x5 x6] T is the state quantity; since formula (8) represents the differential state quantity of the state quantity over time t In formula (9), the differential state quantity To sort out And the control input 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 speed 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 know that the input state of the control model of the dual-motor servo system is the position and speed of the feed-switching mechanism end and the position and speed of the dual motors. The output state is the position and speed of the feed-switching 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 backlash is reflected in the external interference.

7. The anti-backlash control method for the antenna feed switching dual-motor servo system according to claim 6, characterized in that: The position and speed detection of the load and servo motor includes: using sensors to measure the position information of the feed-switching mechanism and the servo motor, establishing a Kalman estimator to obtain more accurate position information for the noise in the measurement process; processing the position information to obtain the speed signals of the load and servo motor; The state prediction model includes: obtaining a predicted value sequence 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; 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 prediction 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 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) of the output of the feed-forward system and the reference value y of the system output pre (k) By comparison, the predicted error e of the reference value of the output of the feed-in-place system relative to the actual situation can be obtained. pre (k); Using the prediction error e pre (k) The reference value y of the system output at the next time 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.

8. The anti-backlash control method for the antenna feed switching dual-motor servo system according to claim 7, 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 conditions of switching triggering, α is the tooth gap width; when |b i |≤α, w(b i )≈1; when |b i |≥β, w(b i )≈0; and when α≤|b i |≤β, the switching function achieves 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.

9. The anti-backlash control method for the 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 a genetic algorithm includes: The NSGA-II genetic algorithm is used to optimize the parameters of the model predictive position tracking controller.

10. A backlash control system for an antenna feed switching dual motor servo system, characterized in that: include: The dead zone model module of tooth clearance is used to establish the dynamic model of the dual-motor servo system, and analyze the dynamic model of the dual-motor servo system to obtain the dead zone model of tooth clearance. The dead zone model of tooth clearance is used to describe the dynamic situation of torque transmission between two gears when the gear transmission passes through the tooth clearance. State space equation model module: used to establish a state space equation model of the dual-motor servo system 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, and used to model the nonlinear effect of the tooth gap as an external disturbance of 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 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 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 through the state values ​​of the load and the 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, when backlash is about to occur, the position difference of the dual motors minus the backlash width is used as the synchronization error, and the reference value of the synchronization error is twice the 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 backlash width, eliminating the influence of the backlash; when there is no backlash, the dual-motor synchronization error is zero, and when the synchronization error reaches the reference value, the dual motors are synchronized and jointly drive the load to rotate.

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