Rotary table dual-motor anti-backlash control method based on ESO observer

Abstract

The invention discloses a rotary table dual-motor anti-backlash control method based on an ESO observer, and belongs to the technical field of rotary table control, and the method comprises the following steps: S1, a controller receives a control instruction to control two motors in a rotary table to drive a gear pair in the rotary table, so that the rotary table rotates; s2, an encoder on the double-tooth-piece mechanism collects and calculates actual position information of the rotary table, and the actual position information serves as system input data and is transmitted to a controller; s3, the controller executes the motion control of the two motors and the superposition effect of the ESO observer; s4, outputting the current loop as system output data, and transmitting the system output data to a motor driver through a CAN communication module to drive the two motors to operate; by improving a motor control strategy, a gap between a motor and a gear is eliminated at a motor driving end.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of turntable control, and particularly relates to a turntable double-motor backlash elimination control method based on an ESO observer. BACKGROUND

[0002] A turntable system is widely applied in the fields of radars and satellite tracking, and double-motor driving can provide greater torque, but the gear backlash can cause nonlinear problems, resulting in a decline in control accuracy.

[0003] Patent No. CN120095768A discloses a high-precision single-axis turntable with a large-diameter hollow shaft hole, which comprises a mechanical table body, a double-tooth piece assembly arranged in the mechanical table body, and two groups of driving assemblies. The mechanical table body comprises a table top, a rotary support gear and a base. The table top is connected to the rotary support gear, and the rotary support gear is arranged on the base. The two groups of driving assemblies are symmetrically arranged on the two sides of the rotary support gear for driving the rotary support gear to rotate. The structure design reduces the difficulty and cost of encoder selection, and two groups of driving assemblies are arranged on the base to eliminate backlash and improve structural rigidity and ensure position accuracy.

[0004] However, the main method for eliminating backlash is to improve the structure, and there is a lack of effective control strategy for motor control. The gear backlash can cause nonlinear problems when the motor is driven, resulting in a decline in control accuracy. Therefore, it is urgent to design a turntable double-motor backlash elimination control method based on an ESO observer, so that the external disturbance of the system or the internal disturbance of the system can be effectively observed, and the estimated results are used as system inputs. The original nonlinear control system becomes a linear control system after disturbance compensation. Whether the object is determined or uncertain, linear or nonlinear, time-varying or time-invariant, the system can be simplified into an integral series system through disturbance compensation, so as to eliminate the static error of the control system through the method of simplifying the system into an integral series system. SUMMARY

[0005] The technical problem to be solved by the present application is to eliminate the gap between the motor and the gear at the motor driving end by improving the motor control strategy.

[0006] The technical scheme adopted by the present application to solve the technical problems is: a turntable double-motor backlash elimination control method based on an ESO observer, the turntable comprising a table body, a double-toothed plate mechanism, two motors, a gear pair, an encoder and a controller, the gear pair, the two motors, the double-toothed plate mechanism and the controller being arranged in the table body, the gear pair being located at the center position of the table body, the two motors being symmetrically arranged and engaged with the gear pair, the double-toothed plate mechanism being engaged with the gear pair, and the encoder being arranged on the double-toothed plate mechanism, the method comprising the following steps:

[0007] S1: the controller receives a control instruction to control the two motors in the turntable to drive the gear pair in the turntable to rotate;

[0008] S2: the encoder on the double-toothed plate mechanism collects the calculated actual position information of the turntable as system input data and transmits the system input data to the controller;

[0009] S3: the controller performs motion control of the two motors and superposition of the ESO observer, the superposition comprising position loop P planning, speed loop PI planning and current loop planning of the two motors through the ESO observer superposition control output;

[0010] The speed output of the position loop P planning is:

[0011] v desire =K pv *(P set -P ssi )

[0012] P ssi =P p *K o

[0013] In the formula, P set is a target position of the turntable, P ssi is an actual position of the turntable collected and calculated by the encoder, k pv is a position loop proportional coefficient, P p is an actual position of the double-toothed plate mechanism collected by the encoder, and K o is a conversion ratio of the actual position of the double-toothed plate mechanism collected by the encoder to the actual position of the turntable;

[0014] The current output of the speed loop PI planning is:

[0015] I pi =k p *e v +k i *∑e v

[0016] ev = v desire -v1

[0017] I eso = -z2 / b

[0018] u = I pi + I eso

[0019] In the formula: I pi is the speed loop output planning current, I eso is the ESO observer output compensation current, k p is the speed loop proportional coefficient, k i is the speed loop integral coefficient, e v is the real-time speed error, ∑e v is the speed cumulative error, v1 is the actual average speed of the double motor, z2 is the expected speed of the motor obtained by the ESO observer, and b is the motor rotational inertia coefficient.

[0020] The current loop output planned by the current loop is:

[0021] I1 = y + I offset

[0022] I2 = u - I offset

[0023] In the formula: I1 is the input current of one motor, I2 is the input current of the other motor, I offset is the bias current, wherein when the difference between the target position of the turntable and the actual turntable position calculated by the encoder is greater than 0.2°, no bias current is added, and when the difference between the target position of the turntable and the actual turntable position calculated by the encoder is less than 0.2°, the bias current I offset is added, and the bias current I offset is 0.2.

[0024] S4: The current loop output is transmitted to the motor driver as system output data through the CAN communication module to drive the two motors to operate.

[0025] As a preferred technical solution of the present application, S1 specifically comprises:

[0026] The controller in the turntable receives the control instruction given by the upper computer to control the two motors in the turntable to drive the gear pair in the turntable to rotate, wherein the transfer function of the motor includes the voltage balance, back electromotive force, torque equation and torque balance equation of the motor.

[0027] As a preferred technical solution of the present application, the voltage balance of the motor is:

[0028]

[0029] wherein v m is the control voltage on the motor armature, E is the back EMF of the motor, i m is the armature current of the motor, R m is the armature resistance of the motor, L m is the armature inductance of the motor, d represents the differential symbol, and t represents the time variable.

[0030] As a preferred technical solution of the present application, the back EMF of the motor is:

[0031] E=k e ω m

[0032] wherein k e is the back EMF constant of the motor, and ω m is the motor speed.

[0033] As a preferred technical solution of the present application, the torque equation of the motor is:

[0034] τ m =k m i m

[0035] wherein τ m is the torque of the motor, and k m is the torque constant of the torque motor.

[0036] As a preferred technical solution of the present application, the torque balance equation of the motor is:

[0037]

[0038] wherein J is the rotor load inertia of the torque motor, F is the friction torque and disturbance torque acting on the torque motor, represents the first derivative of the motor speed.

[0039] As a preferred technical solution of the present application, the Laplace transform of the voltage balance, back EMF, torque equation and torque balance equation of the motor is:

[0040]

[0041] wherein s is the Laplace operator.

[0042] As a preferred technical solution of the present application, the ESO observer includes an observer I and an observer II to obtain the desired speed of the two motors at different times, respectively;

[0043] The mathematical model of the ESO observer is:

[0044] e = z1(k-1) - v1

[0045]

[0046] In the formula: z1(k) is the observer one desired speed at k time, z2(k) is the observer two desired speed at k time, v1 is the double motor actual average speed, e is the speed error, beta1 and beta2 are system disturbance related adjustable parameters, b is the motor rotational inertia coefficient, and u is the output data of the planning current.

[0047] As a preferred technical scheme of the application, the motor rotational inertia formula of the ESO observer mathematical model is:

[0048]

[0049] In the formula: m is mass, r is radius, and v is rotational speed.

[0050] In order to ensure the stability and response speed of the servo system of the turntable, the rotational inertia of the motor must match the rotational inertia of the load.

[0051] As a preferred technical scheme of the application, beta1 and beta2 in the system disturbance related adjustable parameters of the ESO observer mathematical model respectively refer to the friction torque and disturbance torque acting on the torque motor.

[0052] The beneficial effects of the application are embodied in:

[0053] 1. Thus, the specific improvement of the motor drive control algorithm is provided, so as to realize the clearance elimination of the motor drive end and ensure the high-precision requirement of the double-motor turntable. In the clearance elimination of the motor drive end, the output of the speed loop is taken as the input of the extended observer by means of the ESO observer cooperating with the encoder, and the output is superimposed with the bias and then acts on the turntable current loop. In this way, the ESO not only acts as an observer but also directly participates in the control, so as to optimize the control performance and make the double motor reach the clearance elimination target under the action of the positive and negative bias. The clearance elimination control process of the turntable is observed by the ESO, the speed parameters at each time are cyclically iterated, the output current is closely related to the turntable motor position loop and speed loop, the turntable can better adapt to the complex working environment, the double-motor clearance elimination control method based on the ESO observer has advantages in processing nonlinear systems, adaptive control and robustness, and can be combined with expert knowledge and experience for accurate adjustment, so that the system shows good performance under different working conditions.

[0054] 2、Based on the control of the motor drive end clearance, cooperate with the setting of the double tooth piece mechanism, so that the encoder can realize the observation of the rotating position of the rotating table by being arranged on the double tooth piece mechanism, and the installation position of the traditional encoder is avoided, the selection and maintenance of the encoder are facilitated. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 The algorithm flowchart of the present application;

[0056] Figure 2 The system control block diagram of the present application two motor clearance;

[0057] Figure 3 The effect comparison diagram of the present application ESO observer before and after adding the clearance;

[0058] Figure 4 The bottom view structure schematic diagram of the present application rotating table;

[0059] Figure 5 The front view structure schematic diagram of the present application rotating table;

[0060] Figure 6 The front view structure schematic diagram of the present application double tooth piece mechanism and gear pair engagement of the rotating table;

[0061] Figure 7 The front view structure schematic diagram of the present application double tooth piece mechanism and encoder;

[0062] Figure 8 The front view structure schematic diagram of the present application double tooth piece and gear pair engagement;

[0063] Figure 9 The front view structure schematic diagram of the present application double tooth piece mechanism;

[0064] Figure 10 The front view structure schematic diagram of the present application encoder;

[0065] Figure 11 The step process schematic diagram of the present application.

[0066] In the figure: 1, table body; 2, double tooth piece mechanism; 21, first tooth piece; 22, second tooth piece; 23, tooth piece shaft; 24, bearing seat; 25, spring; 3, motor; 4, gear pair; 5, encoder; 51, encoder body; 52, connecting seat; 6, controller. DETAILED DESCRIPTION

[0067] The present application will be further described in detail in combination with the drawings.

[0068] In combination with the drawings Figures 1-11As shown, a turntable double-motor backlash control method based on an ESO observer, the turntable comprising a table body 1, a double-toothed plate mechanism 2, two motors 3, a gear pair 4, an encoder 5, a controller 6, the gear pair 4, the two motors 3, the double-toothed plate mechanism 2 and the controller 6 are all arranged in the table body 1, the gear pair 4 is located at the center position of the table body 1, the two motors 3 are symmetrically arranged and are all engaged with the gear pair 4, the double-toothed plate mechanism 2 is engaged with the gear pair 4, the encoder 5 is arranged on the double-toothed plate mechanism 2, and the method comprises the following steps:

[0069] S1: The controller 6 receives a control instruction to control the two motors 3 in the turntable to drive the gear pair 4 in the turntable to rotate, preferably, the controller 6 receives a control instruction given by a host computer, the control instruction given by the host computer is communicated to the controller 6 via ADS, and the controller 6 performs position planning, speed planning and current planning in the starting stage, and the host computer is an external control machine for arranging instructions for the turntable;

[0070] Specifically,

[0071] The controller 6 in the turntable receives a control instruction given by a host computer to control the two motors 3 in the turntable to drive the gear pair 4 in the turntable to rotate, wherein the transfer function of the motor 3 comprises voltage balance, back electromotive force, torque equation and torque balance equation of the motor 3;

[0072] The voltage balance of the motor 3 is:

[0073]

[0074] In the formula, v m is the control voltage on the motor armature, E is the back electromotive force of the motor, i m is the armature current of the motor, R m is the armature resistance of the motor, L m is the motor armature inductance, d represents the differential symbol, and t represents the time variable;

[0075] The back electromotive force of the motor 3 is:

[0076] E=k e ω m

[0077] In the formula, k e is the motor back electromotive force constant, ω m is the motor speed;

[0078] The torque equation of the motor 3 is:

[0079] τ m =km i m

[0080] where τ is the torque of the motor, k is the torque constant of the motor; m m is the torque constant of the torque motor;

[0081] The torque balance equation of the motor 3 is:

[0082]

[0083] where J is the rotor load inertia of the torque motor, F is the friction torque and disturbance torque acting on the torque motor, represents the first derivative of the motor speed;

[0084] The Laplace transform of the voltage balance, back electromotive force, torque equation and torque balance equation of the motor 3 is:

[0085]

[0086] where s is the Laplace operator;

[0087] S2: The encoder 5 on the double-toothed plate mechanism 2 collects the actual position information of the rotary table as system input and transmits it to the controller 6;

[0088] Specifically, the double-toothed plate mechanism comprises a first toothed plate 21, a second toothed plate 22, a toothed plate shaft 23, and a spring 25. The first toothed plate 21 is fixedly sleeved on the toothed plate shaft 23. The second toothed plate 22 is movably sleeved on the toothed plate shaft 23 and is located above the first toothed plate 21 in parallel. The encoder 5 is connected with the toothed plate shaft 23. The tooth block portions of the first toothed plate 21 and the second toothed plate 22 corresponding to each other are overlapped and located in the same tooth groove of the gear pair 4. One of the two opposite groove surfaces of the same tooth groove is in contact with one surface of the tooth block of the first toothed plate 21, and the other groove surface is in contact with one surface of the tooth block of the second toothed plate 22. One surface of the tooth block of the first toothed plate 21 is opposite to one surface of the tooth block of the second toothed plate 22. Specifically, as shown in Figure 8 ​As shown, the solid line position is the first tooth piece 21, and the dashed line position is the second tooth piece 22. In the fully overlapped state of the first tooth piece 21 and the second tooth piece 22 with the same size, the spring 25 is in a compressed or stretched state. When the corresponding tooth blocks of the first tooth piece 21 and the second tooth piece 22 in the fully overlapped state enter the same tooth groove, the tooth blocks on the same side of the first tooth piece 21 and the second tooth piece 22 are attached to one groove surface of the tooth groove. With the reset of the spring 25, the second tooth piece 22 is further pushed away or pulled, so that the two tooth pieces in the fully overlapped state are changed to a partially overlapped state. At this time, the side of the second tooth piece 22 away from the first tooth piece 21 is attached to the other opposite surface of the tooth groove under the action of the spring 25, and the tensioning operation of the two tooth pieces and the gear pair 4 is completed. The second tooth piece 22 driven by the elastic potential energy of the reset spring 25 rotates along the axis of the tooth piece shaft 23, and the rotation angle range of the second tooth piece 22 on the tooth piece shaft 23 is 0-1°. The spring 25 is located between the first tooth piece 21 and the second tooth piece 22. One end of the spring 25 is connected to the first connecting point of the first tooth piece 21, and the other end is fixed to the second connecting point of the second tooth piece 22. The line between the first connecting point and the second connecting point is perpendicular to the axis of the tooth piece shaft 23, and the line between the first connecting point and the second connecting point is consistent with the tangent direction of the tooth piece. Because there is a height difference between the second tooth piece 22 and the first tooth piece 21, the line between the two connecting points is not completely horizontal to the tangent of the tooth piece. Further, a placing groove is formed on the opposite side of the first tooth piece 21 and the second tooth piece 22, and the first connecting point and the second connecting point are located in the two placing grooves respectively. The setting of the placing groove enables the spring 25 with a certain inclination angle to be as parallel to the tangent as possible, and also as close to perpendicular to the axis of the tooth piece shaft 23 as possible. The tooth piece shaft 23 is installed on the bearing seat 24, and the bearing seat 24 is arranged on the table body 1.

[0089] The encoder 5 adopts an SSI encoder, specifically a high-resolution 24-bit absolute value encoder, with a resolution of 0.0001°, which can accurately feedback the rotation angle of the rotary table and provide accurate position information for the control system, ensuring accurate positioning of the rotary table during rotation. The encoder 5 includes an encoder body 51 and a connecting seat 52. The encoder body 51 includes an encoder rotor and an encoder stator. The connecting seat 52 is connected below the bearing seat 24 and presses the outer ring of the inner bearing of the bearing seat 24. The connecting seat 52 is connected to the encoder stator. The encoder rotor is fixedly connected to the tooth piece shaft 23 in the radial direction through screws. The encoder 5 collects the rotation information of the gear pair 4 with the rotation of the gear shaft.

[0090] The "double gear meshing" structure formed by the two motors 3 and the gear pair 4 makes the two motors 3 drive the gear pair 4 cooperatively, so as to control the output torque of the two motors 3 by adding positive and negative two-direction bias torque, force the two motors 3 to be always "pre-tightened" in opposite directions, force the gear driven by one of the two motors 3 to always lead / lag the gear of the other motor 3, and offset the gear side clearance. Preferably, the gears involved in the turntable all adopt high-precision gears, and the transmission mode is composed of the structure design of the double gear piece mechanism 2, so that the transmission is stable and the noise is low. The two motor shaft ends are each provided with a speed reducer, so as to realize high-efficiency transmission and further improve the transmission accuracy.

[0091] S3: The controller 6 performs motion control of the two motors 3 and superposition of the ESO observer, the superposition including position loop P planning, speed loop PI planning of the two motors 3, and current loop planning through the ESO observer superposition control output. The ESO observer is set to utilize the speed-based analog current compensation law designed based on the ESO observer, and the ESO observer includes observer one and observer two. Through the design of the observer one and the observer two, the speed and process disturbance of the two motors 3 can be synchronously observed, forming "observation redundancy".

[0092] The mathematical model of the ESO observer is:

[0093] e=z1(k-1)-v1

[0094]

[0095] In the formula, z1(k) is the expected speed of the observer one at time k, z2(k) is the expected speed of the observer two at time k, v1 is the actual average speed of the two motors 3, e is the speed error, β1 and β2 are system disturbance related adjustable parameters, b is the motor rotational inertia coefficient, and u is the output data of the planned current.

[0096] The motor rotational inertia formula is:

[0097]

[0098] In the formula, m is the mass, r is the radius, and v is the rotational speed.

[0099] In order to ensure the stability and response speed of the servo system of the turntable, the rotational inertia of the motor 3 must match the rotational inertia of the load.

[0100] β1 and β2 are system disturbance related adjustable parameters, which refer to the friction torque and disturbance torque acting on the torque motor.

[0101] The position loop P plans a velocity output as:

[0102] v desire = K pv * (P set - P ssi )

[0103] P ssi = P p + K o

[0104] Wherein: P set is a target position of the turntable, P ssi is an actual position of the turntable calculated by the encoder, k pv is a position loop proportional coefficient, P p is an actual position of the double-toothed plate mechanism collected by the encoder, K o is a conversion ratio of converting the actual position of the double-toothed plate mechanism collected by the encoder into the actual position of the turntable;

[0105] The velocity loop PI plans a current output as:

[0106] I pi = k p * e v + k i *∑e v

[0107] e v = v desire - v1

[0108] I eso = -z2 / b

[0109] u = I pi + I eso

[0110] Wherein: I pi is a velocity loop output planning current, I eso is an ESO observer output compensation current, k p is a velocity loop proportional coefficient, k i is a velocity loop integral coefficient, e v is a real-time velocity error,∑e v is a velocity cumulative error, v1 is an actual average speed of the double motor, z2 is an expected speed of the motor obtained by the ESO observer, and b is a motor rotational inertia coefficient;

[0111] The current loop plans a current loop output as:

[0112] I1 = u + I offset

[0113] I2 = u - Ioffset

[0114] In the formula: I1 is the input current of one motor 3, I2 is the input current of another motor 3, I offset is a bias current, wherein, when the difference between the target position of the turntable and the actual position of the turntable calculated by the encoder 5 is greater than 0.2°, no bias current is added, and when the difference between the target position of the turntable and the actual position of the turntable calculated by the encoder 5 is less than 0.2°, a bias current is added, and the bias current I offset is 0.2, specifically, when the difference between the target position of the turntable and the actual position of the turntable calculated by the encoder 5 is greater than 0.2°, the turntable is coarsely adjusted, no bias current is added, and when the difference between the target position of the turntable and the actual position of the turntable calculated by the encoder 5 is less than 0.2°, fine adjustment is performed for the purpose of eliminating static error, and a bias current is added;

[0115] P err <0.2

[0116] I offset = 0.2

[0117] In the formula: P err is the position deviation, the position deviation is the difference between the target position of the turntable and the actual position of the turntable calculated by the encoder 5, and the value 0.2 is determined according to the implementation accuracy index 0.1;

[0118] S4: the current loop output is transmitted to the motor driver as system output data through the CAN communication module to drive the two motors 3 to operate, wherein the CAN communication module and the driver are arranged on the table body 1.

[0119] The basic principles, main features and advantages of the present application are shown and described above. It should be understood by those skilled in the art that the present application is not limited by the above embodiments, and the above embodiments and descriptions in the specification are only preferred examples of the present application, and are not intended to limit the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A backlash-eliminating control method for a turntable with dual motors based on an ESO observer, characterized in that: The turntable includes a platform body, a double-toothed gear mechanism, two motors, a gear pair, an encoder, and a controller. The gear pair, two motors, double-toothed gear mechanism, and controller are all housed within the platform body. The gear pair is located at the center of the platform body. The two motors are symmetrically arranged and both mesh with the gear pair. The double-toothed gear mechanism is meshed with the gear pair. The encoder is mounted on the double-toothed gear mechanism. The method includes the following steps: S1: The controller receives a control command and controls the two motors in the turntable to drive the gear pair in the turntable so that the turntable rotates; S2: The encoder on the double-tooth plate mechanism collects and calculates the actual position information of the turntable, which is then transmitted to the controller as system input data. S3: The controller performs motion control of the two motors and superposition of the ESO observer. The superposition includes position loop P planning, speed loop PI planning, and current loop planning of the superposition control output of the two motors. The velocity output of the location loop P-plan is: v desire =K pv *(P set -P ssi ) P ssi =P p *K o In the formula: P set P is the target position of the turntable. ssi k is the actual position of the turntable calculated by the encoder. pv P is the position ring scaling factor. p K represents the actual position of the double-toothed mechanism acquired by the encoder. o The conversion ratio for converting the actual position of the double-tooth mechanism acquired by the encoder into the actual position of the turntable; The current output of the speed loop PI program is: I pi =k p *e v +k i *∑e v yes v =v desire -v1 I eso =-z2 / b u=I pi +I eso In the formula: I pi For the speed loop output planning current, I eso For the ESO observer output compensation current, k p k is the speed loop proportional coefficient. i e is the integral coefficient of the velocity loop. v For real-time speed error, ∑e v It is the speed accumulation error, v1 is the actual average speed of the two motors, z2 is the expected speed of the motors obtained by the ESO observer, and b is the motor rotational inertia coefficient. The current loop output of the current loop planning is: I1=u+I offset I2=u-I offset In the formula: I1 is the input current of one of the motors, I2 is the input current of the other motor, and I... offset The bias current is defined as follows: when the difference between the target position of the turntable and the actual turntable position calculated by the encoder is greater than 0.2°, no bias current is added; when the difference between the target position of the turntable and the actual turntable position calculated by the encoder is less than 0.2°, a bias current is added. The bias current I... offset It is 0.2; S4: The current loop output is transmitted as system output data to the motor driver via the CAN communication module to drive the two motors to operate.

2. The method for backlash-eliminating control of a turntable based on an ESO observer according to claim 1, characterized in that: S1 specifically includes: The controller in the turntable receives control instructions from the host computer and controls the two motors in the turntable to drive the gear pair in the turntable to rotate. The transfer function of the motor includes the voltage balance, back electromotive force, torque equation and torque balance equation of the motor.

3. The method for backlash-eliminating control of a turntable based on an ESO observer according to claim 2, characterized in that: The voltage balance of the motor is: In the formula, v m It is the control voltage on the motor armature, E is the back electromotive force of the motor, and i m It is the armature current of the motor, R m It is the armature resistance of the motor, L m It represents the armature inductance of the motor, d represents the differential symbol, and t represents the time variable.

4. The method for backlash elimination control of a turntable based on an ESO observer according to claim 3, characterized in that: The back electromotive force of the motor is: E=k e oh m In the formula, k e It is the back electromotive force constant of the motor, ω m It refers to the motor speed.

5. The method for backlash elimination control of a turntable based on an ESO observer according to claim 4, characterized in that: The torque equation of the motor is: t m =k m I m In the formula, τ m It is the torque of the motor, k m It is the torque constant of the torque motor.

6. The method for backlash elimination control of a turntable based on an ESO observer according to claim 5, characterized in that: The torque balance equation of the motor is: In the formula, J is the rotor load inertia of the torque motor, and F is the frictional torque and disturbance torque acting on the torque motor. The first derivative represents the motor speed.

7. The method for backlash-eliminating control of a turntable based on an ESO observer according to claim 6, characterized in that: The voltage balance, back electromotive force, torque equation, and torque balance equation of the motor are obtained by performing a Laplace transform: In the formula, s is the Laplace operator.

8. The method for backlash-eliminating control of a turntable based on an ESO observer according to claim 1, characterized in that: The ESO observer includes observer one and observer two, which respectively obtain the desired speeds of the two motors at different times. The mathematical model for the ESO observer is as follows: e = z1(k-1) - v1 In the formula: z1(k) is the expected speed of observer one at time k, z2(k) is the expected speed of observer two at time k, v1 is the actual average speed of the two motors, e is the speed error, β1 and β2 are adjustable parameters related to system disturbance, b is the motor rotational inertia coefficient, and u is the output data of the planned current.

9. The method for backlash-eliminating control of a turntable based on an ESO observer according to claim 8, characterized in that: The formula for the moment of inertia of the motor in the mathematical model of the ESO observer is: In the formula: m is the mass, r is the radius, and v is the rotational speed; In order to ensure the stability and response speed of the turntable's servo system, the rotational inertia of the motor must match the rotational inertia of the load.

10. A turntable dual-motor backlash elimination control method based on an ESO observer according to claim 8, characterized in that: In the mathematical model of the ESO observer, β1 and β2, which are adjustable parameters related to system disturbance, refer to the frictional torque and disturbance torque acting on the torque motor, respectively.

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