A method, system and storage medium for lash control of an exciter drive mechanism

Abstract

The application provides a kind of exciter drive mechanism gapless control method, system and storage medium, the method includes collecting motor and load side angular displacement, driving current and torque instruction, constructs the composite state quantity including angular displacement difference, angular velocity difference and torque residual error, according to which the gap crossing stage is identified and divided into meshing approach, contact transition and stable transmission three sections, based on angular displacement difference and torque residual error construct direction related cost function, variable step size is updated and combined with gradient information to adjust learning rate, according to time window statistical characteristics to generate step length credibility index, optimize angular velocity and angular displacement difference determination threshold, when meeting threshold condition, adjust gradient is obtained by fusing historical gradient and attenuation weight, combined with stage division and step length credibility calculation micro-displacement compensation and torque bias, segmented mapping generates control instruction, realizes exciter drive mechanism gapless precision driving.

Description

Technical Field

[0001] This application belongs to the field of control, and in particular relates to a backlash-free control method, system and storage medium for a vibrator transmission mechanism. Background Technology

[0002] As the power source for engineering vibration equipment, the vibrator's transmission mechanism is primarily responsible for converting the rotational power of the motor into a high-frequency, high-power excitation force output. Under long-term high-frequency reciprocating operation and heavy-load alternating conditions, the internal gear pairs, couplings, and other transmission components inevitably generate and exacerbate mechanical backlash. This nonlinearity of backlash leads to periodic disengagement-free travel-violent collision phenomena in the transmission mechanism during forward and reverse force switching. This causes strong mechanical shocks and high-frequency noise, accelerates fatigue wear and even fracture of transmission components, and results in severe lag and waveform distortion in the actual angular displacement and angular velocity response on the load side, reducing the system's control accuracy and excitation energy transfer efficiency. Therefore, how to reliably suppress the nonlinear oscillation shocks caused by transmission backlash and achieve high-precision backlash-free control of the vibrator's transmission mechanism has become a critical problem that urgently needs to be solved in the field of high-end equipment manufacturing.

[0003] This paper combines sensor detection with control algorithms to establish a gap model by collecting operating data from the motor and load sides, and uses algorithms to estimate and compensate for gap nonlinearity online. However, traditional control strategies fail to perform refined state identification and stage division for the complex process of gap crossing, and only use a globally unified compensation model, which cannot implement differentiated control for different states of the transmission mechanism, such as meshing approximation, contact transition, and stable transmission. Existing variable step size adjustment mechanisms usually rely only on the single error at the current moment, and do not fully combine the angular displacement difference and torque residual to construct a direction-related cost function. When facing high-frequency forward and reverse switching of the exciter, they are prone to learning rate step size oscillations and convergence divergence at the velocity zero crossing point or displacement reversal critical region. Existing methods mostly use fixed state judgment thresholds and lack a reliability assessment and threshold adjustment mechanism based on the historical statistical characteristics of step size updates. This leads to lag or over-adjustment in the generation of micro-displacement compensation and torque bias commands under complex working conditions, and cannot fundamentally achieve smooth, stable, and disturbance-resistant backlash-free transmission. Summary of the Invention

[0004] To address the problems of control oscillation, compensation lag, and mechanical shock caused by the lack of refined identification of the gap crossing stage, fixed threshold determination, and single error variable step size adjustment in existing technologies.

[0005] In a first aspect, the present invention provides a backlash-free control method for a vibrator transmission mechanism, comprising: Collect the angular displacement of the motor side, the angular displacement of the load side, the drive current, and the torque command; construct a composite state quantity based on the difference in angular displacement and angular velocity between the motor side and the load side, as well as the torque residual between the actual torque represented by the drive current and the torque command; identify the gap crossing stage according to the composite state quantity and the rate of change, and divide the transmission process into the meshing approach stage, the contact transition stage, and the stable transmission stage. Based on the angular displacement difference and torque residual, a direction-related cost function is constructed. Variable step size updates are performed on the forward and reverse propagation respectively. The learning rate scaling factor is determined based on the gradient of the cost function and the gradient change rate at adjacent sampling times. A step size reliability index is generated based on the statistical characteristics of the learning rate scaling factor within a preset time window, and the threshold for zero-crossing angular velocity and sign reversal of angular displacement difference are adjusted. When the absolute value of the detected angular displacement difference is less than the adjusted angular displacement difference sign reversal judgment threshold, and the absolute value of the detected angular velocity difference is less than the adjusted angular velocity zero crossing judgment threshold, the adjustment gradient is obtained by combining the historical gradient and memory decay weight; based on the stage division, step size reliability index and adjustment gradient, the micro-displacement compensation amount and torque offset amount are calculated, and the backlash-free control command is generated by segmenting and mapping according to the relative motion direction to drive the exciter transmission mechanism.

[0006] Optionally, the construction of composite state variables based on the angular displacement difference and angular velocity difference between the motor side and the load side, and the torque residual between the actual torque represented by the drive current and the torque command, includes: The angular displacement difference is obtained by acquiring the motor-side angular displacement and the load-side angular displacement at the same sampling time and calculating the difference between the two. The angular velocities of the motor side and the load side are calculated by differentiating the angular displacement of the motor side and the angular displacement of the load side, and the difference between the two is obtained. The actual torque is calculated by multiplying the torque-current conversion constant and the drive current, and the torque residual is obtained by subtracting the torque command from the actual torque. Each of the angular displacement difference, angular velocity difference, and torque residual is assigned an independent preset weighting coefficient; The composite state variables are generated by multiplying the angular displacement difference, angular velocity difference, and torque residual by their respective weighting coefficients and then summing them by weight.

[0007] Optionally, the step of identifying the gap crossing stage based on the composite state quantity and rate of change, and dividing the transmission process into a meshing approach stage, a contact transition stage, and a stable transmission stage, includes: Set a first threshold and a second threshold for the composite state variable, wherein the first threshold is greater than the second threshold; Calculate the absolute value of the composite state quantity and the rate of change of the composite state quantity over time; When the absolute value of the composite state quantity is greater than the first threshold, and the rate of change indicates that the absolute value is decreasing, the transmission process is determined to be in the meshing approach segment. When the absolute value of the composite state quantity is not greater than the first threshold and is greater than the second threshold, and the absolute value of the rate of change is less than the preset rate of change threshold, the transmission process is determined to be in the contact transition section. When the absolute value of the composite state quantity is not greater than the second threshold and the volatility is lower than the preset stability threshold, the transmission process is determined to be in the stable transmission segment.

[0008] Optionally, determining the learning rate scaling factor based on the gradient of the cost function and the rate of change of the gradient at adjacent sampling times includes: Obtain the current gradient of the cost function at the current sampling time, and the historical gradient of the cost function at the previous sampling time; Calculate the difference between the current gradient and the historical gradient to obtain the gradient change rate; The quotient of the absolute value of the current gradient and the sum of the absolute value of the gradient change rate and a preset small positive number is used as the basic adjustment ratio. The basic adjustment ratio is input into a preset nonlinear exponential function for mapping calculation; The learning rate scaling factor is obtained by multiplying the calculation result of the nonlinear exponential function by the base learning rate and the preset scaling constant.

[0009] Optionally, the step of combining historical gradients and memory decay weights to obtain the adjusted gradient includes: By using the data cache queue, extract the historical gradient of the cost function for a preset number of historical periods before the current sampling time; Each extracted historical gradient is assigned a corresponding memory decay weight, which decays exponentially as the time interval from the current sampling time increases. The current gradient of the cost function at the current sampling time is multiplied by the preset current weight to obtain the current weighted gradient; Each extracted historical gradient is multiplied by its corresponding memory decay weight to obtain multiple historical weighted gradients; The adjusted gradient is obtained by summing the current weighted gradient with all historical weighted gradients and dividing by the sum of the current weight and all memory decay weights.

[0010] Optionally, the step of calculating micro-displacement compensation and torque offset based on the stage division, step size reliability index, and adjustment gradient, and generating backlash-free control commands to drive the exciter transmission mechanism by segmenting and mapping according to the relative motion direction, includes: Multiply the adjustment gradient by the step size confidence index to obtain the compensation base coefficient; During the meshing approach phase, a micro-displacement compensation amount is generated based on the compensation baseline coefficient, which is in the same direction as the angular velocity. In the contact transition section, the micro-displacement compensation amount is combined with the attenuation factor to achieve a smooth transition; In the stable transmission section, the micro-displacement compensation is set to zero, and the torque offset is calculated by a proportional-integral regulator based on the torque residual. The micro-displacement compensation amount and the torque offset amount obtained from different stages are superimposed on the position loop and torque loop of the basic control command, respectively, to generate a backlash-free control command that is input to the servo driver of the exciter transmission mechanism for execution.

[0011] Optionally, the step of generating a step size reliability index based on the statistical characteristics of the learning rate scaling factor within a preset time window, and adjusting the angular velocity zero-crossing determination threshold and the angular displacement difference sign flipping determination threshold, includes: Extract all learning rate scaling factors within a preset time window, and calculate the variance and mean; The ratio of the mean to the variance plus a preset small positive number is used as the independent variable and input into the normalized activation function, which outputs the step size confidence index between 0 and 1. Obtain the initial angular velocity zero-crossing threshold and the initial angular displacement difference sign reversal threshold; A threshold adjustment factor is generated based on the step size reliability index; The initial angular velocity zero-crossing determination threshold and the initial angular displacement difference sign reversal determination threshold are multiplied by the threshold adjustment factor to obtain the adjusted angular velocity zero-crossing determination threshold and angular displacement difference sign reversal determination threshold.

[0012] In another aspect, the present invention also provides a backlash-free control system for a vibrator transmission mechanism, comprising: The acquisition module is used to acquire the angular displacement of the motor side, the angular displacement of the load side, the drive current, and the torque command; based on the difference in angular displacement and angular velocity between the motor side and the load side, as well as the torque residual between the actual torque represented by the drive current and the torque command, a composite state quantity is constructed; based on the composite state quantity and the rate of change, the gap crossing stage is identified, and the transmission process is divided into the meshing approach stage, the contact transition stage, and the stable transmission stage. The adjustment module is used to construct a direction-related cost function based on the angular displacement difference and torque residual, perform variable step size updates for forward and reverse propagation respectively, determine the learning rate scaling factor based on the gradient of the cost function and the gradient change rate at adjacent sampling times, generate a step size reliability index based on the statistical characteristics of the learning rate scaling factor within a preset time window, and adjust the angular velocity zero-crossing judgment threshold and the angular displacement difference sign flipping judgment threshold. The generation module is used to obtain an adjustment gradient by combining historical gradients and memory decay weights when the absolute value of the detected angular displacement difference is less than the adjusted angular displacement difference sign reversal judgment threshold and the absolute value of the angular velocity difference is less than the adjusted angular velocity zero crossing judgment threshold; based on the stage division, step size reliability index and adjustment gradient, the micro-displacement compensation amount and torque offset amount are calculated, and backlash-free control commands are generated to drive the exciter transmission mechanism by segmenting and mapping according to the relative motion direction.

[0013] Preferably, the construction of composite state variables based on the angular displacement difference and angular velocity difference between the motor side and the load side, and the torque residual between the actual torque represented by the drive current and the torque command, includes: The angular displacement difference is obtained by acquiring the motor-side angular displacement and the load-side angular displacement at the same sampling time and calculating the difference between the two. The angular velocities of the motor side and the load side are calculated by differentiating the angular displacement of the motor side and the angular displacement of the load side, and the difference between the two is obtained. The actual torque is calculated by multiplying the torque-current conversion constant and the drive current, and the torque residual is obtained by subtracting the torque command from the actual torque. Each of the angular displacement difference, angular velocity difference, and torque residual is assigned an independent preset weighting coefficient; The composite state variables are generated by multiplying the angular displacement difference, angular velocity difference, and torque residual by their respective weighting coefficients and then summing them by weight.

[0014] Preferably, the step of identifying the gap crossing stage based on the composite state quantity and rate of change, and dividing the transmission process into a meshing approach stage, a contact transition stage, and a stable transmission stage, includes: Set a first threshold and a second threshold for the composite state variable, wherein the first threshold is greater than the second threshold; Calculate the absolute value of the composite state quantity and the rate of change of the composite state quantity over time; When the absolute value of the composite state quantity is greater than the first threshold, and the rate of change indicates that the absolute value is decreasing, the transmission process is determined to be in the meshing approach segment. When the absolute value of the composite state quantity is not greater than the first threshold and is greater than the second threshold, and the absolute value of the rate of change is less than the preset rate of change threshold, the transmission process is determined to be in the contact transition section. When the absolute value of the composite state quantity is not greater than the second threshold and the volatility is lower than the preset stability threshold, the transmission process is determined to be in the stable transmission segment.

[0015] Preferably, determining the learning rate scaling factor based on the gradient of the cost function and the rate of change of the gradient at adjacent sampling times includes: Obtain the current gradient of the cost function at the current sampling time, and the historical gradient of the cost function at the previous sampling time; Calculate the difference between the current gradient and the historical gradient to obtain the gradient change rate; The quotient of the absolute value of the current gradient and the sum of the absolute value of the gradient change rate and a preset small positive number is used as the basic adjustment ratio. The basic adjustment ratio is input into a preset nonlinear exponential function for mapping calculation; The learning rate scaling factor is obtained by multiplying the calculation result of the nonlinear exponential function by the base learning rate and the preset scaling constant.

[0016] Preferably, the step of combining historical gradients and memory decay weights to obtain the adjusted gradient includes: By using the data cache queue, extract the historical gradient of the cost function for a preset number of historical periods before the current sampling time; Each extracted historical gradient is assigned a corresponding memory decay weight, which decays exponentially as the time interval from the current sampling time increases. The current gradient of the cost function at the current sampling time is multiplied by the preset current weight to obtain the current weighted gradient; Each extracted historical gradient is multiplied by its corresponding memory decay weight to obtain multiple historical weighted gradients; The adjusted gradient is obtained by summing the current weighted gradient with all historical weighted gradients and dividing by the sum of the current weight and all memory decay weights.

[0017] Preferably, the step of calculating micro-displacement compensation and torque offset based on the stage division, step size reliability index, and adjustment gradient, and generating backlash-free control commands to drive the exciter transmission mechanism by segmenting and mapping according to the relative motion direction includes: Multiply the adjustment gradient by the step size confidence index to obtain the compensation base coefficient; During the meshing approach phase, a micro-displacement compensation amount is generated based on the compensation baseline coefficient, which is in the same direction as the angular velocity. In the contact transition section, the micro-displacement compensation amount is combined with the attenuation factor to achieve a smooth transition; In the stable transmission section, the micro-displacement compensation is set to zero, and the torque offset is calculated by a proportional-integral regulator based on the torque residual. The micro-displacement compensation amount and the torque offset amount obtained from different stages are superimposed on the position loop and torque loop of the basic control command, respectively, to generate a backlash-free control command that is input to the servo driver of the exciter transmission mechanism for execution.

[0018] Preferably, the step of generating a step size reliability index based on the statistical characteristics of the learning rate scaling factor within a preset time window, and adjusting the angular velocity zero-crossing determination threshold and the angular displacement difference sign flipping determination threshold, includes: Extract all learning rate scaling factors within a preset time window, and calculate the variance and mean; The ratio of the mean to the variance plus a preset small positive number is used as the independent variable and input into the normalized activation function, which outputs the step size confidence index between 0 and 1. Obtain the initial angular velocity zero-crossing threshold and the initial angular displacement difference sign reversal threshold; A threshold adjustment factor is generated based on the step size reliability index; The initial angular velocity zero-crossing determination threshold and the initial angular displacement difference sign reversal determination threshold are multiplied by the threshold adjustment factor to obtain the adjusted angular velocity zero-crossing determination threshold and angular displacement difference sign reversal determination threshold.

[0019] This invention constructs a composite state variable by collecting the bilateral motion and torque states of the motor and load, dividing the transmission process into three stages: meshing approximation, contact transition, and stable transmission, thus identifying the true physical characteristics of the system. A direction-dependent cost function is constructed for forward and reverse transmission, and a scaling factor is determined based on the gradient and gradient change rate to generate a step size reliability index, thereby adjusting the judgment thresholds for angular velocity and angular displacement differences in real time. This mechanism not only improves the recognition accuracy and algorithm convergence of gap crossing intervals but also avoids the risks of misjudgment and overshoot oscillation caused by fixed thresholds. When detecting the critical state of the gap, micro-displacement compensation and torque offset are calculated by combining historical gradients and memory decay weights, generating segmented gapless control commands. This reduces mechanical shock and wear, achieves smooth torque transmission, and improves system control accuracy and equipment lifespan. Attached Figure Description

[0020] Figure 1 A flowchart of the first embodiment; Figure 2 This is a schematic diagram illustrating the decay of composite state variables and the stage threshold. Figure 3 This is a schematic diagram of the memory decay weight distribution; Figure 4 This is a schematic diagram comparing contact collision impacts. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this specification will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of them. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this specification.

[0022] In the first embodiment, the present invention proposes a backlash-free control method for a vibrator transmission mechanism, such as... Figure 1 As shown, it includes: S1. Collect the angular displacement of the motor side, the angular displacement of the load side, the drive current, and the torque command; construct a composite state quantity based on the difference in angular displacement and angular velocity between the motor side and the load side, as well as the torque residual between the actual torque represented by the drive current and the torque command; identify the gap crossing stage according to the composite state quantity and the rate of change, and divide the transmission process into the meshing approach stage, the contact transition stage, and the stable transmission stage.

[0023] The angular displacement of the motor side is acquired by an optical encoder mounted on the motor shaft, and the angular displacement of the load side is acquired by an optical encoder mounted on the load end of the exciter. The three-phase drive current output by the motor driver is obtained using a current sensor, and the torque command is read from the host computer. The three-phase drive current is converted into quadrature-axis current using Clark and Park transforms, and the actual torque is calculated by multiplying the quadrature-axis current by the torque current conversion constant. The angular velocities of the motor side and load side are obtained by performing first-order forward differential operations on the angular displacements of the motor side and load side respectively. The angular velocity difference is obtained by subtracting the load side angular velocity from the motor side angular velocity, and the angular displacement difference is obtained by subtracting the load side angular displacement from the motor side angular displacement. The torque residual is obtained by subtracting the torque command from the actual torque. A Kalman filter algorithm is used to filter and denoise the angular displacement difference, angular velocity difference, and torque residual. The denoised angular displacement difference, angular velocity difference, and torque residual are used as feature components to form a three-dimensional column vector as a composite state variable. The rate of change of the composite state variable is calculated by differentiating the composite state variable. A stage identification and classification model is constructed using the support vector machine algorithm. The composite state variables and the rate of change of the composite state variables are input into the support vector machine classification model. When the model output value is -1, it is determined to be the meshing approximation stage; when the model output value is zero, it is determined to be the contact transition stage; and when the model output value is +1, it is determined to be the stable transmission stage, thereby realizing the stage division of the transmission process.

[0024] Optionally, the preferred structure of the support vector machine classification model is that the input features consist of a six-dimensional feature vector composed of three-dimensional composite state variables and their three-dimensional rates of change, and the output consists of three discrete categories: -1 represents the meshing approximation stage, 0 represents the contact transition stage, and +1 represents the stable transmission stage. The model is trained by collecting six-dimensional feature samples under different transmission stages through experiments or simulations, and labeling each sample with the corresponding stage label manually or based on known physical laws. Then, the support vector machine is trained using this labeled data, typically employing a one-to-many or one-to-one strategy to handle the three-class classification problem. An appropriate kernel function, such as the radial basis function, is selected to map the features to a high-dimensional space to construct the optimal classification hyperplane, thereby achieving accurate identification of the three stages of the transmission process.

[0025] In one optional implementation, the construction of composite state variables based on the angular displacement difference and angular velocity difference between the motor side and the load side, and the torque residual between the actual torque represented by the drive current and the torque command, includes: The angular displacement difference is obtained by acquiring the motor-side angular displacement and the load-side angular displacement at the same sampling time and calculating the difference between the two. The angular velocities of the motor side and the load side are calculated by differentiating the angular displacement of the motor side and the angular displacement of the load side, and the difference between the two is obtained. The actual torque is calculated by multiplying the torque-current conversion constant and the drive current, and the torque residual is obtained by subtracting the torque command from the actual torque. Each of the angular displacement difference, angular velocity difference, and torque residual is assigned an independent preset weighting coefficient; The composite state variables are generated by multiplying the angular displacement difference, angular velocity difference, and torque residual by their respective weighting coefficients and then summing them by weight.

[0026] The control system acquires the motor-side angular displacement fed back by the built-in high-precision absolute encoder of the servo motor in real time at a fixed control cycle. Simultaneously, it acquires the load-side angular displacement through an external sensor installed at the load end of the exciter. The two are clock-synchronized and latched, and then the difference is calculated to obtain the angular displacement difference; for example, the angular displacement difference at a certain sampling moment is 0.005 rad. The displacement signal is differentiated using differential operations combined with a first-order low-pass filter with a cutoff frequency of 100 Hz to obtain the angular velocity in rad / s, and the difference is used to generate the angular velocity difference. The quadrature-axis current is read from the current loop of the motor driver as the drive current. This quadrature-axis current is multiplied by a pre-calibrated torque current conversion constant to obtain the actual torque. The torque command issued by the host computer is subtracted to calculate the torque residual in Nm. To eliminate the influence of different dimensions of various physical quantities and to integrate signal characteristics, the controller internally normalizes the calculated angular displacement difference, angular velocity difference, and torque residual to their maximum values, and assigns corresponding dimensionless weighting coefficients to the normalized angular displacement difference, angular velocity difference, and torque residual. For displacement-dominant characteristics, the preferred weighting coefficients are 0.5 to 0.7 for angular displacement difference, 0.2 to 0.4 for angular velocity difference, and 0.05 to 0.15 for torque residual. Preferably, the sum of these weighting coefficients is 1 to maintain the composite state quantity within the normalized range, thereby ensuring the universality of subsequent threshold settings. The three normalized parameters are multiplied by their respective weighting coefficients and linearly superimposed to output a composite state quantity representing the current degree of mechanical clearance closure. This composite state quantity is updated with a 1ms control cycle.

[0027] In one optional implementation, the step of identifying the gap crossing stage based on the composite state quantity and rate of change, and dividing the transmission process into an engagement approach stage, a contact transition stage, and a stable transmission stage, includes: Set a first threshold and a second threshold for the composite state variable, wherein the first threshold is greater than the second threshold; Calculate the absolute value of the composite state quantity and the rate of change of the composite state quantity over time; When the absolute value of the composite state quantity is greater than the first threshold, and the rate of change indicates that the absolute value is decreasing, the transmission process is determined to be in the meshing approach segment. When the absolute value of the composite state quantity is not greater than the first threshold and is greater than the second threshold, and the absolute value of the rate of change is less than the preset rate of change threshold, the transmission process is determined to be in the contact transition section. When the absolute value of the composite state quantity is not greater than the second threshold and the volatility is lower than the preset stability threshold, the transmission process is determined to be in the stable transmission segment.

[0028] Within the servo controller, a first threshold and a second threshold are pre-configured to represent different coupling depths of the composite state quantity in the transmission gap. The preferred setting range for the first threshold is 0.05 to 0.08, and the preferred setting range for the second threshold is 0.01 to 0.03. The controller calculates the absolute value of the composite state quantity in real time during each discrete sampling period and performs a first-order backward difference operation on the absolute value to obtain the rate of change of the composite state quantity over time, in units of... When the status monitoring module detects that the absolute value of the current composite state variable is greater than 0.06 and the rate of change is less than zero, for example, measured as -0.15... This indicates that the system is currently in a state of large backlash deviation and the moving side is rapidly approaching the contact surface. The state machine determines that the current transmission process is in the meshing approach phase. As the transmission process progresses, when the absolute value of the composite state variable decays to the range of 0.015 to 0.06, and the absolute value of the detected rate of change is less than a preset rate of change threshold, which is preferably 0.05,... For example, the current detected change rate is 0.02. When the system enters the region where the tooth surfaces are about to contact or partially contact each other, the nonlinear friction and elastic deformation effects become prominent, and the state flag is immediately set to the contact transition section. When the absolute value of the composite state variable is completely less than or equal to 0.015, and the signal volatility statistically analyzed by the controller within the sliding time window remains below the preset stability threshold, it indicates that the transmission chain stiffness has been fully established and the power transmission performance is stable, automatically switching to the stable transmission section. The signal volatility refers to the ratio of the standard deviation to the mean of the absolute value of the composite state variable in the recent sampling sequence, used to quantify whether the system tends to stabilize, thereby triggering the switching to the stable transmission section. Through a digital logic classification and recognition model, seamless identification of the gap crossing cycle can be achieved, such as... Figure 2 As shown, the curve decays rapidly in the initial stage, passing through the first threshold of 0.06 and the second threshold of 0.015, presenting a complete process from the meshing approach stage, the contact transition stage to the stable transmission stage.

[0029] S2, construct a direction-related cost function based on the angular displacement difference and torque residual, perform variable step size updates for forward and reverse propagation respectively, determine the learning rate scaling factor based on the gradient of the cost function and the gradient change rate at adjacent sampling times, generate a step size reliability index based on the statistical characteristics of the learning rate scaling factor within a preset time window, and adjust the angular velocity zero-crossing judgment threshold and the angular displacement difference sign flipping judgment threshold.

[0030] A direction-dependent cost function is constructed based on the weighted sum of the squares of the angular displacement difference and the squares of the torque residual. Both the angular displacement difference and the torque residual are normalized to eliminate dimensionality effects. When the motor-side angular velocity is greater than zero, it is considered a forward transmission and the first weighted coefficient set is used; when the motor-side angular velocity is less than or equal to zero, it is considered a reverse transmission and the second weighted coefficient set is used. A gradient descent algorithm is used to update the variable step-size parameters for both forward and reverse transmissions. The gradient of the cost function relative to the control variables at the current sampling moment is calculated using a derivative function. The control variables refer to adjustable parameters used to generate micro-displacement compensation and torque bias, such as compensation gain coefficients or step-size iteration weights. The derivative of the cost function is used to optimize the convergence direction of the gap compensation command. The gradient rate of change is obtained by subtracting the gradient from the gradient at the previous sampling moment. A learning rate scaling factor is determined based on the gradient rate of change, automatically shrinking the step size when the gradient changes drastically, appropriately increasing the step size when the gradient changes smoothly, and applying amplitude limiting protection when the gradient rate of change approaches zero to prevent divergence. A preset time window is formed by selecting fifty consecutive sampling periods before the current time. The mean and variance of all learning rate scaling factors within the time window are calculated, and a step size confidence index is generated based on the mean and variance. A threshold adjustment factor that changes inversely with the confidence index is constructed using the step size confidence index. When the step size confidence decreases, the adjustment factor is increased to widen the judgment boundary, thereby suppressing false reverse judgments caused by learning rate oscillations.

[0031] In one implementation, determining the learning rate scaling factor based on the gradient of the cost function and the rate of change of the gradient at adjacent sampling times includes: Obtain the current gradient of the cost function at the current sampling time, and the historical gradient of the cost function at the previous sampling time; Calculate the difference between the current gradient and the historical gradient to obtain the gradient change rate; The quotient of the absolute value of the current gradient and the sum of the absolute value of the gradient change rate and a preset small positive number is used as the basic adjustment ratio. The basic adjustment ratio is input into a preset nonlinear exponential function for mapping calculation; The learning rate scaling factor is obtained by multiplying the calculation result of the nonlinear exponential function by the base learning rate and the preset scaling constant.

[0032] The optimization module of the control system extracts the target cost function based on position tracking error and torque fluctuation within the operating cycle. In the current sampling cycle, it calculates the current gradient value using differential or analytical derivative calculations, for example, a result of 0.85. Simultaneously, it retrieves the historical gradient value from the previous sampling cycle stored in RAM, for example, 0.65. Subtracting the historical gradient from the current gradient yields a gradient change rate of 0.20. To prevent calculation divergence, the absolute value of the current gradient (0.85) is used as the numerator, and the absolute value of the gradient change rate (0.20) is added to a preset small positive number (between 1e-5 and 1e-3, preferably 1e-4) to prevent division by zero. This sum is used as the denominator, and the base adjustment ratio is obtained through division, resulting in a value of approximately 4.247. The controller inputs the calculated base adjustment ratio as an independent variable into a preset nonlinear exponential mapping function. A typical expression for this mapping function is: The decay time constant The preferred configuration is 2.0. Substituting x=4.247 into the typical expression above, the processor calculates a nonlinear mapping output value of approximately 0.88. The processor reads from non-volatile memory a pre-set base learning rate (preferred to be between 0.01 and 0.05, e.g., 0.02) based on the mechanical inertia of the exciter, and a fixed preset scaling constant (e.g., 1.5). A floating-point multiplication operation is then performed on the mapping output value 0.88, the base learning rate 0.02, and the scaling constant 1.5 to generate a learning rate scaling factor of 0.0264 for the current cycle. When the absolute value of the gradient change rate is less than 1e-3, the scaling calculation is skipped, and the base learning rate of 0.02 is directly used as the current learning rate scaling factor. This ensures that the update step size is increased when the cost function is smooth, and automatically contracts in extreme value abrupt regions, avoiding oscillations and divergence during the learning process.

[0033] In one implementation, the step of generating a step size reliability index based on the statistical characteristics of the learning rate scaling factor within a preset time window, and adjusting the angular velocity zero-crossing determination threshold and the angular displacement difference sign flipping determination threshold, includes: Extract all learning rate scaling factors within a preset time window, and calculate the variance and mean; The ratio of the mean to the variance plus a preset small positive number is used as the independent variable and input into the normalized activation function, which outputs the step size confidence index between 0 and 1. Obtain the initial angular velocity zero-crossing threshold and the initial angular displacement difference sign reversal threshold; A threshold adjustment factor is generated based on the step size reliability index; The initial angular velocity zero-crossing determination threshold and the initial angular displacement difference sign reversal determination threshold are multiplied by the threshold adjustment factor to obtain the adjusted angular velocity zero-crossing determination threshold and angular displacement difference sign reversal determination threshold.

[0034] The controller maintains a sliding time data window of length M in the background. The optimal range for M is 20 to 50 sampling points, for example, M=30. The controller updates the sequence within the window during each iteration and simultaneously uses the DSP's built-in statistical algorithm to calculate the statistical mean of 30 learning rate scaling factors within this time window in real time, for example, 0.025, and the statistical variance, for example, 0.0001. Using the statistical mean as the numerator and adding a preset small positive number (preferably 1e-6) to the statistical variance to suppress data underflow as the denominator, a division operation yields a dimensionless independent variable value of approximately 247.5. The controller inputs this independent variable into a typical Sigmoid normalized activation function, and through smooth compression mapping, outputs a step size reliability index strictly limited to the 0-1 interval, for example, the current mapping output is 0.85. This quantitatively evaluates the reliability of the current optimization step size. The controller retrieves the device's factory default initial angular velocity zero-crossing threshold (e.g., 0.05 rad / s) and initial angular displacement difference sign-flipping threshold (e.g., 0.002 rad) from the non-volatile parameter library. The controller then calculates the threshold adjustment factor based on the current step size reliability index, for example... Where β is the amplification factor, preferably ranging from 1.0 to 3.0. When the confidence index is 0.85 and the amplification factor is 1, the adjustment factor is approximately 1.15, the adjusted angular velocity zero-crossing threshold is 0.0575 rad / s, and the angular displacement difference sign reversal threshold is 0.0023 rad. If the step size confidence index drops to 0.4 due to system noise or dead zone disturbance, the adjustment factor is increased to 1.6, and the adjusted thresholds are 0.08 rad / s and 0.0032 rad, respectively. By actively relaxing the judgment threshold and increasing the judgment dead zone during periods of severe learning rate oscillation, the sensitivity of the drive controller to high-frequency measurement noise is reduced, thereby effectively avoiding the problem of frequent false motion reverse judgments caused by noise.

[0035] S3, when the absolute value of the detected angular displacement difference is less than the adjusted angular displacement difference sign reversal judgment threshold, and the absolute value of the angular velocity difference is less than the adjusted angular velocity zero crossing judgment threshold, the adjustment gradient is obtained by combining the historical gradient and memory decay weight; based on the stage division, step size reliability index and adjustment gradient, the micro-displacement compensation amount and torque offset amount are calculated, and the backlash-free control command is generated by segmenting and mapping according to the relative motion direction to drive the exciter transmission mechanism.

[0036] The absolute value calculation function is called to obtain the absolute values ​​of the angular displacement difference and angular velocity difference at the current moment. When the absolute value of the angular displacement difference is less than the adjusted angular displacement difference sign flipping threshold and the absolute value of the angular velocity difference is less than the adjusted angular velocity zero-crossing threshold, the calculation of the adjustment gradient is triggered. Historical gradients from the five most recent sampling moments are selected, and memory decay weights are assigned using an exponential decay algorithm. Gradients closer to the current moment have larger weights. The adjusted gradient is calculated by multiplying the historical gradients by their corresponding memory decay weights and summing the results. During the meshing approach phase, the basic displacement gain is multiplied by the adjustment gradient to obtain the micro-displacement compensation. During the contact transition phase, the step size reliability index is multiplied by the adjustment gradient to calculate the micro-displacement compensation. During the stable transmission phase, the micro-displacement compensation is set to zero. The torque offset is calculated by linearly combining the torque residual and the adjustment gradient using a proportional-integral algorithm. When the relative motion direction is positive, the micro-displacement compensation and torque offset are directly superimposed on the initial position and initial torque commands to generate a backlash-free control command. When the relative motion direction is negative, the micro-displacement compensation and torque offset are inverted and then superimposed on the initial position and initial torque commands to generate a backlash-free control command. A space vector pulse width modulation algorithm is invoked to generate a pulse control signal, which is then sent to the power inverter to drive the exciter transmission mechanism.

[0037] In one implementation, obtaining the adjusted gradient by combining the historical gradient and the memory decay weights includes: By using the data cache queue, extract the historical gradient of the cost function for a preset number of historical periods before the current sampling time; Each extracted historical gradient is assigned a corresponding memory decay weight, which decays exponentially as the time interval from the current sampling time increases. The current gradient of the cost function at the current sampling time is multiplied by the preset current weight to obtain the current weighted gradient; Each extracted historical gradient is multiplied by its corresponding memory decay weight to obtain multiple historical weighted gradients; The adjusted gradient is obtained by summing the current weighted gradient with all historical weighted gradients and dividing by the sum of the current weight and all memory decay weights.

[0038] The controller's underlying layer utilizes a pointer array to construct a data cache queue with a first-in, first-out (FIFO) structure to store the cost function gradients from multiple consecutive control cycles. The queue depth corresponds to a preset number of sampling cycles, preferably configured between 5 and 20 cycles, for example, a length N=10. At each real-time computation cycle, the top 10 historical gradients stored in the cache are extracted and assigned memory decay weights based on an exponential decay model that moves backward by time step. The weight formula is defined as follows: Where i represents the number of historical beats delayed from the current time, i=1 to 10, and the decay factor is... The configuration range is from 0.8 to 0.95, for example, taking... =0.9. Therefore, the weights of the historical data from the 1st to the 10th frame are established as 0.9, 0.81, 0.729, etc., respectively. The influence of the data decreases geometrically as the time period increases. Figure 3 As shown, the weights decay exponentially with increasing time intervals, with the most recent first tick having the highest weight, gradually decreasing with the number of ticks to ensure that gradient calculations balance short-term response and long-term stability. The processor multiplies the newly calculated current gradient within the current sampling period by the system's preset current weight coefficient. To ensure real-time response, this current weight is preferably set to 1.0, resulting in a current weighted gradient of 0.5. Simultaneously, the microprocessor schedules MAC instructions to retrieve historical gradients from the queue; for example, the first three values ​​are 0.48, 0.45, and 0.41, respectively, and match them with the corresponding decay weights. Each gradient is multiplied sequentially to generate a set of historical weighted gradients, such as 0.432, 0.3645, and 0.2988. The controller calls the accumulator to sum the current weighted gradient with all historical weighted gradients and performs normalized division on the summation result to obtain an adjusted gradient with a controlled numerical range. The output adjusted gradient takes into account both short-term momentum and long-term trends, and can filter out high-frequency gradient disturbances caused by mechanical friction collisions in backlash transmissions, thus improving the stability of control optimization.

[0039] In one implementation, the step of calculating micro-displacement compensation and torque offset based on the stage division, step size reliability index, and adjustment gradient, and generating backlash-free control commands to drive the exciter transmission mechanism by segmenting and mapping according to the relative motion direction, includes: Multiply the adjustment gradient by the step size confidence index to obtain the compensation base coefficient; During the meshing approach phase, a micro-displacement compensation amount is generated based on the compensation baseline coefficient, which is in the same direction as the angular velocity. In the contact transition section, the micro-displacement compensation amount is combined with the attenuation factor to achieve a smooth transition; In the stable transmission section, the micro-displacement compensation is set to zero, and the torque offset is calculated by a proportional-integral regulator based on the torque residual. The micro-displacement compensation amount and the torque offset amount obtained from different stages are superimposed on the position loop and torque loop of the basic control command, respectively, to generate a backlash-free control command that is input to the servo driver of the exciter transmission mechanism for execution.

[0040] In each execution cycle of the digital signal processor, the arithmetic logic unit multiplies the previously acquired adjustment gradient, such as the current calculated value of 2.15, with a step confidence index normalized to the 0-1 interval, such as the current evaluation value of 0.8, to calculate a compensation base coefficient with an output size of 1.72. Branching operations are performed based on the flag bit of the currently locked stage of the state machine: When the system is in the meshing approach stage, the controller takes the compensation base coefficient and multiplies it by the system's preset micro-displacement gain coefficient, for example, configured as 0.001 rad, and uses the sign function sign() to convert the base compensation value into the same direction as the current actual angular velocity of the motor, thereby generating a micro-displacement compensation amount in rad to quickly close the free gap; when the detection state transitions to the contact transition stage, the built-in spline interpolation or first-order inertial filter is called to calculate the attenuation factor required for smooth transition. This attenuation factor is related to the ratio of the current composite state quantity to the second threshold, so that the micro-displacement compensation amount adaptively attenuates with the degree of gap closure. For example, the attenuation factor is calculated to drop to 0.4 based on the estimated remaining gap, thereby attenuating the generated micro-displacement compensation amount to 40% of the original, thereby reducing the impact force amplitude and avoiding destructive collisions on the rigid tooth surface. Once the system determines that it has fully entered the stable transmission phase, the controller command register sets the micro-displacement compensation to zero to prevent position loop overshoot, as the physical gap is completely closed and remains stable. Simultaneously, the module activates the torque feedforward control channel, using the torque residual of the current cycle as input, and calculates the torque offset through a proportional-integral regulator to suppress load fluctuations. In the closed-loop distribution phase, the main control chip adds the micro-displacement compensation obtained from each segment mapping as a feedforward to the basic position command generated by the interpolator and sends it to the position regulator. At the same time, it superimposes the calculated torque offset onto the basic torque setpoint command of the inner loop. The resulting backlash-free control command, including dual-loop correction, is input to the servo driver at the end of the vibrator transmission mechanism via industrial fieldbuses such as EtherCAT at a synchronous rate of 1ms to drive the motor rotation.

[0041] A servo motor-driven exciter experimental platform was built, with a high-precision external displacement sensor at the load end and an absolute encoder on the motor side. The control sampling period was set to 1ms. The experiment was divided into a complete scheme group and an ablation control group. The complete scheme group adopted a backlash-free control strategy that included composite state variable stage recognition and step size reliability threshold adjustment. The ablation control group, in addition to the complete scheme, removed the step size reliability threshold adjustment module and used the initial judgment thresholds fixed at the factory throughout the angular velocity zero-crossing determination and angular displacement difference sign reversal determination. During the experiment, the system uniformly received alternating torque commands with an amplitude of 5Nm and a frequency of 10Hz and ran continuously for 200 complete working cycles.

[0042] Experimental data, including the position tracking error and peak impact torque of the transmission mechanism, were recorded in real time using a multi-channel data acquisition card. The results showed that the average position tracking error of the complete scheme group during the gap crossing stage was only 0.015 rad, the average system settling time to reach the stable transmission section was 12 ms, and the peak impact torque generated at the moment of tooth surface contact was strictly limited to within 1.2 Nm. In contrast, the ablation control group showed an increase in average position tracking error to 0.035 rad, an increase in average settling time to 24 ms, and a surge in peak impact torque at the moment of contact to 4.1 Nm. Simultaneously, monitoring revealed that the controller experienced up to 18 false motion reversal misjudgments due to high-frequency measurement noise, leading to high-frequency command divergence. Figure 4 As shown, the peak impact torque of the ablation control group reached 4.1 Nm and exhibited positive and negative oscillations; the peak impact torque of the complete scheme group was suppressed to 1.2 Nm and rapidly decayed to a stable state, verifying the weakening effect of this gapless control strategy on mechanical collision impact.

[0043] The complete solution generates a step size confidence index by extracting the variance and mean of the learning rate scaling factor within the sliding time window. This index automatically generates an amplified threshold adjustment factor when confidence decreases due to dead-zone perturbations or learning rate oscillations. This mechanism, which adaptively widens the decision boundary according to system state, avoids logical misjudgments caused by minute measurement noise. It not only completely eliminates frequent jumps and divergences in backlash-free control commands but also reduces the impact torque of rigid mechanical collisions by approximately 70%, improving the overall smoothness of the drivetrain and servo tracking.

[0044] In a second embodiment, the present invention also provides a backlash-free control system for a vibrator transmission mechanism, comprising: The acquisition module is used to acquire the angular displacement of the motor side, the angular displacement of the load side, the drive current, and the torque command; based on the difference in angular displacement and angular velocity between the motor side and the load side, as well as the torque residual between the actual torque represented by the drive current and the torque command, a composite state quantity is constructed; based on the composite state quantity and the rate of change, the gap crossing stage is identified, and the transmission process is divided into the meshing approach stage, the contact transition stage, and the stable transmission stage. The adjustment module is used to construct a direction-related cost function based on the angular displacement difference and torque residual, perform variable step size updates for forward and reverse propagation respectively, determine the learning rate scaling factor based on the gradient of the cost function and the gradient change rate at adjacent sampling times, generate a step size reliability index based on the statistical characteristics of the learning rate scaling factor within a preset time window, and adjust the angular velocity zero-crossing judgment threshold and the angular displacement difference sign flipping judgment threshold. The generation module is used to obtain an adjustment gradient by combining historical gradients and memory decay weights when the absolute value of the detected angular displacement difference is less than the adjusted angular displacement difference sign reversal judgment threshold and the absolute value of the angular velocity difference is less than the adjusted angular velocity zero crossing judgment threshold; based on the stage division, step size reliability index and adjustment gradient, the micro-displacement compensation amount and torque offset amount are calculated, and backlash-free control commands are generated to drive the exciter transmission mechanism by segmenting and mapping according to the relative motion direction.

[0045] The above description is merely an embodiment of this specification and is not intended to limit this specification. Various modifications and variations can be made to this specification by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of the claims of this specification.

Claims

1. A backlash-free control method for a vibrator transmission mechanism, characterized in that, include: Collect the angular displacement of the motor side, the angular displacement of the load side, the drive current, and the torque command; construct a composite state quantity based on the difference in angular displacement and angular velocity between the motor side and the load side, as well as the torque residual between the actual torque represented by the drive current and the torque command; identify the gap crossing stage according to the composite state quantity and the rate of change, and divide the transmission process into the meshing approach stage, the contact transition stage, and the stable transmission stage. Based on the angular displacement difference and torque residual, a direction-related cost function is constructed. Variable step size updates are performed on the forward and reverse propagations respectively. The learning rate scaling factor is determined based on the gradient of the cost function and the gradient change rate at adjacent sampling times. The step size reliability index is generated based on the statistical characteristics of the learning rate scaling factor within the preset time window, and the threshold for zero crossing of angular velocity and sign reversal of angular displacement difference are adjusted. When the absolute value of the detected angular displacement difference is less than the adjusted angular displacement difference sign reversal judgment threshold, and the absolute value of the detected angular velocity difference is less than the adjusted angular velocity zero crossing judgment threshold, the adjustment gradient is obtained by combining the historical gradient and memory decay weight; based on the stage division, step size reliability index and adjustment gradient, the micro-displacement compensation amount and torque offset amount are calculated, and the backlash-free control command is generated by segmenting and mapping according to the relative motion direction to drive the exciter transmission mechanism.

2. The method according to claim 1, characterized in that, The composite state variables are constructed based on the angular displacement difference and angular velocity difference between the motor side and the load side, as well as the torque residual between the actual torque represented by the drive current and the torque command, including: The angular displacement difference is obtained by acquiring the motor-side angular displacement and the load-side angular displacement at the same sampling time and calculating the difference between the two. The angular velocities of the motor side and the load side are calculated by differentiating the angular displacement of the motor side and the angular displacement of the load side, and the difference between the two is obtained. The actual torque is calculated by multiplying the torque-current conversion constant and the drive current, and the torque residual is obtained by subtracting the torque command from the actual torque. Each of the angular displacement difference, angular velocity difference, and torque residual is assigned an independent preset weighting coefficient; The composite state variables are generated by multiplying the angular displacement difference, angular velocity difference, and torque residual by their respective weighting coefficients and then summing them by weight.

3. The method according to claim 1, characterized in that, The method of identifying the gap crossing stage based on the composite state variables and rate of change divides the transmission process into a meshing approach stage, a contact transition stage, and a stable transmission stage, including: Set a first threshold and a second threshold for the composite state variable, wherein the first threshold is greater than the second threshold; Calculate the absolute value of the composite state quantity and the rate of change of the composite state quantity over time; When the absolute value of the composite state quantity is greater than the first threshold, and the rate of change indicates that the absolute value is decreasing, the transmission process is determined to be in the meshing approach segment. When the absolute value of the composite state quantity is not greater than the first threshold and is greater than the second threshold, and the absolute value of the rate of change is less than the preset rate of change threshold, the transmission process is determined to be in the contact transition section. When the absolute value of the composite state quantity is not greater than the second threshold and the volatility is lower than the preset stability threshold, the transmission process is determined to be in the stable transmission segment.

4. The method according to claim 2, characterized in that, The step of determining the learning rate scaling factor based on the gradient of the cost function and the rate of change of the gradient at adjacent sampling times includes: Obtain the current gradient of the cost function at the current sampling time, and the historical gradient of the cost function at the previous sampling time; Calculate the difference between the current gradient and the historical gradient to obtain the gradient change rate; The quotient of the absolute value of the current gradient and the sum of the absolute value of the gradient change rate and a preset small positive number is used as the basic adjustment ratio. The basic adjustment ratio is input into a preset nonlinear exponential function for mapping calculation; The learning rate scaling factor is obtained by multiplying the calculation result of the nonlinear exponential function by the base learning rate and the preset scaling constant.

5. The method according to claim 1, characterized in that, The process of combining historical gradients and memory decay weights to obtain the adjusted gradient includes: By using the data cache queue, extract the historical gradient of the cost function for a preset number of historical periods before the current sampling time; Each extracted historical gradient is assigned a corresponding memory decay weight, which decays exponentially as the time interval from the current sampling time increases. The current gradient of the cost function at the current sampling time is multiplied by the preset current weight to obtain the current weighted gradient; Each extracted historical gradient is multiplied by its corresponding memory decay weight to obtain multiple historical weighted gradients; The adjusted gradient is obtained by summing the current weighted gradient with all historical weighted gradients and dividing by the sum of the current weight and all memory decay weights.

6. The method according to claim 1, characterized in that, The process involves calculating micro-displacement compensation and torque offset based on the stage division, step size reliability index, and adjustment gradient. Then, it generates backlash-free control commands to drive the exciter transmission mechanism through segmented mapping according to the relative motion direction. This includes: Multiply the adjustment gradient by the step size confidence index to obtain the compensation base coefficient; During the meshing approach phase, a micro-displacement compensation amount is generated based on the compensation baseline coefficient, which is in the same direction as the angular velocity. In the contact transition section, the micro-displacement compensation amount is combined with the attenuation factor to achieve a smooth transition; In the stable transmission section, the micro-displacement compensation is set to zero, and the torque offset is calculated by a proportional-integral regulator based on the torque residual. The micro-displacement compensation amount and the torque offset amount obtained from different stages are superimposed on the position loop and torque loop of the basic control command, respectively, to generate a backlash-free control command that is input to the servo driver of the exciter transmission mechanism for execution.

7. The method according to claim 1, characterized in that, The step size reliability index is generated based on the statistical characteristics of the learning rate scaling factor within a preset time window, and the thresholds for determining zero crossing of angular velocity and sign reversal of angular displacement difference are adjusted, including: Extract all learning rate scaling factors within a preset time window, and calculate the variance and mean; The ratio of the mean to the variance plus a preset small positive number is used as the independent variable and input into the normalized activation function, which outputs the step size confidence index between 0 and 1. Obtain the initial angular velocity zero-crossing threshold and the initial angular displacement difference sign reversal threshold; A threshold adjustment factor is generated based on the step size reliability index; The initial angular velocity zero-crossing determination threshold and the initial angular displacement difference sign reversal determination threshold are multiplied by the threshold adjustment factor to obtain the adjusted angular velocity zero-crossing determination threshold and angular displacement difference sign reversal determination threshold.

8. A backlash-free control system for a vibrator transmission mechanism, characterized in that, include: The acquisition module is used to acquire the angular displacement of the motor side, the angular displacement of the load side, the drive current, and the torque command; based on the difference in angular displacement and angular velocity between the motor side and the load side, as well as the torque residual between the actual torque represented by the drive current and the torque command, a composite state quantity is constructed; based on the composite state quantity and the rate of change, the gap crossing stage is identified, and the transmission process is divided into the meshing approach stage, the contact transition stage, and the stable transmission stage. The adjustment module is used to construct a direction-related cost function based on the angular displacement difference and torque residual, perform variable step size updates for forward and reverse propagation respectively, and determine the learning rate scaling factor based on the gradient of the cost function and the gradient change rate at adjacent sampling times. The step size reliability index is generated based on the statistical characteristics of the learning rate scaling factor within the preset time window, and the threshold for zero crossing of angular velocity and sign reversal of angular displacement difference are adjusted. The generation module is used to obtain an adjustment gradient by combining historical gradients and memory decay weights when the absolute value of the detected angular displacement difference is less than the adjusted angular displacement difference sign reversal judgment threshold and the absolute value of the angular velocity difference is less than the adjusted angular velocity zero crossing judgment threshold; based on the stage division, step size reliability index and adjustment gradient, the micro-displacement compensation amount and torque offset amount are calculated, and backlash-free control commands are generated to drive the exciter transmission mechanism by segmenting and mapping according to the relative motion direction.

9. The system according to claim 8, characterized in that, The composite state variables are constructed based on the angular displacement difference and angular velocity difference between the motor side and the load side, as well as the torque residual between the actual torque represented by the drive current and the torque command, including: The angular displacement difference is obtained by acquiring the motor-side angular displacement and the load-side angular displacement at the same sampling time and calculating the difference between the two. The angular velocities of the motor side and the load side are calculated by differentiating the angular displacement of the motor side and the angular displacement of the load side, and the difference between the two is obtained. The actual torque is calculated by multiplying the torque-current conversion constant and the drive current, and the torque residual is obtained by subtracting the torque command from the actual torque. Each of the angular displacement difference, angular velocity difference, and torque residual is assigned an independent preset weighting coefficient; The composite state variables are generated by multiplying the angular displacement difference, angular velocity difference, and torque residual by their respective weighting coefficients and then summing them by weight.

10. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when executed by a processor, implements the method as described in any one of claims 1-7.

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