Feed rate control method based on real-time parameter identification and model predictive control

Abstract

This application belongs to the field of precision machining technology, specifically disclosing a feed speed control method based on real-time parameter identification and model predictive control. The method includes: establishing a dynamic model of robot feed speed; updating the dynamic model of robot feed speed in real time based on the real-time feed speed during robot operation through an event-triggered mechanism to correct model parameters, resulting in a corrected parameterized model; constructing a model predictive controller, using the actual feed speed to track and schedule the feed speed as the objective, and constructing a multi-objective optimization function by combining the corrected parameterized model and preset feed speed constraints; solving the multi-objective optimization function to obtain the optimal control input sequence, and outputting a control signal based on the optimal control input sequence to achieve robot feed speed control. This application can reduce feed speed tracking errors, ensure speed stability during flat-tail skin machining, and improve machining efficiency while ensuring machining quality.

Description

Technical Field

[0001] This application belongs to the field of precision machining technology, and more specifically, relates to a feed rate control method based on real-time parameter identification and model predictive control. Background Technology

[0002] As a key component in the aerospace field, the machining quality of the horizontal stabilizer skin directly affects the aerodynamic performance and structural integrity of the aircraft. Industrial robots, with their advantages of high flexibility and large working space, have become the mainstream solution for milling large horizontal stabilizer skins. In robotic milling, precise control of the feed rate is crucial for ensuring machining quality and efficiency. On the one hand, precise feed rate control must ensure that the actual feed rate strictly follows the preset scheduling curve to avoid unstable cutting forces due to speed fluctuations, which could lead to workpiece vibration or surface quality defects. On the other hand, the long machining path and wide range of robot motion in the horizontal stabilizer skin, along with factors such as joint coupling, dynamic effects, friction, and inertia, cause the dynamic characteristics of the feed rate to exhibit strong nonlinearity. Traditional controllers with fixed parameters (such as PID controllers and adaptive PI controllers) struggle to adapt to a wide range of operating conditions, easily resulting in tracking lag or overshoot, leading to significant deviations between the actual feed rate and the scheduled rate.

[0003] In existing technologies, some studies employ model predictive control (MPC) for feed rate control. However, this relies on a fixed dynamic model and only achieves good control performance under local conditions, making it difficult to address the time-varying model parameters caused by large-scale robot movements. Other studies fail to consider noise interference in the raw velocity data, directly using identification algorithms to update parameters, resulting in low parameter estimation accuracy and further impacting control performance. These issues make existing feed rate control methods insufficient to meet the speed tracking accuracy requirements of high-precision machining of flat-tail skin, thus hindering improvements in machining quality and efficiency. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this application is to solve the problem that the existing controller is unable to adapt to the nonlinear characteristics of the robot and the time-varying model parameters, resulting in large feed speed tracking errors and unstable processing quality.

[0005] To achieve the above objectives, in a first aspect, this application provides a feed rate control method based on real-time parameter identification and model predictive control, comprising: A dynamic model of robot feed speed is established, which is used to characterize the mapping relationship between scheduled feed speed and actual feed speed; Based on the real-time feed speed during robot operation, the dynamic model of robot feed speed is updated in real time through an event triggering mechanism to correct the model parameters and obtain the corrected parameterized model. A model predictive controller is constructed, which aims to track and schedule the feed rate at the actual feed rate. A multi-objective optimization function is constructed by combining the modified parameterized model and the preset feed rate constraints. The optimal control input sequence is obtained by solving the multi-objective optimization function, and the control signal is output based on the optimal control input sequence to realize the robot's feed speed control.

[0006] Optionally, the process of constructing the dynamic model of the robot's feed speed specifically includes: The dynamic characteristics of the robot's feed speed are approximated as a third-order linear system with two zeros, and the continuous-domain transfer function of the third-order linear system is determined; the continuous-domain transfer function is shown in the following formula:

[0007] in, and These represent the actual feed rate and the scheduled feed rate, respectively, with various coefficients... These are the model parameters to be identified; The continuous domain transfer function is discretized and converted into a discrete state-space model; the discrete state-space model is shown in the following formula:

[0008]

[0009] in, for The system state vector at time t. for The feed rate is scheduled at any given time. for The actual feed rate at any given moment , , This is the model parameter matrix.

[0010] Optionally, the step of updating the robot feed speed dynamic model in real time through an event-triggered mechanism to correct the model parameters includes: Savitzky-Golay filters are used to smooth the raw data of the actual feed rate to filter out measurement noise. Based on the smoothed actual feed rate, the model parameters are updated online using a recursive least squares algorithm, and the weights of new and historical data are balanced by setting a forgetting factor. The normalized relative change rate of the model parameter vector is calculated, and the normalized relative change rate is used as the trigger condition for the event triggering mechanism. When the normalized relative change rate exceeds a preset threshold, it is determined that the trigger condition is met and the parameters are updated to obtain the updated model parameter output.

[0011] Optionally, the smoothing process for the actual feed rate includes: Based on the preset sliding window size, the Savitzky-Golay filter is used to perform polynomial fitting on the raw data of the actual feed rate at each of the m time steps before and after the current time to obtain the fitted value at the current time. The target coefficients of the Savitzky-Golay filter are determined with the goal of minimizing the sum of squared errors between the fitted values ​​and the original data, and the smoothed actual feed rate at the current moment is obtained.

[0012] Optionally, it also includes: Regularly monitor the covariance matrix of the recursive least squares algorithm, and trigger offline least squares method to correct the model parameters when the preset conditions are met; The preset conditions include: the trace of the covariance matrix exceeds a preset multiple of the trace of the covariance matrix at the initial time, and / or the condition number of the covariance matrix exceeds a preset condition threshold.

[0013] Optionally, the construction of the multi-objective optimization function specifically includes: Determine the tracking error sequence and input sequence in the prediction time domain; The tracking error sequence is weighted based on the weight matrix of the control error, and the input sequence is weighted based on the weight matrix of the control input. The multi-objective optimization function is constructed with the goal of minimizing the weighted sum. The constraint condition for determining the input amplitude is based on the maximum value of the control input, and the constraint condition for determining the error amplitude is based on the maximum value of the tracking error.

[0014] Optionally, solving the multi-objective optimization function to obtain the optimal control input sequence includes: Based on the discrete state-space model, the predicted values ​​of the actual feed rate at each moment in the time domain are derived. The predicted values ​​of the actual feed rate are determined based on a linear combination of the current system state vector and the future control input sequence. The multi-objective optimization function is transformed into a quadratic programming problem. The quadratic programming problem takes the future control input sequence as the decision variable, the quadratic form including the prediction matrix, the weight matrix and the reference trajectory as the objective function, and is constrained by a preset constraint matrix and constraint vector. The quadratic programming problem is solved using a numerical optimization algorithm to obtain the optimal control input sequence in the prediction time domain.

[0015] Secondly, this application also provides a feed rate control system based on real-time parameter identification and model predictive control, comprising: The model building module is used to build a dynamic model of the robot's feed speed, which is used to characterize the mapping relationship between the scheduled feed speed and the actual feed speed. The parameter identification module is used to update the dynamic model of the robot's feed speed in real time based on the real-time feed speed during the robot's operation, through an event triggering mechanism, to correct the model parameters and obtain the corrected parameterized model. The controller construction module is used to construct a model predictive controller. The model predictive controller aims to track the actual feed rate and schedule the feed rate. It combines the corrected parameterized model and the preset feed rate constraints to construct a multi-objective optimization function. The control execution module is used to solve the multi-objective optimization function to obtain the optimal control input sequence, and output a control signal based on the optimal control input sequence to realize the robot's feed speed control.

[0016] Thirdly, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0017] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0018] Fifthly, this application provides a computer program product that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0019] It is understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0020] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) This application establishes a dynamic model representing the mapping relationship between the scheduled feed speed and the actual feed speed, and combines an event-triggered real-time parameter update mechanism with model predictive control to achieve precise tracking control of the robot's feed speed. This application overcomes the shortcomings of traditional fixed-parameter controllers that are difficult to adapt to the nonlinearity and time-varying characteristics of robots, significantly reduces feed speed tracking error, ensures speed stability during flat tail skin processing, and ensures processing quality while improving processing efficiency.

[0021] (2) This application approximates the dynamic characteristics of the robot's feed speed as a third-order linear system with two zeros and establishes a discrete state space model. By using the Savitzky-Golay filter to smooth the original velocity data, the interference of measurement noise on parameter identification is effectively filtered out. By combining the recursive least squares algorithm and the normalized relative rate of change event triggering mechanism, the real-time accuracy of the model parameters is guaranteed, the computational overhead is reduced, and the efficiency and reliability of parameter identification are improved.

[0022] (3) This application periodically monitors the state of the covariance matrix of the recursive least squares algorithm and triggers offline least squares correction when the matrix trace or condition number exceeds the preset range, which effectively avoids parameter drift problem and ensures the model accuracy under long-term operation.

[0023] (4) This application achieves a balance between tracking accuracy and control smoothness by constructing a multi-objective optimization function with the goal of minimizing the weighted sum of tracking error and control input, and by combining the dual constraints of control input and system state; by transforming the optimization problem into a quadratic programming form and using a rolling time domain strategy to solve it, high-precision and high-stability control of the robot's feed speed is finally achieved. Attached Figure Description

[0024] Figure 1 This is one of the flowcharts of the feed rate control method based on real-time parameter identification and model predictive control provided in the embodiments of this application; Figure 2 This is the second flowchart of the feed rate control method based on real-time parameter identification and model predictive control provided in the embodiments of this application; Figure 3 This is a schematic diagram of the SG-RLS parameter identification module provided in the embodiments of this application; Figure 4 This is a schematic diagram of the model prediction control framework provided in the embodiments of this application; Figure 5 This is a comparison chart of the feed rate tracking effect provided in the embodiments of this application; Figure 6 This is a schematic diagram of the feed speed control system based on real-time parameter identification and model predictive control provided in the embodiments of this application; Figure 7 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0026] In this article, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The symbol " / " in this article indicates that the related objects are in an "or" relationship; for example, A / B means A or B.

[0027] The terms "first" and "second," etc., used in the specification and claims herein are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0028] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0029] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0030] The embodiments of this application are described below with reference to the accompanying drawings.

[0031] Reference Figure 1 This application provides a feed rate control method based on real-time parameter identification and model predictive control, comprising: S101. Establish a dynamic model of robot feed speed, wherein the dynamic model of robot feed speed is used to characterize the mapping relationship between scheduled feed speed and actual feed speed; S102. Based on the real-time feed speed during robot operation, the robot feed speed dynamic model is updated in real time through an event triggering mechanism to correct the model parameters and obtain the corrected parameterized model; S103. Construct a model predictive controller, and construct a multi-objective optimization function by using the model predictive controller to track the actual feed rate and schedule the feed rate as the objective, combined with the modified parameterized model and the preset feed rate constraint; S104. Solve the multi-objective optimization function to obtain the optimal control input sequence, and output a control signal based on the optimal control input sequence to realize robot feed speed control.

[0032] Specifically, firstly, the dynamic characteristics of the robot's feed speed are approximated as a third-order linear system with two zeros using S101. The coefficients of its continuous domain transfer function are determined by the system identification method. Then, the zero-order hold method is used to discretize the continuous domain transfer function and convert it into a discrete state-space model to accurately describe the dynamic response characteristics of the robot's feed system under different scheduling inputs, thus providing a model basis for subsequent model predictive control.

[0033] Secondly, through S102, during the robot's operation, the actual feed speed data is collected in real time, and the parameters of the dynamic model established in step S101 are updated online through an event triggering mechanism to correct the model parameters, thus obtaining the corrected parameterized model.

[0034] Specifically, the raw feed rate data is first smoothed using a Savitzky-Golay filter to remove measurement noise that could interfere with parameter identification. Then, based on the smoothed feed rate data, a recursive least squares algorithm with a forgetting factor is used to estimate the model parameters online. Simultaneously, the normalized relative rate of change of the model parameter vector is calculated. When this rate of change exceeds a preset threshold, an event trigger condition is met, and the currently estimated model parameters are output as the updated model parameters. This event-triggered mechanism ensures that updates are only performed when the model parameters change significantly, maintaining real-time accuracy while avoiding unnecessary computational overhead.

[0035] Furthermore, a model predictive controller is constructed through S103. This controller takes tracking the scheduled feed rate with the actual feed rate as its core objective and constructs a multi-objective optimization function by combining the corrected parameterized model obtained in step S102 and the preset feed rate constraints.

[0036] Specifically, firstly, the tracking error sequence and input sequence within the prediction time domain are determined based on the preset prediction time domain length; then, the tracking error sequence is weighted by the weight matrix of the control error, and the control input sequence is weighted by the weight matrix of the control input. The objective function is constructed with the goal of minimizing the sum of the two weights, and it is ensured that the control input and the actual feed rate always operate within a safe range.

[0037] Finally, through S104, the multi-objective optimization function constructed in step S103 is solved to obtain the optimal control input sequence, and the control signal is output based on the optimal control input sequence to achieve precise control of the robot's feed speed.

[0038] Specifically, the predicted values ​​of the actual feed rate at each moment in the prediction time domain are derived based on the modified discrete state-space model. Then, the multi-objective optimization function is transformed into a quadratic programming problem with the future control input sequence as the decision variable. Finally, the quadratic programming problem is solved using a numerical optimization algorithm to obtain the optimal control input sequence in the prediction time domain. Based on the rolling time domain control strategy, the control input at the current moment is output as the actual control signal to the robot actuator. The above process is repeated at the next sampling moment to achieve real-time and accurate tracking control of the feed rate.

[0039] Reference Figure 2 , Figure 2 This is a complete flowchart of an embodiment of this application, including the following steps: Step S1: Establish a dynamic model of robot feed speed. The dynamic model of robot feed speed is used to characterize the mapping relationship between scheduled feed speed and actual feed speed. First, the dynamic characteristics of the robot's feed speed are modeled, approximating it as a third-order linear system with two zeros. A state-space model is then established through discretization, providing a foundation for subsequent control.

[0040] Step S2: Design an SG-RLS parameter identification module to update the parameters of the robot feed speed dynamic model in real time based on an event-triggered mechanism; Velocity data is preprocessed using an SG filter, and online parameter updates are achieved by combining the RLS algorithm with an event-triggered mechanism. Offline LS correction is used to avoid parameter drift and ensure model accuracy.

[0041] Step S3: Construct a feed rate controller based on model predictive control. The feed rate controller aims to track and schedule the feed rate based on the actual feed rate. It combines the updated robot feed rate dynamic model and preset feed rate constraints to construct an optimization objective function. With the goals of minimizing tracking error and smoothing control input, an MPC optimization objective function is constructed by combining speed and control input constraints.

[0042] Step S4: Solve the optimization objective function to obtain the optimal control input, and output a control signal based on the optimal control input to achieve precise control of the robot's feed speed.

[0043] The objective function is transformed into a quadratic programming problem to be solved, and a rolling time-domain strategy is used to output control signals to ensure that the actual feed rate accurately tracks the scheduling rate.

[0044] The feed speed control method for milling of variable curvature skinned robots provided in this application, which considers real-time parameter identification and model predictive control, realizes real-time and accurate updating of model parameters through the SG-RLS parameter identification module. Combined with the rolling optimization characteristics of the MPC controller, it effectively adapts to the nonlinearity and time-varying characteristics of the robot parameters, significantly reduces the feed speed tracking error, and ensures the processing quality and efficiency of flat tail skin.

[0045] Optionally, the process of constructing the dynamic model of the robot's feed speed specifically includes: The dynamic characteristics of the robot's feed speed are approximated as a third-order linear system with two zeros, and the continuous-domain transfer function of the third-order linear system is determined; the continuous-domain transfer function is shown in the following formula:

[0046] in, and These represent the actual feed rate and the scheduled feed rate, respectively, with various coefficients... These are the model parameters to be identified; The continuous domain transfer function is discretized and converted into a discrete state-space model; the discrete state-space model is shown in the following formula:

[0047]

[0048] in, for The system state vector at time t. for The feed rate is scheduled at any given time. for The actual feed rate at any given moment , , The model parameter matrix is ​​obtained by identifying initial values ​​based on the initial experimental data.

[0049] Optionally, the step of updating the robot feed speed dynamic model in real time through an event-triggered mechanism to correct the model parameters includes: Savitzky-Golay filters are used to smooth the raw data of the actual feed rate to filter out measurement noise. Based on the smoothed actual feed rate, the model parameters are updated online using a recursive least squares algorithm, and the weights of new and historical data are balanced by setting a forgetting factor. The normalized relative change rate of the model parameter vector is calculated, and the normalized relative change rate is used as the trigger condition for the event triggering mechanism. When the normalized relative change rate exceeds a preset threshold, it is determined that the trigger condition is met and the parameters are updated to obtain the updated model parameter output.

[0050] Optionally, the smoothing process for the actual feed rate includes: Based on the preset sliding window size, the Savitzky-Golay filter is used to perform polynomial fitting on the raw data of the actual feed rate at each of the m time steps before and after the current time to obtain the fitted value at the current time. The target coefficients of the Savitzky-Golay filter are determined with the goal of minimizing the sum of squared errors between the fitted values ​​and the original data, and the smoothed actual feed rate at the current moment is obtained.

[0051] Specifically, in this embodiment, a Savitzky-Golay (SG) filter is used to smooth the raw data of the actual feed rate. The sliding window size of the SG filter satisfies Its expression is:

[0052] in, for The actual feed rate at any given moment Represented as the length of the data sequence, This is the window length. An R-order polynomial can be used. The fitted data points are expressed as a polynomial:

[0053] in, To fit the polynomial at position The value at position j is the index variable of the summation symbol. The filter's first There are several coefficients. The least squares method can be used to find the minimum value of the error:

[0054] To minimize the error equation in each window, system parameters can be identified based on the smoothed sequence using an SG filter, where... For accuracy error, for The raw data of the actual feed rate at time t. For this third-order system, its difference equation can be written as:

[0055] in, It is in time The actual feed rate It is in time Set the feed rate, The model parameters to be identified. and These are the output coefficients and input coefficients, respectively, and the model parameters. and Related to inherent characteristics.

[0056] Furthermore, based on the smoothed feed rate data, the RLS algorithm is used to update the model parameters online. The parameter update formula for the RLS algorithm is:

[0057] in, for Time-based model parameter estimates Let covariance matrix be the variance matrix. This is a forgetting factor used to balance the weights of new and historical data; Furthermore, the normalized relative rate of change is defined as the event triggering condition, and its expression is:

[0058] in, for Normalized relative rate of change at time t.

[0059] It can be used To avoid the denominator becoming zero. When When a specified threshold is exceeded, the model parameters are updated to prevent instability caused by overly frequent controller updates. The expression is:

[0060] in, Indicates the update threshold. Preset trigger threshold. ,when When this happens, RLS parameter updates are triggered to avoid controller instability caused by overly frequent parameter updates.

[0061] Optionally, it also includes: Regularly monitor the covariance matrix of the recursive least squares algorithm, and trigger offline least squares method to correct the model parameters when the preset conditions are met; The preset conditions include: the trace of the covariance matrix exceeds a preset multiple of the trace of the covariance matrix at the initial time, and / or the condition number of the covariance matrix exceeds a preset condition threshold.

[0062] It should be noted that when Recursive Least Squares (RLS) processes high-dimensional parameters, the covariance matrix may lose its symmetric positive definiteness, leading to inaccurate parameter updates. Therefore, it is necessary to periodically correct the RLS update results using an offline LS algorithm.

[0063]

[0064] in, express traces, express The condition number of Indicates the preset multiple. This indicates a preset threshold condition.

[0065] Reference Figure 3 , Figure 3 This is a schematic diagram of the SG-RLS parameter identification module provided in the embodiments of this application. The module sequentially completes the raw data acquisition, SG filtering and smoothing, event trigger judgment, RLS online update and offline LS correction, and outputs accurate model parameters.

[0066] Optionally, the construction of the multi-objective optimization function specifically includes: Determine the tracking error sequence and input sequence in the prediction time domain; The tracking error sequence is weighted based on the weight matrix of the control error, and the input sequence is weighted based on the weight matrix of the control input. The multi-objective optimization function is constructed with the goal of minimizing the weighted sum. The constraint condition for determining the input amplitude is based on the maximum value of the control input, and the constraint condition for determining the error amplitude is based on the maximum value of the tracking error.

[0067] Specifically, this embodiment focuses on minimizing the tracking error between the actual feed rate and the scheduled feed rate. Combined with the requirement for smooth control input, the objective function is optimized as follows:

[0068]

[0069]

[0070] in, It is the weight matrix for controlling the error. It is the weight matrix that controls the input. To track the error sequence, Given the input sequence, For the first in the input sequence The nth value, in order to track the nth error sequence There are several values. To find the optimal value, quadratic programming can be used to minimize the cost function. and These represent the upper limits of the input and output, respectively.

[0071] Reference Figure 4 , Figure 4 This is a schematic diagram of the model predictive control framework provided in this application embodiment. The framework is based on an updated dynamic model, combines preset constraints to solve and optimize the objective function, and outputs the optimal control input. As shown in the diagram, the overall process is as follows: Enter the target working time The feed rate scheduling section outputs a smooth target feed rate. This speed can be input into the controller. Simultaneously, the robot receives its observed position at a fixed frequency. (To obtain the actual feed rate). Within each sampling interval, the SG-RLS module updates the robot's dynamic feed rate model (control cycle is 0.1s). Constraint optimization can be performed within the MPC framework using the updated model and the robot's feed rate constraints. This optimization result can be input into the robot, enabling it to perform milling tasks and ultimately achieving closed-loop control for robot milling.

[0072] Optionally, solving the multi-objective optimization function to obtain the optimal control input sequence includes: Based on the discrete state-space model, the predicted values ​​of the actual feed rate at each moment in the time domain are derived. The predicted values ​​of the actual feed rate are determined based on a linear combination of the current system state vector and the future control input sequence. The multi-objective optimization function is transformed into a quadratic programming problem. The quadratic programming problem takes the future control input sequence as the decision variable, the quadratic form including the prediction matrix, the weight matrix and the reference trajectory as the objective function, and is constrained by a preset constraint matrix and constraint vector. The quadratic programming problem is solved using a numerical optimization algorithm to obtain the optimal control input sequence in the prediction time domain.

[0073] Specifically, in this embodiment of the application, solving the multi-objective optimization function to obtain the optimal control input sequence includes the following process: The objective function is transformed into a quadratic programming problem. Based on the discrete state-space model, the predicted output value in the prediction time domain is derived as follows:

[0074]

[0075]

[0076] in, for The system state vector at time t. Based on the current ( (Time) model, predicting the future (time) The actual feed rate per cycle Future No. Control input for each cycle, and The prediction matrix is ​​given. The objective function is transformed into a standard quadratic programming form:

[0077]

[0078]

[0079]

[0080] in, For the target scheduling speed, and For constraint matrices and constraint vectors, It is the coefficient matrix of the quadratic terms. This is the transpose of the coefficient vector of the linear terms. The target speed.

[0081] The quadratic programming problem is solved using a numerical optimization algorithm to obtain the optimal control sequence. ; A rolling time-domain control strategy is adopted, which only uses the optimal control input at the current moment. The output is sent to the robot's EGM module to achieve real-time control of the actual feed speed, and the above steps are repeated at the next sampling time.

[0082] Figure 5 This is a comparison chart of the feed rate tracking effect provided in the embodiments of this application, such as... Figure 5 As shown, compared with no control, adaptive PI control and fixed parameter MPC control, the actual feed rate (green curve) of the method in this application is closer to the scheduled feed rate (black curve), and the tracking error is significantly reduced.

[0083] In the experimental verification, an ABB IRB 6660 industrial robot, a high-speed spindle, an LK-H008W laser displacement sensor, and a TR-200 roughness tester were used to build an experimental platform for milling two types of flat-tail skin parts: CFRP (200mm×200mm×1mm) and AL6061 (400mm×280mm×2mm). The results show that the average tracking error of the method in this application is reduced by 74.87% (CFRP) and 67.61% (AL6061) compared to the uncontrolled method, by 67.74% and 58.14% compared to adaptive PI control, and by 66.27% and 55.90% compared to fixed-parameter MPC control. Simultaneously, the surface roughness is comparable to that of constant feed rate machining, and the contour error is controlled within ±0.5mm, meeting the quality requirements for flat-tail skin machining, while maintaining optimized machining efficiency.

[0084] Reference Figure 6 This application also provides a feed rate control system based on real-time parameter identification and model predictive control, comprising: The model building module 610 is used to build a dynamic model of the robot's feed speed, which is used to characterize the mapping relationship between the scheduled feed speed and the actual feed speed. The parameter identification module 620 is used to update the dynamic model of the robot's feed speed in real time based on the real-time feed speed during the robot's operation, through an event triggering mechanism, to correct the model parameters and obtain the corrected parameterized model. The controller construction module 630 is used to construct a model predictive controller. The model predictive controller aims to track and schedule the feed rate at the actual feed rate, and constructs a multi-objective optimization function by combining the corrected parameterized model and the preset feed rate constraints. The control execution module 640 is used to solve the multi-objective optimization function to obtain the optimal control input sequence, and output a control signal based on the optimal control input sequence to realize robot feed speed control.

[0085] Optionally, the process of constructing the dynamic model of the robot's feed speed specifically includes: The dynamic characteristics of the robot's feed speed are approximated as a third-order linear system with two zeros, and the continuous-domain transfer function of the third-order linear system is determined; the continuous-domain transfer function is shown in the following formula:

[0086] in, and These represent the actual feed rate and the scheduled feed rate, respectively, with various coefficients... These are the model parameters to be identified; The continuous domain transfer function is discretized and converted into a discrete state-space model; the discrete state-space model is shown in the following formula:

[0087]

[0088] in, for The system state vector at time t. for The feed rate is scheduled at any given time. for The actual feed rate at any given moment , , This is the model parameter matrix.

[0089] Optionally, the step of updating the robot feed speed dynamic model in real time through an event-triggered mechanism to correct the model parameters includes: Savitzky-Golay filters are used to smooth the raw data of the actual feed rate to filter out measurement noise. Based on the smoothed actual feed rate, the model parameters are updated online using a recursive least squares algorithm, and the weights of new and historical data are balanced by setting a forgetting factor. The normalized relative change rate of the model parameter vector is calculated, and the normalized relative change rate is used as the trigger condition for the event triggering mechanism. When the normalized relative change rate exceeds a preset threshold, it is determined that the trigger condition is met and the parameters are updated to obtain the updated model parameter output.

[0090] Optionally, the smoothing process for the actual feed rate includes: Based on the preset sliding window size, the Savitzky-Golay filter is used to perform polynomial fitting on the raw data of the actual feed rate at each of the m time steps before and after the current time to obtain the fitted value at the current time. The target coefficients of the Savitzky-Golay filter are determined with the goal of minimizing the sum of squared errors between the fitted values ​​and the original data, and the smoothed actual feed rate at the current moment is obtained.

[0091] Regularly monitor the covariance matrix of the recursive least squares algorithm, and trigger offline least squares method to correct the model parameters when the preset conditions are met; The preset conditions include: the trace of the covariance matrix exceeds a preset multiple of the trace of the covariance matrix at the initial time, and / or the condition number of the covariance matrix exceeds a preset condition threshold.

[0092] Optionally, the construction of the multi-objective optimization function specifically includes: Determine the tracking error sequence and input sequence in the prediction time domain; The tracking error sequence is weighted based on the weight matrix of the control error, and the input sequence is weighted based on the weight matrix of the control input. The multi-objective optimization function is constructed with the goal of minimizing the weighted sum. The constraint condition for determining the input amplitude is based on the maximum value of the control input, and the constraint condition for determining the error amplitude is based on the maximum value of the tracking error.

[0093] Optionally, solving the multi-objective optimization function to obtain the optimal control input sequence includes: Based on the discrete state-space model, the predicted values ​​of the actual feed rate at each moment in the time domain are derived. The predicted values ​​of the actual feed rate are determined based on a linear combination of the current system state vector and the future control input sequence. The multi-objective optimization function is transformed into a quadratic programming problem. The quadratic programming problem takes the future control input sequence as the decision variable, the quadratic form including the prediction matrix, the weight matrix and the reference trajectory as the objective function, and is constrained by a preset constraint matrix and constraint vector. The quadratic programming problem is solved using a numerical optimization algorithm to obtain the optimal control input sequence in the prediction time domain.

[0094] Reference Figure 7 Based on the methods in the above embodiments, this application provides an electronic device that may include: a processor 710, a communications interface 720, a memory 730, and a communication bus 740. The processor 710, communications interface 720, and memory 730 communicate with each other via the communication bus 740. The processor 710 may call logical instructions stored in the memory 730 to execute the methods in the above embodiments.

[0095] Furthermore, the logical instructions in the aforementioned memory 730 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0096] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0097] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0098] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0099] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0100] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0101] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0102] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A feed rate control method based on real-time parameter identification and model predictive control, characterized in that, include: A dynamic model of robot feed speed is established, which is used to characterize the mapping relationship between scheduled feed speed and actual feed speed; Based on the real-time feed speed during robot operation, the dynamic model of robot feed speed is updated in real time through an event triggering mechanism to correct the model parameters and obtain the corrected parameterized model. A model predictive controller is constructed, which aims to track and schedule the feed rate at the actual feed rate. A multi-objective optimization function is constructed by combining the modified parameterized model and the preset feed rate constraints. The optimal control input sequence is obtained by solving the multi-objective optimization function, and the control signal is output based on the optimal control input sequence to realize the robot's feed speed control.

2. The feed rate control method based on real-time parameter identification and model predictive control according to claim 1, characterized in that, The process of constructing the dynamic model of the robot's feed speed specifically includes: The dynamic characteristics of the robot's feed speed are approximated as a third-order linear system with two zeros, and the continuous-domain transfer function of the third-order linear system is determined; the continuous-domain transfer function is shown in the following formula: wherein, and respectively denote the actual feed speed and the scheduled feed speed, the coefficients are model parameters to be identified; The continuous domain transfer function is discretized and converted into a discrete state-space model; the discrete state-space model is shown in the following formula: wherein is the system state vector at time instant is the scheduled feed speed at time instant is the actual feed speed at time instant , , is the model parameter matrix.

3. The feed rate control method based on real-time parameter identification and model predictive control according to claim 1, characterized in that, The method of updating the robot's feed speed dynamic model in real time through an event-triggered mechanism to correct model parameters includes: Savitzky-Golay filters are used to smooth the raw data of the actual feed rate to filter out measurement noise. Based on the smoothed actual feed rate, the model parameters are updated online using a recursive least squares algorithm, and the weights of new and historical data are balanced by setting a forgetting factor. The normalized relative change rate of the model parameter vector is calculated, and the normalized relative change rate is used as the trigger condition for the event triggering mechanism. When the normalized relative change rate exceeds a preset threshold, it is determined that the trigger condition is met and the parameters are updated to obtain the updated model parameter output.

4. The feed rate control method based on real-time parameter identification and model predictive control according to claim 1, characterized in that, The smoothing process for the actual feed rate includes: Based on the preset sliding window size, the Savitzky-Golay filter is used to perform polynomial fitting on the raw data of the actual feed rate at each of the m time steps before and after the current time to obtain the fitted value at the current time. The target coefficients of the Savitzky-Golay filter are determined with the goal of minimizing the sum of squared errors between the fitted values ​​and the original data, and the smoothed actual feed rate at the current moment is obtained.

5. The feed rate control method based on real-time parameter identification and model predictive control according to claim 1, characterized in that, Also includes: Regularly monitor the covariance matrix of the recursive least squares algorithm, and trigger offline least squares method to correct the model parameters when the preset conditions are met; The preset conditions include: the trace of the covariance matrix exceeds a preset multiple of the trace of the covariance matrix at the initial time, and / or the condition number of the covariance matrix exceeds a preset condition threshold.

6. The feed rate control method based on real-time parameter identification and model predictive control according to claim 1, characterized in that, The construction of the multi-objective optimization function specifically includes: Determine the tracking error sequence and input sequence in the prediction time domain; The tracking error sequence is weighted based on the weight matrix of the control error, and the input sequence is weighted based on the weight matrix of the control input. The multi-objective optimization function is constructed with the goal of minimizing the weighted sum. The constraint condition for determining the input amplitude is based on the maximum value of the control input, and the constraint condition for determining the error amplitude is based on the maximum value of the tracking error.

7. The feed rate control method based on real-time parameter identification and model predictive control according to claim 2, characterized in that, Solving the multi-objective optimization function to obtain the optimal control input sequence includes: Based on the discrete state-space model, the predicted values ​​of the actual feed rate at each moment in the time domain are derived. The predicted values ​​of the actual feed rate are determined based on a linear combination of the current system state vector and the future control input sequence. The multi-objective optimization function is transformed into a quadratic programming problem. The quadratic programming problem takes the future control input sequence as the decision variable, the quadratic form including the prediction matrix, the weight matrix and the reference trajectory as the objective function, and is constrained by a preset constraint matrix and constraint vector. The quadratic programming problem is solved using a numerical optimization algorithm to obtain the optimal control input sequence in the prediction time domain.

8. A feed rate control system based on real-time parameter identification and model predictive control, characterized in that, include: The model building module is used to build a dynamic model of the robot's feed speed, which is used to characterize the mapping relationship between the scheduled feed speed and the actual feed speed. The parameter identification module is used to update the dynamic model of the robot's feed speed in real time based on the real-time feed speed during the robot's operation, through an event triggering mechanism, to correct the model parameters and obtain the corrected parameterized model. The controller construction module is used to construct a model predictive controller. The model predictive controller aims to track the actual feed rate and schedule the feed rate. It combines the corrected parameterized model and the preset feed rate constraints to construct a multi-objective optimization function. The control execution module is used to solve the multi-objective optimization function to obtain the optimal control input sequence, and output a control signal based on the optimal control input sequence to realize the robot's feed speed control.

9. An electronic device, characterized in that, include: At least one memory for storing computer programs; At least one processor is configured to execute a program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is run on the processor, it causes the processor to perform the method as described in any one of claims 1-7.

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