Wafer chamfering machine high-precision multi-parameter collaborative optimization control method and system

Abstract

The application relates to the field of grinding technology, and particularly discloses a high-precision multi-parameter collaborative optimization control method and system of a wafer chamfering machine, aiming at the electromechanical coupling restriction between the mechanical structure rigidity and the servo control dynamic response in the design of the existing wafer chamfering machine, which leads to the problem that the system cannot break through the global performance under strong disturbance and it is difficult to balance the low-frequency nonlinearity and high-frequency narrowband vibration suppression, the application generates a controlled object mixed model by collecting operation data, constructs a feedforward-feedback composite control architecture, combines the structure parameters, the global reference parameters and the fuzzy rule consequent parameters into a mixed collaborative optimization vector, and adopts hierarchical nested optimization to output the optimal parameter combination through stability screening and Pareto screening. The application realizes the best matching of software and hardware, achieves the global optimal balance among the machining precision, the surface quality and the response speed, and significantly improves the comprehensive performance of the wafer chamfering machine under complex working conditions.

Description

Technical Field

[0001] This invention relates to the field of grinding technology, and in particular to a high-precision multi-parameter collaborative optimization control method and system for wafer chamfering machines. Background Technology

[0002] In modern semiconductor manufacturing processes, wafer chamfering is a crucial step in improving semiconductor chip yield. With increasing wafer size and miniaturized chip manufacturing processes, the precision requirements for wafer edge contour processing have become increasingly stringent, reaching the sub-micron level. Wafer chamfering machines typically employ diamond grinding wheels at ultra-high speeds (usually exceeding 30,000 rpm) to precisely grind wafer edges, eliminating edge defects, preventing chipping, and improving the yield of subsequent photolithography processes. It's important to note that a wafer chamfering machine is a typical complex electromechanical system. In this invention, electromechanical does not refer to a simple physical assembly of mechanics and circuits, but rather to the highly dynamic coupling between the mechanical physical entities (including the chamfering arm structure, spindle, grinding wheel, etc., which determine the system's hard characteristics such as stiffness, damping, and inertia) and the active control system (including sensors, servo drives, and control algorithms, which determine the system's soft characteristics such as response bandwidth and correction capability). This coupling means that even small changes in the mechanical structure can directly alter the transfer function of the controlled object, thereby affecting the stability and accuracy of the control algorithm. Similarly, adjusting the control strategy can also change the system's ability to suppress mechanical vibrations.

[0003] However, in the pursuit of ultimate processing precision and surface quality, existing wafer chamfering machine design and control technologies face a series of irreconcilable contradictions and challenges:

[0004] First, the traditional sequential design paradigm limits the global performance of electromechanical systems. Current industrial design processes typically follow a structure-first, control-later sequential approach. Mechanical engineers first determine the stiffness, mass, and damping materials of the chamfered arm based on experience. After the physical prototype is manufactured, control engineers design the control algorithm based on the fixed controlled object. This fragmented design approach ignores the strong dynamic coupling between the mechanical structure and the control system. For example, to suppress vibration, mechanical design tends to increase structural stiffness, but this often leads to increased inertia of moving parts, thus reducing the bandwidth and dynamic response speed of the servo system. Conversely, if stiffness is reduced to pursue lightweight design, it can easily induce structural resonance, making controller tuning difficult. Simply relying on control algorithm optimization cannot compensate for the inherent limitations of mechanical structure design, and vice versa. Therefore, achieving coordinated optimization of mechanical physical parameters (hardware) and control hyperparameters (software) during the design phase is key to breaking through performance bottlenecks.

[0005] Secondly, single-dimensional control strategies struggle to handle complex disturbances across multiple scales and modes. The wafer chamfering process is a typical multi-scale disturbance system, including low-frequency nonlinear disturbances and high-frequency narrowband vibrations. Low-frequency nonlinear disturbances, specifically during grinding, result in highly nonlinear and time-varying grinding forces with varying wheel depth and contact angle, accompanied by significant frictional hysteresis. Traditional PID controllers, with their fixed parameters, struggle to maintain consistent tracking performance under different operating conditions. While fuzzy control can handle nonlinear problems, its heavy reliance on rule bases and its inability to cope with sudden changes in grinding forces in the absence of adaptive adjustment mechanisms are significant challenges.

[0006] High-frequency narrowband vibration is caused by micron-level narrowband harmonic vibration due to the high-speed rotation of the spindle motor and the imbalance of the grinding wheel, which directly affects the surface roughness of the wafer edge. Due to the inherent phase lag and bandwidth limitations of feedback control, it is difficult to effectively eliminate this high-frequency periodic interference.

[0007] Finally, mechatronics co-optimization faces bottlenecks such as the curse of dimensionality and low computational efficiency. If mechanical structural parameters (such as stiffness and damping) and control parameters (such as PID gain, filter coefficients, and fuzzy rules) are placed in the same framework for co-evolutionary optimization, the dimensionality of the optimization variables will expand dramatically. Especially when a fuzzy controller is introduced, dozens or even hundreds of fuzzy rules are often required to achieve fine-grained control effects. In traditional evolutionary algorithms, simultaneously searching for structural parameters and the consequent parameters of each fuzzy rule leads to an exponential increase in the search space, with computation times often lasting days or even weeks. Furthermore, it is highly susceptible to getting trapped in local optima, failing to meet the rapid iteration requirements of engineering applications. While existing fast fuzzy rule learning methods have been applied in single software domains, they have not yet been introduced into the complex field of mechatronics co-design to solve the challenge of simultaneously optimizing hardware and software parameters. Summary of the Invention

[0008] This invention provides a high-precision multi-parameter collaborative optimization control method and system for wafer chamfering machines. The technical problem it solves is that in the existing wafer chamfering machine design, the electromechanical coupling limitation between the rigidity of the mechanical structure and the dynamic response of the servo control makes it impossible for the system to break through the global performance under strong disturbances, and it is impossible to achieve a balance between structural stability, real-time control and high-dimensional optimization efficiency.

[0009] To address the above technical problems, this invention provides a high-precision multi-parameter collaborative optimization control method for wafer chamfering machines, comprising the following steps:

[0010] S1. Collect operating data of the wafer chamfering machine under multiple working conditions and generate a hybrid model of the controlled object;

[0011] S2. Construct a feedforward-feedback composite control architecture for the wafer chamfering machine based on frequency domain divide-and-conquer strategy and fuzzy inference;

[0012] S3. Determine the set of structural parameters to be optimized in the hybrid model of the controlled object, as well as the set of global reference parameters and fuzzy rule consequent parameters to be optimized in the feedforward-feedback composite control architecture, and merge them into a hybrid collaborative optimization vector;

[0013] S4. Employ hierarchical nested optimization, generate an initial population based on the hybrid collaborative optimization vector, and iteratively generate the optimal parameter set after stability screening;

[0014] S5. Calculate multi-objective values ​​in the simulation environment based on the optimal parameter set, and output the optimal combination of structural parameters and control hyperparameters after Pareto screening.

[0015] Furthermore, step S1 specifically includes:

[0016] Collect operating data of the wafer chamfering machine under multiple working conditions, and perform detrending and normalization preprocessing on the operating data to generate a standard dataset;

[0017] The mutual information entropy is calculated based on the standard dataset, the nonlinear correlation between input features and output performance indicators is quantified, features with mutual information entropy greater than a preset threshold are selected, and a nonlinear feature dataset is generated.

[0018] The nonlinear feature dataset is compared with the frequency response residual of the parameterized mechanism model based on the Lagrange equation, and the residual is fitted as an unmodeled dynamic compensation term using system identification.

[0019] The unmodeled dynamic compensation term is fused with the parameterized mechanism model to generate a hybrid model of the controlled object that can be reconstructed in real time with the structural parameters.

[0020] Furthermore, step S2 specifically includes:

[0021] Position tracking error and error change rate data are selected, mapped to the fuzzy domain by quantization factor and a seventh-order linguistic variable is defined. The correction direction of proportional-integral-derivative gain is inferred through a fuzzy inference engine containing multiple rules. After defuzzification, the proportional-integral-derivative gain correction amount is output. The gain correction amount is superimposed with the basic gain to generate a feedback control law.

[0022] Based on the spindle vibration signal, the feedforward controller is decomposed into a nominal feedback part and a free parameter filter through Euler-Kussera parameterization. The free parameter filter is designed as an adaptive filter in the form of finite impulse response. The weights of the adaptive filter are updated online using a recursive least squares algorithm to generate a feedforward compensation signal.

[0023] The feedback control law is superimposed with the feedforward compensation signal to generate a composite control command.

[0024] Furthermore, step S3 specifically includes:

[0025] Define a set of structural parameters including equivalent stiffness, structural damping coefficient and equivalent kinematic mass; define a set of global reference parameters including proportional-integral-differential reference gain, fuzzy quantization factor, filter order and forgetting factor, and consequent parameters of each fuzzy rule in the fuzzy inference engine;

[0026] Upper and lower bound constraints are set for each parameter based on the physical limits of materials, the driving capability of the motor, and the stability criteria.

[0027] The structural parameter set, the global benchmark parameter set, and the fuzzy rule consequent parameters are merged to generate hybrid optimization variable space data.

[0028] Furthermore, step S4 specifically includes:

[0029] The hybrid collaborative optimization vector is encoded as an antibody of the artificial immune algorithm. The initial population is generated by Bernoulli chaotic mapping and mapped to the feasible region of physical parameters to obtain the initial population data.

[0030] The infinite norm index of each antibody is calculated based on the small gain theorem, and individuals that do not meet the stability conditions are removed to generate population data that have passed the stability hard constraint screening.

[0031] The screened population data and typical working condition data are input into the inner loop to calculate the compatibility of each data sample with each fuzzy rule antecedent.

[0032] Using the compatibility as a weight, the instantaneous performance evaluation value is distributed to each rule to generate an independent evaluation value for each rule;

[0033] Based on the independent evaluation values, the consequent parameters of each rule are independently optimized and updated using a parallel framework. The optimized rule parameters are then backfilled into the outer antibody. After receptor editing and iterative convergence, the optimal parameter set data that satisfies the stability constraints is generated.

[0034] Furthermore, step S5 specifically includes:

[0035] The optimal parameter set data is input into the simulation environment to obtain time-domain trajectory tracking error data, frequency-domain power spectral density data, and step response settling time data.

[0036] Based on the time domain data, calculate the integral value of time multiplied by the absolute value of error; based on the frequency domain data, extract the peak power spectral density within a specific frequency band; based on the adjustment time data, obtain the adjustment time value; and generate three multi-objective evaluation function values.

[0037] Based on the multi-objective evaluation function values, non-dominated ranking is performed, dominated individuals are removed, and preferred individuals that cannot be substituted for each other are retained to generate Pareto front data.

[0038] The non-dominated solutions in the Pareto front data are subjected to min-max normalization, and the weighted Euclidean distance from each solution to the origin is calculated by introducing a process preference weight coefficient.

[0039] The individual with the smallest weighted Euclidean distance is selected as the global optimal solution, and the optimal combination of structural parameters and control hyperparameters is output.

[0040] Further, in step S4, the generation of the initial population using the Bernoulli chaotic map specifically includes: generating a normalized chaotic sequence using the Bernoulli displacement map, mapping each element in the normalized chaotic sequence to the feasible domain of the physical parameters of each parameter to be optimized, and constructing a mixed initial population containing chaotic exploration individuals and expert experience individuals, wherein the chaotic exploration individuals account for the majority of the total population and the expert experience individuals account for a small portion of the total population.

[0041] Furthermore, in step S4, the stability screening of the initial population data based on the infinite norm index specifically includes: calculating the infinite norm index of the closed-loop system corresponding to each antibody based on the Euler-Kussera parameterization theory, determining whether the infinite norm index is less than one according to the small gain theorem, and if the infinite norm index is greater than or equal to one, determining that the design scheme is not feasible, directly assigning a range fitness and eliminating it, and skipping all subsequent calculations.

[0042] Furthermore, based on the independent evaluation values, the consequent parameters of each rule are independently optimized and updated using a parallel framework. The optimized rule parameters are then backfilled into the outer antibody. After receptor editing and iterative convergence, an optimal parameter set data satisfying stability constraints is generated, specifically:

[0043] Based on the independent evaluation value, the consequent parameters of each fuzzy rule are independently optimized and updated using a parallel computing framework. The larger the independent evaluation value, the worse the control effect and the larger the adjustment range within the working area corresponding to the rule, and vice versa.

[0044] The optimized rules parameters of the inner loop are backfilled into the outer antibody, and the receptor editing mechanism is executed. Some antibodies are removed according to the affinity ranking, and Bernoulli chaotic mapping is called to generate new antibodies to fill the gap. The process is iterated until the preset termination condition is met, and then the optimal parameter set data that meets the stability constraints is generated.

[0045] The present invention also provides a high-precision multi-parameter collaborative optimization control system for a wafer chamfering machine, the key of which is that it includes an electromechanical modeling module, a composite control construction module, a variable space definition module, a nested optimization module, and a Pareto optimization module, which are respectively used to execute steps S1, S2, S3, S4, and S5 in the high-precision multi-parameter collaborative optimization control method for the wafer chamfering machine.

[0046] The high-precision multi-parameter collaborative optimization control method and system for wafer chamfering machines provided by this invention gradually solves key problems in existing technologies through deep electromechanical integration and progressive optimization: First, by constructing a parameterized structure and a control interaction dynamic environment, key features are screened and the model is calibrated using mutual information entropy, breaking the limitations of traditional static physical models and laying a high-fidelity simulation foundation for collaborative optimization; then, a feedforward-feedback composite control architecture is constructed, integrating the nonlinear adaptability of fuzzy PID and the micro-vibration notch filtering capability of YK feedforward, overcoming the problem that a single control strategy cannot simultaneously handle low-frequency friction and high-frequency narrowband vibration; Building upon this foundation, a nested co-evolutionary and α-FUZZI-ES parallel algorithm is employed to decouple high-dimensional fuzzy rule optimization into independent sub-problems under hard stability constraints, significantly improving the search efficiency in the hybrid space that includes structural physical parameters and control algorithm parameters. Finally, a multi-objective Pareto optimization is introduced to find the globally optimal balance point between processing accuracy, surface quality, and response speed, thereby achieving the integrated optimal matching of the wafer chamfering machine's hardware and software. This solves the problem in existing wafer chamfering machine designs where the electromechanical coupling between the rigidity of the mechanical structure and the dynamic response of the servo control limits the system's inability to break through global performance under strong disturbances. Attached Figure Description

[0047] Figure 1 This is a flowchart of the high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine provided in an embodiment of the present invention;

[0048] Figure 2 This is a diagram of the feedforward-feedback composite control system architecture provided in an embodiment of the present invention;

[0049] Figure 3 This is a nested collaborative optimization flowchart provided in an embodiment of the present invention. Detailed Implementation

[0050] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0051] The high-precision multi-parameter collaborative optimization control method for wafer chamfering machines provided in this embodiment of the invention, such as... Figure 1The flowchart shown includes the following steps:

[0052] S1. Parametric electromechanical modeling: Collect operating data of the wafer chamfering machine under multiple working conditions and generate a hybrid model of the controlled object;

[0053] S2. Constructing a composite control architecture: Constructing a feedforward-feedback composite control architecture for the wafer chamfering machine based on the frequency domain divide-and-conquer strategy and fuzzy inference;

[0054] S3. Definition of Cooperative Variable Space: Determine the set of structural parameters to be optimized in the hybrid model of the controlled object, as well as the set of global baseline parameters and fuzzy rule consequent parameters to be optimized in the feedforward-feedback composite control architecture, and merge them into a hybrid cooperative optimization vector;

[0055] S4. Nested Collaborative Optimization: A hierarchical nested optimization is adopted, and an initial population is generated based on a hybrid collaborative optimization vector. After stability screening, the optimal parameter set is iteratively generated.

[0056] S5. Pareto Multi-Objective Optimization: Based on the optimal parameter set, multi-objective values ​​are calculated in the simulation environment, and the optimal combination of structural parameters and control hyperparameters is output after Pareto screening.

[0057] These five steps generate a hybrid model of the controlled object by collecting operational data, construct a composite control architecture to generate composite control instructions, define a hybrid optimization variable space, generate the optimal parameter set by hierarchical nested optimization iteration, and output the optimal parameter combination through Pareto screening. This achieves deep integration and collaborative optimization of mechanical structure and control parameters, and solves the technical problems in existing wafer chamfering machine designs, such as global performance limitations caused by electromechanical separation, difficulty in suppressing low-frequency nonlinearity and high-frequency narrowband disturbances, and low efficiency in high-dimensional parameter space optimization.

[0058] The following provides a more detailed explanation of each step.

[0059] (1) Step S1: Parametric electromechanical modeling

[0060] This step aims to establish a high-fidelity data twin simulation environment. Unlike traditional simulation models with fixed parameters, the core of this environment lies in its parameterized nature, meaning that the dynamic characteristics of the controlled object can be reconstructed in real time as the mechanical structural parameters to be optimized change, thereby simulating the impact of structural changes on control performance.

[0061] Furthermore, this step includes:

[0062] Collect operating data of the wafer chamfering machine under multiple working conditions, and perform detrending and normalization preprocessing on the operating data to generate a standard dataset;

[0063] The mutual information entropy is calculated based on the standard dataset, the nonlinear correlation between input features and output performance indicators is quantified, features with mutual information entropy greater than a preset threshold are selected, and a nonlinear feature dataset is generated.

[0064] The nonlinear feature dataset is compared with the frequency response residuals of the parameterized mechanism model based on the Lagrange equation, and the residuals are fitted to the unmodeled dynamic compensation term using system identification.

[0065] By fusing unmodeled dynamic compensation terms with a parameterized mechanism model, a hybrid model of the controlled object that can be reconstructed in real time according to structural parameters is generated.

[0066] More specifically, step S1 includes the following steps:

[0067] S11. Establish a mechanistic model for the structural parameters to be optimized: Based on the principles of Lagrange dynamics, establish a mechanistic model for the structural parameters to be optimized.

[0068] First, based on the principles of Lagrange dynamics, the kinetic energy relationship, potential energy relationship, and dissipated energy relationship are determined, and expressed as follows:

[0069] ,

[0070] ,

[0071] ,

[0072] in, As kinetic energy, As potential energy, To dissipate energy, For generalized coordinates (the displacement or rotation of the wafer chamfer arm). For generalized speed (i.e.) Regarding time (first derivative) , , These are the equivalent moving mass, equivalent stiffness, and structural damping coefficient to be optimized, respectively.

[0073] Equivalent moving mass (moment of inertia) Inertial characteristics of the end effector. Optimization while meeting structural strength requirements. This is to balance the acceleration and deceleration capabilities of the servo motor with the system's natural frequency.

[0074] Equivalent structural stiffness The chamfered arm's ability to resist deformation. Higher... It can improve disturbance rejection capability, but may cause high-frequency resonance peaks to move closer to the principal axis rotation frequency; lower It helps reduce manufacturing costs, but requires the control system to have a higher bandwidth.

[0075] Structural damping coefficient Energy dissipation capacity at material and assembly interfaces. Optimization. The aim is to find the optimal level of passive vibration absorption to reduce the burden on the YK feedforward controller.

[0076] Then, based on kinetic energy Potential energy and dissipated energy Construct the Lagrange equation:

[0077] ,

[0078] in, This is the driving torque of the servo motor, serving as the generalized force input of the system. In the electromechanical coupling model, this torque is related to the motor armature current. Proportional, that is ,in This represents the current torque constant of the motor.

[0079] By performing a Laplace transform on the above equations, the continuous-domain transfer function of the controlled object is derived. , This study aims to describe the dynamics of a wafer chamfering machine in the real-time dimension, where s is the Laplace operator. To achieve collaborative optimization, the continuous-domain transfer function is used... The coefficients are defined as functions of the structural parameters to be optimized:

[0080] ,

[0081] in, The set of structural parameters to be optimized. Related , Related damping term This formula establishes an analytical mapping relationship between the structural parameters to be optimized and the pole distribution of the control model, enabling physical changes in the mechanical structure to be reflected in the dynamic characteristics of the controlled object in real time.

[0082] S12. Multi-source data acquisition and preprocessing: In order to make up for the lack of mechanistic models and high-frequency unmodeled dynamics, multi-condition data sampling was performed on a real wafer chamfering machine, and detrending and normalization preprocessing were performed to obtain a standard dataset.

[0083] Multi-condition data acquisition involves setting the spindle speed to cover a typical machining range of 30,000 rpm to 60,000 rpm, using a high-frequency piezoelectric accelerometer to sample end-effector micro-vibration signals, a grating ruler to collect position error signals, and a servo driver to collect current signals, thus obtaining a multi-source raw signal sequence.

[0084] The detrending term is: applying the least squares method to each class of original signal sequences in the multi-source original signal sequence. Perform polynomial fitting to obtain the trend term. (e.g., DC bias caused by thermal deformation), and subtract it to obtain the sequence after eliminating the trend term. .

[0085] Normalization is achieved by using Z-score normalization to map different sequences after the detrended term, including current, vibration, and displacement, to a standard normal distribution space. This eliminates the influence of dimensional differences on subsequent feature selection, resulting in a standard data sequence. ,in The sample mean. This represents the sample standard deviation.

[0086] S13. Nonlinear feature selection based on mutual information entropy: Nonlinear feature selection is performed on the standard dataset based on mutual information entropy to obtain a nonlinear feature dataset.

[0087] Due to the complex nonlinear frictional and hydrodynamic coupling involved in the wafer chamfering process, traditional linear correlation coefficients are insufficient to capture key influencing factors. Therefore, Mutual Information Entropy (MIE) is used to screen for strongly correlated features between input features and output performance in the preprocessed standard dataset.

[0088] For input feature vector A and output index vector B, their mutual information entropy The calculation is as follows:

[0089] ,

[0090] in, Let be the joint probability distribution between any feature 'a' in the input feature vector A and any index 'b' in the output index vector B. and Let be the marginal probability distributions of any feature a in the input feature vector A and any index b in the output index vector B, respectively.

[0091] The MIE values ​​of all acquisition channels in the standard dataset and the processing quality indicators are calculated, and a threshold is set. Key features with MIE values ​​greater than the threshold are retained, while redundant noise with low MIE values ​​is removed, thereby extracting the data subset that truly reflects the electromechanical coupling characteristics, resulting in a nonlinear feature dataset.

[0092] S14. Generation and calibration of interactive simulation environment: Integrate the mechanistic model and nonlinear feature dataset to construct a hybrid model that can dynamically respond to parameter changes.

[0093] This step specifically includes:

[0094] S141, Reference Deviation Extraction: Substitute the initial structural parameters into the mechanism model of step S11. The theoretical frequency response is calculated and compared with the actual data frequency response extracted from S13. The residuals in amplitude and phase frequency characteristics are calculated. These residuals represent higher-order flexible modes, assembly gaps, and nonlinear friction characteristics not included in the mechanistic model.

[0095] S142. Residual Modeling: Using the system identification method, the above residuals are fitted into an independent transfer function, i.e., the unmodeled dynamic compensation term. .

[0096] S143. Hybrid Model Construction: Establishing the final controlled object model:

[0097] ;

[0098] S144. Interaction Mechanism Implementation: In the subsequent collaborative optimization process, whenever the optimization algorithm updates the structural parameters... In the model Part of it updates the pole distribution in real time according to the analytical formula, while It exists as real background noise.

[0099] S15. Mapping and transformation from continuous domain model to discrete domain model: Since the composite control framework of S2 ultimately needs to be implemented through digital algorithms, after completing the continuous domain modeling, it is necessary to map the dynamic characteristics of the controlled object from the continuous time dimension to the discrete time series.

[0100] The sampling period is set to T based on the system's sampling frequency, and then the discretization mapping operator Z is used. Transfer function in continuous domain Convert to discrete domain transfer function z is a discrete transformation operator, ensuring that the digital control instructions designed in S2 are logically aligned with the physical state of the mechanical structure. The discretization formula is:

[0101] ,

[0102] in, It is the natural base.

[0103] The controlled object model constructed in step S1 possesses both the adjustability of a parameterized model and the high fidelity of a data-driven model, thus providing a precise interactive platform for evaluating control algorithms.

[0104] (2) Step S2: Construct a composite control architecture

[0105] To address both low-frequency nonlinear frictional disturbances (caused by grinding wheel cutting contact) and high-frequency narrowband harmonic vibrations (caused by high-speed rotation of the spindle and motor) that occur simultaneously during wafer chamfering, step S2 aims to construct a feedforward-feedback composite control system based on a frequency domain divide-and-conquer strategy. The structure of this system is as follows: Figure 2 As shown, the system comprises two parallel control channels. Based on a frequency domain divide-and-conquer strategy, the feedback channel handles low-frequency grinding nonlinear disturbances, ensuring the system's basic bandwidth and dynamic tracking accuracy. Simultaneously, a feedforward channel based on Youla-Kucera parameterization performs notch filtering for precise removal of high-frequency harmonic vibrations without compressing the main closed-loop phase margin. The outputs of both channels are superimposed to jointly drive the servo motor.

[0106] Furthermore, this step includes:

[0107] Position tracking error and error change rate data are selected, mapped to the fuzzy domain through quantization factors, and seventh-order linguistic variables are defined. The correction direction of proportional-integral-derivative gain is inferred through a fuzzy inference engine containing multiple rules. After defuzzification, the proportional-integral-derivative gain correction amount is output. The gain correction amount is superimposed with the basic gain to generate a feedback control law.

[0108] Based on the spindle vibration signal, the feedforward controller is decomposed into a nominal feedback part and a free parameter filter through Youla-Kucera parameterization. The free parameter filter is designed as an adaptive filter in the form of finite impulse response. The weights of the adaptive filter are updated online using a recursive least squares algorithm to generate the feedforward compensation signal.

[0109] The feedback control law is superimposed with the feedforward compensation signal to generate a composite control command.

[0110] More specifically, step S2 includes:

[0111] S21. Constructing a feedback channel: Select the position tracking error and its rate of change as the input variables of the fuzzy controller, map them to the fuzzy universe of discourse through a quantization factor, and define fuzzy linguistic variables; design a fuzzy inference engine, and infer the correction direction of the PID gain based on the error and the rate of change of error; output the gain correction amount by defuzzification, and synthesize the feedback control law by superimposing it with the basic gain.

[0112] The feedback channel, as the cornerstone of the system, is primarily responsible for ensuring the basic stability of the closed-loop system, the accuracy of trajectory tracking, and its adaptability to changes in nonlinear stiffness. Step S21 specifically includes:

[0113] S211. Input variable definition: Select position tracking error. and error change rate As two input variables of the fuzzy controller and The calculation formulas are as follows:

[0114] ,

[0115] ,

[0116] in, This refers to the chamfering trajectory command, which specifies the precise coordinates that the chamfering arm should reach at each moment. This represents the actual position fed back by the grating ruler, i.e., the true physical position of the chamfering arm at this moment. Indicates the previous moment.

[0117] S212, Fuzzification and Universe Mapping: Setting Quantization Factors and This maps the input from the physical domain to the fuzzy domain and defines the fuzzy linguistic variables as follows: These represent seven fuzzy semantic states: negative large, negative medium, negative small, zero, positive small, positive medium, and positive large, respectively.

[0118] For position tracking error , This indicates that the chamfering arm is significantly lagging behind the trajectory command. This indicates that the chamfer arm is moderately lagging behind the trajectory command. This indicates that the chamfering arm is slightly lagging behind the trajectory command. This indicates that the chamfered arm is severely overshooting. This indicates moderate overshoot in the chamfered arm. This indicates that the chamfering arm has a slight overshoot. This indicates precise location synchronization.

[0119] For the rate of change of error , This indicates that the error is diverging rapidly. This indicates that the error shows a clear divergence trend. This indicates that the error is slowly increasing. This indicates that the error is converging rapidly. This indicates that the error is decreasing at a moderate rate. This indicates that the error is slowly approaching the equilibrium point. This indicates that the error state is stable.

[0120] Fuzzy controller based on and The current state is used to infer the required values ​​from a fuzzy rule base. Parameter correction direction.

[0121] S213. Design a fuzzy inference engine: and To achieve complete coverage of the chamfering machine's state space under all operating conditions and ensure a definite control output under any error combination, a fuzzy inference engine containing 7×7=49 fuzzy rules is designed by combining the states of the two input variables through a Cartesian product. These 49 rules contain dynamic adjustment rules for the precision wafer grinding process, and their core control logic includes:

[0122] When the value is large, the system is in the acceleration phase, where it needs to overcome maximum static friction or quickly track the trajectory. The rule is set to significantly increase... , reduce This provides explosive corrective torque and improves the electrical stiffness of the system;

[0123] At medium time, When the value is large, the system is in the damping braking phase, at which point the system speed is too high, posing a risk of overshoot and collision with the wafer. The rule is set to significantly increase... , reduce The braking system utilizes differential action to provide electronic damping.

[0124] When very small, it is in the steady-state fine grinding stage; now it enters the submicron-level fine grinding stage. The rule is set to increase... , reduce The integral action is used to eliminate the small static error caused by friction.

[0125] S214. Defuzzification and Control Law Synthesis: The centroid method is used to defuzzify the inference results, and the dynamic correction of the PID parameters is output. , , These corrections are then added to the base gain to be optimized, forming the final feedback control law:

[0126] ,

[0127] in, , , Based on PID gain, , , This is the dynamic correction value of the PID gain output by the fuzzy controller.

[0128] The physical meanings of each gain term in the wafer chamfering machine control system are as follows:

[0129] proportional gain This parameter represents the strength of the fuzzy controller's response to the current error. In a wafer chamfering machine, this parameter determines the system's electrical stiffness. A larger proportional gain can improve the chamfering arm's resistance to cutting and grinding forces and speed up the response, but setting it too high can easily lead to high-frequency oscillations in the system.

[0130] Integral gain This parameter represents the fuzzy controller's ability to correct historical accumulated errors. In wafer chamfering machines, this parameter is primarily used to eliminate steady-state errors. When the chamfering arm approaches the target position but is hindered by mechanical friction, the integral action continuously accumulates output torque, ensuring that the diamond wheel can overcome minute resistance and achieve sub-micron level tight contact with the wafer edge.

[0131] Differential gain This parameter represents the fuzzy controller's ability to predict error trends. In a wafer chamfering machine, this parameter is equivalent to providing electronic damping. When the chamfering arm moves rapidly towards the target point, the differential action generates a reverse braking torque to prevent overshoot due to excessive mechanical inertia, thereby avoiding damage to the wafer from grinding wheel collisions.

[0132] For the sake of a unified description of the subsequent composite framework, the feedback logic based on fuzzy rule adaptive adjustment is defined as a feedback controller. This controller is responsible for the basic stability of the system and the suppression of low-frequency disturbances.

[0133] S22. Constructing the feedforward channel: Based on the Youla-Kucera parameterization method, the feedforward controller is decomposed into a nominal feedback part and a free parameter filter; the free parameter filter is designed as an adaptive filter in the form of a finite impulse response; the weights of the adaptive filter are updated online using a recursive least squares algorithm; and an inverse vibration waveform is generated by minimizing the sensitivity function containing the adaptive filter.

[0134] The feedforward channel, acting as a precision vibration damper in the composite control system, aims to address the micron-level narrowband harmonic vibrations caused by the high-speed rotation (>30,000 rpm) of the spindle motor and diamond grinding wheel in the wafer chamfering machine. To effectively suppress vibrations at specific frequencies without compromising the closed-loop stability of the original feedback control loop in S21, an adaptive control architecture based on Youla-Kucera (YK) parameterization is employed. This process specifically includes:

[0135] S221. Establish a feedforward controller model based on Youla-Kucera parameterization: Utilize the Youla-Kucera (YK) parameterization method from modern control theory to restructure the feedforward controller. The core idea is to decompose the controller design into a nominal part that ensures closed-loop stability and a free parameter part that improves disturbance rejection performance, thereby achieving decoupling between stability and dynamics.

[0136] Based on the structural parameters in step S1 Real-time updated discretized transfer function It is decomposed into two stable, properly rational transfer functions. and The ratio form:

[0137] ,

[0138] in, This refers to the set of stable rational numbers whose poles lie within the unit circle. We then introduce two more stable transfer functions. and So that it satisfies Bezout's identity:

[0139] ,

[0140] The physical meaning of this equation lies in the possibility of finding a set of equations that satisfy the above equations. and Then by The constructed nominal feedback controller ensures the internal stability of the closed-loop system. This is achieved using the PID feedback controller already designed in S21. Based on this, the specific parameter selections are as follows:

[0141] ,

[0142] ,

[0143] ,

[0144] .

[0145] The above parameter selection naturally satisfies the Bezout equation, and and These represent the sensitivity function correlation term and the complementary sensitivity function correlation term of the closed-loop system, respectively, and have clear physical meanings.

[0146] According to YK parameterization theory, all objects that can be controlled... Feedforward controller that maintains closed-loop stability The set can be parameterized as:

[0147] ,

[0148] in, For a belonging Free parameter filter.

[0149] Finally, the above theoretical formulas are mapped onto the actual control flow diagram of the wafer chamfering machine, and the output of the feedforward controller is... It consists of two parts: a reference feedforward section and an adaptive correction section. The former is composed of... and A fixed feedforward quantity corresponds to rigid compensation of the foundation, while the latter is determined by... and its related , A defined dynamic compensation amount. Ultimately, the vibration suppression problem is transformed into... Unconstrained optimization problems in parameter space.

[0150] S222, Design an adaptive FIR (FIR) filter : Free parameter filter Designed as an L-order finite impulse response transverse filter to achieve phase and amplitude compensation for vibration signals of a specific frequency. Its transfer function is expressed as:

[0151] ,

[0152] in, Let be the weight vector to be optimized. The unit delay operator represents the delay mapping over a sampling period T. The table executes the first step on the input parameter model. The order L of the historical state. The order L of the filter will be one of the structural parameters to be optimized in step S3, directly affecting the frequency resolution and computation delay of the filter.

[0153] S223. Online Iterative Update of Weights Based on FxRLS: To address the vibration frequency drift caused by slight changes in spindle speed and grinding load during chamfering, the FxRLS algorithm, which has a faster convergence speed than the traditional LMS algorithm, is used to update the weights online. weight vector (n=0,1,2,…,L-1) are updated in real time. The specific update logic and parameter definitions are as follows:

[0154] First, define the sampling time index as n (n=1,2,3... for discrete time steps). The scalar information of the principal shaft reference vibration acquired by the sensor is then processed by the transfer function determined in step S221, which serves as the secondary channel model. After filtering, the scalar filtered reference signal at the current time is obtained, which is defined as the input signal. .

[0155] Based on this, an input data vector that is strictly related to the filter order L is constructed. It is represented as a column vector composed of the current time and the past L-1 historical sample values, with dimension 1. . Specifically, it is expressed as follows:

[0156] .

[0157] Weight vector The update follows the least squares criterion and is implemented recursively as follows:

[0158] ,

[0159] ,

[0160] ,

[0161] in, Let n be the gain vector at time n, with dimension n. ; This is the inverse matrix of the autocorrelation matrix of the input signal at the previous time step, with dimension 1. ; The forgetting factor has a value range of 1. , The smaller the value, the stronger the system's ability to track parameter changes, but the steady-state error may increase. This parameter is also included in the collaborative optimization as a key control hyperparameter in step S3. Let be the optimal weight vector to be solved at time n, with dimension . ; Let n be the scalar value of the system residual vibration error sampled by the sensor at time n; This parameter is the inverse of the autocorrelation matrix of the input signal at the current time. Updating this parameter ensures that the inverse of the autocorrelation matrix is ​​dynamically corrected with time step n, thereby enabling rapid locking of non-stationary vibration frequencies.

[0162] S224, Sensitivity Function Minimization and Disturbance Suppression: Through the above settings, the original vibration suppression problem is transformed into minimizing the vibration function including the adaptive filter. Sensitivity function Question:

[0163] .

[0164] In each control cycle, the FxRLS algorithm searches for the optimal... The parameters enable the reverse vibration waveform generated by the feedforward signal to be precisely canceled out by the actual narrowband harmonic vibration of the spindle at the end of the chamfered arm, thereby achieving notch filtering of high-frequency micro-vibrations without changing the feedback bandwidth (determined by the PID).

[0165] The composite control system constructed through step S2 possesses both the strong adaptive robustness of fuzzy PID for low-frequency nonlinear friction disturbances and the precise counterbalancing capability for high-frequency narrowband vibrations based on YK parameterized feedforward, thus providing robust control assurance for the full-frequency disturbance suppression of the wafer chamfering machine during dynamic grinding.

[0166] (3) Step S3: Definition of the covariate space

[0167] This step aims to construct a unified mathematical space that encompasses both hardware physical properties and software algorithm configurations, thereby breaking the limitation that mechanical parameters are constant in traditional designs.

[0168] Furthermore, step S3 specifically includes:

[0169] Define a set of structural parameters including equivalent stiffness, structural damping coefficient and equivalent kinematic mass; define a set of global reference parameters including proportional-integral-differential reference gain, fuzzy quantization factor, filter order and forgetting factor, and consequent parameters of each fuzzy rule in the fuzzy inference engine;

[0170] Upper and lower bound constraints are set for each parameter based on the physical limits of materials, the driving capability of the motor, and the stability criteria.

[0171] The structural parameter set, the global baseline parameter set, and the fuzzy rule consequent parameters are merged to generate hybrid optimization variable space data.

[0172] More specifically, the steps include:

[0173] S31. Define a hybrid collaborative optimization vector X, which is composed of a set of structural parameters. With control hyperparameter set It consists of two orthogonally combined parts. (Control hyperparameter set) Including the algorithmic variables that determine the performance of the composite control system, this set is further subdivided into a global baseline parameter set to facilitate subsequent nested optimization strategies. With local rule parameter set .

[0174] The global baseline parameter set includes the PID baseline gain, fuzzy quantization factor, and YK adaptive parameters. The PID baseline gain includes... This determines the system's nominal bandwidth and basic stability margin, as well as the system's nominal bandwidth and instruction-following speed; fuzzy quantization factor. and The sensitivity of the fuzzy controller to error signals is determined by the YK adaptive parameters, which include the order L of the FIR filter and the forgetting factor λ of the RLS algorithm.

[0175] Local rule parameters specifically refer to the membership function parameters of the 49 fuzzy rule consequents in the fuzzy inference engine.

[0176] Therefore, the hybrid collaborative optimization vector :

[0177] ,

[0178] in, Specifically refers to the polynomial constant term in the consequent of rule j.

[0179] At the same time, based on actual engineering constraints, including the physical limits of materials, motor driving capability, and stability criteria, upper and lower bound constraints are set for each variable:

[0180] ,

[0181] in, Representing the One parameter to be optimized. , The first The upper and lower bounds of the parameters to be optimized. The total optimization dimension D is calculated as follows:

[0182] ,

[0183] in, For structural parameter set Dimensions For global baseline parameter set Dimensions For local rule parameter set The dimension. In this embodiment, .

[0184] The hybrid collaborative optimization vector defined in step S3 encompasses both the physical design attributes of mechanical structural components and the software configuration parameters of the control algorithm, thus providing a unified mathematical evaluation benchmark for breaking through electromechanical design barriers and exploring the global performance limits of the system.

[0185] (4) Step S4: Nested collaborative optimization

[0186] This step addresses the curse of dimensionality in the electromechanical co-design of wafer chamfering machines, where simultaneously optimizing structural parameters, PID parameters, and dozens of fuzzy rules leads to an exponential expansion of the search space. A layered, nested, derivative-free optimization strategy is employed. This strategy divides the optimization process into two closed loops: an outer macroscopic evolution and an inner microscopic fine-tuning, and introduces a hard constraint screening mechanism based on control theory.

[0187] Further, this step includes: encoding the hybrid cooperative optimization vector into an antibody of the artificial immune algorithm, generating an initial population using Bernoulli chaotic mapping and mapping it to the feasible region of physical parameters to obtain initial population data;

[0188] The infinite norm index of each antibody is calculated based on the small gain theorem, and individuals that do not meet the stability conditions are removed to generate population data that have passed the stability hard constraint screening.

[0189] The screened population data and typical working condition data are input into the inner loop to calculate the compatibility of each data sample with each fuzzy rule antecedent.

[0190] The instantaneous performance evaluation value is distributed to each rule using compatibility as a weight, generating an independent evaluation value for each rule;

[0191] Based on independent evaluation values, a parallel framework is used to independently optimize and update the consequent parameters of each rule. The optimized rule parameters are then backfilled into the outer antibody layer. After receptor editing and iterative convergence, the optimal parameter set data that satisfies stability constraints is generated. The specific process is as follows: Figure 3 As shown.

[0192] More specifically, the steps include:

[0193] S41. Outer Loop Macroevolution: Population initialization and macro-search based on the Artificial Immune System (AIS), optimizing the hybrid collaborative optimization vector to be optimized. Antibodies encoded as part of an artificial immunization algorithm are used to generate initial chaotic sequences using Bernoulli chaotic mapping and mapped to the feasible region of physical parameters. Adaptive cloning and mutation operations are performed by calculating antibody affinity to search for the globally optimal range. Specifically, this includes:

[0194] S411. Hybrid Initialization Based on Bernoulli Chaotic Map: To ensure the ergodicity of the initial solution in multidimensional space and avoid the clustering phenomenon of random initialization, a hybrid collaborative optimization vector is generated using the Bernoulli chaotic map. The corresponding initial population.

[0195] First, a normalized chaotic sequence is generated using the Bernoulli displacement map. The iterative formula is:

[0196] ,

[0197] in, For mapping parameters, The elements in the array are all decimals between 0 and 1, corresponding to the parameters to be optimized defined in step S3. , , They represent equivalent stiffness respectively Relative positions within their respective feasible domains , , Represents the PID reference gain ( , , The relative size of ) , Represents the fuzziness factor The relative size, , Represents the YK adaptive parameters (filter order) The relative magnitude of the forgetting factor (λ). The consequent parameter represents the 49 fuzzy rules.

[0198] Then normalize the chaotic sequence Mapping to the feasible region of physical parameters defined in step S3 The initial physical parameters are obtained as follows:

[0199] ,

[0200] Among them, subscript Indicates the first In terms of dimensions, That is, the first The antibody in the first The initial physical quantity (current value) in the dimension. and Then it is the first The maximum and minimum physical values ​​allowed for each parameter.

[0201] Ultimately, a hybrid initial population was constructed based on the initial physical parameters, consisting of 80% chaotic exploration individuals and 20% expert experience individuals. The chaotic exploration individuals were used to ensure diversity and explore situations untouched by human experience, while the expert experience individuals provided efficient individuals for the algorithm, enabling it to quickly enter the effective search phase.

[0202] S412. Cloning and Mutation Based on Artificial Immune System (AIS): Based on the affinity evaluation results of the previous generation of individuals, perform immune evolution operations to generate a new generation of population.

[0203] Affinity is defined as a metric used to evaluate the quality of antibodies (i.e., candidate co-design schemes). affinity With multi-objective evaluation function They are inversely proportional, and the formula is:

[0204] ,

[0205] in, This is a small constant to prevent division by zero errors. Higher affinity indicates better multi-target comprehensive performance of the antibody.

[0206] Then clone more copies of the high-affinity, high-quality individuals. The clone size of each antibody is The calculation formula is:

[0207] ,

[0208] This formula is used to determine the first... The number of clones that should be replicated during immune evolution for each antibody (i.e., candidate co-design scheme). The maximum clone population size parameter is set to limit the maximum number of clones of a single antibody; This is a rounding function that ensures the number of clones is an integer.

[0209] This formula indicates that antibodies with higher affinity have a higher proportion of clones. The higher the proportion of antibodies with high affinity, the more search resources are available in the next generation of the population; conversely, the fewer antibody clones with low affinity, the more likely they are to be eliminated. This affinity-proportional cloning mechanism mimics the selective amplification of superior antibodies in the biological immune system.

[0210] Finally, the clones are mutated to explore new solutions. An adaptive strategy inversely proportional to affinity is employed: higher affinity results in a smaller variable length (i.e., fine-grained search); lower affinity results in a larger variable length (i.e., global jump). The mutation formula is designed as follows:

[0211] ,

[0212] in, It is the mutated parameter, i.e., the first... The antibody in the first New values ​​in dimensions Normalized affinity (current individual) The performance score is mapped to the [0,1] interval, where 0 represents the worst individual in the population and 1 represents the best individual in the population. These are random numbers from a standard normal distribution. The basic variability rate is the maximum proportionality coefficient representing the variation length, typically taken as 0.1 to 0.3, meaning the maximum allowable jump range is 10% to 30% of the total range; This is the attenuation coefficient, used to control the strength of affinity's suppression of the variation amplitude. If the mutated parameters... Exceeding the boundary If so, then its value will be reset to the boundary value.

[0213] In order to maintain population diversity and prevent premature convergence during the process, the bottom 10% of antibodies are forcibly removed at the end of each generation and replaced with randomly generated new antibodies.

[0214] S42. Stability Hard Constraint Screening: Before entering the time-consuming inner layer optimization, a rapid stability check is first performed on each outer layer individual. This is implemented based on the YK parameterization theory established in S22.

[0215] For any given individual, calculate the closed-loop system. Norm indicator:

[0216] ,

[0217] in, for The stable coprime decomposition factor.

[0218] According to the small gain theorem, if If the value is less than 1, then the system is internally stable. If the calculation result of an individual is less than 1, then the system is internally stable. If the value is ≥1, the design scheme is determined to be physically infeasible. The fitness of the range is directly assigned and the design is discarded, skipping all subsequent calculations, thereby avoiding wasting computing power on invalid solutions.

[0219] S43. Inner Loop Micro-tuning: Employing α-weighted fuzzy rule independent evaluation (α-FUZZI-ES), and utilizing a compatibility-driven performance contribution sharing mechanism, the optimization task of 49 highly coupled fuzzy rules is decoupled into 49 parallel independent subtasks. This process reduces the dimensionality of the search space, which originally grows exponentially with dimensionality, to a linearly growing independent optimization space, fundamentally overcoming the curse of dimensionality in collaborative optimization.

[0220] Input the pre-collected typical operating condition data into the current fuzzy system. Calculate the compatibility of the k-th data sample with the antecedent of the j-th fuzzy rule. This value indicates which rule is activated under the current operating condition and the degree of activation.

[0221] Using compatibility as a weight, the system in the first... Instantaneous performance evaluation value generated at each moment Distribute the burden to each rule. Calculate the... Independent evaluation value of each rule The calculation formula is:

[0222] ,

[0223] in, The total number of samples.

[0224] Independent evaluation value for each rule The consequent parameters of each rule are optimized independently without changing the values ​​of other rules. The optimization algorithm is based on the evaluation value. The search range is dynamically adjusted based on the magnitude. If... If the value is large, then a larger perturbation and variation are applied to the consequent constant term of the rule to quickly escape the inefficient parameter region; otherwise, local fine-tuning is performed.

[0225] Since the evaluation values ​​of each rule are independent, a GPU parallel framework is used to update all 49 rules simultaneously. This step transforms high-dimensional coupled optimization into low-dimensional independent optimization, significantly improving the convergence speed.

[0226] S44, Closed-Loop Iteration and Receptor Editing: The optimal rule parameters optimized from the inner layer are backfilled into the outer layer individuals to form a complete scheme, which is then sent to S5 for evaluation. The evaluation results are fed back to S41 for the next generation of evolution. Simultaneously, receptor editing is performed at the end of each generation, forcibly removing the bottom 10% of antibodies, and the chaotic initialization method in S41 is invoked to generate new antibodies to fill the gaps, thus maintaining population diversity.

[0227] The nested optimization method used in step S4 ensures both the global convergence and closed-loop stability of the high-dimensional parameter search process, and achieves efficient decoupling and precise matching of complex fuzzy rules, thus providing a reliable optimization path for the deep resonance of mechanical structure and control logic.

[0228] (5) Step S5: Pareto multi-objective selection

[0229] The purpose of this step is to conduct a comprehensive performance evaluation of the antibody population generated by nested optimization iterations across multiple dimensions. Since wafer chamfering has different stringent requirements for trajectory accuracy, surface waviness, and processing efficiency, and these objectives often conflict physically, a multi-objective evaluation and Pareto optimization mechanism are employed.

[0230] Furthermore, this step includes:

[0231] Input the optimal parameter set data into the simulation environment to obtain trajectory tracking error data in the time domain, power spectral density data in the frequency domain, and settling time data of the step response;

[0232] The integral value of time multiplied by the absolute value of error is calculated based on time domain data, the peak power spectral density in a specific frequency band is extracted based on frequency domain data, and the adjustment time value is obtained based on adjustment time data to generate three multi-objective evaluation function values.

[0233] Non-dominated ranking is performed based on the multi-objective evaluation function values, dominated individuals are removed, and the best individuals that cannot be substituted for each other are retained to generate Pareto front data.

[0234] The non-dominated solutions in the Pareto front data are subjected to min-max normalization, and the process preference weight coefficient is introduced to calculate the weighted Euclidean distance of each solution to the origin of the coordinate system.

[0235] The individual with the smallest weighted Euclidean distance is selected as the global optimal solution, and the optimal combination of structural parameters and control hyperparameters is output.

[0236] More specifically, step S5 includes:

[0237] S51. Constructing a multi-objective evaluation function set: For each base point co-design scheme (antibody) generated by the outer loop. After fine-tuning the inner fuzzy rules, the comprehensive response data in the time and frequency domains are obtained through a simulation environment, and the following three core optimization objectives are calculated. , , .

[0238] This is a trajectory tracking accuracy index based on the integral of absolute error (ITAE), used to evaluate the macroscopic following capability of the chamfered arm end effector to a preset trajectory set. The evaluation criterion is time multiplied by the integral of absolute error (ITAE), and the calculation formula is as follows:

[0239] ,

[0240] in, For a single chamfering process cycle, For the current simulation time, For a moment The modulus of the difference between the instruction position and the actual feedback position.

[0241] This is a surface micro-vibration index based on the PSD, used to evaluate the microscopic surface quality of the wafer edge and examine the system's ability to suppress narrowband harmonic vibrations caused by high-speed spindle rotation (30,000~60,000 rpm). It also addresses residual position error signals. Perform a Fast Fourier Transform to extract the peak power spectral density (PSD) within a specific frequency band. The calculation formula is as follows:

[0242] ,

[0243] in, For frequency domain analysis, the frequency independent variable is... To optimize the frequency range that the algorithm focuses on detecting, Represents position error signal In frequency Energy density at that location.

[0244] It is a processing efficiency index based on settling time, used to evaluate the dynamic response speed and throughput of the system. The settling time of the system to a step command is used as the evaluation index, and the calculation formula is as follows:

[0245] ,

[0246] That is, the system output enters and remains at the target value. The shortest time required within the error band. It is the time required from the moment the step instruction is issued until the system output no longer exceeds the specified error.

[0247] S52. Pareto Sorting Based on Non-Dominated Ranking: Due to the three objectives , , Since a simple weighted summation cannot be used to uniformly measure the results, a non-dominated sorting mechanism is introduced.

[0248] The definition of non-dominance is: if the scheme The plan is no worse than the original plan in all objectives. And at least one objective is superior to Then it is called Dominate .

[0249] In the selection process, all dominated individuals are eliminated, and the best individuals that cannot be completely substituted for each other are retained.

[0250] S53. Automatic global optimal solution locking based on inflection point strategy: To avoid the subjectivity of manually selecting a solution from the Pareto front, the minimum distance method is used to automatically lock the solution with the best overall performance.

[0251] First, set the three objective values ​​of all non-dominated solutions on the Pareto front. , , Normalize the data and map it to the [0,1] interval.

[0252] We redefine the origin of the coordinate system (0,0,0) as the theoretically highest point that simultaneously achieves the highest accuracy, zero vibration, and fastest speed. Although it is physically unattainable, it serves as a mathematical reference benchmark.

[0253] Next, calculate each solution on the frontier. Euclidean distance to the origin The calculation formula is:

[0254] ,

[0255] in, , , To obtain the normalized performance index, since the original three objectives have completely different physical dimensions and cannot be directly added, the Min-Max normalization method is first used to normalize the performance indexes with different dimensions. The formula for mapping to the interval [0,1] is:

[0256] ,

[0257] in, These correspond to three performance metrics. This indicates taking the minimum value. This indicates taking the maximum value.

[0258] To normalize the trajectory accuracy, representing the contour error level of the k-th scheme, the closer the value is to 0, the more perfect the geometry of the wafer edge; Normalized surface waviness represents the micro-vibration level of the k-th scheme. The closer the value is to 0, the more thoroughly the spindle vibration is suppressed and the smoother the wafer edge. Normalized processing time represents the response speed of the k-th solution. The closer the value is to 0, the more agile the equipment is and the higher the unit output.

[0259] These are the process preference weighting coefficients, namely accuracy weight, quality weight, and efficiency weight. This is a set of parameters set according to specific needs and can be dynamically adjusted according to specific operating conditions to meet [the requirements]. =1, which determines the application direction of the optimization results.

[0260] Final selection The smallest individual is the final globally optimal solution. This solution represents the optimal balance between machining accuracy, surface quality, and production efficiency under current physical limits.

[0261] S54, Optimal Parameter Mapping and Control System Closed-Loop Configuration: Locking S53 The code is parsed into specific engineering instructions and then performs the following physical configuration operations to complete the final implementation of the optimization. This step includes:

[0262] S541. Structural Parameter Output: Extracting the Optimal Structural Parameter Set , These are the optimal equivalent structural stiffness, optimal structural damping coefficient, and optimal equivalent moving mass, respectively.

[0263] S542. Control Parameter Injection: Extracting the Optimal Control Parameter Set The data is injected into the control unit of the wafer chamfering machine, including PID baseline updates, fuzzy rule base reconstruction, and adaptive initial value setting.

[0264] PID benchmark update, i.e., optimal PID benchmark gain , , Write to the gain register of the servo driver.

[0265] The fuzzy rule base reconstruction involves refreshing the optimized 49 sets of consequent parameters into the fuzzy inference table of the motion controller, replacing the original rules.

[0266] Adaptive initial value setting involves setting the optimized forgetting factor. and filter The configuration is then transferred to the YK feedforward module in S2.

[0267] The multi-objective Pareto screening and optimal parameter injection performed in step S5 not only take into account the marginal benefit balance between processing accuracy, surface quality and production efficiency, but also realize the complete closed loop from virtual space simulation optimization to physical entity parameter configuration, thus providing the optimal engineering decision for the best matching of hardware and software integration of wafer chamfering machine under complex working conditions.

[0268] At this point, the system has completed a full closed loop from virtual simulation optimization to physical entity configuration, and the equipment immediately possesses optimal chamfering capabilities.

[0269] It should be noted that the various processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved. This embodiment does not impose any limitations on these steps.

[0270] The present invention also provides a high-precision multi-parameter collaborative optimization control system for a wafer chamfering machine, including an electromechanical modeling module, a composite control construction module, a variable space definition module, a nested optimization module, and a Pareto optimization module, which are respectively used to execute steps S1, S2, S3, S4, and S5 in the high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine.

[0271] The embodiments described in this invention can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with the implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0272] Computer programs for implementing the methods and systems of the present invention may be written in any combination of one or more programming languages ​​and stored in a computer-readable storage medium. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0273] Computer-readable storage media can be tangible media that may contain or store computer programs for use by or in conjunction with an instruction execution system, apparatus, or device. Computer-readable storage media can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. Alternatively, computer-readable storage media can be machine-readable signal media. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, optical disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0274] Table 1 shows a comparison of the results of this invention with existing control methods (pure PID control, feedforward-feedback control, classical fuzzy control, model predictive control (MPC), and reinforcement learning PID control) in multi-condition disturbance scenarios during wafer chamfering. As can be seen from Table 1, this invention does not only lead in a single indicator, but also achieves significant improvements in comprehensive performance across multiple dimensions, including steady-state position error RMS, overfrequency, load disturbance error amplification, and high-frequency noise error amplification, achieving more precise, stable, faster, and more adaptive control objectives. This confirms the effectiveness of the entire process designed in this invention: "parametric electromechanical modeling → constructing a composite control architecture → defining the cooperative variable space → nested cooperative optimization → Pareto multi-objective selection." It successfully solves core problems such as strong electromechanical coupling constraints, difficulty in simultaneously addressing low-frequency nonlinearity and high-frequency vibration, susceptibility to local optima in optimization, and insufficient stability.

[0275] Table 1: Model Comparison Results

[0276]

[0277] In summary, the high-precision multi-parameter collaborative optimization control method and system for a wafer chamfering machine provided by this invention, through deep electromechanical integration and progressive optimization, gradually solves key problems in the prior art: First, by constructing a parameterized structure and a control interaction dynamic environment, key features are screened and the model is calibrated using mutual information entropy, breaking the limitations of traditional static physical models and laying a high-fidelity simulation foundation for collaborative optimization; then, a feedforward-feedback composite control architecture is constructed, integrating the nonlinear adaptability of fuzzy PID and the micro-vibration notch filtering capability of YK feedforward, overcoming the inability of a single control strategy to simultaneously address low-frequency friction and high-frequency narrowband vibration. The challenge lies in addressing this issue. Based on this, a nested co-evolutionary model and the α-FUZZI-ES parallel algorithm are employed to decouple high-dimensional fuzzy rule optimization into independent sub-problems under hard stability constraints, significantly improving the search efficiency in the hybrid space containing structural physical parameters and control algorithm parameters. Finally, a multi-objective Pareto optimization is introduced to find the globally optimal balance between processing accuracy, surface quality, and response speed, thereby achieving the integrated optimal matching of the wafer chamfering machine's hardware and software. This solves the problem in existing wafer chamfering machine designs where the electromechanical coupling between the rigidity of the mechanical structure and the dynamic response of the servo control prevents the system from exceeding its global performance limits under strong disturbances.

[0278] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine, characterized in that, Including the following steps: S1. Collect operating data of the wafer chamfering machine under multiple working conditions and generate a hybrid model of the controlled object; S2. Construct a feedforward-feedback composite control architecture for the wafer chamfering machine based on frequency domain divide-and-conquer strategy and fuzzy inference; S3. Determine the set of structural parameters to be optimized in the hybrid model of the controlled object, as well as the set of global reference parameters and fuzzy rule consequent parameters to be optimized in the feedforward-feedback composite control architecture, and merge them into a hybrid collaborative optimization vector; S4. Employ hierarchical nested optimization, generate an initial population based on the hybrid collaborative optimization vector, and iteratively generate the optimal parameter set after stability screening; S5. Calculate multi-objective values ​​in the simulation environment based on the optimal parameter set, and output the optimal combination of structural parameters and control hyperparameters after Pareto screening.

2. The high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine according to claim 1, characterized in that, Step S1 specifically includes: Collect operating data of the wafer chamfering machine under multiple working conditions, and perform detrending and normalization preprocessing on the operating data to generate a standard dataset; The mutual information entropy is calculated based on the standard dataset, the nonlinear correlation between input features and output performance indicators is quantified, features with mutual information entropy greater than a preset threshold are selected, and a nonlinear feature dataset is generated. The nonlinear feature dataset is compared with the frequency response residual of the parameterized mechanism model based on the Lagrange equation, and the residual is fitted as an unmodeled dynamic compensation term using system identification. The unmodeled dynamic compensation term is fused with the parameterized mechanism model to generate a hybrid model of the controlled object that can be reconstructed in real time with the structural parameters.

3. The high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine according to claim 1, characterized in that, Step S2 specifically includes: Position tracking error and error change rate data are selected, mapped to the fuzzy domain by quantization factor and a seventh-order linguistic variable is defined. The correction direction of proportional-integral-derivative gain is inferred through a fuzzy inference engine containing multiple rules. After defuzzification, the proportional-integral-derivative gain correction amount is output. The gain correction amount is superimposed with the basic gain to generate a feedback control law. Based on the spindle vibration signal, the feedforward controller is decomposed into a nominal feedback part and a free parameter filter through Euler-Kussera parameterization. The free parameter filter is designed as an adaptive filter in the form of finite impulse response. The weights of the adaptive filter are updated online using a recursive least squares algorithm to generate a feedforward compensation signal. The feedback control law is superimposed with the feedforward compensation signal to generate a composite control command.

4. The high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine according to claim 1, characterized in that, Step S3 specifically includes: Define a set of structural parameters including equivalent stiffness, structural damping coefficient and equivalent kinematic mass; define a set of global reference parameters including proportional-integral-differential reference gain, fuzzy quantization factor, filter order and forgetting factor, and consequent parameters of each fuzzy rule in the fuzzy inference engine; Upper and lower bound constraints are set for each parameter based on the physical limits of materials, the driving capability of the motor, and the stability criteria. The structural parameter set, the global benchmark parameter set, and the fuzzy rule consequent parameters are merged to generate hybrid optimization variable space data.

5. The high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine according to claim 1, characterized in that, Step S4 specifically includes: The hybrid collaborative optimization vector is encoded as an antibody of the artificial immune algorithm. The initial population is generated by Bernoulli chaotic mapping and mapped to the feasible region of physical parameters to obtain the initial population data. The infinite norm index of each antibody is calculated based on the small gain theorem, and individuals that do not meet the stability conditions are removed to generate population data that have passed the stability hard constraint screening. The screened population data and typical working condition data are input into the inner loop to calculate the compatibility of each data sample with each fuzzy rule antecedent. Using the compatibility as a weight, the instantaneous performance evaluation value is distributed to each rule to generate an independent evaluation value for each rule; Based on the independent evaluation values, the consequent parameters of each rule are independently optimized and updated using a parallel framework. The optimized rule parameters are then backfilled into the outer antibody. After receptor editing and iterative convergence, the optimal parameter set data that satisfies the stability constraints is generated.

6. The high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine according to claim 1, characterized in that, Step S5 specifically includes: The optimal parameter set data is input into the simulation environment to obtain time-domain trajectory tracking error data, frequency-domain power spectral density data, and step response settling time data. Based on the time domain data, calculate the integral value of time multiplied by the absolute value of error; based on the frequency domain data, extract the peak power spectral density within a specific frequency band; based on the adjustment time data, obtain the adjustment time value; and generate three multi-objective evaluation function values. Based on the multi-objective evaluation function values, non-dominated ranking is performed, dominated individuals are removed, and preferred individuals that cannot be substituted for each other are retained to generate Pareto front data. The non-dominated solutions in the Pareto front data are subjected to min-max normalization, and the weighted Euclidean distance from each solution to the origin is calculated by introducing a process preference weight coefficient. The individual with the smallest weighted Euclidean distance is selected as the global optimal solution, and the optimal combination of structural parameters and control hyperparameters is output.

7. The high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine according to claim 5, characterized in that, In step S4, generating the initial population using the Bernoulli chaotic map specifically includes: generating a normalized chaotic sequence using the Bernoulli displacement map, mapping each element in the normalized chaotic sequence to the feasible domain of the physical parameters of each parameter to be optimized, and constructing a mixed initial population containing chaotic exploration individuals and expert experience individuals, wherein the chaotic exploration individuals account for the majority of the total population and the expert experience individuals account for a small portion of the total population.

8. The high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine according to claim 5, characterized in that, In step S4, the stability screening of the initial population data based on the infinite norm index specifically includes: calculating the infinite norm index of the closed-loop system corresponding to each antibody based on the Euler-Kussera parameterization theory, determining whether the infinite norm index is less than one according to the small gain theorem, and if the infinite norm index is greater than or equal to one, determining that the design scheme is not feasible, directly assigning a range fitness and removing it, and skipping all subsequent calculations.

9. The high-precision multi-parameter collaborative optimization control method for a wafer chamfering machine according to claim 5, characterized in that, Based on the independent evaluation values, the consequent parameters of each rule are independently optimized and updated using a parallel framework. The optimized rule parameters are then backfilled into the outer antibody layer. After receptor editing and iterative convergence, the optimal parameter set data that satisfies stability constraints is generated, specifically as follows: Based on the independent evaluation value, the consequent parameters of each fuzzy rule are independently optimized and updated using a parallel computing framework. The larger the independent evaluation value, the worse the control effect and the larger the adjustment range within the working area corresponding to the rule, and vice versa. The optimized rules parameters of the inner loop are backfilled into the outer antibody, and the receptor editing mechanism is executed. Some antibodies are removed according to the affinity ranking, and Bernoulli chaotic mapping is called to generate new antibodies to fill the gap. The process is iterated until the preset termination condition is met, and then the optimal parameter set data that meets the stability constraints is generated.

10. A high-precision multi-parameter collaborative optimization control system for a wafer chamfering machine, characterized in that: It includes an electromechanical modeling module, a composite control construction module, a variable space definition module, a nested optimization module, and a Pareto optimization module, which are respectively used to execute steps S1, S2, S3, S4, and S5 in the high-precision multi-parameter collaborative optimization control method for the wafer chamfering machine according to any one of claims 1 to 9.

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