Cooperative tool servo diamond turning method and system based on feedforward compensation

Abstract

The application provides a kind of based on feedforward compensation's cooperative tool servo diamond turning method and system, it is related to diamond turning technical field, method includes: constructing master-slave cooperative tool servo system, for main servo shaft Z axis and slave servo shaft W axis configuration cooperative motion relationship;Establish the macro-micro system-oriented data-driven feedforward compensation model capable of predicting the overall tracking error of macro-micro system according to ideal position or trajectory characteristics;The feedforward compensation quantity output by the macro-micro system-oriented feedforward compensation model is superimposed on the target tool trajectory to obtain the compensated trajectory, and then the compensated trajectory is processed by the zero-phase low-pass filter and introduced into the Z-axis controller to drive the diamond tool to complete the workpiece machining;The surface topography error, surface roughness and machining efficiency of the machined workpiece are evaluated;The application can realize ultra-precision turning of microstructure optical elements while considering high speed, high precision and high stability.

Description

Technical Field

[0001] This invention relates to the field of diamond turning technology, and in particular to a collaborative tool servo diamond turning method and system based on feedforward compensation. Background Technology

[0002] In ultra-precision turning, the collaborative tool servo system performs large-stroke motion through the main servo axis (such as the Z-axis), while the slave servo axis (such as the fast tool servo W-axis) compensates in real time for the residual tracking error of the main servo axis Z-axis in the cutting depth direction, thus taking into account both the machining requirements of large stroke and high precision. However, existing technologies still have the following shortcomings: First, when the target surface structure contains high-frequency components, due to the kinematic and dynamic characteristics of the Z-axis, once the spindle speed increases, the tracking error and vibration of the Z-axis will increase sharply, causing the compensation requirement of the W-axis to exceed its effective stroke. The system cannot operate stably at high speeds, severely restricting the improvement of machining efficiency. Second, the W-axis is affected by external disturbances, model uncertainties, and its own structural resonance during actual operation. Conventional feedback control is difficult to suppress these disturbances in a timely manner, and there is obvious phase lag and amplitude attenuation when tracking high-frequency compensation commands, resulting in insufficient compensation accuracy. Third, most existing methods focus on allocating the trajectory between the Z-axis and W-axis and performing local real-time compensation by the W-axis. There is a lack of a feedforward compensation mechanism that can pre-correct the target tool trajectory based on the overall error law of the entire "Z-axis + W-axis" macro-micro composite system before machining, making it difficult to further reduce the overall tracking error of the system. Therefore, how to achieve ultra-precision turning of microstructured optical components while simultaneously ensuring high speed, high precision, and high stability remains a key technical problem that urgently needs to be solved in this field. Summary of the Invention

[0003] To address the aforementioned technical problems, the technical solution adopted by this invention is as follows:

[0004] According to a first aspect of this application, a collaborative tool servo diamond turning method based on feedforward compensation is provided, the method comprising the following steps:

[0005] S100: Construct a master-slave cooperative tool servo system, configure cooperative motion relationship between the master servo axis Z-axis and the slave servo axis W-axis, and design a composite controller for the W-axis including a disturbance observer, a high-bandwidth feedback controller, and a W-axis inverse model controller; at the same time, design a zero-phase low-pass filter based on the kinematic and dynamic constraints of the Z-axis to decompose the tool trajectory in the cutting depth direction into a low-frequency trajectory executed by the Z-axis and a high-frequency compensation trajectory for the difference between the ideal trajectory tracked in real time by the W-axis and the actual trajectory of the Z-axis.

[0006] S200: The frequency sweep trajectory is sent to drive the Z-axis and W-axis to operate in coordination. Error data between the actual position of the macro-micro system composed of the composite displacement of the Z-axis and W-axis and the ideal position obtained by interpolation of the principal axis angle is collected. Based on the error data, a data-driven feedforward compensation model for macro-micro systems is established, which can predict the overall tracking error of the macro-micro system according to the ideal position or trajectory characteristics.

[0007] S300: Based on the target surface structure parameters and the geometric parameters of the diamond tool, the target tool trajectory is planned. The feedforward compensation amount output by the feedforward compensation model for the macro-micro system is superimposed on the target tool trajectory to obtain the compensated trajectory. The compensated trajectory is then processed by the zero-phase low-pass filter and imported into the Z-axis controller. At the same time, the W-axis is controlled to track the difference between the ideal position and the actual position of the macro-micro system to drive the diamond tool to complete the workpiece machining.

[0008] S400 evaluates the surface morphology error, surface roughness, and processing efficiency of the processed workpiece.

[0009] According to another aspect of this application, a collaborative tool servo diamond turning system based on feedforward compensation is also provided, comprising:

[0010] The system construction module is used to build a master-slave cooperative tool servo system. It configures the cooperative motion relationship between the master servo axis Z-axis and the slave servo axis W-axis, and designs a composite controller for the W-axis that includes a disturbance observer, a high-bandwidth feedback controller, and a W-axis inverse model controller. At the same time, based on the kinematic and dynamic constraints of the Z-axis, a zero-phase low-pass filter is designed to decompose the tool trajectory in the cutting depth direction into a low-frequency trajectory executed by the Z-axis and a high-frequency compensation trajectory for the difference between the ideal trajectory tracked in real time by the W-axis and the actual trajectory of the Z-axis.

[0011] The feedforward compensation model construction module is used to send out the frequency sweep trajectory to drive the Z-axis and W-axis to run in coordination, collect error data between the actual position of the macro-micro system composed of the composite displacement of the Z-axis and W-axis and the ideal position obtained by interpolation of the principal axis angle, and establish a data-driven feedforward compensation model for macro-micro systems that can predict the overall tracking error of the macro-micro system according to the ideal position or trajectory characteristics.

[0012] The collaborative machining module is used to plan the target tool trajectory based on the target surface structure parameters and the geometric parameters of the diamond tool. It superimposes the feedforward compensation amount output by the feedforward compensation model for the macro-micro system onto the target tool trajectory to obtain the compensated trajectory. The compensated trajectory is then processed by the zero-phase low-pass filter and imported into the Z-axis controller. At the same time, it controls the W-axis to track the difference between the ideal position and the actual position of the macro-micro system to drive the diamond tool to complete the workpiece machining.

[0013] The evaluation module is used to evaluate the surface morphology error, surface roughness, and processing efficiency of the processed workpiece.

[0014] The present invention has at least the following beneficial effects:

[0015] The present invention provides a collaborative tool servo diamond turning method based on feedforward compensation. First, by integrating a composite controller on the W-axis, including a disturbance observer, a high-bandwidth feedback controller, and a W-axis inverse model controller, the dynamic performance of the servo axis is systematically improved from multiple dimensions. The high-bandwidth feedback controller suppresses resonance and provides a basic high-precision closed-loop response. The disturbance observer cancels external disturbances and model uncertainties in real time. The W-axis inverse model controller is used to pre-compensate for the dynamic hysteresis and amplitude attenuation of the W-axis closed-loop system, thereby improving the tracking response capability and trajectory reproduction accuracy of the W-axis to high-frequency compensated trajectories. Compared with the method of using only feedback control or conventional feedforward compensation, this composite control structure can more fully improve the dynamic tracking performance of the W-axis under high-frequency motion conditions. Secondly, by using a zero-phase low-pass filter designed based on Z-axis kinematics and dynamic constraints to decompose the tool trajectory in the frequency domain, the Z-axis only needs to execute low-frequency trajectories within its physical capabilities, while the W-axis focuses on compensating for high-frequency residuals. This division of labor reduces the burden on the Z-axis in tracking high-frequency commands, reduces vibration and tracking error caused by commands exceeding the dynamic capabilities of the Z-axis, and helps improve the stability of coordinated motion under high spindle speeds, effectively breaking through the bottleneck of machining efficiency. Thirdly, through frequency sweep training and machine learning methods, a data-driven feedforward compensation model for the entire "Z-axis + W-axis" macro-micro system is established. This model can learn and predict the overall error law of the macro-micro system under a specific trajectory, thereby achieving "pre-correction" of the target tool trajectory before machining. This allows the system to pre-compensate the target tool trajectory before machining, forming a complementary dual error elimination mechanism with the real-time compensation of the W-axis during machining, significantly improving the overall tracking accuracy of the system. Finally, this invention organically integrates the above-mentioned control, modeling, and process links into a complete technical closed loop, enabling ultra-precision turning of microstructure optical components while simultaneously achieving high speed, high precision, and high stability. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart of a collaborative tool servo diamond turning method based on feedforward compensation provided in an embodiment of the present invention;

[0018] Figure 2 This is a schematic diagram of the hardware integration of a master-slave cooperative tool servo system based on feedforward compensation, provided in an embodiment of the present invention.

[0019] Figure 3 This is a schematic diagram of a collaborative tool servo system based on feedforward compensation.

[0020] Figure 4 This is a schematic diagram of the W-axis controller structure;

[0021] Figure 5 This is a schematic diagram of the open-loop frequency response of the W-axis provided in an embodiment of the present invention;

[0022] Figure 6 This is a schematic diagram comparing the W-axis trajectory tracking errors under different frequency sinusoidal disturbance signals with and without a disturbance observer, as provided in an embodiment of the present invention.

[0023] Figure 7 This is a schematic diagram comparing the W-axis trajectory tracking errors under the action of a triangular wave disturbance signal with and without a disturbance observer, as provided in an embodiment of the present invention.

[0024] Figure 8 This is a schematic diagram of the Z-axis closed-loop frequency response curve provided in an embodiment of the present invention;

[0025] Figure 9 This is a schematic diagram of the W-axis closed-loop frequency response curve provided in an embodiment of the present invention;

[0026] Figure 10 This is a three-dimensional schematic diagram of the target surface shape of the lens array provided in an embodiment of the present invention;

[0027] Figure 11 A top view of the target surface of the lens array and a schematic diagram of discrete points of the tool path provided in an embodiment of the present invention;

[0028] Figure 12 This is a schematic diagram showing the comparison of the reference tool trajectory, Z-axis tracking results, W-axis tracking results, and W-axis tracking error of the collaborative tool servo system under different spindle speeds in the cutting depth direction, as provided in an embodiment of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] It should be noted that, based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Furthermore, this device and / or practice the method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.

[0031] The following will refer to Figure 1 The flowchart shown is a collaborative tool servo diamond turning method based on feedforward compensation, which introduces a collaborative tool servo diamond turning method based on feedforward compensation.

[0032] The collaborative tool servo diamond turning method based on feedforward compensation includes the following steps:

[0033] S100: Construct a master-slave cooperative tool servo system, configure cooperative motion relationship between the master servo axis Z-axis and the slave servo axis W-axis, and design a composite controller for the W-axis including a disturbance observer, a high-bandwidth feedback controller, and a W-axis inverse model controller; at the same time, design a zero-phase low-pass filter based on the kinematic and dynamic constraints of the Z-axis to decompose the tool trajectory in the cutting depth direction into a low-frequency trajectory executed by the Z-axis and a high-frequency compensation trajectory for the difference between the ideal trajectory tracked in real time by the W-axis and the actual trajectory of the Z-axis.

[0034] The core of this step is to build a "macro-micro composite, master-slave collaborative" hardware and control architecture and to rationally allocate tasks for complex tool trajectories. First, a master-slave collaborative tool servo system is constructed, consisting of a master servo axis (Z-axis) and a slave servo axis (W-axis) connected in series. Based on this, a composite controller integrating a disturbance observer, a high-bandwidth feedback controller, and a W-axis inverse model controller is designed specifically for the W-axis to systematically improve its high-frequency dynamic response and disturbance rejection capabilities. Simultaneously, to fully leverage the advantages of the Z-axis's large stroke and the W-axis's high bandwidth, a zero-phase low-pass filter is designed based on the Z-axis's kinematics (maximum velocity, acceleration) and dynamic constraints. This filter divides the complex tool trajectory along the cutting depth direction into two parts: the low-frequency portion with gradual changes and large stroke is executed by the Z-axis; while the high-frequency residual portion, which the Z-axis cannot track and consists of the difference between the ideal trajectory and the actual Z-axis trajectory, serves as the compensation target command for the W-axis. This division of labor avoids vibration and errors caused by the Z-axis executing high-frequency commands beyond its capabilities from the outset.

[0035] Furthermore, the master-slave cooperative tool servo system constructed in step S100 includes:

[0036] The C-axis of a machine tool is used to drive the main rotational motion of the workpiece.

[0037] like Figure 2 As shown, the C-axis is the workpiece spindle, used to drive the workpiece in its main rotational motion. In practical implementation, the C-axis typically employs a high-precision pneumatic or hydrostatic spindle, equipped with a high-resolution circular encoder as the angle feedback element. The angle signal output by the circular encoder, after being subdivided by an interpolation unit, can obtain the workpiece's current rotational angular position in real time. Its arcsecond or even sub-arcsecond resolution provides a precise time base reference for subsequent toolpath planning and ideal position calculation.

[0038] The X-axis of the machine tool is used to achieve radial feed of the tool.

[0039] The X-axis is the radial feed axis, used to achieve the radial feed motion of the diamond tool along the workpiece. The X-axis is usually driven by a linear motor and equipped with a linear grating ruler to achieve fully closed-loop position feedback. During machining, the X-axis pushes the tool from the edge of the workpiece towards the center step by step according to the preset feed rate, achieving helical coverage of the workpiece end face.

[0040] The Z-axis and W-axis are installed in series in the depth of cut direction to jointly complete the tool feed in the depth of cut direction. The C-axis, X-axis and Z-axis are synchronously controlled by the machine tool multi-axis motion controller, and the W-axis moves in coordination with the machine tool axis through a composite controller, power amplifier and displacement feedback device.

[0041] The Z-axis is the main servo axis, installed in series with the W-axis in the cutting depth direction. Together, they complete the tool's feed motion along this direction. Specifically, the Z-axis is a large-stroke linear motion axis inherent to the machine tool itself, with the W-axis and its tool holder mounted on the slide. The fixed part of the W-axis is rigidly connected to the Z-axis slide, and its motion output end is equipped with a diamond tool. Thus, the final cutting depth position of the tool is the resultant of the superposition of the displacements of the Z-axis and W-axis. The Z-axis stroke can typically reach tens to hundreds of millimeters, but its response bandwidth is relatively low due to its own inertia and drive capability. The W-axis, on the other hand, uses a fast tool servo mechanism driven by smart materials such as piezoelectric ceramics or magnetostrictive materials. Its stroke is generally only tens of micrometers, but its response bandwidth can reach thousands of hertz, enabling it to perform extremely high-frequency reciprocating motion.

[0042] like Figure 3As shown, in the control architecture, the C-axis, X-axis, and Z-axis serve as the basic axes of the machine tool, and are uniformly controlled by the machine tool's multi-axis motion controller for synchronous interpolation and closed-loop control. The multi-axis motion controller coordinates the movement of each axis according to a strict timing relationship based on preset machining codes or trajectory instructions. The W-axis has an independent composite controller, which receives compensation instructions from the upper layer of the system, performs control calculations, and outputs a control signal. This signal is converted into an analog voltage by a digital-to-analog converter, and then driven by a power amplifier to produce displacement by the W-axis actuator. The output displacement of the W-axis is detected in real time by a built-in high-resolution displacement feedback device (such as a capacitive sensor or strain gauge sensor) and fed back to the composite controller to form a closed loop. Simultaneously, the actual displacement signal of the W-axis is also sent to the position synthesis link of the macro-micro system, added to the actual displacement of the Z-axis, to obtain the total actual displacement in the cutting depth direction, which is used for comparison with the ideal position to form the overall tracking error.

[0043] In this embodiment, the aforementioned hardware architecture balances the large stroke capability of the Z-axis and the high-frequency compensation capability of the W-axis. The large-stroke but low-bandwidth Z-axis and the small-stroke but high-bandwidth W-axis are mechanically connected in series but decoupled in control, enabling the entire system to possess both a wide range of motion capabilities and high-frequency dynamic compensation capabilities. High-precision angle feedback on the C-axis provides a position reference for trajectory calculation in the cutting depth direction and multi-axis synchronous control, while the X-axis ensures smooth propagation of the helical trajectory. The independent and dedicated control link for the W-axis—from the composite controller to the power amplifier to the displacement feedback—provides the hardware foundation for achieving sub-micron and even nanometer-level rapid tracking accuracy. This macro-micro composite, master-slave collaborative system architecture provides the hardware foundation for subsequent trajectory decomposition, feedforward compensation, and real-time collaborative machining. Furthermore, the composite controller includes:

[0044] The high-bandwidth feedback controller consists of a damping controller for suppressing the resonant mode of the W-axis micro-motion platform and a high-gain proportional-integral controller for reducing steady-state error and residual tracking error.

[0045] Furthermore, the transfer function of the damping controller ;in, The center angular frequency of the notch filter. and The damping coefficients, which determine the zero-point and pole-point characteristics of the notch filter, are also denoted as [value] in a subsequent specific embodiment. and ; s is a complex frequency variable.

[0046] The transfer function of the high-gain proportional-integral controller ;in, and These are the proportional gain and integral gain, respectively.

[0047] In this embodiment, the high-bandwidth feedback controller is the core feedback path of the W-axis closed-loop system, and it consists of a damping controller and a high-gain proportional-integral controller connected in series.

[0048] The damping controller is specifically designed to address the resonant modes of the mechanical structure of the W-axis micro-motion platform. Because the W-axis fast-tool servo mechanism uses flexible drive components such as piezoelectric ceramics, its mechanical structure exhibits significant resonance peaks near specific frequencies. For example, in one specific embodiment, the W-axis platform has a high-Q resonance peak at approximately 3215Hz. If this resonance peak is not suppressed, it will severely limit the gain margin of the feedback controller, leading to system oscillations or even instability. The damping controller is implemented using a notch filter, and its transfer function is:

[0049] ;

[0050] Where, ω n ζ is the center angular frequency of the notch filter. z and ζ p These are the damping coefficients at the zero and pole points, respectively. In practical implementation, the open-loop frequency response curve along the W axis is first obtained through a frequency sweep test, as shown below. Figure 5 As shown, the exact location of the resonance peak is identified. Then, ω n Set it to the angular frequency corresponding to the resonance frequency, and select a very small ζ. z The value is chosen to generate an extremely narrow notch at the resonant frequency, while selecting an appropriate ζ. p The value controls the bandwidth of the notch filter and the range of its influence on the phase of surrounding frequencies. In a preferred embodiment, the parameter is set to: ω n 2 =4.08×10 8 , ζ z =0.008, ζ p =0.707.

[0051] A high-gain proportional-integral (PI) controller is used to ensure the system's steady-state tracking accuracy and low-frequency stiffness. Its transfer function is:

[0052] ;

[0053] Where, k p For proportional gain, k i The integral gain is the proportional term, which provides an instantaneous response proportional to the instantaneous error, while the integral term eliminates steady-state error by accumulating the error. In practice, the tuning of the PI parameter must be performed under the premise that the damping controller has suppressed resonance. The optimal parameter search can be achieved by constructing a parameter optimization model based on frequency response data. The optimization objective is to make the amplitude-frequency response of the closed-loop transfer function as flat as possible within the target operating bandwidth. Its objective function can be expressed as:

[0054] ;

[0055] Where N is the set of controller parameters to be optimized, ω d Let T(·) be the upper limit of the target operating bandwidth, and T(·) be the closed-loop transfer function. The optimal parameters that make the response of the closed-loop system most flat within its bandwidth can be solved using optimization methods such as genetic algorithms or gradient descent. In a preferred embodiment, the parameters are set as follows: k p =50,k i =0.01.

[0056] In this embodiment, as Figure 4 As shown, the high-bandwidth feedback controller, through the series design of a damped notch filter and a high-gain PI controller, first suppresses the mechanical resonance mode, thereby improving the stability margin of the feedback controller and creating stable conditions for applying high gain subsequently. The high-gain PI controller then further increases the response bandwidth of the closed-loop system, significantly reducing tracking errors in the mid-to-low frequency range. The synergistic effect of these two controllers enables the W-axis closed-loop system to achieve dynamic response capabilities and tracking accuracy far superior to conventional feedback control while ensuring stability.

[0057] The disturbance observer, which includes the nominal model inverse and a low-pass filter, is used to estimate external disturbances and model uncertainties online and feed the estimates back to the control input for compensation.

[0058] In this embodiment, the disturbance observer is used to estimate and compensate for external disturbances and model uncertainties online. Its working principle is to convert the output difference between the actual controlled object and the nominal model into the total disturbance applied to the system and cancel it out through the feedforward channel.

[0059] The implementation of the perturbation observer involves three core steps. The first is the construction of the nominal model inverse. The nominal model P... n (s) is a mathematical description of the controlled object along the W-axis in its ideal or nominal state. In one embodiment, the nominal object along the W-axis adopts a second-order continuous-time model, and its transfer function is:

[0060] ;

[0061] Inverting the nominal model yields P. n -1 (s). In actual control, the actual output displacement y of the W-axis is transmitted through P. n -1 (s) is mapped back to the input side, and then the difference is made with the actual control input u to estimate the equivalent disturbance, which includes external disturbances and model uncertainties.

[0062] Secondly, there is the design of the low-pass filter. Because the nominal model inverse P... n -1(s) often exhibits differential characteristics, amplifying high-frequency measurement noise. Furthermore, to ensure the physical realizability and stability of the entire observer loop, a low-pass filter Q(s) must be connected in series in the disturbance estimation channel. Q(s) can be expressed as:

[0063] ;

[0064] Where τ is the time constant and n is the filter order. The choice of τ requires a trade-off between disturbance suppression bandwidth and noise sensitivity: the smaller τ is, the faster the observer response, but the more significant the noise amplification; the larger τ is, the better the noise suppression, but the lower the high-frequency disturbance compensation capability. In a preferred embodiment, a second-order form is used, τ = 0.00013s, corresponding to a cutoff frequency of approximately 1224Hz.

[0065] Finally, there is the disturbance estimation and compensation stage. The disturbance estimate after Q(s) filtering is superimposed on the control input in the form of negative feedback, that is, the estimate is subtracted from the controller output, so as to cancel the disturbance before it actually affects the controlled object.

[0066] In this embodiment, the introduction of the disturbance observer is equivalent to establishing a "virtual" forward compensation channel for the W-axis control system. This disturbance observer can estimate factors such as external cutting force changes, friction fluctuations, parameter perturbations, and some unmodeled dynamics as equivalent input disturbances, and reduce their impact on W-axis tracking performance through the compensation channel. Figure 6 and Figure 7 The experimental comparison shows that after adding the disturbance observer, the peak and valley values ​​and root mean square values ​​of the W-axis tracking error are significantly reduced, whether it is a sinusoidal disturbance or a triangular wave disturbance containing richer high-frequency components. Especially under the condition of a 600Hz triangular wave disturbance, the peak value of the tracking error is reduced by 65.70% and the root mean square value is reduced by 55.40%, which fully demonstrates the strong robustness of the design to complex disturbance signals.

[0067] The W-axis inverse model controller, obtained by identifying and inverting the W-axis closed-loop transfer function, is used to pre-correct the dynamic lag and amplitude attenuation of the W-axis closed-loop system, thereby improving its ability to track high-frequency compensated trajectories.

[0068] Furthermore, the construction of the W-axis inverse model controller includes the following steps:

[0069] S110 uses a frequency sweep training signal to drive the W-axis motion, collects its input signal and output displacement response, and identifies and establishes the W-axis closed-loop transfer function. ; s is a complex frequency variable.

[0070] S111, for Inverse model to obtain the W-axis inverse model .

[0071] S112, the Connected in series to the W-axis command input, making the adjusted control input... ;in, The desired compensation trajectory is shown on the W-axis.

[0072] In this embodiment, the W-axis inverse model controller is used to pre-correct the dynamic lag and amplitude attenuation of the W-axis closed-loop system itself, thereby further improving its ability to track high-frequency compensated trajectories.

[0073] The construction of the inverse model controller consists of three steps. The first step is system identification. The W-axis motion is driven using a swept-frequency training signal. The input signal uw(t) and output displacement response yw(t) of the W-axis are acquired. Through system identification algorithms such as Fourier transform or subspace identification, the frequency response data of the W-axis closed-loop input-output relationship are obtained and fitted into a closed-loop transfer function Gw(s), which has the following form:

[0074] ;

[0075] The second step is model inversion. The identified Gw(s) is mathematically inverted to obtain the W-axis inverse model:

[0076] ;

[0077] Because physical systems typically have low-pass characteristics, the result obtained by direct inversion may contain leading elements and cannot be directly implemented physically. In practice, Ginv(s) needs to be regularized, for example by adding a high-frequency pole much higher than the operating bandwidth, making it a strictly regular rational function that is easier to implement digitally.

[0078] The third step is feedforward integration. The obtained Ginv(s) is connected in series with the W-axis command input. When the desired compensation trajectory command Rw(s) is given, the actual control input after inverse model adjustment is:

[0079] ;

[0080] This is equivalent to "pre-distorting" the command signal, ensuring that it is precisely restored to the original desired trajectory after passing through the W-axis closed-loop system. In one embodiment, the W-axis controller is implemented using discrete control, with a sampling period Ts = 2 × 10⁻⁶. -5 s corresponds to a sampling frequency of 50kHz. The inverse model is transformed from the continuous domain to the discrete domain through a bilinear transformation.

[0081] In this embodiment, the W-axis inverse model controller addresses signal distortion caused by the inherent dynamic characteristics of the system. The high-bandwidth feedback controller, disturbance observer, and W-axis inverse model controller improve the high-frequency tracking performance of the W-axis from three aspects: closed-loop response, disturbance rejection compensation, and dynamic pre-compensation, respectively. By pre-constructing the inverse of the system's dynamics and implementing pre-compensation at the command input, it effectively eliminates tracking distortion caused by amplitude attenuation and phase lag in the W-axis closed-loop system when tracking high-frequency signals, enabling the W-axis to reproduce high-frequency compensated trajectory commands with higher fidelity. The three controllers work together to construct a complete control system for W-axis high-frequency micro / nano compensated motion from the three dimensions of feedback, disturbance rejection, and feedforward.

[0082] Furthermore, the low-frequency tool trajectory output by the zero-phase low-pass filter designed in step S100 Represented as:

[0083] ;

[0084] in, Let be the component of the trajectory to be decomposed along the cutting depth direction. The impulse response of a zero-phase low-pass filter. This indicates that the sequence is reversed;

[0085] The cutoff frequency of the zero-phase low-pass filter satisfies the following constraint to ensure that the decomposed low-frequency trajectory does not exceed the physical limit of the Z-axis:

[0086] ;

[0087] ;

[0088] in, The velocity along the Z-axis; The acceleration along the Z-axis; and The maximum permissible velocity and acceleration along the Z-axis. This is the filter cutoff frequency. The highest frequency of the Z-axis operating bandwidth. For Z-axis motion error, This represents the maximum permissible error along the Z-axis.

[0089] In this embodiment, the zero-phase low-pass filter plays a crucial role in trajectory frequency domain decomposition. Its function is to decompose the complex tool trajectory along the cutting depth direction into a low-frequency trajectory executed along the Z-axis and a high-frequency compensated trajectory executed along the W-axis. Unlike conventional low-pass filters, the zero-phase filter removes high-frequency components without introducing any phase distortion into the retained low-frequency signal, thus ensuring that the time positioning accuracy of the low-frequency trajectory remains unaffected.

[0090] Zero-phase low-pass filtering is achieved through bidirectional filtering and time reversal. Let the component of the trajectory to be decomposed along the cutting depth direction be... The impulse response of the selected conventional low-pass filter is The low-frequency tool trajectory after zero-phase filtering The calculation process is as follows:

[0091] ;

[0092] in, This represents the convolution operation. This indicates that the sequence is reversed in time (i.e., the sequence is reversed from beginning to end). The impulse response of a conventional low-pass filter is used. Zero-phase filtering is achieved through forward filtering, time reversal, reverse filtering, and reversal again.

[0093] In practice, this operation is performed in four steps:

[0094] The first step is forward filtering. This involves filtering the original trajectory sequence... With filter impulse response Perform convolution to obtain intermediate results At this point, the high-frequency components of the signal are attenuated, but phase lag related to the phase characteristics of the filter is introduced.

[0095] The second step is time reversal. The forward-filtered sequence... Reverse the sequence by flipping the first and last parts to obtain the inverted sequence. .

[0096] The third step is reverse filtering. This involves reversing the sequence... Again with the same filter impulse response Perform convolution to obtain The second filtering further attenuates the remaining high-frequency components, and because it is performed in the time-reversal domain, the phase shift it introduces is in the opposite direction to the phase shift of the first filtering.

[0097] Step four, reverse it again. By performing time reversal again, the final low-frequency trajectory is obtained. After two phase shifts in opposite directions cancel each other out, the output signal... The theoretical phase distortion is zero at all frequencies, preserving only the amplitude attenuation characteristics of the filter.

[0098] In practical digital control systems, the above operations are performed in the form of discrete-time sequences. In one specific embodiment, the sampling period of the W-axis controller is... The corresponding sampling frequency is 50kHz. The trajectory data is also discretized at this sampling rate, and the convolution operation is implemented using a finite impulse response digital filter. To ensure filtering effectiveness, the filter order needs to be reasonably selected based on the cutoff frequency and transition band requirements, typically between tens and hundreds of orders.

[0099] The core design parameter of a zero-phase low-pass filter is the cutoff frequency. . The choice of [aspect] directly determines the "content" of the low-frequency trajectory allocated to the Z-axis, and also determines the amount of high-frequency compensation left for the W-axis. If If the Z-axis is selected too high, it will be required to track high-frequency motions beyond its physical capabilities, leading to increased vibration and errors; if selected too low, the W-axis will bear excessive compensation travel, potentially exceeding its effective operating range. Therefore, An optimal balance must be achieved between the capability boundaries of the Z-axis and W-axis.

[0100] In this embodiment, the selection of the cutoff frequency is formalized into the following multi-constraint optimization problem:

[0101] The first type of constraint is the kinematic constraint. The low-frequency trajectory obtained after zero-phase filtering... velocity at any given moment and acceleration It must not exceed the physical limits that the Z-axis hardware can withstand:

[0102] ;

[0103] in, and These represent the maximum permissible speed and maximum acceleration of the Z-axis drive system, respectively. In practical implementation, this can be achieved by... Numerical difference is used to obtain and The time-domain sequence is obtained, and the maximum absolute value of the sequence is extracted. , Perform a comparison and verification.

[0104] The second type of constraint is the frequency domain constraint. ; Filter cutoff frequency It should not exceed the operating bandwidth limit of the Z-axis servo system. The closed-loop frequency response of the Z-axis typically exhibits low-pass characteristics, such as... Figure 8 and Figure 9As shown, the closed-loop frequency response curves for the Z-axis and W-axis are presented respectively. By comparing the closed-loop frequency responses of the Z-axis and W-axis, it can be seen that the Z-axis is suitable for executing low-frequency trajectories along the cutting depth direction, while the W-axis has a higher response bandwidth and is more suitable for high-frequency residual compensation. This verifies that the master-slave collaborative division of labor in this invention, using a zero-phase low-pass filter to perform frequency domain decomposition of the trajectory and having the Z-axis execute the low-frequency trajectory while the W-axis executes the high-frequency compensation trajectory, is reasonable. Specifically, the Z-axis closed-loop frequency response curve shows... The characteristic point is approximately 136.990 Hz, which can serve as one of the important bases for selecting the cutoff frequency of a zero-phase low-pass filter.

[0105] The third type of constraint is the accuracy constraint. This refers to the actual tracking error of the Z-axis when executing low-frequency trajectories. It must be within the allowable error budget. This error can be estimated using the Z-axis closed-loop transfer function and the spectrum of the input trajectory, or obtained through actual measurement. It should satisfy: ;in, This represents the maximum permissible error allocated to the Z-axis component based on machining accuracy requirements.

[0106] In practical engineering applications, a conservative value can be initially selected based on the bandwidth characteristics of the Z-axis. Then, the above constraints are checked one by one. If the kinematic constraints are not satisfied, the kinematic constraints are reduced. The goal is to reduce the high-frequency components of the trajectory until both velocity and acceleration are within acceptable limits. If the travel or bandwidth of the W-axis cannot meet the remaining high-frequency compensation requirements, iterative adjustments are made at the system design level. This constraint-driven design process ensures the engineering feasibility of the trajectory decomposition results.

[0107] In this embodiment, the introduction and constraint design of a zero-phase low-pass filter solves the coordination problem between the master and slave servo axes from the source. The implementation of bidirectional filtering plus time reversal ensures that the low-frequency trajectory maintains zero-phase characteristics while filtering out high-frequency components, guaranteeing precise temporal alignment between the Z-axis motion and the original trajectory, and avoiding trajectory distortion caused by phase lag in conventional filters. Furthermore, the multi-constraint design based on Z-axis kinematic limits, frequency bandwidth, and tracking accuracy allows the trajectory decomposition process to simultaneously consider signal frequency characteristics and hardware execution capabilities. Through this design, the decomposed low-frequency trajectory is within the stable execution range of the Z-axis, and the remaining high-frequency residuals are compensated by the W-axis, thereby reducing the high-frequency tracking burden on the Z-axis and avoiding increased vibration and error caused by commands exceeding the Z-axis dynamic capabilities, thus providing support for stable collaborative operation at high spindle speeds. S200: The frequency sweep trajectory is sent to drive the Z-axis and W-axis to operate in coordination. Error data between the actual position of the macro-micro system, which is composed of the composite displacement of the Z-axis and W-axis, and the ideal position obtained by interpolation of the principal axis angle is collected. Based on the error data, a data-driven feedforward compensation model for the macro-micro system is established, which can predict the overall tracking error of the macro-micro system according to the ideal position or trajectory characteristics.

[0108] Furthermore, step S200 includes the following steps:

[0109] S210: The actual Z-axis position and the actual W-axis position are read by the Z-axis position feedback device and the W-axis position feedback device respectively, and the actual positions read by the Z-axis position feedback device and the W-axis position feedback device are superimposed to obtain the total actual displacement of the macro-micro system in the cutting depth direction.

[0110] The total actual displacement of the macro-micro system in the cutting depth direction is the superposition of the actual displacements of the Z-axis and W-axis. In practice, the Z-axis position feedback device and the W-axis position feedback device, such as an optical grating ruler, output the actual position signals of their respective moving parts in real time with a high sampling rate. The Z-axis optical grating ruler is usually a linear grating with a resolution down to the nanometer level. It is mounted on the Z-axis guide rail of the machine tool and is used to measure the absolute displacement of the Z-axis slide relative to the machine tool bed. The W-axis position feedback device is usually a capacitive sensor or a resistive strain gauge sensor, integrated inside the fast tool servo mechanism, and is used to measure the micro-displacement of the W-axis output end relative to its fixed end.

[0111] The displacement signals from the two channels, after signal conditioning and analog-to-digital conversion, undergo strict time alignment and superposition in the digital controller. Let the Z-axis grating ruler reading be... The W-axis displacement sensor reading is Then, at that moment, the total actual displacement of the macro-micro system in the cutting depth direction is:

[0112] ;

[0113] It should be noted that the sampling clocks of the Z-axis and W-axis must be synchronized with the sampling clock of the main spindle C-axis to ensure that subsequent comparisons between the ideal and actual positions are performed on the same time reference. In one embodiment, the sampling frequency of the W-axis controller is 50kHz, and the position data of the Z-axis and C-axis are also acquired and interpolated at this frequency, thereby achieving strict synchronization of multi-axis data.

[0114] By acquiring and simultaneously superimposing the actual displacements along the Z-axis and W-axis, a complete description of the tool's true motion trajectory in the cutting depth direction was obtained. This composite displacement signal, which integrates macro and micro motion information, serves as the data foundation for subsequent calculations of the system's overall tracking error, and its accuracy directly determines the effectiveness of the established feedforward compensation model.

[0115] S220 reads the actual position of the C-axis through the spindle position feedback device and obtains the ideal position of the macro-micro system in the cutting depth direction through interpolation calculation.

[0116] The ideal position of the macro-micro system in the cutting depth direction is calculated using the C-axis angle signal as a spatial reference through geometric interpolation. In practical implementation, a high-precision circular encoder is installed on the C-axis, which can output the workpiece's rotational angular position in real time. Let the C-axis angle read by the circular encoder at a certain time t be... Combined with the radial position of the tool at this time (Determined by the X-axis position) and the target surface shape function of the surface to be processed. Then, the ideal target position of the tool in the cutting depth direction at that moment can be calculated by interpolation:

[0117] ;

[0118] in, This is a depth-of-cutting mapping function based on target surface structure parameters and tool geometry parameters. In practical implementation, since the angle values ​​output by the circular grating are discrete in time, time-dimensional interpolation may be required to accurately align with the sampling times of the Z and W axes. Commonly used interpolation methods include linear interpolation and cubic spline interpolation, which are selected based on the required accuracy and computational resources.

[0119] In this embodiment, the angle signal of the C-axis circular grating is used as the absolute spatial reference for calculating the ideal position. This fully utilizes the high resolution characteristics of the circular grating at the arcsecond or even sub-arcsecond level, ensuring that the ideal target position at every instant has extremely high spatial certainty. This position setting method based on the spindle angle guarantees a strict synchronization between the tool movement and the workpiece rotation, laying the foundation for the accuracy of subsequent error calculations.

[0120] S230, the difference between the ideal position and the total actual displacement is used to obtain the overall tracking error of the macro-micro system.

[0121] The ideal position obtained by S220 is compared with the total actual displacement obtained by S210 at the same time. The difference between the two is the overall tracking error of the macro-micro system. Let there be a sampling time t, and the overall tracking error be... for:

[0122] ;

[0123] Performing this operation at all sampling times yields the error time series of the entire sweep trajectory. This error signal includes the Z-axis tracking error, the W-axis tracking error, and all error components resulting from their coupling effect, representing a comprehensive system-level error. To construct a high-quality training dataset, the sweep trajectory should cover multiple frequency components and amplitude combinations within the system's operating frequency range, fully stimulating the system's error characteristics under various operating conditions.

[0124] In this embodiment, the overall tracking error of the entire macro-micro system is used as the modeling object, rather than modeling the errors of the Z-axis and W-axis separately. This system-level error definition method includes all factors affecting the final machining accuracy, such as macro-micro coupling effects, mechanical backlash, and sensor noise, enabling the subsequently established feedforward compensation model to reflect the full picture of errors under actual machining conditions.

[0125] S240, based on the ideal macro-micro system position-measured macro-micro system error dataset, an offline machine learning model is trained to establish the mapping relationship between the machining trajectory in the cutting depth direction and the overall tracking error, thereby forming the data-driven feedforward compensation model for macro-micro systems.

[0126] Based on the "ideal macro-micro system position - measured macro-micro system error" dataset accumulated by S230, a machine learning model is trained offline to establish the mapping relationship between the machining trajectory in the cutting depth direction and the overall tracking error, that is, a feedforward compensation model for macro-micro systems.

[0127] In practical implementation, the input features of the model are usually selected as ideal locations. The model output label is a combination of its historical and future values, or a selection of statistical features describing the frequency, amplitude, rate of change, and other characteristics of the current trajectory segment, to fully characterize the trajectory state at the current moment. Or its equivalent compensation (inverted). Optional machine learning models include, but are not limited to, Gaussian process regression, support vector regression, or shallow neural networks. After model training, its mathematical form can be abstracted as a mapping function. ,satisfy:

[0128] ;

[0129] in, This is the feedforward compensation amount. In step S300, the model can directly receive the target tool trajectory as input and output the corresponding feedforward compensation sequence, which is used to pre-correct the original target trajectory.

[0130] By combining frequency sweep training and machine learning, this invention addresses the challenge of describing the overall error of macro- and micro-systems using precise physical models through a data-driven approach. The trained model learns and captures complex nonlinear error patterns hidden within the data, enabling error prediction of processing trajectories with similar trajectory characteristics to the training data. Compared to traditional error compensation methods based on physical models, this data-driven paradigm eliminates the need for tedious individual calibration and analytical modeling of error sources in each component of the system, simplifying the implementation process while often achieving higher compensation accuracy. Furthermore, the offline training and online application architecture ensures that the feedforward compensation model does not consume additional computing resources during processing, guaranteeing the determinism of the real-time control system.

[0131] S300: Based on the target surface structure parameters and the geometric parameters of the diamond tool, the target tool trajectory is planned. The feedforward compensation amount output by the feedforward compensation model for the macro-micro system is superimposed on the target tool trajectory to obtain the compensated trajectory. The compensated trajectory is then processed by the zero-phase low-pass filter and imported into the Z-axis controller. At the same time, the W-axis is controlled to track the difference between the ideal position and the actual position of the macro-micro system to drive the diamond tool to complete the workpiece machining.

[0132] Furthermore, step S300 includes the following steps:

[0133] S310, using the target surface structure parameters and diamond tool geometric parameters, plans the target tool trajectory in polar coordinates through equal-angle discretization and Z-axis projection; the component of the target tool trajectory in polar coordinates along the cutting depth direction is expressed as... .

[0134] This step involves planning a complete tool motion path in polar coordinates based on the target shape parameters of the microstructure surface to be machined and the geometric parameters of the diamond tool used.

[0135] In practice, the objects being processed are typically the surfaces of rotationally symmetric or periodically arranged microstructured optical elements, such as... Figure 10 and Figure 11The microlens array is shown. First, the target surface morphology is expressed as a mathematical function. Let the radial position be ρ and the angular position be θ in the workpiece polar coordinate system. Then, the morphology height of the target surface along the cutting depth direction can be expressed as a function. At the same time, it is also necessary to consider the influence of the geometric parameters of the diamond tool—including the tip radius, rake angle, clearance angle, and cutting edge radius—on the actual cutting point position, and establish a tool geometric compensation model.

[0136] Trajectory planning is performed using equal-angle discretization and Z-axis projection, i.e., at a constant rotational speed ω along the C-axis. c Under rotational conditions, the X-axis feeds at a speed f x The machining path is formed by advancing radially from the outer edge of the workpiece towards the center, creating an Archimedean spiral. Discrete sampling is performed along this path at fixed time intervals Δt. Let the index of the discrete point be n. Then, at the nth discrete point, the workpiece rotation angle position θ(n), the tool radial position ρ(n), and the target position y in the depth of cut direction are determined. d (n) are respectively:

[0137] ;

[0138] ;

[0139] ;

[0140] Among them, R w Let L be the workpiece radius, and L(·) be the cutting depth mapping function that combines the surface topography function S(θ,ρ) with the tool geometry compensation model. In actual operation, for surfaces with discrete periodic characteristics such as microlens arrays, it is necessary to divide the trajectory segment according to the sub-aperture boundary of each microlens unit to ensure that the cutting depth variation of the tool in each unit corresponds precisely to the surface shape of that unit.

[0141] The use of equal-angle discretization and Z-axis projection for trajectory planning in polar coordinates naturally adapts to the motion pattern of workpiece rotation and tool radial feed in diamond turning, ensuring precise synchronization between the tool path and workpiece rotation. Simultaneously, incorporating tool geometry parameters into the trajectory calculation effectively compensates for cutting point offsets caused by tool tip shape, fundamentally improving the theoretical accuracy of the target tool trajectory.

[0142] S320, the feedforward compensation amount predicted by the feedforward compensation model for macro-micro systems. The compensated trajectory is obtained by directly superimposing it onto the target toolpath. .

[0143] This step puts the feedforward compensation model for macro-micro systems trained in step S200 into practical use to pre-correct the target tool trajectory.

[0144] In practical implementation, the target tool trajectory sequence y obtained from S310 planning will be used. d (n) Input to the pre-trained feedforward compensation model. This model predicts the overall tracking error that the macro-micro system will generate at the current trajectory point based on its ideal position and surrounding trajectory characteristics, and outputs the inverted result as the feedforward compensation amount y. ff (n). Add the two at their corresponding discrete point indices n to obtain the compensated trajectory sequence:

[0145] ;

[0146] This calculation process is completed offline before machining, without consuming the computing resources of the real-time controller. It should be noted that the training trajectory of the feedforward compensation model should match the characteristics of the actual machining trajectory. If the surface structure type of the target workpiece differs significantly from the training sweep trajectory, more diverse trajectory patterns can be introduced during the model training phase, or the generalization performance of the model can be improved through transfer learning, incremental learning, or other methods.

[0147] The introduction of feedforward compensation enables "proactive prevention" rather than "post-mortem correction" of machining errors. By reverse-correcting the target trajectory based on the overall error patterns already exposed by the system before formal cutting, it is equivalent to pre-setting a "counter-error" signal with the same magnitude but opposite direction as the expected error. This global pre-correction strategy complements the real-time local compensation of the W-axis during subsequent machining in both time and space, significantly improving the overall tracking accuracy of the system.

[0148] S330, Frequency domain decomposition is performed using a zero-phase low-pass filter to obtain a low-frequency trajectory executed along the Z-axis.

[0149] This step will compensate for the trajectory y after feedforward pre-correction. c (n) The zero-phase low-pass filter designed in step S100 is fed into the filter and decomposed into a low-frequency trajectory executed on the Z-axis and a high-frequency compensation trajectory executed on the W-axis.

[0150] In practical implementation, the zero-phase low-pass filter is implemented as described in step S100, using a bidirectional filtering method with time reversal, and its output low-frequency trajectory z d (n) is:

[0151] ;

[0152] Where h is the impulse response of the zero-phase low-pass filter, and R represents the inversion of the sequence. The filter's cutoff frequency f cut The maximum permissible speed v along the Z-axis has been determined in S100. max,zMaximum permissible acceleration a max,z Working bandwidth f max,z and maximum permissible error e max,z Constraints are predetermined.

[0153] At the digital implementation level, the impulse response h of the filter needs to be pre-designed and stored as a coefficient table for a finite impulse response filter. For each machining trajectory sequence, the above convolution operation is performed offline. After filtering, z d (n) The reference input command for the Z-axis controller is sent to the machine tool's multi-axis motion controller; the remaining high-frequency residual—the difference between the compensated trajectory and the low-frequency trajectory—is used as the desired compensated trajectory R for the W-axis. w (n), to be tracked in real time in S340 later.

[0154] A key design element of this step is the cascading execution of feedforward pre-correction and frequency domain decomposition. c (n) Simultaneously includes target surface information and system error pre-compensation information, which are uniformly subjected to zero-phase filtering. This ensures that the low-frequency error pre-compensation is executed along with the large stroke of the Z-axis, while the high-frequency error pre-compensation is handled by the W-axis in the real-time compensation stage. This "superposition followed by decomposition" processing order guarantees the complete transmission and accurate implementation of the feedforward compensation across the entire frequency domain.

[0155] S340, the W-axis uses the difference between the ideal position in the cutting depth direction of the macro-micro system and the total actual displacement synthesized from the actual positions of the Z-axis and W-axis as a command to perform real-time tracking compensation.

[0156] This step constitutes the closed loop of macro-micro collaborative machining. Along the Z-axis, following the low-frequency trajectory z... d (n) While moving, the W-axis tracks the transient difference between the ideal position and the actual position of the macro-micro system in real time, and fine-tunes the remaining error.

[0157] In practice, for each control cycle, the system performs the following closed-loop operation:

[0158] First, the current C-axis angle θ is read using the main spindle circular grating. actual Combined with the current position ρ on the X-axis actual Using the target surface shape function, interpolation is performed to calculate the ideal position y in the cutting depth direction at this moment. ideal .

[0159] Secondly, the actual Z-axis position z is read using a Z-axis grating ruler. actual The actual position of the W-axis is read by the W-axis displacement sensor. actual The sum of the two gives the total actual position y. actual =zactual +w actual .

[0160] Then, calculate the transient tracking error e=y ideal -y actual This error is the compensation command for the W-axis at the current moment.

[0161] Finally, the compensation command is sent to the W-axis composite controller designed in step S100. The W-axis inverse model controller in the composite controller first performs pre-distortion processing on the command to compensate for the dynamic hysteresis of the W-axis itself. The disturbance observer estimates and compensates for external disturbances in real time, while the high-bandwidth feedback controller ensures the high-speed, high-precision response of the closed-loop system. After being driven by the power amplifier, the W-axis actuator outputs displacement, completing the real-time compensation for the transient error.

[0162] The entire closed-loop operation of the S340 is executed cyclically at an extremely high frequency. In one embodiment, the sampling frequency of the W-axis controller is 50kHz, which means that the above-mentioned complete sensing-calculation-execution cycle is completed once every 20 microseconds, ensuring timely response to high-frequency error components.

[0163] This step establishes a rigorous two-layer error compensation system. From a temporal perspective, the feedforward pre-correction of S320 is a strategic compensation completed before machining, while the real-time tracking of S340 is a tactical fine-tuning performed during machining. From a spatial perspective, the Z-axis executes the pre-corrected low-frequency main motion, while the W-axis, as the final link, captures and eliminates all remaining errors with extremely high dynamic response capabilities. By combining feedforward pre-compensation before machining with real-time W-axis compensation during machining, the residual tracking error of the macro-micro system in the cutting depth direction can be reduced, improving the machining accuracy and motion stability of microstructured optical components under high spindle speeds. Figure 12 The tracking results shown further verify the applicability and effectiveness of the method under different processing speed conditions.

[0164] S400 evaluates the surface morphology error, surface roughness, and processing efficiency of the processed workpiece.

[0165] Furthermore, the evaluation in step S400 is aimed at the microstructure optical element processing object, comprehensively considering surface morphology error, surface roughness, and processing efficiency that can be achieved while ensuring processing accuracy.

[0166] This step verifies and evaluates the final effect of the entire technical solution. After processing, the obtained microstructured optical components and other workpieces are comprehensively evaluated using three core indicators: surface morphology error, surface roughness, and processing efficiency. Surface morphology error and surface roughness directly reflect processing accuracy and surface quality, while processing efficiency is measured by the highest spindle speed achievable by the system while maintaining the aforementioned accuracy. This evaluation system comprehensively and objectively verifies the superiority of the method of this invention in simultaneously achieving high speed, high precision, and high stability.

[0167] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0168] Embodiments of the present invention also provide a cooperative tool servo diamond turning system based on feedforward compensation, comprising:

[0169] The system construction module is used to build a master-slave cooperative tool servo system. It configures the cooperative motion relationship between the master servo axis (Z-axis) and the slave servo axis (W-axis), and designs a composite controller for the W-axis that includes a disturbance observer, a high-bandwidth feedback controller, and a W-axis inverse model controller. At the same time, based on the kinematic and dynamic constraints of the Z-axis, a zero-phase low-pass filter is designed to decompose the tool trajectory in the cutting depth direction into a low-frequency trajectory executed by the Z-axis and a high-frequency compensation trajectory for the difference between the ideal trajectory tracked in real time by the W-axis and the actual trajectory of the Z-axis.

[0170] The feedforward compensation model construction module is used to send out frequency sweep trajectory to drive the Z-axis and W-axis to operate in coordination, collect error data between the actual position of the macro-micro system composed of the composite displacement of the Z-axis and W-axis and the ideal position obtained by interpolation of the principal axis angle, and establish a data-driven feedforward compensation model for macro-micro systems that can predict the overall tracking error of the macro-micro system according to the ideal position or trajectory characteristics.

[0171] The collaborative machining module is used to plan the target tool trajectory based on the target surface structure parameters and the geometric parameters of the diamond tool. It superimposes the feedforward compensation amount output by the feedforward compensation model for the macro-micro system onto the target tool trajectory to obtain the compensated trajectory. The compensated trajectory is then processed by the zero-phase low-pass filter and imported into the Z-axis controller. At the same time, it controls the W-axis to track the difference between the ideal position and the actual position of the macro-micro system to drive the diamond tool to complete the workpiece machining.

[0172] The evaluation module is used to evaluate the surface morphology error, surface roughness, and processing efficiency of the processed workpiece.

[0173] While specific embodiments of the invention have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and are not intended to limit the scope of the invention. Those skilled in the art should also understand that various modifications can be made to the embodiments without departing from the scope and spirit of the invention.

Claims

1. A collaborative tool servo diamond turning method based on feedforward compensation, characterized in that, The method includes the following steps: S100: Construct a master-slave cooperative tool servo system, configure cooperative motion relationship between the master servo axis Z-axis and the slave servo axis W-axis, and design a composite controller for the W-axis including a disturbance observer, a high-bandwidth feedback controller, and a W-axis inverse model controller; at the same time, design a zero-phase low-pass filter based on the kinematic and dynamic constraints of the Z-axis to decompose the tool trajectory in the cutting depth direction into a low-frequency trajectory executed by the Z-axis and a high-frequency compensation trajectory for the difference between the ideal trajectory tracked in real time by the W-axis and the actual trajectory of the Z-axis. S200: The frequency sweep trajectory is sent to drive the Z-axis and W-axis to operate in coordination. Error data between the actual position of the macro-micro system composed of the composite displacement of the Z-axis and W-axis and the ideal position obtained by interpolation of the principal axis angle is collected. Based on the error data, a data-driven feedforward compensation model for macro-micro systems is established, which can predict the overall tracking error of the macro-micro system according to the ideal position or trajectory characteristics. S300: Based on the target surface structure parameters and the geometric parameters of the diamond tool, the target tool trajectory is planned. The feedforward compensation amount output by the feedforward compensation model for the macro-micro system is superimposed on the target tool trajectory to obtain the compensated trajectory. The compensated trajectory is then processed by the zero-phase low-pass filter and imported into the Z-axis controller. At the same time, the W-axis is controlled to track the difference between the ideal position and the actual position of the macro-micro system to drive the diamond tool to complete the workpiece machining. S400 evaluates the surface morphology error, surface roughness, and processing efficiency of the processed workpiece.

2. The method for cooperative tool servo diamond turning based on feedforward compensation according to claim 1, characterized in that, The master-slave cooperative tool servo system constructed in step S100 includes: The C-axis of a machine tool is used to drive the main rotational motion of the workpiece; The X-axis of the machine tool is used to achieve radial feed of the tool. The Z-axis and W-axis are installed in series in the depth of cut direction to jointly complete the tool feed in the depth of cut direction. The C-axis, X-axis and Z-axis are synchronously controlled by the machine tool multi-axis motion controller, and the W-axis moves in coordination with the machine tool axis through a composite controller, power amplifier and displacement feedback device.

3. The method for cooperative tool servo diamond turning based on feedforward compensation according to claim 1, characterized in that, The composite controller includes: The high-bandwidth feedback controller consists of a damping controller for suppressing the resonant mode of the W-axis micro-motion platform and a high-gain proportional-integral controller for reducing steady-state error and residual tracking error; The disturbance observer, which includes the nominal model inverse and a low-pass filter, is used to estimate external disturbances and model uncertainties online and feed the estimates back to the control input for compensation. The W-axis inverse model controller, obtained by identifying and inverting the W-axis closed-loop transfer function, is used to pre-correct the dynamic lag and amplitude attenuation of the W-axis closed-loop system, thereby improving its ability to track high-frequency compensated trajectories.

4. The method for cooperative tool servo diamond turning based on feedforward compensation according to claim 3, characterized in that, The transfer function of the damping controller ;in, The center angular frequency of the notch filter. and The damping coefficient; It is a complex frequency variable; The transfer function of the high-gain proportional-integral controller ;in, and These are the proportional gain and integral gain, respectively.

5. The method for cooperative tool servo diamond turning based on feedforward compensation according to claim 3, characterized in that, The construction of the W-axis inverse model controller includes the following steps: S110 uses a frequency sweep training signal to drive the W-axis motion, collects its input signal and output displacement response, and identifies and establishes the W-axis closed-loop transfer function. ; s is a complex frequency variable; S111, for Inverse model to obtain the W-axis inverse model ; S112, the Connected in series to the W-axis command input, making the adjusted control input... ;in, The desired compensation trajectory is shown on the W-axis.

6. The method for cooperative tool servo diamond turning based on feedforward compensation according to claim 1, characterized in that, The low-frequency tool path output by the zero-phase low-pass filter designed in step S100 Represented as: ； in, Let be the component of the trajectory to be decomposed along the cutting depth direction. The impulse response of a zero-phase low-pass filter. This indicates that the sequence is reversed; The cutoff frequency of the zero-phase low-pass filter satisfies the following constraint to ensure that the decomposed low-frequency trajectory does not exceed the physical limit of the Z-axis: ； ； in, The velocity along the Z-axis; The acceleration along the Z-axis; and The maximum permissible velocity and acceleration along the Z-axis. This is the filter cutoff frequency. The highest frequency of the Z-axis operating bandwidth. For Z-axis motion error, This represents the maximum permissible error along the Z-axis.

7. The method for cooperative tool servo diamond turning based on feedforward compensation according to claim 1, characterized in that, Step S200 includes the following steps: S210: The actual Z-axis position and the actual W-axis position are read by the Z-axis position feedback device and the W-axis position feedback device respectively, and the actual positions read by the Z-axis position feedback device and the W-axis position feedback device are superimposed to obtain the total actual displacement of the macro-micro system in the cutting depth direction. S220 reads the actual position of the C-axis through the spindle position feedback device and obtains the ideal position of the macro-micro system in the cutting depth direction through interpolation calculation; S230, the difference between the ideal position and the total actual displacement is used to obtain the overall tracking error of the macro-micro system; S240, based on the ideal macro-micro system position-measured macro-micro system error dataset, an offline machine learning model is trained to establish the mapping relationship between the machining trajectory in the cutting depth direction and the overall tracking error, thereby forming the data-driven feedforward compensation model for macro-micro systems.

8. The method for cooperative tool servo diamond turning based on feedforward compensation according to claim 1, characterized in that, Step S300 includes the following steps: S310, using the target surface structure parameters and diamond tool geometric parameters, plans the target tool trajectory in polar coordinates through equal-angle discretization and Z-axis projection; the component of the target tool trajectory in polar coordinates along the cutting depth direction is expressed as... ; S320, the feedforward compensation amount predicted by the feedforward compensation model for macro-micro systems. The compensated trajectory is obtained by directly superimposing it onto the target toolpath. ; S330, Frequency domain decomposition is performed using a zero-phase low-pass filter to obtain a low-frequency trajectory executed along the Z-axis; S340, the W-axis uses the difference between the ideal position in the cutting depth direction of the macro-micro system and the total actual displacement synthesized from the actual positions of the Z-axis and W-axis as a command to perform real-time tracking compensation.

9. The method for cooperative tool servo diamond turning based on feedforward compensation according to claim 1, characterized in that, The evaluation in step S400 is aimed at the microstructure optical element processing object, comprehensively considering surface morphology error, surface roughness, and processing efficiency that can be achieved while ensuring processing accuracy.

10. A cooperative tool servo diamond turning system based on feedforward compensation, characterized in that, include: The system construction module is used to build a master-slave cooperative tool servo system. It configures the cooperative motion relationship between the master servo axis Z-axis and the slave servo axis W-axis, and designs a composite controller for the W-axis that includes a disturbance observer, a high-bandwidth feedback controller, and a W-axis inverse model controller. At the same time, based on the kinematic and dynamic constraints of the Z-axis, a zero-phase low-pass filter is designed to decompose the tool trajectory in the cutting depth direction into a low-frequency trajectory executed by the Z-axis and a high-frequency compensation trajectory for the difference between the ideal trajectory tracked in real time by the W-axis and the actual trajectory of the Z-axis. The feedforward compensation model construction module is used to send out the frequency sweep trajectory to drive the Z-axis and W-axis to run in coordination, collect error data between the actual position of the macro-micro system composed of the composite displacement of the Z-axis and W-axis and the ideal position obtained by interpolation of the principal axis angle, and establish a data-driven feedforward compensation model for macro-micro systems that can predict the overall tracking error of the macro-micro system according to the ideal position or trajectory characteristics. The collaborative machining module is used to plan the target tool trajectory based on the target surface structure parameters and the geometric parameters of the diamond tool. It superimposes the feedforward compensation amount output by the feedforward compensation model for the macro-micro system onto the target tool trajectory to obtain the compensated trajectory. The compensated trajectory is then processed by the zero-phase low-pass filter and imported into the Z-axis controller. At the same time, it controls the W-axis to track the difference between the ideal position and the actual position of the macro-micro system to drive the diamond tool to complete the workpiece machining. The evaluation module is used to evaluate the surface morphology error, surface roughness, and processing efficiency of the processed workpiece.

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