Loop attack modeling and stability compensation method for precise motion control

Abstract

The invention relates to a precise motion control-oriented loop attack modeling and stability compensation method, which comprises the following steps of: acquiring operation parameters of a precise motion control loop in real time, establishing a loop attack model comprising a delay injection attack and a noise superposition attack, and constructing a closed-loop control model comprising a feed-forward channel; performing frequency domain analysis according to the closed-loop control model, calculating a phase margin of a control loop, and triggering an instability alarm when the phase margin is lower than a preset margin threshold value; in response to the instability alarm, modeling a dynamic behavior of an attacked control loop into a state equation containing a feed-forward channel; and designing a feedforward compensation item by using a stability theory, dynamically adjusting a compensation parameter, and recovering a phase margin of a control loop to a stable interval, so as to achieve the purposes of attack real-time detection and dynamic stability compensation of the precise motion control system in an industrial Internet of Things environment.

Description

Technical Field

[0001] The present invention relates to the field of industrial Internet of Things security and intelligent control technology, and in particular to a loop attack modeling and stability compensation method for precision motion control. Background Art

[0002] With the deep integration of the Industrial Internet of Things (IIoT), precision motion control systems face increasingly complex security threats, especially from new attack vectors such as delayed injection and noise superposition within control loops. Traditional defense mechanisms are now demonstrating significant limitations. Existing technologies often rely on static threshold detection or single parameter adjustment strategies, such as abnormal fluctuation determination based on a fixed threshold or adaptive adjustment of conventional PID parameters. While these approaches can address known attack patterns, they struggle to dynamically adapt to time-varying disturbances and are unable to effectively restore stability when an attack causes the system phase margin to fall below a critical value. More critically, static strategies lack quantitative modeling of the coupling relationship between attack disturbances and system stability, resulting in delayed defense responses and difficulty meeting the stringent control robustness and real-time requirements of high-precision equipment, such as semiconductor manufacturing equipment. Summary of the Invention

[0003] The main purpose of the present invention is to provide a loop attack modeling and stability compensation method for precision motion control, so as to achieve the purpose of real-time attack detection and dynamic stability compensation of precision motion control systems in the industrial Internet of Things environment.

[0004] To achieve the above objectives, the present invention provides a loop attack modeling and stability compensation method for precision motion control, comprising the following steps: Collect the operating parameters of the precision motion control loop in real time, establish a loop attack model that includes delay injection attack and noise superposition attack, and build a closed-loop control model that includes a feedforward channel; Perform frequency domain analysis based on the closed-loop control model to calculate the control loop phase margin, and trigger an instability alarm when the phase margin is lower than a preset margin threshold; In response to the instability alarm, modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel; Design feedforward compensation terms, dynamically adjust compensation parameters, and restore the phase margin of the control loop to the stable range.

[0005] Furthermore, the steps of establishing a loop attack model including a delay injection attack and a noise superposition attack and constructing a closed-loop control model including a feedforward channel include: By monitoring the real-time data flow of the control loop, a time-varying disturbance term in the control loop is identified, wherein the time-varying disturbance term characterizes the disturbance characteristics of the delay injection attack; Model the noise superposition attack as a random noise term that conforms to the historical statistical distribution; A closed-loop control model is constructed based on the time-varying disturbance term and the random noise term to quantify the dynamic impact of the attack on the loop output.

[0006] Furthermore, the steps of constructing a closed-loop control model include: fusing the original transfer characteristic of the control loop with the time-varying disturbance term and the random noise term to form a closed-loop control model including a feedforward channel; The closed-loop control model is used for phase margin analysis and compensation parameter design.

[0007] Furthermore, the step of performing frequency domain analysis according to the closed-loop control model to calculate the control loop phase margin, and triggering an instability alarm when the phase margin is lower than a preset margin threshold, includes: generating a Bode diagram based on the closed-loop control model, analyzing and obtaining an initial phase margin of the control loop in a non-attack state; Based on the initial phase margin and actual equipment stability test results, calibrate a preset margin threshold for triggering an instability alarm; When the real-time phase margin is lower than the preset margin threshold, an alarm signal is generated.

[0008] Furthermore, in response to the instability alarm, the step of modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel includes: After receiving the instability warning information, the amplitude crossover frequency point is located on the phase curve of the open-loop transfer characteristic of the control loop; Calculating the difference between the phase value corresponding to the amplitude crossover frequency point and the critical instability value to obtain a real-time phase margin; When the real-time phase margin is lower than a preset attack threshold within a continuous preset number of control cycles, a multi-level alarm is triggered and a state equation including a time-varying disturbance term and a random noise term is constructed.

[0009] Furthermore, the steps of designing a feedforward compensation term using stability theory, dynamically adjusting the compensation parameters, and restoring the phase margin of the control loop to a stable range include: Dynamically adjusting a feedforward gain coefficient based on a phase margin analysis result of the closed-loop control model; The state convergence of the compensated control loop is verified by the derivative constraint of the Lyapunov function; The feedforward compensation term is added to the control signal input to generate a disturbance-resistant closed-loop control signal.

[0010] Furthermore, the step of dynamically adjusting the feedforward gain coefficient includes: Based on the real-time monitored time-varying disturbance term and the real-time monitored value of the phase margin, the gain coefficient range is adaptively adjusted; After dynamically adjusting the gain coefficient, verify whether the compensated phase margin reaches the stable range; If stability is not achieved, the gain adjustment strategy is iteratively optimized in combination with the changing trend of the time-varying disturbance term until the system stability requirement is met.

[0011] Furthermore, the step of designing the feedforward compensation term using stability theory also includes: Deploying the calculation logic of the feedforward compensation term via a programmable logic device, wherein the programmable logic device is driven by a high-speed clock signal and performs a low-latency response; The low-latency response is used to counteract the effects of attack disturbances on the precision motion control loop in real time.

[0012] Furthermore, the step of designing the feedforward compensation term using stability theory also includes: Dynamically loading the gain parameter of the feedforward compensation term in a real-time operating system; The gain parameter is adjusted through an online update module to adapt to the stability requirements of different attack scenarios.

[0013] The present invention also provides a loop attack modeling and stability compensation system for precision motion control, comprising: A model building unit is used to collect the operating parameters of the precision motion control loop in real time, establish a loop attack model including delay injection attack and noise superposition attack, and build a closed-loop control model including a feedforward channel; a stability analysis unit, configured to perform frequency domain analysis based on the closed-loop control model, calculate a control loop phase margin, and trigger an instability alarm when the phase margin is lower than a preset margin threshold; In response to the instability alarm, modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel; The compensation optimization unit is used to design the feedforward compensation term, dynamically adjust the compensation parameters, and restore the phase margin of the control loop to the stable range.

[0014] The loop attack modeling and stability compensation method for precision motion control provided by the present invention has the following beneficial effects: By innovatively integrating attack dynamic modeling with Lyapunov stability theory, the present invention constructs a multi-level defense system, improving the security and robustness of precision motion control systems. Based on a closed-loop model of time-varying perturbations and random noise, the present invention accurately quantifies the impact of complex attacks, breaking through the traditional static threshold detection's blind spot in detecting dynamic attacks. Secondly, through the collaborative design of feedforward compensation terms and phase margin recovery mechanisms, system stability is quickly reconstructed after an attack is triggered, resolving the technical bottleneck of single parameter adjustment being unable to maintain phase margin. Furthermore, through a collaborative hardware and software architecture, the compensation algorithm achieves microsecond-level real-time response and dynamic parameter loading capabilities, enabling the system to adaptively respond to diverse attack modes such as step and ramp attacks. Furthermore, the multi-level alarm mechanism and iterative optimization strategy proposed in the present invention establish a full-process defense closed loop for industrial control loops, from attack identification, dynamic modeling, to compensation control. This not only significantly reduces the false alarm rate and the risk of missed detection, but also provides a universal solution for the long-term reliable operation of high-value equipment, with broad industrial application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 1 is a flow chart of a loop attack modeling and stability compensation method for precision motion control according to an embodiment of the present invention; Figure 2 1 is a structural block diagram of a loop attack modeling and stability compensation system for precision motion control in one embodiment of the present invention.

[0016] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0018] Reference Figure 1 , which is a flow chart of a loop attack modeling and stability compensation method for precision motion control proposed by the present invention, comprising the following steps: S1, real-time acquisition of operating parameters of the precision motion control loop, establishment of a loop attack model including delay injection attack and noise superposition attack, and construction of a closed-loop control model including a feedforward channel; S2, performing frequency domain analysis according to the closed-loop control model, calculating the control loop phase margin, and triggering an instability alarm when the phase margin is lower than a preset margin threshold; S3, in response to the instability alarm, modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel; S4, design the feedforward compensation term, dynamically adjust the compensation parameters, and restore the phase margin of the control loop to the stable range.

[0019] In one embodiment, for step S1, The steps of establishing a loop attack model including delay injection attack and noise superposition attack and building a closed-loop control model including a feedforward channel include: By monitoring the real-time data flow of the control loop, a time-varying disturbance term in the control loop is identified, wherein the time-varying disturbance term characterizes the disturbance characteristics of the delay injection attack; Model the noise superposition attack as a random noise term that conforms to the historical statistical distribution; A closed-loop control model is constructed based on the time-varying disturbance term and the random noise term to quantify the dynamic impact of the attack on the loop output.

[0020] In specific implementation, multi-source sensing units acquire the operating parameters of the precision motion control loop in real time: a high-precision optical encoder continuously monitors the Z-axis position feedback signal with a resolution of ±0.1 μm, a Hall effect current sensor captures the servo motor drive current spectrum with a 10 kHz bandwidth, and an FPGA-embedded probe records the transmission delay fluctuations of the position command signal with a 10 ns timestamp accuracy. This real-time data flows through the edge computing node, undergoes Kalman filtering for noise reduction and sliding window normalization, and is then input into the attack feature extraction module for in-depth analysis. This module identifies abnormally increased communication delay fluctuations in the control loop. The delay injection attack is modeled as a time-varying perturbation term, characterized by a periodic perturbation with a randomly varying amplitude (±0.3 ms) superimposed on a normal communication delay baseline value (approximately 0.5 ms). This perturbation term is strongly correlated with the frequency of the malicious commands injected by the attacker. Modeling the noise superposition attack: By analyzing noise data captured from a historical attack sample library and statistically analyzing its amplitude distribution characteristics, it was found that the attack noise conforms to a Gaussian distribution with a mean of zero and a standard deviation of 0.12μm. This noise is then modeled as a random noise term with the same statistical characteristics. Based on this attack model, the original transfer function of the Z-axis servo system (including physical parameters such as motor inertia and damping coefficient) is integrated with the attack disturbance term to construct a closed-loop control model with a feedforward channel. When constructing the closed-loop model in a simulation environment, the time-varying disturbance term is embedded in the feedforward channel in the form of a variable transmission delay module, and the random noise term is superimposed on the position feedback signal via a Gaussian noise generator. This embodiment deeply couples real-time data acquisition (grating encoder + current sensor + FPGA probe) with attack feature extraction (joint time-frequency analysis), overcoming the shortcomings of traditional methods in modeling the correlation between attack disturbances and system states. This achieves an end-to-end mapping from physical signals to control models, establishing a scalable technical framework for active defense in industrial IoT environments.

[0021] In one embodiment, the step of constructing a closed-loop control model includes: fusing the original transfer characteristic of the control loop with the time-varying disturbance term and the random noise term to form a closed-loop control model including a feedforward channel; The closed-loop control model is used for phase margin analysis and compensation parameter design.

[0022] Specifically, the transfer function model of the original control loop is established, and the open-loop transfer characteristics of the Z-axis servo system are assumed to be:

[0023] Where, is the motor rotor inertia, is the damping coefficient, is the proportional gain, is the Laplace operator, which is used to convert the time domain signal into the complex frequency domain for analysis. To prevent delay injection attacks, a time-varying disturbance term is introduced into the control command channel. , the physical manifestation is the random fluctuation of transmission delay (in the actual attack scenario The noise superposition attack is modeled as Gaussian white noise, and its statistical characteristics are calibrated to have a mean of zero and a variance of . Closed-loop transfer function modeling: , the coupling effect of attack disturbance on the system is characterized by the closed-loop transfer function model, and the delayed disturbance term Causes phase lag when When the measured phase lag reaches 34°, the noise disturbance term This resulted in a ±0.15 μm random fluctuation in the position feedback signal, consistent with the measured error distribution of the Z-axis scale. Frequency domain analysis and stability verification based on a closed-loop model revealed a Bode plot showing an uncompensated phase margin of 28°, significantly below the preset safety threshold of 45°. Time domain response testing revealed a position tracking error of ±5 μm under step input (compared to ±0.5 μm under normal operating conditions), with overshoot increasing from 3% to 22%.

[0024] In one embodiment, for step S2, The step of performing frequency domain analysis according to the closed-loop control model, calculating the control loop phase margin, and triggering an instability alarm when the phase margin is lower than a preset margin threshold, includes: generating a Bode diagram based on the closed-loop control model, analyzing and obtaining an initial phase margin of the control loop in a non-attack state; Based on the initial phase margin and actual equipment stability test results, calibrate a preset margin threshold for triggering an instability alarm; When the real-time phase margin is lower than the preset margin threshold, an alarm signal is generated.

[0025] In the specific implementation, based on the closed-loop control model constructed in step S1 , generate the Bode diagram through the control system toolbox and analyze the initial phase margin under the non-attack state. The initial phase margin of the Bangtou Z-axis servo system under normal working conditions is measured by experiment. , corresponding to the open-loop transfer function Amplitude crossover frequency At this time, the Z-axis position tracking error is ±0.5μm (laser interferometer measured data). The phase margin critical value is verified by actual equipment stability test. and noise Under the combined attack of , at this time, the Z-axis position oscillation amplitude reaches ±5μm, and the servo motor current fluctuation exceeds the limit (the peak value reaches 120% of the rated value). Further experiments show that when the phase margin When the system Lyapunov index changes from negative to positive ( ), it is determined to be a critical state of instability, so the preset margin threshold is calibrated as Deploy an FPGA-based online monitoring module to calculate the phase margin value in real time, collect open-loop frequency response data every 10 ms, and update the amplitude crossover frequency through fast Fourier transform (FFT). , located on the Bode diagram phase curve The corresponding phase value , calculate the real-time phase margin , when within 3 consecutive sampling periods When , the third level instability alarm (yellow / orange / red) is triggered, and the feedforward compensation algorithm of step S3 is started.

[0026] In one embodiment, for step S3, In response to the instability alarm, the step of modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel comprises: After receiving the instability warning information, the amplitude crossover frequency point is located on the phase curve of the open-loop transfer characteristic of the control loop; Calculating the difference between the phase value corresponding to the amplitude crossover frequency point and the critical instability value to obtain a real-time phase margin; When the real-time phase margin is lower than a preset attack threshold within a continuous preset number of control cycles, a multi-level alarm is triggered and a state equation including a time-varying disturbance term and a random noise term is constructed.

[0027] In a specific implementation, when the online monitoring module detects the real-time phase margin When the open loop transfer characteristic The amplitude crossover frequency is precisely located on the phase curve of the Bode plot. (corresponding to the point where the gain is 0dB), then read Phase value at And calculate the real-time phase margin When the margin value is within 3 consecutive control cycles (cycle ) is continuously lower than When the system triggers the yellow ( ),orange( ),red( ) three-level alarm, this multi-level alarm mechanism provides an accurate time window for subsequent modeling. Based on this alarm signal, the system immediately starts the dynamic modeling process and constructs the state equation including the feedforward channel , where the state variable ,in is the Z-axis angular displacement of the Bang head, is the angular velocity (the actual measurement accuracy of the laser encoder is ±0.1μrad). The matrix parameters obtained through system identification, the time-varying disturbance term The delay fluctuation data collected by FPGA is driven in real time (update rate 10kHz), and the random noise term Then through the variance This embodiment uses Bode plot analysis and state-space modeling to ensure both the engineering feasibility of the phase margin threshold (a three-cycle delay effectively balances false alarm suppression and response speed) and the precise correspondence between the mathematical model and the physical system (all parameters are derived from the equipment technical manual and measured data). This ultimately enables automated processing of the entire process, from instability detection and dynamic modeling to compensation control.

[0028] In one embodiment, for step S4, The steps of using stability theory to design feedforward compensation terms, dynamically adjusting compensation parameters, and restoring the phase margin of the control loop to a stable range include: Dynamically adjusting a feedforward gain coefficient based on a phase margin analysis result of the closed-loop control model; The state convergence of the compensated control loop is verified by the derivative constraint of the Lyapunov function; The feedforward compensation term is added to the control signal input to generate a disturbance-resistant closed-loop control signal.

[0029] In a specific implementation, based on the phase margin analysis results of the closed-loop control model, when the phase margin is detected When the temperature drops to 28°, the system starts the dynamic compensation mechanism. The quadratic function is constructed by Lyapunov stability theory. , where the state variable is the Z-axis angular displacement of the Bang head, the positive definite matrix P is obtained by solving the Riccati equation (Pick ) is determined. Based on this function, the feedforward compensation term is designed , where the gain coefficient By ensuring the Lyapunov function derivative constraint The compensation term is calculated in real time by FPGA hardware at a 200MHz clock frequency, with a response delay within 0.8μs. After being added to the control signal, the phase margin is restored to 48°.

[0030] In one embodiment, the step of dynamically adjusting the feedforward gain coefficient includes: Based on the real-time monitored time-varying disturbance term and the real-time monitored value of the phase margin, the gain coefficient range is adaptively adjusted; After dynamically adjusting the gain coefficient, verify whether the compensated phase margin reaches the stable range; If stability is not achieved, the gain adjustment strategy is iteratively optimized in combination with the changing trend of the time-varying disturbance term until the system stability requirement is met.

[0031] Specifically, real-time monitoring of time-varying disturbances (sampling rate 10 kHz) and phase margin (Update period 1ms), establish the gain coefficient Adaptive adjustment rules: When Fluctuations exceeding ±0.2 ms or When The gain range is adjusted at a rate of 0.000. After each adjustment, the phase margin is verified by the real-time updated Bode diagram. If the 45° stable range is not reached, the phase margin is combined with the The historical trend of change (predicted by ARIMA model) is iteratively optimized until Stable within the range.

[0032] In one embodiment, the step of designing the feedforward compensation term using stability theory further includes: Deploying the calculation logic of the feedforward compensation term via a programmable logic device, wherein the programmable logic device is driven by a high-speed clock signal and performs a low-latency response; The low-latency response is used to counteract the effects of attack disturbances on the precision motion control loop in real time.

[0033] Specifically, by using a Xilinx Kintex-7 FPGA to implement pipeline processing of the compensation algorithm, the critical path delay was optimized to 37 ns, ensuring that the calculation was completed within a 1 ms control cycle: ,in The computational logic is implemented in a hardware description language (VHDL), meeting the requirement for real-time offset of attack disturbances. The low-latency response reduces the transition time required to restore the phase margin to 48° to just 1.2 ms.

[0034] In one embodiment, the step of designing the feedforward compensation term using stability theory further includes: Dynamically loading the gain parameter of the feedforward compensation term in a real-time operating system; The gain parameter is adjusted through an online update module to adapt to the stability requirements of different attack scenarios.

[0035] Specifically, deploy dynamic loading modules in the real-time operating system to support online updates via the EtherCAT bus Parameter group (stores 8 preset values). Automatically switches to optimal parameters for different attack modes, such as step and ramp. Step attacks use higher gains for rapid disturbance suppression, matching the transient characteristics of sudden attacks; ramp attacks use dynamically adjusted medium gains to balance response speed and long-term stability. Through adaptive parameter switching, the system can intelligently respond to diverse attack modes, avoiding the performance limitations of single fixed parameters and significantly improving the comprehensive defense capabilities of IIoT control loops.

[0036] Reference Figure 2 , is a structural block diagram of a loop attack modeling and stability compensation system for precision motion control in one embodiment of the present invention, including: A model building unit is used to collect the operating parameters of the precision motion control loop in real time, establish a loop attack model including delay injection attack and noise superposition attack, and build a closed-loop control model including a feedforward channel; a stability analysis unit, configured to perform frequency domain analysis based on the closed-loop control model, calculate a control loop phase margin, and trigger an instability alarm when the phase margin is lower than a preset margin threshold; In response to the instability alarm, modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel; The compensation optimization unit is used to design the feedforward compensation term, dynamically adjust the compensation parameters, and restore the phase margin of the control loop to the stable range.

[0037] For the specific implementation of each unit in the above device example, please refer to the above method embodiment, which will not be repeated here.

[0038] In summary, the present invention acquires the operating parameters of the precision motion control loop in real time, establishes a loop attack model including delay injection attack and noise superposition attack, and constructs a closed-loop control model including a feedforward channel; performs frequency domain analysis based on the closed-loop control model, calculates the phase margin of the control loop, and triggers an instability alarm when the phase margin is lower than a preset margin threshold; in response to the instability alarm, models the dynamic behavior of the attacked control loop as a state equation including a feedforward channel; uses stability theory to design a feedforward compensation term, dynamically adjusts the compensation parameters, and restores the phase margin of the control loop to a stable range, so as to achieve the purpose of real-time attack detection and dynamic stability compensation of the precision motion control system in the industrial Internet of Things environment.

[0039] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware using a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the above-described method embodiments. Any reference to memory, storage, database, or other media provided herein and used in the embodiments may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double-speed SDRAM (SSRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct RAMbus dynamic RAM (DRDRAM), and RAMbus dynamic RAM.

[0040] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, apparatus, article, or method comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, apparatus, article, or method. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, apparatus, article, or method comprising the element.

[0041] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A loop attack modeling and stability compensation method for precision motion control, characterized in that: The following steps are involved: Collect the operating parameters of the precision motion control loop in real time, establish a loop attack model that includes delay injection attack and noise superposition attack, and build a closed-loop control model that includes a feedforward channel; Perform frequency domain analysis based on the closed-loop control model to calculate the control loop phase margin, and trigger an instability alarm when the phase margin is lower than a preset margin threshold; In response to the instability alarm, modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel; Design feedforward compensation terms, dynamically adjust compensation parameters, and restore the phase margin of the control loop to the stable range.

2. The loop attack modeling and stability compensation method for precision motion control according to claim 1 is characterized in that: The steps of establishing a loop attack model including a delay injection attack and a noise superposition attack, and constructing a closed-loop control model including a feedforward channel include: By monitoring the real-time data flow of the control loop, a time-varying disturbance term in the control loop is identified, wherein the time-varying disturbance term characterizes the disturbance characteristics of the delay injection attack; Model the noise superposition attack as a random noise term that conforms to the historical statistical distribution; A closed-loop control model is constructed based on the time-varying disturbance term and the random noise term to quantify the dynamic impact of the attack on the loop output.

3. The loop attack modeling and stability compensation method for precision motion control according to claim 2 is characterized in that: The step of constructing a closed-loop control model includes: fusing the original transfer characteristic of the control loop with the time-varying disturbance term and the random noise term to form a closed-loop control model including a feedforward channel; The closed-loop control model is used for phase margin analysis and compensation parameter design.

4. The loop attack modeling and stability compensation method for precision motion control according to claim 1 is characterized in that: The step of performing frequency domain analysis according to the closed-loop control model, calculating the control loop phase margin, and triggering an instability alarm when the phase margin is lower than a preset margin threshold, includes: generating a Bode diagram based on the closed-loop control model, analyzing and obtaining an initial phase margin of the control loop in a non-attack state; Based on the initial phase margin and actual equipment stability test results, calibrate a preset margin threshold for triggering an instability alarm; When the real-time phase margin is lower than the preset margin threshold, an alarm signal is generated.

5. The loop attack modeling and stability compensation method for precision motion control according to claim 1 is characterized in that: The step of modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel in response to the instability alarm comprises: After receiving the instability warning information, the amplitude crossover frequency point is located on the phase curve of the open-loop transfer characteristic of the control loop; Calculating the difference between the phase value corresponding to the amplitude crossover frequency point and the critical instability value to obtain a real-time phase margin; When the real-time phase margin is lower than a preset attack threshold within a continuous preset number of control cycles, a multi-level alarm is triggered and a state equation including a time-varying disturbance term and a random noise term is constructed.

6. The loop attack modeling and stability compensation method for precision motion control according to claim 1, characterized in that: The steps of designing a feedforward compensation term, dynamically adjusting the compensation parameters, and restoring the phase margin of the control loop to a stable range include: Dynamically adjusting a feedforward gain coefficient based on a phase margin analysis result of the closed-loop control model; The state convergence of the compensated control loop is verified by the derivative constraint of the Lyapunov function; The feedforward compensation term is added to the control signal input to generate a disturbance-resistant closed-loop control signal.

7. The loop attack modeling and stability compensation method for precision motion control according to claim 6, characterized in that: The step of dynamically adjusting the feedforward gain coefficient comprises: Based on the real-time monitored time-varying disturbance term and the real-time monitored value of the phase margin, the gain coefficient range is adaptively adjusted; After dynamically adjusting the gain coefficient, verify whether the compensated phase margin reaches the stable range; If stability is not achieved, the gain adjustment strategy is iteratively optimized in combination with the changing trend of the time-varying disturbance term until the system stability requirement is met.

8. The loop attack modeling and stability compensation method for precision motion control according to claim 1, characterized in that: The step of designing the feedforward compensation term further includes: Deploying the calculation logic of the feedforward compensation term via a programmable logic device, wherein the programmable logic device is driven by a high-speed clock signal and performs a low-latency response; The low-latency response is used to counteract the effects of attack disturbances on the precision motion control loop in real time.

9. The loop attack modeling and stability compensation method for precision motion control according to claim 1, characterized in that: The step of designing the feedforward compensation term further includes: Dynamically loading the gain parameter of the feedforward compensation term in a real-time operating system; The gain parameter is adjusted through an online update module to adapt to the stability requirements of different attack scenarios.

10. A loop attack modeling and stability compensation system for precision motion control, characterized in that: include: A model building unit is used to collect the operating parameters of the precision motion control loop in real time, establish a loop attack model including delay injection attack and noise superposition attack, and build a closed-loop control model including a feedforward channel; a stability analysis unit, configured to perform frequency domain analysis based on the closed-loop control model, calculate a control loop phase margin, and trigger an instability alarm when the phase margin is lower than a preset margin threshold; In response to the instability alarm, modeling the dynamic behavior of the attacked control loop as a state equation including a feedforward channel; The compensation optimization unit is used to design the feedforward compensation term, dynamically adjust the compensation parameters, and restore the phase margin of the control loop to the stable range.

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