A vibration compensation effect simulation evaluation system and method based on VCO phase accumulation

Abstract

The present application relates to a kind of vibration compensation effect simulation evaluation system and method based on VCO phase accumulation, system includes arbitrary waveform generator, analog differentiator, voltage-controlled oscillator, real-time compensation module, oscilloscope and host computer, arbitrary waveform generator generates a sine wave signal as analog speed quantity, and input voltage-controlled foot of voltage-controlled oscillator and analog differentiator, analog differentiator will signal after processing input to real-time compensation module, integral follow-up signal exported by real-time compensation module and the modulation signal output by voltage-controlled oscillator enter oscilloscope and be collected record, oscilloscope is connected with host computer by USB, data stream is transmitted to host computer and is carried out automatic calculation processing.The present application adopts pure electronic signal simulation scheme, vibration signal is generated by signal generator, while input is measured compensation module and the phase accumulation reference circuit based on VCO, constructs double-path parallel processing verification architecture.The system significantly improves the development test efficiency of compensation system.

Description

Technical Field

[0001] This invention is a vibration compensation effect simulation and evaluation system and method based on VCO phase accumulation, which is mainly used to perform high-precision, all-electronic equivalent testing and verification of the performance of vibration compensation modules in the laboratory. Background Technology

[0002] For vibration real-time compensation modules used in precision measurement systems, their performance (such as compensation accuracy, dynamic response, and delay time) directly determines the noise level of the entire dynamic atomic gravity measurement system. Therefore, before integrating the compensation module into expensive and complex optical-physical systems, it must undergo thorough and reliable independent testing and verification. The core of verification is to simulate carrier vibration and accurately assess whether the compensation module's output can keep up with the ideal compensation amount required by the simulated vibration.

[0003] Traditional methods, such as using precision mechanical vibration tables for verification, can test compensation modules by physically reproducing the acceleration spectrum. However, their inherent limitations significantly restrict the effectiveness and practicality of the verification. This approach relies on expensive, high-precision, long-stroke vibration tables and associated infrastructure. In terms of performance, the vibration table's response capabilities at high frequencies (e.g., >1kHz) and large dynamic ranges (e.g., >±2g) are severely limited, making it difficult to realistically simulate the broadband random vibration environment encountered by the carrier. Furthermore, the accuracy of the verification benchmark is constrained by the vibration table's own performance; motion control errors, table surface unevenness, and multi-axis coupling issues directly introduce these problems into the reference signal, thus affecting the accuracy of the evaluation results.

[0004] Therefore, there is an urgent need for a fully electronic, high-precision dynamic signal generation and verification system. This system should be able to accurately simulate the phase accumulation process caused by carrier vibration, providing the compensation module with an electronic reference comparable to actual optical measurement standards, thereby enabling comprehensive, efficient, and low-cost verification of the compensation module's performance in the laboratory.

[0005] Chinese patent "Phase Modulation Synchronous Integration Phase Shift Interferometry Method and Apparatus," authorized publication number CN102353341 B, proposes a phase shift interferometry method based on sinusoidal phase modulation and synchronous integration algorithms. It achieves sinusoidal wavelength variation through laser modulation and acquires multiple interferometric images through synchronous integration within the modulation period using a CCD camera. The core of this method lies in the introduction of real-time measurement and feedback control technology for the phase modulation degree, and precise synchronous control of the phase difference between the CCD camera exposure signal and the phase modulation signal. Through multi-channel bandpass filtering, multiplicative demodulation, and iterative optimization of the Bessel function, dynamic locking of the phase modulation degree is achieved, thereby improving the accuracy and anti-interference capability of the interferometry. This method has good application potential in high-precision dynamic measurements such as optical surface morphology and wave aberration. However, this technology is highly dependent on the synchronous integration performance of the CCD camera and the linearity of the laser modulation. The system is complex and costly, and its real-time performance is limited by the image acquisition and processing speed, making it difficult to adapt to the rapid phase compensation requirements in high-frequency dynamic vibration environments. Its closed-loop control is mainly for static or quasi-static optical measurements and does not involve a real-time feedforward compensation mechanism for phase noise caused by carrier vibration. Therefore, it is not suitable for strong dynamic interference scenarios such as mobile platform cold atom gravimeters.

[0006] Currently, quantum sensing devices such as cold atom gravimeters require efficient and reliable verification of the performance of their real-time vibration compensation modules when used on mobile platforms. Therefore, a dedicated verification system is needed that is highly integrated, easy to operate, capable of simulating large dynamic vibration signals, and achieving high-precision phase accumulation and comparison. This system would support rapid laboratory research and development as well as on-site engineering testing of the compensation module, filling a gap in existing technology for this application scenario. Summary of the Invention

[0007] To address the aforementioned technical problems, the first objective of this invention is to provide a vibration compensation effect simulation and evaluation system based on VCO phase accumulation. This system features a purely electronic architecture that enables real-time signal generation and synchronous acquisition, allowing for rapid evaluation of compensation effects without relying on large mechanical platforms. It is particularly suitable for rapid testing and iterative optimization in engineering projects. The second objective of this invention is to provide a vibration compensation effect simulation and evaluation method based on VCO phase accumulation.

[0008] To achieve the first objective of the invention, the present invention adopts the following technical solution:

[0009] A vibration compensation effect simulation and evaluation system based on VCO phase accumulation includes an arbitrary waveform generator, an analog differentiator, a voltage-controlled oscillator (VCO), a real-time compensation module, an oscilloscope, and a host computer. The arbitrary waveform generator generates a sine wave signal as an analog velocity quantity and inputs it to the voltage control pins of the analog differentiator and the VCO. The analog differentiator inputs the processed signal to the real-time compensation module. The integral follower signal output by the real-time compensation module and the modulation signal output by the VCO are collected and recorded by the oscilloscope. The oscilloscope is connected to the host computer via USB to transmit the data stream to the host computer for automated calculation and processing.

[0010] As a preferred embodiment: the real-time compensation module is a heterogeneous FPGA, which includes an analog-to-digital conversion driver module, an AXI-FIFO1 register, a velocity integral calculation module, a timer module, a frequency word calculation module, and a direct frequency generation driver module. The analog-to-digital conversion driver module is used to receive the data stream from the analog differentiator. The data stream is connected to the AXI-FIFO1 register via the AXI bus. The real-time velocity value calculated by the velocity integral calculation module is connected to the frequency word calculation module. The frequency word calculation module is implemented through high-level synthesis. Based on the atomic velocity measurement value and the timing of the interference sequence, it dynamically calculates and outputs the frequency word. The frequency word data stream is transmitted to the direct frequency generation driver module, which converts the frequency word into an integral follower signal received by the external module and then transmits it through the parallel interface.

[0011] As a preferred embodiment, the heterogeneous FPGA also includes a timer module, which is implemented through high-level synthesis to precisely control the key pulse sequence timing signal of cold atom interferometry. The pulse signal is connected to the frequency word calculation module.

[0012] As a preferred solution: the speed integral calculation module is implemented through high-level synthesis, and outputs the speed value through ADC data normalization and dimension conversion, 31st-order FIR digital filtering, 10x CIC downsampling and first-order IIR approximate integral operation; all processing units are transmitted in a pipeline, and can complete multi-level signal processing in parallel within a single clock cycle.

[0013] As a preferred embodiment, the heterogeneous FPGA also includes an AXI-FIFO2 register and an on-chip system. The key parameters of the speed integral calculation module are configured online through the AXI-Lite interface, and a data stream for intermediate calculation variables is provided. The data stream is connected to the AXI-FIFO2 register, read in real time by the on-chip system, and transmitted via TCP network communication.

[0014] As a preferred embodiment: the oscilloscope is set to edge-triggered mode, the trigger source is the synchronous output signal of an arbitrary waveform generator, and after acquiring the signals of the modulated voltage-controlled oscillator and the real-time compensation module with integral compensation, the data stream is transmitted to the host computer via USB bus. The host computer automatically evaluates the compensation effect of the real-time compensation module.

[0015] As a preferred embodiment, the real-time compensation module is connected to the host computer via a TCP network interface for status monitoring, parameter configuration, and data acquisition.

[0016] As a preferred embodiment, the analog differentiator is constructed using a precision operational amplifier circuit, and the operational amplifier model is ADA4898-1.

[0017] As a preferred embodiment, the voltage-controlled oscillator is model CVSS-945, with a center frequency of 100MHz, a tuning voltage range of 2.5±2.5V, and a tuning rate of +25ppm / V.

[0018] To achieve the second objective of the invention, the present invention adopts the following technical solution:

[0019] A vibration compensation effect simulation and evaluation method based on VCO phase accumulation, employing the system described above, and comprising the following steps:

[0020] Step S1, Data Stream Input: The host computer reads two signals from the voltage-controlled oscillator and the real-time compensation module from the oscilloscope to confirm the sampling rate and the time interval between data points;

[0021] Step S2, Hilbert Transform: The host computer applies the Hilbert transform to the original signal to construct an analytic complex signal to extract the instantaneous phase; analytic signal Defined as: ,in, Represents the Hilbert transform. Represents the original signal. The imaginary unit;

[0022] Step S3, Phase Extraction, Unfolding and Correction: Extract the instantaneous phase from the analytical signal and eliminate the 2π phase jump;

[0023] Instantaneous phase: ,in, Indicates the instantaneous phase of the signal. To analyze the imaginary part of the signal, This represents the real part of the analytic signal;

[0024] Phase expansion algorithm:

[0025] ,

[0026] ,

[0027] in, Indicates the phase of the expansion. The phase deviation is obtained by subtracting the ideal linear phase corresponding to the 100MHz carrier frequency from the 2π phase transition number.

[0028] Ideal linear phase: ,in, , ,

[0029] Phase correction: ;

[0030] Step S4, Differential Calculation and Polynomial Correction: Differentiate the downsampled phase to obtain the frequency deviation;

[0031] ,

[0032] ,

[0033] in, It is the phase difference between adjacent points. It is the frequency difference between adjacent points;

[0034] Then, polynomial correction is performed on the VCO frequency deviation data to compensate for the modulation nonlinearity of the VCO.

[0035] Step S5, Integration and Feature Extraction: Perform trapezoidal integration on the corrected frequency deviation to reconstruct the phase. ;

[0036] ,

[0037] The phase is recorded at key time points based on the pulse sequence defined by the atomic interferometer.

[0038] Trigger starting point, =500,

[0039] π / 2 pulse point =2500, record VCO phase DDS phase ;

[0040] π pulse point, =4500, record VCO phase DDS phase ;

[0041] π / 2 pulse point =6500, record VCO phase DDS phase ;

[0042] Step S6, Differential Phase Output: Calculate the second-order phase difference sensitive to key time points;

[0043] Voltage-controlled oscillator phase difference:

[0044] ,

[0045] Compensation for phase difference:

[0046] ,

[0047] in, The VCO phase at point 2500. The VCO phase at point 6500. The VCO phase at point 4500. The DDS phase at point 2500. The DDS phase at point 6500. This is the DDS phase at point 4500.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] This invention employs a purely electronic signal simulation scheme. A vibration signal is generated by a signal generator, converted by a differentiating circuit, and simultaneously input to the compensation module under test and a VCO-based phase accumulation reference circuit, constructing a dual-channel parallel processing verification architecture. The system utilizes the voltage, frequency, and phase integration characteristics of the VCO, combined with nonlinear correction algorithms and scaling factor calibration techniques, to generate a high-precision displacement reference signal as an evaluation benchmark. A high-sampling-rate multi-channel synchronous acquisition system synchronously captures the DDS output, reference signal, and original vibration signal, and integrates an automated analysis system to complete phase deviation calculation, frequency jump detection, and quantitative evaluation of the compensation effect. This system can simulate large dynamic vibration environments without large equipment such as mechanical vibration tables, supports parameterized configuration of various vibration waveforms, and enables rapid deployment and accurate verification of vibration compensation modules, significantly improving the development and testing efficiency of the compensation system. Attached Figure Description

[0050] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute a limitation thereof.

[0051] Figure 1 This is a schematic diagram of the system of the present invention;

[0052] Figure 2 This is a schematic diagram of the real-time compensation module of the system of the present invention;

[0053] Figure 3 This is an automation flowchart of the system of the present invention;

[0054] Figure 4 This is a modulation phase follower diagram of the system of the present invention;

[0055] Figure 5 This is the differential phase fitting diagram of the system of the present invention.

[0056] The labels in the attached diagram are as follows: 1101, Arbitrary waveform generator; 1102, Analog differentiator; 1103, Voltage-controlled oscillator; 1104, Real-time compensation module; 1105, Oscilloscope; 1106, Host computer; 102, Analog-to-digital conversion driver module; 103, AXI-FIFO1 register; 104, Speed ​​integral calculation module; 105, AXI-FIFO2 register; 106, System-on-a-chip; 107, Timer module; 108, Frequency word calculation module; 109, Direct frequency generation driver module. Detailed Implementation

[0057] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0058] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0059] Furthermore, in the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0060] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more, unless explicitly defined otherwise.

[0061] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0062] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0063] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0064] like Figure 1 and Figure 2As shown, a vibration compensation effect simulation and evaluation system based on VCO phase accumulation includes an arbitrary waveform generator 1101, an analog differentiator 1102, a voltage-controlled oscillator 1103, a real-time compensation module 1104, an oscilloscope 1105, and a host computer 1106. The arbitrary waveform generator 1101 generates a sine wave signal as an analog velocity quantity. The analog differentiator 1102 is built using a precision operational amplifier circuit. The operational amplifier model is ADA4898-1, which has a linear low-noise input stage and built-in compensation circuit, enabling high slew rate and low noise. The differentiated analog signal is considered as an acceleration signal. The voltage-controlled oscillator 1103 is a CVSS-945 model, with a center frequency of 100MHz, a tuning voltage range of 2.5±2.5V, and a tuning rate of +25ppm / V. When the arbitrary waveform generator produces 2Vpp, the resulting frequency modulation is Δf = 100MHz × 25ppm / V × 2V = 5kHz. This frequency modulation simulates the actual effect of carrier vibration on the Raman laser frequency. The real-time compensation module 1104 is a vibration real-time compensation module for precision measurement systems. It can acquire the analog acceleration signal output by the differentiator in real time and output an integrally followed frequency signal. The oscilloscope 1105 is set to edge-triggered mode, with the trigger source being the synchronous output signal of the arbitrary waveform generator 1101. After acquiring the signals from the modulated voltage-controlled oscillator 1103 and the integrally compensated real-time compensation module 1104, the data stream is transmitted to the host computer via USB bus. The host computer 1106 automatically evaluates the compensation effect of the real-time compensation module.

[0065] The real-time compensation module 1104 is a heterogeneous FPGA, which includes an analog-to-digital conversion driver module 102, an AXI-FIFO1 register 103, a velocity integral calculation module 104, a timer module 107, a frequency word calculation module 108, and a direct frequency generation driver module 109. The analog-to-digital conversion driver module 102 receives the data stream from the analog differentiator 1102. The data stream is connected to the AXI-FIFO1 register 103 via an AXI bus. The real-time velocity value calculated by the velocity integral calculation module 104 is connected to the frequency word calculation module 108. The frequency word calculation module 108 is implemented through high-level synthesis. Based on the atomic velocity measurement value and the timing of the interference sequence, it dynamically calculates and outputs the frequency word. The frequency word data stream is transmitted to the direct frequency generation driver module 109, which converts the frequency word into an integral follower signal received by an external module and then transmits it through a parallel interface.

[0066] A heterogeneous FPGA is used as the core of the real-time compensation module. The parallel processing capability of the FPGA, combined with its dedicated internal signal processing chain (ADC driver, FIFO, integral calculation, frequency word calculation, DDS driver), forms a complete hardware pipeline. This means that the delay from data acquisition to output compensation signal can be minimized (nanosecond to microsecond level), which is crucial for real-time compensation systems that need to track rapid vibrations (such as high-frequency noise).

[0067] The AXI-FIFO1 register in the heterogeneous FPGA acts as a data buffer, which not only solves the cross-clock domain problem that may exist between the ADC acquisition clock and the FPGA internal processing clock, but also plays a buffering role when the instantaneous data flow is too large, preventing data loss and ensuring the reliability of the signal processing link.

[0068] The introduction of a timer module in a heterogeneous FPGA is crucial. It is responsible for accurately simulating or synchronizing the pulse sequence timing (such as π / 2 pulses, π pulses) of the cold atom interferometer. Based on this precise timing and the velocity value obtained by integration, the frequency word calculation module dynamically calculates the frequency word, ensuring that the compensation signal can be applied precisely at the specific moment of the interaction between the atom and the laser, which is a prerequisite for effective compensation.

[0069] The direct frequency generation driver module in the heterogeneous FPGA receives the calculated frequency word and converts it into an "integral follower signal" to drive external modules (such as a real DDS chip or analog signals). This module simulates the final step of the conversion from digital compensation signal to analog physical quantity in a real system, enabling the entire evaluation process to cover the complete signal chain from sensor input to compensation drive output.

[0070] The heterogeneous FPGA also includes a timer module 107, which is implemented through high-level synthesis to precisely control the timing signals of the key pulse sequence in cold atom interferometry. These pulse signals are connected to the frequency word calculation module 108. The timer module 107 uses a pulse sequence (e.g., Raman pulse sequence) specific to the atomic interferometer and requiring extremely high timing accuracy as a trigger signal, directly connecting it to the frequency word calculation module. This ensures that the generation and output of the compensation signal are strictly synchronized with the atomic interferometry process, accurately providing the required phase compensation at each pulse action moment (e.g., π / 2, π, π / 2), achieving an integrated design of timing and compensation.

[0071] The frequency word calculation module and timer module in the heterogeneous FPGA are implemented using High-Level Synthesis (HLS). HLS allows developers to describe complex algorithms (such as compensation algorithms and sequential logic) using high-level languages ​​such as C / C++ and automatically generates optimized RTL code. This significantly shortens the development cycle, improves the efficiency of algorithm portability and iteration, and ensures hardware acceleration performance when running on the FPGA.

[0072] The speed integral calculation module 104 is implemented through high-level synthesis. It outputs the speed value through ADC data normalization and dimension conversion, 31st-order FIR digital filtering, 10x CIC downsampling, and first-order IIR approximate integral operation. All processing units are transmitted in a pipeline and can complete multi-level signal processing in parallel within a single clock cycle.

[0073] The heterogeneous FPGA also includes an AXI-FIFO2 register 105 and a system-on-chip 106. The key parameters of the speed integral calculation module 104 are configured online through the AXI-Lite interface, and a data stream for intermediate calculation variables is provided. The data stream is connected to the AXI-FIFO2 register 105, read in real time by the system-on-chip 106, and transmitted via TCP network communication.

[0074] Through the AXI-Lite interface, the host computer can dynamically modify key parameters in the velocity integral calculation module in real time, such as FIR filter coefficients, integrator coefficients, and dimension conversion factors. This allows the algorithm to be adjusted without system downtime during the evaluation process, and the impact of different parameters on the compensation effect can be observed, greatly facilitating algorithm debugging and optimization.

[0075] Furthermore, the data stream of intermediate computational variables is transmitted to the host computer via the AXI-FIFO2 register and the on-chip system through a TCP / IP network. This is equivalent to opening a "window" into the complex signal processing within the FPGA. Developers can observe the filtered acceleration data, velocity values ​​during integration, etc., in real time, thereby gaining a deeper understanding of the algorithm's internal behavior, diagnosing potential problems (such as integration drift, filtering distortion, etc.), and providing valuable debugging information for algorithm improvement.

[0076] The real-time compensation module 1104 is connected to the host computer 1106 via a TCP network interface for status monitoring, parameter configuration, and data acquisition. The host computer software, through the TCP network interface, can both send configuration parameters and receive monitoring data, forming a closed-loop development and evaluation platform with a graphical interface, thus improving the system's usability and operability.

[0077] like Figure 3As shown, a method for simulating and evaluating vibration compensation effects based on VCO phase accumulation is employed using the aforementioned system and includes the following steps:

[0078] Step S1, Data Stream Input: The host computer 1106 reads two signals from the voltage-controlled oscillator 1103 and the real-time compensation module 1104, namely the VCO signal and the DDS signal, from the oscilloscope 1105 to confirm the sampling rate and the time interval between data points.

[0079] Step S2, Hilbert Transform: The host computer applies the Hilbert transform to the original signal to construct an analytic complex signal to extract the instantaneous phase; analytic signal Defined as: ,in, Represents the Hilbert transform. Represents the original signal. The imaginary unit;

[0080] Step S3, Phase Extraction, Unfolding and Correction: Extract the instantaneous phase from the analytical signal and eliminate the 2π phase jump;

[0081] Instantaneous phase: ,in, Indicates the instantaneous phase of the signal. To analyze the imaginary part of the signal, This represents the real part of the analytic signal;

[0082] Phase expansion algorithm:

[0083] ,

[0084] ,

[0085] in, Indicates the phase of the expansion. The phase deviation is obtained by subtracting the ideal linear phase corresponding to the 100MHz carrier frequency from the 2π phase transition number.

[0086] Ideal linear phase: ,in, , ,

[0087] Phase correction: ;

[0088] Step S4, Differential Calculation and Polynomial Correction: Differentiate the downsampled phase to obtain the frequency deviation;

[0089] ,

[0090] ,

[0091] in, It is the phase difference between adjacent points. It is the frequency difference between adjacent points;

[0092] Then, polynomial correction is performed on the VCO frequency deviation data to compensate for the modulation nonlinearity of the VCO.

[0093] Step S5, Integration and Feature Extraction: Perform trapezoidal integration on the corrected frequency deviation to reconstruct the phase. ;

[0094] ,

[0095] The phase is recorded at key time points based on the pulse sequence defined by the atomic interferometer.

[0096] Trigger starting point, =500,

[0097] π / 2 pulse point =2500, record VCO phase DDS phase ;

[0098] π pulse point, =4500, record VCO phase DDS phase ;

[0099] π / 2 pulse point =6500, record VCO phase DDS phase ;

[0100] Step S6, Differential Phase Output: Calculate the second-order phase difference sensitive to key time points;

[0101] Voltage-controlled oscillator phase difference:

[0102] ,

[0103] Compensation for phase difference:

[0104] ,

[0105] in, The VCO phase at point 2500. The VCO phase at point 6500. The VCO phase at point 4500. The DDS phase at point 2500. The DDS phase at point 6500. This is the DDS phase at point 4500.

[0106] Figure 4 The phase-following diagram of the compensation module in actual testing is shown. The VCO signal, after phase expansion and differentiation, represents the frequency modulation response of the voltage-controlled oscillator under simulated vibration excitation, reflecting the actual impact of carrier vibration on the Raman laser frequency. The DDS signal is the frequency compensation signal output by the real-time compensation module. In the initial stage of the system, the DDS signal is in its initial state and has not yet tracked the VCO modulation. When the system enables phase following, the DDS signal quickly converges and closely follows the VCO modulation signal. The two signal waveforms are highly consistent in the time domain, and the phase difference remains constant, indicating that the real-time compensation system can reconstruct the frequency modulation caused by vibration and achieve effective compensation for carrier vibration.

[0107] Figure 5 This paper presents the correlation analysis results of VCO differential phase and DDS differential phase data obtained through repeated tests in an embodiment of the present invention. The scatter plot contains multiple sets of independent test data points, and the quantitative relationship between the system input and output is compensated through linear regression analysis. A least-squares linear fit is performed on the scatter data, yielding a correlation coefficient squared (R²) of 0.998448, indicating a high linear correlation between the VCO differential phase and the DDS differential phase. The standard deviation of the residuals between the data points and the fitted line is approximately 6.14 rad.

[0108] This invention constructs a vibration compensation verification system using a purely electronic signal simulation scheme. The system employs an arbitrary waveform generator and a voltage-controlled oscillator (VCO) to collaboratively build a high-precision phase reference. A dual-path parallel processing architecture synchronously acquires the VCO phase signal and the compensation module's output signal. Combined with Hilbert transform phase extraction, polynomial nonlinear correction, and automated analysis algorithms, it achieves efficient quantitative evaluation of the vibration compensation module's compensation accuracy, dynamic response, and linearity. This system completely eliminates the reliance on large mechanical vibration tables and complex optical measurement devices, enabling the simulation of large dynamic vibration environments under conventional experimental conditions.

[0109] This system uses VCO phase accumulation as the displacement reference benchmark. Compared with displacement measurement based on laser interferometers, it significantly reduces system complexity while maintaining sub-milliradian phase accuracy, making it more suitable for rapid verification in engineering fields. By introducing a nonlinear correction algorithm and scaling factor calibration process, the phase accumulation linearity is improved compared to an uncorrected VCO reference system. The system integrates automated analysis software, which, compared with traditional manual data recording and processing methods, automates the entire process from signal acquisition to evaluation report generation. The time for a single test is reduced to less than 10 minutes, and it supports batch testing and data traceability, greatly improving the verification efficiency and reliability of the compensation module. This provides a standardized and replicable verification solution for the development of vibration compensation modules for quantum sensing devices such as mobile platform cold atom interferometers.

[0110] This invention employs a fully electronic VCO phase accumulation reference architecture, generating analog vibration acceleration signals through an arbitrary waveform generator and an analog differentiating circuit. Vibration acceleration is physically a direct representation of the motion disturbance of the carrier, and its instantaneous measurement itself has no integral drift or cumulative error. Through a parallel processing path, this signal is synchronously input to the compensation module under test and the phase accumulation reference unit built based on a voltage-controlled oscillator. The VCO, through its inherent voltage, frequency, and phase integration characteristics, combined with a discrete-time correction algorithm, can reconstruct the acceleration signal into a high-precision accumulated phase reference within microsecond delays. This mechanism effectively avoids the reference signal distortion introduced by the limitations of the table response bandwidth, nonlinearity of the mechanical transfer function, and multi-axis coupling in traditional mechanical vibration table verification schemes.

[0111] This invention designs a dual-path parallel, phase-comparison evaluation architecture. The core of this architecture lies in constructing an electronic phase accumulation reference equivalent to the actual optical interferometry process, and achieving strictly synchronized acquisition and analysis with the compensation output. In the reference path, the instantaneous phase of the VCO signal is extracted through Hilbert transform, and combined with nonlinear correction and phase expansion algorithms, the ideal phase accumulation trajectory caused by vibration is reconstructed. The evaluation path synchronously acquires the frequency output of the compensation module and converts it into a phase sequence. By latching and performing second-order difference calculations on the two phases at key time points of the atomic interferometer (such as Raman π / 2 and π pulse moments), the residual error of the compensation can be directly quantified.

[0112] This invention integrates a fully automated signal processing and data analysis pipeline into the evaluation system, and designs a software analysis platform that includes multi-stage data visualization and configurable parameters. This enables the system to achieve transparent processing and repeatable analysis throughout the entire process, from raw signal acquisition, phase extraction, nonlinear compensation to performance index generation. This design not only achieves efficient quantitative evaluation of the compensation effect, but also allows for self-verification of the system's linearity, dynamic range, and stability through parametric testing and regression analysis. It provides a complete hardware and software integrated verification foundation for iterative optimization, field calibration, and long-term reliability verification of the compensation module.

[0113] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0114] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for simulating and evaluating the vibration compensation effect based on VCO phase accumulation, characterized in that: The vibration compensation effect simulation and evaluation system includes an arbitrary waveform generator (1101), an analog differentiator (1102), a voltage-controlled oscillator (1103), a real-time compensation module (1104), an oscilloscope (1105), and a host computer (1106). The arbitrary waveform generator (1101) generates a sine wave signal as an analog velocity quantity and inputs it to the voltage control pins of the analog differentiator (1102) and the voltage-controlled oscillator (1103). The analog differentiator (1102) inputs the processed signal to the real-time compensation module (1104). The integral follower signal output by the real-time compensation module (1104) and the modulation signal output by the voltage-controlled oscillator (1103) are collected and recorded by the oscilloscope (1105). The oscilloscope (1105) is connected to the host computer (1106) via USB to transmit the data stream to the host computer (1106) for automated calculation and processing. The system includes the following steps: Step S1, Data Stream Input: The host computer (1106) reads two signals from the voltage-controlled oscillator (1103) and the real-time compensation module (1104) from the oscilloscope (1105) to confirm the sampling rate and the time interval between data points; Step S2, Hilbert Transform: The host computer (1106) applies the Hilbert transform to the original signal to construct an analytic complex signal to extract the instantaneous phase; the analytic signal... Defined as: ,in, Represents the Hilbert transform. Represents the original signal. The imaginary unit; Step S3, Phase Extraction, Unfolding and Correction: Extract the instantaneous phase from the analytical signal and eliminate the 2π phase jump; Instantaneous phase: ,in, Indicates the instantaneous phase of the signal. To analyze the imaginary part of the signal, This represents the real part of the analytic signal; Phase expansion algorithm: ， ， in, Indicates the phase of the expansion. The phase deviation is obtained by subtracting the ideal linear phase corresponding to the 100MHz carrier frequency from the 2π phase transition number. Ideal linear phase: ,in, , , Correction phase: ; Step S4, Differential Calculation and Polynomial Correction: Differentiate the downsampled phase to obtain the frequency deviation; ， ， in, It is the phase difference between adjacent points. It is the frequency difference between adjacent points; Then, polynomial correction is performed on the VCO frequency deviation data to compensate for the modulation nonlinearity of the VCO. Step S5, Integration and Feature Extraction: Perform trapezoidal integration on the corrected frequency deviation to reconstruct the phase. ; ， The phase is recorded at key time points based on the pulse sequence defined by the atomic interferometer. Trigger starting point, =500, π / 2 pulse point =2500, record VCO phase DDS phase ; π pulse point, =4500, record VCO phase DDS phase ; π / 2 pulse point =6500, record VCO phase DDS phase ; Step S6, Differential Phase Output: Calculate the second-order phase difference sensitive to key time points; Voltage-controlled oscillator phase difference: ， Compensation for phase difference: ， in, The VCO phase at point 2500. The VCO phase at point 6500. The VCO phase at point 4500. The DDS phase at point 2500. The DDS phase at point 6500. This is the DDS phase at point 4500.

2. The vibration compensation effect simulation and evaluation method based on VCO phase accumulation according to claim 1, characterized in that: The real-time compensation module (1104) is a heterogeneous FPGA. The heterogeneous FPGA includes an analog-to-digital conversion driver module (102), an AXI-FIFO1 register (103), a velocity integral calculation module (104), a timer module (107), a frequency word calculation module (108), and a direct frequency generation driver module (109). The analog-to-digital conversion driver module (102) is used to receive the data stream from the analog differentiator (1102). The data stream is connected to the AXI-FIFO1 register (103) via the AXI bus. The real-time velocity value calculated by the velocity integral calculation module (104) is connected to the frequency word calculation module (108). The frequency word calculation module (108) is implemented through high-level synthesis. Based on the atomic velocity measurement value and the timing of the interference sequence, it dynamically calculates and outputs the frequency word. The frequency word data stream is transmitted to the direct frequency generation driver module (109). This module converts the frequency word into an integral follower signal received by the external module and then transmits it through the parallel interface.

3. The vibration compensation effect simulation and evaluation method based on VCO phase accumulation according to claim 2, characterized in that: The heterogeneous FPGA also includes a timer module (107), which is implemented through high-level synthesis to precisely control the key pulse sequence timing signal of cold atom interferometry. The pulse signal is connected to the frequency word calculation module (108).

4. The vibration compensation effect simulation and evaluation method based on VCO phase accumulation according to claim 2, characterized in that: The speed integral calculation module (104) is implemented through high-level synthesis. It outputs the speed value through ADC data normalization and dimension conversion, 31st-order FIR digital filtering, 10x CIC downsampling and first-order IIR approximate integral operation. All processing units are transmitted in a pipeline and can complete multi-level signal processing in parallel within a single clock cycle.

5. The vibration compensation effect simulation and evaluation method based on VCO phase accumulation according to claim 2, characterized in that: The heterogeneous FPGA also includes an AXI-FIFO2 register (105) and a system-on-a-chip (106). The key parameters of the speed integral calculation module (104) are configured online through the AXI-Lite interface, and a data stream for intermediate calculation variables is provided. The data stream is connected to the AXI-FIFO2 register (105), read in real time through the system-on-a-chip (106), and transmitted via TCP network communication.

6. The vibration compensation effect simulation and evaluation method based on VCO phase accumulation according to claim 1, characterized in that: The oscilloscope (1105) is set to edge trigger mode, and the trigger source is the synchronous output signal of the arbitrary waveform generator (1101). After acquiring the signals of the modulated voltage-controlled oscillator (1103) and the real-time compensation module (1104) with integral compensation, the data stream is transmitted to the host computer via the USB bus. The host computer automatically evaluates the compensation effect of the real-time compensation module.

7. The vibration compensation effect simulation and evaluation method based on VCO phase accumulation according to claim 1, characterized in that: The real-time compensation module (1104) is connected to the host computer (1106) via a TCP network interface and is used for status monitoring, parameter configuration and data acquisition of the real-time compensation module (1104).

8. The vibration compensation effect simulation and evaluation method based on VCO phase accumulation according to claim 1, characterized in that: The analog differentiator (1102) is built using a precision operational amplifier circuit, and the operational amplifier model is ADA4898-1.

9. The vibration compensation effect simulation and evaluation method based on VCO phase accumulation according to claim 1, characterized in that: The voltage-controlled oscillator (1103) is model CVSS-945, with a center frequency of 100MHz, a tuning voltage range of 2.5±2.5V, and a tuning rate of +25ppm / V.

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