Vertical noise rejection platform for airborne gravity gradiometry and control method

Abstract

This application belongs to the field of active vibration isolation technology, and is a vertical noise suppression platform and control method for airborne gravity gradient measurement. It includes: a passive vibration isolation unit for pre-attenuating high-frequency vibrations of the airborne foundation and providing static support for the load; a horizontal constraint mechanical unit for retaining only the vertical linear motion degree of freedom of the vibration isolation platform base; a vibration signal acquisition unit for acquiring vibration signals from the airborne foundation and the load; a drive execution unit for synchronously outputting a vertical bidirectional control force based on the drive current; and a control unit for calculating the control quantity based on the foundation vibration signal and the load vibration signal, and controlling the drive execution unit to output the corresponding vertical bidirectional control force to counteract the disturbance of the load caused by airborne vibration. This application is adapted to airborne scenarios, and through a feedforward feedback dual-sensor architecture and full-state control, it adapts to complex dynamic disturbances on the airborne surface, solving the problem of poor adaptability to the airborne environment in traditional solutions.

Description

Technical Field

[0001] This application belongs to the field of active vibration isolation technology, specifically a vertical noise suppression platform and control method for airborne gravity gradient measurement. Background Technology

[0002] Gravity gradiometers are a new type of high-precision measuring instrument widely used in precision measurement fields such as geophysics, oceanographic exploration, airborne geophysical surveying, and inertial navigation. In airborne dynamic measurement scenarios, complex vibrations such as aircraft engine vibration, low-frequency airflow turbulence, takeoff and landing impacts, and fuselage structural resonance affect the stability and accuracy of measurements. Among these, the 0.1-10Hz ultra-low frequency band is the core sensitive frequency band of gravity gradiometers, where vibrations will couple into the measurement results. Passive vibration isolation can only effectively attenuate high-frequency vibrations, and its effect on suppressing low-frequency vibrations is poor. In fact, it may even amplify the transmission of vibrations in the system's resonant frequency band. Therefore, it is necessary to compensate for low-frequency vibrations through an active vibration isolation system.

[0003] Currently, research has been conducted on vibration isolation schemes for gravity gradiometers. Existing vibration isolation platforms are all designed for ground-based experimental environments and have significant limitations in airborne scenarios: First, existing schemes mostly use pendulum-type velocity seismometers to achieve high-precision vibration detection, but the vibration amplitude in the airborne environment can reach several grams, exceeding the range of most high-precision seismometers. Moreover, the kilogram-level weight of the seismometer is not conducive to the miniaturization of the vibration isolation platform and cannot adapt to the load and space constraints of airborne environments. Second, existing schemes are based on PID control, and the control effect is highly dependent on manual parameter tuning. They have poor adaptability and anti-interference ability to time-varying disturbances and nonlinear interference in airborne scenarios and are difficult to cope with complex airborne dynamic environments.

[0004] Model predictive control (MPC) can achieve rolling optimization under explicit constraints and can effectively adapt to hardware constraints such as the stroke and output range of a coil motor. However, its control accuracy is highly dependent on the accuracy of the dynamic model. In aviation scenarios, non-ideal factors such as motor temperature rise and structural deformation can lead to model mismatch, resulting in prediction residual errors and a decline in control performance. Reinforcement learning can learn the model error and disturbance law through data-driven methods. Among them, the deep deterministic policy gradient (TD3) algorithm is suitable for continuous motion control scenarios and can effectively solve problems such as value function overestimation and policy oscillation. However, its direct output of control quantity is difficult to guarantee system stability and constraint compliance. Summary of the Invention

[0005] This application provides an airborne active vibration isolation system and control method to solve the problems of difficulty in suppressing ultra-low frequency vibration, mismatch between sensor range and miniaturization requirements, and poor anti-interference leading to decreased control performance in airborne atomic gravity measurement scenarios.

[0006] The first aspect of this application provides a vertical noise suppression platform for airborne gravity gradient measurement, comprising: a passive vibration isolation unit, a horizontal constraint mechanical unit, a vibration signal acquisition unit, a control unit, and a drive execution unit; wherein: The passive vibration isolation unit uses a compression spring as a vibration isolation element and is set between the vibration isolation platform base and the platform to pre-attenuate the high-frequency vibration of the airborne foundation and provide static support for the load. The horizontal constraint mechanical unit includes a limiting guide rod and a linear bearing. The linear bearing is fixed on the platform, the limiting guide rod is vertically fixed to the vibration isolation platform base, and the linear bearing is sleeved on the outside of the limiting guide rod and slides in cooperation with the limiting guide rod, so as to retain only the vertical linear motion degree of freedom of the vibration isolation platform base. The vibration signal acquisition unit is used to acquire airborne foundation vibration signals and load vibration signals; The drive execution unit includes a voice coil motor disposed between the stage and the vibration isolation platform base, used to synchronously output vertical bidirectional control force according to the drive current; The control unit is used to calculate the control quantity based on the foundation vibration signal and the load vibration signal, and control the drive execution unit to output the corresponding vertical bidirectional control force to counteract the disturbance of the load by the airborne vibration.

[0007] Furthermore, the vibration signal acquisition unit includes a feedforward accelerometer and a feedback accelerometer. The feedforward accelerometer is mounted on the base of the vibration isolation platform, and the feedback accelerometer is mounted on the platform surface of the loading stage.

[0008] Furthermore, there are four voice coil motors, which are evenly distributed at 90° orthogonal around the vibration isolation platform base.

[0009] Furthermore, the control unit includes a system identification module, a model prediction control module, a reinforcement learning correction module, and a visualization analysis module; wherein: The system identification module is used to collect system input and output datasets through hammer impact tests and sinusoidal excitation tests in the offline stage, and to identify the nominal dynamic model of the active vibration isolation system with a vertical single degree of freedom using the N4SID subspace method algorithm, obtain the parameters of the nominal dynamic model and complete the calibration. The model predictive control module is used to predict the system output for multiple future sampling times based on the nominal dynamic model after obtaining the system state at the current time by iterating the state update equation in the nominal dynamic model. It constructs a cost function using the weighted sum of squares of the deviation between the predicted output and the expected reference trajectory, and the weighted sum of squares of the control increment. It solves for the optimal control sequence that minimizes the cost function and uses the first component of the optimal control sequence as the initial control quantity at the current time. The reinforcement learning correction module is used to receive the prediction residual error and initial control quantity from the model prediction control module. After processing by the actor-critic network, the stiffness correction quantity, damping correction quantity, and correction quantity of the initial control quantity of the nominal dynamic model are obtained. The initial control quantity and the correction quantity are superimposed to obtain the final control quantity. The visualization analysis module is used to display the vibration signal time-domain curve, the vibration isolation transmissibility frequency-domain curve, and the final control and correction variable change curves in real time.

[0010] Furthermore, the N4SID subspace method algorithm is used to identify the nominal dynamic model of the active vibration isolation system with a single vertical degree of freedom, including: Impulse response data of the active vibration isolation system is obtained through hammer impact test, and frequency response data of the active vibration isolation system within a set frequency band is obtained through sinusoidal excitation test. Excitation signal and acceleration response signal are collected to construct input-output dataset. Based on the input and output dataset, a past input matrix, a past output matrix, a future input matrix, and a future output matrix are constructed. The future output matrix is ​​obliquely projected to extract system state information. Singular value decomposition is performed on the obliquely projected future output matrix. The system order is determined based on the magnitude of the singular values. The state transition matrix A and the output matrix C are solved using the shift invariance of the observability matrix. The number of columns in the observability matrix is ​​determined by the system order. The input matrix B and the feedforward matrix D are solved by least squares fitting to obtain the nominal dynamic model. Modal frequencies and damping ratios are extracted from the eigenvalues ​​of the identified state transition matrix A. Stiffness coefficients and damping coefficients are calculated based on the known load mass 4, thus completing the parameter extraction and calibration of the nominal dynamic model.

[0011] Furthermore, in the model predictive control module, under the condition of including physical constraints, the cost function and constraint conditions are transformed into a standard quadratic programming problem for solution. The quadratic programming solver is called to solve the above standard quadratic programming problem to obtain the optimal control increment sequence in the control time domain. Only the first component of the optimal control increment sequence is taken as the optimal control increment at the current time. It is then superimposed on the control quantity at the previous time to form the initial control quantity at the current time.

[0012] Furthermore, the state space of the actor-critic network includes foundation displacement, foundation velocity, foundation acceleration, load displacement, load velocity, load acceleration, the prediction residual error of the model predictive control module, and the initial control quantity output by the model predictive control module. The state space is processed to output a three-dimensional action vector, which includes stiffness correction, damping correction and initial control correction for the nominal dynamic model. The stiffness correction and the damping correction are fed back to the nominal dynamic model to correct the stiffness and damping parameters of the nominal dynamic model online. The updated nominal dynamic model is used for the output prediction of the model prediction control module in the next control cycle. The correction amount of the initial control quantity is added to the initial control quantity to form the final control quantity.

[0013] The first aspect of this application provides a control method for a vertical noise suppression platform for airborne gravity gradient measurement, comprising: In the offline phase, the system input and output datasets were collected through hammer impact tests and sinusoidal excitation tests. The N4SID algorithm of the subspace method was used to identify the nominal dynamic model of the active vibration isolation system with a vertical single degree of freedom, obtain the parameters of the nominal dynamic model, and complete the calibration. Based on the nominal dynamics model, after obtaining the system state at the current moment, the system output at multiple future sampling moments is predicted by iterating the state update equation in the nominal dynamics model. A cost function is constructed using the weighted sum of squares of the deviation between the predicted output and the expected reference trajectory, and the weighted sum of squares of the control increment. The optimal control sequence that minimizes the cost function is solved, and the first component of the optimal control sequence is used as the initial control quantity at the current moment. The predicted residual error and initial control quantity are processed by an actor-critic network to obtain the stiffness correction, damping correction, and correction to the initial control quantity of the nominal dynamic model. The initial control quantity and the correction are then superimposed to obtain the final control quantity.

[0014] Furthermore, the stiffness correction and the damping correction are fed back to the nominal dynamic model to perform online correction of the stiffness and damping parameters of the nominal dynamic model.

[0015] Compared with the prior art, the advantages of this application are as follows: This application is adapted to airborne scenarios. Through a feedforward dual-sensor architecture and full-state control, it adapts to complex dynamic disturbances on the air and solves the problem of poor adaptability to the aviation environment of traditional solutions.

[0016] Achieve full-band vibration suppression: Passive vibration isolation using compression springs attenuates high-frequency vibrations, while active vibration isolation compensates for ultra-low-frequency vibrations in the 0.1-10Hz range. This solves the inherent defects of poor low-frequency effect and resonance peak amplification in passive vibration isolation, and covers the entire sensitive frequency band of gravity gradient measurement.

[0017] The platform in this application strictly meets hardware constraints to ensure system control stability; it corrects model prediction errors online through reinforcement learning, adapts to continuous motion control scenarios, solves the problems of value function overestimation and policy oscillation, and has a strong adaptive capability to time-varying disturbances and nonlinear characteristics in aviation scenarios. Attached Figure Description

[0018] Figure 1 A schematic diagram of a vertical noise suppression platform for airborne gravity gradient measurement provided in this application embodiment; Figure 2 This is a structural block diagram of the control unit provided in an embodiment of this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0020] The design load mass selected in this embodiment is 250g, and the core is adapted to the sensitive frequency band of gravity gradient measurement of 0.1-10Hz. It can be adapted to dynamic measurement scenarios in the entire flight phase, such as aircraft cruise, take-off and landing. The overall weight of the system is ≤1.5kg, which is fully adapted to the load and space miniaturization constraints of airborne aircraft.

[0021] See Figure 1 As shown, a vertical noise suppression platform for airborne gravity gradient measurement includes: a passive vibration isolation unit, a horizontal constraint mechanical unit, a vibration signal acquisition unit, a control unit, and a drive execution unit; wherein: The passive vibration isolation unit uses a compression spring 8 as a vibration isolation element, which is set between the vibration isolation platform base 1 and the platform 2 to pre-attenuate the high-frequency vibration of the airborne foundation and provide static support for the load 4. The horizontal constraint mechanical unit includes a limiting guide rod 6 and a linear bearing 7. The linear bearing 7 is fixed on the platform 2. The limiting guide rod 6 is vertically fixed to the vibration isolation platform base 1. The linear bearing 7 is sleeved on the outside of the limiting guide rod 6 and slides in cooperation with the limiting guide rod 6, so as to retain only the vertical linear motion degree of freedom of the vibration isolation platform base 1. The vibration signal acquisition unit is used to acquire the vibration signal of the airborne foundation and the vibration signal of the load 4; The drive execution unit includes a voice coil motor 9 disposed between the stage 2 and the vibration isolation platform base 1, which is used to synchronously output vertical bidirectional control force according to the drive current; The control unit is used to calculate the control quantity based on the foundation vibration signal and the load vibration signal, and control the drive execution unit to output the corresponding vertical bidirectional control force to counteract the disturbance of the airborne vibration on the load 4.

[0022] The core working principle is as follows: a vibration signal acquisition unit is used to collect vibration signals from the airborne foundation and the load; the control unit calculates the control quantity in real time through an embedded control algorithm based on the feedforward information of the foundation vibration and the feedback information of the load 4 vibration; the drive execution unit outputs the corresponding vertical control force according to the control quantity; the control force and the spring force of the passive vibration isolation unit work together to counteract the disturbance of the airborne vibration to the load 4. This structure achieves ultra-low frequency vibration suppression of the precision load 4 in the airborne environment through active and passive coordinated vibration isolation.

[0023] In some embodiments, the passive vibration isolation unit uses a compression spring 8 as the vibration isolation element, disposed between the vibration isolation platform base 1 and the platform 2. The compression spring 8 is symmetrically arranged at multiple positions between the vibration isolation platform base 1 and the platform 2, with its upper end abutting the lower surface of the platform 2 and its lower end abutting the upper surface of the vibration isolation platform base 1, providing static support for the platform 2 and its load 4. In the airborne environment, high-frequency vibrations of the foundation are first pre-attenuated by the elastic deformation of the compression spring 8. The stiffness coefficient of the compression spring 8 is matched to ensure that the system's natural frequency is much lower than the dominant frequency of the airborne vibration, thus achieving initial isolation of high-frequency vibrations at the passive level.

[0024] In a typical embodiment of this application, the compression spring 8 is sleeved outside the limiting guide rod 6 of the horizontal constraint mechanical unit. The limiting guide rod 6 guides the extension and retraction direction of the compression spring 8, preventing lateral bending of the compression spring 8 during compression or extension. The number and stiffness coefficient of the compression spring 8 are jointly determined based on the total mass of the load 4 (including the mass of the stage 2, the mass of the load 4, and the equivalent mass of the mover of the voice coil motor 9) and the design natural frequency, ensuring that the compression amount of the compression spring 8 is within the linear operating range under static equilibrium conditions.

[0025] In some embodiments, the horizontal constraint mechanical unit includes a limiting guide rod 6 and a linear bearing 7, used to constrain the non-vertical degrees of freedom of the vibration isolation platform, retaining only the vertical linear motion degree of freedom. The limiting guide rod 6 is vertically fixed to the vibration isolation platform base 1 and extends vertically. The linear bearing 7 is fixedly installed on the platform 2 through a bearing seat, and the linear bearing 7 is sleeved outside the limiting guide rod 6 and forms a sliding fit with the limiting guide rod 6. The cooperation relationship between the limiting guide rod 6 and the linear bearing 7 is as follows: when the platform 2 is subjected to a horizontal component force, the rigid contact between the linear bearing 7 and the limiting guide rod 6 prevents the platform 2 from undergoing horizontal displacement; when the platform 2 is subjected to a torque about the horizontal axis, multiple limiting guide rods 6 and linear bearings 7 work together to prevent the platform 2 from pitching and rolling; when the platform 2 is subjected to vertical vibration, the linear bearing 7 slides freely along the limiting guide rod 6, so that the platform 2 retains only the vertical linear motion degree of freedom.

[0026] In a typical embodiment of this application, four limiting guide rods 6 are arranged in a rectangular pattern around the vibration isolation platform base 1, and four linear bearings 7 are correspondingly provided to each of them. The four limiting guide rods 6 together constrain the horizontal displacement and rotational degrees of freedom, while evenly bearing the horizontal load and overturning moment of the platform 2. The limiting guide rods 6 and the linear bearings 7 are made of low-friction coefficient materials (such as chrome-plated steel guide rods and self-lubricating linear bearings 7) to minimize the sliding resistance during vertical movement and ensure the sensitivity of the vibration isolation system.

[0027] In some embodiments, the vibration signal acquisition unit includes a feedforward accelerometer 3 and a feedback accelerometer 5, both of which are MEMS capacitive accelerometers. They have the advantages of small size, light weight, strong shock resistance and good DC response characteristics, making them suitable for the application requirements of airborne environments.

[0028] The feedforward accelerometer 3 is mounted on the vibration isolation platform base 1 to collect the original vibration signal of the airborne foundation. This original vibration signal includes composite vibration components such as aircraft engine vibration, airflow turbulence excitation, and takeoff and landing impact, serving as the disturbance input for feedforward control. The feedback accelerometer 5 is mounted on the platform 2 to collect the actual vibration response signal of the load 4, including the residual vibration after passive vibration isolation attenuation and the residual vibration after the application of active control force, serving as the error input for feedback control.

[0029] In a typical embodiment of this application, the outputs of both accelerometers are connected to an AD7606 synchronous sampling chip. The AD7606 synchronous sampling chip is an eight-channel synchronous sampling analog-to-digital converter that supports parallel interface output. It can synchronously sample and convert the two acceleration signals, ensuring strict time alignment between the feedforward and feedback signals and eliminating phase errors introduced by sampling time deviations. The sampling rate is set to 1000Hz, covering the main frequency band of airborne vibration from 0.1Hz to 100Hz.

[0030] In some embodiments, the control unit is the core of the entire platform and is implemented using the ZYNQ7020 chip. The ZYNQ7020 has a built-in PS (processing system, i.e., dual-core ARM Cortex-A9 processor) and PL (programmable logic, i.e. FPGA resources) collaborative architecture, and all acquisition, calculation and control are completed in a closed loop within a single chip, without the need for an external processor or FPGA.

[0031] In terms of functional allocation, the PL end is responsible for the underlying high-speed real-time tasks, including the AD7606 synchronous sampling chip acquisition driver, controlling the sampling timing of the AD7606 synchronous sampling chip and reading the converted data through a parallel interface; digital filtering, performing bandpass filtering on the acceleration signal to remove DC bias and power frequency interference; acceleration integration, performing time-domain integration on the filtered acceleration signal to obtain velocity and displacement signals; and drive execution unit driving and data buffering, outputting the calculated digital control quantities in parallel according to the timing requirements of the drive execution unit, and buffering data to match the rate difference between the PS end and the PL end.

[0032] The PS (Power Supply) module runs an operating system or a bare-metal program, undertaking the computation and control decision-making tasks of complex algorithms. This includes a system identification module, which identifies the nominal dynamic model of the system through hammer tests and sinusoidal excitation tests in the offline phase; a model predictive control module, which calculates the initial control quantity based on the nominal dynamic model through rolling optimization in each control cycle; a reinforcement learning correction module, which corrects the prediction residual error of the model predictive control module online; and a visualization analysis module, which displays the vibration time-domain curve, the vibration isolation transmissibility frequency-domain curve, and the curves showing the changes in control and correction quantities in real time.

[0033] In one embodiment, the drive execution unit includes a digital-to-analog converter module, a voltage-controlled constant current source, and a voice coil motor 9, used to convert the digital control quantity output by the control unit into actual driving force.

[0034] The digital-to-analog converter module uses the DAC904 chip, a 14-bit high-speed digital-to-analog converter that supports parallel data input. The PL terminal directly outputs a 14-bit digital control signal in parallel to the DAC904 chip, which converts the digital signal into an analog voltage signal. The voltage range is designed to match the input range of the voltage-controlled constant current source.

[0035] The voltage-controlled constant current source is constructed using an operational amplifier (such as the OPA547 chip) to linearly convert the analog voltage signal output from the DAC904 chip into a drive current. The output current of the constant current source is proportional to the input voltage, and the proportionality coefficient is calibrated to ensure accurate and linear conversion between control voltage and drive current.

[0036] Four voice coil motors 9 are arranged in a 90° orthogonal uniform distribution around the vibration isolation platform base 1. The four motors are electrically connected in parallel and receive the same drive current command. Each voice coil motor 9 includes a permanent magnet stator and a movable coil. When the drive current passes through the coil, the coil experiences a Lorentz force in the magnetic field, generating a vertical thrust or pull force; the direction of the current determines the direction of the force. The four motors synchronously output a vertical bidirectional control force, the resultant of which acts on the platform 2 to counteract the disturbance of the load 4 caused by airborne vibration. The voice coil motors 9 have the advantages of being contactless, frictionless, having a fast response speed, and exhibiting a linear relationship between control force and current, making them suitable as high-frequency response actuators for active vibration isolation.

[0037] In some embodiments, see Figure 2 As shown, the PS terminal of the control unit includes a system identification module, a model prediction control module, a reinforcement learning correction module, and a visualization analysis module; wherein: The system identification module is used to collect system input and output datasets through hammer impact tests and sinusoidal excitation tests in the offline stage. It uses the N4SID subspace method algorithm to identify the nominal dynamic model of the active vibration isolation system with a vertical single degree of freedom, obtain the parameters of the nominal dynamic model, and complete the calibration. The model predictive control module is used to predict the system output for multiple future sampling times based on the nominal dynamic model after obtaining the system state at the current time by iterating the state update equation in the nominal dynamic model. It constructs a cost function using the weighted sum of squares of the deviation between the predicted output and the expected reference trajectory, and the weighted sum of squares of the control increment. It solves for the optimal control sequence that minimizes the cost function and uses the first component of the optimal control sequence as the initial control quantity at the current time. The reinforcement learning correction module receives the prediction residual error and initial control quantity from the model prediction control module. After processing by the actor-critic network, it obtains the stiffness correction, damping correction, and correction of the initial control quantity of the nominal dynamic model. The initial control quantity and the correction are superimposed to obtain the final control quantity. The visualization analysis module is used to display the vibration signal time-domain curve, the vibration isolation transmissibility frequency-domain curve, and the curves showing the changes in the final control and correction quantities in real time.

[0038] The system identification module employs the subspace method N4SID algorithm to identify the vertical single-degree-of-freedom nominal dynamic model of the active vibration isolation system. The full name of the subspace method N4SID algorithm is Numerical Algorithm for Subspace State-Space System Identification, which includes: The impulse response data of the active vibration isolation system is obtained through hammer impact tests, and the frequency response data of the system within a set frequency band is obtained through sinusoidal excitation tests. Excitation signals and acceleration response signals are collected to construct an input-output dataset. The hammer impact test is used to obtain the impulse response characteristics of the system. Its principle is to apply a very short-duration pulse force, approximately a half-sine wave, to the vibration isolation platform using a hammer equipped with a force sensor. The spectrum of this pulse force remains flat over a wide frequency band, thus enabling simultaneous excitation of multiple modes of the system. Before the test, the following preparations must be completed: install the platform on the aerospace vibration simulation table, ensuring a secure connection between the base and the simulation table surface; check the installation status of the feedforward accelerometer 3 and the feedback accelerometer 5, confirming the correct correspondence between the sensors and the acquisition channels; connect the force sensor signal line of the hammer to the input channel of the AD7606 synchronous sampling chip.

[0039] The material of the hammer cap and the weight of the hammer head should be selected appropriately according to the target frequency band (0.1Hz to 100Hz).

[0040] The operator uses a hammer to strike the platform 2 or base of the vibration isolation platform vertically. The striking position should be near the center of the platform to ensure that the excitation force is evenly transmitted to all modes of the system. Each strike should be crisp and clean, with the hammer lifted quickly after contact with the platform to avoid secondary or multiple impacts that could contaminate the signal.

[0041] The piezoelectric sensor built into the hammer collects the excitation force signal in real time, which is proportional to the pulse force applied to the system. Simultaneously, the feedforward accelerometer 3 mounted on the vibration isolation platform base 1 and the feedback accelerometer 5 mounted on the platform 2 synchronously collect the system's acceleration response signal. These two acceleration signals reflect the vibration response on the foundation side and the load side, respectively, and together constitute the system's input and output data under pulse excitation.

[0042] To ensure the data quality of the hammer impact test, the following measures were taken: Averaging of multiple strikes. To reduce statistical bias caused by random errors and operational inconsistencies, 5 to 10 strikes are performed under identical conditions and averaged to improve the accuracy of signal-to-noise ratio and frequency response function estimation. After each strike, the amplitude and waveform shape of the force pulse are checked, and obviously abnormal strike data (such as secondary impacts or data points with excessively low amplitude) are discarded.

[0043] Second, windowing processing. Force window and exponential window are applied to the acquired force signal and response signal. The force window is used to suppress noise in the force signal, and the exponential window is used to ensure that the response signal decays to zero before the end of the sampling window, thereby reducing spectral leakage.

[0044] Sine excitation tests are used to obtain the steady-state response characteristics of a system at a specific frequency point. They are more accurate than hammer tests and are especially suitable for fine characterization of frequency characteristics near the resonance peak.

[0045] A single-frequency sinusoidal sweep signal is applied to the active vibration isolation system via the voice coil motor 9 of the drive unit or an external exciter. The sweep range covers 0.1Hz to 100Hz, encompassing the entire frequency band of airborne vibration. The frequency step size is tightened in the resonance region and loosened in the non-resonance region according to accuracy requirements. A smaller frequency step size (e.g., 0.1Hz) is used near the natural frequency initially identified by the hammer impact test to accurately capture the shape and amplitude of the resonance peak; a larger frequency step size (e.g., 1Hz) is used in the frequency band far from the resonance frequency to improve test efficiency.

[0046] At each frequency point, the system needs sufficient time to reach steady state. The steady-state criterion is that the rate of change of the response signal amplitude over multiple consecutive cycles is less than a set threshold. After the system reaches steady state, the amplitude and phase information of the input force / current signal and the output acceleration / displacement signal are acquired. The amplitude information is used to calculate the transmissibility at that frequency point, and the phase information is used to evaluate the phase hysteresis characteristics of the system. Two accelerometers acquire the base response and the load response respectively, which together constitute the input-output data pair at that frequency point.

[0047] When the frequency sweep approaches the system's natural frequency, the response amplitude will increase sharply. At this time, it is necessary to appropriately reduce the excitation amplitude to avoid the voice coil motor 9 exceeding its stroke or the accelerometer saturating. At the same time, the frequency step size should be increased to obtain a high-resolution resonance peak curve.

[0048] The hammer impact test and the sinusoidal excitation test together constitute a complete input-output dataset. The input data includes the hammer impact force signal sequence and the sinusoidal excitation signal sequence, while the output data includes the acceleration response signal sequence synchronously acquired by feedforward accelerometer 3 and feedback accelerometer 5. The sampling of the two sets of data must be time-synchronized, which is achieved through the synchronous sampling function of the AD7606 synchronous sampling chip to ensure that there is no time delay error between the input and output.

[0049] Based on the input and output dataset, a past input matrix, a past output matrix, a future input matrix, and a future output matrix are constructed. The future output matrix is ​​obliquely projected to extract system state information. Singular value decomposition is performed on the obliquely projected future output matrix. The system order is determined based on the magnitude of the singular values. The shift invariance of the observability matrix is ​​used to solve for the state transition matrix A and the output matrix C. Then, the input matrix B and the feedforward matrix D are solved by least squares fitting to complete the state space model identification. Modal frequencies and damping ratios are extracted from the eigenvalues ​​of the identified state transition matrix A. The stiffness coefficients are calculated by combining the known mass of load 4, thus completing the parameter extraction and calibration of the nominal dynamic model.

[0050] In one example, the input and output data in the time domain are constructed into block-based Hankel matrices, including four Hankel matrices: the past output matrix, the past output matrix, the future input matrix, and the future output matrix.

[0051] Choose a time window length (usually greater than the system order), defined as follows: ; ; in, For the past input matrix, For the past output matrix, For the past input matrix, the first The input data in row j, For the past output matrix, the first Output data in row j; Construct the future input matrix by shifting the past input matrix backward. A matrix for each sampling period, i.e.: , in, For the future input matrix, for translate backward Input data for one sampling period.

[0052] The past input matrix and the past output matrix are stacked along the row direction to form a past data joint matrix, which contains all the input and output information of the past time. Oblique projection is performed on the future output matrix to extract system state information. Oblique projection projects the row vectors of the future output matrix onto the space of the past data joint matrix, but along the direction of the future input matrix. Singular value decomposition (SVD) is then performed on the obliquely projected future output matrix, decomposing it into the product of a left singular vector matrix, a diagonal singular value matrix, and a right singular vector matrix. The singular values ​​are arranged in descending order, and their magnitudes reflect the energy proportion of the corresponding mode in the system's dynamic characteristics.

[0053] In an ideal, noise-free environment, the system order equals the number of non-zero singular values. However, in practical engineering, due to measurement noise and modeling errors, singular values ​​that should be zero may exhibit small, non-zero amplitudes. For a vertical single-degree-of-freedom vibration isolation system, its physical order is 2. Therefore, in the singular value sequence, the amplitudes of the first two singular values ​​are significantly larger than those of subsequent singular values, and there is a clear amplitude jump between the second and third order singular values.

[0054] At this point, we can observe the inflection point where the singular values ​​transition from large to small amplitudes. Large amplitudes correspond to the dominant mode of the system, while small amplitudes correspond to negligible noise modes.

[0055] In practice, the system order is determined by calculating the logarithmic gap between adjacent singular values ​​and searching for the maximum value. The position where this maximum value appears is the system order. Cross-validation can be performed using the AIC (Akaike Information Criterion), and the order that minimizes the AIC value is selected as the final decision. After determining the system order, the system's state vector dimension is confirmed to be 2, corresponding to the two state variables of vertical motion: displacement and velocity.

[0056] After determining the system order, the estimated value of the extended observability matrix is ​​extracted from the singular value decomposition results.

[0057] Take before The extended observability matrix is ​​constructed from the singular vectors and singular values ​​on the left column, and is expressed as follows: , in, The observability matrix, For the front Left singular vectors, For the front A diagonal matrix composed of singular values.

[0058] The shift invariance of the observability matrix refers to dividing the observability matrix into two submatrices, one of which is an increasing matrix (remove the last part). (rows) and descent matrix (before deletion) The first row block of the observability matrix is ​​the descent matrix, which is equal to the product of the ascending matrix and the state transition matrix A. Thus, the state transition matrix A can be obtained from the ascending matrix and the descent matrix. The output matrix C is the first row block of the observability matrix.

[0059] Based on the shift invariance of the observability matrix, after extracting the state transition matrix A, the output matrix C is directly taken from the first row block of the observability matrix (corresponding to the output dimension l rows), that is, C = the first l rows of the observability matrix.

[0060] Furthermore, the input matrix B and feedforward matrix D are solved using the least squares method. Substituting the identified state transition matrix A and output matrix C into the state-space equations (including the state update equations and output equations), and utilizing the known input-output dataset, a least squares problem is constructed: a system of linear equations is built from the past and current input-output data and the estimated state sequence. The estimated state sequence refers to a set of estimated values ​​of the system's state variables at each discrete time step, obtained by back-calculating from the known input-output data using the N4SID subspace identification method during the system identification process. The formula for calculating the estimated state sequence is: , It is an increasing matrix. This is the matrix of oblique projection results. To estimate the state sequence, the state update equation at each time step is... and output equation By combining the equations, a system of linear equations is constructed. The optimal estimates of the input matrix B and the feedforward matrix D are then obtained through batch least squares fitting, thus yielding the complete discrete nominal dynamic model, expressed as: , , in , , , The system matrix is ​​the discretized matrix. Discrete time The state vector. For the next discrete time step +1 state vector, Discrete time Input data, Discrete time The output data.

[0061] The system's modal parameters are extracted from the eigenvalues ​​of the identified state transition matrix A. Eigenvalue decomposition is performed on the state transition matrix A to obtain the eigenvalues. Calculate the natural frequency using eigenvalues: , in, The sampling period is It is the natural frequency.

[0062] Calculate the damping ratio using the natural frequency: , in, is the damping ratio.

[0063] Based on the obtained natural frequency Given the known load of mass m (250g), using the single-degree-of-freedom vibration theory formula: Calculate the stiffness coefficient of the system The damping coefficient is calculated using the relationship between the damping ratio and the damping coefficient. : , The identified stiffness coefficients Damping coefficient The nominal dynamic model is compared and calibrated with the nominal design value. If the deviation is within the set threshold range, the nominal dynamic model is confirmed to have passed the calibration. If the deviation exceeds the limit, the identification parameters are adjusted and re-identified until the extracted physical parameters match the nominal design value, thus completing the parameter extraction and calibration of the nominal dynamic model.

[0064] The model parameters obtained from the offline identification above (state transition matrix A, input matrix B, output matrix C, feedforward matrix D, and stiffness coefficients) Damping coefficient It is burned and solidified into the storage unit as the basis of the nominal dynamic model of the model prediction and control module.

[0065] The model predictive control module is used to predict the system output for multiple future sampling times based on the nominal dynamic model after acquiring the system state at the current time. It iterates the state update equation in the nominal dynamic model and constructs a cost function using the weighted sum of squares of the deviation between the predicted output and the expected reference trajectory, and the weighted sum of squares of the control increment. It solves for the optimal control sequence that minimizes the cost function and uses the first component of the optimal control sequence as the initial control quantity output at the current time.

[0066] The detailed implementation process of the model predictive control module is as follows: First, define the prediction time domain of the model predictive control module. =20 and control time domain =5. Within each control cycle, based on the current time... The system state and nominal dynamics model, for the future The system output at each sampling time is predicted. By iterating the state update equation, the predicted output can be written as a linear function in matrix form: , in, To predict the output vector, from the future It is composed of stacked output data. For the current moment Predicted, future The load 4 acceleration value of the step, which is the final predicted value in the prediction time domain. For the control vector, from the future It is composed of stacked control variables. Indicates at time Decision-making, control time within the time domain Control quantity, free response matrix And the forced response matrix: All of them are constant matrices composed of state transition matrix A, input matrix B, output matrix C, and feedforward matrix D.

[0067] Next, we construct the following quadratic cost function. : , in, For the future The reference input vector for the step. It is the output error weight matrix. It is the control increment weight matrix. It is the control increment vector, and the output error weight matrix includes displacement error weights and velocity error weights.

[0068] The cost function consists of two terms: the first is the output tracking error term, which is the deviation between the predicted output vector and the reference input vector, calculated by squaring this deviation and multiplying it by the output error weight matrix. The reference input vector is zero in this system because the control objective is to completely suppress the load vibration acceleration to zero. The physical meaning of this term is to penalize the degree to which the load acceleration deviates from zero in the prediction time domain; the greater the predicted acceleration, the higher this cost, and the controller will tend to output a larger control force to suppress vibration.

[0069] The second term is the control increment penalty term, which is the sum of the squares of the elements in the control increment vector multiplied by the control increment weight matrix. The control increment is defined as the difference between the control quantity at the current moment and the control quantity at the previous moment. The physical meaning of this term is to penalize the magnitude of change in the control quantity between adjacent moments. The larger the control increment, the more drastic the change in the control command, and the higher the cost of this term. The controller will tend to output a control quantity with a gradual change to protect the actuator.

[0070] The two factors are weighted using their respective weight matrices. The output error weight matrix is ​​a diagonal matrix, with its diagonal elements corresponding to the weight coefficients of the output error at each time point in the prediction time domain. These include displacement error weights and velocity error weights, which are used to adjust the relative importance of different prediction times in the optimization objective.

[0071] The diagonal elements of the control increment weight matrix correspond to the weight coefficients of the control increment at each time point in the control time domain, which are used to adjust the penalty for changes in the control quantity.

[0072] The control increment vector is represented as: , , For a moment The control increment, For a moment The control quantity, For a moment The control quantity, For at any time Decision-making, control time within the time domain The control increment.

[0073] If physical constraints are ignored, the analytical solution can be obtained by directly differentiating the equations: [The predicted equations are then transformed into the analytical solution]. Substituting the cost function, the cost function is rearranged into a standard quadratic form: ; at this time , ; in, For the Hessian matrix, The gradient vector, The forced response matrix is ​​in incremental form. This indicates transpose.

[0074] Setting the gradient to zero, we obtain the optimal control increment sequence: , in, This is the optimal control increment sequence.

[0075] However, when physical constraints are included, the above cost function and constraints are transformed into a standard quadratic programming (QP) problem: , , Wherein, the constraint matrix and constraint boundary vector Used to express: , , in, To control the amplitude constraint, To control the quantity to the minimum, To control the maximum value; To control the incremental amplitude constraint, at time The control increment, To control the minimum increment, To control the maximum increment.

[0076] The above control magnitude constraint and control increment magnitude constraint are converted into standard form. We obtained the following respectively: ,as well as , To control the amplitude constraint matrix, To control the magnitude of the constraint boundary vector, To control the incremental amplitude constraint matrix, To control the incremental magnitude constraint boundary vector.

[0077] Combining the cost function and constraints described above forms a standard quadratic programming problem. The optimization variable is the future sequence of control increments, the objective function is a quadratic form with respect to the control increments, and the constraints are a system of linear inequalities related to the control increments. When physical constraints are not considered, simply setting the gradient of the cost function with respect to the control increments to zero yields an analytical solution for the optimal control increment sequence. However, in practical engineering, due to the physical limitations of the actuators, a constrained quadratic programming approach is used.

[0078] In each control cycle, a quadratic programming solver (such as MATLAB's quadprog module or Python's cvxopt module) is invoked to solve the standard quadratic programming problem described above, obtaining the optimal control increment sequence. At this point, although the optimal control increment sequence for the future NC steps has been calculated, only the current time step is considered. The first control increment applied to the system is called rolling optimization.

[0079] Current moment The initial control quantity is: , in, For the current moment The initial control quantity, For the current moment The initial control quantity, Current moment The optimal control increment. The initial control input is output to the reinforcement learning correction module.

[0080] The output of the model predictive control module in each control cycle is the initial control quantity for the current moment, which is fed into the reinforcement learning correction module as one of the inputs. Simultaneously, the prediction residual error generated by the model predictive control module during the prediction process—the deviation between the actual feedback output and the model prediction output—is also fed into the reinforcement learning correction module. This prediction residual error reflects the degree of mismatch between the nominal dynamic model and the actual system, and is a key basis for the reinforcement learning correction module to determine the stiffness and damping correction amounts. The final control quantity is obtained by superimposing the initial control quantity from the model predictive control module and the correction amount from the initial control quantity from the reinforcement learning correction module, jointly driving the voice coil motor 9 to output a vertical bidirectional control force.

[0081] In some embodiments, the reinforcement learning correction module employs the TD3 (Twin Delayed Deep Deterministic Policy Gradient) algorithm architecture to correct the prediction residual error of the model predictive control module online. The reinforcement learning correction module takes the initial control input and prediction residual error from the model predictive control module as input, and outputs stiffness corrections, damping corrections, and corrections to the initial control input for the nominal dynamic model. The final control input is obtained by superimposing the initial control input and the corrections.

[0082] First, configure the TD3 agent using an Actor-Critic network architecture. The Actor-Critic network consists of an Actor network (a two-layer fully connected network with an 8-dimensional state vector as input and a 3-dimensional action vector as output) and a dual Critic network (two independent Critic networks, each with a structure consistent with the Actor). The Q-values ​​of the two networks are calculated independently, and the smaller value is used when updating the target. The state space of the actor-critic network includes the foundation vibration state (displacement, velocity, acceleration), the load vibration state (displacement, velocity, acceleration), the prediction residual error, and the initial control quantity, for a total of 8 dimensions. , in, This is the foundation displacement. For the foundation velocity, For foundation acceleration, For a load displacement of 4, For a load of 4 speed, For load 4, vibration acceleration, To predict residual error, This is the initial control variable. is a state space vector.

[0083] The three-dimensional action space is 3-dimensional: , These correspond to the correction amounts for stiffness, damping, and initial control, respectively. Let be the action space vector. The reward function comprehensively considers the residual error suppression effect, load acceleration amplitude, correction fluctuation amplitude, and constraint violation penalty to guide the TD3 agent to maintain system stability while ensuring control effectiveness. Reward function: , in Residual error weights : Load 4 acceleration weight, Correction amount fluctuation penalty weight, : Constraints on the penalty weight for violations As a reward value, To predict residual error, For load vibration acceleration, This is the absolute value of the stiffness correction. This is the absolute value of the damping correction. To constrain the penalty for violations, the reward function includes... For actuator constraint penalty terms, and This is a penalty term for parameter fluctuations.

[0084] Next, the reinforcement learning correction module is pre-trained offline. The detailed process is as follows: Based on the nominal dynamic model obtained from system identification, a digital twin model of the active vibration isolation system is constructed in a simulation environment. A time-varying disturbance model matching the actual aviation environment is introduced, including: white noise component to simulate sensor measurement noise, low-frequency sinusoidal component to simulate airflow turbulence disturbance, and random pulse component to simulate takeoff and landing impact, synthesizing an airborne composite vibration signal of 0.1-100Hz as environmental excitation. Then, an experience playback buffer with a capacity of [missing information] is initialized. One approach is to randomly initialize the parameters of the Actor network and the dual Critic network, while keeping the target network parameters consistent with the current network parameters. Then, calculate the total number of training steps. Each offline pre-training iteration performs the following operation at each step: obtain the current state from the digital twin environment. The Actor network is based on the current state. Output Action Adding Ornstein-Uhlenbeck exploratory noise yields the actual execution action: , in, For the actual execution of actions, The value decreases linearly from 0.3 to 0.02 with each training step to balance exploration and exploitation. To explore noise for Ornstein-Uhlenbeck, The mean regression rate, For volatility. Digital twin environment execution. Update to the next status And calculate the current reward value. Transfer tuples Store in the experience replay buffer. Randomly sample batch size from the buffer. Based on this experience, calculate the target Q value: , in, For the target Q value, As a discount factor, and These are the two outputs of the bi-objective Critic network. For the next state, For the target action, and All of these are parameters of the target Critic network.

[0085] Update the dual Critic network separately to minimize the mean squared error loss. , The loss function value of the Critic network. For mathematical expectation, For the first The current output of the Critic network.

[0086] Every Update the Actor network step by step, and do so using a soft update method. , To delay updating the number of steps, For the target Critic network parameters, These are the current online network parameters. To update the coefficients softly, update the target Critic network parameters. Repeat the above process until complete. After training, the converged network weights are saved to the storage unit.

[0087] The pre-trained model is loaded into the controller for no-load and load calibration. The cost function weights and the action range of the TD3 agent are adjusted to ensure that the voice coil motor 9 operates normally, the stage 2 has no overtravel, and the vertical movement of the vibration isolation platform is stable without self-excited vibration.

[0088] The specific steps for adjusting the cost function weights and the action range of the TD3 agent are as follows: No-load calibration phase: Performed without a gravity gradient meter load (250g simulated mass block). Adjust the displacement error weight, velocity error weight, and control increment weight in the model predictive control module, and observe the load displacement time-domain curve and the vibration isolation transmissibility frequency-domain curve until the system motion is stable and there is no self-excited vibration; at the same time, calibrate the constraint boundaries to ensure that the voice coil motor's 9-stroke is within the specified range. Within the design range, the drive current is Within the range, and quadratic programming is feasible.

[0089] Load calibration phase: Further calibration is performed after installing a 250g simulated load. The initial operating range of the TD3 agent output layer is set as follows: stiffness correction is [-50, 50] N / m, damping correction is [-5, 5] Ns / m, and initial control quantity correction is [-0.5, 0.5] A. The system is run and observed: if the correction frequently touches the boundary value, it indicates that the operating range is too small and needs to be appropriately expanded to provide sufficient correction capability; if the fluctuation amplitude of the correction is much smaller than the boundary of the operating range, the range can be appropriately reduced to improve control stability.

[0090] System performance verification: After parameter adjustment, apply single-frequency sinusoidal disturbances (0.1Hz, 1Hz, 5Hz, and 10Hz, a total of 4 frequency points) and broadband random disturbances respectively, and record the vibration attenuation rate, peak load displacement, and control current curves at each frequency. Requirements: The vibration attenuation rate across the entire frequency band should not be less than 70% (i.e., the vibration isolation transmissibility should not exceed 0.3), the vertical displacement of the load should always be within the design stroke, and there should be no self-excited vibration.

[0091] After offline pre-training and calibration, the reinforcement learning correction module is deployed to the control unit. During airborne operation, this module takes the initial control quantity and prediction residual error output by the model predictive control module as input. After processing by its internal actor-critic network, it outputs in real time the stiffness correction quantity, damping correction quantity, and correction quantity of the initial control quantity to the nominal dynamic model. Among them, the stiffness correction quantity and damping correction quantity are fed back to the nominal dynamic model to correct its stiffness and damping parameters online. The correction quantity of the initial control quantity is superimposed on the initial control quantity to form the final control quantity. It is converted into driving current by the digital-to-analog converter module and the voltage-controlled constant current source, which drives the voice coil motor 9 to output vertical bidirectional control force to achieve closed-loop adaptive vibration isolation.

[0092] The visualization analysis module runs on the PS terminal and connects to the host computer (such as a personal computer or ground monitoring terminal) via Ethernet or serial communication interface. It is used to display the operating status data and performance evaluation results of the vibration isolation system in real time, providing operators with intuitive system monitoring and data analysis tools.

[0093] The visualization analysis module receives and displays two control-related curves in real time: The first curve is the final control quantity curve, which is the curve of the final control current command after reinforcement learning correction as a function of time, in amperes; The second curve is the correction curve, which is the curve showing the change of the correction amount of the initial control quantity output by the reinforcement learning correction module over time, in amperes.

[0094] The two curves are superimposed on the same coordinate system, facilitating the observation of the superposition relationship between the initial control variable, the reinforcement learning correction variable, and the final control variable. Furthermore, according to the operator's needs, the curves showing the variation of the stiffness correction variable and the damping correction variable can be displayed, in units of Newtons per meter and Newton-seconds per meter, to monitor the online adjustment behavior of the reinforcement learning correction module on the model parameters.

[0095] Another aspect of this application provides a control method for a vertical noise suppression platform for airborne gravity gradient measurement, including: In the offline phase, the system input and output datasets were collected through hammer impact tests and sinusoidal excitation tests. The N4SID algorithm of the subspace method was used to identify the nominal dynamic model of the active vibration isolation system with a vertical single degree of freedom, obtain the parameters of the nominal dynamic model, and complete the calibration. Based on the nominal dynamics model, after obtaining the system state at the current moment, the system output at multiple future sampling moments is predicted by iterating the state update equation in the nominal dynamics model. A cost function is constructed using the weighted sum of squares of the deviation between the predicted output and the expected reference trajectory, and the weighted sum of squares of the control increment. The optimal control sequence that minimizes the cost function is solved, and the first component of the optimal control sequence is used as the initial control quantity at the current moment. The predicted residual error and initial control quantity are processed by an actor-critic network to obtain the stiffness correction, damping correction, and correction to the initial control quantity of the nominal dynamic model. The initial control quantity and the correction are then superimposed to obtain the final control quantity.

[0096] In some embodiments, the stiffness correction and the damping correction are fed back to the nominal dynamic model to perform online correction of the stiffness parameters and damping parameters of the nominal dynamic model.

[0097] Specifically, the system identification phase was completed under offline laboratory conditions to obtain the nominal dynamic model of the active vibration isolation system with a single vertical degree of freedom.

[0098] First, the input and output datasets of the system are acquired through hammer impact tests and sinusoidal excitation tests. In the hammer impact test, a hammer equipped with a force sensor strikes the vibration isolation platform vertically. The force sensor built into the hammer collects the excitation force signal, while the feedforward accelerometer 3 installed on the base 1 of the vibration isolation platform and the feedback accelerometer 5 installed on the stage 2 simultaneously collect the acceleration response signal. Multiple hammer impacts are performed under the same conditions, and the average is taken to improve the signal-to-noise ratio. In the sinusoidal excitation test, a single-frequency sinusoidal sweep signal is applied to the system through a voice coil motor 9 or an external exciter. The sweep frequency range covers 0.1Hz to 100Hz. After the system reaches steady state at each frequency point, the amplitude and phase information of the input and output signals are collected. The two test data together constitute a complete input and output dataset.

[0099] Secondly, the N4SID subspace method algorithm was used to identify the nominal dynamic model of the active vibration isolation system with a vertical single degree of freedom. The specific steps were as follows: The time-domain input and output data were constructed into block-based Hankel matrices, including past input matrices, past output matrices, future input matrices, and future output matrices; the past input and output matrices were stacked along the row direction to form a joint matrix of past data; the future output matrix was obliquely projected to extract system state information; the obliquely projected matrix was subjected to singular value decomposition, and the system order was determined based on the singular value magnitudes; the shift invariance of the observability matrix was used to solve for the state transition matrix A and the output matrix C; and the input matrix B and the feedforward matrix D were solved using least-squares fitting.

[0100] Finally, modal frequencies and damping ratios are extracted from the eigenvalues ​​of the identified state transition matrix A, and stiffness and damping coefficients are calculated using the known load mass. The identified stiffness and damping coefficients are then compared with the nominal design values ​​for verification: if the deviation is within a set threshold range, the nominal dynamic model is confirmed to have passed calibration; if the deviation exceeds the limit, the identification parameters are adjusted and re-identification is performed until the extracted physical parameters match the nominal design values. The model parameters obtained from offline identification are burned and stored in the storage unit.

[0101] The model predictive control phase is executed during real-time airborne operation, calculating the initial control quantity at the current moment based on the nominal dynamic model.

[0102] At the beginning of each control cycle, the current system state is first acquired, including the vertical displacement and vertical velocity of load 4. This state is obtained by integrating the signals collected by the accelerometer in the time domain. The prediction time domain is defined as 20 sampling periods, and the control time domain as 5 sampling periods. Based on the current state and the nominal dynamic model, the system output for the next 20 sampling moments is predicted through iterative state update equations. The predicted output is then presented as a linear function in matrix form, consisting of a free response matrix and a forced response matrix.

[0103] A cost function is constructed using the weighted sum of squares of the output error and the weighted sum of squares of the control increment. The output error is the deviation between the predicted output and the desired reference trajectory, which is the zero vector; the control increment is the difference in control values ​​between adjacent time steps. With physical constraints included, the cost function and constraints are transformed into a standard quadratic programming problem. The constraints include control magnitude constraints and control increment magnitude constraints. The control magnitude constraint limits the voice coil motor 9 drive current to a set range, and the control increment magnitude constraint limits the change in control value between adjacent time steps to a set range.

[0104] The control magnitude constraints and control increment magnitude constraints are transformed into systems of linear inequalities and stacked to form a complete constraint matrix and constraint boundary vector. A quadratic programming solver is invoked in each control cycle to obtain the optimal control increment sequence for the next five time steps. Only the first component of the sequence is taken as the optimal control increment for the current time step, superimposed on the initial control quantity from the previous time step, forming the initial control quantity for the current time step, which is then output to the reinforcement learning correction module. Unused subsequent control increments are discarded, and the optimization problem is reconstructed and solved in the next control cycle based on new state measurements, achieving rolling optimization.

[0105] The reinforcement learning correction phase receives the initial control input and prediction residual error from the model predictive control module, processes them, and outputs the correction amount for the model parameters and the initial control input.

[0106] First, an eight-dimensional state space is constructed, including foundation displacement, foundation velocity, foundation acceleration, load displacement, load velocity, load acceleration, model prediction residual error, and initial control input. The foundation displacement, foundation velocity, and foundation acceleration are acquired and integrated by feedforward accelerometer 3, while the load displacement, load velocity, and load acceleration are acquired and integrated by feedback accelerometer 5. The prediction residual error is the deviation between the predicted output of the model predictive control module and the actual feedback.

[0107] The aforementioned state-space vector is input into the actor-critic network. A three-dimensional motion vector is output. This three-dimensional motion vector is then trimmed to satisfy preset motion boundary constraints, yielding the final stiffness correction, damping correction, and initial control value corrections.

[0108] The reward function takes minimizing the model prediction residual error and load vibration acceleration as the core optimization objective, while incorporating actuator constraint penalty terms and parameter fluctuation penalty terms.

[0109] The stiffness and damping corrections are fed back to the nominal dynamic model to correct its stiffness and damping parameters online. The updated nominal dynamic model is used by the model predictive control module to predict the output of the next control cycle. The corrected control values ​​are then added to the initial control value to form the final control value.

[0110] The final control quantity is converted into driving current through the digital-to-analog converter module and the voltage-controlled constant current source, driving four voice coil motors 9 to output compensation force synchronously to counteract the disturbance of the load 4 caused by the airborne vibration.

[0111] During airborne operation, the online identification module continuously updates the model parameters. When the predicted residual error exceeds the set threshold, the online model update process is triggered. The recursive least squares method is used to correct the parameters of the nominal dynamic model online, so that the nominal model always approximates the dynamic characteristics of the actual system and realizes closed-loop adaptive vibration isolation.

[0112] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A vertical noise rejection platform for airborne gravity gradiometry, characterized by, include: Passive vibration isolation unit, horizontal constraint mechanical unit, vibration signal acquisition unit, control unit, and drive execution unit; wherein: The passive vibration isolation unit uses a compression spring (8) as a vibration isolation element, which is set between the vibration isolation platform base (1) and the platform (2) to pre-attenuate the high-frequency vibration of the airborne foundation and provide static support for the load (4); The horizontal constraint mechanical unit includes a limiting guide rod (6) and a linear bearing (7). The linear bearing (7) is fixed on the platform (2). The limiting guide rod (6) is vertically fixed on the vibration isolation platform base (1). The linear bearing (7) is sleeved on the outside of the limiting guide rod (6) and slides with the limiting guide rod (6) to retain only the vertical linear motion degree of freedom of the vibration isolation platform base (1). The vibration signal acquisition unit is used to acquire airborne foundation vibration signals and load vibration signals; The drive execution unit includes a voice coil motor (9) disposed between the stage (2) and the vibration isolation platform base (1), which is used to synchronously output vertical bidirectional control force according to the drive current; The control unit is used to calculate the control quantity based on the foundation vibration signal and the load vibration signal, and control the drive execution unit to output the corresponding vertical bidirectional control force to counteract the disturbance of the load (4) by the airborne vibration.

2. The airborne gravity gradiometry-oriented vertical noise suppression platform according to claim 1, wherein, The vibration signal acquisition unit includes a feedforward accelerometer (3) and a feedback accelerometer (5). The feedforward accelerometer (3) is installed on the base (1) of the vibration isolation platform, and the feedback accelerometer (5) is installed on the platform (2).

3. The airborne gravity gradiometry-oriented vertical noise suppression platform according to claim 1, wherein, The voice coil motors (9) are four in number and are evenly distributed at 90° orthogonal around the vibration isolation platform base (1).

4. The airborne gravity gradiometry-oriented vertical noise suppression platform according to claim 1, wherein, The control unit includes a system identification module, a model prediction control module, a reinforcement learning correction module, and a visualization analysis module; wherein: The system identification module is used to collect system input and output datasets through hammer impact tests and sinusoidal excitation tests in the offline stage, and to identify the nominal dynamic model of the active vibration isolation system with a vertical single degree of freedom using the N4SID subspace method algorithm, obtain the parameters of the nominal dynamic model and complete the calibration. The model predictive control module is used to predict the system output for multiple future sampling times based on the nominal dynamic model after obtaining the system state at the current time by iterating the state update equation in the nominal dynamic model. It constructs a cost function using the weighted sum of squares of the deviation between the predicted output and the expected reference trajectory, and the weighted sum of squares of the control increment. It solves for the optimal control sequence that minimizes the cost function and uses the first component of the optimal control sequence as the initial control quantity at the current time. The reinforcement learning correction module is used to receive the prediction residual error and initial control quantity from the model prediction control module. After processing by the actor-critic network, the stiffness correction quantity, damping correction quantity, and correction quantity of the initial control quantity of the nominal dynamic model are obtained. The initial control quantity and the correction quantity are superimposed to obtain the final control quantity. The visualization analysis module is used to display the vibration signal time-domain curve, the vibration isolation transmissibility frequency-domain curve, and the final control and correction variable change curves in real time.

5. The vertical noise suppression platform for airborne gravity gradient measurement according to claim 4, characterized in that, The N4SID algorithm using the subspace method was employed to identify the nominal dynamic model of the active vibration isolation system with a single vertical degree of freedom, including: Impulse response data of the active vibration isolation system is obtained through hammer impact test, and frequency response data of the active vibration isolation system within a set frequency band is obtained through sinusoidal excitation test. Excitation signal and acceleration response signal are collected to construct input-output dataset. Based on the input and output dataset, a past input matrix, a past output matrix, a future input matrix, and a future output matrix are constructed. The future output matrix is ​​obliquely projected to extract system state information. Singular value decomposition is performed on the obliquely projected future output matrix. The system order is determined based on the magnitude of the singular values. The state transition matrix A and the output matrix C are solved using the shift invariance of the observability matrix. The number of columns in the observability matrix is ​​determined by the system order. The input matrix B and the feedforward matrix D are solved by least squares fitting to obtain the nominal dynamic model. Modal frequencies and damping ratios are extracted from the eigenvalues ​​of the identified state transition matrix A. Stiffness coefficients and damping coefficients are calculated based on the known load mass 4, thus completing the parameter extraction and calibration of the nominal dynamic model.

6. The airborne gravity gradiometry-oriented vertical noise suppression platform according to claim 4, wherein, In the model predictive control module, with physical constraints included, the cost function and constraints are transformed into a standard quadratic programming problem for solution. The quadratic programming solver is called to solve the standard quadratic programming problem to obtain the optimal control increment sequence in the control time domain. Only the first component of the optimal control increment sequence is taken as the optimal control increment at the current time, and it is superimposed on the control quantity at the previous time to form the initial control quantity at the current time.

7. The vertical noise suppression platform for airborne gravity gradient measurement according to claim 4, characterized in that, The state space of the actor-critic network includes foundation displacement, foundation velocity, foundation acceleration, load displacement, load velocity, load acceleration, the prediction residual error of the model predictive control module, and the initial control quantity output by the model predictive control module. The state space is processed to output a three-dimensional action vector, which includes stiffness correction, damping correction and initial control correction for the nominal dynamic model. The stiffness correction and the damping correction are fed back to the nominal dynamic model to correct the stiffness and damping parameters of the nominal dynamic model online. The updated nominal dynamic model is used for the output prediction of the model prediction control module in the next control cycle. The correction amount of the initial control quantity is added to the initial control quantity to form the final control quantity.

8. A control method for a vertical noise suppression platform for airborne gravity gradient measurement, used in the vertical noise suppression platform for airborne gravity gradient measurement as described in any one of claims 1-7, characterized in that: include: In the offline phase, the system input and output datasets were collected through hammer impact tests and sinusoidal excitation tests. The N4SID algorithm of the subspace method was used to identify the nominal dynamic model of the active vibration isolation system with a vertical single degree of freedom, obtain the parameters of the nominal dynamic model, and complete the calibration. Based on the nominal dynamics model, after obtaining the system state at the current moment, the system output at multiple future sampling moments is predicted by iterating the state update equation in the nominal dynamics model. A cost function is constructed using the weighted sum of squares of the deviation between the predicted output and the expected reference trajectory, and the weighted sum of squares of the control increment. The optimal control sequence that minimizes the cost function is solved, and the first component of the optimal control sequence is used as the initial control quantity at the current moment. The predicted residual error and initial control quantity are processed by an actor-critic network to obtain the stiffness correction, damping correction, and correction to the initial control quantity of the nominal dynamic model. The initial control quantity and the correction are then superimposed to obtain the final control quantity.

9. The control method for a vertical noise suppression platform for airborne gravity gradient measurement according to claim 8, characterized in that, The stiffness correction and the damping correction are fed back to the nominal dynamic model to correct the stiffness and damping parameters of the nominal dynamic model online.

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