Wind tunnel magnetic suspension balance multi-layer finite time composite disturbance rejection control method and system

Abstract

The application discloses a wind tunnel magnetic suspension balance multilayer finite time composite disturbance rejection control method and system, the method comprises the following steps: obtaining the displacement signal of the magnetic suspension balance suspension model, and decomposing the displacement signal into multiple time domain signals; performing spectrum analysis on the displacement signal to obtain the real-time energy of each frequency band; dynamically adjusting the fusion weight of each layer observer according to the relative size of the real-time energy of each frequency band; constructing a multilayer parallel finite time extended state observer, obtaining each layer disturbance estimation value and weighted sum, and obtaining the total disturbance estimation value; constructing a non-singular double power integral type fast terminal sliding mode controller, and designing a sliding mode control law; the total disturbance estimation value is superimposed into the sliding mode control law as a feedforward compensation term to generate a final control signal to drive an actuator. The application can effectively suppress multi-frequency airflow disturbance, has strong robust stability, and provides a solution with fast response and strong robustness for a large-gap magnetic suspension balance system.

Description

Technical Field

[0001] This invention mainly relates to the technical field of wind tunnel magnetic suspension balance systems, specifically to a multi-layer finite-time composite disturbance rejection control method and system for wind tunnel magnetic suspension balances. Background Technology

[0002] The Magnetic Suspension and Balance System (MSBS) is a novel wind tunnel testing device that uses electromagnetic force to achieve contactless support for the model. It completely eliminates the interference of traditional mechanical support on the flow field and improves the accuracy of flow field observation and aerodynamic measurement. Under this configuration, the MSBS faces severe challenges: (1) the inherent quasi-steady, unsteady and broadband airflow disturbances in the wind tunnel flow field; (2) the large gap magnetic circuit designed to ensure the duty cycle requirement of the flow field, which leads to a severe attenuation of electromagnetic force gain (current stiffness), low open-loop gain and limited dynamic response of the system; (3) the complex magnetic coupling effect between multiple degrees of freedom caused by the large gap. These factors, as well as the aerodynamic, electromagnetic and structural multi-field coupling, exacerbate the uncertainty of the system, leading to increased steady-state error, limit loop oscillation or even instability in traditional controllers (such as PID and LQR) designed based on linearized models.

[0003] In low-speed wind tunnels, especially open-type wind tunnels, magnetic suspension balance systems under large-gap suspension conditions suffer from limited dynamic response and stability degradation due to airflow disturbances, multi-degree-of-freedom magnetic coupling, and electromagnetic force gain attenuation caused by the large gap. Therefore, the following core technical problems exist: (1) The problem of suppressing unsteady disturbances in the wind tunnel shear layer Low-speed wind tunnels, especially open-type wind tunnels, experience airflow disturbances caused by a free shear layer, which exhibits complex unsteady structural features. Related studies have shown that the shear layer contains various complex flow phenomena, including small-scale Kelvin-Helmholtz vortex convection, vortex pairing, and multi-vortex convection. These vortex structures cause fluctuations in the shear layer position, and the frequency of these fluctuations is highly consistent with the characteristic frequency of lift fluctuations, indicating that the unsteady motion of the shear layer is the primary disturbance source acting on the suspension model. Furthermore, when shear layer instability couples with the wind tunnel's acoustic resonant frequency, it generates low-frequency, large-amplitude pressure fluctuations (lock-in phenomenon), further deteriorating suspension stability. Effectively suppressing this broadband, unsteady aerodynamic disturbance induced by the shear layer vortex structure is one of the core challenges of this invention.

[0004] (2) Difficulty in suppressing multi-frequency disturbances In addition to shear layer disturbances, wind tunnels also contain disturbances of various frequencies, including mainstream airflow forces, quasi-steady airflow fluctuations, and boundary layer turbulent pressure fluctuations. These disturbances enter the system through multi-field coupling channels of air, electromagnetic, and structure, leading to amplified steady-state errors, limit cycle oscillations, and even instability in traditional controllers.

[0005] (3) Dynamic limitation caused by large gaps To ensure flow field quality and reduce interference from the tunnel walls, the magnetic suspension balance has a large levitation gap, resulting in a severe attenuation of the electromagnetic force current stiffness and a low open-loop gain. This significantly reduces the system's ability to suppress high-frequency disturbances and leads to a sluggish dynamic response.

[0006] (4) Limitations of traditional observers A single extended state observer (ESO) inherently presents a trade-off between estimation bandwidth and noise sensitivity, making it difficult to simultaneously guarantee high-frequency estimation accuracy and low-frequency steady-state performance under wideband perturbations. Cascading ESOs sacrifices high-level dynamics, while directly cascading ESOs in parallel leads to frequency domain overlap and increased estimation errors.

[0007] (5) The chattering and convergence speed of sliding mode control are contradictory. Traditional sliding mode control often requires a large switching gain to achieve fast convergence, which can exacerbate control signal chattering and easily excite unmodeled high-frequency modes in large-gap systems, leading to instability.

[0008] Existing technologies mainly adopt the following approach, but they all show significant shortcomings in low-speed wind tunnels, especially in open wind tunnels under shear layer disturbance conditions: (1) Linear control methods (PID, LQR / LQG) A fixed-gain controller is designed by linearizing the system model. However, this approach is effective near the design point, but gain decay under large gaps leads to a significant decrease in control performance when deviating from the design point. More importantly, unsteady disturbances in the shear layer exhibit wideband and time-varying characteristics. The linear method degrades the suspension control performance when suppressing these complex disturbances caused by the evolution of vortex structures, ultimately resulting in decreased accuracy in flow field observations and aerodynamic measurements.

[0009] (2) Combining a single extended state observer (ESO) with nonlinear control The total disturbance is estimated using an ESO and then fed forward compensation is applied. However, traditional single-layer ESOs have inherent limitations: increasing the bandwidth to accelerate high-frequency disturbance estimation introduces more measurement noise, worsening the already weak signal-to-noise ratio; decreasing the bandwidth, on the other hand, causes severe phase lag in high-frequency disturbances. For multi-scale vortex disturbances induced by shear layers, single-layer ESOs cannot simultaneously ensure the estimation accuracy across all frequency bands.

[0010] (3) Cascaded Extended State Observer (CESO) Multiple ESOs are cascaded to reduce the load on a single layer. However, this cascaded structure sacrifices the dynamic response performance of higher layers (higher frequencies). The input of a later-stage observer depends on the output of the previous stage, leading to a significant increase in high-frequency disturbance estimation errors and a slower response. This hysteresis is fatal for high-frequency, small-scale vortex disturbances in the shear layer.

[0011] (4) Traditional Sliding Mode Control (SMC) and its Improvements Convergence speed can be improved by designing a nonlinear sliding surface. However, a drawback remains: the fundamental contradiction between convergence speed and chattering suppression is not resolved. A large switching gain is required to achieve fast convergence, which exacerbates chattering. Under continuous excitation by shear layer perturbations, chattering is more likely to induce unmodeled high-frequency modes in the system, leading to instability.

[0012] (5) Adaptive method based on frequency identification An adaptive notch filter is used to estimate the disturbance frequency online for narrowband filtering. However, this method has drawbacks: it is largely based on gradient descent algorithms, which suffer from large estimation variance, accuracy, and stability issues in the low signal-to-noise ratio environment common in wind tunnel testing. Furthermore, the gradient descent mechanism has an inherent convergence lag, making it difficult to balance dynamic response and steady-state tracking accuracy for the rapid evolution of shear layer vortex structures.

[0013] (6) Existing MSBS control research Domestic and international research on MSBS mainly focuses on the suspension control of the system itself, employing methods such as PI control, sliding mode control, and disturbance observer-based feedforward control. However, existing methods fail to adequately consider the impact of multi-frequency, unsteady disturbances induced by multi-frequency airflow disturbances on suspension stability.

[0014] In summary, existing methods lack a composite control architecture that can specifically address the combined challenges of "large gap + wideband unsteady disturbance" without relying on high-precision models and real-time frequency estimation, for the shear layer disturbance characteristics of low-speed wind tunnels, especially open wind tunnels. This architecture would enable rapid decoupling of wideband disturbances, accurate tracking of dominant disturbances, and ensure fast, stable, and robust convergence of the system. Summary of the Invention

[0015] To address the technical problems existing in the prior art, this invention provides a multi-layer finite-time composite anti-disturbance control method and system for wind tunnel magnetic suspension balances that effectively suppresses airflow disturbances.

[0016] To solve the above-mentioned technical problems, the technical solution proposed by this invention is as follows: A multi-layer finite-time composite disturbance rejection control method for a wind tunnel magnetic suspension balance includes the following steps: The displacement signal of the magnetic suspension balance levitation model is acquired in real time and decomposed into multiple time-domain signals; Real-time spectrum analysis of the displacement signal is performed, and the spectrum information corresponding to each frequency band is recursively calculated by sliding window discrete Fourier transform to obtain the real-time energy of each frequency band. Based on the relative magnitude of the real-time energy of each frequency band, the fusion weight of the observer outputs of each layer in the total disturbance estimation is dynamically adjusted so that the observer with the highest weight corresponds to the current dominant disturbance frequency band. Construct a multi-layer parallel finite-time extended state observer. Each layer of the observer is input with a corresponding time-domain signal and the disturbance component is estimated independently to obtain the disturbance estimate of each layer of the observer. The perturbation estimates of each layer of observers are weighted and summed according to their corresponding fusion weights to obtain the total perturbation estimate; Construct a non-singular double power integral fast terminal sliding mode controller and design a sliding mode control law; The total disturbance estimate is superimposed as a feedforward compensation term into the sliding mode control law to generate the final control signal, which is then output to the actuator of the magnetic suspension balance system.

[0017] Preferably, the spectral information corresponding to each frequency band is calculated using the sliding window discrete Fourier transform recursive formula, the specific formula being:

[0018] in The spectral value at sampling time n; The spectral value at the next sampling time n+1; This is the most recently sampled displacement signal; This is the first sampling point in the current window; N The length of the sliding window; Frequency point index; is the rotation factor.

[0019] Preferably, each time-domain signal corresponds to a preset perturbation frequency sub-band; wherein, based on the spectral characteristics of multi-degree-of-freedom magnetic coupling interference and wind tunnel shear layer perturbation, the perturbation frequency is divided into low-frequency band, mid-frequency band, mid-high frequency band and high-frequency band.

[0020] Preferably, the real-time energy of each frequency band is obtained by multi-point sampling within the frequency band. Specifically, multiple representative frequency points are selected uniformly or adaptively within each frequency band, the instantaneous energy of the multiple representative frequency points is calculated, and the summation or weighted average is used as the real-time energy of that frequency band.

[0021] Preferably, the real-time energy of each frequency band is obtained by the full-spectrum accumulation method within the frequency band, specifically: the energy of all DFT spectral lines within each frequency band is accumulated to obtain the real-time energy of each frequency band.

[0022] Preferably, the specific process of dynamically adjusting the fusion weights of the observer outputs of each layer in the total perturbation estimation is as follows: The relative magnitude of real-time energy in each frequency band is compared at fixed intervals. The frequency band with the largest real-time energy is identified as the current dominant disturbance frequency band. The fusion weight of the observer in the corresponding layer of this frequency band is increased, while the weights of other layers are decreased. The sum of the fusion weights of all layer observers is 1.

[0023] Preferably, the finite-time extended state observer uses the arctangent power function; the mathematical model of the finite-time extended state observer is:

[0024] in, For the first Displacement estimates from a layer-wise finite-time extended state observer; For the first Velocity estimates for a layered finite-time extended state observer; For the first Perturbation estimates for a layered finite-time extended state observer; , , They are respectively , , The first derivative with respect to time; For power-order parameters; This is the gain parameter; This is the nominal gain; This refers to the position observation error; This is the core function of the finite-time extended state observer.

[0025] Preferably, the sliding surface of the non-singular double-power integral type fast terminal sliding mode controller is:

[0026] in, For sliding mode variables; This refers to displacement tracking error; For speed tracking error; for e Gain coefficient of 1 The gain coefficient of the sliding surface. The gain is the power term; It is a power function. This is the amplitude-limited integral term; For micro-offset; These are boundary layer parameters; for Fixed gain; for The variable gain coefficient.

[0027] Preferably, the non-singular double-power integral type fast terminal sliding mode controller adopts a variable gain arctangent double-power reaching law:

[0028] in, For sliding mode variables The first derivative with respect to time; For adaptive gain; , These are boundary layer parameters; , It is a power function.

[0029] The present invention also discloses a multi-layer finite-time composite anti-disturbance control system for a wind tunnel magnetic suspension balance, comprising an interconnected memory and a processor, wherein the memory stores a computer program, and the computer program executes the steps of the method described above when run by the processor.

[0030] Compared with the prior art, the advantages of the present invention are as follows: This invention addresses the broadband airflow disturbance characteristics of low-speed wind tunnels, especially low-speed open wind tunnels, including shear layer disturbances. It constructs a high-, medium-, and low-frequency layered observation architecture through frequency domain decoupling; dynamically identifies the dominant disturbance frequency band and updates the weights of each layer using sliding window DFT (recursive update) frequency domain analysis; and combines finite-time sliding mode control with a variable damping composite sliding mode surface and a variable gain double power-law approaching law to effectively suppress unsteady, multi-frequency airflow disturbances, providing a solution for large-gap magnetic suspension balance systems that combines fast response and strong robustness. Attached Figure Description

[0031] Figure 1 This is a block diagram of the multi-layer finite-time composite disturbance rejection control system for a wind tunnel magnetic suspension balance according to an embodiment of the present invention.

[0032] Figure 2 This is a flowchart of the multi-layer finite-time composite disturbance rejection control method for a wind tunnel magnetic suspension balance according to an embodiment of the present invention.

[0033] Figure 3 The diagram shows the displacement response of the method of the present invention and existing methods under step disturbance.

[0034] Figure 4 This is a graph showing the frequency perturbation estimation error between the method of the present invention and existing methods.

[0035] Figure 5 This is a diagram showing the estimation error between the method of the present invention and existing methods under multi-frequency composite disturbances.

[0036] Figure 6 The diagram shows the displacement response of the method of the present invention and existing methods under multi-frequency composite disturbance.

[0037] Figure 7 The diagram shows the displacement and attitude response of this invention under a quasi-steady disturbance of 72 m / s.

[0038] Figure 8 The diagram shows the displacement and attitude response of the present invention under unsteady shear disturbance. Detailed Implementation

[0039] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0040] The wind tunnel magnetic suspension balance multi-layer finite-time composite disturbance rejection control method provided in this embodiment of the invention is based on, as Figure 1 The control system shown is used to implement this, and the control system includes a multi-layer parallel finite-time convergent extended state observer, such as... Figure 1 MPFTESO, a non-singular double power integral fast terminal sliding mode controller (MPFTESO), Figure 1 In the NDPITFSMC), high-bandwidth current loop (High Bandwidth Current Control), Figure 1 HBCC in the middle) and the magnetic suspension balance body ( Figure 1 MSBS in the middle); where each layer of finite-time convergent dilation state observer includes frequency domain segmentation and sliding window DFT of each layer ( Figure 1 The parameters are Filter1 / DFT1, Filter2 / DFT2, ..., Filterk / DFTk, where Filterk is the k-th layer Filter and DFTk is the k-th layer sliding window DFT) and a finite-time dilated state observer. Figure 1 (1-FTESO, 2-FTESO, ..., k-FTESO in the control quantity). u The input is sent to the HBCC, which controls and tracks the electromagnet's rapid current commands, providing real-time adjustable levitation electromagnetic force.

[0041] like Figure 2 As shown, based on the above control system, the multi-layer finite-time composite disturbance rejection control method for wind tunnel magnetic suspension balances provided in this embodiment of the invention includes the following steps: S1. Signal Acquisition and Frequency Domain Decomposition S101. Displacement Signal Acquisition: The displacement signal of the magnetic suspension balance levitation model is acquired in real time using a linear charge-coupled device (CCD) position sensor. ,in The displacement signal is a time variable. It includes the dynamic response of the model under airflow disturbance and multi-degree-of-freedom magnetic coupling.

[0042] S102. Frequency Band Division: Based on the spectral characteristics of multi-degree-of-freedom magnetic coupling interference and low-speed wind tunnel shear layer disturbance, the disturbance frequency range is divided into several sub-frequency bands. In this embodiment, the frequency band division is as follows: Low frequency: f 1≤30Hz; covering low-frequency mainstream airflow disturbance frequencies (<2Hz), shear layer position fluctuation dominant frequencies, and possible acoustic resonance frequencies (<30Hz). Mid-frequency: 30Hz f 2≤70Hz; including periodic disturbances (<60Hz, originating from the blower impeller rotation frequency and its low-order harmonics) and magnetic circuit coupling disturbances (<100Hz, magnetic coupling force between multiple degrees of freedom, whose spectrum is related to the system control bandwidth and mechanical resonant frequency). Mid-to-high frequency: 70Hz f 3≤150Hz; High frequency: >150Hz, corresponding to small-scale vortices and turbulent pulsations.

[0043] The above frequency band division can be adaptively adjusted according to the actual wind tunnel conditions and suspension system parameters.

[0044] S103. Signal frequency domain decomposition; displacement signal Through a set of parallel bandpass filters Decomposed into The frequency domain signal is divided into several frequency bands; the frequency domain segmentation is based on the frequency range of wind tunnel airflow disturbance and the frequency range of magnetic coupling disturbance, so that each sub-band corresponds to the disturbance frequency range.

[0045] Each filter needs to have sufficient stopband attenuation to reduce inter-band coupling. (Filter bank) satisfy:

[0046] And frequency band decoupling constraints:

[0047] in These are all filter layer numbers, ranging from 1, 2... ,and ;in The total number of bandpass filters in the filter bank is equal to the number of perturbation frequency sub-bands. For the first The transfer function (Laplace domain) of a layered bandpass filter. For the Laplace operator, ; Angular frequency, in rad / s; For the first The frequency response function of the layer filter will Substitution get; The condition for complete reconstruction of the filter bank is that the sum of the transfer functions of all filters is 1, which ensures that the original signal can be reconstructed without distortion after decomposition. For all frequencies The product of the frequency response amplitude gain of two different filters; To characterize the first Layer and First Positive real-valued parameters representing the frequency domain decoupling performance between layer filters, used to constrain the upper limit of the amplitude product between frequency bands; This is the maximum allowable amplitude product (i.e., the upper bound of the product of the gains of the two filters); the smaller this value, the less overlap between frequency bands and the weaker the energy coupling. To indicate by , ,…, The set of filter banks that constitutes the filter bank.

[0048] The filter bank can use conventional low-order low-pass and band-pass filters, or it can use low-pass and band-pass filters composed of high-order finite impulse response (FIR) filters, or frequency segmentation paths composed of wavelet transform methods.

[0049] S2. Bandwidth energy monitoring based on real-time spectrum To dynamically identify the dominant disturbance frequency band under the current operating condition, the displacement signal... Real-time spectrum analysis is performed using a sliding-window Discrete Fourier Transform (DFT) to recursively calculate the spectral information corresponding to each frequency band. The recursive formula is as follows:

[0050] in The spectral value at sampling time n; The spectral value at the next sampling time n+1; This is the most recently sampled displacement signal; This is the first sampling point in the current window; N The length of the sliding window; Frequency point index; is the rotation factor.

[0051] This algorithm updates the spectral value of a specified frequency point with constant time complexity for each new input sampling point, resulting in a constant and extremely low computational cost, making it suitable for embedded real-time control systems. To avoid redundant calculations across the entire spectrum, this invention focuses only on a few frequency points related to a preset frequency band.

[0052] The real-time energy of each frequency band is obtained through the following two preferred methods: Method A (Multi-point sampling within a frequency band): Uniform or adaptive selection within each frequency band L Representative frequency points ( L ≥2), the corresponding set of integer indices Calculate the instantaneous energy at these sampling points and sum or take a weighted average to obtain an approximate value for the energy of that frequency band:

[0053] in, Representing the Instantaneous energy (or power spectral density) at a frequency point; For the first The frequency band in the first n The sum of the instantaneous energies of all spectral lines at each sampling point.

[0054] This approach strikes a balance between computational complexity and accuracy: compared to the single-point center frequency method, multi-point sampling can more reliably reflect the overall energy of the frequency band and avoid energy underestimation caused by the perturbation frequency deviating from the center; compared to the full-spectrum accumulation method, the computational complexity is significantly reduced, making it suitable for resource-constrained embedded platforms.

[0055] Method B (Full-Spectrum Accumulation Method within the Frequency Band): The energies of all DFT spectral lines within the frequency band are accumulated, i.e.:

[0056] in For the first The complete set of indexes corresponding to each frequency band.

[0057] This method can most accurately reflect the total energy of the frequency band, and is especially suitable for scenarios where the disturbance energy distribution is complex and may occur at any frequency within the frequency band.

[0058] Regardless of the method used, instantaneous energy can be smoothed by first-order low-pass filtering to obtain a stable real-time energy estimate, thereby suppressing the impact of instantaneous fluctuations on weight updates.

[0059] S3. Weight Adaptive Adjustment Based on the above real-time energy estimation, the initial weights of each layer of finite-time extended state observer (FTESO) can be determined (e.g., according to the energy ratio within the initial time period), and the sliding window DFT is continuously updated during operation to dynamically adjust the fusion weights of each layer of FTESO, so that FTESO always focuses on the dominant perturbation frequency band measured at the current time, thereby achieving adaptive tracking of time-varying perturbations in the shear layer.

[0060] Specifically, the real-time energy of each frequency band is compared at fixed intervals. E i The relative magnitude of the frequencies determines the frequency band with the highest energy, which is then identified as the current dominant disturbance frequency band. The fusion weights of each layer's FTESO output in the total perturbation estimation are dynamically adjusted based on the current dominant perturbation frequency band. This allows the observation architecture to adaptively focus on the dominant perturbation frequency band. Specifically, if the first... If the energy of a frequency band is the highest, then increase Accordingly, reduce other weights, and satisfy the following conditions: .

[0061] This mechanism enables online tracking of time-varying disturbances without requiring identification of the precise frequency of the airflow disturbance force. It only needs to compare the relative magnitude of the energy in each frequency band to effectively guide the weight allocation. This greatly reduces the dependence on real-time frequency estimation and effectively avoids the performance degradation and dynamic lag problems of traditional frequency estimation algorithms under low signal-to-noise ratio.

[0062] S4. Design of Multi-Level Parallel Finite-Time Sliding Mode Controller The result obtained from step S1 Each frequency band time domain signal is input respectively A layered, parallel finite-time extended state observer (FTESO) architecture is used, with each layer independently estimating the perturbation component for its corresponding frequency band. This structure achieves hierarchical estimation of broadband perturbations, effectively overcoming the bandwidth-noise trade-off in single-layer FTESO estimation. Ideally, each layer of FTESO can handle the corresponding frequency band perturbation approximately independently, and the inter-layer coupling allows it to be treated as part of the perturbation, decoupled through the observer estimates.

[0063] Specifically, a finite-time extended state observer (FTESO) is designed for each sub-band. Traditional FTESOs using sign power functions are prone to control signal jitter, leading to position observation errors. The fact that FTESO functions are not differentiable at zero points hinders the construction of Lyapunov functions. This invention uses the arctangent power function to replace the traditional sign power function, thus solving the problem that the traditional FTESO function is not differentiable at zero points and easily leads to control signal jitter.

[0064] No. k The mathematical model of layer FTESO is:

[0065] in For the first k The actual displacement corresponding to the layer finite-time extended state observer (FTESO); For the first k The actual speed corresponding to layer FTESO; The perturbation is the output of the k-th layer FTESO; For the first Displacement estimates from a layer-wise finite-time extended state observer; For the first Velocity estimates for a layered finite-time extended state observer; For the first Perturbation estimates for a layered finite-time extended state observer; , , They are respectively , , The first derivative with respect to time; For power-order parameters; This is the gain parameter; This is the nominal gain; This refers to the position observation error; The improved FTESO core function approximates a linear function in the small error region and a sign function in the large error region, achieving a smooth transition; This is the steepness factor. It should be noted that letters with dots (such as...) ) indicates that the variable The first derivative with respect to time; letters with pointed caps (e.g.) ) indicates that the variable The estimated value; the symbol definitions for the following parameters are consistent with those here.

[0066] Define estimation error :

[0067] The error dynamic equation is:

[0068] in This refers to the position observation error; This is the error in velocity observation; This is to account for observational errors caused by disturbances. For the first The actual total disturbance corresponding to the layer frequency band.

[0069] Furthermore, by selecting an appropriate observer gain and utilizing the hierarchical homogeneity theory, it can be proven that each layer of ESO can converge in a finite time, and the upper bound of the convergence time can be explicitly expressed.

[0070] The Multi-parallel Finite-time Extended State Observer (MPFTESO) is obtained by combining multiple FTESOs.

[0071] Through frequency domain decoupling and parallel observation, MPFTESO can quickly and coarsely decompose broadband complex airflow disturbances, providing high-quality feedforward compensation signals for subsequent sliding mode control. The weight update mechanism based on sliding window DFT ensures that the observer can adaptively track changes in the frequency band of the airflow disturbance.

[0072] S5. Total Disturbance Estimation and Feedforward Compensation The perturbation estimates of each layer are weighted according to the fusion weight coefficient. Weighted summation yields the broadband total disturbance estimate. : ; Similarly, the displacement estimates of each layer of FTESO are calculated according to the fusion weights. Weighted summation yields the estimated total displacement. : ; Similarly, the velocity estimates of each layer of FTESO are calculated according to the fusion weights. Weighted summation yields the estimated total speed. :

[0073] S6. Design of Nonsingular Double-Power Integral Fast Terminal Sliding Mode Control (NDPITFSMC); Design of a composite sliding surface with variable damping: Construct a composite sliding surface that integrates variable damping, integral and power terms, the expression of which can be summarized as: = The variable damping term, integral term, and power term are specifically as follows:

[0074] in, For sliding mode variables, For displacement tracking error, , For reference displacement; For speed tracking error, , For reference speed; for Gain coefficient, The gain coefficient of the sliding surface. The gain is the power term; The function is a power function, used to improve the terminal convergence speed and achieve finite-time convergence from the sliding surface to the equilibrium point; the integral is limited to prevent saturation, i.e., the integral term is limited. , Preset boundary layer parameters; For micro-offsets, to avoid singularities; These are boundary layer parameters; for Fixed gain, for The variable gain coefficient.

[0075] The variable damping term adjusts the damping coefficient according to the system state error, which is based on... S In terms of the error velocity coefficient in the derivative, it can improve the convergence speed; the integral term is used to eliminate steady-state error; the power term guarantees finite-time convergence within the sliding surface. The sliding surface design ensures that the system state converges to the equilibrium point within a finite time after reaching the sliding surface.

[0076] Based on this, its equivalent control for:

[0077] in, This is the displacement stiffness coefficient after linearizing the electromagnetic force of the electromagnet. is the current stiffness coefficient after linearizing the electromagnetic force of the electromagnet, and m is the mass of the suspension model.

[0078] The sliding mode controller employs a variable gain arctangent double power-law approach: an improved approach law is designed, the form of which can be summarized as follows: =Variable gain term multiplied by power term (power less than 1) + Variable gain term multiplied by power term (power equal to 1) + Variable gain term multiplied by non-power term, specifically:

[0079] in, For sliding mode variables The first derivative with respect to time, , These are boundary layer parameters; , Both are power functions. ; For adaptive gain, it is adaptively adjusted according to the system state error norm, specifically as follows:

[0080] in Based on the gain, For dynamic gain, state1 is the nonlinear state in the large error region, and state2 is the steady state in the small error region.

[0081] Since the derivative of the equivalent control is zero, therefore The switching control can be obtained. :

[0082] in , To determine the system state error and sliding surface S Adaptive adjustment of switching gain, , .

[0083] Low-power terms ensure rapid approach when far from the sliding surface, while high-power terms ensure rapid convergence and low chattering when approaching the sliding surface. The adaptive gain mechanism enables the controller to provide strong control when the error is large, and reduces the gain when the error is small to save energy and suppress chattering. The arctangent saturation function replaces the traditional sign function to further smooth the control signal and suppress chattering at its source.

[0084] Main controller output:

[0085] Airflow disturbance feedforward compensation: This adjusts the total disturbance estimate of MPFTESO. The weighted fusion of FTESO estimates from each layer is directly superimposed onto the sliding mode control law as a feedforward compensation control variable, achieving active compensation for broadband disturbances induced by the shear layer. This significantly reduces the burden on the sliding mode feedback control, allowing for the use of smaller switching gains and further suppressing chattering.

[0086] Based on this global estimate, the feedforward compensation control quantity as follows:

[0087] At this point, the overall control output is:

[0088] By combining feedforward compensation and robust feedback control, the contradictory requirements of rapid dynamic response and high-precision vibration suppression in large-clearance systems are structurally resolved in a coordinated manner. The finite-time convergence characteristic provides a definite guarantee for the system's dynamic performance.

[0089] S7. Output the final control signal obtained in step S6 to the high-bandwidth current loop HBCC, and convert it into a suspension model of the magnetic suspension balance body MSBS acting with the corresponding electromagnetic force. Figure 1 The action of MSBS (total disturbance value), enabling fast and robust suppression of broadband unsteady disturbances.

[0090] The system repeats steps S1-S7 at a fixed sampling period to form a closed-loop control.

[0091] This invention addresses the broadband airflow disturbance characteristics of low-speed wind tunnels, particularly open wind tunnels, including shear layer disturbances. It constructs a high-, medium-, and low-frequency layered observation architecture through frequency domain decoupling; dynamically identifies the dominant disturbance frequency band and updates the weights of each layer using sliding window DFT (recursive update) frequency domain analysis; and combines finite-time sliding mode control with a variable-damping composite sliding surface and a variable-gain double-power-law approaching law to effectively suppress unsteady, multi-frequency airflow disturbances. This provides a solution for large-gap magnetic suspension balance systems that combines fast response and strong robustness. Specific technical effects are reflected in the following aspects: 1. A multi-layer parallel finite-time ESO architecture of "frequency domain segmentation + parallel sliding window DFT weight identification" is proposed to address the characteristics of wind tunnel airflow disturbances: This invention addresses the broadband and unsteady disturbance characteristics of multi-degree-of-freedom magnetically coupled disturbances and low-speed wind tunnel shear layer disturbances. It abandons the complex path of pursuing precise frequency estimation and instead adopts a strategy of estimating only the frequency range of the disturbance (through sliding window DFT energy analysis) and dynamically adjusting the weights of each ESO layer accordingly. This shift fundamentally avoids the shortcomings of traditional frequency estimation algorithms, such as dynamic lag and poor noise resistance, and significantly reduces the algorithm's complexity.

[0092] 2. Innovatively establishes an adaptive partitioning mechanism for disturbance frequency band weights, including shear layer airflow disturbances, based on real-time CCD measurements: This invention utilizes the inherent CCD position sensor of the MSBS system to acquire micro-displacement signals of the model under shear layer disturbances in real time; through real-time sliding window DFT spectrum analysis of the signal, the actual disturbance energy distribution excited on the model by the current airflow disturbance is identified online; based on this, the observation frequency bands of each layer of ESO are dynamically partitioned, so that the controller design is directly based on the measured disturbance characteristics at the current moment, with a clear physical background and real-time flow physics basis, rather than purely black-box parameter tuning or offline data dependence.

[0093] 3. An improved finite-time ESO is designed, employing an arctangent power function to achieve smooth transition: Traditional FTESO uses a sign power function, which is non-differentiable at zero, easily leading to control signal jitter. This invention introduces an arctangent power function, utilizing its linearity in the small error region and saturation characteristics in the large error region to achieve smooth switching of the observer error dynamics, effectively suppressing high-frequency jitter introduced by the observer itself.

[0094] 4. A non-singular double-power integral fast terminal sliding mode controller is designed, integrating a variable-damping sliding surface, a variable-gain double-power reaching law, and an arctangent saturation function: This invention addresses the contradiction between fast convergence and low chattering from multiple perspectives. Variable damping sliding surface: The damping is dynamically adjusted according to the state error to accelerate convergence; Variable gain double power-order reaching law: It utilizes the advantages of both low-power and high-power terms to achieve global fast reaching; Arctangent saturation function: replaces the traditional sign function, fundamentally smoothing the control signal; Perturbation feedforward fusion: The perturbations estimated by multiple ESOs are used as feedforwards, which greatly reduces the gain burden of sliding mode switching.

[0095] 5. A composite disturbance rejection control framework of "frequency domain observation + finite-time sliding mode" is constructed to eliminate the dependence on accurate models: This framework achieves accurate estimation of broadband disturbances purely based on system input and output data (CCD measured displacement) using MPFTESO, and then uses NDPITFSMC for robust stabilization. This "data-driven observation + robust control" mode avoids the impact of model parameter perturbations caused by large gaps on control performance, providing a vibration suppression solution with strong engineering practicality and complete theoretical support for low-speed wind tunnels, especially open wind tunnel magnetic suspension balance systems.

[0096] To verify the effectiveness of this invention, the following results were obtained through relevant simulation experiments: 1. Improved accuracy and suppression capability of disturbance estimation: In step disturbances, by Figure 3It can be seen that the displacement response amplitude of the method of the present invention is reduced by up to 34.1% compared with the existing methods. This is due to the high-precision estimation of broadband disturbances in the shear layer by MPFTESO and the effective compensation of NDPITFSMC. The method of the present invention is a nonsingular double-power integral fast terminal sliding mode control (MPFTESO-NDPIFTSMC) based on a multi-parallel finite-time extended state observer; the existing methods include linear active disturbance rejection control (LADRC) based on a linear extended state observer and nonsingular fast terminal sliding mode control (SLESO-NFTSMC) based on a single-layer linear extended state observer.

[0097] During single-frequency perturbation force frequency sweep, by Figure 4 , Figure 5 and Figure 6 It can be seen that the proposed method improves the disturbance suppression performance in the mid-to-high frequencies while ensuring low-frequency performance; at 50Hz and 130Hz, the disturbance estimation error is reduced by 39%. Figure 5 and Figure 6 It can be seen that the disturbance force error is the smallest, the axial displacement fluctuation value is the smallest, and the performance is the best.

[0098] 2. Effectively overcomes dynamic limitations and accelerates response speed: by Figure 3 In simulations of large-gap conditions and step disturbances, the convergence time of the method of this invention is reduced by 72.2% and 50% compared to existing mainstream methods (such as LADRC and SLESO-NFTSMC). This directly proves that the method effectively overcomes the problem of slow system response caused by gain attenuation due to large gaps.

[0099] 3. Improved steady-state accuracy and faster convergence time in actual wind tunnel experiments: When the wind tunnel operates at speeds of 0–72 m / s, the MSBS suspension model exhibits broadband quasi-steady disturbances and unsteady shear disturbances. Figure 7 and Figure 8It can be seen that the steady-state accuracy of MPFTESO-NDPIFTSMC when statically suspended is 10um and 17m°, the steady-state accuracy when blowing air is 40um and 40m°, the maximum displacement under strong airflow disturbance is 0.5mm and 0.53°, and the convergence time is 40ms.

[0100] 4. Strong robustness ensures levitation stability: This method can effectively cope with the time-varying disturbance characteristics caused by airflow disturbance and multi-degree-of-freedom magnetic coupling disturbance, as well as the severe perturbation of model parameters under large gaps, effectively preventing the system from becoming unstable due to the accumulation of disturbances and ensuring stable levitation under a wide range of operating conditions.

[0101] 5. Significantly optimized real-time performance and computational complexity: By adopting the strategy of "frequency domain segmentation + sliding window DFT weight identification", the real-time tracking of the precise frequency of airflow disturbance forces, including the shear layer, is bypassed. The online computational burden and implementation complexity of this method are greatly reduced compared with the traditional scheme based on adaptive notch filters, making it easier to implement in engineering.

[0102] 6. Strong real-time adaptive capability: Based on the frequency band division mechanism of CCD measured data, the controller can automatically adjust the observation frequency band and weight according to changes in operating conditions such as current wind speed and model position, effectively cope with frequency drift caused by shear layer airflow disturbance, and maintain high performance under different wind speed conditions.

[0103] 7. Effectively resolves the contradiction between chattering and speed: Through the coordinated design of variable damping sliding surface, variable gain double power-law approach, arctangent saturation function and disturbance feedforward compensation, while achieving fast response, chattering of control signal is effectively suppressed, avoiding chattering from exciting potential weakly damped modes in large-gap systems, and ensuring stable system operation.

[0104] It should be noted that although this invention is described in detail using a low-speed open wind tunnel as a typical application scenario (in which unsteady shear layer disturbances are typical representatives of broadband disturbances), the core technical concept of this invention—namely, the composite disturbance rejection architecture based on a multi-layer parallel finite-time observer and sliding-window DFT frequency band energy monitoring—is also applicable to other scenarios with similar disturbance spectrum characteristics to low-speed open wind tunnels. For example, broadband disturbances induced by turbulent boundary layer fluctuations in low-speed closed wind tunnels, and multi-frequency mechanical vibrations in industrial magnetic suspension devices, can all be addressed by adaptively adjusting the frequency band division parameters and controller parameters using the method of this invention.

[0105] This invention also discloses a multi-layer finite-time composite disturbance rejection control system for a wind tunnel magnetic suspension balance, comprising an interconnected memory and a processor. The memory stores a computer program, which, when run by the processor, executes the steps of the method described above. The control system of this invention corresponds to the control method described above and also possesses the advantages described therein.

[0106] The present invention can implement all or part of the processes in the methods of the above embodiments, or it can be implemented by hardware related to computer program instructions. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of the above method embodiments. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable storage medium includes: any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. The memory is used to store computer programs and / or modules. The processor implements various functions by running or executing the computer programs and / or modules stored in the memory, and by calling data stored in the memory. The memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0107] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A multi-layer finite-time composite disturbance rejection control method for a wind tunnel magnetic suspension balance, characterized in that, Including the following steps: The displacement signal of the magnetic suspension balance levitation model is acquired in real time and decomposed into multiple time-domain signals; Real-time spectrum analysis of the displacement signal is performed, and the spectrum information corresponding to each frequency band is recursively calculated by sliding window discrete Fourier transform to obtain the real-time energy of each frequency band. Based on the relative magnitude of the real-time energy of each frequency band, the fusion weight of the observer output of each layer in the total disturbance estimation is dynamically adjusted so that the observer with the highest fusion weight corresponds to the current dominant disturbance frequency band. Construct a multi-layer parallel finite-time extended state observer. Each layer of the observer is input with a corresponding time-domain signal and the disturbance component is estimated independently to obtain the disturbance estimate of each layer of the observer. The perturbation estimates of each layer of observers are weighted and summed according to their corresponding fusion weights to obtain the total perturbation estimate; Construct a non-singular double power integral fast terminal sliding mode controller and design a sliding mode control law; The total disturbance estimate is superimposed on the sliding mode control law as a feedforward compensation term to generate the final control signal, which is then output to the actuator of the magnetic suspension balance system. The spectral information corresponding to each frequency band is calculated using the sliding window discrete Fourier transform recursive formula. The specific formula is as follows: in The spectral value at sampling time n; The spectral value at the next sampling time n+1; This is the most recently sampled displacement signal; This is the first sampling point in the current window; N The length of the sliding window; Frequency point index; The rotation factor; Each time-domain signal corresponds to a preset perturbation frequency sub-band; based on the spectral characteristics of multi-degree-of-freedom magnetic coupling interference and wind tunnel shear layer perturbation, the perturbation frequency is divided into low-frequency band, mid-frequency band, mid-high frequency band and high-frequency band.

2. The multi-layer finite-time composite disturbance rejection control method for wind tunnel magnetic suspension balances according to claim 1, characterized in that, The real-time energy of each frequency band is obtained by multi-point sampling within the frequency band. Specifically, multiple representative frequency points are selected uniformly or adaptively within each frequency band, the instantaneous energy of the multiple representative frequency points is calculated, and the sum or weighted average is used as the real-time energy of that frequency band.

3. The multi-layer finite-time composite disturbance rejection control method for wind tunnel magnetic suspension balances according to claim 1, characterized in that, The real-time energy of each frequency band is obtained by the full-spectrum accumulation method within the frequency band. Specifically, the energy of all DFT spectral lines within each frequency band is accumulated to obtain the real-time energy of each frequency band.

4. The multi-layer finite-time composite disturbance rejection control method for wind tunnel magnetic suspension balances according to claim 1, 2, or 3, characterized in that, The specific process of dynamically adjusting the fusion weights of the observer outputs of each layer in the total perturbation estimation is as follows: The relative magnitude of real-time energy in each frequency band is compared at fixed intervals. The frequency band with the largest real-time energy is identified as the current dominant disturbance frequency band. The fusion weight of the observer in the corresponding layer of this frequency band is increased, while the fusion weight of other layers is decreased. The sum of the fusion weights of all layer observers is 1.

5. The multi-layer finite-time composite disturbance rejection control method for wind tunnel magnetic suspension balances according to claim 1, 2, or 3, characterized in that, The finite-time extended state observer uses the arctangent power function; the mathematical model of the finite-time extended state observer is: in, For the first Displacement estimates from a layer-wise finite-time extended state observer; For the first Velocity estimates for a layered finite-time extended state observer; For the first Perturbation estimates for a layered finite-time extended state observer; , , They are respectively , , The first derivative with respect to time; For power-order parameters; This is the gain parameter; This is the nominal gain; This refers to the position observation error; This is the core function of the finite-time extended state observer.

6. The multi-layer finite-time composite disturbance rejection control method for wind tunnel magnetic suspension balances according to claim 1, 2, or 3, characterized in that, The sliding surface of a non-singular double-power integral type fast terminal sliding mode controller is: in, For sliding mode variables, This refers to displacement tracking error; For speed tracking error; for e Gain coefficient of 1 The gain coefficient of the sliding surface. The gain is the power term; It is a power function. This is the amplitude-limited integral term; For micro-offset; These are boundary layer parameters; for Fixed gain, for The variable gain coefficient.

7. The multi-layer finite-time composite disturbance rejection control method for wind tunnel magnetic suspension balances according to claim 6, characterized in that, The non-singular double-power integral fast terminal sliding mode controller employs a variable gain arctangent double-power reaching law: in, For sliding mode variables The first derivative with respect to time; For adaptive gain; , These are boundary layer parameters; , It is a power function.

8. A multi-layer finite-time composite disturbance rejection control system for a wind tunnel magnetic suspension balance, comprising an interconnected memory and a processor, wherein the memory stores a computer program, characterized in that, When the computer program is run by the processor, it executes the steps of the multi-layer finite-time composite disturbance rejection control method for wind tunnel magnetic suspension balance as described in any one of claims 1-7.

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