The application relates to a quasi-resonant ESO control method and system combining a Hilbert algorithm of an axial magnetic bearing and a frequency observation of a quadrature phase-locked loop

Abstract

This invention relates to a quasi-resonant ESO control method and system combining Hilbert's algorithm with orthogonal phase-locked loop (PLL) frequency observation for axial magnetic bearings, belonging to the field of magnetic levitation bearing control. Addressing the hardware limitations of a single displacement signal for axial magnetic bearings and the stability issues caused by frequency shifts in periodic disturbance suppression, this invention constructs an improved extended state observer (FESO) assisted by a fractional-order model, connecting a quasi-resonant controller (QRC) to the total disturbance estimation channel of the FESO. The single displacement signal is orthogonally processed using Hilbert's algorithm to generate orthogonal signals, which are then input into the PLL to observe the disturbance frequency in real time, and the resonant frequency of the QRC is adjusted accordingly. This system can be used for periodic disturbance control scenarios of solid magnetic bearings.

Description

Technical Field

[0001] This invention belongs to the field of magnetic levitation bearing control, specifically relating to a quasi-resonant ESO control method and system that combines Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings. Background Technology

[0002] Magnetic levitation bearings utilize electromagnetic force to levitate the rotor, enabling contactless operation between the rotor and stator. They are characterized by being frictionless, pollution-free, and having a long lifespan, making them suitable for high-speed, ultra-high-speed, and high-performance transmission applications requiring contactless, lubrication-free, and pollution-free operation.

[0003] In practical engineering, solid magnetic bearing systems are often subjected to periodic disturbances at specific frequencies, such as geometric eccentricity caused by thrust disk end face runout, harmonic interference in the drive circuit, and periodic axial force fluctuations transmitted from the load side. If these disturbances are not effectively suppressed, they will directly affect the rotor's rotational accuracy. Therefore, this paper further introduces a quasi-resonant ESO algorithm with frequency observation, aiming to achieve adaptive and precise suppression of specific frequency disturbances while maintaining the excellent performance of FESO. Summary of the Invention

[0004] The purpose of this invention is to address the hardware limitations of axial magnetic bearings with only a single displacement signal and the stability problem caused by frequency shift in periodic disturbance suppression. It provides a quasi-resonant ESO control method and system that combines the Hilbert algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings. This method not only exhibits excellent disturbance suppression performance over a wide frequency range but also achieves high-precision vibration control at specific frequency points. Furthermore, the frequency observation algorithm can track the disturbance frequency in real time and accurately, providing an effective solution for periodic disturbance suppression in solid magnetic bearing systems.

[0005] This invention discloses a quasi-resonant ESO control method and system that combines Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings. It includes selective enhancement for specific frequencies (especially the system's mechanical resonance frequency or periodic disturbance frequency). While maintaining the excellent performance of the fractional-order model-assisted extended state observer (FESO), it achieves adaptive and precise suppression of disturbances at specific frequencies. The frequency observation algorithm can also track the disturbance frequency in real time and accurately, providing an effective solution for suppressing periodic disturbances in solid magnetic bearing systems.

[0006] To achieve the above objectives, the technical solution of this invention is: a quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings, comprising:

[0007] An improved extended state observer FESO assisted by a fractional-order model is constructed, which outputs the system state estimate and the total disturbance estimate z3;

[0008] The quasi-resonant controller QRC is connected in parallel to the z3 channel of the FESO to form a quasi-resonant ESO;

[0009] A single-channel displacement signal of the axial magnetic bearing is acquired, and the single-channel displacement signal is orthogonalized using the Hilbert algorithm to generate a pair of orthogonal signals.

[0010] The orthogonal signal is input into the orthogonal phase-locked loop, and the disturbance frequency of the axial rotor is observed through the orthogonal phase-locked loop;

[0011] The resonant frequency of the QRC is adjusted based on the disturbance frequency output by the quadrature phase-locked loop.

[0012] Furthermore, the FESO is constructed based on a fractional-order model of solid magnetic bearings and is used to estimate the dynamic characteristics of solid magnetic bearings.

[0013] Furthermore, the QRC is constructed by introducing a damping term into the resonant controller. The resonant controller is based on the idea of ​​introducing an internal mode of a corresponding frequency into the controller. By embedding a resonant element in the control loop, the system exhibits high gain characteristics for specific frequency signals. Its transfer function expression is:

[0014]

[0015] RC at resonant frequency ω r The gain at that frequency is infinite, thus exhibiting a very strong ability to suppress disturbances at that frequency.

[0016] After introducing the damping term, the transfer function of the quasi-resonant controller QRC is:

[0017]

[0018] Where, k r For the resonant controller gain, ω r ω is the resonant frequency. c The cutoff frequency is defined as the frequency range. The QRC reduces the infinite gain to a finite value, maintaining strong suppression of resonant frequency disturbances while decreasing the sensitivity of the resonant controller to frequency shifts and improving the frequency characteristics near the resonant frequency, thereby ensuring system stability.

[0019] Furthermore, adjusting the resonant frequency of the QRC specifically involves using the disturbance frequency output by the quadrature phase-locked loop as the resonant frequency ω of the QRC. r .

[0020] Furthermore, QRC is introduced into the ESO access point z3. z3, as an extended state, is essentially an estimate of the total system disturbance and does not require strict physical meaning. Incorporating QRC into the z3 channel enhances the observation capability of specific frequency components in the total disturbance estimation, enabling the ESO to accurately compensate for this type of periodic disturbance while ensuring the accuracy of the ESO reference model.

[0021] Furthermore, the Hilbert algorithm employs an IIR implementation based on all-pass filter pairs, specifically including:

[0022] Two all-pass filters, A1(s) and A2(s), with different time constants are used, where the geometric mean of the time constants of A1(s) and A2(s) is equal to the reciprocal of the target center angular frequency; the orthogonal signal is calculated using the following formula:

[0023]

[0024] Where u(t) is a single-channel displacement signal, For signals that are in phase with u(t), Let be a virtual signal orthogonal to u(t).

[0025] Furthermore, the first-order expression of the all-pass filter A(s) is:

[0026]

[0027] in, is the time constant.

[0028] Furthermore, in the frequency observation algorithm, an orthogonal phase-locked loop is used to ensure that the resonant frequency corresponds accurately to the frequency of the periodic disturbance, preventing a certain deviation between the resonant frequency and the actual disturbance frequency, which could cause the QRC to have a significant negative effect and lead to a decrease in system stability.

[0029] Furthermore, the quadrature phase-locked loop eliminates the influence of the input signal amplitude on phase detection by constructing two quadrature signals, and outputs a disturbance frequency.

[0030] Furthermore, by constructing two orthogonal signals using a quadrature phase-locked loop, the influence of the input signal amplitude on phase detection can be effectively eliminated, thus maintaining high frequency estimation accuracy even under amplitude fluctuations or noise interference. Moreover, the closed-loop feedback structure gives it good dynamic tracking performance, enabling it to respond to frequency changes in real time.

[0031] This invention also provides a quasi-resonant ESO control system combining Hilbert's algorithm for axial magnetic bearings with orthogonal phase-locked loop frequency observation, comprising:

[0032] An improved extended state observer FESO module assisted by fractional-order model is used to output system state estimates and total disturbance estimates z3;

[0033] The quasi-resonant controller QRC module is connected to the z3 channel of the FESO module to form a quasi-resonant ESO;

[0034] The Hilbert processing module is used to acquire single-channel displacement signals of the axial magnetic bearing and perform orthogonalization processing to generate a pair of orthogonal signals;

[0035] An orthogonal phase-locked loop module is used to receive the orthogonal signal and observe the disturbance frequency of the axial rotor;

[0036] The frequency adjustment module is used to adjust the resonant frequency of the QRC module according to the disturbance frequency output by the quadrature phase-locked loop module.

[0037] Furthermore, the Hilbert processing module adopts an IIR implementation based on an all-pass filter pair, including two all-pass filters A1(s) and A2(s) with different time constants, wherein the geometric mean of the time constants of A1(s) and A2(s) is equal to the reciprocal of the target center angular frequency.

[0038] Furthermore, the transfer function of the QRC module is:

[0039]

[0040] Where, k r For the resonant controller gain, ω r ω is the resonant frequency. c The cutoff frequency is set by the frequency adjustment module based on the output of the quadrature phase-locked loop module.

[0041] Compared with the prior art, the present invention has the following advantages: the present invention not only has good disturbance suppression performance in a wide frequency range, but also can achieve high-precision vibration control at a specific frequency point. The frequency observation algorithm can also track the disturbance frequency in real time and accurately, providing an effective solution for the periodic disturbance suppression of solid magnetic bearing systems. Attached Figure Description

[0042] Figure 1 This is a FESO control block diagram of a magnetic levitation bearing system applicable to an example of the present invention.

[0043] Figure 2 This is a block diagram of a FESO control system with an added resonant controller, applicable to an example of the present invention.

[0044] Figure 3 This is a QR-FESO control block diagram that incorporates the Hilbert algorithm, applicable to examples of this invention.

[0045] Figure 4 This is a block diagram of an orthogonal phase-locked loop control applicable to an example of the present invention. Detailed Implementation

[0046] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0047] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0048] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0049] This invention provides a quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings, comprising:

[0050] An improved extended state observer FESO assisted by a fractional-order model is constructed, which outputs the system state estimate and the total disturbance estimate z3;

[0051] The FESO expression is:

[0052]

[0053] Where x1 is the rotor displacement, z1 is the observed rotor displacement, z2 is the observed rotor speed, z3 is the observed total system disturbance estimate, β1, β2, and β3 are the observer gain coefficients, and k i k is the current stiffness of the magnetic bearing. x For the displacement stiffness of the magnetic bearing, i c To control the current.

[0054] The quasi-resonant controller QRC is connected to the z3 channel of the FESO to form a quasi-resonant ESO;

[0055] A single-channel displacement signal of the axial magnetic bearing is acquired, and the single-channel displacement signal is orthogonalized using the Hilbert algorithm to generate a pair of orthogonal signals.

[0056] The orthogonal signal is input into the orthogonal phase-locked loop, and the disturbance frequency of the axial rotor is observed through the orthogonal phase-locked loop;

[0057] The resonant frequency of the QRC is adjusted based on the disturbance frequency output by the quadrature phase-locked loop.

[0058] This invention also provides a quasi-resonant ESO control system combining Hilbert's algorithm for axial magnetic bearings with orthogonal phase-locked loop frequency observation, comprising:

[0059] An improved extended state observer FESO module assisted by fractional-order model is used to output system state estimates and total disturbance estimates z3;

[0060] A quasi-resonant controller QRC module is connected in parallel to the z3 channel of the FESO module to form a quasi-resonant ESO;

[0061] The Hilbert processing module is used to acquire single-channel displacement signals of the axial magnetic bearing and perform orthogonalization processing to generate a pair of orthogonal signals;

[0062] An orthogonal phase-locked loop module is used to receive the orthogonal signal and observe the disturbance frequency of the axial rotor;

[0063] The frequency adjustment module is used to adjust the resonant frequency of the QRC module according to the disturbance frequency output by the quadrature phase-locked loop module.

[0064] The following is a detailed implementation process of the present invention.

[0065] like Figure 1 As shown, traditional ESOs struggle to suppress complex generalized disturbances caused by eddy current effects, exhibiting limited estimation accuracy and robustness. To address this issue, this invention proposes an improved ESO (FESO) based on a fractional-order model of solid magnetic bearings. By incorporating this model into the ESO design framework, the aim is to more accurately estimate the dynamic characteristics of solid magnetic bearings, thereby enhancing the vibration suppression effect of ESOs on solid magnetic bearing systems.

[0066] like Figure 2 As shown, the resonant controller (RC) is based on the idea of ​​introducing an internal mode of a corresponding frequency into the controller. By embedding a resonant element in the control loop, the system exhibits high gain characteristics for specific frequency signals. Its transfer function expression is:

[0067]

[0068] Where k r For the resonant controller gain, ω r ω is the resonant frequency. RC at the resonant frequency ω rThe gain at that frequency is infinite, thus exhibiting extremely strong suppression capability against disturbances at that frequency. Introducing a damping term into the resonant controller constitutes a quasi-resonant controller (QRC), whose transfer function expression is:

[0069]

[0070] Where ω c At the cutoff frequency, QRC reduces the infinite gain to a finite value. While maintaining strong suppression of resonant frequency disturbances, it reduces the sensitivity of the resonant controller to frequency shifts and improves the frequency characteristics near the resonant frequency, thus ensuring system stability. Introducing QRC into the ESO in parallel with z3, where z3 represents the extended state, is essentially an estimate of the total system disturbance and does not require strict physical meaning. Incorporating QRC into the z3 channel enhances the observation capability of specific frequency components in the total disturbance estimation, enabling the ESO to accurately compensate for such periodic disturbances while ensuring the accuracy of the ESO reference model.

[0071] like Figure 3 As shown, in the frequency observation algorithm, an orthogonal phase-locked loop (QL) is used to accurately correspond the resonant frequency to the frequency of the periodic disturbance, preventing a certain deviation between the resonant frequency and the actual disturbance frequency. This would prevent the QL from having a significant negative effect, leading to a decrease in system stability. Using an QL to construct two orthogonal signals effectively eliminates the influence of the input signal amplitude on phase detection, thus maintaining high frequency estimation accuracy even under amplitude fluctuations or noise interference. Furthermore, the closed-loop feedback structure provides excellent dynamic tracking performance, enabling real-time response to frequency changes. The Hilbert algorithm is introduced to orthogonalize the single-channel displacement signal of the axial magnetic bearing, generating a pair of orthogonal signals that meet the input requirements of the QL, enabling real-time observation of the axial rotor disturbance frequency.

[0072] For a real signal u(t), its Hilbert transform is defined as:

[0073]

[0074] This integral has a singularity τ=t, therefore its Cauchy principal value is usually used for calculation, and its expression is:

[0075]

[0076] Where PV is the Cauchy principal value integral. The time-domain expression of the above equation is insufficient for analyzing the impact of Hilbert's algorithm on the signal. Applying a Fourier transform, we obtain the frequency-domain transfer function of Hilbert's algorithm:

[0077]

[0078] The commonly used discretized implementation of Hilbert's algorithm is based on an IIR implementation using a pair of all-pass filters, i.e., using two all-pass filters to form a 90° phase-shift network. The expression for a first-order all-pass filter is:

[0079]

[0080] Where τ is the time constant. As the signal frequency increases, the amplitude of the filter remains constant at 1, while the phase frequency response changes from 0° to -180°. The expression for the IIR implementation based on the all-pass filter pair can be obtained as follows:

[0081]

[0082] Here, A1(s) and A2(s) are all-pass filters with different time constants, requiring that the geometric mean of the two time constants be equal to the reciprocal of the target center angular frequency. This enables the designed Hilbert algorithm to accurately achieve a 90° phase shift while maintaining the integrity of the output signal amplitude. Addressing the hardware limitation of axial magnetic bearings having only one displacement signal, this method successfully constructs a virtual signal orthogonal to the original signal, thus allowing the quadrature phase-locked loop (PLL) to be applied to frequency observation scenarios in axial magnetic bearing systems.

[0083] like Figure 4 As shown, in a quadrature phase-locked loop (QLL), the input signals are a pair of mutually orthogonal signals. First, a normalization factor is introduced. The input signal amplitude is normalized to eliminate the influence of amplitude variations on the phase detection results. After normalization, the PI parameters of the phase-locked loop (PLL) do not need to be adjusted with the input signal amplitude, thus simplifying the parameter tuning process. The output of the PI controller is the angular frequency of the observed signal. The integral of the angular frequency is the phase estimate, which is fed back to the input terminal for phase comparison with the input signal, forming a closed-loop phase-locked loop.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings, characterized in that, include: An improved extended state observer FESO assisted by a fractional-order model is constructed, which outputs the system state estimate and the total disturbance estimate z3; The quasi-resonant controller QRC is connected in parallel to the z3 channel of the FESO to form a quasi-resonant ESO; A single-channel displacement signal of the axial magnetic bearing is acquired, and the single-channel displacement signal is orthogonalized using the Hilbert algorithm to generate a pair of orthogonal signals. The orthogonal signal is input into the orthogonal phase-locked loop, and the disturbance frequency of the axial rotor is observed through the orthogonal phase-locked loop; The resonant frequency of the QRC is adjusted based on the disturbance frequency output by the quadrature phase-locked loop.

2. The quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings as described in claim 1, is characterized in that... The FESO is constructed based on a fractional-order model of solid magnetic bearings and is used to estimate the dynamic characteristics of solid magnetic bearings.

3. The quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings as described in claim 1, is characterized in that... The transfer function of the QRC is: Where, k r For the resonant controller gain, ω r ω is the resonant frequency. c This is the cutoff frequency.

4. The quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings as described in claim 1, is characterized in that... The adjustment of the resonant frequency of the QRC specifically involves using the perturbation frequency output by the quadrature phase-locked loop as the resonant frequency ω of the QRC. r .

5. The quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings as described in claim 1, characterized in that... The Hilbert algorithm is implemented using an IIR method based on all-pass filter pairs, specifically including: Two all-pass filters, A1(s) and A2(s), with different time constants are used, where the geometric mean of the time constants of A1(s) and A2(s) is equal to the reciprocal of the target center angular frequency; the orthogonal signal is calculated using the following formula: Where u(t) is a single-channel displacement signal, For signals that are in phase with u(t), Let be a virtual signal orthogonal to u(t).

6. The quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings as described in claim 1, is characterized in that... The first-order expression for the all-pass filter A(s) is: in, is the time constant.

7. The quasi-resonant ESO control method combining Hilbert's algorithm with orthogonal phase-locked loop frequency observation for axial magnetic bearings as described in claim 1, characterized in that... The quadrature phase-locked loop eliminates the influence of the input signal amplitude on phase detection by constructing two quadrature signals and outputs a disturbance frequency.

8. A quasi-resonant ESO control system combining Hilbert's algorithm for axial magnetic bearings with orthogonal phase-locked loop frequency observation, characterized in that... include: An improved extended state observer FESO module assisted by fractional-order model is used to output system state estimates and total disturbance estimates z3; The quasi-resonant controller QRC module is connected to the z3 channel of the FESO module to form a quasi-resonant ESO; The Hilbert processing module is used to acquire single-channel displacement signals of the axial magnetic bearing and perform orthogonalization processing to generate a pair of orthogonal signals; An orthogonal phase-locked loop module is used to receive the orthogonal signal and observe the disturbance frequency of the axial rotor; The frequency adjustment module is used to adjust the resonant frequency of the QRC module according to the disturbance frequency output by the quadrature phase-locked loop module.

9. The quasi-resonant ESO control system combining Hilbert's algorithm for axial magnetic bearings with orthogonal phase-locked loop frequency observation as described in claim 8, is characterized in that... The Hilbert processing module adopts an IIR implementation based on an all-pass filter pair, including two all-pass filters A1(s) and A2(s) with different time constants, wherein the geometric mean of the time constants of A1(s) and A2(s) is equal to the reciprocal of the target center angular frequency.

10. The quasi-resonant ESO control system combining Hilbert's algorithm for axial magnetic bearings with orthogonal phase-locked loop frequency observation as described in claim 8, is characterized in that... The transfer function of the QRC module is: Where, k r For the resonant controller gain, ω r ω is the resonant frequency. c The cutoff frequency is set by the frequency adjustment module based on the output of the quadrature phase-locked loop module.

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