On-line time-lag identification method for magnetic suspension rotor system based on correlation analysis

Abstract

The invention discloses a correlation analysis-based magnetic suspension rotor system on-line time-lag identification method, which comprises the following steps of: generating a sine excitation signal through an excitation signal generator to excite a magnetic suspension rotor system, collecting a control voltage and a displacement signal, and introducing the control voltage and the displacement signal into a cross-correlation time-lag identifier to carry out time-lag identification. The time-delay identifier is composed of a band-pass filter, a conversion transfer function, a data storage module and a cross-correlation time-delay identification operation module. Voltage and displacement signals which are introduced into the cross-correlation time-lag identifier are firstly filtered through a band-pass filter and then converted into homologous signals through a conversion transfer function, then data storage and iteration are carried out by utilizing a data storage module, and finally the required time-lag amount is identified by utilizing a cross-correlation operation module. According to the method, the advantage that the magnetic suspension rotor system is active and controllable is utilized, extra testing equipment does not need to be used, the structure is simple, few computing resources are occupied, time delay information in the system can be obtained online, and time delay identification of the magnetic suspension rotor system is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic levitation bearings, and particularly to an online time-delay identification method for a magnetic levitation rotor system based on correlation analysis. Background Art

[0002] As a typical mechatronic product, various time-delay links inevitably exist inside a magnetic levitation rotor system. In a mechatronic system, even a tiny time delay may have a great impact on the stability and dynamic performance of the rotor system. Currently, in the design of the controller for a magnetic levitation rotor system, the influence of the internal time-delay amount of the system is usually ignored. When the internal time-delay amount of the system is small or the requirement for control accuracy is not high, this consideration will not affect the stability of the system. However, with the continuous expansion of the application fields of magnetic levitation bearings, some application scenarios that need to work in harsh environments for a long time have emerged, such as magnetic levitation subsea compressors, offshore wind turbines, and magnetic levitation pipeline compressors for long-distance natural gas pipelines. In these situations, the controller is usually separated from the magnetic levitation bearing body and placed in a safer place. However, this distributed design will make the internal time-delay problem of the system prominent. In order to consider the time-delay factor in the controller, it is particularly crucial to obtain an accurate system time-delay amount. However, there is little research on the identification of the internal time delay of a magnetic levitation bearing system in existing theories. Summary of the Invention

[0003] The purpose of the present invention is to address the above deficiencies in the prior art. The present invention proposes an online time-delay identification method for a magnetic levitation rotor system based on correlation analysis. This method has a simple structure and strong real-time performance, and can obtain the internal time-delay amount of the system online.

[0004] The present invention adopts the following technical solutions to solve the above technical problems:

[0005] An online time-delay identification method for a magnetic levitation rotor system based on correlation analysis, characterized in that: it consists of two parts, an excitation signal generator and a cross-correlation time-delay identifier; the magnetic levitation rotor system mainly includes four parts: a magnetic levitation bearing-rotor, a controller, a power amplifier, and a displacement sensor; the input signals of the cross-correlation time-delay identifier are respectively a control voltage signal U(s) and a displacement signal Y(s); the specific steps of cross-correlation time-delay identification are as follows:

[0006] Step S1: Generate a sinusoidal excitation signal through the excitation signal generator to excite the magnetic levitation rotor system, and collect the control voltage and displacement signals during operation;

[0007] Step S2: Use a band-pass filter to process the collected voltage and displacement signals, extract the response signals in the signals caused by the excitation signal, and remove other irrelevant signal interferences;

[0008] Step S3: Convert and transfer the voltage and displacement signals into homologous signals through the transfer functions G u (s) and G y (s);

[0009] Step S4: Store and iterate the data converted in Step S3; establish two arrays U and Y with length L, define the sampling time of the data, which is generally consistent with the sampling time of the controller, and the time interval for performing a cross-correlation identification; as the data sampling continues, store the preprocessed voltage and displacement signals collected into the arrays U and Y;

[0010] Step S5: Perform a cross-correlation time-delay identification operation on the data in the arrays U and Y.

[0011] Furthermore, the expressions of the transfer functions G u (s) and G y (s) are respectively:

[0012]

[0013] where b is the system gain, k xx is the displacement stiffness per unit mass, and its magnitude is: b = k a k i k s / m, k xx = k x / m; k a and k s are respectively the power amplifier gain and the sensor gain, k i and k x are respectively the current stiffness and the displacement stiffness, m is the rotor mass; 1 / (1 + Ts) 2 is a low-pass filter, and T is the time constant of the low-pass filter; in addition to the signal filtering effect, the low-pass filter also has the effect of meeting physical implementation; therefore, the order of the low-pass filter should be greater than or equal to 2 so that the numerator order of G y (s) is not greater than the denominator;

[0014] For a time-delay magnetic levitation rotor system, its transfer function Y(s) can be expressed as:

[0015]

[0016] where W(s) is the transfer function of the interference signal, and τ is the magnitude of the system time delay;

[0017] Therefore, when the extracted voltage and displacement signals are converted by G u (s) and G y (s), they can be expressed as:

[0018]

[0019] At this time, Y f (s) and U f (s) are converted into a homologous signal, and there is only a time-delay difference e except for the interference signal -τs .

[0020] Furthermore, in the array U, the form of data storage and iteration is as follows:

[0021] U(i) = U(i + 1), i ∈ [1, L - 1]

[0022] U(L) = u f (t), i = L

[0023] wherein, u f (t) is the time-domain signal of U f (s); by continuously iterating the data content of the array, the data in the array is updated in real time.

[0024] Furthermore, the specific operation principle of performing cross-correlation time-delay identification operation on the data in the arrays U and Y is as follows:

[0025] Assume that there are two groups of signals U and Y to be identified, and Y is regarded as being converted from signal U through the following system:

[0026] H(f) = exp(-j[2πft d + θ c )

[0027] wherein, t d is the group delay, θ c is the center-frequency phase shift, and exp represents the exponential function; the phase delay is defined as:

[0028]

[0029] Then, at the center frequency, the above formula can be rewritten as:

[0030] H(f) = exp(-j2πf[t d + t p )

[0031] Furthermore, the total time delay between the signals U and Y is τ = t d + t p ; therefore, the time-delay amount between the signals U and Y can be obtained by finding the group delay and the phase delay, and these two parameters can be obtained by performing cross-correlation function calculation in the frequency domain. The specific steps are as follows:

[0032] First, convert the signal U from the complex-valued baseband signal b(t) = br (t) + jb i (t) frequency shift representation; here, b r (t) is the real part of the complex baseband signal, b i (t) is the imaginary part of the complex baseband signal:

[0033] U(f) = B(f - f c ) / 2 + B * (-f - f c ) / 2

[0034] In the formula, f c is the center frequency, B(f - f c ) represents the spectrum of the baseband signal shifted to the right by f c , B * (-f - f c ) then represents the conjugate symmetric part of the baseband signal spectrum shifted to the left by f c , ensuring that the time-domain signal is real; taking the inverse Fourier transform of the above formula gives the relationship of U:

[0035] U = b r (t) cos(2πft c t) - b i (t) sin(2πft c t)

[0036] Y is obtained from U through the system H(f), that is:

[0037] Y = b r (t - t d ) cos(2πf c [t - t d + θ c ) - b i (t - t d ) sin(2πf c [t - t d + θ c )

[0038] The cross-correlation function C UY (f) is defined in the frequency domain as:

[0039]

[0040] where, * represents conjugate; the above formula can be rewritten for bandpass signals as:

[0041]

[0042] Taking the inverse Fourier transform of the above formula, we have:

[0043]

[0044] Among them, is the autocorrelation function of b(t); among them, and are respectively the real part and the imaginary part of c bb (t), and can be defined in the frequency domain as C bb (f) = B(f)B * (f) = |B(f)| 2 , is the envelope function, is the phase angle function;

[0045] According to the above formula, the envelope function c UY (t) of the cross-correlation function c UY1 (t) is:

[0046] c UY1 (t) = 2e bb (t - t d )

[0047] When t = t d , the envelope function generates a peak; therefore, the group delay of the signal can be obtained by calculating the abscissa corresponding to the peak of the envelope function; when the group delay t d is determined, the phase shift θ d of the center frequency is determined by analyzing the phase parameter of the cross-correlation function at t c , that is:

[0048]

[0049] Among them, arctan(·) represents the arctangent function, Im[c UY (t d )] represents taking the imaginary part of c UY (t d ), and Re[c UY (t d )] represents taking the real part of c UY (t d );

[0050] In summary, the estimated value τ* of the time delay between the two signals to be identified is:

[0051]

[0052] Furthermore, since the external disturbance of the controlled object contains the unbalanced disturbance amount of the rotor, which is of the same frequency as the system input and output signals and will affect the phase difference between the input and output signals, it is necessary to combine the excitation signal generator with the band-pass filter. The excitation signal generator generates a sinusoidal excitation signal with a small amplitude and a frequency different from the rotational frequency of the rotor. The frequency of the sinusoidal excitation signal is exactly the center frequency of the band-pass filter, which can ensure that the band-pass filter extracts only the response signal generated by the excitation signal generator from U(s) and Y(s), avoiding the influence of the rotor unbalanced disturbance amount on the time-delay identification result.

[0053] Furthermore, the excitation signal generator generates a sinusoidal excitation signal Asin(ωt), which mainly includes two parameters: the excitation signal amplitude A and the excitation frequency ω. The excitation signal amplitude A needs to ensure that the amplitude is as small as possible without affecting the stable operation of the rotor and is greater than the noise signal in the system so that it can be extracted by the band-pass filter Q(s). The excitation frequency ω needs to be far from the rotational frequency of the rotor.

[0054] Furthermore, the center frequency of the band-pass filter Q(s) needs to be equal to the excitation frequency ω of the sinusoidal excitation signal, and the bandwidth can be adjusted according to the actual situation.

[0055] Compared with the prior art, the present invention adopts the above technical solutions and has the following beneficial effects:

[0056] 1. An online time-delay identification method for a magnetic levitation rotor system based on correlation analysis proposed by the present invention gives full play to the advantages of the active controllability of the magnetic levitation rotor system, uses the magnetic levitation bearing as the excitation source, does not require additional testing instruments, and saves costs.

[0057] 2. An online time-delay identification method for a magnetic levitation rotor system based on correlation analysis proposed by the present invention adopts the combination of an excitation signal generator and a band-pass filter, effectively avoiding the influence of unbalanced interference during the rotor operation on the time-delay identification.

[0058] 3. An online time-delay identification method for a magnetic levitation rotor system based on correlation analysis proposed by the present invention has a simple structure, small computational complexity, and is applicable to all magnetic levitation rotating machinery; it has strong real-time performance, can perform time-delay identification during the operation of the system, has high efficiency, and is convenient to operate. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is the principle block diagram of an online time-delay identification method for a magnetic levitation rotor system based on correlation analysis of the present invention;

[0060] Figure 2 is the frequency response fitting curve of the magnetic levitation rotor system;

[0061] Figure 3 It is an identification algorithm verification program;

[0062] Figure 4 It is the result curve of online time-delay identification on a magnetic levitation rotor test bench;

[0063] Figure 5 It is the result curve of variable time-delay identification at 0 Hz;

[0064] Figure 6 It is the result curve of variable time-delay identification at 30 Hz;

[0065] Figure 7 It is the result curve of variable time-delay identification at 60 Hz;

[0066] Figure 8 It is the result curve of variable time-delay identification at 90 Hz. Specific implementation manner

[0067] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0068] As Figure 1 shown, it is the principle block diagram of an online time-delay identification method for a magnetic levitation rotor system based on correlation analysis. The online time-delay identification method consists of two parts: an excitation signal generator and a cross-correlation time-delay identifier. The magnetic levitation rotor system mainly includes four parts: a magnetic levitation bearing-rotor, a controller, a power amplifier, and a displacement sensor. Figure 1 In it, a simplified expression is used for this part, where the total internal time-delay of the system is τ, G(s) = b / (s 2 - k xx ), b = k a k i k s / m, k xx = k x / m. k a is the power amplifier gain, k s is the sensor gain, k i is the current stiffness of the magnetic levitation bearing-rotor part, k x is the displacement stiffness of the magnetic levitation bearing-rotor part. The input signals of the cross-correlation time-delay identifier are the control voltage signal U(s) and the displacement signal Y(s) respectively. The cross-correlation time-delay identifier consists of a band-pass filter (Q(s)), a conversion transfer function (G u (s) and G y(s)), data storage iterative arrays (U and Y), and cross-correlation time-delay identification operations.

[0069] The function of the excitation signal generator is to generate a sinusoidal signal with an amplitude of A and an angular velocity of ω. The excitation signal needs to be far from the working rotation frequency of the rotor and have a small amplitude so as not to affect the stability of the rotor during operation. The center frequency of the band-pass filter needs to be the same as the frequency generated by the excitation signal generator to facilitate the extraction of the response signal of the excitation noise from the signal and avoid interference from other signals.

[0070] When the system control voltage signal and displacement signal pass through the band-pass filter, they are converted into homologous signals through the transfer functions G u (s) and G y (s). The expressions of G u (s) and G y (s) are respectively:

[0071]

[0072] Among them, b is the system gain, k xx is the displacement stiffness per unit mass, and its magnitude is: b = k a k i k s / m, k xx = k x / m; k a and k s are respectively the power amplifier gain and the sensor gain, k i and k x are respectively the current stiffness and the displacement stiffness, m is the rotor mass; 1 / (1 + Ts) 2 is a low-pass filter, and T is the time constant of the low-pass filter; in addition to the signal filtering function, the low-pass filter also has the function of meeting physical implementation; therefore, the order of the low-pass filter should be greater than or equal to 2 so that the numerator order of G y (s) is not greater than the denominator;

[0073] For the magnetic levitation rotor system, traditional linearization expressions often ignore the phase information inside the system. To avoid this problem, the present invention models the system as a second-order plus time-delay system, and its transfer function can be expressed as:

[0074]

[0075] Among them, W(s) is the interference signal. When the extracted voltage and displacement signals pass through G u (s) and G y (s) for conversion, they can be expressed as:

[0076]

[0077] At this time, Y f (s) and U f (s) are converted into homologous signals, and there is only a time-delay difference e except for the interference signal -τs .

[0078] Store and iterate the converted data. Establish two arrays U and Y with a length of L, define the sampling time of the data (generally consistent with the sampling time of the controller), and the time interval for performing a cross-correlation identification. As the data sampling continues, the preprocessed voltage and displacement signals collected are stored in the arrays U and Y. Taking the array U as an example, the specific form of data storage is as follows:

[0079] U(i) = U(i + 1), i ∈ [1, L - 1]

[0080] U(L) = u f (t), i = L

[0081] where, u f (t) is the time-domain signal of U f (s). By continuously iterating the data content in the array, the data in the array is updated in real time.

[0082] Perform a cross-correlation time-delay identification operation on the data in the arrays U and Y. The specific operation principle is as follows:

[0083] Suppose there are two groups of signals U and Y to be identified. Y is regarded as being converted from the signal U through the following system:

[0084] H(f) = exp(-j[2πft d + θ c )

[0085] where, t d is the group delay, θ c is the central frequency phase shift, and exp represents the exponential function. Define the phase delay as:

[0086]

[0087] Then at the central frequency, the above formula can be rewritten as:

[0088] H(f) = exp(-j2πf[t d + t p )

[0089] In summary, the total time delay between the signals U and Y is τ = t d + t pTherefore, the time delay between signals U and Y can be obtained by calculating the group delay and phase delay, and these two parameters can be obtained by calculating the cross-correlation function in the frequency domain.

[0090] First, the signal U is represented by frequency shifting of the complex baseband signal b(t) = b r (t) + jb i (t) (here, b r (t) is the real part of the complex baseband signal, and b i (t) is the imaginary part of the complex baseband signal):

[0091] U(f) = B(f - f c ) / 2 + B * (-f - f c ) / 2

[0092] where f c is the center frequency, B(f - f c ) represents the spectrum of the baseband signal shifted to the right by f c , and B * (-f - f c ) represents the conjugate symmetric part of the baseband signal spectrum shifted to the left by f c to ensure that the time-domain signal is real; taking the inverse Fourier transform of the above equation gives the relationship between U and b(t):

[0093] U = b r (t)cos(2πf c t) - b i (t)sin(2πf c t)

[0094] Y is obtained from U through the system H(f), i.e.:

[0095] Y = b r (t - t d )cos(2πf c [t - t d + θ c ) - b i (t - t d )sin(2πf c [t - t d + θ c )

[0096] The definition of the cross-correlation function in the frequency domain is:

[0097]

[0098] where * denotes the conjugate. The above equation can be rewritten for a bandpass signal as:

[0099]

[0100] Performing the inverse Fourier transform on the above equation, we have:

[0101]

[0102] where is the autocorrelation function of b(t) ( and are the real and imaginary parts of c bb (t), respectively), and in the frequency domain, it can be defined as C bb (f) = B(f)B * (f) = |B(f)| 2 . is the envelope function, is the phase angle function.

[0103] According to the above equation, the envelope function c UY (t) of the cross-correlation function c UY1 (t) is:

[0104] c UY1 (t) = 2e bb (t - t d )

[0105] When t = t d , the envelope function generates a peak. Therefore, the group delay of the signal can be obtained by calculating the abscissa corresponding to the peak of the envelope function. When the group delay t d is determined, the central frequency phase shift θ d is determined by analyzing the phase parameter of the cross-correlation function at t c , that is:

[0106]

[0107] where arctan(·) represents the arctangent function, Im[c UY (t d )] represents taking the imaginary part of c UY (t d ), and Re[c UY (t d )] represents taking the real part of c UY (t d );

[0108] In summary, the estimated value τ* of the time delay between the two signals to be identified is:

[0109]

[0110] Online time-delay identification of the magnetic levitation rotor system is achieved by continuously storing and iterating the collected signals and identifying the system time-delay using cross-correlation time-delay identification operation.

[0111] Implementation method: experimental identification.

[0112] The experimental frequency response from the control voltage U(s) to Y(s) of the magnetic levitation rotor system is plotted using a swept-frequency test, and fitting is performed using a traditional second-order model and the second-order plus time-delay model proposed in the present invention, as Figure 2 shown. It can be seen that the fitting effect of the second-order plus time-delay model proposed in the present invention is better, complementing the phase information ignored by the conventional second-order model. The fitting results show that the time-delay amount contained in the system is 182.2 μs.

[0113] Time-delay identification operation is performed under the static floating state of the system, and the identification algorithm verification program is as Figure 3 shown. Among them, 1 represents the identification result of the total time-delay, 2 represents the identification result of the time-delay amount contained in the system, and 3 represents the identification result of the 50 μs time-delay amount added to the controller. From Figure 4 the results, it can be seen that the three groups of identification results all fluctuate around the theoretical value, indicating that the algorithm proposed in this paper can effectively identify the time-delay amount inside the system. Although there are fluctuations, the maximum error does not exceed 25 μs, and the error range is small, which will not have a significant impact on the results. Specifically, the identification result of 2 fluctuates around 182.2 μs, which is consistent with the result of frequency response fitting; the steady-state value of the identification result of 3 is consistent with the added 50 μs time-delay amount; the steady-state value of the identification result of 1 is 232.2 μs, which is consistent with the sum of the identification results of 2 and 3. In addition, the identification result of 3 fluctuates less, mainly because the signal it collects contains fewer modules and less interference.

[0114] Time-delay identification operation is performed at various rotational speeds, as Figures 5 to 8 shown. Among them, a time-varying time-delay of 50 - 200 μs is added after the controller, that is, the total time-delay will vary between 232.2 - 382.2 μs. Figure 5 is the identification result when the rotational frequency is 0 Hz (i.e., during static floating), Figure 6 , Figure 7 and Figure 8 are the identification results at 30 Hz, 60 Hz, and 90 Hz respectively. The average error rates at the four frequencies are 0.63%, 0.67%, 0.64%, and 0.43% respectively. It can be seen that when the rotor operates at various rotational frequencies, the identification algorithm of the present invention can track the time-delay changes of the system. Therefore, the identification algorithm proposed in the present invention can perform time-delay identification operation during the stable operation of the rotor and can respond in a timely manner to the possible time-delay changes inside the system.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the various embodiments of the present invention.

Claims

1. An online time delay identification method for a magnetic suspension rotor system based on correlation analysis, characterized in that: It consists of two parts: an excitation signal generator and a cross-correlation time-delay identifier. The magnetic suspension rotor system mainly includes four parts: a magnetic suspension bearing-rotor, a controller, a power amplifier, and a displacement sensor. The input signals of the cross-correlation time-delay identifier are the control voltage signal U(s) and the displacement signal Y(s). The specific steps of cross-correlation time-delay identification are as follows: Step S1: generating a sinusoidal excitation signal through an excitation signal generator to excite the magnetic suspension rotor system, and collecting control voltage and displacement signals during operation; Step S2: using a bandpass filter to process the collected voltage and displacement signals, extracting the response signal caused by the excitation signal, and removing other irrelevant signal interference; Step S3: By converting the transfer function G u (s) and G y (s) converting voltage and displacement signals into homologous signals; Step S4: storing and iterating the data converted in step S3; establishing two arrays U and Y of length L, defining the data sampling time, which is generally consistent with the sampling time of the controller, and the time interval for performing a cross-correlation identification; as data sampling continues, the collected pre-processed voltage and displacement signals are stored in the arrays U and Y; Step S5: performing a cross-correlation time-delay identification operation on the data in the arrays U and Y.

2. According to claim 1, the method for online time delay identification of a magnetic suspension rotor system based on correlation analysis is characterized in that: The conversion transfer function G u (s) and G y The expressions of (s) are: Where b is the system gain, k xx is the unit mass displacement stiffness, and its magnitude is: b = k a k i k s / m,k xx =k x / m;k a and k s are the power amplifier gain and sensor gain, k i and k x are the current stiffness and displacement stiffness respectively, m is the rotor mass; 1 / (1+Ts) 2 is a low-pass filter, T is the time constant of the low-pass filter; in addition to signal filtering, the low-pass filter also has the function of satisfying physical realization; therefore, the order of the low-pass filter must be greater than or equal to 2, so that G y The numerator of (s) is not greater than the denominator; For the magnetically suspended rotor system with time lag, its transfer function Y(s) can be expressed as: Among them, W(s) is the transfer function of the interference signal, and τ is the system time delay; Therefore, when the extracted voltage and displacement signals pass through G u (s) and G y After conversion, (s) can be expressed as: At this time, Y f (s) and U f (s) is transformed into a homologous signal, and only the time lag difference e exists besides the interference signal -τs .

3. The method for online time delay identification of a magnetic suspension rotor system based on correlation analysis according to claim 1 is characterized in that: In the array U, the data is stored and iterated in the following form: U(i)=U(i+1),i∈[1,L-1] U(L)=u f (t),i=L Among them, u f (t) is U f (s) time domain signal; by continuously iterating the array content data, the data in the array can be updated in real time.

4. The method for online time delay identification of a magnetic suspension rotor system based on correlation analysis according to claim 1 is characterized in that: The specific operation principle of performing the cross-correlation time-delay identification operation on the data in the arrays U and Y is as follows: Assume that there are two sets of signals to be identified, U and Y, and Y is regarded as the signal U converted by the following system: H(f)=exp(-j[2πft d +θ c ]) Among them, t d is the group delay, θ c is the center frequency phase shift, exp represents the exponential function; the phase delay is defined as: At the center frequency, the above formula can be rewritten as: H(f)=exp(-j2πf[t d +t p ])。 5. The method for online time delay identification of a magnetically suspended rotor system based on correlation analysis according to claim 1 is characterized in that: The total time lag between the signals U and Y is τ=t d +t p ; Therefore, the time delay between signals U and Y can be obtained by calculating the group delay and phase delay, and these two parameters can be obtained by calculating the cross-correlation function in the frequency domain. The specific steps are as follows: First, the signal U is transformed from the complex-valued baseband signal b(t)=b r (t)+jb i (t) is represented by the frequency shift; here, b r (t) is the real part of the complex baseband signal, b i (t) is the imaginary part of the complex baseband signal: U(f)=B(f-f c ) / 2+B * (-f-f c ) / 2 In the formula, f c is the center frequency, B(ff c ) indicates that the spectrum of the baseband signal is shifted to the right by f c , B * (-ff c ) means that the conjugate symmetric part of the baseband signal spectrum is shifted to the left by f c , ensuring that the time domain signal is a real number; performing an inverse Fourier transform on the above formula can obtain the relationship of U: U=b r (t)cos(2πf c t)-b i (t)sin(2πf c t) Y is obtained from U through the system H(f), that is: Y=b r (t-t d )cos(2πf c [t-t d ]+θ c )-b i (t-t d )sin(2πf c [t-t d ]+θ c ) Cross-correlation function C UY (f) is defined in the frequency domain as: Where * represents conjugation; the above formula can be rewritten as: Perform inverse Fourier transform on the above formula, we have: in, is the autocorrelation function of b(t); and c bb The real and imaginary parts of (t) can be defined in the frequency domain as C bb (f) = B(f)B * (f)=|B(f)| 2 , is the envelope function, is the phase angle function; According to the above formula, the cross-correlation function c UY (t) envelope function c UY1 (t) is: c UY1 (t)=2e bb (t-t d ) When t = t d When , the envelope function produces a peak value; therefore, the group delay of the signal can be obtained by calculating the horizontal coordinate corresponding to the peak value of the envelope function; when the group delay t d After determination, by analyzing t d The phase parameter of the cross-correlation function at the center frequency is used to determine the phase shift θ c ,Right now: Where arctan(·) represents the inverse tangent function, Im[c UY (t d )] means taking c UY (t d )'s imaginary part, Re[c UY (t d )] means taking c UY (t d ) In summary, the estimated value τ* of the delay between two signals to be identified is:

6. The method for online time delay identification of a magnetic suspension rotor system based on correlation analysis according to claim 1 is characterized in that: Since the external disturbance of the controlled object contains the rotor unbalance disturbance, which is at the same frequency as the system input and output signals, it will affect the phase difference between the input and output signals; therefore, it is necessary to combine the excitation signal generator with the bandpass filter; the excitation signal generator generates a sinusoidal excitation signal with a small amplitude and a different frequency from the rotor rotation frequency; the frequency of the sinusoidal excitation signal is exactly the center frequency of the bandpass filter, which can ensure that the bandpass filter only extracts the response signal generated by the excitation signal generator from U(s) and Y(s), avoiding the influence of the rotor unbalance disturbance on the time-delay identification result.

7. The method for online time delay identification of a magnetically suspended rotor system based on correlation analysis according to claim 1 is characterized in that: The excitation signal generator generates a sinusoidal excitation signal Asin(ωt), which mainly includes two parameters: the excitation signal amplitude A and the excitation frequency ω; the excitation signal amplitude A needs to ensure that the amplitude is as small as possible so as not to affect the stable operation of the rotor, and is larger than the noise signal in the system and can be extracted by the bandpass filter Q(s); the excitation frequency ω needs to be far away from the rotor rotation frequency.

8. The method for online time delay identification of a magnetically suspended rotor system based on correlation analysis according to claim 1 is characterized in that: The center frequency of the bandpass filter Q(s) needs to be equal to the excitation frequency ω of the sinusoidal excitation signal; the bandwidth can be adjusted according to actual conditions.

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