Design method and device of AMB rigid rotor system based on wave trap

Abstract

The invention belongs to the technical field of active magnetic suspension bearings, and discloses a design method and device for an AMB rigid rotor system based on wave traps, and the method comprises the steps: enabling a plurality of cascaded phase-shift wave traps to be embedded into the AMB rigid rotor system, and setting the wave trapping fundamental frequency of the cascaded phase-shift wave traps as the rotor rotating speed frequency; establishing a closed loop characteristic equation of the AMB rigid rotor system embedded with the cascade phase shift wave trap; setting a system stability condition that roots of all closed-loop characteristic equations have negative real parts; solving partial derivative of the closed-loop characteristic equation to obtain a variation trend equation; and inputting the closed-loop characteristic equation into the cascade phase-shift wave trap, performing phase shift through the change trend equation, and controlling the AMB rigid rotor system through the cascade phase-shift wave trap to obtain the AMB rigid rotor system based on the cascade phase-shift wave trap. The AMBs rigid rotor system using the phase shift wave trap does not need polarity switching when crossing a critical rotating speed, and the control difficulty can be reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of active magnetic suspension bearing, and particularly relates to a design method and device of an AMB rigid rotor system based on a wave trap. BACKGROUND

[0002] The combination of high-speed motor and electromagnetic bearing (AMB) is a key technical solution for improving the performance of rotating machinery, and is particularly suitable for application occasions with extremely high requirements for operation accuracy, rotating speed and reliability. However, in an actual control system, a low-pass filter is often used to suppress high-frequency noise and reduce its interference on the controller. However, the introduction of the low-pass filter will cause phase lag, which will adversely affect the control performance of the system. Therefore, developing an efficient vibration control strategy has become a key research direction for improving the performance of AMBs system.

[0003] A patent application with the name of magnetic suspension rotor vibration harmonic suppression method and system of multiple wave traps in parallel, and the patent number CN109976403A, discloses a magnetic suspension rotor vibration harmonic suppression method and system of multiple wave traps in parallel, which comprises a parallel phase shift wave trap, a magnetic suspension controller and a magnetic bearing rotor connected in turn. The signal extraction point of the parallel phase shift wave trap is placed at the input end of the magnetic suspension controller, and the signal insertion point of the parallel phase shift wave trap is placed at the displacement error signal. The application considers the influence of rotor mass imbalance and sensor vibration on the magnetic suspension rotor, establishes a magnetic suspension rotor dynamics model containing harmonic disturbance, and effectively suppresses the different frequency disturbance components of the harmonic current at the variable rotating speed frequency through multiple wave traps with different phase shifts in parallel. The patent application does not consider the influence of the low-pass filter on the phase and stability of the system, and in the case where the low-pass filter is not used, multiple phase shift wave traps need to be connected in parallel to effectively suppress the current harmonic at each frequency, which increases the hardware calculation load and is not conducive to online implementation of the system. SUMMARY

[0004] In order to overcome the problems existing in the prior art, the purpose of the present application is to provide a design method and device of an AMB rigid rotor system based on a wave trap, which effectively compensates for the phase lag introduced by the low-pass filter and optimizes the control performance of the system by providing a design method of an AMB rigid rotor system based on a wave trap.

[0005] To achieve the above purpose, the technical scheme adopted by the present application is as follows: In a first aspect, the present application provides a design method of an AMB rigid rotor system based on a wave trap, comprising the following steps: Embed multiple phase shift wave traps in the AMB rigid rotor system and cascade them, and set the wave trap base frequency of the cascaded phase shift wave trap to the rotor rotating speed frequency. Establish the closed-loop characteristic equation of the AMB rigid rotor system with cascaded phase-shifting notch filters; The system stability condition is set such that the roots of all closed-loop characteristic equations have negative real parts; by taking the partial derivatives of the closed-loop characteristic equations, the trend equations are obtained. The closed-loop characteristic equation of the AMB rigid rotor system with an embedded cascaded phase-shift notch filter is input into the cascaded phase-shift notch filter, and phase shift is performed by the change trend equation. The AMB rigid rotor system is then controlled by the cascaded phase-shift notch filter to obtain the AMB rigid rotor system based on the cascaded phase-shift notch filter.

[0006] Optionally, when establishing the closed-loop characteristic equation of the AMB rigid rotor system, the closed-loop characteristic equation can be established based on a first-order low-pass filter.

[0007] Alternatively, the closed-loop characteristic equation of the AMB rigid rotor system is:

[0008] Where kp is the power amplifier gain; ki is the current stiffness coefficient; ks is the sensor sensitivity gain; m is the rotor mass; kh is the displacement stiffness coefficient; P, I, D are the controller parameters; i is the harmonic order; ωn is the notch filter fundamental frequency; η is the notch filter gain parameter; θ is the compensation phase angle; and ωc is the cutoff frequency of the first-order low-pass filter.

[0009] Optionally, the system stability condition is:

[0010] Where s is the root of the closed-loop characteristic equation; η is the notch filter gain parameter.

[0011] Optionally, the trend equation is:

[0012] Where s is the root of the closed-loop characteristic equation; η is the notch filter gain parameter; kp is the power amplifier gain; ki is the current stiffness coefficient; ks is the sensor sensitivity gain; m is the rotor mass; kh is the displacement stiffness coefficient; P, I, D are the controller parameters; i is the harmonic order; ω is the rotor speed frequency; θ is the compensation phase angle; and ωc is the cutoff frequency of the first-order low-pass filter.

[0013] Secondly, the present invention provides an AMB rigid rotor system based on a notch filter, which is designed using the aforementioned design method for an AMB rigid rotor system based on a notch filter.

[0014] Thirdly, the present invention provides a design system for an AMB rigid rotor system based on a notch filter, comprising: The system setup module is used to embed multiple phase-shift notch filters into the AMB rigid rotor system and cascade them, setting the notch fundamental frequency of the cascaded phase-shift notch filters to the rotor speed frequency. The equation-building module is used to build the closed-loop characteristic equations of the AMB rigid rotor system with cascaded phase-shifting notch filters. The calculation module is used to set the system stability condition as all roots of the closed-loop characteristic equations having negative real parts; and to obtain the trend equation by taking the partial derivatives of the closed-loop characteristic equations. The system setting module is used to input the closed-loop characteristic equation of the AMB rigid rotor system with a cascaded phase-shift notch filter into the cascaded phase-shift notch filter, and to perform phase shifting through the change trend equation. The AMB rigid rotor system is controlled by the cascaded phase-shift notch filter to obtain the AMB rigid rotor system based on the cascaded phase-shift notch filter.

[0015] Fourthly, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method when executing the design computer program for the notch filter-based AMB rigid rotor system.

[0016] Fifthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the design method of the notch filter-based AMB rigid rotor system.

[0017] In a sixth aspect, the present invention provides a computer program product including a computer-readable medium, wherein computer-readable program code is contained on the computer-readable medium, the program code executing the design method of the notch filter-based AMB rigid rotor system.

[0018] Compared with the prior art, the present invention has the following beneficial effects: The phase-shift notch filter used in this invention can simultaneously and effectively compensate for the system's lag phase, and effectively suppress same-frequency and harmonic vibrations caused by rotor imbalance forces and sensor fluctuations. The derived equivalent stiffness and equivalent damping models provide practical guidance for the selection of control parameters for AMBs systems. Compared with classic notch filters, AMBs rigid rotor systems using phase-shift notch filters do not require polarity switching when crossing critical speeds, reducing control difficulty. The control method proposed in this invention demonstrates good control performance in practical AMBs systems, significantly reducing vibration amplitude and harmonic components within a wide speed range of 0-400 Hz, and exhibiting more stable current response.

[0019] In this invention, the signal extraction point of the parallel phase-shift notch filter is placed at the rotor displacement signal, and the signal insertion point is placed at the displacement error signal. After considering the influence of the low-pass filter, this invention achieves higher phase compensation accuracy. By using a combination of a low-pass filter and a cascaded phase-shift notch filter, if the low-pass filter cutoff frequency is set to four times the system input frequency, only three cascaded phase-shift notch filters are needed to achieve multi-frequency suppression, reducing hardware stress. Attached Figure Description

[0020] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way.

[0021] In the attached diagram: Figure 1 This is a diagram of a five-degree-of-freedom AMBs rigid rotor system under unbalanced conditions according to an embodiment of the present invention; Figure 2 These are the controller parameters in the embodiments of the present invention. P right k eq and d eq The influence of the three-dimensional diagram; Figure 3 These are the controller parameters in the embodiments of the present invention. I right k eq and d eq The influence of the three-dimensional diagram; Figure 4 These are the controller parameters in the embodiments of the present invention. D right k eq and d eq The influence of the three-dimensional diagram; Figure 5 This is a block diagram of the automatic balancing strategy control of the AMB rigid rotor system based on cascaded phase-shift notch filters according to an embodiment of the present invention. Figure 6 This is the rotor closed-loop root locus diagram using a first-order low-pass filter in an embodiment of the present invention; Figure 7 These are simulation curves of rotor response under various strategies below the rigid body critical speed according to embodiments of the present invention; Figure 8 This is a frequency domain diagram of the rotor response under various strategies below the rigid body critical speed according to an embodiment of the present invention; Figure 9 These are simulation curves of rotor response under various strategies at speeds above the rigid body critical speed according to embodiments of the present invention. Figure 10 These are frequency domain diagrams of the rotor response under various strategies at speeds above the rigid body critical speed according to embodiments of the present invention. Figure 11 These are simulation curves of the rotor response under various strategies at full speed according to embodiments of the present invention; Figure 12 This is a frequency domain diagram of the rotor response under various strategies at full speed according to an embodiment of the present invention. Detailed Implementation

[0022] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0023] Unless otherwise defined, 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 invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0024] It should be noted that any reference signs placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. This application can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified. The present invention will now be described in detail with reference to the accompanying drawings.

[0025] The present invention provides a design method for an AMB rigid rotor system based on a notch filter, comprising the following steps: Several cascaded phase-shift notch filters are embedded in the AMB rigid rotor system, and the notch fundamental frequency of the cascaded phase-shift notch filters is set to the rotor speed frequency. Establish the closed-loop characteristic equation of the AMB rigid rotor system with cascaded phase-shifting notch filters; The system stability condition is set such that the roots of all closed-loop characteristic equations have negative real parts; by taking the partial derivatives of the closed-loop characteristic equations, the trend equations are obtained. The closed-loop characteristic equation of the AMB rigid rotor system with an embedded cascaded phase-shift notch filter is input into the cascaded phase-shift notch filter, and phase shift is performed by the change trend equation. The AMB rigid rotor system is then controlled by the cascaded phase-shift notch filter to obtain the AMB rigid rotor system based on the cascaded phase-shift notch filter.

[0026] The phase-shift notch filter used in this invention can simultaneously and effectively compensate for the system's lag phase, and effectively suppress same-frequency and harmonic vibrations caused by rotor imbalance forces and sensor fluctuations. The derived equivalent stiffness and equivalent damping models provide practical guidance for the selection of control parameters for AMBs systems. Compared with classic notch filters, AMBs rigid rotor systems using phase-shift notch filters do not require polarity switching when crossing critical speeds, reducing control difficulty. The control method proposed in this invention demonstrates good control performance in practical AMBs systems, significantly reducing vibration amplitude and harmonic components within a wide speed range of 0-400 Hz, and exhibiting more stable current response.

[0027] Example 1 Proportional-Integral-Derivative (PID) control, a classic control method, is widely used in various control systems due to its simple structure, ease of implementation, and convenient parameter tuning. PID obtains precise control actions through accurate proportional-integral-derivative calculations, which are applied to magnetic levitation bearings to achieve stable levitation, thereby optimizing system performance. PID is typically used as the main controller in AMB (Automatic Bragg Bearing) rigid rotor systems to ensure system stability.

[0028] Low-pass filters (LPFs), as a fundamental and crucial signal conditioning unit, are widely integrated into various control systems due to their effective attenuation of high-frequency noise. In AMB (Automatic Signal Processor) systems, LPFs are typically placed in the feedback loop to filter out high-frequency interference such as sensor signals and power amplifier switching noise, thereby improving the purity of the control signal. However, the phase response of a low-pass filter exhibits a monotonically decreasing characteristic, which means that while effectively filtering out high-frequency noise, it introduces a non-negligible phase lag in the mid-to-low frequencies of the system.

[0029] A notch filter (NF) is a band-stop filter with an extremely narrow stopband. Its core function is to deeply attenuate specific frequency components in a signal. Based on this characteristic, it is widely used in vibration control of rotating machinery to eliminate synchronous vibrations caused by rotor imbalance, etc. The main types of notch filters used for vibration suppression in magnetic levitation systems are classic notch filters, generalized notch filters, and phase-shift notch filters.

[0030] Step 1: Analyze the impact of rotor unbalance force and sensor vibration on the system, and establish a model for the five-degree-of-freedom AMBs system under unbalanced conditions.

[0031] Figure 1 This is a five-DOF AMBs rigid rotor system operating in an unbalanced state. When the actual rotor position deviates from the target position, the displacement sensor feeds back the real-time position signal to the controller. The controller calculates a control signal based on a preset algorithm. This signal is amplified by a power amplifier and drives the electromagnetic bearing to generate a corresponding electromagnetic force, thereby correcting the rotor position in real time and ultimately stabilizing it at the target operating point.

[0032] Figure 1 The diagram shows a five-degree-of-freedom active magnetic bearing rigid rotor system model. The system consists of an axial electromagnetic bearing, a displacement sensor, a digital controller, and a power amplifier. The origin is established with the rotor's center of mass as the starting point. XYZ Coordinate system. x a , x b , y a , y b The rotor is located along the two radial magnetic bearings. X , Y Displacement on the axis. z c For the rotor along the axial magnetic bearing Z Displacement along the axis. Center of mass. O The generalized coordinates are as follows q =[ x c , y c , z c , θ x , θ y ] T The displacement vector of the rotor at the electromagnetic bearing is denoted as... q m =[ x a , x b ,y a , y b , z c ] T The displacement vector at the sensor is denoted as q s =[ x sa , x sb , y sa , y sb , z sc ] T .

[0033] Because the relationship between the magnitude of the electromagnetic force and the current and air gap is nonlinear, it is necessary to linearize the electromagnetic force for easier control. The electromagnetic forces in the five degrees of freedom are as follows: Formula 1 In Equation 1, where, F m =[ f xa , f xb , f ya , f yb , f zc ] T This is the electromagnetic force vector. I =[ i xa ,i xb , i ya , i yb , i zc ] T This is the coil current vector. K h =diag[ k hxa , k hxb , k hya , k hyb , k hzc ] is the displacement stiffness coefficient matrix. K i =diag[ k ixa, k ixb , k iya , k iyb , k izc ] is the current stiffness coefficient matrix.

[0034] Due to rotor winding Z Rotation in the axial direction is controlled by an electric motor; therefore, only the rotor's rotation along the axis is considered. X , Y Translational displacement along the Z-axis x c , y c , z c And around X , Y Rotation angle in the axial direction θ x , θ y .

[0035] Formula 2 In Equation 2, l ma , l mb These are the distances from the center of the two radial magnetic bearings to their centroids, respectively.

[0036] Considering the effects of rotor imbalance and acceleration, according to rotor dynamics theory, the equation of motion for a five-degree-of-freedom active magnetic bearing rigid rotor system is: Formula 3 In Equation 3, m For rotor mass, m e This refers to unbalanced mass. J x , J y , J z Rotor winding X , Y , Z Moment of inertia of the shaft. μ z for c Click O The distance between points is Z Projection on the axis ε for c Click O The projection of the point distance onto the central plane containing the centroid. φ The rotation angle of the rotor. ωω is the angular velocity of the rotor.

[0037] Combining Equations 1 and 3, they can be simplified as follows: Formula 4 In Equation 4, M For the quality matrix, G For gyroscope matrices, L f This is the lever arm coefficient matrix. F u It is a generalized unbalanced vector.

[0038] Since the displacement and rotation angle of the rotor's center of mass in each direction cannot be directly obtained, they need to be measured indirectly through displacement sensors. However, there is a certain distance between the displacement sensor and the electromagnetic bearing, so further coordinate transformation is required.

[0039] Formula 5 Formula 6 Combining equations 4 and 5, the dynamic model of the open-loop five-degree-of-freedom AMB rigid rotor system in generalized coordinates can be obtained as follows: Formula 7 make , The state-space expression of the AMB rigid rotor open-loop system is: Formula 8 In Equation 8, E is the identity matrix. .

[0040] Unbalanced mass can cause rotor displacement q m It contains unbalanced vibration signals with the same frequency as the rotational speed. F u In addition, sensor fluctuations will further introduce vibration signals into the system that are multiples of the rotational speed. F s The controller will... F s The signal generates a response and implements control, thereby controlling the current. I The corresponding sensor interference current is generated in the middle. I s Formula 9 In Equation 9, i This represents the harmonic order. K s =[ f sxai , f sxbi , fsyai , f sybi , f szci ] T For the interference of each degree of freedom sensor at an angular frequency of i The magnitude vector of the Fourier decomposition. H θ =[ θ sxai , θ sxbi , θ syai , θ sybi , θ szci ] T Phase vector. C ( iω )and c ( iω ) are the transfer functions of the controller. G C ( s At a frequency of iω The amplitude and phase at that time.

[0041] The dynamic model of the AMB rigid rotor open-loop system considering both co-frequency and harmonic interference is as follows: Formula 10 In Equation 10, This is the total disturbance vector.

[0042] Step 2: Derive the system under PD control k eq and d eq The expression and stability condition are given, and a first-order low-pass filter is introduced to correct the time delay effect.

[0043] A distributed PD controller is used to perform closed-loop control on the AMB open-loop rotor system, and combined with Equation 8, we have: Formula 11 In Equation 11, This is a proportionality coefficient matrix. This is the differential coefficient matrix.

[0044] Combining equations 10 and 12, and neglecting the influence of disturbances, the motion equations of the AMB closed-loop rotor system under PD control in the generalized coordinate system are as follows: Formula 12 Because radial bearings and axial bearings have different structures, their corresponding current stiffness coefficients and displacement stiffness coefficients are also different.

[0045] Let k ixa =k ixb =k iya =k iyb =k i rad k hxa =k hxb =k hya =k hyb =k h rad k izc =k i axi k hzc =k h axi In the actual control of the system, the radial and axial control parameters are independent of each other. Ignoring the coupling between the system's translational and conical modes, let P... xa =P xb =P ya =P yb =P rad D xa =D xb =D ya =D yb =D rad P zc =P axi D zc =D axi If l ma =l mb =l m , l sa =l sb =l s J x =J y =J, Equation 12 can be written as: Formula 13 Consider the control parameters of the radial bearing. Select the damping ratio in the translational mode. ξ 1 tra and natural frequency ω 1 tra ,but P rad and D rad It can be represented as: Formula 14 Ignoring gyroscopic effects, select the damping ratio under the conical mode. ξ 1 con and natural frequencyω 1 con ,but P rad and D rad It can be represented as: Formula 15 Furthermore, the relationship between the damping ratio and the natural frequency in the translational and conical modes is as follows: Formula 16 Consider the control parameters of the axial bearing. Select the damping ratio in the translational mode. ξ 2 tra and natural frequency ω 2 tra ,but P axi and D axi It can be represented as Formula 17 Based on the definitions of stiffness and damping in a second-order linear damped mass-spring system, the equivalent stiffness of the AMB rigid rotor system under PD control can be derived by analogy. k eq With equivalent damping d eq They are respectively: Formula 18 To reduce the steady-state error of rotor vibration, an integral term needs to be introduced. I In addition, because the control loop of the AMB rigid rotor system contains high-frequency noise introduced by the power amplifier, sensors and other components, a first-order low-pass filter needs to be added to improve the system's controllability.

[0046] Formula 19 In Equation 19, k p =1A / V is the power amplifier gain. k s =10V / mm is the sensor sensitivity gain. ω c =2kHz is the cutoff frequency of the low-pass filter.

[0047] make The system is switched to the frequency domain. Formula 20 In Equation 20, .

[0048] The equivalent stiffness and equivalent damping of the AMB rigid rotor system considering the first-order time delay are: Formula 21 The hysteresis phase when a first-order low-pass filter is introduced is: Formula 22 As can be seen from Equation 22, at the cutoff frequency ω c At the input frequency ω = ω c The phase lag is 45°. When ω far below ω c When the phase lag is close to 0°, ω Much higher Figure 2 c At this point, the phase lag is close to 90°. The phase response of a first-order filter is monotonically decreasing, with a maximum lag of no more than 90 degrees.

[0049] Step 3: Analyze the influence of controller parameters on the equivalent stiffness and damping of the AMBs rigid rotor system.

[0050] Equation 21 yields the PID controller parameters in the presence of a first-order low-pass filter. P , I , D Equivalent stiffness of AMB rigid rotor system k eq With equivalent damping d eq The impact.

[0051] 1) Control parameters P right k eq and d eq The impact.

[0052] Figure 2 Display controller parameters P For AMB rigid rotor systems k eq and d eq The impact. ω (a) Display, ω Constant time k eq Follow P Increase and increase, P Constant time ω It increases with increasing frequency. As shown in Equation 21, the low-frequency band... ω Small, ,and Item and The item is also relatively small. D and I rightk eq Small impact P This is the main influencing parameter. When ω Exceed ω c back, The impact surged. Figure 3 It has also become a major influencing parameter. ω (b) Display ω When constant, d eq Follow P It increases and decreases, but the impact is relatively small. d eq Follow ω It increases and decreases because... Xiang Sui Figure 3 It increases as it grows.

[0053] 2) Control parameters I right k eq and d eq The impact.

[0054] Figure 3 Display controller parameters I For AMB rigid rotor systems k eq and d eq The impact of parameters. P and D Set them to 5000 and 10 respectively. ω (a) Display, at constant frequency I right k eq Basically no impact. I When unchanged k eq Follow Figure 3 It increases as it grows. ω (b) shows that at a constant frequency I right d eq Basically no impact. I When unchanged d eq Follow Figure 4 The increase is followed by a period of no change.

[0055] 3) Control parameters D right k eq and d eq The impact.

[0056] Figure 4 Display controller parametersD For AMB rigid rotor systems k eq and d eq The impact of parameters. P and I Set them to 5000 and 200 respectively. ω (a) It can be seen that in the low frequency band D right k eq Basically no impact. Figure 4 After enlargement D The influence is gradually increasing, and in Under the action of the item, k eq Follow D Increase rapidly. (From) ω (b) It can be seen that at any frequency, due to item, d eq Follow D Increase the basic linear growth. D When =2, ω Increase from 0 to 1200, d eq From 779 N·s·m -1 Reduced to 695 N·s·m -1 ,because Xiang Sui θ It increases and therefore increases. D When unchanged d eq It will decrease in the high-frequency range.

[0057] Step 4: Design an automatic balancing strategy for the AMB rigid rotor system based on cascaded phase-shifting notch filters.

[0058] To overcome the limitation of the non-configurable damping angle of classic notch filters, this invention employs a phase-shift notch filter and configures its compensation angle. Unlike classic notch filters, the phase-shift notch filter introduces a compensating phase angle. Figure 5 Its transfer function expression is: Formula 23 Similar to a classic notch filter, the phase-shift notch filter maintains the same filtering effect, but its pole damping angle is... Multiple phase-shifting notch filters are embedded in the AMB rigid rotor system to suppress simultaneous and multi-frequency disturbances, such as... ω As shown.

[0059] The transfer function of the cascaded phase-shift notch filter is: Formula 24 The closed-loop characteristic equation of the AMB rigid rotor system is: Formula 25 In Equation 25, G L ( s ) is the transfer function of the low-pass filter.

[0060] To suppress in-frequency and harmonic disturbances, a cascaded phase-shift notch filter is used. N c ( s The notch filter frequency should be set to the rotor speed frequency, i.e. ω n = jω When a first-order low-pass filter is used, the closed-loop characteristic equation of the system can be written as: Formula 26 when When, the roots of the closed-loop characteristic equation of the system are s =± j2ω , s =± jiω , ..., s =± ω To ensure the stability of the system, the roots of all its closed-loop characteristic equations must have negative real parts. The system stability condition is: Formula 27 Taking the partial derivative of the closed-loop characteristic equation, we obtain the trend of the poles on the imaginary axis when a first-order low-pass filter exists: Formula 28 According to Equation 26, the root locus of the closed-loop transfer function of the system using a first-order low-pass filter in the range of 0~1200Hz is shown in Figure 6, where the settings are as follows: Figure 7 c = 2 kHz. As shown in the figure, when CNF (Cascaded Notch Filter) control is used, the closed-loop transfer function of the rotor system has a right-half-plane pole, which causes the system to become unstable across the entire speed range.

[0061] After further phase compensation based on Equation 28, PSNF (Phase-Shift Notch Filter) control can ensure that all poles of the system are located in the left half-plane, thereby ensuring system stability.

[0062] Example 2 The stability of the AMBs rigid rotor system under automatic balancing strategy control based on cascaded phase-shift notch filters was verified by simulation. Dynamic simulations of the system were performed using MATLAB / Simulink, and the displacement response of the AMBs rigid rotor system under conditions below the rigid body critical speed, above the rigid body critical speed, and full-speed acceleration was investigated to verify the feasibility of the strategy. For ease of description, simulation model A1 represents basic PID control, A2 introduces a low-pass filter on top of A1, and A3 and A4 further introduce CNF and PSNF respectively on top of A2. The rigid body critical speed range is 4200 rpm to 5400 rpm.

[0063] The rotor response simulation curves for each strategy below the rigid body critical speed in this embodiment are as follows: Figure 7 As shown in the figure, the maximum value of the rotor vibration amplitude is marked. (From...) Figure 8 (a) It can be seen that the rotor vibration amplitude is reduced after the introduction of the low-pass filter, but it introduces a phase lag of approximately 30°. Combined with... Figure 8 Analysis of (a) and (b) shows that although the filter suppressed the 6th and 7th harmonic components of the system, the change in rotor displacement amplitude was not significant due to the small proportion of high-frequency components. The subsequently introduced CNF further filtered out the mid- and low-frequency components, causing the amplitude to decrease further; however, its notch filter itself also caused phase hysteresis, leading to an increase in the overall phase delay of the system. In contrast, PSNF effectively offset the hysteresis effect through phase compensation, enhancing the tracking filtering performance of the notch filter feedback, thereby further suppressing the rotor vibration amplitude.

[0064] Figure 8 This is the frequency domain plot of the rotor displacement response. (Comparison) Figure 9 As shown in (c) and (d), PSNF is more effective than CNF in suppressing low-frequency disturbance components in rotor displacement. Specifically, the second harmonic component decreases from 0.419 μm to 0.377 μm, a reduction of 10%, and the third harmonic component decreases from 0.279 μm to 0.233 μm, a reduction of 16.4%. In addition, the high-frequency components of the system are also reduced compared to A1.

[0065] The rotor response simulation curves for each strategy above the rigid body critical speed in this embodiment are as follows: Figure 9 As shown. By Figure 10 (b) It can be seen that the introduction of a low-pass filter also introduces a phase lag of nearly 30 degrees. This is because the phase lag of a first-order low-pass filter depends only on the ratio of the input frequency to the cutoff frequency, which can also be verified according to Equation 22. Compared to CNF, the rotor displacement amplitude decreased from 1.85 μm to 1.65 μm after using PSNF, a reduction of 10.8%. Similarly, FFT analysis of the rotor displacement response yielded the following results: Figure 11As shown, compared to strategy A2, strategy A4 significantly improves harmonic suppression in the high-frequency band. Compared to A3, PSNF effectively overcomes the phase lag problem through phase compensation, achieving a significant reduction in rotor vibration amplitude. Specifically, the synchronization component decreased from 0.861 μm to 0.689 μm, a reduction of 20%.

[0066] The rotor response simulation curves under various strategies at full speed in this embodiment are as follows: Figure 11 As shown. By Figure 11 (a) As can be seen, after introducing the notch filter, the system can gradually filter out the harmonic overtone components, thus gradually reducing the vibration across the entire speed range, with a particularly significant amplitude reduction in the critical speed region. Specifically, in the 200-400 Hz acceleration range, the PSNF reduces the steady-state amplitude of the vibration from 2.13 μm under CNF to 1.52 μm, a reduction of 28.6%. Furthermore, from... Figure 12 (b) It can be observed that PSNF can effectively compensate for the phase lag introduced by the first-order low-pass filter during the acceleration process.

[0067] Figure 12 This demonstrates the suppression effects of different control strategies on harmonic components of the rotor system. From Figure 12 (a) It can be seen that after adding a first-order low-pass filter, the higher harmonics of the system are effectively filtered out, while the first three harmonics are basically not suppressed. Taking the first harmonic as an example, its amplitude is still 1.981 μm. Figure 12 (b) shows that after introducing CNF on the basis of A2, the first three harmonics of the rotor are rapidly suppressed, with the first harmonic decreasing from 1.787 μm to 1.166 μm and the second harmonic decreasing from 0.997 μm to 0.424 μm. Further by... Figure 1 (c) It can be seen that the control effect of PSNF is better than that of CNF, and it can further filter out residual harmonics. Its first harmonic amplitude is reduced from 1.166 μm to 1.020 μm, a reduction of 12.5%.

[0068] Example 3 This embodiment of the AMB rigid rotor system based on a notch filter is designed using the design method of the AMB rigid rotor system based on a notch filter in Embodiment 1.

[0069] Example 4 Based on the design method of the AMB rigid rotor system based on notch filter in Embodiment 1, a design system for the AMB rigid rotor system based on notch filter is disclosed, including: The system setup module is used to embed multiple phase-shift notch filters into the AMB rigid rotor system and cascade them, setting the notch fundamental frequency of the cascaded phase-shift notch filters to the rotor speed frequency. The equation-building module is used to build the closed-loop characteristic equations of the AMB rigid rotor system with cascaded phase-shifting notch filters. The calculation module is used to set the system stability condition as all roots of the closed-loop characteristic equations having negative real parts; and to obtain the trend equation by taking the partial derivatives of the closed-loop characteristic equations. The system setting module is used to input the closed-loop characteristic equation of the AMB rigid rotor system with a cascaded phase-shift notch filter into the cascaded phase-shift notch filter, and to perform phase shifting through the change trend equation. The AMB rigid rotor system is controlled by the cascaded phase-shift notch filter to obtain the AMB rigid rotor system based on the cascaded phase-shift notch filter.

[0070] Example 5 The purpose of this embodiment is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the design method of the notch filter-based AMB rigid rotor system.

[0071] Example 6 The purpose of this embodiment is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the design method of the AMB rigid rotor system based on a notch filter.

[0072] Example 7 The purpose of this embodiment is to provide a computer program product including a computer-readable medium, wherein the computer-readable medium contains computer-readable program code that executes the design method of the notch filter-based AMB rigid rotor system.

[0073] The steps and methods involved in the apparatuses of the above embodiments 4, 5, 6 and 7 correspond to those in embodiment 1. For specific implementation details, please refer to the relevant description section of embodiment 1.

[0074] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes. These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes ​ The steps of the function specified in one or more boxes.

[0075] Unless otherwise specified, the working methods or control methods involved in the above embodiments are conventional working methods or control methods in the art.

[0076] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application. Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention, as long as they do not depart from the spirit and scope of the technical solutions of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A design method for an AMB rigid rotor system based on a notch filter, characterized in that, Includes the following steps: Multiple phase-shift notch filters are embedded in the AMB rigid rotor system and cascaded, with the notch fundamental frequency of the cascaded phase-shift notch filters set to the rotor speed frequency. Establish the closed-loop characteristic equation of the AMB rigid rotor system with cascaded phase-shifting notch filters; The system stability condition is set such that the roots of all closed-loop characteristic equations have negative real parts; by taking the partial derivatives of the closed-loop characteristic equations, the trend equations are obtained. The closed-loop characteristic equation of the AMB rigid rotor system with an embedded cascaded phase-shift notch filter is input into the cascaded phase-shift notch filter, and phase shift is performed by the change trend equation. The AMB rigid rotor system is then controlled by the cascaded phase-shift notch filter to obtain the AMB rigid rotor system based on the cascaded phase-shift notch filter.

2. The design method of an AMB rigid rotor system based on a notch filter according to claim 1, characterized in that, When establishing the closed-loop characteristic equation of the AMB rigid rotor system, the closed-loop characteristic equation is established based on a first-order low-pass filter.

3. The design method of an AMB rigid rotor system based on a notch filter according to claim 2, characterized in that, The closed-loop characteristic equation of the AMB rigid rotor system is: Where kp is the power amplifier gain; ki is the current stiffness coefficient; ks is the sensor sensitivity gain; m is the rotor mass; kh is the displacement stiffness coefficient; P, I, D are the controller parameters; i is the harmonic order; ωn is the notch filter fundamental frequency; η is the notch filter gain parameter; θ is the compensation phase angle; and ωc is the cutoff frequency of the first-order low-pass filter.

4. The design method of an AMB rigid rotor system based on a notch filter according to claim 1, characterized in that, The system stability condition is Where s is the root of the closed-loop characteristic equation; η is the notch filter gain parameter.

5. The design method of an AMB rigid rotor system based on a notch filter according to claim 1, characterized in that, The trend equation is Where s is the root of the closed-loop characteristic equation; η is the notch filter gain parameter; kp is the power amplifier gain; ki is the current stiffness coefficient; ks is the sensor sensitivity gain; m is the rotor mass; kh is the displacement stiffness coefficient; P, I, D are the controller parameters; i is the harmonic order; ω is the rotor speed frequency; θ is the compensation phase angle; and ωc is the cutoff frequency of the first-order low-pass filter.

6. An AMB rigid rotor system based on a notch filter, characterized in that, The design method of the AMB rigid rotor system based on notch filter as described in any one of claims 1 to 5 is adopted.

7. A design system for an AMB rigid rotor system based on a notch filter, characterized in that, include: The system setup module is used to embed multiple phase-shift notch filters into the AMB rigid rotor system and cascade them, setting the notch fundamental frequency of the cascaded phase-shift notch filters to the rotor speed frequency. The equation-building module is used to build the closed-loop characteristic equations of the AMB rigid rotor system with cascaded phase-shifting notch filters. The calculation module is used to set the system stability condition as all roots of the closed-loop characteristic equations having negative real parts; and to obtain the trend equation by taking the partial derivatives of the closed-loop characteristic equations. The system setting module is used to input the closed-loop characteristic equation of the AMB rigid rotor system with a cascaded phase-shift notch filter into the cascaded phase-shift notch filter, and to perform phase shifting through the change trend equation. The AMB rigid rotor system is controlled by the cascaded phase-shift notch filter to obtain the AMB rigid rotor system based on the cascaded phase-shift notch filter.

8. An electronic device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the design method of the AMB rigid rotor system based on a notch filter as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the design method of the AMB rigid rotor system based on a notch filter as described in any one of claims 1-6.

10. A computer program product comprising a computer-readable medium, characterized in that, The computer-readable medium contains computer-readable program code that performs the design method of the notch filter-based AMB rigid rotor system according to any one of claims 1-6.

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