Magnetic bearing-rotor system moving base interference suppression method and system

Abstract

The invention discloses a magnetic bearing-rotor system moving base interference suppression method and system. The method comprises the following steps: establishing a magnetic bearing-rotor system rotation equivalent kinetic model; establishing a magnetic bearing-rotor system dynamic model containing base interference; based on the magnetic bearing-rotor system rotation equivalent dynamical model and the magnetic bearing-rotor system dynamical model containing base interference, obtaining a magnetic bearing-rotor system rotation dynamical model containing interference terms; obtaining an extended state observer based on a magnetic bearing-rotor system rotation dynamic model containing interference terms; obtaining an extended state observer based on model reference adaptive compensation through the extended state observer and the model reference adaptive compensator; and interference suppression on the moving base of the magnetic bearing-rotor system is completed through an expansion state observer based on model reference adaptive compensation. The anti-interference performance of the system is improved, and the influence of the interference of the movable base on the system is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of magnetic bearing-rotor systems, and particularly relates to a method and system for suppressing dynamic base interference of a magnetic bearing-rotor system. Background Art

[0002] Ultra-agile maneuvering satellites represented by space radiation measurement reference satellites must have the ability to track the attitude of space moving targets in order to quickly track target satellites. In such satellite platforms, a control moment gyro group composed of multiple magnetic levitation control moment gyros is often used to meet the requirements of large-angle ultra-agile maneuvers of the satellites. When the ultra-agile satellite platform performs an attitude maneuver task, the attitude angular velocity of the satellite often needs to be adjusted in real time according to the position of the aerospace target satellite. The magnetic levitation control moment gyro base is fixedly connected to the platform cabin, and the magnetic bearing-rotor system will be affected by the attitude rotation of the platform cabin. In this case, the magnetic bearing-rotor system of the magnetic levitation control moment gyro is not only affected by the dynamic frame interference, but also affected by the interference transmitted from the satellite platform rotation to the base, and this interference is called the dynamic base interference of the magnetic bearing-rotor system.

[0003] Both the dynamic frame effect and the dynamic base interference of the magnetic bearing-rotor system will bring strong torque interference to the system, causing the rotor suspension position to deviate seriously, and even hitting the protection bearing, affecting the stability of the control system and reducing the service life of the magnetic levitation control moment gyro. The difference is that the amplitude and frequency of the dynamic frame torque interference are often higher than those of the dynamic base interference, and the impact on the magnetic bearing is also greater, but the interference information can be obtained through the frame servo system. However, the dynamic base interference has a complex transmission path and the interference information is not easy to obtain, and the interference information can only be estimated through the state variables of the control system. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention proposes a method and system for suppressing dynamic base interference of a magnetic bearing-rotor system. It is intended to establish a dynamic model of the magnetic bearing-rotor system under dynamic base interference, and propose a dynamic base interference compensation method based on the combination of an extended state observer and an adaptive compensator to improve the anti-interference performance of the system and reduce the impact of dynamic base interference on the system.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for suppressing dynamic base interference of a magnetic bearing-rotor system includes the following steps:

[0007] Establish a rotational equivalent dynamic model of the magnetic bearing-rotor system;

[0008] Establish a dynamic model of the magnetic bearing-rotor system containing base interference;

[0009] Based on the rotational equivalent dynamic model of the magnetic bearing-rotor system and the dynamic model of the magnetic bearing-rotor system with base disturbance, the rotational dynamic model of the magnetic bearing-rotor system with disturbance terms is obtained;

[0010] Based on the rotational dynamic model of the magnetic bearing-rotor system with disturbance terms, an extended state observer is obtained;

[0011] Through the extended state observer and the model reference adaptive compensator, an extended state observer based on model reference adaptive compensation is obtained;

[0012] Through the extended state observer based on model reference adaptive compensation, the suppression of the dynamic base disturbance of the magnetic bearing-rotor system is completed.

[0013] Preferably, the extended state observer includes: an extended state observer without model parameters and an extended state observer based on model parameters.

[0014] Preferably, the operation method of the extended state observer based on model parameters includes:

[0015]

[0016] Among them, J is the moment of inertia of the rotor in the radial direction, k i is the force-current stiffness coefficient of the magnetic bearing, k h is the force-displacement stiffness coefficient of the magnetic bearing, l m is the distance from the center of mass of the rotor to the center of the drive coil, l s is the distance from the center of mass of the rotor to the center of the sensor, R is the resistance of the drive coil, L is the inductance of the drive coil, and M d is the observer estimator, α is the observer input, I α is the control current of the α channel, and E1 to E3 are the values of the observer gain matrix.

[0017] Preferably, the adaptive tracking rate and the compensation control voltage differential compensation method in the self-adaptive compensation link include:

[0018]

[0019] Among them, δ kc is a small constant used to prevent the denominator from being zero, γ eso is the ESO model reference adaptive compensation coefficient, e d is the compensation error, k c_eso is the model reference adaptive tracking rate, u eso is the control voltage, and M d is the disturbance observation estimator.

[0020] The present invention also provides a dynamic base disturbance suppression system for a magnetic bearing-rotor system, including: a first construction module, a second construction module, a third construction module, a fourth construction module, a fifth construction module, and a suppression module. The first construction module is used to establish a rotational equivalent dynamic model of the magnetic bearing-rotor system;

[0021] The second construction module is used to establish a dynamic model of the magnetic bearing-rotor system containing base disturbance;

[0022] The third construction module is used to obtain a rotational dynamic model of the magnetic bearing-rotor system containing disturbance terms based on the rotational equivalent dynamic model of the magnetic bearing-rotor system and the dynamic model of the magnetic bearing-rotor system containing base disturbance;

[0023] The fourth construction module is used to obtain an extended state observer based on the rotational dynamic model of the magnetic bearing-rotor system containing disturbance terms;

[0024] The fifth construction module is used to obtain an extended state observer based on model reference adaptive compensation through the extended state observer and the model reference adaptive compensator;

[0025] The suppression module is used to complete the suppression of the dynamic base disturbance of the magnetic bearing-rotor system through the extended state observer based on model reference adaptive compensation.

[0026] Preferably, the extended state observer includes: an extended state observer without model parameters and an extended state observer based on model parameters.

[0027] Preferably, the operation process of the extended state observer based on model parameters includes:

[0028]

[0029] Among them, J is the moment of inertia of the rotor in the radial direction, k i is the force-current stiffness coefficient of the magnetic bearing, k h is the force-displacement stiffness coefficient of the magnetic bearing, l m is the distance from the center of mass of the rotor to the center of the drive coil, l s is the distance from the center of mass of the rotor to the center of the sensor, R is the resistance of the drive coil, L is the inductance of the drive coil, and M d is the observer estimator, α is the observer input, I α is the control current of the α channel, and E1 to E3 are the values of the observer gain matrix.

[0030] Preferably, the adaptive tracking rate and the compensation control voltage differential compensation process in the self-adaptive compensation link include:

[0031]

[0032] Among them, δ kc is a small constant used to prevent the denominator from being zero, and γ eso is the ESO model reference adaptive compensation coefficient, e d is the compensation error, k c_eso is the model reference adaptive tracking rate, u eso is the control voltage, and M d is the disturbance observation estimator.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] Aiming at the serious deviation problem of the magnetic bearing-rotor suspension position caused by the dynamic base interference of the magnetic suspension control moment gyro under the super-agile maneuvering satellite platform, the present invention analyzes the transmission path of the dynamic base interference, establishes the dynamic model of the magnetic bearing-rotor system under the dynamic base interference, discusses the influence of two types of extended state observers with and without model parameters on the system, optimizes the model reference adaptive compensation algorithm based on the extended state observer, designs an interference compensation method combining an extended state observer and an adaptive compensator, and finally conducts an experiment on suppressing the dynamic base interference on the magnetic suspension control moment gyro experimental platform to verify the effectiveness of the algorithm. The present invention improves the anti-interference performance of the system and reduces the influence of the dynamic base interference on the system. Description of the Drawings

[0035] In order to more clearly illustrate the technical solutions of the present invention, the following briefly introduces the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0036] Figure 1 is a schematic flow chart of the method for suppressing the dynamic base interference of the magnetic bearing-rotor system according to the embodiment of the present invention;

[0037] Figure 2 is a schematic diagram of the coordinate system definition of the magnetic suspension control moment gyro under the rotation of the base according to the embodiment of the present invention;

[0038] Figure 3 is a schematic diagram of the high-speed rotor system rotating around the Xp axis according to the embodiment of the present invention;

[0039] Figure 4 is a schematic diagram of the high-speed rotor system rotating around the Yox axis according to the embodiment of the present invention;

[0040] Figure 5 is a schematic diagram of the high-speed rotor system rotating around the Zoy axis according to the embodiment of the present invention;

[0041] Figure 6 It is the rotational equivalent structure block diagram of the magnetic bearing-rotor system containing a model-free parameter Extended State Observer (ESO) in the embodiment of the present invention;

[0042] Figure 7 It is the block diagram of the magnetic bearing rotation system under a single degree of freedom with a model-free parameter ESO in the embodiment of the present invention;

[0043] Figure 8 It is the signal flow diagram of the magnetic bearing rotation system under a single degree of freedom with a model-free parameter ESO in the embodiment of the present invention;

[0044] Figure 9 It is the block diagram of the rotational equivalent system of the magnetic bearing-rotor based on a model parameter ESO in the embodiment of the present invention;

[0045] Figure 10 It is the schematic diagram of the pole region configuration of the Extended State Observer in the embodiment of the present invention;

[0046] Figure 11 It is the variation diagram of the current stiffness coefficient with displacement and current in the embodiment of the present invention;

[0047] Figure 12 It is the schematic diagram of the pole configuration result in the region of the Extended State Observer in the embodiment of the present invention;

[0048] Figure 13 It is the schematic diagram of the performance simulation of the disturbance observer in the embodiment of the present invention;

[0049] Figure 14 It is the schematic diagram of the change of the adaptive compensation coefficient at different χ values in the embodiment of the present invention;

[0050] Figure 15 It is the schematic diagram of the displacement change trend at different χ values in the embodiment of the present invention;

[0051] Figure 16 It is the rotor displacement signal diagram after no compensation, model-based ESO compensation, and ESOMRAC compensation in the embodiment of the present invention. Detailed implementation manners

[0052] 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. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0053] To make the above objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Embodiment 1

[0055] As Figure 1 shown, the present invention provides a method for suppressing the dynamic base disturbance of a magnetic bearing-rotor system, including the following steps:

[0056] Establish a rotational equivalent dynamic model of the magnetic bearing-rotor system;

[0057] Establish a dynamic model of the magnetic bearing-rotor system containing base disturbance;

[0058] Based on the rotational equivalent dynamic model of the magnetic bearing-rotor system and the dynamic model of the magnetic bearing-rotor system containing base disturbance, obtain a rotational dynamic model of the magnetic bearing-rotor system containing disturbance terms;

[0059] Based on the rotational dynamic model of the magnetic bearing-rotor system containing disturbance terms, obtain an extended state observer;

[0060] Through the extended state observer and the model reference adaptive compensator, obtain an extended state observer based on model reference adaptive compensation;

[0061] Through the extended state observer based on model reference adaptive compensation, complete the suppression of the dynamic base disturbance of the magnetic bearing-rotor system.

[0062] In this embodiment, the method for obtaining the rotational equivalent dynamic model of the magnetic bearing-rotor system includes:

[0063] In the super-agile maneuvering condition, the dynamic base disturbance of the magnetic suspension control moment gyro is mainly transmitted to the magnetic bearing-rotor system in the form of rotation. The radial magnetic bearing can control both the radial translation and the radial rotation of the rotor. To more intuitively analyze the dynamic base disturbance transmission characteristics, a rotational equivalent dynamic model of the system can be established based on the dynamic formula of the magnetic bearing-rotor system, and the dynamic base disturbance characteristics can be analyzed with this, and a dynamic base disturbance observation-compensation control method can be designed.

[0064] In the open-loop magnetic bearing-rotor system, the four displacement signals in the sensor coordinate system at both ends are described by (x as , x bs , y as , y bs ). The rotor displacement in the stator coordinate system is described by (x, y, α, β). The displacement stiffness forces received by the four radial degrees of freedom of the rotor in the sensor coordinate system are:

[0065]

[0066] The relationship between the stator coordinate system (x, y, α, β) and the sensor coordinate system (x as , x bs , y as , y bs ) is as follows:

[0067]

[0068] The dynamic formula of the rotating magnetic bearing rotor is:

[0069]

[0070] The transfer function of the power amplifier link of the magnetic bearing-rotor system is:

[0071]

[0072] The control current of the magnetic bearing-rotor system is:

[0073]

[0074] Let Simplify the controller K to G c , then the radial translational controller is transformed into the closed-loop dynamic model of the equivalent magnetic bearing-rotor system under radial rotation as:

[0075]

[0076] The two-degree-of-freedom rotational equivalent dynamic model in (6) can be modeled and abbreviated as:

[0077]

[0078] The magnetic bearing-rotor dynamic model shown in Equation (7) can lay a foundation for analyzing the influence of dynamic base interference on the magnetic bearing-rotor system.

[0079] In this embodiment, the method for obtaining the dynamic model of the magnetic bearing-rotor system containing base interference includes:

[0080] In order to further analyze the characteristics of dynamic base interference, it is necessary to establish a magnetic bearing-rotor dynamic equation containing rotational interference. To describe the rotation of the magnetic suspension control moment gyro on the satellite platform, as Figure 2 shown, an absolute space coordinate system, a virtual outer frame X coordinate system, a virtual outer frame Y coordinate system, and a virtual outer frame Z coordinate system can be established.

[0081] (1) The absolute space coordinate system OoXoYoZo, which is used to describe the relative motion of the base of the magnetic suspension control moment gyro in space and is a stationary reference system

[0082] (2) Inner frame coordinate system P coordinate system OpXpYpZp, a coordinate system used to describe the relationship between the three-degree-of-freedom rotational angular velocity of the magnetic suspension control moment gyro base and the magnetic bearing-rotor dynamic equation.

[0083] (3) Virtual outer frame X coordinate system OoxXoxYoxZox, which only rotates around the Xp axis of the inner frame coordinate system P in space, and the rotational angular velocity can be expressed as

[0084] (4) Virtual outer frame Y coordinate system OoyXoyYoyZoy, which only rotates around the Yox axis of the virtual outer frame X coordinate system in space, and the rotational angular velocity can be expressed as

[0085] (5) Virtual outer frame Z coordinate system OozXozYozZoz, which only rotates around the Zoy axis of the virtual outer frame Y coordinate system in space, and the rotational angular velocity can be expressed as

[0086] As Figure 2 shown, in the initial state, the origin (Oo, Ooz, Ooy, and Oox) and the X-axis (Xo, Xoz, Xoy, and Xox), Y-axis (Yo, Yoz, Yoy, and Yox), and Z-axis (Zo, Zoz, Zoy, and Zox) of the absolute space coordinate, virtual outer frame Z coordinate system, virtual outer frame Y coordinate system, and virtual outer frame X coordinate system are consistent with the origin Op and the Xp, Yp, and Zp axes of the inner frame coordinate system P.

[0087] The relative motion angular velocity of the virtual outer frame X coordinate system rotating around the Xp axis of the inner frame P coordinate system is:

[0088]

[0089] The relative motion angular velocity of the virtual outer frame Y coordinate system rotating around the Yox axis of the virtual outer frame X coordinate system is:

[0090]

[0091] The relative motion angular velocity of the virtual outer frame Z coordinate system rotating around the Zoy axis of the virtual outer frame Y coordinate system is:

[0092]

[0093] The angular velocity of rotation around the Xp axis projected into the inner frame coordinate system P is:

[0094]

[0095] The angular velocity of rotation around the Yox axis projected into the inner frame coordinate system P is:

[0096]

[0097] The angular velocity of rotation about the Zoy axis projected onto the inner frame coordinate system P is as follows:

[0098]

[0099] As Figure 3 、 Figure 4 、 Figure 5 shown, the motions of the three rotational degrees of freedom in the inner frame coordinate system P are:

[0100]

[0101] In the stator coordinate system, the rotational motion of the rotor can be described as:

[0102]

[0103] Since there is no relative motion between the stator coordinate system and the inner frame coordinate system, and the Z axes of the stator coordinate system and the inner frame coordinate system are the same, and there is only a 45° angular relationship, according to Euler's formula, the relationship between the two coordinate systems is:

[0104]

[0105] Wherein,

[0106] Then there is:

[0107]

[0108] Wherein,

[0109]

[0110] Then the dynamic equation of the magnetic bearing-rotor system with pedestal interference in the magnetic bearing stator coordinate system is:

[0111]

[0112] According to Equation (18), the three-degree-of-freedom rotation of the pedestal is transmitted to the magnetic bearing-rotor system in the form of torque interference. Although it is similar to the frame servo interference in the manifestation of rotor dynamics, this interference is a combination of three-degree-of-freedom rotational motions and has a large randomness and cannot be directly compensated. Therefore, the characteristics of this interference should be fully considered when designing the compensator.

[0113] In this embodiment, the method for obtaining the rotational dynamic model of the magnetic bearing-rotor system containing the interference term includes:

[0114] After substituting Equation (18) into Equation (7), the rotational dynamics model of the magnetic bearing-rotor system with interference terms can be obtained as follows:

[0115]

[0116] Among them, is the angular velocity of the moving base.

[0117] Equation (19) can be adjusted to:

[0118]

[0119] It can be seen from Equation (20) that the disturbance torque of the moving base of the magnetic bearing-rotor system has the characteristics of low frequency and unknown. To achieve precise compensation for the disturbance of the moving base, it is necessary to design a suitable observer according to the measurable state of the magnetic bearing-rotor system to observe the disturbance of the moving base. The extended state observer has the characteristics of precise estimation of low-frequency disturbances, simple design and small computational load, and is an ideal observer for the disturbance of the moving base of the magnetic bearing-rotor system.

[0120] Ignoring the closed-loop controller term, further arranging Equation (20) gives:

[0121]

[0122] The above rotational dynamics equation of the magnetic bearing-rotor system base is established under the condition that the frame servo system does not rotate, that is, the magnetic levitation control moment gyro in model (18) does not actively output torque.

[0123] When the frame outputs torque, the dynamics model of the magnetic bearing-rotor system containing the moving frame disturbance and the moving base disturbance is:

[0124]

[0125] It should be noted that when describing the movement of the base, a virtual outer frame Y coordinate system is established. This coordinate system coincides with the frame coordinate system at the initial position, and the relative movement of the frame servo system driving the gyro housing is consistent with the relative rotation of the gyro housing around the Yo axis.

[0126] In this embodiment, the extended state observer includes: an extended state observer without model parameters and an extended state observer based on model parameters.

[0127] Furthermore, regarding the design and analysis of the extended state observer without model parameters: In the control system (21), the coupling term is used as the internal disturbance term of the system. After being decoupled and suppressed by the robust feedback linearization controller, its influence can be ignored. Therefore, the system can be approximated as:

[0128]

[0129] The same model-free extended state observer (model-free ESO) is designed for both the α channel and the β channel of the magnetic bearing. Taking the α channel as an example, the model-free ESO observation state is selected as α, M iα , then the model-free parameter ESO of the α channel is:

[0130]

[0131] Among them, the system input of the observer is [αM iα ] T .

[0132] After adding the model-free parameter ESO to the magnetic bearing-rotor rotation system, the system equivalent structure block diagram is as follows: Figure 6 shown.

[0133] Figure 6 The input quantity of the system is:

[0134]

[0135] According to formula (7), we can know that:

[0136]

[0137] The rotation compensation of the two degrees of freedom can be designed as:

[0138]

[0139] The transfer function of the compensation link is:

[0140]

[0141] Since the α and β channels of the magnetic bearing-rotor system are similar, in order to analyze the influence of the model-free parameter ESO on the magnetic bearing-rotor system, the α rotation channel will be taken as an example for research. M iα Substituting x1, x2, and x3, and performing Laplace transform on Equation (24), we can obtain:

[0142]

[0143] According to formula (29), the input-output equation of ESO without model parameters is established:

[0144]

[0145] make The control system can be simplified as follows Figure 7 The system structure diagram shown in Figure 1 is as follows. dxIt is the disturbance torque caused by the movement of the outer base.

[0146] To analyze the transfer function of the system, the Figure 7 structural block diagram shown can be represented as an equivalent system signal flow diagram as Figure 8 shown.

[0147] According to Figure 8 the system signal flow diagram, the transfer function of the system can be obtained as:

[0148]

[0149] After simplifying Equation (31), it can be obtained that:

[0150]

[0151] Analyzing (32), it can be seen that G old is the control transfer function in the original system, and G new is the additional control system transfer function after introducing the model-free parameter ESO. Therefore, the stability of G eso is mainly determined by the stability of the new generalized controller G new link of the system.

[0152]

[0153] In Equation (33), the position of the system poles in the denominator determines the stability of the system. Observing (33), it can be seen that the new generalized controller G new of the system is composed of the denominator of the power amplifier link and the denominator of the observer link. The denominator of the power amplifier link is stable by itself. Therefore, only by ensuring the stability of the denominator of the observer can the stability of G eso be ensured.

[0154] For the stability analysis of the denominator link (s 3 + E1s 2 + E2s + 2E3) of the third-order observer, according to the Routh criterion, the condition for the stability of the G eso (s) system is that E1E2 > 2E4. The displacement negative stiffness instability factor existing in the system is solved by the differential control link in the radial controller.

[0155] Furthermore, regarding the design and analysis of the extended state observer based on model parameters: According to Equation (23), it can be known that when designing the observer, the α channel and the β channel can be designed and analyzed separately. Taking the α channel as an example, let I α = [i by - i ay , and the ESO can be designed as:

[0156]

[0157] where J is the moment of inertia of the rotor in the radial direction, k i is the force-current stiffness coefficient of the magnetic bearing, k h is the force-displacement stiffness coefficient of the magnetic bearing, l m is the distance from the center of mass of the rotor to the center of the drive coil, l s is the distance from the center of mass of the rotor to the center of the sensor, R is the resistance of the drive coil, and L is the inductance of the drive coil, and M d is the observer estimator, α is the observer input, I α is the control current of the α channel, and E1 to E3 are the observer gain matrix values.

[0158] Denote the observer state by and α by y1. Taking the Laplace transform of Equation (34) gives:

[0159]

[0160] According to Equation (35), the observer output can be simplified to:

[0161]

[0162] From Equation (36), it can be seen that the transfer function of the observer output based on the model parameters can be divided into two parts, G1(s) and G2(s), which are the influence links of the rotor displacement y1 and the control current I α respectively.

[0163] To further analyze the influence of the ESO based on the model parameters on the magnetic bearing-rotor control system, the single-degree-of-freedom rotational model of the magnetic bearing-rotor system containing the ESO based on the model parameters is expressed as the magnetic bearing-rotor rotational equivalent system block diagram shown in Figure 9 Figure.

[0164] Calculating the transfer function of the shaded part in the figure shows that:

[0165]

[0166] From Equation (37), it can be seen that the main influence of the observer on the magnetic bearing-rotor system is:

[0167]

[0168] Substituting G1(s) and G2(s) in Equation (36) into Equation (37) gives:

[0169]

[0170] As can be seen from Equation (39), after the observer based on model parameters is introduced into the system, the controlled object remains unchanged, which is also conducive to the stability analysis after adding other algorithms. However, the configuration of the observer after introducing the model will also become a new difficulty in the design of such an observer. Therefore, the present invention adopts the method of regional pole placement to configure the closed-loop observer matrix [A r -E r C r in Equation (34).

[0171] In the present invention, the desired closed-loop pole region of the observer is jointly determined by the region D1 surrounded by the straight line α in the left half plane e and the region D2 surrounded by the lines a, b and the included angle θ e , as shown in Figure 10 .

[0172] The description equation of region D1 is:

[0173]

[0174] The description equation of region D2 is:

[0175]

[0176] Figure 10 As shown, the observer pole positions can be configured through Equations (40) and (41) and obtained by calculation using LMItools in MATLAB. In addition, the compensating link of the observer without model parameters is the same as the compensating link of Equation (28) designed for the observer based on model parameters.

[0177] By observing the observer without model parameters and the observer based on model parameters, it can be seen that the introduction of the observer without model parameters will destroy the transfer function of the controlled object, but will not affect the stability of the system. On the contrary, the introduction of the observer based on model parameters will not only have no impact on the controlled model of the control system, but also will not destroy the stability of the original system. However, considering the characteristics that the observer based on model parameters is easy to combine with other algorithms, the present invention finally selects the extended state observer based on model parameters as the moving base disturbance observer of the present invention. For the sake of convenient description, after selecting the extended state observer based on model parameters as the main observer studied in the present invention, unless otherwise specified in the following text, all extended state observers represent the extended state observer based on model parameters.

[0178] In this embodiment, the design and analysis of the model reference adaptive compensator: The present invention designs the direct compensating link shown in Equation (28), but there is an easily perturbed current stiffness coefficient in the denominator of this link. Therefore, the current stiffness accuracy will directly affect the accuracy of disturbance compensation. The change trend diagram of the system current stiffness coefficient k i is as shown in Figure 11 .

[0179] Depend on Figure 11 It can be seen that the current stiffness k i There is a serious perturbation problem, and the accuracy of the direct compensation model shown in Equation (28) is difficult to guarantee. To address the low accuracy of dynamic base disturbance compensation caused by current stiffness coefficient perturbations, the ESO can be combined with a model reference adaptive compensator (MRAC) to suppress it. This extended state observer based on model reference adaptive compensation can be abbreviated as ESOMRAC. The ESO is responsible for observing the disturbance torque, and the MRAC compensates based on the disturbance torque.

[0180] After the observer observes the interference, since the compensation link needs to calculate the inverse function of the power amplifier link (28), the compensation process involves pure differential calculation, and the compensation noise is too large. A low-pass link can be added in engineering to improve the compensation accuracy of the system. In order to make the stability of the adaptive algorithm independent of the input signal amplitude correlation, the adaptive tracking rate is normalized to obtain:

[0181]

[0182] Among them, δ kc is a smaller constant used to prevent the denominator from being 0, γ eso is the ESO model reference adaptive compensation coefficient, e d Compensation error, k c Adaptive tracking rate.

[0183] In order to avoid computational saturation, a limiting link needs to be introduced, and equation (42) becomes:

[0184]

[0185] Where, χ is the peak value of the limiting link,

[0186] The adaptive tracking rate in the adaptive compensation link is and compensation control voltage differential for:

[0187]

[0188] Model reference adaptive tracking rate k c_eso And control voltage u eso The recursive formula is:

[0189]

[0190] Among them, δ kc is a smaller constant used to prevent the denominator from being 0, γ eso is the ESO model reference adaptive compensation coefficient, ed To compensate for the error, k c_eso is the model reference adaptive tracking rate, and u eso is the control voltage, and M d is the disturbance observation estimator.

[0191] In the time domain, the control system can be expressed as:

[0192]

[0193] The characteristic equation of the above system is:

[0194]

[0195] Then the main condition for the system to be stable is That is:

[0196]

[0197] At this time, after adding the compensation link, the stability of the system will no longer be affected by the disturbance input and is only related to the inherent parameters of the magnetic bearing-rotor closed-loop control system.

[0198] Embodiment 2

[0199] The present invention also provides a dynamic base disturbance suppression system for a magnetic bearing-rotor system, including: a first construction module, a second construction module, a third construction module, a fourth construction module, a fifth construction module, and a suppression module.

[0200] The first construction module is used to establish a rotational equivalent dynamic model of the magnetic bearing-rotor system;

[0201] The second construction module is used to establish a dynamic model of the magnetic bearing-rotor system containing base disturbance;

[0202] The third construction module is used to obtain a rotational dynamic model of the magnetic bearing-rotor system containing disturbance terms based on the rotational equivalent dynamic model of the magnetic bearing-rotor system and the dynamic model of the magnetic bearing-rotor system containing base disturbance;

[0203] The fourth construction module is used to obtain an extended state observer based on the rotational dynamic model of the magnetic bearing-rotor system containing disturbance terms;

[0204] The fifth construction module is used to obtain an extended state observer based on model reference adaptive compensation through the extended state observer and the model reference adaptive compensator;

[0205] The suppression module is used to complete the suppression of the dynamic base disturbance of the magnetic bearing-rotor system through the extended state observer based on model reference adaptive compensation.

[0206] In this embodiment, the extended state observer includes: a model - free - parameter extended state observer and a model - parameter - based extended state observer.

[0207] In this embodiment, the operation process of the model - parameter - based extended state observer includes:

[0208]

[0209] Among them, J is the moment of inertia of the rotor in the radial direction, k i is the magnetic bearing force - current stiffness coefficient, k h is the magnetic bearing force - displacement stiffness coefficient, l m is the distance from the centroid of the rotor to the center of the drive coil, l s is the distance from the centroid of the rotor to the center of the sensor, R is the resistance of the drive coil, L is the inductance of the drive coil, and M d is the observer estimator, α is the observer input, I α is the control current of the α channel, and E1 - E3 are the values of the observer gain matrix.

[0210] In this embodiment, the adaptive tracking rate and the compensation control voltage differential compensation process in the adaptive compensation link include:

[0211]

[0212] Among them, δ kc is a small constant used to prevent the denominator from being 0, γ eso is the ESO model - reference adaptive compensation coefficient, e d is the compensation error, k c_eso is the model - reference adaptive tracking rate, u eso is the control voltage, M d is the disturbance observation estimator. [[ID=4!6]]

[0213] Embodiment III

[0214] This embodiment presents the process of simulation and experimental verification of the extended state observer based on model - reference adaptive compensation.

[0215] In this embodiment, the simulation verification of the extended state observer based on model - reference adaptive compensation:

[0216] To verify the effectiveness of the method proposed in the present invention, the extended state observer can be configured for regional pole placement according to Equations (43) and (44), and the configuration results of the observer are shown in the table.

[0217] Table 1 Configuration parameters and configuration results of the extended state observer

[0218]

[0219] According to the configuration results shown in the table, the observer region pole diagram as shown in Figure 12 can be obtained. It can be seen from Figure 12 that the observer poles consist of a pole falling on the main axis and a pair of conjugate poles, and the positions of the poles are constrained within the overlapping region described by Eqs. (40) and (41).

[0220] Table 1 Rotor dynamic parameters of the magnetic bearing-rotor system

[0221]

[0222] To test the performance of the extended state observer designed in the present invention, a dynamic base simulation model of the magnetic levitation control moment gyro was built according to the dynamic parameters and observer parameters of the magnetic bearing-rotor system shown in the table and Table 1. After applying 30 Nm interference torques of 0.1 Hz and 1 Hz to the magnetic bearing-rotor system respectively, the time series signal diagrams of the interference input signal, the observer output signal and the observer error signal were plotted in the same virtual oscilloscope as shown in Figure 13 . When the system is subjected to interference with a frequency of 0.1 Hz, the maximum observation error is 0.17 Nm (the error is 0.57%). When the frequency is 1.0 Hz, the error is 1.69 Nm (the error is 5.63%). The observer parameters are designed to keep the observation error of the interference between 0 and 1 Hz below 10%, indicating that the observer has good performance.

[0223] The design of the extended state observer based on model information has been completed. Next, the simulation of the model reference adaptive compensation link is carried out. The stability of the model reference adaptation is greatly affected by the adaptive step size, and the adaptive step size must be less than the upper limit value determined by the amplitude of the adaptive tracking signal source. In the algorithm proposed in the present invention, the adaptive tracking source is the output of the observer. Since the interference of the dynamic base is unknown, it is difficult to determine the stable critical value of the adaptive step size in the adaptive step size link. Therefore, Eq. (44) proposes a normalization processing method for the output signal of the ESO. However, in Eq. (44), the two parameters χ and δ kc have great influence on the system performance, and the values of the parameters χ and δ need to be further determined through simulation analysis kc .

[0224] As Figure 14 shown is the influence of different χ values on the adaptive compensation coefficient. It can be seen from the simulation results that the model reference adaptive compensation coefficient under the state observer information changes in a "comb-like" manner. It can be seen from Figure 14 that among the three cases where the χ value is 2, 100, and 500, the larger the χ value, the adaptive compensation coefficient k cThe faster the convergence speed is. Therefore, when designing the normalization parameter, the value of χ should be appropriately increased. However, the value of χ is not the higher the better. For example, Figure 15 shows the change state diagram of the rotor suspension deviation displacement during the adaptive compensation process when the value of χ is 2, 100, and 500.

[0225] It can be seen from Figure 15 that although the larger the value of χ is, the faster the convergence speed of the adaptive compensation algorithm is, when χ increases to 500, the peak-to-peak value of the rotor displacement shows a state of first decreasing and then increasing. Although the displacement of the rotor can still be stabilized within a certain range, this change should be avoided in the actual control system. After comprehensive consideration, the normalization parameter in the model reference adaptive controller is designed as χ = 80, δ kc = 0.005.

[0226] To verify the compensation effect of the extended state observer - model reference adaptive controller, after determining the normalization parameter of the model reference adaptive, the step size of the model reference adaptive is determined to be 0.003, and the comparison diagram of the dynamic base disturbance suppression of three control methods (no compensation, model parameter - based ESO controller, and ESOMRAC controller) can be obtained. Since the signals of the four radial channels are similar, taking the Bx end of the magnetic bearing as an example, the displacement states of the three control methods are as Figure 16 shown. It can be seen from the simulation results that in the case of no external compensator, affected by the dynamic base disturbance, the peak-to-peak value of the rotor displacement reaches 1.7×10 -5 m, and the peak-to-peak value of the displacement directly compensated by the model parameter ESO observer is 1.1×10 -6 m. Compared with before compensation, the peak-to-peak value of the displacement has decreased by about 93.5%. And under the ESOMRAC controller, the peak-to-peak value of the displacement under the same base disturbance is 5.6×10 -7 m. Compared with the model parameter - based ESO compensator, the peak-to-peak value of the displacement has decreased by 49.1% again. It can be seen that compared with before compensation, the peak-to-peak value of the displacement has decreased by 96.7%. It can be seen from the simulation results that most of the disturbances brought by the dynamic base to the magnetic bearing - rotor system have been eliminated.

[0227] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. Method for suppressing interference of a moving base of a magnetic bearing-rotor system, characterized in that, It includes the following steps: Establish a rotational equivalent dynamic model of the magnetic bearing-rotor system; Establish a dynamic model of the magnetic bearing-rotor system with pedestal interference; Based on the rotational equivalent dynamic model of the magnetic bearing-rotor system and the dynamic model of the magnetic bearing-rotor system with pedestal interference, obtain a rotational dynamic model of the magnetic bearing-rotor system with interference terms; Based on the rotational dynamic model of the magnetic bearing-rotor system with interference terms, obtain an extended state observer; Through the extended state observer and the model reference adaptive compensator, obtain an extended state observer based on model reference adaptive compensation; Through the extended state observer based on model reference adaptive compensation, complete the suppression of the dynamic pedestal interference of the magnetic bearing-rotor system.

2. The method for suppressing the interference of a moving base of a magnetic bearing-rotor system according to claim 1, wherein The extended state observer includes: an extended state observer without model parameters and an extended state observer based on model parameters.

3. The method for suppressing the interference of the moving base of the magnetic bearing-rotor system according to claim 2, characterized in that, The operation method of the extended state observer based on model parameters includes: where J is the moment of inertia of the rotor in the radial direction, k i is the force-current stiffness coefficient of the magnetic bearing, k h is the force-displacement stiffness coefficient of the magnetic bearing, l m is the distance from the center of mass of the rotor to the center of the drive coil, l s is the distance from the center of mass of the rotor to the center of the sensor, R is the resistance of the drive coil, L is the inductance of the drive coil, and M d is the observer estimator, α is the observer input, I α is the control current of the α channel, and E1 to E3 are the values of the observer gain matrix.

4. The method for suppressing the interference of a moving base of a magnetic bearing-rotor system according to claim 1, characterized in that, The adaptive tracking rate and the differential compensation method of the compensation control voltage in the adaptive compensation link include: Among them, δ kc is a relatively small constant used to prevent the denominator from being zero, and γ eso is the ESO model reference adaptive compensation coefficient, e d is the compensation error, k c_eso is the model reference adaptive tracking rate, u eso is the control voltage, and M d is the disturbance observation estimator.

5. Active base disturbance rejection system for magnetic bearing-rotor system, characterized in that, It includes: The first construction module, the second construction module, the third construction module, the fourth construction module, the fifth construction module and the suppression module, The first construction module is used to establish a rotational equivalent dynamic model of the magnetic bearing-rotor system; The second construction module is used to establish a dynamic model of the magnetic bearing-rotor system with pedestal interference; The third construction module is used to obtain a rotational dynamic model of the magnetic bearing-rotor system with interference terms based on the rotational equivalent dynamic model of the magnetic bearing-rotor system and the dynamic model of the magnetic bearing-rotor system with pedestal interference; The fourth construction module is used to obtain an extended state observer based on the rotational dynamic model of the magnetic bearing-rotor system with interference terms; The fifth construction module is used to obtain an extended state observer based on model reference adaptive compensation through the extended state observer and the model reference adaptive compensator; The suppression module is used to complete the suppression of the dynamic pedestal interference of the magnetic bearing-rotor system through the extended state observer based on model reference adaptive compensation.

6. The magnetic bearing-rotor system dynamic base interference suppression system according to claim 5, characterized in that, The extended state observer includes: an extended state observer without model parameters and an extended state observer based on model parameters.

7. The magnetic bearing-rotor system dynamic base interference suppression system according to claim 6, characterized in that The operation process of the extended state observer based on model parameters includes: where J is the moment of inertia of the rotor in the radial direction, k i is the force-current stiffness coefficient of the magnetic bearing, k h is the force-displacement stiffness coefficient of the magnetic bearing, l m is the distance from the center of mass of the rotor to the center of the drive coil, l s is the distance from the center of mass of the rotor to the center of the sensor, R is the resistance of the drive coil, L is the inductance of the drive coil, and M d is the observer estimator, α is the observer input, I α is the control current of the α channel, and E1 to E3 are the observer gain matrix values.

8. The magnetic bearing-rotor system dynamic base interference suppression system according to claim 5, characterized in that The adaptive tracking rate and the differential compensation process of the compensation control voltage in the adaptive compensation link include: Among them, δ kc is a relatively small constant used to prevent the denominator from being zero, and γ eso is the ESO model reference adaptive compensation coefficient, e d is the compensation error, k c_eso is the model reference adaptive tracking rate, u eso is the control voltage, and M d is the disturbance observation estimator.

Images