Control system and method of active electromagnetic bearing

Abstract

The invention belongs to the technical field of active magnetic suspension bearings, and discloses a control system and method for an active electromagnetic bearing, and the system comprises a first subtracter, a second subtracter, a third subtracter, a first multiplier, a second multiplier, a third multiplier, a fourth multiplier, a first integrator, a second integrator, and an SOGI-LADRC controller. A linear expansion state observer of a control system of the active electromagnetic bearing is replaced by a second-order generalized integrator, linear configuration is carried out on an observation value of the linear expansion state observer based on the second-order generalized integrator, and through a linear active disturbance rejection controller based on the second-order generalized integrator, the linear expansion state observer of the control system of the active electromagnetic bearing is subjected to linear configuration; root locus analysis can be carried out on a closed-loop system under the controller method, and the stability of the system is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of active magnetic bearings, and in particular relates to a control system and method for an active electromagnetic bearing. Background Art

[0002] Active magnetic bearings (AMBs), referred to as electromagnetic bearings, have many advantages. However, if the geometric axis of the rotor does not coincide with its inertial axis, the rotor mass is unbalanced, which will generate unbalanced forces, and then cause the rotor to generate unbalanced vibrations with the same frequency as the unbalanced forces. Unbalanced vibration control in electromagnetic bearing rotor systems can be divided into two methods: automatic balancing control and unbalance compensation. Automatic balancing control is to offset or filter the unbalanced displacement signal in the sensor output signal so that the controller does not exert control force on the signal, thereby causing the rotor to rotate around its inertial axis. Automatic balancing often uses various notch filters to output speed frequency compensation signals to offset the speed frequency in the sensor output signal, so that the controller does not respond to the speed frequency signal. In actual working conditions, as the temperature of the electromagnetic bearing rotor system increases, the system parameters will be affected, and the algorithm in the automatic balancing method is more dependent on the accurate model of the system, which will make the unbalance suppression effect worse.

[0003] Unbalance compensation is to generate a control force equal to the unbalance force in magnitude and opposite in direction through a certain algorithm, which offsets the effect of the unbalance force and forces the rotor to rotate around its geometric axis. Another method of unbalance compensation is the linear self-disturbance rejection control method, the core of which is to use ESO to observe the unbalance force and other unknown disturbances as a lumped disturbance and compensate them to the system.

[0004] The Chinese patent publication number is CN115750592A, and the name is a patent application for a method for controlling the unbalanced vibration of an active magnetic suspension bearing rotor. The patent application includes the following steps: first, according to the rotor dynamics equation, a system model of the unbalanced vibration of the rotor is established, and the position coupling, gyroscopic effect coupling, and unbalanced vibration coupling components existing in the system model are all treated as disturbance signals. A state observer is designed to estimate and compensate for this disturbance, so that the four position freedom degree subsystems are independent of each other; a control method combining an adaptive notch filter and a nonlinear feedback control law is used to derive a closed-loop feedback simplified structure of the subsystem, analyze its frequency characteristics, and analyze the reasons for selecting the controller parameters from the BODE diagram, and finally achieve stable control of the magnetic suspension rotor. Although this patent application can control active magnetic suspension bearings, it cannot achieve the effect of anti-interference and improving observation accuracy. Summary of the invention

[0005] In order to overcome the problems existing in the above-mentioned prior art, the object of the present invention is to provide a control system and method for active electromagnetic bearings, by replacing the ordinary integral with SOGI, so as to improve the observation accuracy of LESO. The present invention uses SOGI-LADRC to perform root locus analysis on the closed-loop system under the controller method to ensure the stability of the system.

[0006] To achieve the above object, the technical solution adopted by the present invention is: In a first aspect, the present invention provides a control system for an active electromagnetic bearing, comprising: The first subtractor is used to calculate the output displacement of the active electromagnetic bearing system x 1 and system state observation z 1 difference variable θ1; A first multiplier, used for calculating the product of a first gain L1 of the LESO observer and a variable θ1; The second subtractor is used to calculate the system state observation value z 2 and Difference in θ1 ; The first integrator is used to Integrate to obtain the system state observation value z 1; a second multiplier, used for calculating the product of a second gain L2 of the LESO observer and a variable θ1; The third subtractor is used to calculate the system state observation value z 3 and The sum of the two multipliers and the output of the second multiplier Difference in θ1 ; The third multiplier is used to calculate the product of the third gain L3 of the LESO observer, the variable θ1 and the system input Laplace transform R(s), and calculate the system state observation value z 3; The second integrator is used to calculate the result of the third subtractor. Integrate to obtain the system state observation value ; SOGI-LADRC controller, used to input the result obtained by the first integrator z 1. The result obtained by the second integrator , the result obtained by the third multiplier z 3 and system reference displacement x r , calculate the variable ; The fourth multiplier is used to multiply the variable With the lumped disturbance parameter Multiply to get the reference currenti。

[0007] Optionally, the control system of the active electromagnetic bearing further includes a LESO observer, and the first gain L1 of the LESO observer is 3ω o , the second gain L2 of the LESO observer is 3ω o 2 , the third gain L3 of the LESO observer is -ω o 3 ,ω o is the observer bandwidth.

[0008] Optionally, the active electromagnetic bearing system outputs a displacement x 1Measured by SOGI-LADRC controller for active electromagnetic bearings.

[0009] Optionally, the linear control rate formula of the SOGI-LADRC controller is:

[0010] Where: c is the controller bandwidth; x r is the system reference displacement; bo is the lumped disturbance parameter.

[0011] Optionally, the observed value z 1. z 2. z The calculation formula for 3 is:

[0012] Among them, the calculation formulas of M1 and M2 are:

[0013]

[0014] Among them, ω o is the observer bandwidth, is the pull-type change of the system input, s is the complex frequency variable; bo is the lumped disturbance parameter.

[0015] Optionally, the linear control rate of SOGI-LADRC is:

[0016] Where: ;

[0017] Among them, ω c is the controller bandwidth; s is the complex frequency variable; i is the current; ω o is the observer bandwidth; G IL is the transfer function of current and displacement.

[0018] Optionally, the active electromagnetic bearing system outputs the displacement x The calculation formula for 1 is: ; Where b0 is the lumped disturbance parameter.

[0019] Optionally, the closed-loop transfer function of the system is:

[0020] Where: k 21 , k 11 To simplify the variables, ; , It is the pull-type change of the output displacement of the active electromagnetic bearing system; is the pull-type variation of the lumped disturbance.

[0021] In a second aspect, the present invention provides a control method for an active electromagnetic bearing, using the control system of the active electromagnetic bearing, comprising the following steps: The output displacement x1 of the active electromagnetic bearing system and the system state observation value are calculated by the first subtractor z 1 difference variable θ1; Calculate the product of the first gain L1 of the LESO observer and the variable θ1 by a first multiplier; The system state observation value is calculated by the second subtractor z 2 and Difference in θ1 ; Through the first integrator Integrate to obtain the system state observation value z 1; Calculate the product of the second gain L2 of the LESO observer and the variable θ1 by a second multiplier; The system state observation value is calculated by the third subtractor z 3 and The sum of the two multipliers and the output of the second multiplier Difference in θ1 ; The third multiplier calculates the third gain L3 of the LESO observer, the product of the variable θ1 and the system input pull-type change R (s) to calculate the system state observation value z 3; The calculation result of the third subtractor is calculated by the second integrator Integrate to obtain the system state observation value ; Input the result of the first integrator z 1. The result obtained by the second integrator , the result obtained by the third multiplier z 3 and system reference displacement x r To the SOGI-LADRC controller, calculate the variables ; The variable With the lumped disturbance parameter Multiply to get the reference current i ; The reference current i The input is sent to the active electromagnetic bearing system for circulation, and the active electromagnetic bearing continues to output displacement x1.

[0022] Optionally, during operation, the bandwidth of the SOGI-LADRC controller is maintained at c >0.

[0023] Compared with the prior art, the present invention has the following beneficial effects: The present invention discloses a control system for an active electromagnetic bearing. By replacing the LESO (Linear Extended State Observer) of the control system of the active electromagnetic bearing with a SOGI (Second-Order Generalized Integrator), since the observation accuracy of the observer determines the effect of the controller, the observation accuracy of the lumped disturbance directly affects the suppression performance of the anti-disturbance controller for disturbances. The overall control effect of the active electromagnetic bearing can be enhanced by the improvement. Since the disturbance observation value and the observation error information are in an integral relationship, in order to improve the observation accuracy of the observation, SOGI-LESO (linear extended state observer based on second-order generalized integrator) is proposed. The principle is to change the original integrator to SOGI. After analyzing the Bode diagram of the linear extended state observer, the observation accuracy of the linear extended state observer based on the second-order generalized integrator is better than that of LESO. The present invention linearly configures the observation value of the linear extended state observer based on the second-order generalized integrator. Through SOGI-LADRC (linear anti-disturbance controller based on the second-order generalized integrator), the closed-loop system under the controller method can be root locus analyzed to ensure the stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The drawings described herein are for explanation purposes only and are not intended to limit the scope of the present invention in any way. In addition, the shapes and proportional dimensions of the components in the drawings are only for illustration purposes to help understand the present invention, and are not intended to specifically limit the shapes and proportional dimensions of the components of the present invention. In the drawings: Figure 1 The electromagnetic bearing rotor structure is as follows Figure 1 As shown; Figure 2 It is a schematic diagram of rotor imbalance; Figure 3 Comparison of two extended state observers Figure 4 This is the SOGI-LADRC framework diagram; Figure 5 It is the electromagnetic bearing vibration based on SOGI-LADRC controller when ω=100; Figure 6 is ω=50 for electromagnetic bearing vibration of SOGI-LADRC controller; Figure 7 is ω=25 for electromagnetic bearing vibration of SOGI-LADRC controller; Figure 8 It is ω=75 for electromagnetic bearing vibration of SOGI-LADRC controller; Fig. 9 is the electromagnetic bearing vibration based on LESO controller when ω=100; Fig.10 It is a PID controller for electromagnetic bearing vibration. DETAILED DESCRIPTION

[0025] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0026] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0027] In the description of the embodiments of the present invention, it should be noted that if the terms "upper", "lower", "horizontal", "inner", etc. appear, the orientation or position relationship indicated is based on the orientation or position relationship shown in the accompanying drawings, or is the orientation or position relationship in which the product of the invention is usually placed when used. It is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0028] When an element is referred to as being "disposed on" another element, it may be directly on the other element or there may also be a central element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may also be a central element. The terms "vertical", "horizontal", "left", "right" and similar expressions used herein are for illustrative purposes only and are not intended to be the only embodiments. If the term "horizontal" appears, it does not mean that the component is required to be absolutely horizontal, but it can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", which does not mean that the structure must be completely horizontal, but it can be slightly tilted.

[0029] It should be noted that similar reference numerals and letters represent similar items in the following figures, so once an item is defined in one figure, it does not need to be further defined and explained in the subsequent figures. In the description of the present invention, it is to be understood that the terms "include" and "comprise" indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or their collections.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art of the technical field of the present invention. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, the singular forms of "a", "an" and "the" are intended to include plural forms unless the context clearly indicates otherwise.

[0031] The present invention is described in detail below with reference to the accompanying drawings.

[0032] like Figure 4 As shown, a control system of an active electromagnetic bearing of the present invention comprises: The first subtractor is used to calculate the output displacement of the active electromagnetic bearing system x 1 and system state observation z 1 difference variable θ1; A first multiplier, used for calculating the product of a first gain L1 of the LESO observer and a variable θ1; The second subtractor is used to calculate the system state observation value z 2 and Difference in θ1 ; The first integrator is used to Integrate to obtain the system state observation value z 1; a second multiplier, used for calculating the product of a second gain L2 of the LESO observer and a variable θ1; The third subtractor is used to calculate the system state observation value z 3 and The sum of the two multipliers and the output of the second multiplier Difference in θ1 ; The third multiplier is used to calculate the product of the third gain L3 of the LESO observer, the variable θ1 and the system input Laplace transform R(s), and calculate the system state observation value z 3; The second integrator is used to calculate the result of the third subtractor. Integrate to obtain the system state observation value ; SOGI-LADRC controller, used to input the result obtained by the first integrator z 1. The result obtained by the second integrator , the result obtained by the third multiplier z 3 and system reference displacement x r , calculate the variable ; The fourth multiplier is used to multiply the variable With the lumped disturbance parameter Multiply to get the reference current i。

[0033] A control method for a control system of an active electromagnetic bearing of the present invention comprises the following steps: The output displacement x1 of the active electromagnetic bearing system and the system state observation value are calculated by the first subtractor z 1 difference variable θ1; Calculate the product of the first gain L1 of the LESO observer and the variable θ1 by a first multiplier; The system state observation value is calculated by the second subtractor z 2 and Difference in θ1 ; Through the first integrator Integrate to obtain the system state observation value z 1; Calculate the product of the second gain L2 of the LESO observer and the variable θ1 by a second multiplier; The system state observation value is calculated by the third subtractor z 3 and The sum of the two multipliers and the output of the second multiplier Difference in θ1 ; The third multiplier calculates the third gain L3 of the LESO observer, the product of the variable θ1 and the system input pull-type change R (s) to calculate the system state observation value z 3; The calculation result of the third subtractor is calculated by the second integrator Integrate to obtain the system state observation value ; Input the result of the first integrator z 1. The result obtained by the second integrator , the result obtained by the third multiplier z 3 and system reference displacement x r To the SOGI-LADRC controller, calculate the variables ; The variable With the lumped disturbance parameter Multiply to get the reference current i ; The reference current i The input is sent to the active electromagnetic bearing system for circulation, and the active electromagnetic bearing continues to output displacement x1.

[0034] The present invention discloses a control system for an active electromagnetic bearing. By replacing the LESO (Linear Extended State Observer) of the control system of the active electromagnetic bearing with a SOGI (Second-Order Generalized Integrator), since the observation accuracy of the observer determines the effect of the controller, the observation accuracy of the lumped disturbance directly affects the suppression performance of the anti-disturbance controller for disturbances. The overall control effect of the active electromagnetic bearing can be enhanced by the improvement. Since the disturbance observation value and the observation error information are in an integral relationship, in order to improve the observation accuracy of the observation, SOGI-LESO (linear extended state observer based on second-order generalized integrator) is proposed. The principle is to change the original integrator to SOGI. After analyzing the Bode diagram of the linear extended state observer, the observation accuracy of the linear extended state observer based on the second-order generalized integrator is better than that of LESO. The present invention linearly configures the observation value of the linear extended state observer based on the second-order generalized integrator. Through SOGI-LADRC (linear anti-disturbance controller based on the second-order generalized integrator), the closed-loop system under the controller method can be analyzed by root locus, thereby ensuring the stability of the system.

[0035] Example 1 The electromagnetic bearing rotor structure used in the magnetic levitation high-speed motor system is as follows: Figure 1 As shown. Where c is the center of mass of the rotor;f xa , f ya , f xb , f yb They are a and b respectively. x , y Electromagnetic force on l a , l b are the distances from the geometric center c to the electromagnetic bearings at both ends a and b, respectively: Formula 1 x and y are the displacements of the rotor geometric center c respectively.

[0036] Rotor winding x , y The angle of the axis rotating counterclockwise is: Formula 2 in, , For the rotor x , y The angle of the axis's counterclockwise rotation, x a and x b Respectively indicate that end a and end b are x The displacement of the axis, y a and y b Respectively indicate that end a and end b are y Displacement of the axis.

[0037] like Figure 2 As shown in the figure, if the rotor unbalanced mass is at point G', the projection of G' on the end a of the geometric center plane of the balanced rotor is G. Oz The projection length on the axis is , the eccentricity from point G to point c is ε, and r is the distance from point c to point O.

[0038] Point G' is the reference point; the instantaneous rotation angle of G is φ , when the rotor is running stably ,φ=ωt Considering the influence of rotor imbalance and rotor acceleration, and based on rotor dynamics, the motion differential equation of the four-degree-of-freedom electromagnetic bearing rotor system is: Formula 3 in, ω is the angular velocity, t is the time; J For the rotorx , y Moment of inertia in direction; J z For the rotor z Moment of inertia in direction; m is the rotor mass; f d1 , f d2 , f d3 , f d For unbalanced force.

[0039] f xa For the a end x electromagnetic force at a distance; f xb is the electromagnetic force at distance x from end b; f ya is the unbalanced force at distance y from end a; f yb For the B side y Unbalanced forces at distance.

[0040] The expression of unbalanced force is: Formula 4 Where: m e is the unbalanced mass; ε is the eccentricity from point G to point c.

[0041] Formula 3 is written as a matrix formula, and we have: Formula 5 Where: ; ; ; . ; in, J For the rotor x , y Moment of inertia in direction; J z For the rotor z Moment of inertia in direction; m is the rotor mass.

[0042] The generalized displacement vector of the rotor mass center c q =[θ y , x ,θ x , y ]T , rotor geometric center displacement vector q b= [ x a , x b , y a , y b ] T The relationship between them is: Formula 6 Where:

[0043] Combining Formula 5 and Formula 6, Formula 5 is now rewritten as: Formula 7 in, is the rotor geometric center displacement vector; T represents the magnetic bearing distance matrix; M is the moment of inertia and rotor mass matrix; L f is the transpose of the magnetic bearing distance matrix; F is the electromagnetic force matrix; F d is the unbalanced force matrix.

[0044] To simplify the model, let l a = l b = l o , where l o To simplify the variables, Formula 7 is expanded to: Formula 8 Where: ; ; ; ;

[0045] in, For end a x The second derivative of the shaft displacement; For the B side x The second derivative of the shaft displacement; For end a y The second derivative of the shaft displacement; For the B side y Second derivative of shaft displacement; B0 is a simplified variable.

[0046] Taking the x-direction of the rotor a-end as an example, the rotor is not only affected by the internal influence of the electromagnetic force in the x-direction of the a-end, but also by the external influences of the electromagnetic force in the x-direction of the b-end, the coupling in the y-direction, and the unbalanced force.

[0047] Without considering the sensor misalignment effect, the electromagnetic bearing adopts a differential drive mode, that is, the two opposing magnets in each direction are driven by a fixed bias current in the same direction and an adjustable control current in the opposite direction. Since the displacement of the rotor in a stable suspension state is very small, the electromagnetic force can generally be linearized at the steady-state position.

[0048] Rotor end A x Direction, for example, electromagnetic force f xa It is expressed as: Formula 9 in, k i is the current proportional parameter of end a in the x direction; ks is the distance variable proportional parameter of end a in the x direction; i xa is the current at terminal a in the x direction; x xa is the distance variable of end a on x.

[0049] According to formula 9, formula 8 can be written as: Formula 10 Where: a 0= A 1 k s ; b 0= A 1 k i ; d xa , d xb , d ya , d yb They are the lumped disturbances in four degrees of freedom except the controllable electromagnetic force itself.

[0050] Through equation 10, decentralized control of each electromagnetic bearing rotor system is achieved.

[0051] The principle of Linear Active Disturbance Rejection Control (LADRC) is to treat the unknown disturbances inside and outside the system as a lumped disturbance, expand it into a new state, and then design a linear extended state observer (LESO) based on the relationship between the system input and output. This new state is observed through LESO, and then the lumped disturbance is compensated in the controller to reduce the impact of the lumped disturbance on the system.

[0052] For the electromagnetic bearing rotor system in formula 10, now the rotor x Taking the LESO design as an example, there are: Formula 11 Where: x 3= a 0 x 1+ d xa , h for x 3Rate of change.

[0053] According to formula 11, the LESO is designed as: Formula 12 Where: L 1. L 2. L 3 is the gain of LESO; z 1. z 2. z 3 are system status x 1. x 2. x 3 Observations; θ 1= z 1- x 1.

[0054] Subtracting Equation 11 from Equation 12 yields the error state equation: Formula 13 Where: θ 2= z 2- x 2; θ 3= z 3- x 3.

[0055] Performing Laplace transform on equation 13, we have: Formula 14 Then get z 3 and x The transfer function between 3 is: Formula 15 in, z 3 is the system state observation value; x 3 is a simplified variable; s is a complex frequency variable; In order to make the system stable, that is: z 3 and xThe transfer function poles between 3 are all located in the left half plane. Assuming that the three poles of equation 15 are all -ω0, ω0 is the bandwidth and is greater than 0, then: Formula 16 The solution is: Formula 17 Substituting Equation 17 into Equation 15: Formula 18 The linear control rate of LADRC is: Formula 19 Where: c is the controller bandwidth; bo is the lumped disturbance parameter.

[0056] The frequency domain expression of the second order generalized integrator SOGI (Second Order Generalized Integrator) is: Formula 20 Where: n is the adjustment coefficient of SOGI, and s is the complex frequency variable.

[0057] According to the improvement idea, the same observer gain is used, and the specific expression of SOGI-LESO is: Formula 21 Where: R(t) is the time domain expression of R(s).

[0058] Subtract equation 11 from equation 21 and perform Laplace transform to obtain z 3 and x The transfer function of 3 is: Formula 22 Where: ; ; ; . Draw the Bode diagrams of LESO and SOGI-LESO with the same bandwidth ω0, where k 1, k 2, k 3, k 4 is a simplified variable, such as Figure 3 As shown: from Figure 3 First, we can see that SOGI-LESO is better than LESO in both amplitude and phase angle observation accuracy, and the observation accuracy of SOGI-LESO increases with the increase of ω0. In addition, both observers can effectively observe disturbances in the low frequency band. x3. Starting from the mid-frequency band, the two observers react to the disturbance x The amplitude and phase observation accuracy of 3 will deteriorate as the frequency increases.

[0059] According to Equation 19 and Equation 21, the framework of the linear active disturbance rejection control second-order generalized integrator SOGI-LADRC (Second Order Generalized Integrator-Linear Active Disturbance Rejection Control) is obtained as follows Figure 4 shown.

[0060] According to formula 11 and formula 21, the specific expressions of the observed values ​​z1, z2, and z3 are obtained:

[0061] Where:

[0062]

[0063] The linear control rate of SOGI-LADRC adopts Equation 19, which can be obtained by substituting:

[0064] Where: ; . According to formula 11, the system output is:

[0065] Lian Li i , x 1, we can get:

[0066] It can be seen from the above formula that the output displacement x1 of the active electromagnetic bearing system is not only related to the system reference displacement x r Also related to the lumped disturbance x 3. If the influence of disturbance on the system is ignored, the closed-loop transfer function of the system is:

[0067] Analyzing the above formula, we can see that the system stability is only related to the controller bandwidth ω c and as long as the controller bandwidth ω c >0, then the system output can be stable.

[0068] If the influence of disturbance on system output is considered, the closed-loop transfer function of the system is:

[0069] Where: ; ,The parameters of the electromagnetic bearing rotor system are shown in Table 1.

[0070] Table 1

[0071] Example 2 In order to compare the effects of the present invention, based on the control system of an active electromagnetic bearing described in Example 1, two controllers, LADRC and SOGI-LADRC, are used to control the electromagnetic bearing rotor system, and the results are compared to verify the superiority of SOGI-LADRC. c The values ​​are the same.

[0072] In order to better measure the control effect, the calculation formula of the average displacement is now defined as: Formula 23 Where: N is the number of sampling points.

[0073] Figure 5 This is a simulation experiment of the electromagnetic bearing vibration based on the SOGI-LADRC controller when ω=100. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 3.88m.

[0074] Figure 6 This is a simulation experiment of the electromagnetic bearing vibration based on the SOGI-LADRC controller when ω=50. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 4.77m.

[0075] Figure 7 This is a simulation experiment of the electromagnetic bearing vibration based on the SOGI-LADRC controller when ω=25. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 5.02m.

[0076] Figure 8 This is a simulation experiment of the electromagnetic bearing vibration based on the SOGI-LADRC controller when ω=75. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 4.97m.

[0077] From the analysis of the above figure, we can see that the amplitude of the electromagnetic bearing is the smallest when ω=100. Next, we will perform simulations under the LESO controller and PID controller respectively when ω=100.

[0078] Fig. 9This is a simulation experiment of the electromagnetic bearing vibration based on the LESO controller when ω=100. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 4.91m.

[0079] Fig.10 This is a simulation experiment of the vibration of the electromagnetic bearing with a PID controller. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 5.06m.

[0080] Therefore: Compared with the traditional LADRC, the SOGI-LADRC controller can better observe and compensate for the lumped disturbance, and is suitable for the inherently unstable AMBs-rotor system.

[0081] The SOGI-LADRC controller designed in the present invention can effectively suppress rotor vibration within the first-order critical speed and second-order critical speed frequency bands.

[0082] In actual working conditions, since the power amplifier and sensor have a delay effect, this will affect the observation effect of the observer and may eventually affect the rotor vibration suppression effect. Therefore, phase compensation of the controller should be considered in practical applications.

[0083] Unless otherwise specified, the device elements involved in the above embodiments are all conventional device elements, and the structural settings, working modes or control modes involved are all conventional settings, working modes or control modes in the art unless otherwise specified.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in the field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims

1. A control system for an active electromagnetic bearing, characterized in that: include: The first subtractor is used to calculate the output displacement of the active electromagnetic bearing system x 1 and system state observation z 1 difference variable θ1; A first multiplier, used for calculating the product of a first gain L1 of the LESO observer and a variable θ1; The second subtractor is used to calculate the system state observation value z 2 and Difference in θ1 ; The first integrator is used to Integrate to obtain the system state observation value z 1; a second multiplier, for calculating the product of a second gain L2 of the LESO observer and a variable θ1; The third subtractor is used to calculate the system state observation value z 3 and The sum of the two multipliers and the output of the second multiplier Difference in θ1 ; The third multiplier is used to calculate the product of the third gain L3 of the LESO observer, the variable θ1 and the system input Laplace transform R(s), and calculate the system state observation value z 3; The second integrator is used to calculate the result of the third subtractor. Integrate to obtain the system state observation value ; SOGI-LADRC controller, used to input the result obtained by the first integrator z 1. The result obtained by the second integrator , the result obtained by the third multiplier z 3 and system reference displacement x r , calculate the variable ; The fourth multiplier is used to multiply the variable With the lumped disturbance parameter Multiply to get the reference current i .

2. The control system of an active electromagnetic bearing according to claim 1, characterized in that: The control system of the active electromagnetic bearing further includes a LESO observer, wherein the first gain L1 of the LESO observer is 3ω o , the second gain L2 of the LESO observer is 3ω o 2 , the third gain L3 of the LESO observer is -ω o 3 ,ω o is the observer bandwidth.

3. The control system of an active electromagnetic bearing according to claim 1, characterized in that: The active electromagnetic bearing system output displacement x 1Measured by SOGI-LADRC controller for active electromagnetic bearings.

4. The control system of an active electromagnetic bearing according to claim 1, characterized in that: The linear control rate formula of the SOGI-LADRC controller is: Where: c is the controller bandwidth; x r is the system reference displacement; bo is the lumped disturbance parameter.

5. The control system of an active electromagnetic bearing according to claim 1, characterized in that: Observations z 1. z 2. z The calculation formula for 3 is: Among them, the calculation formulas of M1 and M2 are: Among them, ω o is the observer bandwidth, is the pull-type change of the system input, s is the complex frequency variable; bo is the lumped disturbance parameter.

6. The control system of an active electromagnetic bearing according to claim 1, characterized in that: The linear control rate of SOGI-LADRC is: Where: ; Among them, ω c is the controller bandwidth; s is the complex frequency variable; i is the current; ω o is the observer bandwidth; G IL is the transfer function of current and displacement.

7. The control system of an active electromagnetic bearing according to claim 1, characterized in that: Active electromagnetic bearing system output displacement x The calculation formula for 1 is: ; Where b0 is the lumped disturbance parameter.

8. The control system of an active electromagnetic bearing according to claim 1, characterized in that: The closed-loop transfer function of the system is: Where: k 21 , k 11 To simplify the variables, ; , It is the pull-type change of the output displacement of the active electromagnetic bearing system; is the pull-type variation of the lumped disturbance.

9. A control method for an active electromagnetic bearing, characterized in that: The control system using the active electromagnetic bearing comprises the following steps: The output displacement x1 of the active electromagnetic bearing system and the system state observation value are calculated by the first subtractor z 1 difference variable θ1; Calculate the product of the first gain L1 of the LESO observer and the variable θ1 by a first multiplier; The system state observation value is calculated by the second subtractor z 2 and Difference in θ1 ; Through the first integrator Integrate to obtain the system state observation value z 1; Calculate the product of the second gain L2 of the LESO observer and the variable θ1 by a second multiplier; The system state observation value is calculated by the third subtractor z 3 and The sum of the two multipliers and the output of the second multiplier Difference in θ1 ; The third multiplier calculates the third gain L3 of the LESO observer, the product of the variable θ1 and the system input pull-type change R (s) to calculate the system state observation value z 3; The calculation result of the third subtractor is calculated by the second integrator Integrate to obtain the system state observation value ; Input the result of the first integrator z 1. The result obtained by the second integrator , the result obtained by the third multiplier z 3 and system reference displacement x r To the SOGI-LADRC controller, calculate the variables ; The variable With the lumped disturbance parameter Multiply to get the reference current i ; The reference current i The input is sent to the active electromagnetic bearing system for circulation, and the active electromagnetic bearing continues to output displacement x1.

10. The control method of an active electromagnetic bearing according to claim 9, characterized in that: During operation, the bandwidth of the SOGI-LADRC controller is maintained c >0.

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