A control system and method for an active electromagnetic bearing

Abstract

The present invention belongs to the technical field of active magnetic bearings and discloses a control system and method for an active electromagnetic bearing, comprising a first subtractor, a second subtractor, a third subtractor, a first multiplier, a second multiplier, a third multiplier, a fourth multiplier, a first integrator, a second integrator, and a SOGI-LADRC controller. The present invention replaces the linear extended state observer of the active electromagnetic bearing control system with a second-order generalized integrator. The present invention linearly configures the observation values ​​of the linear extended state observer based on the second-order generalized integrator. Using a linear active disturbance rejection controller based on the second-order generalized integrator, root locus analysis of the closed-loop system under this controller method can be performed, thereby ensuring system stability.

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), often referred to as EMBs, offer numerous advantages. However, if the rotor's geometric axis does not coincide with its inertial axis, resulting in an imbalanced rotor mass, this can generate unbalanced forces, which in turn cause the rotor to vibrate at the same frequency as the unbalanced forces. Unbalanced vibration control in EMB rotor systems can be divided into two approaches: automatic balancing control and imbalance compensation. Automatic balancing control eliminates or filters the unbalanced displacement signal in the sensor output signal, preventing the controller from exerting control over it and causing the rotor to rotate about its inertial axis. Automatic balancing often uses various notch filters to output a speed-synchronization compensation signal, offsetting the speed-synchronization component in the sensor output signal and preventing the controller from responding to the speed-synchronization signal. In actual operating conditions, as the temperature of the EMB rotor system increases, system parameters are affected. The algorithms used in automatic balancing rely heavily on a precise model of the system, which can reduce the effectiveness of imbalance suppression.

[0003] Unbalance compensation uses an algorithm to generate a control force equal in magnitude and opposite in direction to the unbalanced force, counteracting the effect of the unbalanced force and forcing the rotor to rotate about its geometric axis. Another method for unbalance compensation is linear active disturbance rejection control (ADRC). Its core approach is to use an ESO to observe the unbalanced force and other unknown disturbances as a lumped disturbance and compensate for them in the system.

[0004] The Chinese patent application, CN115750592A, is titled "A Method for Controlling Unbalanced Vibration of an Active Magnetic Bearing Rotor by Decoupling." The patent application includes the following steps: First, a system model of the rotor's unbalanced vibration is established based on the rotor dynamics equations. The position coupling, gyroscopic coupling, and unbalanced vibration coupling components present in the system model are treated as disturbance signals. A state observer is designed to estimate and compensate for this disturbance, making the four position degree-of-freedom subsystems independent. A control method combining an adaptive notch filter and a nonlinear feedback control law is employed to derive a simplified closed-loop feedback structure for the subsystems, analyze their frequency characteristics, and analyze the rationale for controller parameter selection from a BODE diagram, ultimately achieving stable control of the magnetically suspended rotor. While this patent application is capable of controlling active magnetic bearings, it fails to achieve the desired interference rejection or improve observation accuracy. Summary of the Invention

[0005] To overcome the aforementioned problems in the prior art, the present invention provides a control system and method for an active electromagnetic bearing (AEB). This method improves the observation accuracy of LESO by replacing conventional integration with SOGI. Using SOGI-LADRC, the present invention performs root locus analysis on the closed-loop system of this controller, ensuring system stability.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] In a first aspect, the present invention provides a control system for an active electromagnetic bearing, comprising:

[0008] The first subtractor is used to calculate the output displacement of the active electromagnetic bearing system x 1 and system state observation value z 1 difference variable θ1;

[0009] a first multiplier for calculating the product of a first gain L1 of the LESO observer and a variable θ1;

[0010] The second subtractor is used to calculate the system state observation value z 2 and Difference in θ1 ;

[0011] The first integrator is used to Integrate to obtain the system state observation value z 1;

[0012] a second multiplier for calculating the product of a second gain L2 of the LESO observer and a variable θ1;

[0013] 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 ;

[0014] 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;

[0015] The second integrator is used to calculate the result of the third subtractor Integrate to obtain the system state observation value ;

[0016] 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 z3 and system reference displacement x r , calculate the variable ;

[0017] The fourth multiplier is used to multiply the variable With the lumped disturbance parameter Multiply and get the reference current i。

[0018] 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.

[0019] Optionally, the active electromagnetic bearing system outputs a displacement x 1Measured by SOGI-LADRC controller for active electromagnetic bearings.

[0020] Optionally, the linear control rate formula of the SOGI-LADRC controller is:

[0021]

[0022] Where: ω c is the controller bandwidth; x r is the system reference displacement; bo is the lumped disturbance parameter.

[0023] Optionally, the observation z 1. z 2. z The calculation formula for 3 is:

[0024]

[0025] The calculation formulas for M1 and M2 are:

[0026]

[0027] 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.

[0028] Optionally, the linear control rate of SOGI-LADRC is:

[0029]

[0030] Where: ;

[0031] 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.

[0032] Optionally, the active electromagnetic bearing system outputs displacement x The calculation formula for 1 is: ; Where b0 is the lumped disturbance parameter.

[0033] Optionally, the closed-loop transfer function of the system is:

[0034]

[0035] 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.

[0036] In a second aspect, the present invention provides a control method for an active electromagnetic bearing, which uses the control system of the active electromagnetic bearing, comprising the following steps:

[0037] 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;

[0038] Calculate the product of the first gain L1 of the LESO observer and the variable θ1 through the first multiplier;

[0039] The system state observation value is calculated by the second subtractor z 2 and Difference in θ1 ;

[0040] Through the first integrator Integrate to obtain the system state observation value z 1;

[0041] Calculate the product of the second gain L2 of the LESO observer and the variable θ1 through the second multiplier;

[0042] 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 ;

[0043] The system state observation value is calculated by calculating the product of the third gain L3 of the LESO observer, the variable θ1 and the system input pull-type change R(s) through the third multiplier z 3;

[0044] The calculation result of the third subtractor is calculated by the second integrator Integrate to obtain the system state observation value ;

[0045] 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 SOGI-LADRC controller, calculate the variable ;

[0046] The variable With the lumped disturbance parameter Multiply and get the reference current i ;

[0047] 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.

[0048] Optionally, during operation, the bandwidth of the SOGI-LADRC controller is maintained at c >0.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present invention proposes a control system for an active electromagnetic bearing (AEB). This system replaces the Linear Extended State Observer (LESO) in the AEB control system with a Second-Order Generalized Integrator (SOGI). Since the observer's observation accuracy determines the controller's effectiveness, the observation accuracy of lumped disturbances directly affects the disturbance rejection performance of the active disturbance rejection controller. This improvement enhances the overall control effectiveness of the AEB. Since the disturbance observation value and the observation error information are in an integral relationship, a SOGI-LESO (Linear Extended State Observer based on a Second-Order Generalized Integrator) is proposed to improve observation accuracy. This approach replaces the original integrator with the SOGI. Bode plot analysis of the LESO demonstrates that the LESO- ... BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The drawings described herein are for illustrative 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 schematic and are used 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:

[0052] Figure 1 The electromagnetic bearing rotor structure is as follows Figure 1 As shown;

[0053] Figure 2 It is a schematic diagram of rotor imbalance;

[0054] Figure 3 Comparison of two extended state observers

[0055] Figure 4 This is the SOGI-LADRC framework diagram;

[0056] Figure 5 is the electromagnetic bearing vibration based on SOGI-LADRC controller when ω=100;

[0057] Figure 6 Is ω = 50 in SOGI-LADRC controller electromagnetic bearing vibration;

[0058] Figure 7Is ω = 25 in SOGI-LADRC controller electromagnetic bearing vibration;

[0059] Figure 8 Is ω = 75 in SOGI-LADRC controller electromagnetic bearing vibration;

[0060] Figure 9 is the vibration of the electromagnetic bearing based on the LESO controller when ω=100;

[0061] Figure 10 It is a PID controller for electromagnetic bearing vibration. DETAILED DESCRIPTION

[0062] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the embodiments described 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 making creative efforts should fall within the scope of protection of the present invention.

[0063] 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 as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0064] 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 in use. 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. Therefore, it cannot be understood as a limitation on the present invention.

[0065] 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 an intermediate 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 an intermediate 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", and it does not mean that the structure must be completely horizontal, but it can be slightly tilted.

[0066] It should be noted that similar reference numerals and letters denote similar items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further defined or explained in the subsequent figures. In the description of the present invention, it should be understood that the terms "comprises" and "comprising" indicate the presence of the described features, integers, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their collections.

[0067] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention pertains. The terms used herein in the specification of the present invention are for the purpose of describing specific embodiments only 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 "a," "an," and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0068] The present invention will be described in detail below with reference to the accompanying drawings.

[0069] like Figure 4 As shown, a control system of an active electromagnetic bearing of the present invention includes:

[0070] The first subtractor is used to calculate the output displacement of the active electromagnetic bearing system x 1 and system state observation value z 1 difference variable θ1;

[0071] a first multiplier for calculating the product of a first gain L1 of the LESO observer and a variable θ1;

[0072] The second subtractor is used to calculate the system state observation value z 2 and Difference in θ1 ;

[0073] The first integrator is used to Integrate to obtain the system state observation value z 1;

[0074] a second multiplier for calculating the product of a second gain L2 of the LESO observer and a variable θ1;

[0075] 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 ;

[0076] 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;

[0077] The second integrator is used to calculate the result of the third subtractor Integrate to obtain the system state observation value ;

[0078] 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 ;

[0079] The fourth multiplier is used to multiply the variable With the lumped disturbance parameter Multiply and get the reference current i。

[0080] A control method for a control system of an active electromagnetic bearing according to the present invention comprises the following steps:

[0081] 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;

[0082] Calculate the product of the first gain L1 of the LESO observer and the variable θ1 through the first multiplier;

[0083] The system state observation value is calculated by the second subtractor z 2 and Difference in θ1 ;

[0084] Through the first integrator Integrate to obtain the system state observation value z 1;

[0085] Calculate the product of the second gain L2 of the LESO observer and the variable θ1 through the second multiplier;

[0086] 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 ;

[0087] The system state observation value is calculated by calculating the product of the third gain L3 of the LESO observer, the variable θ1 and the system input pull-type change R(s) through the third multiplier z 3;

[0088] The calculation result of the third subtractor is obtained by the second integrator Integrate to obtain the system state observation value ;

[0089] 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 SOGI-LADRC controller, calculate the variables ;

[0090] The variable With the lumped disturbance parameter Multiply and get the reference current i ;

[0091] 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.

[0092] The present invention proposes a control system for an active electromagnetic bearing (AEB). This system replaces the Linear Extended State Observer (LESO) in the AEB control system with a Second-Order Generalized Integrator (SOGI). Since the observer's observation accuracy determines the controller's effectiveness, the observation accuracy of lumped disturbances directly affects the disturbance rejection performance of the active disturbance rejection controller. This improvement enhances the overall control effectiveness of the AEB. Since the disturbance observation value and the observation error information are in an integral relationship, a SOGI-LESO (Linear Extended State Observer based on a Second-Order Generalized Integrator) is proposed to improve observation accuracy. This approach replaces the original integrator with the SOGI. Bode plot analysis of the LESO demonstrates that the observation accuracy of the LESO- ...

[0093] Example 1

[0094] 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 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. Then:

[0095] Formula 1

[0096] x and y are the displacements of the rotor geometric center c respectively.

[0097] Rotor winding x 、 y The angle of the axis rotating counterclockwise is:

[0098] Formula 2

[0099] 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.

[0100] like Figure 2 As shown, if the rotor unbalance 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.

[0101] Point G' is the reference point; the instantaneous rotation angle of G is φ , when the rotor is running stably ,φ=ωtConsidering 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:

[0102] Formula 3

[0103] in, ω is the angular velocity, t is the time; J For the rotor x 、 y moment of inertia in the direction; J z For the rotor z moment of inertia in the direction; m is the rotor mass; f d1 、 f d2 、 f d3 、 f d For unbalanced force.

[0104] f xa For end a x electromagnetic forces 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 distances.

[0105] The expression of unbalanced force is:

[0106] Formula 4

[0107] Where: m e is the unbalanced mass; ε is the eccentricity from point G to point C.

[0108] Formula 3 is written as a matrix formula, which is:

[0109] Formula 5

[0110] Where: ; ;

[0111] ;

[0112] .

[0113] ;

[0114] in, J For the rotor x 、 y moment of inertia in the direction; J z For the rotor z moment of inertia in the direction; m is the rotor mass.

[0115] The generalized displacement vector of the rotor mass center c q =[θ y 、 x ,θ x 、 y ] T , rotor geometric center displacement vector

[0116] q b= [ x a 、 x b 、 y a 、 y b ] T The relationship between them is:

[0117] Formula 6

[0118] Where:

[0119] Combining Formula 5 and Formula 6, Formula 5 can now be rewritten as:

[0120] Formula 7

[0121] 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.

[0122] To simplify the model, let l a = l b = l o , where l o To simplify the variables, Equation 7 is expanded to:

[0123] Formula 8

[0124] Where: ; ;

[0125] ; ;

[0126] in, For end a x Second derivative of shaft displacement; For the B side x Second derivative of shaft displacement; For end a y Second derivative of shaft displacement; For the B side y The second derivative of the shaft displacement; B0 is a simplified variable.

[0127] 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.

[0128] 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.

[0129] End A of the rotor x direction, for example, electromagnetic force f xa Expressed as:

[0130] Formula 9

[0131] 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.

[0132] According to formula 9, formula 8 can be written as:

[0133] Formula 10

[0134] 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 the four degrees of freedom except the controllable electromagnetic force itself.

[0135] Through Equation 10, decentralized control of each electromagnetic bearing rotor system is achieved.

[0136] The principle of Linear Active Disturbance Rejection Control (LADRC) is to treat 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 by LESO, and the lumped disturbance is then compensated in the controller to reduce the impact of the lumped disturbance on the system.

[0137] For the electromagnetic bearing rotor system in formula 10, the rotor x Taking one end of the direction as an example, the LESO is designed with:

[0138] Formula 11

[0139] Where: x 3= a 0 x 1+ d xa , h for x 3 rate of change.

[0140] According to formula 11, the LESO is designed as:

[0141] Formula 12

[0142] 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.

[0143] Subtracting Equation 11 from Equation 12 yields the error state equation:

[0144] Formula 13

[0145] Where: θ 2= z 2- x 2; θ 3= z 3- x 3.

[0146] Performing Laplace transform on Equation 13, we have:

[0147] Formula 14

[0148] Then get z 3 and x The transfer function between 3 is:

[0149] Formula 15

[0150] in, z 3 is the system state observation value; x 3 is a simplified variable; s is a complex frequency variable;

[0151] In order to make the system stable, that is: z 3 and x The 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:

[0152] Formula 16

[0153] The solution is:

[0154] Formula 17

[0155] Substituting Equation 17 into Equation 15:

[0156] Formula 18

[0157] The linear control rate of LADRC is:

[0158] Formula 19

[0159] Where: ω c is the controller bandwidth; bo is the lumped disturbance parameter.

[0160] The frequency domain expression of the second-order generalized integrator SOGI (Second Order Generalized Integrator) is:

[0161] Formula 20

[0162] Where: ω n is the adjustment coefficient of SOGI, and s is the complex frequency variable.

[0163] According to the improvement idea, the same observer gain is used. The specific expression of SOGI-LESO is:

[0164] Formula 21

[0165] Where: R(t) is the time domain expression of R(s).

[0166] Subtract Equation 11 from Equation 21 and perform Laplace transform to obtain z 3 and x The transfer function of 3 is:

[0167] Formula 22

[0168] 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:

[0169] from Figure 3 First, we can see that SOGI-LESO is superior to 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. x 3. Starting from the mid-frequency band, the two observers react to the disturbance x The amplitude and phase observation accuracy of 3 will deteriorate with the increase of frequency.

[0170] According to Equations 19 and 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.

[0171] According to formula 11 and formula 21, the specific expressions of the observation values ​​z1, z2, and z3 are obtained:

[0172]

[0173] Where:

[0174]

[0175] The linear control rate of SOGI-LADRC adopts Equation 19, which can be obtained by substituting:

[0176]

[0177] Where: ;

[0178] .

[0179] According to formula 11, the system output is:

[0180]

[0181] Joint i 、 x 1, we can get:

[0182]

[0183] 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:

[0184]

[0185] 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.

[0186] If the influence of disturbance on system output is considered, the closed-loop transfer function of the system is:

[0187]

[0188] Where: ; ,The parameters of the electromagnetic bearing rotor system are shown in Table 1.

[0189] Table 1

[0190]

[0191] Example 2

[0192] 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.

[0193] In order to better measure the control effect, the calculation formula of the average displacement is now defined as:

[0194] Formula 23

[0195] Where: N is the number of sampling points.

[0196] Figure 5 The simulation experiment of electromagnetic bearing vibration based on SOGI-LADRC controller when ω=100. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 3.88m.

[0197] Figure 6 The simulation experiment of electromagnetic bearing vibration based on SOGI-LADRC controller when ω=50. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 4.77m.

[0198] Figure 7 The simulation experiment of electromagnetic bearing vibration based on SOGI-LADRC controller when ω=25. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 5.02m.

[0199] Figure 8 The simulation experiment of electromagnetic bearing vibration based on SOGI-LADRC controller when ω=75. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 4.97m.

[0200] 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 simulate under the LESO controller and PID controller respectively under the state of ω=100.

[0201] Figure 9 The simulation experiment of electromagnetic bearing vibration based on LESO controller when ω=100. From the figure we can see that the maximum amplitude of the electromagnetic bearing is about 4.91m.

[0202] Figure 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.

[0203] Therefore, compared with the traditional LADRC, the SOGI-LADRC controller is more capable of observing and compensating the lumped disturbance, and is suitable for the inherently unstable AMBs-rotor system.

[0204] 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.

[0205] In actual working conditions, the power amplifier and sensor have a delay effect, which 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.

[0206] Unless otherwise specified, the device components involved in the above embodiments are all conventional device components, 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.

[0207] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention and are not limiting. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in this 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 value z 1 difference variable θ1; a first multiplier 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 and get the reference current i； 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; Active electromagnetic bearing system output displacement x The calculation formula for 1 is: ; Where b0 is the lumped disturbance parameter; The closed-loop transfer function of the system is: Where: k 21 , k 11 To simplify the variables, ; , The pull-type change of the output displacement of the active electromagnetic bearing system; is the pull-type variation of the lumped disturbance.

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: ω 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: The calculation formulas for 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. A control method for an active electromagnetic bearing, characterized in that: A control system for an active electromagnetic bearing according to any one of claims 1 to 5 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 through the 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 through the 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 system state observation value is calculated by calculating the product of the third gain L3 of the LESO observer, the variable θ1 and the system input pull-type change R(s) through the third multiplier z 3; The calculation result of the third subtractor is obtained 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 SOGI-LADRC controller, calculate the variable ; The variable With the lumped disturbance parameter Multiply and 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.

7. The control method of an active electromagnetic bearing according to claim 6, characterized in that: During operation, maintain the bandwidth of SOGI-LADRC controller c >0.

Images