Control method for solid thrust magnetic bearing affected by eddy current effect

Abstract

The present application provides a control method for a solid thrust magnetic bearing affected by eddy current effects, and relates to the field of magnetic bearing control. The method includes constructing a fractional-order anti-disturbance control architecture of a controller in a solid thrust magnetic bearing system, the architecture including a precompensator, a low-pass filter, and an expectation module; determining the transfer functions of the precompensator, the low-pass filter, the expectation module, and the controlled object; performing stability analysis on the solid thrust magnetic bearing system based on the transfer functions of the precompensator, the low-pass filter, the expectation module, and the controlled object, and determining stability conditions; adjusting control parameters based on the stability conditions; substituting the adjusted control parameters into the transfer function of the precompensator and the transfer function of the low-pass filter, compensating for the total disturbance of the system, and realizing anti-disturbance control of the controlled object. The method simplifies the control parameter adjustment process and improves the stability and anti-disturbance performance of the solid thrust magnetic bearing system.

Description

Technical Field

[0001] The present application relates to the field of magnetic suspension bearing control, and in particular to a control method for a solid thrust magnetic suspension bearing affected by eddy current effects. Background Art

[0002] Magnetic bearing technology plays a vital role in modern industry, particularly in high-speed rotating machinery, such as turbomolecular pumps, magnetically suspended blowers, and magnetically suspended centrifugal compressors. Active magnetic bearings utilize electromagnetic force to suspend the rotor, achieving contactless support. These bearings offer significant advantages, including zero friction, no lubrication requirements, and a long service life.

[0003] However, due to their structural characteristics, solid thrust magnetic bearings are susceptible to eddy current effects. These eddy current effects can enhance the nonlinear characteristics of the system, increasing the complexity of the control system and the difficulty of dynamic response. Related technologies have designed controller parameters based on the frequency response of the fractional-order model of the magnetic bearing, which can achieve better control performance for solid thrust magnetic bearing control systems. However, this method involves a complex parameter design process and a high computational effort, and has not yet explored the system's anti-interference performance. Summary of the Invention

[0004] Based on this, it is necessary to provide a control method for a solid thrust magnetic bearing affected by eddy current effect to address the above technical problems. This method can simplify the control parameter adjustment process and improve the stability and anti-interference performance of the solid thrust magnetic bearing system.

[0005] In a first aspect, the present application provides a control method for a solid thrust magnetic bearing affected by an eddy current effect. The method is applied to a controller of a solid thrust magnetic bearing system. The solid thrust magnetic bearing system also includes a solid thrust magnetic bearing, and the solid thrust magnetic bearing is a controlled object. The method includes:

[0006] A fractional-order anti-disturbance control architecture for the controller in a solid thrust magnetic bearing system is constructed. The architecture includes a precompensator, a low-pass filter, and an expectation module. The precompensator is a fractional-order PD controller.

[0007] determining a transfer function of a precompensator, a transfer function of a low-pass filter, a transfer function of a desired module, and a transfer function of the controlled object;

[0008] Based on the transfer functions of the precompensator, low-pass filter, desired module, and controlled object, the system stability analysis of the solid thrust magnetic bearing system is carried out to determine the stability conditions.

[0009] Based on the stability conditions, the control parameters in the fractional-order disturbance rejection control architecture are adjusted. The control parameters include the differential term proportional coefficient, differential coefficient, and fractional differential order of the precompensator, as well as the time constant of the low-pass filter.

[0010] The adjusted control parameters are substituted into the transfer function of the precompensator and the transfer function of the low-pass filter, and the total disturbance of the solid thrust magnetic bearing system is observed and compensated to achieve anti-disturbance control of the controlled object.

[0011] In one embodiment, by Square root conversion to the second parameter , The complex plane consists of the imaginary axis and the real axis. The complex plane includes stable and unstable regions. The complex plane is divided into the right half plane and the left half plane with the imaginary axis as the dividing line. The unstable region is located in the right half plane, the stable region is larger than the unstable region, and the stable region includes the left half plane and part of the right half plane.

[0012] The stability condition is that there is a target constant greater than zero when Greater than zero and less than the target constant:

[0013] Condition a: The order of the controlled object transfer function after pre-compensation matches the expected module transfer function;

[0014] Condition b: The zero point of the controlled object in the complex plane is located in the stable region;

[0015] Condition c: The zero point of the precompensator in the complex plane is located in the stable region.

[0016] In one embodiment, a system stability analysis is performed on a solid thrust magnetic bearing system based on the transfer functions of a precompensator, a low-pass filter, a desired module, and a controlled object to determine stability conditions, including:

[0017] The open-loop transfer function expression of the solid thrust magnetic bearing system is derived based on the transfer functions of the precompensator, low-pass filter, expectation module and the controlled object. ;in, Used to indicate The proportional coefficient, differential coefficient and fractional differential order of the differential term in the complex plane and Impact on the stability of solid thrust magnetic bearing system;

[0018] based on , by Square root converted to ,get The transformation expression of ;

[0019] By determining when The distribution area of ​​the roots of the characteristic polynomial equal to zero when it approaches zero is used to determine conditions b and c in the stability condition; among them, the characteristic polynomial and the transformation expression related.

[0020] In one embodiment, by determining when The distribution area of ​​the roots of the characteristic polynomial equal to zero when , to determine the conditions b and c in the stability conditions, including:

[0021] The root of the characteristic polynomial equal to zero is equivalent to the target expression The root equal to zero; where the target expression It is the sum of two parts, one part is related to the differential term proportional coefficient and differential coefficient, and the other part is related to related;

[0022] when Approaching zero, the target expression Split into first target expression and the second target expression The product of

[0023] based on The distribution area of ​​the roots determines conditions b and c in the stability conditions.

[0024] In one embodiment, based on The root distribution area determines the stability conditions b and c, including:

[0025] Will The specific formula is decomposed into a first expression and a second expression; wherein the parameters in the first expression are the same as the parameters in the precompensator transfer function, and some parameters in the second expression are the same as some parameters in the controlled object expression;

[0026] Condition c among the stability conditions is determined based on the root distribution area of ​​the first expression, and condition b among the stability conditions is determined based on the root distribution area of ​​the second expression.

[0027] In one embodiment, Rewrite it to include two variables Integrate into an expectation expression containing a target variable ;Expected expression It also includes the matching degree between the transfer function of the controlled object after pre-compensation and the transfer function of the expected module;

[0028] Among them, the stability condition also includes condition d: the expected expression A root equal to zero is a negative real number.

[0029] In one embodiment, determining the condition d in the stability condition includes:

[0030] Assume that the first value is the expected expression A root of , the second value and the third value are the second target expression The two roots of

[0031] According to Rouchet's theorem, we get When it is greater than zero and close to zero, the square of the second value is The product of the square of the third value and The product of is equal to the first value;

[0032] By square of the second value and The product of the square of the third value and The product of is equal to the first value, and we get When the value is greater than zero and approaches zero, the square of the second value and the square of the third value are equal to the sum of the first value and The ratio of

[0033] The square of the second value and the square of the third value are both equal to the first value and The ratio of Zero and first value In this case, the second and third values ​​are both pure imaginary numbers and are located in the stable region.

[0034] In one embodiment, adjusting control parameters in a fractional-order disturbance rejection control architecture based on a stability condition includes:

[0035] when When the matching degree approaches zero, the transfer function of the controlled object after precompensation and the transfer function of the desired module have a matching degree higher than the matching threshold in the high frequency band. By setting the differential coefficient of the precompensator , derive the proportional coefficient of the differential term of the precompensator Transfer function and differential coefficient of controlled object and desired module The relationship between the differential term and the proportional coefficient is determined based on this relationship. .

[0036] Determined according to stability conditions The upper limit value of the characteristic polynomial is the minimum value when the root of the characteristic polynomial is located at the boundary between the stable region and the unstable region. The time constant Select between zero and the upper limit.

[0037] In one embodiment, It is obtained through dynamic adjustment. Specifically include:

[0038] Building a simulation model based on the transfer function of the controlled object, the simulation model includes a displacement outer loop and a current inner loop;

[0039] When the simulation model is running, an impact disturbance is applied to the step response, and the displacement drop value and recovery time of the transfer function of the pre-compensated controlled object after receiving the impact disturbance are observed;

[0040] Between zero and the upper limit, gradually decrease Until the displacement drop is less than the drop threshold and the recovery time is less than the recovery threshold.

[0041] In the second aspect, the present application also provides a solid thrust magnetic bearing system affected by eddy current effect, the system including a controller and a solid thrust magnetic bearing, the solid thrust magnetic bearing being the controlled object, and the controller being capable of executing the solid thrust magnetic bearing control method affected by eddy current effect of the first aspect.

[0042] The above-mentioned control method for a solid thrust magnetic bearing affected by eddy current effect is applied to a controller of a solid thrust magnetic bearing system, and specifically includes: constructing a fractional-order anti-disturbance control architecture of the controller, which specifically includes a precompensator, a low-pass filter and an expectation module, wherein the precompensator is a fractional-order PD controller; determining the various transfer functions of the precompensator, the low-pass filter, the expectation module and the controlled object; further performing a system stability analysis on the solid thrust magnetic bearing system based on the various transfer functions of the precompensator, the low-pass filter, the expectation module and the controlled object to determine the stability conditions; adjusting the control parameters in the fractional-order anti-disturbance control architecture according to the stability conditions, including the differential term proportional coefficient, differential coefficient and fractional differential order of the precompensator and the time constant of the low-pass filter; substituting the adjusted control parameters into the transfer function of the precompensator and the transfer function of the low-pass filter, and realizing anti-disturbance control of the controlled object by observing and compensating the total disturbance of the solid thrust magnetic bearing system. This method can simplify the adjustment process of control parameters, improve the stability and anti-interference performance of the solid thrust magnetic bearing system, and ensure that the solid thrust magnetic bearing system can maintain stable operation when disturbed. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flow chart of a control method for a solid thrust magnetic bearing affected by eddy current effect in one embodiment;

[0044] Figure 2A framework diagram of a solid thrust magnetic bearing system according to an embodiment;

[0045] Figure 3 A schematic diagram of a stable region and an unstable region in one embodiment;

[0046] Figure 4 A flow chart for determining stability conditions in one embodiment;

[0047] Figure 5 A flowchart for determining conditions b and c in the stability condition in one embodiment;

[0048] Figure 6 Obtaining the time constant for one embodiment Flowchart of

[0049] Figure 7 FIG. 4 is a diagram of simulation results in one embodiment. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0051] In one embodiment, a control method for a solid thrust magnetic bearing affected by eddy current effect is provided. The method is applied to a controller of a solid thrust magnetic bearing system. The solid thrust magnetic bearing system also includes a solid thrust magnetic bearing, and the solid thrust magnetic bearing is a controlled object. Figure 1 As shown, the method includes the following steps:

[0052] Step 101: Construct a fractional-order anti-disturbance control architecture for a controller in a solid thrust magnetic bearing system, the architecture including a precompensator, a low-pass filter, and an expectation module; wherein the precompensator is a fractional-order PD controller.

[0053] Figure 2 This is the framework diagram of the solid thrust magnetic bearing system. Figure 2The figure shows that the controller in a solid thrust magnetic bearing system includes a precompensator, a low-pass filter, and an expectation module, with the solid thrust magnetic bearing as the controlled object. It should be noted that the precompensator is a fractional-order PD controller, which is used to precompensate the solid thrust magnetic bearing system, adjust and optimize the solid thrust magnetic bearing system in advance, and reduce the mismatch between the solid thrust magnetic bearing system and the expectation model; the low-pass filter can be used to reduce the impact of high-frequency noise on the disturbance observer, ensuring that external high-frequency noise during the anti-disturbance process does not significantly interfere with the normal operation of the solid thrust magnetic bearing system; the expectation module can express the expected dynamic response characteristics of the solid thrust magnetic bearing system and provide a performance target for the controller. This performance target can describe the input-output relationship of the solid thrust magnetic bearing system under ideal conditions, allowing the controller to adjust the actual response of the solid thrust magnetic bearing system based on this performance target.

[0054] Step 102: Determine the transfer function of the precompensator, the transfer function of the low-pass filter, the transfer function of the desired module, and the transfer function of the controlled object.

[0055] In the embodiment of the present application, the expression of the precompensator can be the transfer function of the fractional-order PD controller, and the precompensator can be expressed as , the transfer function of the precompensator is:

[0056] ;

[0057] in, is the differential term proportional coefficient of the precompensator, is the differential coefficient of the precompensator, is the fractional differential term, and 1.5 is the fractional differential order. It should be noted that the fractional differential order is set to 1.5 in the embodiment of the present application, but this fractional differential order is not fixed. The selection of the fractional differential order can be adjusted according to the specific system characteristics and control requirements, with the aim of optimizing the performance of the controller so that it can provide better control effects over a wider frequency range, thereby enhancing the stability and anti-interference capability of the solid thrust magnetic suspension bearing system.

[0058] The low-pass filter can be expressed as , the transfer function of the low-pass filter is:

[0059] ;

[0060] in, is the time constant of the low-pass filter, The invention is used to limit the influence of high-frequency noise on the solid thrust magnetic bearing system, ensure the accuracy of disturbance observation, and not affect the low-frequency response characteristics of the solid thrust magnetic bearing system.

[0061] The transfer function of the desired module can be set according to the design requirements of the solid thrust magnetic bearing system, which is usually a stable transfer function with desired dynamic characteristics. The desired module can be expressed as , the transfer function of the expected module is:

[0062] = ;

[0063] in, is the time constant of the desired module, which determines the speed of response of the solid thrust magnetic bearing system. The larger the time constant, the slower the response. The smaller it is, the faster the response.

[0064] The controlled object can be represented as , the transfer function of the controlled object is:

[0065] ;

[0066] in, 、 and All of them are known quantities obtained through parameter identification of solid thrust magnetic bearing system.

[0067] It should be noted that is the Laplace operator.

[0068] Step 103: Based on the transfer functions of the precompensator, the low-pass filter, the desired module, and the controlled object, a system stability analysis is performed on the solid thrust magnetic bearing system to determine the stability conditions.

[0069] For example, the transfer function of the precompensator, the transfer function of the low-pass filter, the transfer function of the desired module, and the transfer function of the controlled object can be substituted into the expression of the closed-loop transfer function of the entire solid thrust magnetic bearing system to construct the characteristic polynomial of the solid thrust magnetic bearing system. Using stability criteria, such as Matignon's theorem, the roots of the characteristic polynomial in the complex plane (which can be referred to as The distribution of the characteristic polynomial on the complex plane (or other parameters) is determined. By ensuring that all roots of the characteristic polynomial lie within the stable region of the complex plane, the stability conditions of the solid thrust magnetic bearing system are determined. These conditions include the relationships or ranges that the control parameters of the precompensator, low-pass filter, desired module, and controlled object must satisfy, as well as the degree of match between the controlled object transfer function and the desired module transfer function. This ensures the stable operation of the entire solid thrust magnetic bearing system under various operating conditions.

[0070] Step 104: Based on the stability condition, adjust the control parameters in the fractional-order disturbance rejection control architecture; wherein the control parameters include the differential term proportional coefficient, differential coefficient and fractional differential order of the precompensator and the time constant of the low-pass filter .

[0071] Specifically, the control parameters include the differential term proportional coefficient of the precompensator , differential coefficient and fractional differential order and time constant of the low-pass filter The purpose of adjusting these control parameters is to ensure that the entire solid thrust magnetic bearing system meets the stability conditions and optimize the dynamic response performance of the solid thrust magnetic bearing system.

[0072] Based on the stability condition, the control parameters of the precompensator, low-pass filter, and desired module can be adjusted to ensure that the roots of the characteristic equation of the solid thrust magnetic bearing system fall within the stable region, thereby ensuring stable operation of the solid thrust magnetic bearing system. Exemplarily, the adjustment method may include successive approximation, iterative optimization, or the use of specific control theory tools to find the optimal parameter combination that satisfies the stability condition.

[0073] Step 105: Substitute the adjusted control parameters into the transfer function of the precompensator and the transfer function of the low-pass filter, and observe and compensate for the total disturbance of the solid thrust magnetic bearing system to achieve anti-disturbance control of the controlled object.

[0074] The updated precompensator inherits the new derivative term scaling factor , differential coefficient and fractional differential orders, the low-pass filter applies a new time constant Through the synergistic effect of the expectation module, precompensator, and low-pass filter, the solid thrust magnetic bearing system can observe and compensate for the total disturbance affecting the solid thrust magnetic bearing in real time. This process effectively reduces the impact of disturbances on the solid thrust magnetic bearing system, ensuring its stable operation and successfully achieving the anti-disturbance control goal for the controlled object.

[0075] In this embodiment, the method is applied to a controller of a solid thrust magnetic bearing system, specifically comprising: constructing a fractional-order anti-disturbance control architecture of the controller, the architecture specifically comprising a precompensator, a low-pass filter, and an expectation module, wherein the precompensator is a fractional-order PD controller; determining the transfer functions of the precompensator, the low-pass filter, the expectation module, and the controlled object; further performing a system stability analysis of the solid thrust magnetic bearing system based on the transfer functions of the precompensator, the low-pass filter, the expectation module, and the controlled object to determine the stability conditions; adjusting the control parameters in the fractional-order anti-disturbance control architecture according to the stability conditions, including the differential term proportional coefficient, differential coefficient, fractional differential order of the precompensator, and the time constant of the low-pass filter; substituting the adjusted control parameters into the precompensator and the low-pass filter, and realizing anti-disturbance control of the controlled object by observing and compensating the total disturbance of the solid thrust magnetic bearing system. This method can simplify the control parameter adjustment process, improve the stability and anti-disturbance performance of the solid thrust magnetic bearing system, and ensure that the solid thrust magnetic bearing system can maintain stable operation when disturbed.

[0076] In one embodiment, by Square root conversion to the second parameter , The complex plane consists of the imaginary axis and the real axis. The complex plane includes stable and unstable regions. The complex plane is divided into the right half plane and the left half plane with the imaginary axis as the dividing line. The unstable region is located in the right half plane, the stable region is larger than the unstable region, and the stable region includes the left half plane and part of the right half plane.

[0077] The stability condition is that there exists a target constant ,when Greater than zero and less than the target constant:

[0078] Condition a: The relative order of the controlled object transfer function after pre-compensation matches the expected transfer function;

[0079] Condition b: The zero point of the controlled object in the complex plane is located in the stable region;

[0080] Condition c: The zero point of the precompensator in the complex plane is located in the stable region.

[0081] Specifically, by setting the first parameter Square root conversion to the second parameter ,Right now Among them, the first parameter is the Laplace operator parameter in the above steps. Figure 3 As shown, The complex plane consists of the real axis and the imaginary axis. The complex plane is divided into the left half plane and the right half plane by the imaginary axis. The left half plane (the shaded part in the figure) is the stable region, and the blank part of the right half plane is the unstable region. The stable region is larger than the unstable region, and the stable region includes the left half plane and part of the right half plane. There are two dividing lines between the stable region (the shaded part) and the unstable region (the blank part), which are located in the first quadrant and the fourth quadrant respectively. The angles between the two dividing lines and the real axis are both It should be noted that the angle between the dividing line and the real axis is not fixed and can be adjusted according to the specific system characteristics.

[0082] It should be noted that condition a requires that the transfer function of the controlled object after adjustment by the precompensator and the desired transfer function of the desired module should be consistent in relative order. The relative order can be defined as the order of the highest order term in the denominator minus the order of the highest order term in the numerator of the transfer function. For example, if the relative order of the transfer function of the desired module is 1st order (e.g. ), the relative order of the controlled object transfer function is 2.5 (for example ), then when the differential order of the precompensator is 1.5 (for example ), The relative order of is 1, which matches the relative order of the transfer function of the desired module.

[0083] Condition b is The zero point of the controlled object in the complex plane is located in the stable region. The zero point refers to the zero point of the controlled object transfer function, that is, the root of the numerator polynomial. The stable region refers to The left half plane and part of the right half plane of the complex plane (such as Figure 3 (shaded area in the middle). Therefore, condition b requires that the zero points of the controlled object all lie in the stable region. If the zero points of the controlled object are in the stable region, the response characteristics of the solid thrust magnetic bearing system are controllable, without undesirable oscillations or unstable behavior.

[0084] Condition c is The zero point of the precompensator in the complex plane is located in the stable region. Similarly, the zero point of the precompensator should also be located in The left half plane and part of the right half plane of the complex plane (such as Figure 3 The precompensator adjusts the centrifugal thrust magnetic bearing system to achieve the desired performance. If the precompensator's zero point is within the stable region, no new instability factors will be introduced, thus ensuring the stability of the magnetic bearing system.

[0085] In one embodiment, Figure 4As shown, based on the precompensator, low-pass filter, expectation module and various transfer functions of the controlled object, a system stability analysis is performed on the solid thrust magnetic bearing system to determine the stability conditions, including the following steps:

[0086] Step 401: Derive the open-loop transfer function expression of the solid thrust magnetic bearing system based on the transfer functions of the precompensator, the low-pass filter, the desired module, and the controlled object. ; Used to indicate The proportional coefficient, differential coefficient and fractional differential order of the differential term in the complex plane and Impact on bearing system stability.

[0087] It should be noted that the controlled object Can represent the physical characteristics of solid thrust magnetic bearings, precompensators It can be used to adjust the dynamic characteristics of the solid thrust magnetic bearing system, low-pass filter Can be used to reduce the impact of high frequency noise, the expected module The desired dynamic response of the solid thrust magnetic bearing system can be defined. By combining these expressions, the open-loop transfer function of the solid thrust magnetic bearing system can be obtained. , open-loop transfer function The input-output relationship of the solid thrust magnetic bearing system without feedback can be described.

[0088] For example, assuming 、 、 and The transfer function is as follows:

[0089] , , , ;

[0090] based on 、 、 as well as The transfer function of the solid thrust magnetic bearing system can be derived from the open-loop transfer function expression for:

[0091] .

[0092] Can be used to indicate The proportional coefficient of the differential term of the precompensator in the complex plane is , differential coefficient and fractional differential order and time constant of the low-pass filter Impact on bearing system stability.

[0093] Step 402: Based on By Square root converted to ,get The transformation expression of .

[0094] Specifically, the open-loop transfer function expression of the solid thrust magnetic bearing system is: , and perform parameter transformation by Square root converted to , that is, By parameter transformation, the original open-loop transfer function expression can be Convert to Transformation Expression , transform expression for:

[0095] .

[0096] Step 403: Determine when the low-pass filter The distribution area of ​​the roots of the characteristic polynomial equal to zero when , in order to determine the conditions b and c in the stability condition, where the characteristic polynomial and the transformation expression related.

[0097] Specifically, when the low-pass filter Approaching zero (i.e. ), the influence of the low-pass filter on the stability of the solid thrust magnetic bearing system can be ignored. The characteristic polynomial is , the root of the characteristic polynomial equal to zero is Root.

[0098] Through analysis The distribution area of ​​the roots of can be used to determine the stability of the solid thrust magnetic bearing system. If all roots of the characteristic polynomial are equal to zero, they are located in If the stable region of the complex plane is satisfied, conditions b and c are satisfied, that is, the zero point of the controlled object and the zero point of the precompensator are both located in the stable region, ensuring the stability of the solid thrust magnetic bearing system.

[0099] In one embodiment, Figure 5 As shown, The distribution area of ​​the roots of the characteristic polynomial equal to zero when approaching zero is used to determine conditions b and c in the stability condition, including the following steps:

[0100] Step 501: Equivalently convert the root of the characteristic polynomial equal to zero to the target expression Root equal to zero; target expression It is the sum of two parts, one of which is related to the differential term proportional coefficient and differential coefficient of the precompensator, and the other is related to the time constant related.

[0101] Specifically, according to Matignon's theorem, the stability condition of the solid thrust magnetic bearing system is that the roots of the characteristic polynomial are equal to zero. Figure 3 In the stable region shown, the root of the characteristic polynomial equal to zero is equivalent to the target expression The root of zero.

[0102] It should be noted that the expression of the root of the characteristic polynomial equal to zero is:

[0103] .

[0104] Furthermore, the equivalent target expression The root of is equal to zero as follows:

[0105] .

[0106] The target expression The sum of the two parts, the first half and the differential term of the precompensator are proportional coefficients , differential coefficient of the precompensator The second half is related to the time constant of the low-pass filter. related.

[0107] Step 502: When Approaching zero, the target expression Split into first target expression and the second target expression The product of .

[0108] Specifically, the target expression Can be split into the first target expression and the second target expression The first target expression and the second target expression The specific formula is as follows:

[0109] .

[0110] Step 503: Based on The distribution area of ​​the roots determines conditions b and c in the stability conditions.

[0111] Specifically, the stability condition of the solid thrust magnetic bearing system is the target expression The root of is located in the stable region, that is, the first target expression and the second target expression The roots are located in the stable area.

[0112] when When it is equal to zero, and The roots of are the same. is the first target expression The root, is the target expression The root of So that the curve First target expression only A solution, the first objective expression and On the curve Continuous, and as well as , we get the existence constant , so that when hour, Established. , , according to Rouchet's theorem, we get the first objective expression and the target expression On the curve have the same number of roots; and at the same time , get the limit , Established.

[0113] First target expression The roots of include the zero point of the precompensator and the zero point of the controlled object. The stability of the solid thrust magnetic bearing system requires the first objective expression The root of is located in the stable region, so the zero point of the precompensator and the zero point of the controlled object must both be located in the stable region.

[0114] By analyzing the first target expression The roots are The distribution on the complex plane ensures that the first objective expression The roots of are all located in the stable region, thus ensuring the stability of the solid thrust magnetic bearing system. Condition b requires that the zero point of the controlled object is located in the stable region, while condition c requires that the zero point of the precompensator is also located in the stable region. The root distribution can ensure that these two conditions are met, thereby ensuring the stability of the entire solid thrust magnetic bearing system.

[0115] In one embodiment, based on the first target expression The root distribution area determines the stability conditions b and c, including:

[0116] The first target expression The specific formula is decomposed into a first expression and a second expression; wherein the parameters in the first expression are the same as the parameters in the precompensator transfer function, and some parameters in the second expression are the same as some parameters in the controlled object expression;

[0117] Condition c among the stability conditions is determined based on the root distribution area of ​​the first expression, and condition b among the stability conditions is determined based on the root distribution area of ​​the second expression.

[0118] Specifically, the first target expression The formula is as follows:

[0119] .

[0120] The first target expression Decomposed into the first expression and the second expression. The first expression is Among them, the parameters in the first expression, such as the differential term proportional coefficient , differential coefficient , which is the same as the parameters in the expression of the precompensator; it should be noted that the first expression is the same as the expression of the precompensator. By analyzing the first expression The roots are The distribution of the complex plane determines the condition c, that is, whether the zero point of the precompensator is in the stable region.

[0121] The second expression is Among them, some parameters in the second expression, such as , and the parameters in the expression of the controlled object The same. By analyzing the root of the second expression in The distribution of the complex plane determines the condition b, that is, whether the zero point of the controlled object is in the stable region. By decomposing the first objective expression And analyze the roots of each part separately The distribution of the complex plane can effectively determine the stability conditions of the solid thrust magnetic bearing system.

[0122] In one embodiment, Rewrite it to include two variables Integrate into an expectation expression containing a target variable ;Expected expression It also includes the matching degree between the transfer function of the controlled object after pre-compensation and the transfer function of the expected module;

[0123] The stability condition also includes condition d: the expected expression A root equal to zero is a negative real number.

[0124] Specifically, To rewrite, you can use the command , when the time constant When it approaches zero, the variable This transformation can include two variables The second target expression Convert to contain a variable The second target expression .

[0125] New second target expression is obtained by taking the time constant In the limit case, is simplified to:

[0126] ;

[0127] in, , It is the matching degree between the transfer function of the controlled object after pre-compensation and the expected module transfer function.

[0128] In one embodiment, determining the condition d in the stability condition includes:

[0129] Assume that the first value is the expected expression A root of , the second value and the third value are the second target expression The two roots of

[0130] According to Rouchet's theorem, we have When it is greater than zero and close to zero, the square of the second value is The product of the square of the third value and The product of is equal to the first value;

[0131] By square of the second value and The product of the square of the third value and The product of is equal to the first value, and we get When the value is greater than zero and approaches zero, the square of the second value and the square of the third value are equal to the sum of the first value and The ratio of

[0132] The square of the second value and the square of the third value are both equal to the first value and The ratio of Zero and first value In this case, the second and third values ​​are both pure imaginary numbers and are located in the stable region.

[0133] Specifically, assuming that the first value for A root of, the second value , the third value The second target expression There are two roots of . Then there is a small , making , .

[0134] make , .Will Expand to get:

[0135] .

[0136] For a very small , , making According to Rouchet's theorem, we can get hour, The second value of the two roots , the third value , which is the limit , Established.

[0137] When the first value The second value , the third value Located in the stable area. , we can get the first value , so you need .

[0138] Established. , Established, , the first value The second value can be obtained and the third value Located on the imaginary axis, that is, the second value and the third value are all pure imaginary numbers, located Figure 3 Stable area shown.

[0139] Furthermore, we can get Approaching zero , the system model of solid thrust magnetic bearing system has no The zero point of the complex plane unstable region, the precompensator has no When the zero point of the complex plane unstable region is The roots are located in Figure 3 The stable region shown; when hour, The roots of are negative real numbers, that is The roots are located in Figure 3 In the stable region shown, the solid thrust magnetic bearing system is stable.

[0140] In one embodiment, based on the stability condition, adjusting the control parameters in the fractional-order disturbance rejection control architecture includes:

[0141] when Approaching zero and matching When it approaches zero, the transfer function of the controlled object after precompensation and the transfer function of the desired module have a matching degree higher than the matching threshold in the high frequency band. By setting the differential coefficient of the precompensator , derive the proportional coefficient of the differential term of the precompensator Transfer function and differential coefficient of controlled object and desired module The relationship between the differential term and the proportional coefficient is determined based on this relationship. .

[0142] Determine the time constant of the low-pass filter based on the stability condition The upper limit value is the minimum value when the root of the characteristic polynomial is located at the boundary between the stable region and the unstable region. The time constant Select between zero and the upper limit.

[0143] Specifically, when And matching When , which will further reduce the internal disturbance of the solid thrust magnetic bearing system, and the transfer function of the controlled object and the transfer function of the desired module have a matching degree higher than the matching threshold in the high frequency band. Among them, the precompensator can correct the phase and amplitude of the solid thrust magnetic bearing system, making the transfer function closer to the desired dynamic characteristics in the high frequency band, thereby improving the matching degree. By setting the differential coefficient of the precompensator , derive the proportional coefficient of the differential term of the precompensator Transfer function and differential coefficient of controlled object and desired module Furthermore, the proportional coefficient of the differential term can be derived Transfer function and differential coefficient of controlled object and desired module The relationship between them is:

[0144] in, .

[0145] At this time, only the time constant Not yet determined, as long as the time constant If is chosen to be small enough, the solid thrust magnetic bearing system can be stable. The conditions for the stability of the solid thrust magnetic bearing system are All roots of Figure 3 The stable region shown in The root is or When the solid thrust magnetic bearing system is in a critical stable state, the time constant The upper limit of is the minimum value when the root of the characteristic polynomial is located at the boundary between the stable region and the unstable region. and is a positive real number. Then Selected upper limit for:

[0146] .

[0147] therefore, Select as The value should be as small as possible to meet performance requirements.

[0148] In one embodiment, Figure 6 As shown, the time constant It is obtained through dynamic adjustment. The specific steps include:

[0149] Step 601: Based on the controlled object The simulation model is constructed based on the transfer function, which includes the displacement outer loop and the current inner loop.

[0150] Specifically, based on the controlled object The transfer function can be used to build a simulation model, which can be used to simulate and analyze the dynamic behavior of the solid thrust magnetic bearing system.

[0151] The simulation model consists of an outer displacement loop and an inner current loop. The outer displacement loop primarily controls the rotor's position, ensuring stable suspension within the desired range. The inner current loop precisely controls the current in the electromagnet, rapidly responding to displacement changes and providing the corresponding electromagnetic force. Through the coordinated operation of these two loops, the solid thrust magnetic bearing system achieves precise control of the rotor's position and ensures its stability and dynamic performance.

[0152] Step 602: When the simulation model is running, an impact disturbance is applied to the step response, and the displacement drop value and recovery time of the transfer function of the pre-compensated controlled object after receiving the impact disturbance are observed.

[0153] A step response is applied to the solid thrust magnetic bearing system, causing the rotor to levitate at the center. Furthermore, an impact disturbance is applied to simulate conditions such as sudden loads or collisions that may occur during actual operation. This approach allows for realistic simulation of the disturbances that a solid thrust magnetic bearing system might encounter under actual operating conditions.

[0154] After an impact disturbance is applied, the solid thrust magnetic bearing system reacts to it, allowing observation of its dynamic response characteristics. The displacement drop in the controlled object's transfer function after the impact disturbance—that is, the maximum deviation of the rotor position from the set point—can be observed, reflecting the stability and anti-interference capability of the solid thrust magnetic bearing system under disturbance. The time required for the solid thrust magnetic bearing system to return to a stable state, known as the recovery time, can also be recorded, reflecting the dynamic response speed and regulation capability of the solid thrust magnetic bearing system.

[0155] Step 603: gradually reduce the time parameter between zero and the upper limit value Until the displacement drop is less than the drop threshold and the recovery time is less than the recovery threshold.

[0156] It should be noted that Select as By continuously reducing , you can change the low-pass filter The characteristics of the solid thrust magnetic bearing system will affect its dynamic response. In the simulation process, the displacement drop value and recovery time of the solid thrust magnetic bearing system after the impact disturbance are observed, and the requirements are found. At this time, the solid thrust magnetic bearing system shows good anti-disturbance performance.

[0157] In one embodiment, after parameter identification, the transfer function of the solid thrust magnetic bearing system is expressed as follows:

[0158] .

[0159] Select ,but The value range of is: , select The simulation process is to first give a step response to make the rotor levitate at the center position, and then apply an impact force of 250N with a duration of 1ms at 0.5s. The displacement waveform simulation results of the solid thrust magnetic bearing system are as follows: Figure 7 shown.

[0160] like Figure 7 As shown in the figure, the horizontal axis represents time (s) and the vertical axis represents displacement (μm). The vertical axis represents the displacement of the system after the impact. The displacement of the solid thrust magnetic bearing system drops by approximately 10.3485 μm after the impact, with peak-to-peak oscillation of approximately 14.90 μm. The time required for the displacement to recover to within ±1 μm is 10.3 ms. The solid thrust magnetic bearing system operates stably and can return to a steady state after the impact, with minimal displacement drop and adjustment time.

[0161] Based on the same concept, an embodiment of the present application also provides a solid thrust magnetic bearing system affected by eddy current effect. The solid thrust magnetic bearing system includes a controller and a solid thrust magnetic bearing. The solid thrust magnetic bearing is a controlled object, and the controller can execute the above-mentioned solid thrust magnetic bearing control method affected by eddy current effect.

[0162] As a controlled object, solid thrust magnetic bearings are susceptible to eddy current effects. The controller's function is to implement the aforementioned control method to effectively control the solid thrust magnetic bearing. By implementing this method, the controller can precisely control the solid thrust magnetic bearing, even when subject to eddy current effects, thereby ensuring system stability and reliability.

[0163] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0164] The above embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A control method for a solid thrust magnetic bearing affected by eddy current effect, characterized in that: The method is applied to a controller of a solid thrust magnetic suspension bearing system, wherein the solid thrust magnetic suspension bearing system further comprises a solid thrust magnetic suspension bearing, and the solid thrust magnetic suspension bearing is a controlled object. The method comprises: Constructing a fractional-order anti-disturbance control architecture of the controller in the solid thrust magnetic bearing system, the architecture comprising a precompensator, a low-pass filter, and an expectation module; wherein the precompensator is a fractional-order PD controller; determining a transfer function of the precompensator, a transfer function of the low-pass filter, a transfer function of the desired module, and a transfer function of the controlled object; performing a system stability analysis on the solid thrust magnetic bearing system based on the transfer functions of the precompensator, the low-pass filter, the desired module, and the controlled object to determine a stability condition; Based on the stability condition, the control parameters in the fractional-order disturbance rejection control architecture are adjusted; wherein the control parameters include the differential term proportional coefficient, differential coefficient and fractional differential order of the precompensator and the time constant of the low-pass filter ; The adjusted control parameters are substituted into the transfer function of the precompensator and the transfer function of the low-pass filter, and the total disturbance of the solid thrust magnetic bearing system is observed and compensated to achieve anti-disturbance control of the controlled object.

2. The control method for a solid thrust magnetic bearing affected by eddy current effect according to claim 1, characterized in that: By passing the first parameter Square root conversion to the second parameter , The complex plane consists of an imaginary axis and a real axis. The complex plane includes stable and unstable regions. The complex plane is divided into a right half plane and a left half plane with the imaginary axis as the dividing line, the unstable region is located in the right half plane, the stable region is larger than the unstable region, and the stable region includes the left half plane and part of the right half plane; The stability condition is that there is a target constant greater than zero when the Greater than zero and less than the target constant: Condition a: The order of the controlled object transfer function after pre-compensation matches the expected module transfer function; Condition b: in the The zero point of the controlled object in the complex plane is located in the stable region; Condition c: in the The zero points of the precompensator in the complex plane are located in the stable region.

3. The control method for a solid thrust magnetic bearing affected by eddy current effect according to claim 2, characterized in that: Based on the transfer functions of the precompensator, the low-pass filter, the desired module, and the controlled object, a system stability analysis is performed on the solid thrust magnetic bearing system to determine a stability condition, including: The open-loop transfer function expression of the solid thrust magnetic bearing system is derived based on the transfer functions of the precompensator, the low-pass filter, the desired module, and the controlled object. ; wherein, Used to indicate the The differential term proportional coefficient, the differential coefficient and the fractional differential order in the complex plane and the Impact on the stability of the solid thrust magnetic bearing system; Based on the , by putting the The square root is converted into , get the The transformation expression of ; By determining when the The distribution area of ​​the roots of the characteristic polynomial equal to zero when approaching zero is used to determine the conditions b and c in the stability condition; wherein the characteristic polynomial and the transformation expression related.

4. The control method for a solid thrust magnetic bearing affected by eddy current effect according to claim 3, characterized in that: The method is determined by The distribution area of ​​the roots of the characteristic polynomial equal to zero when the characteristic polynomial is equal to zero, in order to determine the conditions b and c in the stability conditions, include: The characteristic polynomial is equal to the root of zero, which is equivalent to the target expression The root of zero; wherein the target expression is the sum of two parts, one part is related to the differential term proportional coefficient and the differential coefficient, and the other part is related to the related; When the Approaching zero, the target expression Split into first target expression and the second target expression The product of Based on the The distribution area of ​​the roots determines conditions b and c in the stability conditions.

5. The control method for a solid thrust magnetic bearing affected by eddy current effect according to claim 4, characterized in that: Based on the The root distribution area determines the stability conditions b and c, including: The The specific formula is decomposed into a first expression and a second expression; wherein the parameters in the first expression are the same as the parameters in the precompensator transfer function, and some parameters in the second expression are the same as some parameters in the controlled object expression; Condition c among the stability conditions is determined based on the root distribution area of ​​the first expression, and condition b among the stability conditions is determined based on the root distribution area of ​​the second expression.

6. The control method for a solid thrust magnetic bearing affected by eddy current effect according to claim 4, characterized in that: The method further comprises: Rewrite the above statement containing two variables. Integrate into an expectation expression containing a target variable ; The expected expression It also includes the matching degree between the transfer function of the controlled object after pre-compensation and the transfer function of the expected module; Among them, the stability condition also includes condition d: the expected expression A root equal to zero is a negative real number.

7. The control method for a solid thrust magnetic bearing affected by eddy current effect according to claim 6, characterized in that: Determining the condition d in the stability condition includes: Assume that the first value is the expected expression A root of , the second value and the third value are the second target expression The two roots of According to Rouchet's theorem, we can get the existence of When the value is greater than zero and approaches zero, the square of the second value is equal to the The product of the square of the third value and the The product of is equal to the first value; By the square of the second value and the The product of the square of the third value and the The product of is equal to the first value, and the When the square of the second value and the square of the third value are both equal to the square of the first value and the third value, The ratio of The square of the second value and the square of the third value are both equal to the sum of the first value and the The ratio of Zero and the first value In this case, the second value and the third value are both pure imaginary numbers and are located in the stable region.

8. The control method for a solid thrust magnetic bearing affected by eddy current effect according to claim 2, characterized in that: Adjusting control parameters in the fractional-order disturbance rejection control architecture based on the stability condition includes: When the When the matching degree approaches zero, the transfer function of the controlled object after precompensation and the transfer function of the desired module have a matching degree higher than the matching threshold in the high frequency band. , derive the differential term proportional coefficient of the precompensator Transfer function and differential coefficient of controlled object and desired module The relationship between the differential term proportional coefficient is determined based on the relationship ; Determine the stability condition The upper limit value is the minimum value when the root of the characteristic polynomial is located at the boundary between the stable region and the unstable region, and the time constant Select between zero and the upper limit.

9. The control method for a solid thrust magnetic bearing affected by eddy current effect according to claim 8, characterized in that: described is obtained by dynamic adjustment, dynamically adjusting the Specifically include: Building a simulation model based on the transfer function of the controlled object, wherein the simulation model includes a displacement outer loop and a current inner loop; When the simulation model is running, an impact disturbance is applied to the step response, and a displacement drop value and a recovery time of the transfer function of the pre-compensated controlled object after receiving the impact disturbance are observed; Between zero and the upper limit, gradually reduce the Until the displacement drop is less than the drop threshold and the recovery time is less than the recovery threshold.

10. A solid thrust magnetic bearing system for use under eddy current effects, characterized in that: A solid thrust magnetic bearing system includes a controller and a solid thrust magnetic bearing, wherein the solid thrust magnetic bearing is a controlled object, and the controller can execute the control method for a solid thrust magnetic bearing affected by eddy current effect according to any one of claims 1 to 9.

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