Single-winding magnetic suspension motor SWBSRM-radial magnetic bearing integrated strong interference resisting method

Abstract

The invention provides a single-winding magnetic suspension motor SWBSRM-radial magnetic bearing integrated strong disturbance resisting method, which is used for a radial magnetic bearing and SWBSRM combined suspension system, and is characterized in that magnetic bearing suspension force control is taken as a main part, SWBSRM single-winding suspension force control is taken as a slave part, the suspension force is independently provided by a magnetic bearing under general conditions, and the magnetic bearing and the radial magnetic bearing are combined. And when the disturbance exceeds the bearing capacity of the radial magnetic bearing, the suspension force of the SWBSRM is dynamically cut in. According to the SWBSRM-radial magnetic bearing integrated strong disturbance resisting method, suspension force control of a collaborative magnetic bearing and a single-winding switched reluctance motor is combined with precise disturbance estimation of an extended state disturbance observer and a generalized extended state observer and intelligent adjustment of a self-adaptive neural network sliding mode controller; the stable operation of the system in a high-disturbance environment is realized, and the robustness and the anti-interference capability of the system are remarkably enhanced.

Description

Technical Field

[0001] The present invention integrates multiple technical fields such as control theory, electrical engineering, artificial intelligence, and mechanical design, and relates to the comprehensive application of advanced control technology and motor drive systems. Specifically, it relates to an intelligent suspension control method and device for a radial magnetic bearing system. Background Art

[0002] With the rapid development of modern industrial technology, higher requirements are put forward for the suspension accuracy, dynamic response speed, and stability of rotating machinery systems. As a non-contact and non-wearing support technology, radial magnetic bearings have attracted much attention because they can achieve high-precision, high-speed, and long-life rotation control. However, in practical applications, the radial magnetic bearing system faces many challenges. Especially under complex and changing working conditions, how to effectively suppress external disturbances and internal coupling disturbances to ensure the stable suspension of the system has become an urgent problem to be solved.

[0003] First of all, external disturbances such as load changes, mechanical vibrations, and electromagnetic interference will directly affect the suspension performance of the radial magnetic bearing, resulting in rotor position deviation, and further affecting the accuracy and stability of the entire system. Traditional control methods often have difficulty observing and compensating these disturbances in real time and accurately, resulting in poor control effects of the system.

[0004] Secondly, internal coupling disturbances are also important factors affecting the performance of radial magnetic bearings. Since radial magnetic bearings usually consist of multiple degrees of freedom, there are certain coupling relationships between the degrees of freedom. When one degree of freedom is disturbed, it will affect other degrees of freedom through the coupling effect, thereby reducing the control accuracy of the entire system.

[0005] In addition, when external disturbances or internal coupling disturbances are too large and exceed the bearing capacity of the radial magnetic bearing, traditional control methods often cannot effectively cope with them, resulting in system instability or even damage. Therefore, a compensation mechanism that can provide additional suspension force when the disturbance exceeds the bearing capacity is needed to ensure the stable operation of the system. Summary of the Invention

[0006] Based on the above background, the present invention proposes an innovative suspension control method for radial magnetic bearings, which realizes the effective suppression of external disturbances and internal coupling disturbances, as well as the dynamic suspension force compensation when the disturbance exceeds the bearing capacity, significantly improving the suspension accuracy, dynamic response ability, and robustness of the radial magnetic bearing system.

[0007] The technical solution of the present invention is: a single-winding magnetic suspension motor SWBSRM-radial magnetic bearing integrated strong disturbance resistance method. This control method includes magnetic bearing suspension force control and single-winding suspension force control, where the magnetic bearing control is the main and the single-winding control is the auxiliary, and the two cooperate to control to improve the disturbance resistance of the system; the specific process is as follows:

[0008] Based on the mathematical model of the radial magnetic bearing, a two-degree-of-freedom extended state disturbance observer is designed respectively to realize the online observation of external disturbances and internal coupling disturbances in each degree of freedom;

[0009] The fuzzy system is used to adjust the observer gain online to make it always match the total disturbance, improving the estimation performance of the observer;

[0010] By reconstructing the total disturbance and introducing the generalized extended state, a generalized extended state observer reflecting the known components in the disturbance is designed;

[0011] Using diffeomorphic transformation to reconstruct the disturbed system, establishing a generalized model of the internal state of the original system and the state of the disturbed system, and designing a generalized nonlinear extended state observer ESO reflecting the known components in the disturbance;

[0012] Improve the Fal function in the nonlinear extended state observer, and design a fixed-time convergence nonlinear extended state observer with an exponential spiral structure to further improve the observer performance.

[0013] Compared with the prior art, the present invention has the following beneficial effects after adopting the above technical solutions:

[0014] 1. Significantly improve the disturbance observation and compensation accuracy: The two-degree-of-freedom extended state disturbance observer designed by the present invention, combined with the strategy of online adjusting the gain by the fuzzy system, can observe and compensate external disturbances and internal coupling disturbances more accurately. This dynamic adjustment mechanism enables the observer to adapt to the changes of the system state in real time, ensuring the accuracy and robustness of the disturbance estimation, thus significantly improving the control accuracy and stability of the system.

[0015] 2. Enhance the system robustness and adaptability: By introducing a generalized extended state observer, through reconstructing the disturbed system and establishing a generalized model, the system's ability to handle complex disturbances is further improved. This method not only reflects the known components in the disturbance but also enhances the system's adaptability to unknown disturbances, enabling the system to maintain stable suspension performance under various working conditions.

[0016] 3. Realize the dynamic suspension force compensation under overload disturbances: When the disturbance exceeds the bearing capacity of the radial magnetic bearing, the present invention uses SWBSRM (or similar switched reluctance motor) for dynamic suspension force compensation. By accurately calculating and distributing the current in the three-phase windings, the generated suspension force can compensate for the deficiency of the magnetic bearing in real time, ensuring that the system can maintain stable suspension even under extreme working conditions and avoiding the risk of system instability or damage.

[0017] 4. Reduce control chattering and improve control quality: An adaptive neural network sliding mode control strategy is adopted. The switching gain of the sliding mode controller is adjusted by the neural network, enabling the switching gain to be adaptively adjusted according to the changes in disturbances. This method effectively reduces the chattering problem caused by sliding mode control while enhancing the anti-disturbance performance of the system, improving the smoothness and quality of control.

[0018] 5. Improve the overall performance and reliability of the system: By comprehensively applying the above technical solutions, the present invention not only improves the suspension accuracy, dynamic response ability, and robustness of the radial magnetic bearing system but also reduces the maintenance cost and failure rate of the system. At the same time, this technical solution has strong scalability and flexibility, can be customized and optimized according to the requirements of different application scenarios, and provides a new, more efficient, and reliable solution for the field of high-precision suspension control. Description of the Drawings

[0019] Figure 1 It is the equivalent magnetic circuit diagram for suspension, where (a) is the equivalent magnetic circuit diagram of the bias magnetic flux, and (b) is the equivalent magnetic circuit diagram of the control magnetic flux;

[0020] Figure 2 It is the structure diagram of the ESO;

[0021] Figure 3 It is the block diagram of the fuzzy system structure in the FESO;

[0022] Figure 4 It is the control system diagram under the cooperation of the suspension force of the single-winding system;

[0023] Figure 5 It is the diagram of the learning process of the RBF neural network;

[0024] Figure 6 It is the structure diagram of the RBF neural network sliding mode controller;

[0025] Figure 7 It is the schematic diagram of the method for the present invention to resist strong disturbances Detailed Embodiment

[0026] Next, according to the attached drawings of the specification Figure 1-7 The technical solutions of the present invention will be clearly and completely described.

[0027] The present invention proposes an innovative suspension control method for radial magnetic bearings, and the main technical features include:

[0028] 1. Intelligent disturbance observation and compensation: Based on the mathematical model of the radial magnetic bearing, a two-degree-of-freedom extended state disturbance observer is designed to realize the online observation of external disturbances and internal coupling disturbances. The observer gain is adjusted online by the fuzzy system to ensure that the observer always matches the total disturbance, improving the accuracy and robustness of disturbance estimation.

[0029] 2. Design of Generalized Extended State Observer: By reconstructing the total disturbance and introducing the generalized extended state, a generalized extended state observer that reflects the known components in the disturbance is designed. The differential homeomorphism transformation is used to reconstruct the disturbed system, and the generalized models of the original system and the disturbed system are established, further improving the performance of the observer.

[0030] 3. Dynamic Compensation of Suspension Force of SWBSRM: When the observed total disturbance value exceeds the bearing capacity of the radial magnetic bearing, SWBSRM (assumed to be a specifically designed switched reluctance motor or a similar device) is automatically started for dynamic compensation of the suspension force. By accurately calculating and distributing the current in the three-phase windings, the generated suspension force can compensate for the deficiency of the radial magnetic bearing in real time, ensuring the stable suspension of the system.

[0031] 4. Adaptive Neural Network Sliding Mode Control: To further improve the disturbance rejection performance of the system and reduce the chattering problem caused by sliding mode control, this invention introduces a neural network to adjust the switching gain of the traditional sliding mode controller. The switching gain can be adaptively adjusted with the change of the disturbance and always remains above the current disturbance value, achieving a smoother and more stable control effect.

[0032] Step 1, Construction of the Mathematical Model of the Magnetic Bearing and Design of the Extended State Observer.

[0033] First, based on the mathematical model of the radial magnetic bearing, a two-degree-of-freedom extended state disturbance observer is designed to realize the online observation of external disturbances and internal coupling disturbances in each degree of freedom. The specific design is as follows:

[0034] (1) Construction of the Mathematical Model of the Magnetic Bearing

[0035] The magnetic bearing suspension system can provide stable suspension with four degrees of freedom in the radial direction for the rotor through the cooperation between two suspension stators. The stable suspension of the rotor is achieved by the mutual cooperation of the bias magnetic flux and the control magnetic flux. Therefore, the equivalent magnetic circuit of the suspension system can be divided into two parts, namely the equivalent bias magnetic circuit and the equivalent control magnetic circuit, for discussion. The mathematical model of the entire suspension system is established using the equivalent magnetic circuit method.

[0036] The equivalent magnetic circuit diagram of the bias magnetic circuit of the suspension system is as Figure 1 shown.

[0037] Among them, F m is the magnetomotive force of the permanent magnet ring, R m is the magnetic resistance of the permanent magnet ring, Φ m is the total bias magnetic flux, is the sum of the air gap magnetic resistance and leakage magnetic flux in the x and y directions of the front stator, and are the sums of the air gap magnetic resistance and leakage magnetic flux in the x and y directions of the rear stator. is the magnetic flux at the air gaps in the x and y directions of the front stator, and is the magnetic flux at the air gaps in the x and y directions of the rear stator. For the biased magnetic circuit, there are

[0038]

[0039] And the magnetomotive force and reluctance of the permanent magnet material are respectively:

[0040]

[0041] In Equation (2), the magnetized thickness l of the permanent magnet m , the coercivity coefficient H c , μ r is the relative permeability of the permanent magnet, A m is the axial cross-sectional area of the permanent magnet ring, μ 0 is the permeability of vacuum. Due to the characteristics of the permanent magnet, H c = B r / μ 0 . Substituting into the above formula, we can get where B r is the remanence of the permanent magnet.

[0042] When the rotor is stably suspended, the sizes of all working air gaps are equal, all being g 0 . Assume that the rotor is disturbed by the outside world, causing the rotor to shift in the negative x direction, and the shift amount is x 0 . At this time, the reluctances at the working air gaps are respectively:

[0043]

[0044] where S is the effective magnetic flux area of each pole.

[0045] Analyzing the equivalent magnetic circuit diagram, the magnetic circuit equation of the biased magnetic circuit can be obtained as:

[0046] c 1 F m = (R L + R R + R m ) Φ m (4)

[0047] where c 1 is the leakage coefficient, R L and R R Their expressions are as follows:

[0048]

[0049] By solving each magnetic circuit equation, the biased magnetic fluxes at the working air gaps can be obtained as

[0050]

[0051] The equivalent magnetic circuit diagram of the suspension system control magnetic circuit is as shown in Figure 2 Figure.

[0052] The working air gap lengths of the control flux path and the bias flux path are the same. Therefore, the magnetic resistance of the control flux is the same as that of the bias flux.

[0053] Combined with Figure 2 the equivalent magnetic circuit shown in Figure, the equations of the control magnetic circuit at each working air gap in the x direction can be obtained as

[0054]

[0055] where N x is the number of turns of the suspension winding, i x is the control current of the suspension winding, 2N x i x is the magnetomotive force of the suspension current, Φ Lcx is the control flux at the left suspension stator air gap, Φ Rcx is the control flux at the right suspension stator air gap. Then:

[0056]

[0057] At any moment, the suspension force is provided by the cooperation of the bias flux and the control flux. By combining equations (7) and (8), the suspension force F x in the x direction generated by the suspension system can be derived as:

[0058]

[0059] and are the bias magnetic fluxes at each air gap of the left suspension stator, and are the bias magnetic fluxes at each air gap of the right suspension stator, B Lcx is the control magnetic flux density at the left suspension stator air gap, B Rcx are the control magnetic flux densities at the right suspension stator air gap respectively. and are the total magnetic flux densities at each air gap of the left suspension stator, and are the total magnetic flux densities at each air gap of the right suspension stator.

[0060]

[0061] The magnetic induction intensity of the bias flux is

[0062]

[0063] The magnetic induction intensity for controlling the magnetic flux is

[0064]

[0065] Substituting formula (10) into formula (9), we can obtain

[0066]

[0067] Using the Taylor formula to linearly approximate the suspension force F at the equilibrium position in the x direction x , we can obtain

[0068]

[0069] Where k xx is the displacement stiffness coefficient, and k ix is the current stiffness coefficient. The expressions for both are

[0070]

[0071] (2) Design of the extended state observer.

[0072] The extended state refers to new state variables outside the system itself. ADRC (active disturbance rejection control) regards the disturbance quantity as an extended state for observation and control. The core of active disturbance rejection control is the ESO (extended state observer), and the observation accuracy of the ESO determines the quality of the control system. For an n-order system, the schematic diagram of the structure of the ESO is as Figure 2 shown.

[0073] The state expression of an n-order nonlinear system is as follows:

[0074]

[0075] Where x i (i = 1, 2... n) represents the system state variables, g(x 1 , x 2 , …, x n , t) is the internal uncertainty dynamics of the system, ω(t) represents the external disturbance, u(t) represents the input quantity of the control system, and b is the input gain of the controlled object. According to formula (17), the combined disturbance is defined as f = g(x 1 , x 2 , …, x n , t) + ω(t), and the reconstructed system is obtained:

[0076]

[0077] The extended state x n+1 is the combined disturbance quantity. According to formula (18), a nonlinear ESO is designed:

[0078]

[0079] In the formula, fal n (e) is a non - linear function, and β i (i = 1, 2…n) is the observer gain, is the estimated value of the system state.

[0080] Step 2: Use the fuzzy system to adjust the observer gain online.

[0081] Since the disturbances and dynamic characteristics of the system may change during operation, fixed ESO gains may be difficult to adapt to all situations. Therefore, the fuzzy system is used to adjust the observer gain online to always match the total disturbance, improving the observer's estimation performance.

[0082] The following specifically introduces the design idea of the fuzzy extended state observer:

[0083] The non - linear system is as follows:

[0084]

[0085] Among them, n is the order of the system, y is the system output, u is the system input, h(·) is the known system function, ω(t) is the external disturbance, g(·) is the unknown system function, f(t) is the system error, and b is a constant.

[0086] The state - space expression is:

[0087]

[0088] Define the extended state variable Then the new state - space expression is:

[0089]

[0090] Among them, is an unknown bounded function.

[0091] The FESO (fuzzy extended state observer) is designed as follows:

[0092]

[0093] In the formula, e is the system state estimation error, z n (n = 1, 2, ···) is the system estimated value, z n is the state variable, β n is the observer gain, and h(·) is the known system function.

[0094] Select β according to pole - zero configuration 1 , β 2 , …βn+1 Make (s + ω 0 ) n+1 = s n+1 + β 1 s n + β 2 s n-1 + … + β n+1 hold, where ω 0 is the observer bandwidth. The size of the observer bandwidth is closely related to the observer performance. Considering the need to balance between the convergence speed and the peak phenomenon, the observer bandwidth value is generally adjusted manually according to experience. Here, a simple single-input single-output fuzzy system is designed, and using the rules of this fuzzy system, the observer bandwidth of the traditional ESO is intelligently adjusted according to the system state error function.

[0095] Among them, the fuzzy logic system mainly consists of fuzzification, fuzzy inference, defuzzification, and the knowledge base. Fuzzification is to perform fuzzy processing on the input variables of the fuzzy system, convert the crisp quantity into a fuzzy quantity, and represent it with the corresponding fuzzy set. The knowledge base contains the relevant knowledge in the control application field and the control objectives to be achieved, reflecting the empirical knowledge of control experts. Fuzzy inference is to design fuzzy control rules according to the knowledge base and then perform fuzzy logic operations. Defuzzification is to convert the output quantity of the fuzzy inference into a crisp quantity. Since the output quantity obtained through fuzzy inference is a fuzzy quantity and the actual bandwidth value of the observer is a crisp quantity, defuzzification is required.

[0096] Define where x represents the system state, represents the estimated value of the system state, and the system state estimation error is e. The input of the designed fuzzy system is a function of the system state estimation error: where, k 1 , k 2 are the input scaling factors, and the output of the fuzzy system is the observer bandwidth. The input fuzzy sets corresponding to the fuzzy system input are designed as: Negative Large (NL), Negative Medium (NM), Zero (ZO), Positive Medium (PM), Positive Large (PL).

[0097] The fuzzy sets NM, ZO, and PM in the FESO system correspond to Gaussian functions, and the fuzzy sets N and PL correspond to the Z function and the S function respectively. The corresponding output fuzzy sets are designed as: Small (S), Medium (M), Large (L). The output fuzzy sets S and L correspond to the Z function and the S function respectively, and the fuzzy set M corresponds to the Gaussian function.

[0098] To achieve the desired control objectives of the control system, the following five rules are designed based on control experience knowledge for fuzzy inference:

[0099] Rule 1: If is PL, then ω 0 is S;

[0100] Rule 2: If is PM, then ω 0 is M;

[0101] Rule 3: If is ZO, then ω 0 is L;

[0102] Rule 4: If is NM, then ω 0 is M;

[0103] Rule 5: If is NL, then ω 0 is S.

[0104] The above rules describe that when the input of the fuzzy system belongs to the two fuzzy sets of PL and NL, the corresponding fuzzy output observer bandwidth ω 0 belongs to the output fuzzy set S; when the input of the fuzzy system belongs to the two fuzzy sets of PM and NM, the corresponding fuzzy output observer bandwidth ω 0 belongs to the output fuzzy set M; when the input of the fuzzy system belongs to the ZO fuzzy set, the corresponding fuzzy output observer bandwidth ω 0 belongs to the output fuzzy set L, realizing the real-time adjustment of the observer bandwidth ω 0 .

[0105] When the system state estimation error e is large, FESO obtains a smaller observer bandwidth through fuzzy rules, thereby suppressing the peak phenomenon. If f(e) is also large when the system state estimation error e is large and f(e) is small when e is small, then the designed f(e) can reflect the change of the system state estimation error e, so the design of the fuzzy input is reasonable.

[0106] In FESO, by introducing a fuzzy system, the observer bandwidth of the traditional ESO is designed as a variable bandwidth. When the initial estimation error is large, a smaller observer bandwidth value can be obtained through fuzzy rules to weaken the peak phenomenon, so as to obtain a good estimation effect and further reduce the impact of the peak phenomenon on the performance of the control system. FESO provides a mechanism to change the observer bandwidth according to system conditions, and this method can effectively achieve an appropriate balance between the peak phenomenon and the convergence speed.

[0107] Step 3: Design the generalized extended state observer through diffeomorphism transformation

[0108] Introduce the generalized extended state to reconstruct the total disturbance, and design a generalized extended state observer that reflects the known components. The specific method is to use diffeomorphism transformation to reconstruct the disturbed system, establish a generalized model of the internal state of the original system and the state of the disturbed system, and design a generalized nonlinear ESO that reflects the known components in the disturbance to analyze the total disturbance of the system. The specific design idea is as follows:

[0109] Define the nonlinear uncertainty and external disturbance as

[0110]

[0111] Regard the total disturbance as the output function of a single-input single-output affine nonlinear system, and assume the following disturbed system model

[0112]

[0113] where: θ ∈ R m is the state of the disturbed system, θ ∈ R is the input of the disturbed system, is a function related to the external disturbance ω(t) and the system state x, D ∈ R m is the output of the disturbed system, p, q ∈ R m →R m are two smooth vector fields, s ∈ R m →R is a smooth mapping. The relative degree r of the disturbed system = m.

[0114] Define the Lie derivative of the system:

[0115] L p s(θ) = <ds(θ), p(θ)> (26)

[0116] where ds is the gradient of the mapping s(θ), and there is The relative degree of the disturbed system is r, which means that for any θ ∈ R m , there exists: Under this definition, there exists a diffeomorphism mapping: Ψ: R m →R m ,

[0117] Are defined as follows:

[0118]

[0119] L p s(θ) is the system Lie derivative, and r is the relative order of the perturbed system.

[0120] The system can be expressed in the new coordinate system as

[0121]

[0122] Where: ξ 1 , … ξ r are the system perturbation states. Since p, q, and s are known functions and μ is an unknown function, define

[0123] ξ r+1 = b(ξ)μ (29)

[0124] Then

[0125]

[0126] Regarding the perturbed system states ξ 1 , ……, ξ r+1 as the generalized extended states of the system, and denoting the generalized state as The generalized model of the system obtained after reconstruction is:

[0127]

[0128] Where:

[0129]

[0130] Where:

[0131] For the reconstructed system model, design the following generalized ESO:

[0132]

[0133] Where: ε is the adjustable parameter of the ESO, and g i (·) (i = 1, 2, …, n + 1) are nonlinear functions and satisfy x i (t) is the system state, the estimated value of the system state, and e i (t) is the system state estimation error.

[0134] Define:

[0135] The observed error dynamic system of the system can be obtained as

[0136]

[0137] which is the observed error state equation.

[0138] In fact, the generalized ESO makes the observer expansion order higher by using the system after disturbance decoupling, expanding by r + 1 orders, which contains the prior information of time-varying disturbances. When partial disturbance information is known, such as periodic disturbances of a certain frequency, the total disturbance is reconstructed at this time. Based on this, a generalized model of the system is constructed and a generalized nonlinear ESO is designed, which can compensate for the known disturbance components and improve the tracking accuracy.

[0139] Step 4, improvement of the fal function

[0140] In the traditional extended state observer based on the fal function, the fal function is a non-finite-time convergence function, and there is a judgment term in the function, so the calculation time is long. When the value in the fal function is small, the large gain term in the fal function can better make the observer amplify the small error in the system, but amplifying the error is more likely to cause the vulnerability of the observer. At the same time, the relevant design parameters can only be adjusted by experience, which is very cumbersome. Therefore, the Fal function (nonlinear function) in the nonlinear extended state observer is improved, and a fixed-time convergence nonlinear extended state observer is designed by using an exponential spiral structure to further improve the performance of the observer. Specifically:

[0141]

[0142] where a and b are the design parameters of the exponential spiral convergence function, a i1,j1 > 0, b i1,j1 > 0, i 1 = 0, 1; j 1 = 1, 2, 3,...; q 0 > 0; p 0 > 0; q 1 > 0; p 1 > 0; q 0 / p 0 ∈(0, 1); q 1 / p 1 ∈(0, 1). sgn(·) is the sign function, and e 1 is the tracking error of the system

[0143] There is no judgment term in the convergence function of the exponential spiral convergence function, and it is fixed-time convergence. Therefore, in the case of observing large errors and disturbances, it has a faster convergence speed and higher steady-state accuracy.

[0144] The improved model is as follows:

[0145]

[0146] where Z 1 is the observed value of X; B 0 is a constant, and a, b, a 0 , b 0 , a 1 , b 1 are the design parameters of the exponential spiral convergence function, and X is the system state variable.

[0147] Step Five, Dynamic Cut-in Strategy for Levitation Force

[0148] When the total disturbance value observed by the disturbance observer is greater than the radial magnetic bearing load capacity, the SWBSRM levitation force dynamically cuts in. At this time, the difference between the disturbance value and the magnetic bearing load capacity is used as the given value of the SWBSRM levitation system. The specific idea is as follows:

[0149] The total disturbance value F d of the system (including external disturbances and internal unmodeled dynamics) is monitored in real time through a Generalized Extended State Observer (GESO). Define the maximum load capacity F max of the magnetic bearing, and compare the output F d of the disturbance observer with F max in real time.

[0150] When F d > F max , the magnetic bearing cannot completely offset the disturbance. At this time, the SWBSRM levitation system is started to provide additional levitation force:

[0151] F swbsrm = F d - F max (37)

[0152] where: F swbsrm is the compensation force provided by the SWBSRM levitation system. F max is the maximum load capacity of the magnetic bearing.

[0153] The magnetic bearing and the SWBSRM work together to stabilize the rotor position. Among them, the magnetic bearing is responsible for basic levitation, and the SWBSRM dynamically compensates for excessive disturbances. When the disturbance value exceeds the load capacity of the magnetic bearing, the SWBSRM can accurately provide the levitation force for the difference part, thus ensuring the stability of the overall system.

[0154] Since the compensation levitation force value of the SWBSRM (Single-Winding Bearingless Reluctance Motor) is related to the rotor position range, a two-phase rectangular coordinate system is established based on the levitation force directions of two degrees of freedom of the radial magnetic bearing. The coordinate axes are defined as the x-axis and the y-axis. Based on the three-phase stator axes of the single-winding bearingless reluctance motor, a three-phase coordinate system of A, B, and C that is spatially separated by 30° is established. The mapping relationship of the levitation force between the two-phase coordinate system and the three-phase coordinate system is established, and the corresponding phase sequence is selected according to the rotor position of the SWBSRM. The given values of the levitation forces in the x and y directions of freedom are converted into the given values in the three-phase coordinate system according to the coordinate mapping relationship. Based on the given values of the levitation force in the three-phase coordinate system, the current of each winding in the conducting phase is calculated and forms a closed loop with the feedback current. The generated levitation force can simultaneously meet the requirements for compensating the levitation force of two degrees of freedom of the radial magnetic bearing. The specific method is as follows;

[0155] A two-phase rectangular coordinate system is established based on the levitation force directions of two degrees of freedom of the radial magnetic bearing. The coordinate axes are defined as the x-axis and the y-axis. Based on the phase axes of the three-phase stator of the SWBSRM, a three-phase coordinate system of A, B, and C that is spatially separated by 30° is established. Phase A: As the reference phase, the included angle relative to the x-axis is 0°. Phase B: Offset -120° relative to Phase A. Phase C: Offset +120° relative to Phase A.

[0156] To achieve the conversion of the levitation force between the two-phase coordinate system (x, y axes) and the three-phase coordinate system (A, B, C axes), a coordinate transformation matrix is used to convert the levitation forces F x , F y in the x and y directions into the levitation force generated by the three-phase stator current.

[0157] Assume that the three-phase winding currents of the SWBSRM are i A , i B , i C . The components of the resultant force F generated by the three-phase levitation force in the x and y directions can be calculated through the following relationships

[0158]

[0159] where the definition of the mapping matrix T is:

[0160] The inverse mapping is used to convert the required levitation forces in the x and y directions into the current reference values of the three-phase windings of the SWBSRM. Through the inverse matrix T -1 of the mapping matrix T, the following relationship is achieved:

[0161]

[0162] According to the x and y coordinates output by the rotor position detection system, the required levitation forces F x and F yUsing the above mapping relationship, F x and F y are converted into the three-phase current values i A i B i C , dynamically adjusting the current input of the SWBSRM.

[0163] The three-phase current is regulated by the SWBSRM controller to ensure that the levitation force generated by the current precisely matches the required compensation force, maintaining the stable levitation of the rotor.

[0164] In the x 1 degree of freedom, the levitation force set value F x * is obtained by processing the error between the displacement detection value and the set value through the controller. Further, the levitation force set value F x * is collaboratively allocated to the wide-bearing system and the single-winding system. Among them, F Bx * is the set value of the wide-bearing system in the x 1 degree of freedom, and F SW * is the levitation force set value of the single-winding system. And there is

[0165] F x * = F Bx * + (F SW * / cosα) (40)

[0166] where α is the mechanical angle in space between stator A1 of the single-winding system and stator S1 of the wide-bearing system.

[0167] For the x 1 degree of freedom control system of the wide-bearing system, based on the levitation force set value F Bx * , the required winding current is obtained by adopting the direct levitation force control strategy. For the calculation of the winding current of the single-winding system, the classical constant current - constant conduction width control of the single-winding magnetic levitation switched reluctance motor is adopted. The speed error obtains a constant equivalent torque current through the controller, and then the single-winding current is calculated by combining with the levitation current to complete the levitation control of the single-winding system.

[0168] Based on the traditional levitation force modeling method of the single-winding magnetic levitation switched reluctance motor, a levitation force mathematical model of the single-winding system is established

[0169]

[0170] The independent variables of this model include: K 1 (θ), K 2($\theta$) is a function of the rotor position angle $\theta$, and the torque current component $i$ m , $x$ 1 -axis suspension current component $i$ s1 and the $y$-axis suspension current component $i$ s2 . Among them, the relationships between the torque current component and the suspension current components and the actual control current of the single winding are as follows:

[0171]

[0172] Among them, $i$ m为 is the torque current component, $x$ 1 -axis suspension current component is $i$ s1 and the $y$-axis suspension current component is $i$ s2 , is the actual control current of the single winding in the $x$ and $y$ directions.

[0173] From equations (41) and (42), the value of the single-winding control current can be obtained. Due to the cut-in of the suspension force of the single-winding system, a coupled suspension force will be generated in the $y$ 1 -axis. Therefore, the coupled suspension force $F$ cy * is compensated as a disturbance into the wide-bearing $y$ 1 -axis control system, and the direct suspension force control strategy is adopted to obtain the winding current required for this axis.

[0174] Step 7: Design of the neural network magnetic bearing controller

[0175] In order to make the switching gain adaptively change with the change of the disturbance and always be greater than the current disturbance value, while increasing the disturbance rejection performance and reducing the chattering problem caused by the sliding mode, a neural network is further introduced to adjust the switching gain of the traditional sliding mode controller, thus forming an adaptive neural network sliding mode controller. The design steps are as follows:

[0176] Rewrite the magnetic suspension bearing system into a state equation, which can be expressed as:

[0177]

[0178] Among them, $x(t)$ is the system state vector, $u(t)$ is the control input, and $A$, $B$ are the system matrices.

[0179] In the system, the position signal of the rotor is represented by $r$. Under the current-mode control, the state variables are selected. The rotor position is represented by $x$, and the change speed of the rotor displacement is represented by . On the other hand, in the sliding mode control, the state variables are selected. The position error is represented by $e(t)$, regarded as the error between the current position of the rotor and the desired position, and the speed error is represented by Denote it as the error between the rotor displacement change and the expected change speed. Let x r (t) represent the expected position of the rotor, which is the expected speed of the rotor displacement. We can obtain:

[0180]

[0181] When designing the control law, the convergence of the motion is first considered in the sliding mode motion. The curve equation of the sliding mode motion can be regarded as the above switching function. The control function can make the points far from the sliding mode surface return to the sliding mode surface and move along the sliding mode surface. Generally, the choice of the sliding mode surface is relatively fixed, but the reaching law is different. Different reaching methods have different control laws. Taking the exponential reaching law as an example:

[0182]

[0183] where k is the control gain, sgn(s) is the sign function, s is the sliding mode surface, and ε represents the rate of approaching the sliding mode surface s = 0.

[0184] The constant velocity approaching term tracks all position motion points and ensures their reachability when approaching the switching surface. In addition, there is also which is the exponential approaching term. We can get s = s(0)e -kt . It can be seen from the time domain solution that when the motion point is far from the switching surface, its convergence speed is relatively large. When the motion point is close to the switching surface, the convergence speed is also relatively small, but the speed is not zero, but ε because of the existence of the constant velocity approaching term The motion points far from the switching surface can quickly return to the vicinity of the switching surface, and the points close to the switching surface can also return to the switching surface in a finite time.

[0185] The magnetic levitation bearing system can be expressed as:

[0186]

[0187] where b is the known system input coefficient

[0188] According to the above formula, the sliding mode function can be known:

[0189]

[0190] where c is a constant, the current speed of the rotor, which is the expected speed of the rotor displacement, is the second derivative of x(t), is x r (t) second derivative.

[0191] Combining the above two equations, it can be deduced that:

[0192]

[0193] is the current speed of the rotor, c is a constant, x is the desired position of the rotor, b is the known system input coefficient, u is the control input, and ε represents the rate of approaching the sliding mode surface.

[0194] After sorting and simplifying, it can be obtained that:

[0195]

[0196] Since the RBF network consists of three layers, the input layer, the hidden layer, and the output layer. The hidden layer is composed of radial basis functions and contains two variables. The Gaussian basis function is:

[0197]

[0198] In the formula, the output of the hidden layer is denoted as h j ; X represents the input of the network; c j = [c j1 c j2 … c jn is the radial basis center vector of the jth node, and b j is the variance of the radial basis function of the jth node. When training the RBF neural network, some parameters need to be given and initialized first. The steps are as follows:

[0199] (1) Input the parameter X = [x 1 x 2 … x n ;

[0200] (2) Output the vector Y and the output reference vector R (output target vector Y), Y = [y 1 y 2 … y q , R = [r 1 r 2 … r q , and q represents the number of units in the output layer;

[0201] (3) The weight W k = [w k1 w k2 … w kn , k = 1, 2, 3…q;

[0202] (4) For subsequent training updates, initialize the center vector c j = [c j1 c j2 … cjn T , the base width vector B = [b 1 b 2 ... b n T , and the output of the j-th node in the hidden layer can be calculated according to Equation (44).

[0203] The output of the RBF network is:

[0204]

[0205] In the RBF network structure, the weight vector of the network is W = [w 1 w 2 … w m . Among them, the larger the value of b is selected, the larger the width of the Gaussian basis function is, and the better the mapping effect on the input. On the contrary, the mapping effect is poor. In the design process of the RBF network controller, the node center, base vector width, and weight of the hidden layer neurons are crucial. The above parameters are the key to its identification performance. If the selected parameters are inappropriate, it will cause the RBF neural network not to reflect the identification law and will also reduce the network performance.

[0206] Because different layers are very different from each other, even the same learning algorithm will perform differently for different layers. Therefore, in the design, the number of hidden layers, the center points, and the base width vector of the RBF network are generally selected first, and then the weights between the hidden layer and the output layer are determined. Commonly used learning algorithms include self-organizing learning, random selection, gradient descent, etc.

[0207] The performance index function of the RBF network is:

[0208]

[0209] Among them, y m (t) is the output of the radial basis function neural network at the t-th moment, and y(t) is the output of the system to be identified at the t-th moment.

[0210] According to the gradient descent method, the iterative algorithms for the output weights, node centers, and base width parameters are as follows:

[0211]

[0212] bj(t) = bj(t - 1) + ηΔbj + α[bj(t - 1) - bj(t - 2)] (55)

[0213]

[0214] c ji (t) = c ji (t - 1) + ηΔc ji ​​+α[c ji (t - 1)-c ji (t - 2)] (57)

[0215] where the learning rate is η, α is the momentum factor, and its value range is usually between 0 and 1. Since the magnetic levitation system can also be written in the following form:

[0216]

[0217] where x 1 , x 2 represent the rotor position and speed respectively, and u is the control speed.

[0218] Let the position command still be r(t), and the switching function be:

[0219]

[0220] where:

[0221]

[0222] Design the sliding mode controller as the output of the RBF network:

[0223]

[0224] where n is the number of neurons in the hidden layer. The control objective of SMC is Then the RBF network

[0225] The weight adjustment of the network is:

[0226]

[0227] Then:

[0228]

[0229] Then the RBF network weight learning algorithm is:

[0230]

[0231] Take the switching function as the input of the RBF network and the sliding mode controller as the output of the RBF network, and utilize the learning function of the neural network to achieve neural sliding mode control.

[0232] By completing the above steps, the integrated anti-strong interference method of SWBSRM (single-winding magnetic levitation motor)-radial magnetic bearing is realized. When the magnetic bearing is not sufficient to completely compensate for the disturbance, SWBSRM provides the compensation levitation force, thereby enhancing the robustness and stability of the system, enabling the rotor to still operate stably in a high-disturbance environment.

Claims

1. A single-winding magnetic suspension motor SWBSRM-radial magnetic bearing integrated anti-interference method, characterized in that: The control method includes magnetic bearing suspension force control and single winding suspension force control, wherein the magnetic bearing control is the main control and the single winding control is the slave control, and the coordinated control of the two improves the anti-interference performance of the system; the specific process is: Based on the mathematical model of radial magnetic bearings, two-degree-of-freedom extended state disturbance observers are designed to achieve online observation of external disturbances and internal coupling disturbances in each degree of freedom. The observer gain is adjusted online using the fuzzy system to always match the total disturbance, thus improving the observer estimation performance. By reconstructing the total disturbance and introducing the generalized extended state, a generalized extended state observer is designed to reflect the known components in the disturbance. The perturbation system is reconstructed using differential homeomorphism transformation, a generalized model of the internal state of the original system and the state of the perturbation system is established, and a generalized nonlinear extended state observer (ESO) is designed to reflect the known components in the perturbation. The Fal function in the nonlinear extended state observer is improved, and an exponential spiral structure is used to design a fixed-time convergence nonlinear extended state observer to further improve the observer performance.

2. The method according to claim 1, characterized in that: When the total disturbance value observed by the disturbance observer is greater than the radial magnetic bearing capacity, the single-winding magnetic suspension motor SWBSRM suspension force is dynamically cut in. At this time, the difference between the disturbance value and the magnetic bearing capacity is used as the given value of the SWBSRM suspension system.

3. The method according to claim 1, characterized in that: In view of the fact that the SWBSRM compensation suspension force value is related to the rotor position range, a two-phase rectangular coordinate system is established based on the direction of the two-degree-of-freedom suspension force of the radial magnetic bearing. The coordinate axes are defined as the x-axis and the y-axis. The three-phase stator axis of the 12 / 8SWBSRM (12 / 8 single-winding magnetic suspension motor) is used as the reference to establish a three-phase coordinate system A, B, and C separated by 30° in space, and the mapping relationship between the suspension force between the two-phase coordinate system and the three-phase coordinate system is established.

4. The method according to claim 1, characterized in that: The corresponding phase sequence is selected by the SWBSRM rotor position, and the given values ​​of the suspension force in the x and y directions are converted into given values ​​in the three-phase coordinate system according to the coordinate mapping relationship. The current of each winding in the conduction phase is calculated based on the given value of the suspension force in the three-phase coordinate system, and a closed loop is formed with the feedback current. The generated suspension force can simultaneously meet the requirements of suspension force compensation for the two degrees of freedom of the radial magnetic bearing.

5. The method according to claim 1, characterized in that: A neural network is introduced to adjust the switching gain of the sliding mode controller, so that the switching gain changes adaptively with the change of disturbance and is always greater than the current disturbance value. This increases the anti-disturbance performance while reducing the jitter problem caused by the sliding mode, forming an adaptive neural network sliding mode controller.

6. The method according to claim 1, characterized in that: When the magnetic bearings are not sufficient to fully compensate for the disturbance, the SWBSRM provides compensating suspension force, thereby enhancing the robustness and stability of the system, allowing the rotor to still operate stably in a high disturbance environment.

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