Torque system and suspension system decoupling method of single-winding magnetic suspension permanent magnet synchronous motor

Abstract

The invention discloses a torque system and suspension system decoupling method of a single-winding magnetic suspension permanent magnet synchronous motor, the motor adopts a suspension parallel single-winding structure, the torque system decouples suspension current, permanent magnets adopt consequent poles, and the suspension system decouples a rotor position angle; aiming at a current loop of the suspension system, regarding a coupling item of a torque system to the suspension system as disturbance, designing a sliding mode disturbance observer based on an improved superhelix algorithm, observing and compensating the disturbance, and realizing decoupling of the suspension system and torque control; aiming at the displacement / suspension force ring of the suspension system, designing a sliding-mode active-disturbance-rejection controller, observing the disturbance of the rotor displacement and compensating the suspension force to realize decoupling among different suspension degrees of freedom; the residual coupling factors of the torque system are regarded as system disturbance, and the disturbance is observed and compensated in real time by using a sliding mode-active disturbance rejection composite control method, so that decoupling of the residual coupling factors is realized. According to the invention, comprehensive decoupling of the torque system and the suspension system is realized.

Description

Technical Field

[0001] The present invention relates to the field of motor body design and control technology, and in particular to a decoupling method between a torque system and a suspension system of a single-winding magnetic levitation permanent magnet synchronous motor. The method achieves complete decoupling of various coupling variables in the motor system through topological design and control methods. Background Art

[0002] Magnetic levitation permanent magnet synchronous motors are widely used in high-speed rotating machinery, vacuum environments and special environments because they can achieve frictionless suspension of the rotor without the need for mechanical bearings. However, the traditional single-winding magnetic levitation permanent magnet synchronous motor has a coupling problem between the torque system and the suspension system. This coupling complicates the design of the control system and affects the performance and stability of the motor.

[0003] Existing decoupling methods usually improve the control strategy by adding complex decoupling algorithms to reduce the mutual influence between torque and suspension system. However, these methods often rely on complex models and control algorithms, making it difficult to achieve ideal results in practical applications. In addition, although some methods can achieve a certain degree of decoupling, they do not fully consider the system coupling problem in the design of the motor topology, resulting in unsatisfactory decoupling effect. Summary of the invention

[0004] In view of the shortcomings in the prior art, the present invention provides a method for decoupling the torque system and suspension system of a single-winding magnetic levitation permanent magnet synchronous motor. By optimizing the topological structure and control strategy of the motor, comprehensive decoupling of the torque system and suspension system in the single-winding magnetic levitation permanent magnet synchronous motor is achieved.

[0005] The present invention achieves the above technical objectives through the following technical means.

[0006] Decoupling method of torque system and suspension system of single-winding magnetic suspension permanent magnet synchronous motor:

[0007] The motor adopts a suspended parallel single winding structure to achieve decoupling of the torque system from the suspension current;

[0008] The permanent magnet adopts an alternating pole design to achieve decoupling of the suspension system from the rotor position angle;

[0009] In the current loop of the suspension system, the voltage at the torque inverter terminal is regarded as a disturbance term, and together with other disturbance factors affecting the suspension current control, it is regarded as a system disturbance. A sliding mode disturbance observer is designed to observe the disturbance in real time and compensate the suspension current to achieve decoupling of the suspension current control from the torque system.

[0010] In the displacement / suspension force loop of the suspension system, the coupling between different suspension degrees of freedom and other displacement disturbances are regarded as system disturbances. A sliding mode anti-disturbance controller is designed to observe and compensate the suspension force to achieve control decoupling between different suspension degrees of freedom.

[0011] The internal disturbances unknown in the mathematical model of the torque control system and the external disturbances caused by the external environment and operating conditions are regarded as disturbances that affect the stable operation of the motor torque system. The sliding mode-auto-disturbance rejection composite control method is used to observe and compensate for the disturbances in real time to achieve high-performance and highly robust torque system control.

[0012] Furthermore, the motor adopts a suspended parallel single winding structure to achieve decoupling of the suspension current by the torque system, specifically: each phase torque winding is connected in series, and the torque inverter only provides a three-phase torque current i mA 、i mB 、i mC , the suspension inverter provides suspension current i s and where i s Including three-phase suspension current i sA 、i sB 、i sC , the i sA 、i sB 、i sC The torque is injected from the midpoint of each phase winding. Connects to the torque inverter and injects torque into the winding.

[0013] Furthermore, the permanent magnet adopts an alternating pole design, specifically: the permanent magnet adopts a surface insertion type, and the number of permanent magnet pole pairs is ≥4; the magnetization direction of the permanent magnet is arranged with the same polarity along the rotor surface, and the rotor core part adjacent to the permanent magnet is magnetized to the opposite polarity.

[0014] Furthermore, in the sliding mode disturbance observer, the designed linear sliding mode surface s is: Among them, e ix is the suspension current observation error, i sx is the actual suspension current generated by the motor in the x-axis direction, is the estimated suspension current in the x-axis direction.

[0015] Furthermore, in the sliding mode disturbance observer, the sliding mode reaching law of the improved super spiral algorithm is: Among them, k1 and k2 are superhelical sliding mode gains, v is the state variable, ρ1 and ρ2 are external disturbances, t is time, λ is the exponential power term gain, and α is a constant.

[0016] Furthermore, the perturbation observation error e diConsidered as a disturbance term, the control law of the sliding mode disturbance observer based on the improved super-helical algorithm is:

[0017] Furthermore, the sliding mode active disturbance rejection controller is:

[0018]

[0019] Among them, the sliding surface s = c2e x1 +e x2 , the intermediate quantity e x1 =x1-z x1 、e x2 =x2-z x2 , z x1 、z x2 、z x3 is the output of the sliding mode disturbance observer of the displacement / suspension force loop, k3, λ1, c2 are constants greater than 0, u f0 (t) is the feedback control law of the sliding mode active disturbance rejection controller, is disturbance compensation, b1 is system parameter, and f0 represents disturbance.

[0020] Furthermore, the feedback control law of the sliding mode ADRC satisfies:

[0021]

[0022] Among them, the intermediate x is the displacement of the motor rotor in the positive direction of the x-axis, and the coefficient k ecc It is related to the air gap magnetic field characteristics and air gap magnetic permeability, and m is the rotor mass.

[0023] Furthermore, the sliding mode-ADR composite control method is specifically as follows: Assume that the sliding mode control surface s = e ω , select parameter k4, use the sliding mode control design method to design the sliding mode active disturbance rejection controller of the speed loop:

[0024]

[0025] Among them, e ω is the speed error, is the control law of the speed loop, is the first-order derivative of the state variable z1.

[0026] Furthermore, the extended state observer is used to compensate the reference torque current calculated by the sliding mode anti-disturbance controller of the speed loop. The compensated current command i q * for:

[0027]

[0028] Among them, b2 is the system control gain, z2 is the state variable, The tracking signal ω represents the given speed v1 The derivative with respect to time.

[0029] Compared with the prior art, the present invention has the following beneficial effects after adopting the above technical solution:

[0030] 1. Effectively decouple the torque and suspension systems: The present invention effectively decouples the torque system from the suspension system by designing a suspended parallel single winding structure and adopting an alternating-pole permanent magnet design, thereby solving the problem of mutual interference between torque control and suspension control in traditional magnetic levitation permanent magnet synchronous motors, simplifying system design, and improving control effects.

[0031] 2. Improve system stability and control accuracy: The present invention uses a sliding mode observer and a sliding mode anti-disturbance controller based on an improved superhelix algorithm to observe and compensate for disturbances in the system in real time, further enhancing the stability and anti-disturbance capability of the system and improving the accuracy of the suspension system and torque control.

[0032] 3. Simplified suspension control system: By decoupling the suspension system from the rotor position angle, the design of the suspension control system is simplified, making the control more intuitive and easy to implement, which helps to improve the reliability and response speed of the motor in practical applications.

[0033] 4. Enhance the robustness of the control system: The present invention designs a highly robust torque operation control strategy that can cope with the remaining coupling factors in the torque system, achieve comprehensive decoupling of torque control, ensure that the system can still operate stably under complex working conditions, and have good robustness.

[0034] 5. Adaptable to various application environments: Since the topology-control collaborative decoupling method of the present invention can achieve efficient torque and suspension decoupling, it is particularly suitable for application in high-speed rotating machinery, vacuum environments and other special environments with high requirements on precision and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a schematic diagram of the structure of the alternating-pole magnetic suspension permanent magnet synchronous motor of the present invention;

[0036] FIG2( a ) is a schematic diagram showing the principle of generating levitation force of an alternating-pole magnetic levitation permanent magnet synchronous motor when the rotation angle is 0° in the present invention;

[0037] FIG2( b ) is a schematic diagram showing the principle of generating levitation force of the alternating-pole magnetic levitation permanent magnet synchronous motor when the rotation angle is 45° in the present invention;

[0038] FIG2( c ) is a finite element magnetic flux density simulation diagram of the present invention when the rotation angle is 0°;

[0039] FIG2( d ) is a finite element magnetic flux density simulation diagram of the present invention when the rotation angle is 45°;

[0040] Figure 3 This is the single winding topology diagram of the present invention;

[0041] Figure 4 The air gap magnetic permeability distribution diagram of the present invention;

[0042] Figure 5 This is a control block diagram of the suspension system based on sliding mode active disturbance rejection according to the present invention;

[0043] Figure 6 This is a structural block diagram of the sliding mode disturbance observer of the suspension current loop of the present invention;

[0044] Figure 7 This is a structural block diagram of the displacement loop sliding mode observer of the present invention;

[0045] Figure 8 This is a block diagram of the speed auto-disturbance rejection control based on magnetic field orientation according to the present invention;

[0046] Fig. 9 This is a block diagram of the principle of the speed loop sliding mode auto-disturbance rejection control of the present invention;

[0047] Fig.10 The present invention is a flowchart of a method for decoupling a torque system and a suspension system of a single-winding magnetically suspended permanent magnet synchronous motor. DETAILED DESCRIPTION

[0048] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0049] like Fig.10 As shown, the method for decoupling the torque system and suspension system of the single-winding magnetic suspension permanent magnet synchronous motor of the present invention is as follows:

[0050] In terms of topological design, the present invention proposes a suspended parallel single winding structure, so that when the suspension force changes within a certain range, the torque control decouples the suspension current. The motor permanent magnet adopts an alternating pole design, and the structural characteristics of the alternating pole permanent magnet synchronous motor are utilized to realize the decoupling of the suspension system from the rotor position angle, thereby simplifying the control of the suspension system.

[0051] In terms of control strategy, for the current loop of the suspension system, the present invention regards the coupling term of the torque system to the suspension system as a disturbance, and observes and compensates for the disturbance in real time by designing a sliding mode disturbance observer based on the improved superhelix algorithm, thereby realizing the decoupling of the motor suspension system and torque control. For the displacement / suspension force loop of the suspension system, the present invention designs a sliding mode anti-disturbance control controller, which realizes the control decoupling between different suspension degrees of freedom by observing the disturbance of the rotor displacement and compensating the suspension force in real time. The remaining coupling factors of the torque system are regarded as system disturbances, and the sliding mode-anti-disturbance control composite method is used to observe and compensate for the disturbance in real time, thereby realizing high-performance and strong robustness torque system control and decoupling of the remaining coupling factors.

[0052] The specific contents include the following:

[0053] (1) The design prototype is a 48-slot, 8-pole alternating-pole permanent magnet synchronous motor. The cross-sectional diagram of the alternating-pole permanent magnet synchronous motor structure is shown in Figure 2. Figure 1 The stator part is the same as the traditional permanent magnet synchronous motor. The permanent magnets in the rotor are surface-inserted. The magnetization direction of the permanent magnets is arranged with the same polarity along the rotor surface, and the rotor core part adjacent to the permanent magnets is magnetized to the opposite polarity. The magnetized part is called the "iron pole".

[0054] Since the magnetic permeability of the rotor core is much greater than that of the permanent magnet, the magnetic flux generated by the stator winding almost entirely passes through the rotor core, and the bias magnetic field of the rotor's suspension force is actually a unipolar magnetic field in the "iron pole". To obtain a stable and controllable suspension force, the pole pair number p of the suspension winding should be s is 1, and the torque winding pole pair number no longer has to follow p s =p m ±1 relationship.

[0055] Figure 2(a) and (b) illustrate the principle of the levitation force generated by the alternating pole magnetic levitation permanent magnet synchronous motor. The air gap magnetic field of the alternating pole magnetic levitation permanent magnet synchronous motor is the superposition of the magnetic fields excited by the permanent magnet, torque current and levitation current. The thin dotted lines in Figure 2(a) and Figure 2(b) represent the magnetic field flux generated by the permanent magnet, and the dotted lines represent the levitation winding N y The magnetic field flux generated. In one electrical cycle, when the rotor rotates to different positions, the magnetic field generated by the suspension winding and the magnetic field generated by the permanent magnet are superimposed, the magnetic flux density at air gap 1 increases, and the magnetic flux density at air gap 2 decreases, generating a radial force along the positive direction of the y-axis; when a reverse current is passed, a radial force along the negative direction of the y-axis is generated. The principle of generating radial force in the x-axis direction is similar to that of the y-axis.

[0056] Let p m is the number of permanent magnet pole pairs (i.e. the number of torque winding pole pairs), A p , A sare the magnetomotive force generated by the permanent magnet and the suspension winding, G is the air gap length, r is the average radius of the air gap, l is the rotor core length, μ0 is the vacuum permeability, θ m is the pole arc angle of the permanent magnet in each pair of poles (including the permanent magnet and the rotor core on one side), with a value range of (0, 2π), and there are the permanent magnet pole arc angle and the iron pole pole arc angle in each pair of poles (θ i ) is 2π / p m When p m When ≥4, the expression of the rotor suspension force can be written as:

[0057]

[0058] It can be seen from equation (1) that the suspension force F is independent of the rotor position angle and the rotating magnetic field excited by the torque current. Finite element simulation is performed on Figure 2(a) and (b), and the magnetic density cloud diagrams obtained are shown in Figure 2(c) and (d). When the rotor position is at different angles, the suspension winding can generate a controllable and stable suspension force.

[0059] (2) Alternating pole magnetic suspension permanent magnet synchronous motor single winding topology Figure 3 The motor torque inverter only provides three-phase torque current i mA 、i mB 、i mC , each phase torque winding of the motor is connected in series, similar to a dual-winding motor; the suspension inverter provides a suspension current i s (including three-phase suspension current i sA 、i sB 、i sC )and where i sA 、i sB 、i sC Injected from the midpoint of each phase torque winding, Connects to the torque inverter and injects torque into the winding.

[0060] From the perspective of the suspension inverter, each phase torque winding is divided into two parallel coil groups, and the suspension current flows in opposite directions in the coil groups. Taking the A phase winding as an example, the currents in the two coil groups are:

[0061]

[0062] The different current excitations in the two coil groups break the air gap magnetic field balance and generate radial force. sx 、i sy The levitation current required to generate the levitation force in the x direction or y direction is adjusted. sx 、i sy Generate different F x 、F y, we can get any required radial force vector F. The three-phase suspension current can be converted by formula (3), where: is the initial position angle of the A-phase suspension current space vector.

[0063]

[0064] Take phase A as an example. Figure 3 , assuming the torque inverter terminal voltage v m , suspension inverter terminal voltage v s , the voltages of the two coil groups of the A phase winding are v1 and v2, R is the resistance of the coil group, L is the self-inductance of the coil group, M is the mutual inductance between the coil groups A1 and A2, i m is the torque current, ω is the rotor electrical angular velocity, Ψ is the magnetic flux in a coil group, and:

[0065]

[0066] Torque inverter end v m and the voltage v at the suspended inverter end s They can be written as:

[0067] v m =v1+v2

[0068]

[0069] Equations (6) and (7) show that the voltage at the motor winding suspension inverter terminal is coupled with the voltage at the torque inverter terminal. The control of the suspension inverter terminal should consider torque decoupling. The torque inverter terminal voltage is decoupled from the suspension inverter terminal, and the torque control system is not affected by the suspension control.

[0070] (3) According to the characteristics of the suspended parallel single winding structure of the designed motor, the mathematical model of the motor is analyzed and established, and the following assumptions are made first:

[0071] ① The magnetic permeability of the magnetic material is infinite, and the magnetic flux all passes through the air gap radially;

[0072] ② The air gap magnetomotive force is sinusoidally distributed, and higher harmonics are ignored;

[0073] ③ Ignore magnetic saturation;

[0074] ④ Ignore eddy current, friction and other losses;

[0075] ⑤The stator surface is smooth, the slot effect is ignored, and the winding end effect is ignored.

[0076] 1) Suspension motion model of alternating-pole magnetic suspension permanent magnet synchronous motor

[0077] The air gap magnetic field of the alternating pole magnetic suspension permanent magnet synchronous motor is mainly generated by three excitations: permanent magnet, torque current and suspension current. Assume that the torque current is i m , the suspension current is i s The magnetomotive force of the magnetic field generated by the three excitations is A f , A m , A s , the magnetic flux density is recorded as B f , B m , B s Then the air gap magnetic field magnetomotive force of the motor can be expressed as:

[0078] A(φ,t)=A f +A m cos(p m φ-p m ωt-μ)+A s cos(φ-λ)(8)

[0079] Among them, φ is the stator spatial position, ωt is the rotor position angle, μ is the angle between the rotating magnetic motive force and the A-phase winding current, and λ is the angle between the suspension magnetic motive force and the A-phase winding current. In order to make the alternating-pole magnetic suspension permanent magnet synchronous motor produce a stable suspension force, the suspension current is set to DC, so A s Does not include the ωt term.

[0080] Based on the structure of the alternating-pole magnetic levitation permanent magnet synchronous motor, its air gap permeance per unit area is:

[0081]

[0082] Considering the air gap eccentricity, the air gap permeance per unit area is written as:

[0083] Λ(φ,ωt,θ r )=μ0G -1 (φ,ωt,θ r )(10)

[0084] Among them, θ r is the rotor electrical angle.

[0085] Based on the structure of the alternating pole magnetic levitation permanent magnet synchronous motor, the magnetic flux densities of its torque magnetic field and suspension magnetic field are:

[0086]

[0087] B m and B s The fundamental amplitudes are:

[0088]

[0089] Among them, Imm ,I sm are the torque current winding amplitude and the suspension current winding amplitude, k m , k s are the fundamental wave winding coefficients of the torque winding and the suspension winding respectively, and N is the number of series turns of each phase of the winding.

[0090] The application of Maxwell tensor method can obtain the radial suspension force per unit area on the rotor surface:

[0091]

[0092] Among them, B n For B m and B s Resultant magnetic flux, S is the rotor surface area, and B is the air gap magnetic flux of the motor.

[0093] The components of the radial suspension force on the rotor in the positive directions of the x-axis and y-axis are:

[0094]

[0095] Figure 4 The air gap permeance distribution diagram of the alternating pole magnetic levitation permanent magnet synchronous motor on the stator circumference is given.

[0096] Depend on Figure 4 , write the air gap permeability P(φ) of the motor on the stator circumference into a piecewise function form:

[0097]

[0098] Where G is the length of the air gap at the core, θ m is the pole arc of the permanent magnet in one electrical cycle, h m is the thickness of the permanent magnet, μ rPM is the relative magnetic permeability of the permanent magnet, k = 1, 2, 3...p m .

[0099] The air gap flux density expression of the alternating pole magnetic levitation motor is:

[0100] B(φ)=A(φ)p(φ)(16)

[0101] Substituting equations (15) and (16) into equation (14), integrating φ and accumulating, we can obtain:

[0102]

[0103] Since it is assumed that the magnetic material has infinite permeability and the magnetic flux all passes through the air gap radially, it can be seen that the magnetic lines of force basically all enter and exit the core surface vertically, so the second term of the above two equations can be ignored. m=4, suspension winding pole pair number p s =1, we can get:

[0104]

[0105] From equation (19), it can be seen that the suspension force is independent of the motor rotor position angle ωt. When the angles between the torque current magnetic field, the suspension current magnetic field vector and the A phase are all 0 (i.e., μ = 0, λ = 0), the suspension force in the x-axis direction can be simplified as:

[0106]

[0107] In equation (20), the air gap magnetic field generated by the suspension current and the torque current is coupled. The torque current is decomposed into i md 、i mq .i md The magnetomotive force generated by the magnetic field and the magnetomotive force generated by the permanent magnet are combined to form A F ,i mq The generated rotating magnetic field magnetomotive force is A q , rewrite formula (8) as:

[0108] A(φ,t)=A F +A q sin(p m φ-p m ωt-μ)+A s cos(φ-λ)(21)

[0109] Therefore, formula (19) can be rewritten as:

[0110]

[0111] When μ or λ is zero, F x Only the first term on the right side of the equal sign exists. When λ=0 or μ=λ=0, the suspension force is written as:

[0112]

[0113] If a suspension current i is applied that only generates a suspension force in the y direction y , we can get:

[0114]

[0115] In addition to the controllable suspension force generated by the suspension current, the motor suspension force also includes the unilateral magnetic pull caused by the imbalance of the air gap magnetic field caused by the air gap eccentricity. Taking into account the influence of the air gap eccentricity on the suspension force in the x-axis direction, it can be written as:

[0116]

[0117] Where x is the projection of the rotor eccentricity in the x-axis direction, and the coefficient k is ecc It is related to the air gap magnetic field characteristics and air gap permeance. When the motor parameters are constant, the external excitation is given, and the air gap permeance Fourier expansion takes a certain number of terms, the coefficient is a constant. In addition, the air gap permeance is related to the rotor eccentricity type. Formula (15) gives the dynamic eccentricity. When the rotor is statically eccentric, vibrating eccentric, mixed eccentric, etc., the coefficient k ecc They are all different and the expressions are relatively complicated. The coefficient can be obtained through finite element simulation or experimental testing according to the actual situation of the prototype.

[0118] Therefore, the radial suspension force on the rotor can be written as:

[0119]

[0120] Among them, k s is the motor current stiffness coefficient, which is a quantity related to the motor structure.

[0121] Based on formula (26), the suspension motion model of the alternating-pole magnetic suspension permanent magnet synchronous motor is:

[0122]

[0123] Where m is the rotor mass, F zx 、F zy are the external radial loads in the x and y directions, respectively, sx 、F sy is the Maxwell force which is proportional to the eccentric displacement.

[0124] The suspension motion model of formula (27) is derived based on the structural characteristics of the motor body. If the power electronic devices, namely the torque inverter and the suspension inverter, are considered, then combined with formula (7), it can be seen that the suspension current equation of the motor includes both the suspension inverter terminal voltage v s , also includes the torque inverter terminal voltage v m , substituting equations (6) and (7) into the suspension force equation (equation (26)), equation (27) can be written as:

[0125]

[0126] It can be seen that there is a torque-current coupling term in the motor suspension control, and the coupling factors also include the rotor eccentric displacement and external disturbance force.

[0127] 2) Torque mathematical model of alternating-pole magnetic levitation permanent magnet synchronous motor

[0128] a. Voltage equation

[0129] Analyzing the motor torque performance, ignoring magnetic saturation, eddy current loss, and hysteresis loss, the three-phase voltage of the torque inverter can be written as:

[0130]

[0131] In the formula, R s is the stator winding resistance, Ψ mA is the flux linkage of the air gap magnetic field excited by the A-phase stator current, Ψ mB is the flux linkage of the air gap magnetic field excited by the B-phase stator current, Ψ mC is the flux linkage of the air gap magnetic field excited by the C-phase stator current.

[0132] Using the dq axis mathematical model to analyze the motor, the voltage equation of the torque inverter can be written as:

[0133]

[0134] In the formula, Ψ md ,Ψ mq are the stator flux of d and q axes respectively, i md 、i mq They are the d-axis and q-axis components of the torque current, u d 、u q is the stator voltage in the rotating coordinate system.

[0135] b. Magnetic flux equation

[0136] The air gap magnetic field flux generated by the three-phase torque current is:

[0137]

[0138] In the formula, Ψ f is the flux generated by the permanent magnet, L AA is the self-inductance of phase A, L AB is the mutual inductance of A relative to B, L AC is the mutual inductance of A relative to C, L BA is the mutual inductance of B relative to A, L BB is the self-inductance of phase B, L BC is the mutual inductance of B relative to C, L CA is the mutual inductance of C relative to A, L CB is the mutual inductance of C relative to B, L CC It is the self-inductance of phase C.

[0139] In the rotating coordinate system, the torque flux equation can be written as:

[0140]

[0141] Where, L md , L mq is the excitation inductance of the d and q axis coils, if is the equivalent excitation current of the permanent magnet, which can be regarded as a constant without considering the influence of temperature on the performance of the permanent magnet.

[0142] c. Torque equation

[0143] Assuming that the air gap magnetic field flux excited by the torque current and the air gap magnetic field generated by the permanent magnet have a spatial angle of β, the electromagnetic torque of the motor can be written as:

[0144]

[0145] Where, T em is the electromagnetic torque, L d , L q is the inductance component of the d and q axes; the second item in the brackets is the reluctance torque caused by the rotor salient poles.

[0146] d. Equations of motion

[0147] Note that the motor load torque T L , moment of inertia J, friction coefficient K, the mechanical motion equation of the motor is:

[0148]

[0149] In the formula, is the mechanical angular velocity of the motor.

[0150] The establishment of the motor mathematical model provides a basis for the study of motor control systems.

[0151] (4) Analysis of coupling characteristics of alternating-pole magnetic levitation permanent magnet synchronous motor.

[0152] The analysis of the topological design, operating principle and mathematical model of the alternating pole magnetic suspension permanent magnet synchronous motor shows that from the topological structure of the motor body, the suspension system of the motor and the rotor position angle θ e Decoupling, suspension current i s The current i that produces torque mq Decoupling; The alternating-pole magnetic suspension permanent magnet synchronous motor requires a torque inverter and a suspension inverter to drive the torque and suspension operation of the motor respectively. From the torque inverter end, the torque system is decoupled from the suspension current i s , but from the suspension inverter end, the suspension system includes the torque inverter end voltage v m From the suspension force motion model of the alternating-pole magnetic suspension permanent magnet synchronous motor, it can be seen that there is no coupling between the radial suspension forces in the x and y directions in theory. However, in fact, due to the existence of air gap magnetic field harmonics and other reasons, there is a certain coupling between the suspension forces of these two suspension degrees of freedom. sx When i sxIncrease and increase.

[0153] The topology of the alternating-pole magnetic levitation permanent magnet synchronous motor determines that this problem is not easy to be solved by optimizing the winding structure. The suspension force / current F of two different suspension degrees of freedom can be controlled by a suitable control method. x and i sy 、F y and i sx Decoupling between them.

[0154] (5) Research on suspension system control strategy.

[0155] In order to achieve complete decoupling of the suspension system and the torque system, the present invention proposes a decoupling control based on a sliding mode disturbance observer. m As a disturbance term, it is combined with other factors affecting the suspension current i s The disturbance factors of the control are taken as system disturbances, and a sliding mode disturbance observer is designed to observe the disturbances in real time and compensate them to the given signal i of the suspension current. * s middle.

[0156] In order to suppress the inherent chattering problem of sliding mode, the suspension current sliding mode observer adopts and improves the super-twisting algorithm (STW) to improve the accuracy and response speed of disturbance observation. In the displacement / suspension force loop, the coupling between different suspension degrees of freedom and other displacement disturbances are regarded as system disturbances, and a sliding mode anti-disturbance controller is designed for observation, compensation is performed at the given suspension force, and the sliding mode variable structure approach rate is used to improve the nonlinear characteristic function in the nonlinear state error feedback law.

[0157] The control structure block diagram of the suspension system of the alternating-pole magnetic suspension permanent magnet synchronous motor is as follows: Figure 5 In the figure, x * ,y * Indicates the desired position of the motor rotor in the x-axis and y-axis directions, which is used to define the target position of the suspension system; represents the reference suspension force in the x-axis and y-axis directions calculated by the sliding mode ADRC, yes Compensated suspension force; is the reference current, which is the current signal obtained by converting the suspension force control signal through the proportional coefficient F / i; They are The current signal after compensation; i sx 、i sy is the actual suspension current generated by the motor in the x-axis and y-axis directions; is the estimated suspension current in the x-axis and y-axis directions; is the output of the sliding mode disturbance observer; is the reference suspension voltage, and these two signals are the adjustment results of the suspension current obtained after calculation by the PID controller; v sx 、v sy is the actual suspension voltage.

[0158] 1) Design of torque-voltage decoupling strategy for suspension system.

[0159] The suspension control system of the alternating-pole magnetic suspension permanent magnet synchronous motor is a double closed-loop structure of current loop and displacement / suspension force loop. s The torque inverter terminal voltage v m In engineering, these disturbances can be regarded as bounded noise, and a sliding mode disturbance observer is designed to observe the disturbance. In this way, the torque voltage coupling that originally needs to be measured online can be obtained by the observer, and its influence can be compensated to i sx * 、i sy * In this paper, the decoupling of the suspension current control from the torque system is realized.

[0160] According to the analysis of the suspension motion model, the voltage relationship (7) at the suspension inverter end is rewritten as (35):

[0161]

[0162] In the formula, v sx 、v sy are the suspension voltages in the x and y directions, v mx 、v my They are the torque voltages in the x and y directions respectively.

[0163] The torque inverter terminal voltage v m is regarded as a known disturbance of the system, and together with other disturbances affecting the suspension current, is regarded as the total disturbance of the suspension current control link, set as d i . With the suspension current i x As an example, the suspension current and disturbance are taken as state variables, and the suspension inverter terminal voltage v s As the system input, equation (35) is written as follows:

[0164]

[0165] In the formula, f i is the disturbance change rate.

[0166] Taking the suspension current and disturbance as observation objects, let u0 be the designed sliding mode control law, g be the observation gain, and the superscript “^” indicates that the quantity is an observation value. The designed current sliding mode observer can be expressed as:

[0167]

[0168] Assume that the suspension current observation error and disturbance observation error are as follows:

[0169]

[0170] In the formula, e ix is the suspension current observation error, e di is the disturbance observation error.

[0171] Then, by combining equations (36) and (37), we can obtain the current sliding mode observer error:

[0172]

[0173] The designed linear sliding surface is:

[0174]

[0175] The sliding mode observer is highly robust and easy to implement, but it has a chattering problem. The integrator in the high-order sliding mode of the superhelical algorithm can smooth the discontinuous signal, improve the dynamic performance of the system, and effectively suppress chattering. Therefore, in order to suppress the chattering of the sliding mode system and improve the observation accuracy, the sliding mode convergence rate based on the superhelical algorithm is used to make the state trajectory converge to the sliding mode surface. The general form of the sliding mode convergence law of the superhelical algorithm is shown in formula (41):

[0176]

[0177] In order to further suppress the system chattering, the approach rate is improved and the power function of the system switching surface is introduced, so that the approach rate of the moving point on the sliding surface can be adaptively increased or decreased as the system state variable is closer to the sliding mode switching surface. The sliding mode approach law of the improved super spiral algorithm is as follows:

[0178]

[0179] In the formula, k1 and k2 are superhelical sliding mode gains, and k1 and k2>0; s is the sliding surface, v is the state variable, ρ1 and ρ2 are external disturbances, and t is time; λ>0, which is the exponential power term gain; 0<α<1 / 2.

[0180] The perturbation observation error e di Considered as a disturbance term, the control law of the sliding mode disturbance observer based on the improved super-helical algorithm is:

[0181]

[0182] The structural block diagram of the suspension current sliding mode disturbance observer based on the improved super-helical algorithm is as follows: Figure 6 In the figure For a given suspension

[0183] flow, To observe the suspension current, e is is the suspension current error.

[0184] 2) Design of two-degree-of-freedom decoupling strategy for suspension system.

[0185] The alternating-pole magnetic suspension permanent magnet synchronous motor is a complex nonlinear system. The suspension force F in the x and y directions is x 、F y There is actual coupling between the two, and it is not easy to establish an accurate mathematical model; the motor speed regulation range is wide, and there are many position disturbance factors that affect the suspension performance, making it difficult for traditional control methods to achieve good results. The use of ADRC technology can regard the known and unknown coupling factors of the system as "total disturbance", and use the disturbance observer to observe. According to the system input, output information and observed disturbance information, the given quantity is compensated in real time to achieve strong robust decoupling control. At the same time, in view of the situation where there are many adjustable parameters and difficult setting in ADRC, the advantages of sliding mode variable structure control technology are combined. In the displacement / suspension force control link of the suspension control system, the sliding mode control technology is introduced into the disturbance observer and ADRC controller design, so that the adjustable parameters of the controller can smoothly transition when switching, reduce the system error, and improve the anti-disturbance capability of the system.

[0186] a. Design of displacement ring transition link

[0187] In order to avoid the contradiction between overshoot and rapidity of the control system, a "transition process" needs to be arranged according to the control target so that the actual behavior of the system can track this "transition process" to ultimately achieve the control target. In the suspension control system of the motor, in order to obtain better control effect, the current inner loop responds quickly and the output of the displacement / force outer loop is relatively smooth and gentle. Based on this idea, a transition process is set for the outer loop control link.

[0188] Assume the given signal of rotor displacement is x * (t), the rotor displacement tracking signal x1(t) and the rotor displacement approximate differential x2(t) have the following differential equations:

[0189]

[0190] When t→∞, x1(t)→0, x2(t)→0, and the function f satisfies |f(x1(t),(x2(t))|≤r.

[0191] Formula (44) is written in discrete form, and we can get:

[0192]

[0193] In the formula, h is the integration step length, and the function f uses the nonlinear comprehensive control function fal(·), and its specific form is:

[0194]

[0195] In the formula, α is the nonlinear factor and δ is the filtering factor.

[0196] The discrete form of the rotor position tracking differentiator of the motor suspension control system is as follows:

[0197]

[0198] The filter factor δ of TD can also be taken as the step size h. r is the speed factor. Adjusting the size of r can adjust the speed of the transition process. The larger the r, the faster the tracking speed, but too large r value will cause system oscillation.

[0199] b. Design of sliding mode disturbance observer for displacement / suspension force loop

[0200] The alternating pole magnetic levitation permanent magnet synchronous motor is designed as an alternating pole structure. In theory, the motor is decoupled in the two suspension degrees of freedom in the x-axis and y-axis directions. However, in actual operation, due to the existence of magnetomotive force harmonics, there is coupling between the suspension forces in the x-axis and y-axis directions, and it is not easy to accurately model. This coupling effect and other disturbance factors that affect the control of the rotor suspension force are taken as the system disturbance of the suspension force control in the suspension control, and are recorded as d in the x-axis and y-axis directions respectively. x ,d y , the suspension force mathematical model (Equation (27)) is rewritten as follows:

[0201]

[0202] The design method of the extended state observer takes the x-direction displacement / suspension force as an example. The variable x is the displacement of the motor rotor in the positive direction of the x-axis. The state variable of the sliding mode disturbance observer is assumed to be:

[0203]

[0204] Substituting into formula (48), we have:

[0205]

[0206] Assume u1 is the control rate to be designed, and the sliding mode disturbance observer is designed as:

[0207]

[0208] From equations (49) and (51), we can get the error of the sliding mode disturbance observer:

[0209]

[0210] In the formula, is the rotor displacement disturbance observation error, g1 is the observation gain.

[0211] Design sliding surface:

[0212] s=c1e1+e2=0(53)

[0213] The selection of constant c1 should satisfy Hurwitz stability and c1>0.

[0214] In order to eliminate chattering and improve the robustness and stability of the system, the sliding mode reaching law designed based on the super helical algorithm is as shown in Equation (54), where k 21 >0,k 22 >0.

[0215]

[0216] The sliding mode disturbance observer is designed as Figure 7 shown.

[0217] c. Design of sliding mode active disturbance rejection controller

[0218] The coupling of the rotor in the x and y degrees of freedom of suspension in the suspension control system and other interference factors are regarded as system disturbances. The second-order system of the displacement / force control loop is subjected to the anti-disturbance control technology, combined with the sliding mode nonlinear state error feedback control law, to achieve the decoupling control of the rotor suspension. The output of the sliding mode disturbance observer in 2) is written as [z x1 z x2 z x3 ] T , let the intermediate quantity e x1 =x1-z x1 、e x2 =x2-z x2 , design sliding surface s = c2e x1 +e x2 , where c2>0; combined with sliding mode technology to design the sliding mode feedback control law u of the active disturbance rejection controller f 0(t) is as follows:

[0219]

[0220] Where k3>0, λ1>0,

[0221] The disturbance compensation is:

[0222]

[0223] The designed sliding mode active disturbance rejection controller is as follows:

[0224]

[0225] Where b1 is the system parameter and f0 represents the disturbance.

[0226] (6) Research on torque system control strategy.

[0227] The alternating pole magnetic levitation permanent magnet synchronous motor designed by the present invention has good decoupling performance, and the torque system is decoupled from the suspension current and is less affected by the eccentricity of the rotor displacement. The classic control method can meet the torque performance requirements. However, when the motor is interfered by strong external factors, the suspension current and the rotor displacement exceeding a certain numerical range will also have a greater impact on the stable operation of the torque system. Therefore, it is considered to adopt a control method with better anti-interference and stronger robustness. The internal disturbances unknown to the precise mathematical model of the motor in the torque control system ("precise model" refers to the derived torque mathematical model, and "unknown internal disturbances" refer to complex nonlinear factors or uncertainty factors that cannot be reflected in the precise model) and the external disturbances caused by the external environment and operating conditions are regarded as disturbances that affect the stable operation of the motor torque system. The sliding mode-self-anti-disturbance composite control method is used to observe and compensate for the disturbance in real time, so as to achieve high-performance and strong robustness torque system control. The control principle block diagram is shown in the figure. Figure 8 As shown in the figure. r * is the given speed of the motor, ω r is the actual speed, is the torque reference current in the d and q axis coordinate system, i md 、i mq is the actual measured d and q axis torque current, is the torque voltage reference voltage in the d and q axis coordinate system, is the torque reference voltage in the α and β coordinate systems, θ e The rotor electrical angle, ω is the electrical angular velocity.

[0228] 1) Transition process design

[0229] In order to extract the signal more accurately, a nonlinear tracking differentiator is used to arrange the transition process. Assume that the given speed of the motor is ω r * , the tracking signal ω of a given speed is obtained through a nonlinear tracking differentiator v1 and the derivative signal ω v2 The design of the fastest tracking differentiator for the motor speed is as follows:

[0230]

[0231] Where h is the integration step size.

[0232] The specific expression of the discrete system fastest comprehensive function fhan(·) is as follows:

[0233]

[0234] Where r is the speed factor, which determines the speed of tracking; the transition interval is defined as d=rh, the saturation interval is defined as d0=hd, a represents the adjustment amount, a0 represents the adjustment factor, and y represents the intermediate variable.

[0235] 2) Extended State Observer Design

[0236] The state equation of the speed loop of the motor torque system can be written as:

[0237]

[0238] The motor speed is affected by known and unknown disturbance factors such as load torque changes, operating conditions changes, and motor parameters changes due to the external environment. Let w in equation (60) be the unknown external disturbance of the speed loop, and the first two terms on the right side of the equal sign are known disturbances, denoted as f(ω1). The sum of the two is regarded as the total disturbance f(t, ω1, w) of the speed loop control system, which is used as the expanded state quantity of the state observer, denoted as z ω , then the speed loop state equation after state expansion can be written as:

[0239]

[0240] In the formula, g ω is the total derivative of the expanded state variable. For the actual system g ω Bounded; It is the system control gain determined by the motor structure.

[0241] Considering the limited variation range of the total disturbance of the system, designing a high-gain state observer can make the structure simpler, reduce the number of parameters that need to be debugged, and have a low system order, so the gain will not be much higher than that of the nonlinear observer. The second-order speed ESO (extended state observer) is designed as follows:

[0242]

[0243] Among them, β 01 , β 02 is the gain factor.

[0244] 3) Design of sliding mode active disturbance rejection controller

[0245] Speed ​​setting of speed loop ω * r The tracking signal is ω v1, the output z1 of ESO, then the error between the given speed and the speed feedback is:

[0246] e ω =ω v1 -z1(63)

[0247] Assume that the sliding mode control surface s = e ω , Select parameter k4, and according to formula (61), use the sliding mode control design method to design the SM-NLSEF (sliding mode active disturbance rejection controller) of the speed loop as follows:

[0248]

[0249] in, is the control law of the speed loop (outer loop);

[0250] Since the SM-NLSEF (sliding mode active disturbance rejection controller) cannot offset the disturbance and uncertainty in the system, the reference torque current calculated by the SM-NLSEF is analyzed using the extended state observer (ESO). After compensation, the current command i q * (Inner loop), used to offset disturbances and uncertainties in the system and improve the steady-state and dynamic performance of the system;

[0251]

[0252] The designed speed sliding mode anti-disturbance control can make the system stable, the error converges to the sliding mode surface in a limited time, and the design parameters are relatively few and the structure is simple; its control principle diagram is as follows Fig. 9 The target speed signal is converted into a smooth speed reference signal through a first-order tracking differentiator (TD), which is convenient for the controller to process. Fig. 9 middle, Represents ω v1 The derivative with respect to time; ω is the actual motor speed, which indicates the actual running speed of the motor, which is measured in real time by a sensor or estimator and fed back to the control system for closed-loop regulation; e ω is the speed error; Represents the reference torque current, the reference current signal calculated by the sliding mode anti-disturbance controller, which is used to control the output torque of the motor to achieve the desired dynamic performance; i q is the actual q-axis current of the motor (the current component used to generate torque); z1 and z2 are state variables, which are the state feedback variables inside the sliding mode ADRC, representing the internal dynamics of the controller and used to improve control performance and suppress disturbances.

[0253] According to the above ideas, based on the concept of topology-control collaborative decoupling, the designed alternating-pole suspended parallel single-winding magnetic levitation permanent magnet synchronous motor can realize full coupled variable decoupling of the torque system and the suspension system, and at the same time has the application advantages of high power density and high torque output.

[0254] The embodiments are preferred implementations of the present invention, but the present invention is not limited to the above-mentioned implementations. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essential content of the present invention belong to the protection scope of the present invention.

Claims

1. A method for decoupling the torque system and suspension system of a single-winding magnetic suspension permanent magnet synchronous motor, characterized in that: The motor adopts a suspended parallel single winding structure to achieve decoupling of the torque system from the suspension current; The permanent magnet adopts an alternating pole design to achieve decoupling of the suspension system from the rotor position angle; In the current loop of the suspension system, the voltage at the torque inverter terminal is regarded as a disturbance term, and together with other disturbance factors affecting the suspension current control, it is regarded as a system disturbance. A sliding mode disturbance observer is designed to observe the disturbance in real time and compensate the suspension current to achieve decoupling of the suspension current control from the torque system. In the displacement / suspension force loop of the suspension system, the coupling between different suspension degrees of freedom and other displacement disturbances are regarded as system disturbances. A sliding mode anti-disturbance controller is designed to observe and compensate the suspension force to achieve control decoupling between different suspension degrees of freedom. The internal disturbances unknown in the mathematical model of the torque control system and the external disturbances caused by the external environment and operating conditions are regarded as disturbances that affect the stable operation of the motor torque system. The sliding mode-auto-disturbance rejection composite control method is used to observe and compensate for the disturbances in real time to achieve high-performance and highly robust torque system control.

2. The method for decoupling a torque system from a suspension system according to claim 1, characterized in that: The motor adopts a suspended parallel single winding structure to achieve decoupling of the suspension current by the torque system. Specifically, each phase torque winding is connected in series, and the torque inverter only provides a three-phase torque current i mA 、i mB 、i mC , the suspension inverter provides suspension current i s and where i s Including three-phase suspension current i sA 、i sB 、i sC , the i sA 、i sB 、i sC The torque is injected from the midpoint of each phase winding. Connects to the torque inverter and injects torque into the winding.

3. The method for decoupling a torque system from a suspension system according to claim 1, characterized in that: The permanent magnet adopts an alternating pole design, specifically: the permanent magnet adopts a surface insertion type, and the number of permanent magnet pole pairs is ≥4; the magnetization direction of the permanent magnet is arranged with the same polarity along the rotor surface, and the rotor core part adjacent to the permanent magnet is magnetized with opposite polarity.

4. The method for decoupling a torque system from a suspension system according to claim 1, characterized in that: In the sliding mode disturbance observer, the designed linear sliding mode surface s is: Among them, e ix is the suspension current observation error, i sx is the actual suspension current generated by the motor in the x-axis direction, is the estimated suspension current in the x-axis direction.

5. The method for decoupling a torque system from a suspension system according to claim 4, characterized in that: In the sliding mode disturbance observer, the sliding mode reaching law of the improved super spiral algorithm is: Among them, k1 and k2 are superhelical sliding mode gains, v is the state variable, ρ1 and ρ2 are external disturbances, t is time, λ is the exponential power term gain, and α is a constant.

6. The method for decoupling a torque system from a suspension system according to claim 5, characterized in that: The perturbation observation error e di Considered as a disturbance term, the control law of the sliding mode disturbance observer based on the improved super-helical algorithm is:

7. The method for decoupling a torque system from a suspension system according to claim 1, characterized in that: The sliding mode active disturbance rejection controller is: Among them, the sliding surface s = c2e x1 +e x2 , the intermediate quantity e x1 =x1-z x1 、e x2 =x2-z x2 , z x1 、z x2 、z x3 is the output of the sliding mode disturbance observer of the displacement / suspension force loop, k3, λ1, c2 are constants greater than 0, u f0 (t) is the feedback control law of the sliding mode ADRC, u * f (t) is the disturbance compensation, b1 is the system parameter, and f0 represents the disturbance.

8. The method for decoupling a torque system from a suspension system according to claim 7, characterized in that: The feedback control law of the sliding mode active disturbance rejection controller satisfies: Among them, the intermediate x is the displacement of the motor rotor in the positive direction of the x-axis, and the coefficient k ecc It is related to the air gap magnetic field characteristics and air gap magnetic permeability, and m is the rotor mass.

9. The method for decoupling a torque system from a suspension system according to claim 1, characterized in that: The sliding mode-ADR composite control method is specifically as follows: Suppose the sliding mode control surface s = e ω , select parameter k4, use the sliding mode control design method to design the sliding mode active disturbance rejection controller of the speed loop: Among them, e ω is the speed error, is the control law of the speed loop, is the first-order derivative of the state variable z1.

10. The method for decoupling a torque system from a suspension system according to claim 9, characterized in that: The reference torque current calculated by the sliding mode anti-disturbance controller of the speed loop is compensated by the extended state observer. The compensated current command i q * for: Among them, b2 is the system control gain, z2 is the state variable, The tracking signal ω represents the given speed v1 The derivative with respect to time.

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