CN111650975A - Magnetic suspension rotor harmonic current suppression method based on multi-order repetitive controller - Google Patents
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Abstract
The invention discloses a magnetic suspension rotor harmonic current suppression method based on a multi-order repetitive controller, which aims at a magnetic suspension control torque gyroscope, firstly establishes a magnetic suspension rotor dynamic model containing mass unbalance and sensor harmonic, and secondly adopts the multi-order repetitive controller to process signals of the first three periods so as to adjust the current, thereby realizing the effective suppression of harmonic current under fixed frequency. The invention can realize effective suppression of harmonic current at any fixed rotating speed, and is suitable for suppression of harmonic current of the magnetic suspension rotor with mass unbalance and sensor harmonic. The repetitive controller is applied, so that accurate suppression of harmonic current is guaranteed, and meanwhile, a wide notch width is provided at each frequency point, and the frequency robustness of the control system is improved.
Description
Technical Field
The invention relates to the technical field of magnetic suspension rotor harmonic current suppression, in particular to a magnetic suspension rotor harmonic current suppression method based on a multi-order repetitive controller, which is used for suppressing harmonic current in a magnetic suspension control moment gyroscope rotor system and providing technical support for the application of a magnetic suspension control moment gyroscope on an 'ultra-stable and ultra-static' satellite platform.
Background
The magnetic suspension rotor system has the characteristics of no friction, long service life, controllable active vibration and the like, and has good application in the aspects of magnetic suspension control moment gyros, magnetic suspension flywheels, magnetic suspension molecular pumps and the like. Because the processing precision is limited, the magnetic suspension rotor inevitably has mass unbalance, and the same-frequency control current with the rotating speed and the frequency is generated in the high-speed rotating process; on the other hand, due to the fact that the unsmooth magnetic characteristics of the detection surface and the detection surface of the sensor are not consistent, the detection signal of the sensor contains same-frequency and frequency-doubling noise, namely sensor harmonic, and the sensor harmonic can cause harmonic control current. Due to the unbalanced mass of the magnetic suspension rotor and the harmonic control current generated by the harmonic of the sensor, the magnetic suspension rotor system can generate harmonic vibration force, and the harmonic vibration force is further transmitted to the base to influence the attitude control precision of the hyperstable hyperstatic satellite platform.
Harmonic vibration suppression can be divided into two broad categories, one of which includes control methods for single frequency suppression, such as traps, resonant controllers, and the like. Aiming at the vibration caused by the harmonic wave of the sensor, the method is characterized in that the harmonic wave of fundamental frequency and multiple frequency multiplication is existed, so that the harmonic wave suppression can not be realized by using a simple structure aiming at the control method of single frequency. The other type refers to a method for simultaneously suppressing fundamental frequency and frequency multiplication, such as a state observer, a repetitive controller, etc., which can simultaneously suppress vibrations of different frequency components without connecting multiple filters in parallel, wherein the state observer needs to estimate the disturbance quantity, and thus needs a complex structure and a large amount of calculation. The repetitive controller based on the internal model principle can realize the complete inhibition of frequency doubling harmonic waves, and the existing method has no frequency robustness.
Disclosure of Invention
The purpose of the invention is as follows: the method for suppressing the harmonic current of the magnetic suspension rotor based on the multi-order repetitive controller overcomes the defects of the prior art, and achieves accurate suppression of the harmonic current insensitive to fundamental frequency fluctuation at any constant rotating speed.
The technical scheme adopted by the invention is as follows: a magnetic suspension rotor harmonic current suppression method based on a multi-order repetitive controller comprises the following steps:
step (1) establishing a magnetic suspension rotor dynamics model containing mass unbalance and sensor harmonic
According to the structure diagram of the magnetic suspension rotor, three coordinate systems, namely a generalized coordinate system, a magnet coordinate system and a displacement sensor coordinate system, are established for the rotor, and a rotor motion equation is obtained according to the Newton's law of mechanics:
where M is the generalized mass, G is the gyro matrix, qIIs the displacement of the rotor inertia axis in a generalized coordinate system. f is a generalized force vector, and the force vector in the magnet coordinate system is represented as fmDenoted f in the displacement sensor coordinate systemsThere is a conversion relationship:
f＝Tffm
wherein the transformation matrix TfDistance l from centroid of radial magnetic bearing to origin of three coordinatesmConverted out ofmCan be expressed as:
fm＝kiim+kxqm
definition kiTo the current stiffness, kxDisplacement q in magnet coordinate system for displacement stiffnessmAnd q under a displacement coordinate systemsHaving a conversion relation Tfqm＝qG，qs＝TsqG，qGIs the displacement of the geometric axis of the rotor under a generalized coordinate system, and converts the matrix TsFrom the magnification of the displacement sensor and the center of mass of the displacement sensor to the seatThe distance of the origin point is converted, and the coil current i is represented by the geometric axis displacementm：
im＝function(0-qs)
function(s)＝Gw(s)Gm(s)
Gw(s) and Gm(s) represents the equivalent transfer functions of the controller and the power amplifier, respectively, and the basic model of the magnetic levitation rotor system can be expressed as:
defining the unbalance amount of the rotor as deltaq, and expressing the value as follows:
wherein, Ω is the angular velocity of the rotor, t is the time, cos (Ω t + χ) and sin (Ω t + χ) represent the static unbalance amount (the offset displacement of the geometric axis and the inertial axis) of the rotor, χ sum is the initial phase and amplitude of the static unbalance amount, σ sin (Ω t +) and- σ cos (Ω t +) represent the dynamic unbalance amount (the deflection angle of the geometric axis and the inertial axis) of the rotor, and σ is the initial phase and amplitude of the dynamic unbalance amount, and are substituted into the basic model to obtain the dynamic model of the magnetic bearing system under the influence of the rotor unbalance factor: (Ms)2+Gs)[qG(s)+Δq(s)]＝-ki[Gw1(s)TfTsGs(s)+Gw2(s)TfTf T]qG(s)+kxTfTf TqG(s)
In the above formula Gw1(s) and Gw2(s) is a power amplifier Gw(s) the equivalent values of the forward channel and the feedback channel, wherein s is a parameter after the Laplace transform and is a complex number s. Because the curvature exists on the detection surface which is difficult to avoid in the processing process, the output signal of the sensor can have harmonic waves, and the harmonic waves q are defined under the coordinate system of the displacement sensorsr：
i represents the number of harmonics, n is a positive integer, harmonics below 7 in an actual system are obvious, and sasiAnd sbsiRespectively representing the magnitude of the ith harmonic component at the ends ab, αsiAnd βsiRespectively representing the phase of the ith harmonic component at the two ends ab. The actual output signal of the displacement sensor is then represented, which in turn yields the kinetic equation of the rotor system under rotor imbalance and sensor harmonic factors:
(Ms2+Gs)[qG(s)+Δq(s)]
＝-ki{Gw1(s)TfTsGs(s)[qG(s)+Ts -1qsr(s)]+Gw2(s)TfTf TqG(s)}+kxTfTf TqG(s)
by combining the analysis, the rotor mass imbalance and the sensor error can cause the magnetic suspension rotor system to generate harmonic control current, so that harmonic vibration force is generated;
step (2) design of harmonic current suppression algorithm based on multi-order repetitive controller to carry out magnetic suspension rotor harmonic current suppression
Taking the harmonic current as a control target, and converting the harmonic current ixThe harmonic fundamental frequency is not fixed and does not change in an actual magnetic bearing control system, and fluctuation exists in a fundamental frequency small range.
Further, the harmonic current suppression algorithm in step (2) is as follows:
the nested MORC is an internal mold structure with three closed rings, w1，w2，w3The delay links on each closed loop are connectedThe input weight reflects the influence level of the error values at different moments on the output signal at the current moment; the low-pass filter q (z) is used to ensure system convergence; l (z) ═ zlIs a linear phase filter leading the phase angle thetaL(ω) is derived from the value of the variable l and ωnT is calculated to obtain omeganIs the fluctuation frequency, T is the sampling period of the system discretization, which is used for offsetting the phase angle lag of the high-frequency position, and the phase compensation function C (z) is used for phase compensation of the middle-low frequency position, thereby ensuring the system stability. By adopting the controller with the structure, on one hand, harmonic current at each frequency doubling position can be completely inhibited; on the other hand, the method can reduce the error caused by the fluctuation of the disturbance frequency near the fundamental frequency, and realize the accurate suppression of the harmonic current of the magnetic suspension rotor system with frequency robustness.
Further, the harmonic current suppression algorithm takes the reference input signal r (z) and the equivalent harmonic disturbance signal d (z) as inputs, and the sensitivity function s (z) of the magnetic bearing coil current i (z) as output can be expressed as follows:
wherein W (z) ═ w1z-N+w2z-2N+w3z-3N，krcIs the controller gain, N is the ratio of the rotor rotation period to the sampling period T, F is the system function, when ω isnN Ω, n is a positive integer,
then, when w1+w2+w3＝1，1-Q(z)W(z)z-NAnd the gain is approximately equal to 0, namely, the controller is ensured to have infinite gain at each harmonic vibration frequency point with the same frequency and multiple frequency.
The basic principle of the invention is as follows: for a magnetic suspension flywheel, high-frequency vibration can reduce the pointing accuracy and stability of a satellite platform and must be suppressed. Among the major sources of vibration are mass imbalance and sensor harmonics. The invention restrains the harmonic current and reduces the harmonic vibration. Due to the existence of mass unbalance and sensor harmonic waves, the control current contains harmonic waves, namely harmonic wave current, so that the magnetic suspension control moment gyro contains harmonic wave vibration. A magnetic suspension rotor dynamic model containing mass unbalance and sensor harmonic is established, harmonic current is analyzed, a repetitive controller is provided to realize harmonic current suppression of a magnetic suspension rotor at a high rotating speed, and the three aspects are mainly researched: designing a nested repetitive control structure with a plurality of closed loops to realize frequency multiplication harmonic suppression at a fixed rotating speed; carrying out frequency robustness analysis on the controller, and selecting proper weights on each closed loop; and a phase compensation link is designed, the stability of the controller is analyzed, the stability is ensured by designing the phase compensation link, and the accurate suppression of the harmonic current of the magnetic suspension rotor at a fixed rotating speed is finally realized.
Compared with the prior art, the invention has the advantages that:
(1) in order to effectively suppress harmonic current in a magnetic suspension rotor system, the invention provides a magnetic suspension rotor harmonic current suppression method based on a multi-order repetitive controller, which can realize effective suppression of harmonic current of a rotor at a fixed rotating speed by using three closed-loop internal model structures respectively comprising first three periodic signals and is suitable for suppression of harmonic current of a magnetic suspension rotor with mass imbalance and sensor harmonic.
(2) The multi-order repetitive controller provided by the invention has larger notch width, has better robustness on current harmonic suppression under base frequency perturbation, and provides a new stability analysis method to ensure the stability of the whole system.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a cross-sectional view of a magnetically levitated control moment gyro rotor system;
FIG. 3 is a schematic view of a rotor mass imbalance;
FIG. 4 is a schematic diagram of sensor harmonics;
FIG. 5 is a basic block diagram of a magnetically levitated rotor control system;
FIG. 6 is a block diagram of a multi-level repetitive controller;
FIG. 7 is GmorcThe amplitude-frequency characteristic curve of (1);
FIG. 8 is a structural view of a magnetic levitation rotor system with an inserted MORC;
fig. 9 is a phase compensation graph of the system.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
As shown in fig. 1, the magnetic suspension rotor rotates around the shaft at a high speed in a working state, and four pairs of radial magnets and displacement sensors are symmetrically distributed at two ends of the rotor AB and used for detecting radial displacement deviation.
The implementation process of the magnetic suspension rotor harmonic current suppression method based on the multi-order repetitive controller is as follows:
step (1) establishing a magnetic suspension rotor dynamic model containing mass unbalance and sensor harmonic;
and (2) designing a magnetic suspension rotor harmonic current suppression method based on a multi-order repetitive controller.
The method specifically comprises the following steps:
step (1) establishing a magnetic suspension rotor dynamics model containing mass unbalance and sensor harmonic
According to the structure diagram of the magnetic suspension rotor shown in the figure 2, three coordinate systems, namely a generalized coordinate system, a magnet coordinate system and a displacement sensor coordinate system, are established for the rotor, wherein the three coordinate systems all use the center of a magnet as an origin, and the X axis and the Y axis of the generalized coordinate system are parallel to a radial displacement sensor, so that the right-hand rule is met; the XY axis of the magnet coordinate system is in the magnetic bearing coil plane, and the Z axis is vertical to the plane; the XY axes of the displacement sensor coordinate system are respectively parallel to the connecting lines of the two opposite displacement sensors. And obtaining a rotor motion equation according to the Newton's law of mechanics:
where M is the generalized mass, G is the gyro matrix, qIIs the displacement of the rotor inertia axis in a generalized coordinate system. f is a generalized force vector, and the force vector in the magnet coordinate system is represented as fmDenoted f in the displacement sensor coordinate systemsThere is a conversion relationship:
f＝Tffm
wherein the transformation matrix TfDistance l from centroid of radial magnetic bearing to origin of three coordinatesmConverted out ofmCan be expressed as:
fm＝kiim+kxqm
definition kiTo the current stiffness, kxDisplacement q in magnet coordinate system for displacement stiffnessmAnd q under a displacement coordinate systemsHaving a conversion relation Tfqm＝qG，qs＝TsqG，qGIs the displacement of the geometric axis of the rotor under a generalized coordinate system, and converts the matrix TsThe current i of the coil is represented by the displacement of the geometric axism：
im＝function(0-qs)
function(s)＝Gw(s)Gm(s)
function (-) is a function of the rotor system controller and the power amplifier in series, Gw(s) and Gm(s) represents the equivalent transfer functions of the controller and the power amplifier, respectively, and the basic model of the magnetic levitation rotor system can be expressed as:
imbalance in rotor mass can cause misalignment of the geometric axis with the inertial axis, thereby generating harmonics (fig. 3), defining the rotor imbalance quantity as Δ q, expressed as:
wherein, Ω is the angular velocity of the rotor, t is the time, cos (Ω t + χ) and sin (Ω t + χ) represent the static unbalance amount (the offset displacement of the geometric axis and the inertial axis) of the rotor, χ sum is the initial phase and amplitude of the static unbalance amount, σ sin (Ω t +) and- σ cos (Ω t +) represent the dynamic unbalance amount (the deflection angle of the geometric axis and the inertial axis) of the rotor, and σ is the initial phase and amplitude of the dynamic unbalance amount, and are substituted into the basic model to obtain the dynamic model of the magnetic bearing system under the influence of the rotor unbalance factor:
(Ms2+Gs)[qG(s)+Δq(s)]＝-ki[Gw1(s)TfTsGs(s)+Gw2(s)TfTf T]qG(s)+kxTfTf TqG(s)
in the above formula Gw1(s) and Gw2(s) is a power amplifier Gw(s) equivalent values of a forward channel and a feedback channel, wherein s is a parameter after Ralstonian transformation and is a complex number s, the curvature of a detection surface exists in the processing process, so that a sensor output signal can have harmonic waves, and the harmonic waves q are defined under a displacement sensor coordinate systemsr(FIG. 4):
i represents the number of harmonics, n is a positive integer, harmonics below 7 in an actual system are obvious, and sasiAnd sbsiRespectively representing the amplitude of the ith harmonic component at the two ends AB of the magnetic suspension rotor, αsiAnd βsiRespectively representing the phase of the ith harmonic component at both ends of the AB. The actual output signal of the displacement sensor is then represented and the control system block diagram is shown in fig. 5, which in turn yields the rotor system dynamics equations under rotor imbalance and sensor harmonic factors:
(Ms2+Gs)[qG(s)+Δq(s)]
＝-ki{Gw1(s)TfTsGs(s)[qG(s)+Ts -1qsr(s)]+Gw2(s)TfTf TqG(s)}+kxTfTf TqG(s)
by combining the analysis, the rotor mass imbalance and the sensor error can cause the magnetic suspension rotor system to generate harmonic control current, so that harmonic vibration force is generated;
(2) magnetic suspension rotor harmonic current suppression method based on multi-order repetitive controller
Aiming at the problem that harmonic current exists in the coil current in the step (1), the invention adopts a magnetic suspension rotor harmonic current suppression method based on a multi-order repetitive controller. Taking the harmonic current as a control target, and converting the harmonic current ixThe harmonic fundamental frequency is not fixed and does not change in an actual magnetic bearing control system, and fluctuation exists in a fundamental frequency small range.
As shown in FIG. 6, the nested multistage repetitive controller MORC is an internal model structure with three closed loops, w1，w2，w3The weight value is accessed after the delay link on each closed loop, and reflects the influence level of the error value at different moments on the output signal at the current moment; the low-pass filter q (z) is used to ensure system convergence; l (z) ═ zlIs provided with a lead angle thetaL(ω)＝lωnLinear phase filter of T for canceling phase angle lag, omega, at high frequency positionsnIs the fluctuation frequency, T is the sampling period of the system discretization, and the phase compensation function C (z) is used for the phase compensation of the middle and low frequency bands to ensure the stability of the system. The controller with the structure can completely suppress harmonic current at each frequency multiplication part on one handPreparing; on the other hand, the method can reduce the error caused by the fluctuation of the disturbance frequency near the fundamental frequency, and realize the accurate suppression of the harmonic current of the magnetic suspension rotor system with frequency robustness.
Further, the harmonic current suppression algorithm takes the reference input signal r (z) and the equivalent harmonic disturbance signal d (z) as inputs, and the sensitivity function s (z) of the magnetic bearing coil current i (z) as output can be expressed as follows:
wherein W (z) ═ w1z-N+w2z-2N+w3z-3N，krcIs the controller gain, N is the ratio of the rotor rotation period to the sampling period T, F is the system function, when ω isnN Ω, n is a positive integer,
then, when w1+w2+w3＝1，1-Q(z)W(z)z-NAnd the gain is approximately equal to 0, namely, the controller is ensured to have infinite gain at each harmonic vibration frequency point with the same frequency and multiple frequency.
The method is analyzed below, according to one embodiment of the present invention.
1. Robust analysis
Compared with the widely-used traditional repetitive controller, the multi-order repetitive controller provided by the invention has good frequency robustness, omeganK Ω (k is a positive integer) is a target frequency point that needs to be suppressed, and the frequency at which the ripple occurs can be expressed as ω ═ ωn(1+). The requirement is less than 1, the amplitude G of the multi-stage repetitive controller is compared by taking 0.01 as the valuemorc(omega) and conventional repetitive controller GcrcAmplitude of (ω):
formula (II)
The robustness of the multi-order repetitive controller is better than that of the traditional controller, and the following conditions are met:
-4w2 2+4w2+(6w2-4w2+2w3)(1-cos(2πk))＞0
further, w is fixed within the range defined by the above formula30.5 pairs of different w2The amplitude-frequency characteristic curve of the transfer function under the influence of the weight is analyzed, and the observation of figure 7 shows that w2When too large, the notch width of the controller at the frequency point will be narrower, and w2Too small may cause the controller to produce negative gain at non-harmonic frequency points, with w being chosen for trade-off considerations2＝0.7。
2. Stability analysis
The low-pass filter is simplified by q (z) 1, and the transfer function is expressed as:
according to w1，w2，w3Is defined relationship w1+w2+w3At 1, introduce α to re-represent the transfer function as follows:
FIG. 8 is a model of the rotor system after insertion of the MORC, wherein Gp(s) represents a transfer function of the magnetically levitated rotor; gc(s) a controller, often a PID, for stabilizing the suspension of the magnetic suspension rotor; gw(s) is the transfer function of the power amplifier; ksIs the displacement sensor transfer function. Defining:
is a system function of a closed loop system.
Assuming that the frequency response of the phase compensation function C (z) is
Wherein A isk(ω) is the amplitude, θk(ω) is the phase; similarly, let
Wherein A isf(ω) is the amplitude, θfAnd (ω) is its phase. Definition M (ω) ═ Ak(ω)Af(ω) and θ (ω) ═ θk(ω)+θf(ω)+lωTs。
For a closed loop system as shown in fig. 8, the closed loop system is asymptotically stable if the following conditions are simultaneously satisfied:
condition 1: the magnetic suspension rotor system without the repeated controller is gradually stabilized;
condition 2: when gain k in closed loop systemrcAnd w1、w2、w3MORC is progressively stable when the following conditions are met:
wherein α + β is w1-1，αβ＝w3，w1+w2+w3＝1.
Condition 3: the MORC is asymptotically stable when the closed loop system phase θ satisfies the following condition:
θ∈(90°，270°)
in conclusion, by selecting appropriate gain and weight and designing a reasonable phase compensation scheme, the stability of the system after the algorithm is added can be ensured.
3. Phase compensation design
According to the stability of the controllerAnalytically, the phase angle θ needs to satisfy θ ∈ (90 °, 270 °). from fig. 9, it can be seen that the initial phase of the system ranges from 270 ° to-90 °, so it is necessary to design a suitable phase compensation method to compensate the phase angle to around 180 °lThe (ω) ═ l ω T is used to compensate the phase of the high band, which needs to be compensated by about 270 °, so l ═ 5 is selected, and for the phase compensation of the middle and low band, the compensation function c (z) is designed as follows, and the dashed line in fig. 9 represents the result of the phase compensation.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but various changes may be apparent to those skilled in the art, and it is intended that all inventive concepts utilizing the inventive concepts set forth herein be protected without departing from the spirit and scope of the present invention as defined and limited by the appended claims.
Claims (4)
1. A magnetic suspension rotor harmonic current suppression method based on a multi-order repetitive controller is characterized by comprising the following steps: the method comprises the following steps:
step (1) establishing a magnetic suspension rotor dynamic model containing mass unbalance and sensor harmonic;
designing a harmonic current suppression algorithm based on a multistage repetitive controller MORC to suppress the harmonic current of the magnetic suspension rotor, and taking the harmonic current as a control target to suppress the harmonic current ixThe harmonic wave quantity in the input signal is eliminated by the repetitive controller based on an internal model principle, and a rotor system containing the controller is stable by adopting a multi-closed-loop repetitive control structure and a phase compensation method.
2. The method for suppressing the harmonic current of the magnetic levitation rotor based on the multi-order repetitive controller as claimed in claim 1, wherein:
firstly, establishing a generalized coordinate system, a magnet coordinate system and a displacement sensor coordinate system for a rotor, and obtaining a rotor motion equation according to a Newton's law of mechanics:
where M is the generalized mass, G is the gyro matrix, qIIs the displacement of the rotor inertia axis under the generalized coordinate system; f is a generalized force vector, and the force vector in the magnet coordinate system is represented as fmDenoted f in the displacement sensor coordinate systemsThere is a conversion relationship:
f＝Tffm
wherein the transformation matrix TfDistance l from centroid of radial magnetic bearing to origin of three coordinatesmConverted out ofmExpressed as:
fm＝kiim+kxqm
definition kiTo the current stiffness, kxDisplacement q in magnet coordinate system for displacement stiffnessmAnd q under a displacement coordinate systemsHaving a conversion relation Tsqm＝qG，qs＝TsqG，qGIs the displacement of the geometric axis of the rotor under a generalized coordinate system, and converts the matrix TsThe current i of the coil is represented by the displacement of the geometric axism：
im＝function(0-qs)
function(s)＝Gw(s)Gm(s)
function (-) is a function of the rotor system controller and the power amplifier in series, Gw(s) and Gm(s) equivalent transfer functions of controller and power amplifier, respectively, magnetic levitation rotor systemThe basic model of (a) is expressed as:
defining the unbalance amount of the rotor as deltaq, and expressing the value as follows:
wherein, Ω is the rotor angular velocity, t is time, cos (Ω t + χ) and sin (Ω t + χ) represent the static unbalance of the rotor caused by the deviation of the geometric axis and the inertial axis, χ sum is the initial phase and amplitude of the static unbalance, σ sin (Ω t +) and- σ cos (Ω t +) represent the dynamic unbalance of the rotor caused by the deflection of the geometric axis and the inertial axis, and σ is the initial phase and amplitude of the dynamic unbalance, and are substituted into the basic model to obtain the dynamic model of the magnetic suspension rotor system under the influence of the rotor unbalance factor:
(Ms2+Gs)[qG(s)+Δq(s)]＝-ki[Gw1(s)TfTsGs(s)+Gw2(s)TfTf T]qG(s)+kxTfTf TqG(s) in the above formula Gw1(s) and Gw2(s) is a power amplifier Gw(s) the equivalent values of the forward and feedback channels, s being the parameters after the Ralsberg transform and being the complex number s, and for the curvature of the detection surface caused by the machining process, the output signal of the sensor is provided with harmonics, and the harmonics q are defined under the coordinate system of the displacement sensorsr：
i denotes the order of the harmonic, n is a positive integer, sasiAnd sbsiRespectively representing the amplitude of the ith harmonic component at both ends of the magnetic levitation rotor AB, αsiAnd βsiRespectively representing the phases of ith harmonic components at two ends of the AB; the actual output signal of the displacement sensor is represented, and thenObtaining a dynamic equation of the rotor system under the rotor unbalance and sensor harmonic factors:
(Ms2+Gs)[qG(s)+Δq(s)]
＝-ki{Gw1(s)TfTsGs(s)[qG(s)+Ts -1qsr(s)]+Gw2(s)TfTf TqG(s)}+kxTfTf TqG(s)
rotor mass imbalance and sensor errors can cause a magnetic suspension rotor system to generate harmonic control currents, thereby generating harmonic vibration forces.
3. The method for suppressing the harmonic current of the magnetic levitation rotor based on the multi-order repetitive controller as claimed in claim 1, wherein: the harmonic current suppression algorithm in the step (2) is as follows:
the embedded multi-order repetitive controller MORC is an internal mold structure with three closed loops, and the structure comprises three delay links, a first-order delay link and a weight w1Forming a first closed loop, a second-order delay link and a weight w2Forming a second closed loop, a third-order delay link and a weight w3Form a third closed loop, w1，w2，w3The weight value is accessed after the delay link on each closed loop, reflects the influence level of the error values of the signals of the previous three periods on the output signal at the current moment, and realizes the correction of the current signal by using the errors of the previous three periods; the discretized parameter of the system is z, and a low-pass filter Q (z) is used for ensuring the convergence of the system; l (z) ═ zlIs a linear phase filter leading the phase angle thetaL(ω) is derived from the value of the variable l and ωnT is calculated to obtain omeganIs the ripple frequency, T is the sampling period of the system discretization for canceling the phase angle lag of the high frequency position, and the phase compensation function c (z) is used for phase compensation of the medium and low frequency.
4. The method for suppressing the harmonic current of the magnetic levitation rotor based on the multi-order repetitive controller as claimed in claim 1, wherein: the step (2) designs a compensation function C (z) as follows,
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| CN112525179A (en) * | 2020-11-30 | 2021-03-19 | 北京航空航天大学 | Harmonic current suppression method based on virtual sampling second-order repetitive control |
| CN115217847A (en) * | 2022-07-12 | 2022-10-21 | 珠海格力电器股份有限公司 | Magnetic suspension control system, control method and device thereof and storage medium |
| CN115333425A (en) * | 2022-10-10 | 2022-11-11 | 希望森兰科技股份有限公司 | Current harmonic suppression algorithm of high-performance permanent magnet synchronous motor |
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