CN114735240B - Method and device for compensating measurable basic motion disturbance of magnetic bearing - Google Patents
Method and device for compensating measurable basic motion disturbance of magnetic bearing Download PDFInfo
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Abstract
The invention discloses a measurable basic motion disturbance compensation method and a measurable basic motion disturbance compensation device for a magnetic bearing, wherein the measurable basic motion disturbance compensation method comprises the following steps: step S1, taking the MIT model reference control voltage quantity as the self-adaptive feedforward system control quantity of the magnetic bearing system at the moment n; s2, obtaining a disturbance displacement error of the bearing-rotor system at the n moment according to the self-adaptive feedforward system control quantity of the magnetic bearing system at the n moment; s3, obtaining a disturbance power error at the n moment according to the disturbance displacement error of the bearing-rotor system at the n moment; s4, obtaining feedforward control gain at the n +1 moment according to the disturbance force error at the n moment; s5, obtaining the self-adaptive feedforward system control quantity of the magnetic bearing system at the n +1 moment according to the feedforward control gain at the n +1 moment; and S6, repeating the steps S1 to S5 until the disturbance error of the magnetic bearing-rotor system is zero. By adopting the technical scheme of the invention, the stable operation of the magnetic bearing system under the basic motion working condition can be ensured.
Description
Technical Field
The invention belongs to the technical field of spacecraft attitude control, and particularly relates to a measurable basic motion disturbance compensation method and device for a magnetic bearing.
Background
The control moment gyroscope is a satellite attitude actuator and is widely applied to the field of attitude execution of spacecrafts. The magnetic suspension control moment gyro is a control moment gyro using magnetic suspension support. As shown in fig. 1, the system structure of a single-frame control force gyroscope is shown, the base of the control force gyroscope at the bottom of the outermost layer is responsible for fixing the control force gyroscope, and the frame servo system of the system is arranged in the middle of the outer layer and can drive the rotor base to rotate along the rotating shaft of the servo system. The X and Y directions of the rotor and the moving direction of the frame form an included angle of 45 degrees, the Z axis is the rotating axis of the rotor, and omega g Which represents the angular velocity of the base rotation of the rotor, and alpha and beta represent the rotational angle of the rotor along the X-axis and Y-axis, respectively.
Normally, the magnetic bearing-rotor dynamics model is:
H＝J z w z is the angular momentum of the rotor, m is the mass of the rotor, X, Y represent the displacement of the rotor in the X and Y directions,
representing the acceleration of the rotor in the x and y directions, f ax Representing the force of the rotor on the magnetic bearing in the direction of the a-terminal X, f bx Representing the force of the magnetic bearing on the rotor in the x-direction of the B-terminal, f ay Showing the force of the magnetic bearing on the rotor in the A-terminal Y-direction, f by Indicating that the rotor is subjected to the forces of the magnetic bearing in the B-terminal y-direction,
and
representing angular acceleration of the rotor about the X-bearing and Y-axis, respectively. M represents the moment values in the directions of the x and y inertia axes. l m Is the magnetic gap of the magnetic bearing. Unfolding the magnetic bearing force model into a linear model:
wherein k is i As current stiffness (force/current proportionality coefficient), k h Is the displacement stiffness (force/displacement proportionality coefficient).
When the frame servo system rotates with the rotor base, the rotor of the rotor base is relatively deviated in the stator. Because the basic motion of the magnetic bearing has six degrees of freedom, namely rotation with three degrees of freedom and translation with three degrees of freedom, the degrees of freedom alpha and beta of the two magnetic bearings which have the greatest influence on the magnetic bearing system and are also most difficult to compensate exist. The main effects are as follows:
influence 1: the moments of the basic motion are coupled into the mechanical model of the magnetic bearing:
in this model, if ω is g The disturbance term is too large, which can directly cause the stability of the magnetic bearing to cause magnetismInstability of the bearing control system.
Influence 2: the base motion rotation causes the rotor gravity to couple into the mechanical model of the bearing:
the basic motion has a large influence on the magnetic bearing rotor system, and the basic motion is comprehensive and can be obtained as follows:
for a magnetic bearing rotor system, the magnetic bearing kinetic equations for base motion and high speed rotor conditions can be written in the form of disturbance forces and moments:
wherein the content of the first and second substances,
and
the disturbance resultant force of the large current of the magnetic bearing and the gravity coupling quantity of the rotor in the basic motion state,
and
the disturbance moment generated on the rotor by the rotation of the basic motion is used.
At present, aiming at the complex influence of the dynamic coupling basic motion of the magnetic bearing rotor, the stable operation of the magnetic bearing system under the basic motion working condition can not be ensured.
Disclosure of Invention
The invention provides a measurable basic motion disturbance compensation method and device for a magnetic bearing, which can ensure that a magnetic bearing system stably operates under the working condition of basic motion.
In order to realize the purpose, the invention adopts the following technical scheme:
a method for compensating measurable basic motion disturbance of a magnetic bearing comprises the following steps:
s1, obtaining an MIT model reference control voltage quantity at n moment according to a projection value of a frame rotation angular speed at an ax end of a magnetic bearing at n moment, and taking the MIT model reference control voltage quantity as a self-adaptive feedforward system control quantity of a magnetic bearing system at n moment;
s2, obtaining a disturbance displacement error of the bearing-rotor system at the n moment according to the self-adaptive feedforward system control quantity of the magnetic bearing system at the n moment;
s3, obtaining a disturbance power error at the n moment according to the disturbance displacement error of the bearing-rotor system at the n moment;
s4, obtaining feedforward control gain at the n +1 moment according to the disturbance force error at the n moment;
s5, obtaining the self-adaptive feedforward system control quantity of the magnetic bearing system at the n +1 moment according to the feedforward control gain at the n +1 moment;
and S6, repeating the steps S1 to S5 until the disturbance error of the magnetic bearing-rotor system is zero.
Preferably, in step S1, the calculation process of the MIT model reference control voltage amount at the n-th moment is:
u(n)＝G p (s)*ω g (n)*k c (n)
wherein u (n) is the adaptive feedforward system control quantity, omega, of the magnetic bearing system at time n g (n) is the projection value of the frame rotation angular velocity on the ax end of the magnetic bearing at the moment n, G p (s) is a controlled object model, k c And (n) is the feedforward control gain at the n moment.
Preferably, in step S3, the process of calculating the disturbance force error at time n is as follows:
wherein e is f (n) is the disturbance force error at time n, e s (n) is the disturbance displacement error of the bearing-rotor system at time n, G r T is a numerical conversion coefficient for the transfer function of the rotor system.
Preferably, in step S4, the calculation process of the feedforward control gain at the time n +1 is as follows:
k c (n+1)＝k c (n)+χ·γe f (n)f d (n)
wherein k is c (n + 1) is feedforward control gain at the moment of n +1, chi is sampling time, gamma is step length, e f (n) is the disturbance force error at the moment n; f. of d (n) is the base disturbance force sense caused by the frame servo at time n.
The invention also provides a device for compensating measurable basic motion disturbance of a magnetic bearing, which comprises:
the first calculation module is used for obtaining an MIT model reference control voltage quantity at n moment according to a projection value of the frame rotation angular speed at the ax end of the magnetic bearing at n moment, and meanwhile, the MIT model reference control voltage quantity is used as a self-adaptive feedforward system control quantity of the magnetic bearing system at n moment;
the second calculation module is used for obtaining the disturbance error of the bearing-rotor system at the n moment according to the self-adaptive feedforward system control quantity of the magnetic bearing system at the n moment;
the third calculation module is used for obtaining the disturbance force displacement error at the n moment according to the disturbance error of the bearing-rotor system at the n moment;
the first updating module is used for obtaining feedforward control gain at the n +1 moment according to the disturbance force displacement error at the n moment;
the second updating module is used for obtaining the self-adaptive feedforward system control quantity of the magnetic bearing system at the moment of n +1 according to the feedforward control gain at the moment of n + 1;
wherein the process of the first calculation module, the second calculation module, the third calculation module, the first update module and the second update module is repeated until the disturbance error of the magnetic bearing-rotor system is zero.
Preferably, the calculation formula of the reference control voltage amount of the MIT model at the n-time is:
u(n)＝G p (s)*ω g (n)*k c (n)
wherein u (n) is the adaptive feedforward system control quantity, omega, of the magnetic bearing system at time n g (n) is the projected value of the angular velocity of the frame rotation at the ax end of the magnetic bearing at n moments, G p (s) is a controlled object model, k c And (n) is the feedforward control gain at the moment n.
Preferably, the formula for calculating the disturbance force error at the time n is as follows:
wherein e is f (n) is the disturbance force error at time n, e s (n) is the disturbance displacement error of the bearing-rotor system at time n, G r T is a numerical conversion coefficient for the transfer function of the rotor system.
Preferably, the calculation formula of the feedforward control gain at the time n +1 is as follows:
k c (n+1)＝k c (n)+χ·γe f (n)f d (n)
wherein k is c (n + 1) is feedforward control gain at the moment of n +1, chi is sampling time, gamma is step length, e f (n) is the disturbance force error at the moment n; f. of d And (n) is a basic disturbance force caused by the frame servo at the time n.
The invention adopts the MIT model reference adaptive controller to realize the adaptive feedforward compensation so as to ensure the stable operation of the magnetic bearing system under the basic motion working condition.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the embodiments are briefly introduced below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a block diagram of a prior art system for controlling a force gyro with a single frame;
FIG. 2 is a flow chart of a method for compensating for measurable basic motion disturbance of a magnetic bearing in accordance with the present invention;
FIG. 3 is a schematic diagram of the architecture of the MIT model reference adaptive feedforward compensation control;
FIG. 4 is a simulation diagram of disturbance adaptive tracking, in which FIG. 4 (a) shows a disturbance tracking result; FIG. 4 (b) shows the disturbance tracking error result;
FIG. 5 is a graph of simulation results of a process incorporating adaptive feedforward compensation.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the 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, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
Example 1:
as shown in fig. 2, the present invention provides a compensation method for measurable basic motion disturbance of a magnetic bearing, when a magnetic suspension control moment gyro needs to output a moment to the outside, a frame servo system rotates a gyro room, thereby changing the direction of angular momentum of a rotor in the gyro room and realizing the output of the moment. In this process, the magnetic bearing rotor system will be subject to servo frame induced magnetic bearing base disturbances, and the source of the magnetic bearing base disturbance is known, including:
s1, obtaining an MIT model reference control voltage quantity at n moment according to a projection value of a frame rotation angular speed at an ax end of a magnetic bearing at n moment, and taking the MIT model reference control voltage quantity as an adaptive feedforward system control quantity of a magnetic bearing system at n moment;
s2, obtaining a disturbance displacement error of the bearing-rotor system at the n moment according to the self-adaptive feedforward system control quantity of the magnetic bearing system at the n moment;
s3, obtaining a disturbance power error at the n moment according to the disturbance displacement error of the bearing-rotor system at the n moment;
s4, obtaining feedforward control gain at the n +1 moment according to the disturbance force error at the n moment;
s5, obtaining the self-adaptive feedforward system control quantity of the magnetic bearing system at the moment of n +1 according to the feedforward control gain at the moment of n + 1;
and S6, repeating the steps S1 to S5 until the disturbance error of the magnetic bearing-rotor system is zero.
As an implementation manner of this embodiment, as shown in fig. 3, in step S1, the process of calculating the MIT model reference control voltage amount at n-th time is as follows:
u(n)＝G p (s)*ω g (n)*k c (n)
wherein u (n) is the adaptive feedforward system control quantity, omega, of the magnetic bearing system at time n g (n) is the projected value of the angular velocity of the frame rotation at the ax end of the magnetic bearing at n moments, G p (s) is a controlled object model, k c And (n) is the feedforward control gain at the moment n.
As an embodiment of this embodiment, as shown in fig. 3, in step S2, after the control voltage u is output, a feedforward control current i is generated through the driving coil of the electromagnetic bearing, and due to the existence of the current, the rotor receives a feedforward electromagnetic attraction force f generated by the driving coil, the feedforward electromagnetic force and the disturbance force cooperate to correct the position of the rotor, and the rotor position signal can acquire the rotor displacement at the time n through the displacement sensor, and can calculate the error e from the target displacement s 。
As an embodiment of the present embodiment, as shown in fig. 3, in step S3, the process of calculating the disturbance power error at time n is as follows:
wherein e is f (n) is the disturbance force error at time n, e s (n) is n bearing-rotating timeDisturbance displacement error of the subsystem, G r T is a numerical conversion coefficient for the transfer function of the rotor system.
As an implementation manner of this embodiment, as shown in fig. 3, in step S4, the process of calculating the feedforward control gain at the time n +1 is as follows:
k c (n+1)＝k c (n)+χ·γe f (n)f d (n)
wherein k is c (n + 1) is feedforward control gain at the moment of n +1, chi is sampling time, gamma is step length, e f (n) is the disturbance force error at the moment n; f. of d And (n) is a basic disturbance force caused by the frame servo at the time n.
As an embodiment of the present embodiment, as shown in fig. 3, in step S5, the calculation process of obtaining the adaptive feedforward control amount of the magnetic bearing system at the time point n +1 is as follows:
u(n+1)＝G p (s)*ω g (n+1)*k c (n+1)
wherein u (n + 1) is the adaptive feedforward system control quantity, omega, of the magnetic bearing system at the moment n +1 g Projection of frame rotation angular speed on ax end of magnetic bearing when (n + 1) is n +1
As shown in FIG. 3, as an embodiment of this embodiment, in the feedforward control system, the transfer function G from the basic angular velocity of motion to the radial disturbed force of the magnetic bearing m (s) is:
wherein f is d The basic disturbance force caused by the frame servo is determined.
When the feedforward control force can compensate the disturbance force brought by the frame, the following requirements are met:
f＝f d
wherein f is the feedforward compensation force.
If feed forward is enabled, it is satisfied that:
k c k p G p (z)G ui (s)G f (s)＝k m G m (s)
wherein k is m To perturb the gain of the channel, k c For adjustable gain, G ui For the power amplifier transfer function, G, of the input voltage u to the control current i in the magnetic bearing control system f (s) is a transfer function of the control current i to the output force, k p Gp (z) is a discrete form of the controlled object model and is the equivalent gain of the controlled object model.
Wherein, in the magnetic bearing control system, the power amplifier transfer function G from the input voltage u to the output current i ui Comprises the following steps:
wherein k is ui To control the proportionality coefficient from pwm value to voltage u, L, R of digital power amplifier.
Wherein at the displacement h m When =0, the transfer function G of the control current i to the output force f f (s) is:
G f (s)＝k i
the controlled object model transfer function Gp(s) is designed in the form of:
as a preferable mode of the present embodiment, k c Is set to k as the initial value of 0 c (0)＝0，k p Is set to 1,k m Set to 1.3, step γ =0.00001.
In order to verify the effectiveness of the adoption of the MIT model reference adaptive feedforward in the embodiment, simulation and experiment are respectively performed to verify the effectiveness of the MIT model reference adaptive on the tracking of the basic motion disturbance. The four-degree-of-freedom experimental phenomena of the radial magnetic bearing are substantially similar, and the validity of the experimental algorithm is illustrated herein by way of example only at the ax end.
As shown in fig. 4, which is a simulation result diagram of MIT model reference adaptive control to basic motion tracking, it can be known from the simulation result that adaptive control can quickly track disturbance force according to errors, thereby ensuring the effectiveness of the algorithm in feedforward application. Fig. 5 is a graph of experimental results of the process after the adaptive feedforward compensation is added, and the experimental results show that the adaptive controller can achieve stable disturbance suppression in 4s after the adaptive compensation algorithm is added.
Example 2:
the invention also provides a device for compensating measurable basic motion disturbance of a magnetic bearing, which comprises:
the first calculation module is used for obtaining an MIT model reference control voltage quantity at the n moment according to a projection value of the frame rotation angular speed at the ax end of the magnetic bearing at the n moment, and meanwhile, the MIT model reference control voltage quantity is used as an adaptive feedforward system control quantity of the magnetic bearing system at the n moment;
the second calculation module is used for obtaining the disturbance error of the bearing-rotor system at the n moment according to the self-adaptive feedforward system control quantity of the magnetic bearing system at the n moment;
the third calculation module is used for obtaining the disturbance power error at the n moment according to the disturbance error of the bearing-rotor system at the n moment;
the first updating module is used for obtaining the feedforward control gain at the n +1 moment according to the disturbance power error at the n moment;
the second updating module is used for obtaining the self-adaptive feedforward system control quantity of the magnetic bearing system at the moment of n +1 according to the feedforward control gain at the moment of n + 1;
wherein the processes of the first calculation module, the second calculation module, the third calculation module, the first update module and the second update module are repeated until the disturbance error of the magnetic bearing-rotor system is zero.
The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solutions of the present invention can be made by those skilled in the art without departing from the spirit of the present invention, and the technical solutions of the present invention are within the scope of the present invention defined by the claims.
Claims (2)
1. A measurable basic motion disturbance compensation method for a magnetic bearing is characterized by comprising the following steps:
s1, obtaining an MIT model reference control voltage quantity at n moment according to a projection value of a frame rotation angular speed at an ax end of a magnetic bearing at n moment, and taking the MIT model reference control voltage quantity as a self-adaptive feedforward system control quantity of a magnetic bearing system at n moment;
s2, obtaining a disturbance displacement error of the bearing-rotor system at the n moment according to the self-adaptive feedforward system control quantity of the magnetic bearing system at the n moment;
s3, obtaining a disturbance power error at the n moment according to the disturbance displacement error of the bearing-rotor system at the n moment;
s4, obtaining feedforward control gain at the n +1 moment according to the disturbance force error at the n moment;
s5, obtaining the self-adaptive feedforward system control quantity of the magnetic bearing system at the moment of n +1 according to the feedforward control gain at the moment of n + 1;
s6, repeating the steps S1 to S5 until the disturbance error of the magnetic bearing-rotor system is zero; wherein the content of the first and second substances,
in step S1, the calculation process of the MIT model reference control voltage quantity at the n-time includes:
u(n)＝G p (s)*ω g (n)*k c (n)
wherein u (n) is the adaptive feedforward system control quantity, omega, of the magnetic bearing system at time n g (n) is the projection value of the frame rotation angular velocity on the ax end of the magnetic bearing at the moment n, G p (s) is a controlled object model, k c (n) is the feedforward control gain at n moments;
in step S2, after the control voltage u (n) is output, feedforward control current i is generated through a driving coil of an electromagnetic bearing, meanwhile, the rotor is subjected to feedforward electromagnetic attraction force f generated by the driving coil, the feedforward electromagnetic force and disturbance force act together to correct the position of the rotor, rotor position signals are collected through a displacement sensor to the rotor displacement at the moment of n, and the error e between the rotor position signals and the target displacement can be calculated s ；
In step S3, the calculation process of the disturbance force error at the time n is as follows:
wherein e is f (n) is the disturbance force error at time n, e s (n) is the disturbance displacement error of the bearing-rotor system at time n, G r T is a numerical conversion coefficient, and is a transfer function of the rotor system;
in step S4, the calculation process of the feedforward control gain at the time n +1 is as follows:
k c (n+1)＝k c (n)+χ·γe f (n)f d (n)
wherein k is c (n + 1) is feedforward control gain at the moment of n +1, chi is sampling time, gamma is step length, e f (n) is the disturbance force error at the moment n; f. of d (n) is the base disturbance force caused by the frame servo at time n;
in step S5, the calculation process for obtaining the adaptive feedforward system control quantity of the magnetic bearing system at the time of n +1 is as follows:
u(n+1)＝G p (s)*ω g (n+1)*k c (n+1)
wherein u (n + 1) is the adaptive feedforward system control quantity, omega, of the magnetic bearing system at the moment n +1 g And (n + 1) is the projection of the frame rotation angular speed at the ax end of the magnetic bearing at the moment of n + 1.
2. A device for compensating measurable basic motion disturbance of a magnetic bearing, comprising:
the first calculation module is used for obtaining an MIT model reference control voltage quantity at n moment according to a projection value of the frame rotation angular speed at the ax end of the magnetic bearing at n moment, and meanwhile, the MIT model reference control voltage quantity is used as a self-adaptive feedforward system control quantity of the magnetic bearing system at n moment;
the second calculation module is used for obtaining the disturbance displacement error of the bearing-rotor system at the n moment according to the self-adaptive feedforward system control quantity of the magnetic bearing system at the n moment;
the third calculation module is used for obtaining the disturbance power error at the n moment according to the disturbance displacement error of the bearing-rotor system at the n moment;
the first updating module is used for obtaining the feedforward control gain at the n +1 moment according to the disturbance power error at the n moment;
the second updating module is used for obtaining the self-adaptive feedforward system control quantity of the magnetic bearing system at the moment of n +1 according to the feedforward control gain at the moment of n + 1;
wherein the processes of the first calculation module, the second calculation module, the third calculation module, the first update module and the second update module are repeated until the disturbance error of the magnetic bearing-rotor system is zero; wherein, the first and the second end of the pipe are connected with each other,
in the first calculation module, a calculation formula of the reference control voltage quantity of the MIT model at the n moment is as follows:
u(n)＝G p (s)*ω g (n)*k c (n)
wherein u (n) is the adaptive feedforward system control, ω, of the magnetic bearing system at time n g (n) is the projection value of the frame rotation angular velocity on the ax end of the magnetic bearing at the moment n, G p (s) is a controlled object model, k c (n) is the feedforward control gain at n moments;
in the second calculation module, after the control voltage u (n) is output, feedforward control current i is generated through a driving coil of an electromagnetic bearing, meanwhile, the rotor is subjected to feedforward electromagnetic attraction force f generated by the driving coil, the feedforward electromagnetic force and disturbance force act together to correct the position of the rotor, rotor position signals are collected to rotor displacement at n moments through a displacement sensor, and an error e between the rotor position signals and target displacement can be calculated s ；
In the third calculation module, the calculation formula of the disturbance power error at the time n is as follows:
wherein e is f (n) is the disturbance force error at time n, e s (n) is the disturbance displacement error of the bearing-rotor system at time n, G r (s) is the transfer function of the rotor system, and T is the numerical conversion coefficient;
in the first updating module, the calculation formula of the feedforward control gain at the moment of n +1 is as follows:
k c (n+1)＝k c (n)+χ·γe f (n)f d (n)
wherein k is c (n + 1) is feedforward control gain at the moment of n +1, chi is sampling time, gamma is step length, e f (n) is the disturbance force error at the moment n; f. of d (n) is the base disturbance force caused by the frame servo at time n;
in the second updating module, the calculation process for obtaining the self-adaptive feedforward system control quantity of the magnetic bearing system at the moment of n +1 is as follows:
u(n+1)＝G p (s)*ω g (n+1)*k c (n+1)
wherein u (n + 1) is the adaptive feedforward system control quantity, omega, of the magnetic bearing system at the moment n +1 g And (n + 1) is the projection of the frame rotation angular speed at the ax end of the magnetic bearing at the moment of n + 1.
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| CN114735240A (en) | 2022-07-12 |
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