CN112857348A - Angular velocity measuring method using magnetic suspension bearing - Google Patents
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- 239000000725 suspension Substances 0.000 title claims abstract description 28
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- 238000013528 artificial neural network Methods 0.000 claims abstract description 44
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G1/00—Cosmonautic vehicles
- B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
- B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
- B64G1/244—Spacecraft control systems
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G1/00—Cosmonautic vehicles
- B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
- B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
- B64G1/36—Guiding or controlling apparatus, e.g. for attitude control using sensors, e.g. sun-sensors, horizon sensors
- B64G1/369—Guiding or controlling apparatus, e.g. for attitude control using sensors, e.g. sun-sensors, horizon sensors using gyroscopes as attitude sensors
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
- G01C19/02—Rotary gyroscopes
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
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- G06N3/02—Neural networks
- G06N3/08—Learning methods
- G06N3/084—Backpropagation, e.g. using gradient descent
Abstract
The invention discloses an angular velocity measuring method using a magnetic suspension bearing, which realizes inverse solution of spacecraft attitude angles by training a neural network, takes two radial paths of displacement signals and electromagnetic driving current signals of a magnetic bearing control system as training samples and the attitude angular velocity of a spacecraft as a label of the training samples when the neural network is trained, and adopts a BP neural network based on convolution data preprocessing to train in order to avoid the attitude inverse solution error, and can take the current signals at the last moment and the next moment of the current moment into account by convolution of the electromagnetic torque current signals, and then trains the BP neural network based on convolution data preprocessing by using a gradient descent method to determine the weight of the convolution BP network and the value of an offset term, and finally the BP neural network is programmed into a gyroscope attitude control system to detect the attitude angular velocity of the spacecraft in real time, the reliability of the attitude control system is improved.
Description
Technical Field
The invention relates to the field of spacecraft attitude control and detection, in particular to an angular velocity measurement method by using a magnetic suspension bearing.
Background
The attitude control system is an important subsystem for realizing attitude maneuver and attitude stabilization of the three-axis stabilized spacecraft and comprises three parts, namely an attitude sensor, a controller and an actuating mechanism. With the continuous expansion of the application range of the space spacecraft, higher requirements are put forward on the rapid maneuver of the spacecraft attitude. However, since a damping isolation device is often arranged between the detection device and the execution device, control and detection are asynchronous, and the requirement for fast and high-precision control is difficult to meet, so that the integration of attitude measurement and control with high reliability is an important development trend.
The attitude of the existing spacecraft is changed mainly by the following modes: the control actuator of the spacecraft, namely the double-frame magnetic suspension CMG high-speed gyroscope, utilizes the moment output realized by the moment of the gyroscope, a rotor of the moment gyroscope is supported by adopting a five-degree-of-freedom permanent magnet biased hybrid magnetic bearing, and when the axisymmetric rotor rotates around a symmetric axis at a high speed, the attitude of the spacecraft is changed by changing the angles of two frames of the magnetic suspension gyroscope and utilizing the resistance moment expressed by the change of the direction of the current rotating shaft in space. In the process, the magnetic bearing control system generates corresponding electromagnetic force to prevent the gyro rotor and the gyro room from generating relative motion by controlling the current of the coil, so that the rotor is suspended in the center of the gap. When the magnetically suspended moment gyroscope is in a working state, the moment borne by the magnetically suspended rotor is caused by the rotation of the spacecraft, the rotation of the gyroscope frame and the relative displacement of the rotor, and the magnitude of the moment borne by the magnetically suspended rotor in the magnetically suspended moment gyroscope is uniquely determined by the magnetic bearing force. Therefore, the three-axis angular velocity of the spacecraft can be obtained by detecting the current of the magnetic bearing and the displacement information of the rotor in real time.
However, the magnetic suspension high-speed rotor system based on five degrees of freedom is actually a multi-input multi-output closed-loop system in attitude measurement, and can measure the attitude angular speed of two input shafts along the radial direction. However, due to the high-speed rotor dynamics, there is a coupling between the two measurement axes, which is dual, that is, the input angular velocity on one axis can generate the gyro rotor deflection angle and the gyro moment on the two axes, so there is always a cross coupling between the two measurement axes, and if only the dynamic equation of the magnetic suspension rotor is used, it is difficult to solve the attitude angular velocity of the spacecraft indirectly by an inverse solution method.
Therefore, the invention provides an inverse solution method for realizing the attitude angle of the spacecraft by training a neural network.
Disclosure of Invention
The invention aims to provide an angular velocity measuring method utilizing a magnetic suspension bearing, which can take current signals at the last moment and the next moment of the current moment into account by convolution of electromagnetic torque current signals, train a BP neural network based on convolution data preprocessing by using a gradient descent method, determine weights and offset items of the convolution BP network, and finally program the BP neural network into a magnetic suspension torque gyro attitude control system to detect the real-time attitude angular velocity of a spacecraft in real time, thereby realizing integration of detection and control and improving the reliability of the attitude control system.
In order to achieve the above object, the present invention provides a method for measuring angular velocity of a magnetic suspension bearing, comprising the steps of:
s1, calculating attitude angular velocity
S1-1, setting the rotation speed of the gyro rotor to be omega, and assuming the initial attitude angular velocity and the initial rotation angle to be omega according to the dynamic and static mechanics principleZero when the external attitude angular velocity is respectively equal to the rotor x axis and the rotor y axis
And
its corresponding moment equation is expressed as:
wherein, the rotor angular momentum H ═ JZΩ，JzIs rotor pole moment of inertia; j. the design is a squarerAs the moment of inertia at the equator of the rotor,
and
the gyroscopic precession moment terms of the high-speed rotor along the x axis and the y axis respectively,
and
the inertia moment terms of the rotor along the x axis and the y axis respectively;
s1-2, Laplace transform is carried out on the formula (1) to obtain:
wherein the precession moment
Mgx(s) and Mgy(s) are each MgxAnd MgyThe laplace transform of (a) is performed,
and
are respectively as
And
s is a laplace transform operator;
s1-3, the estimated value of attitude angular velocity is expressed as:
s2, measuring a pair of pyramid-shaped radial magnetic bearing control currents i of the double-frame magnetic suspension CMG installed on the spacecraftl＝(ilax，ilbx，ilay，ilby)、ir＝(irax，irbx，iray，irby) And sensor coordinates q of a pair of rotorsls＝(hlax，hlbx，hlay，hlby)、qrs＝(hrax，hrbx，hray，hrby)；
S3, constructing a neural network model
S3-1, selecting a fitted neural network as a two-layer neural network, wherein the two-layer neural network is a BP neural network for convolution data preprocessing and comprises a single-layer convolution pooled forward transfer network and an error reverse transfer network, and the single-layer convolution pooled forward transfer network comprises a single-layer convolution pooled layer, a hidden layer and an output layer;
and the parameters of the convolution pooling layer are set to be [1, 0.3, -0.5, -0.9, -1, -0.5, 1, 1.3, 1.5], and the operation formula of the data at a certain moment is as follows:
xi＝(Ii-4+0.3*Ii-3-0.5*Ii-2-0.9*Ii-1-Ii-0.5*Ii+1+Ii+2+1.3*Ii+3+1.5*Ii+4)/2 (4)
s3-2, a single-layer convolution pooled forward transfer network;
s3-3, an error reverse transfer network;
the method comprises the steps of taking a radial magnetic bearing control current and the output of a displacement sensor as input training samples, taking spacecraft attitude angular velocity accurately measured by an inertia element as a training label, performing single-dimensional convolution pooling on radial magnetic bearing control current data and the displacement sensor, and then performing reverse transmission on errors;
s4, training the BP neural network based on convolution data preprocessing by using a gradient descent method;
s4-1, determining the connection weight and bias of the BP neural network preprocessed by the convolution data;
s4-2, calculating a global error E under a training sample by taking the adjusted hidden layer weight w and the adjusted output layer weight v as a new forward-direction transmission neural network, judging whether the global error E meets a target, if not, continuously adjusting the hidden layer weight w and the output layer weight v and continuously training until a threshold value of the global error E is met, finishing training, and outputting w, b, v and l under the current network as a finally trained neural network;
and S5, obtaining connection weight and bias according to the training of the step S4-2, and programming a convolution pooling data preprocessing formula and a formula into the DSP, thereby realizing the real-time detection of the three-axis attitude angular velocity of the spacecraft.
Preferably, the specific step of step S3-2 includes:
in the process of forward transmission of the neural network, n nodes are output after input training samples pass through a convolution pooling layer, q nodes are output from a hidden layer, m nodes are output from an output layer, and a weight value between the convolution pooling layer and the hidden layer is vkiOffset is bkThe weight between the hidden layer and the output layer is wkjOffset is ljThe activation function of the hidden layer is f1(.), the activation function of the output layer is f2(.)；
The net input of the k-th neuron in the q neurons in the hidden layer and the j-th neuron in the m neurons in the output layer are respectively
And
the output of the k-th node of the hidden layer after the activation function is f1 (.):
the activation function is f2(.) the output of the jth node of the post-output layer is:
thus, the approximate mapping of the n-dimensional space vector of the B-P network to the m-dimensional space is completed.
Preferably, step S3-3 specifically includes the following steps:
s3-3-1, error calculation
Let the input be P learning samples, use x1，x2，x3，…xpTo show that the P-th sample is input into the B-P network to obtain the output yj pJ ═ 1, 2, 3, using the mean square error function, then the error Ep for the p-th sample is obtained:
wherein, tj pIs the desired output;
for p samples, the global error is:
s3-3-2, adjusting weight of output layer
Training the network by using a gradient descent method, and continuously adjusting wjkTo achieve a global error E minimization, i.e.
Wherein eta is the learning rate;
the error signal is defined as:
wherein the content of the first and second substances,
partial differentiation of the output layer activation function:
and then, pushing out:
derived from the chain theorem:
the weight value adjustment formula of each neuron of the output layer is as follows:
s3-3-3 hidden layer weight adjustment
Adjusting the weight of the hidden layer:
the error signal is defined as:
wherein the content of the first and second substances,
derived from the chain theorem:
partial differentiation of the hidden layer transfer function:
and then, pushing out:
derived from the chain theorem:
the weight value adjustment formula of each neuron of the hidden layer is obtained as follows:
preferably, in step S3-2: the number of nodes of the input layer is 16 ([ i [ ])l，ir，qls，qrs]T) The number of hidden layer nodes is 80, and the number of output layer nodes is 3;
the learning rate is 0.01 in step S3-3.
Preferably, the actual output of the output layer is set to be in step S3-2
The activation functions of the hidden layer and the output layer are both unipolar sigmoid functions
Preferably, the data preprocessing described in step S4-1 includes the steps of:
before training input training samples, normalizing the data, and after processing, X0＝[X01，X02，X03…X016]TBy X0iWherein i is 1, 2, 3 · 16.
Preferably, step S4-1 specifically includes: after training the BP neural network, extracting the connection weight v between the input layer neuron i and the hidden layer neuron k trained in the step S3-3kiAnd bias bkAnd the connection weight w between hidden layer neuron k and output layer neuron jjkAnd an offset lj。
Preferably, the convolution pooling layer in step S3-1 is a single-latitude convolution pooling layer.
Therefore, the invention adopts the angular velocity measuring method using the magnetic suspension bearing, current signals at the last moment and the next moment of the current moment can be taken into account by convolution of electromagnetic torque current signals, a BP neural network based on convolution data preprocessing is trained by using a gradient descent method, the weight value and the offset value of the convolution BP network are determined, finally the BP neural network is programmed into a gyroscope attitude control system, the attitude angular velocity of the spacecraft on the day can be detected in real time, when the attitude of the spacecraft is changed, the peak value of a control current signal can be caused due to the active control action of the control system on a magnetic bearing, in order to avoid the influence of the peak value on the training network, the peak wave suppression of the current signal is realized by using a convolution pooling layer, the influence of a current error on an effective signal is avoided, and the synchronization of detection and control is realized, the reliability of the attitude control system is improved.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a BP neural network diagram of an angular velocity measurement method using a magnetic bearing according to an embodiment of the present invention;
fig. 2 is a schematic diagram of convolution pooling data processing using an angular velocity measurement method of a magnetic bearing according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, and it should be noted that the present embodiment is based on the technical solution, and the detailed implementation and the specific operation process are provided, but the protection scope of the present invention is not limited to the present embodiment.
FIG. 1 is a BP neural network diagram of an angular velocity measurement method using a magnetic bearing according to an embodiment of the present invention; fig. 2 is a schematic diagram of convolution pooling data processing of an angular velocity measurement method using a magnetic bearing according to an embodiment of the present invention, as shown in fig. 1 and 2, the present invention includes the following steps:
s1, calculating attitude angular velocity
S1-1, setting the gyro rotor rotation speed to be omega, according to the dynamic and static mechanics principle, assuming that the initial attitude angular velocity and the initial rotation angle are zero, when the external attitude angular velocity is respectively equal to the rotation angle along the x axis and the y axis of the rotor
And
its corresponding moment equation is expressed as:
wherein, the rotor angular momentum H ═ JZΩ，JzIs rotor pole moment of inertia; j. the design is a squarerAs the moment of inertia at the equator of the rotor,
and
the gyroscopic precession moment terms of the high-speed rotor along the x axis and the y axis respectively,
and
the inertia moment terms of the rotor along the x axis and the y axis respectively;
s1-2, in the formula (1), the moment mainly includes two parts, one is the gyroscopic precession moment caused by the attitude angular velocity, and the other is the inertia moment term caused by the attitude angular acceleration, because the rotor usually runs at a very high rotation speed, and has a very large angular momentum, and the attitude angular acceleration of the spacecraft is very small, the inertia moment term as a tiny amount can be ignored, so the laplace transform is performed on the formula (1):
wherein the precession moment
Mgx(s) and Mgy(s) are each MgxAnd MgyThe laplace transform of (a) is performed,
and
are respectively as
And
s is a laplace transform operator;
s1-3, the estimated value of attitude angular velocity is expressed as:
according to the formula (3), the attitude angular velocity is only related to precession moment Mg, the attitude of the magnetic suspension CMG high-speed rotor can be changed at the moment of changing the attitude of the spacecraft, at the moment, the magnetic bearing control system can generate corresponding electromagnetic force to eliminate the influence of gyro moment on the magnetic suspension CMG high-speed rotor, so that the magnetic suspension CMG high-speed rotor is positioned at the central position, and the control system decouples and controls two radial translational degrees of freedom and two rotational degrees of freedom of the magnetic suspension rotor mainly by controlling 4 radial control quantities (respectively represented by ax, ay, bx and by) of the magnetic suspension CMG rotor in the process. Because the axial bearing channel (indicated by z) controls a translation degree of freedom, the rotation degree of freedom is driven by the motor, the angular momentum of the rotor is provided, and the angular momentum does not participate in the torque control of the magnetic suspension CMG rotor, the output torque of the double-frame magnetic suspension CMG can be considered to be mainly influenced by the radial channel of the magnetic bearing.
For research and analysis convenience, the radial magnetic bearings, the power amplifier and the control system in each channel are assumed to have the same performance, and the installation positions of the radial magnetic bearings are symmetrical relative to the mass center of the rotor.
Therefore, the angular velocity of the spacecraft under the action of force can be known
And
at the moment of change, the double-frame magnetic suspension CMG can generate precession torque Mg, and then the high-speed rotor of the magnetic suspension CMG displaces q under a bearing coordinate systemmChanging, and thus high speed, the sensor coordinate q of the rotorsFinally, the displacement q under the bearing coordinate system of the high-speed rotor is changed through a magnetic suspension bearing control system under the action of a radial magnetic bearing control current i ═ (iax, ibx, iay, iby)mReturning to the original value, the rotor remains centered on the magnetic bearing.
S2, according to the description, the angular velocities of two shafts of the spacecraft are determined in the context of single double-frame magnetic levitation CMG
And
the current i ═ can be controlled by the radial magnetic bearingax，ibx，iay，iby) And the sensor coordinate qs of the rotor, so that a pair of pyramid-shaped radial magnetic bearing control currents i of the double-frame magnetic suspension CMG installed on the spacecraft is measuredl＝(ilax，ilbx，ilay，ilby)、ir＝(irax，irbx，iray，irby) And sensor coordinates q of a pair of rotorsls＝(hlax，hlbx，hlay，hlby)、qrs＝(hrax，hrbx，hray，hrby) (ii) a In the embodiment, the double-frame magnetic suspension CMG is a two-degree-of-freedom gyroscope composed of a high-speed gyroscope rotor, an inner frame and an outer frame.
S3, constructing a neural network model
S3-1, selecting a fitted neural network as a two-layer neural network, wherein the two-layer neural network is a BP neural network for convolution data preprocessing and comprises a single-layer convolution pooled forward transfer network and an error reverse transfer network, and the single-layer convolution pooled forward transfer network comprises a single-layer convolution pooled layer, a hidden layer and an output layer;
and the parameters of the convolution pooling layer are set to be [1, 0.3, -0.5, -0.9, -1, -0.5, 1, 1.3, 1.5], and the operation formula of the data at a certain moment is as follows:
xi＝(Ii-4+0.3*Ii-3-0.5*Ii-2-0.9*Ii-1-Ii-0.5*Ii+1+Ii+2+1.3*Ii+3+1.5*Ii+4)/2 (4)
preferably, the convolution pooling layer in step S3-1 is a single-latitude convolution pooling layer.
S3-2, a single-layer convolution pooled forward transfer network;
preferably, the specific step of step S3-2 includes:
in the process of forward transmission of the neural network, n nodes are output after input training samples pass through a convolution pooling layer, q nodes are output from a hidden layer, m nodes are output from an output layer, and a weight value between the convolution pooling layer and the hidden layer is vkiOffset is bkThe weight between the hidden layer and the output layer is wkiOffset is ljThe activation function of the hidden layer is f1(.), the activation function of the output layer is f2(.)；
The net input of the k-th neuron in the q neurons in the hidden layer and the j-th neuron in the m neurons in the output layer are respectively
And
the output of the k-th node of the hidden layer after the activation function is f1 (.):
the activation function is f2(.) the output of the jth node of the post-output layer is:
thus, the approximate mapping of the n-dimensional space vector of the B-P network to the m-dimensional space is completed.
Preferably, the actual output of the output layer is set to be in step S3-2
The activation functions of the hidden layer and the output layer are both unipolar sigmoid functions
S3-3, an error reverse transfer network;
the method comprises the steps of taking a radial magnetic bearing control current and the output of a displacement sensor as input training samples, taking spacecraft attitude angular velocity accurately measured by an inertia element as a training label, performing single-dimensional convolution pooling on radial magnetic bearing control current data and the displacement sensor, and then performing reverse transmission on errors;
preferably, step S3-3 specifically includes the following steps:
s3-3-1, error calculation
Let the input be P learning samples, use x1，x2，x3，…xpTo show that the P-th sample is input into the B-P network to obtain the output yj pUsing the mean square error function, j ═ 1, 2, 3, and then the error E of the p-th sample is obtainedp：
Wherein, tj pIs the desired output;
for p samples, the global error is:
s3-3-2, adjusting weight of output layer
Training the network by using a gradient descent method, and continuously adjusting wjkTo achieve a global error E minimization, i.e.
Wherein eta is the learning rate;
the error signal is defined as:
wherein the content of the first and second substances,
partial differentiation of the output layer activation function:
and then, pushing out:
derived from the chain theorem:
the weight value adjustment formula of each neuron of the output layer is as follows:
s3-3-3 hidden layer weight adjustment
Adjusting the weight of the hidden layer:
the error signal is defined as:
wherein the content of the first and second substances,
derived from the chain theorem:
partial differentiation of the hidden layer transfer function:
and then, pushing out:
derived from the chain theorem:
the weight value adjustment formula of each neuron of the hidden layer is obtained as follows:
preferably, in step S3-2: the number of nodes of the input layer is 16 ([ i [ ])l，ir，qls，qrs]T) The number of hidden layer nodes is 80, and the number of output layer nodes is 3;
the learning rate is 0.01 in step S3-3.
S4, training the BP neural network based on convolution data preprocessing by using a gradient descent method;
s4-1, determining the connection weight and bias of the BP neural network preprocessed by the convolution data;
preferably, the data preprocessing described in step S4-1 includes the steps of:
before training input training samples, normalizing the data, and after processing, X0＝[X01，X02，X03…X016]TBy X0iWherein i is 1, 2, 3 · 16.
Preferably, step S4-1 specifically includes: after training the BP neural network, extracting the connection weight v between the input layer neuron i and the hidden layer neuron k trained in the step S3-3kiAnd bias bkAnd the connection weight w between hidden layer neuron k and output layer neuron jjkAnd an offset lj。
S4-2, calculating a global error E under a training sample by taking the adjusted hidden layer weight w and the adjusted output layer weight v as a new forward-direction transmission neural network, judging whether the global error E meets a target, if not, continuously adjusting the hidden layer weight w and the output layer weight v and continuously training until a threshold value of the global error E is met, finishing training, and outputting w, b, v and l under the current network as a finally trained neural network;
and S5, obtaining connection weight and bias according to the training of the step S4-2, and programming a convolution pooling data preprocessing formula and the formulas (4), (5) and (6) into a DSP (digital signal processor), thereby realizing the real-time detection of the three-axis attitude angular velocity of the spacecraft.
Therefore, by adopting the angular velocity measuring method using the magnetic suspension bearing, the current signals at the last moment and the next moment of the current moment can be taken into account by convolution of the electromagnetic torque current signals, then the BP neural network based on convolution data preprocessing is trained by using a gradient descent method, the weight value and the offset item value of the convolution BP network are determined, and finally the BP neural network is programmed into a gyroscope attitude control system, so that the attitude angular velocity of the spacecraft on the same day can be detected in real time, the synchronization of detection and control is realized, and the reliability of the attitude control system is improved.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the invention without departing from the spirit and scope of the invention.
Claims (8)
1. An angular velocity measurement method using a magnetic suspension bearing is characterized in that: the method comprises the following steps:
s1, calculating attitude angular velocity
S1-1, setting the gyro rotor rotation speed to be omega, according to the dynamic and static mechanics principle, assuming that the initial attitude angular velocity and the initial rotation angle are zero, when the external attitude angular velocity is respectively equal to the rotation angle along the x axis and the y axis of the rotor
And
its corresponding moment equation is expressed as:
wherein, the rotor angular momentum H ═ JZΩ，JzIs rotor pole moment of inertia; j. the design is a squarerIs the rotor equator moment of inertia;
and
are respectively high-speed rotorsThe gyroscopic precession moment terms along the x-axis and the y-axis,
and
the inertia moment terms of the rotor along the x axis and the y axis respectively;
s1-2, Laplace transform is carried out on the formula (1) to obtain:
wherein the precession moment
Mgx(s) and Mgy(s) are each MgxAnd MgyThe laplace transform of (a) is performed,
and
are respectively as
And
s is a laplace transform operator;
s1-3, the estimated value of attitude angular velocity is expressed as:
s2, measuring a pair of pyramid-shaped radial magnetic bearings of the double-frame magnetic suspension CMG installed on the spacecraftStream il＝(ilax，ilbx，ilay，ilby)、ir＝(irax，irbx，iray，irby) And sensor coordinates q of a pair of rotorsls＝(hlax，hlbx，hlay，hlby)、qrs＝(hrax，hrbx，hray，hrby)；
S3, constructing a neural network model
S3-1, selecting a fitted neural network as a two-layer neural network, wherein the two-layer neural network is a BP neural network for convolution data preprocessing and comprises a single-layer convolution pooled forward transfer network and an error reverse transfer network, and the single-layer convolution pooled forward transfer network comprises a single-layer convolution pooled layer, a hidden layer and an output layer;
and the parameters of the convolution pooling layer are set to be [1, 0.3, -0.5, -0.9, -1, -0.5, 1, 1.3, 1.5], and the operation formula of the data at a certain moment is as follows:
xi＝(Ii-4+0.3*Ii-3-0.5*Ii-2-0.9*Ii-1-Ii-0.5*Ii+1+Ii+2+1.3*Ii+3+1.5*Ii+4)/2 (4)
s3-2, a single-layer convolution pooled forward transfer network;
s3-3, an error reverse transfer network;
the method comprises the steps of taking a radial magnetic bearing control current and the output of a displacement sensor as input training samples, taking spacecraft attitude angular velocity accurately measured by an inertia element as a training label, performing single-dimensional convolution pooling on radial magnetic bearing control current data and the displacement sensor, and then performing reverse transmission on errors;
s4, training the BP neural network based on convolution data preprocessing by using a gradient descent method;
s4-1, determining the connection weight and bias of the BP neural network preprocessed by the convolution data;
s4-2, calculating a global error E under a training sample by taking the adjusted hidden layer weight w and the adjusted output layer weight v as a new forward-direction transmission neural network, judging whether the global error E meets a target, if not, continuously adjusting the hidden layer weight w and the output layer weight v and continuously training until a threshold value of the global error E is met, finishing training, and outputting w, b, v and l under the current network as a finally trained neural network;
and S5, obtaining connection weight and bias according to the training of the step S4-2, and programming a convolution pooling data preprocessing formula and a formula into the DSP, thereby realizing the real-time detection of the three-axis attitude angular velocity of the spacecraft.
2. The angular velocity measurement method using a magnetic bearing according to claim 1, wherein: the specific steps of step S3-2 include:
in the process of forward transmission of the neural network, n nodes are output after input training samples pass through a convolution pooling layer, q nodes are output from a hidden layer, m nodes are output from an output layer, and a weight value between the convolution pooling layer and the hidden layer is vkiOffset is bkThe weight between the hidden layer and the output layer is wkjOffset is ljThe activation function of the hidden layer is f1(.), the activation function of the output layer is f2(.)；
The net input of the k-th neuron in the q neurons in the hidden layer and the j-th neuron in the m neurons in the output layer are respectively
And
the activation function is f1(.) the output of the k-th node of the rear hidden layer is:
the activation function is f2(.) the output of the jth node of the post-output layer is:
thus, the approximate mapping of the n-dimensional space vector of the B-P network to the m-dimensional space is completed.
3. The angular velocity measurement method using a magnetic bearing according to claim 2, wherein: step S3-3 specifically includes the following steps:
s3-3-1, error calculation
Let the input be P learning samples, use x1，x2，x3，…xpTo show that the P-th sample is input into the B-P network to obtain the output yj pJ ═ 1, 2, 3, using the mean square error function, and then the error E for the p-th sample is obtainedp：
Wherein, tj pIs the desired output;
for p samples, the global error is:
s3-3-2, adjusting weight of output layer
Training the network by using a gradient descent method, and continuously adjusting wjkTo achieve a global error E minimization, i.e.
Wherein eta is the learning rate;
the error signal is defined as:
wherein the content of the first and second substances,
partial differentiation of the output layer activation function:
and then, pushing out:
derived from the chain theorem:
the weight value adjustment formula of each neuron of the output layer is as follows:
s3-3-3 hidden layer weight adjustment
Adjusting the weight of the hidden layer:
the error signal is defined as:
wherein the content of the first and second substances,
derived from the chain theorem:
partial differentiation of the hidden layer transfer function:
and then, pushing out:
derived from the chain theorem:
the weight value adjustment formula of each neuron of the hidden layer is obtained as follows:
4. the angular velocity measurement method using a magnetic bearing according to claim 3, wherein: in step S3-2: the number of nodes of the input layer is 16 ([ i [ ])l，ir，qls，qrs]T) The number of hidden layer nodes is 80, and the number of output layer nodes is 3;
the learning rate is 0.01 in step S3-3.
5. The angular velocity measurement method using a magnetic bearing according to claim 2, wherein: the actual output of the output layer is set to be in step S3-2
The activation functions of the hidden layer and the output layer are both unipolar sigmoid functions
6. The angular velocity measurement method using a magnetic bearing according to claim 1, wherein: the data preprocessing described in step S4-1 includes the steps of:
before training input training samples, normalizing the data, and after processing, X0＝[X01，X02，X03…X016]TBy X0iWherein i is 1, 2, 3 … 16.
7. The angular velocity measurement method using a magnetic bearing according to claim 3, wherein: step S4-1 specifically includes: after training the BP neural network, extracting the connection weight v between the input layer neuron i and the hidden layer neuron k trained in the step S3-3kiAnd bias bkAnd the connection weight w between hidden layer neuron k and output layer neuron jjkAnd an offset lj。
8. The angular velocity measurement method using a magnetic bearing according to any one of claims 1 to 7, wherein: the convolution pooling layer in step S3-1 is a convolution pooling layer of a single latitude.
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