CN115079566A - Self-adaptive radial basis function neural network control method for carrier rocket attitude system - Google Patents

Self-adaptive radial basis function neural network control method for carrier rocket attitude system Download PDF

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CN115079566A
CN115079566A CN202110293507.0A CN202110293507A CN115079566A CN 115079566 A CN115079566 A CN 115079566A CN 202110293507 A CN202110293507 A CN 202110293507A CN 115079566 A CN115079566 A CN 115079566A
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attitude
carrier rocket
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刘华华
胡昌华
刘晨
王青
马艳如
张连怡
杨涵博
谢宝娣
李伟夫
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Abstract

The invention provides a self-adaptive radial basis function neural network control method of a carrier rocket attitude system, which comprises the following steps: establishing a dynamic model of a carrier rocket attitude control system; step two: establishing a dynamic model of the attitude control system under the fault of the carrier rocket, and establishing the dynamic model of the attitude control system under the fault by considering the fault of an actuator on the basis of the model in the first establishing step; step three: designing a nonsingular terminal sliding mode surface, and enabling the attitude tracking error to be converged to zero within limited time by designing a terminal sliding mode control law; step four: and designing a radial basis function neural network to approach unknown system parameters, and adding a self-adaptive control item for compensating errors in the disturbance and approximation processes, so that the attitude tracking error is converged to zero in a limited time. The method considers the influence of interference, actuator faults and model uncertainty factors, and designs the control rate to ensure that the error of the carrier rocket attitude tracking system converges to zero in limited time.

Description

Self-adaptive radial basis function neural network control method for carrier rocket attitude system
Technical Field
The invention belongs to the field of flight control systems, and particularly relates to a self-adaptive radial basis function neural network control method for a carrier rocket attitude system.
Background
The launch vehicle is an important tool for space exploration and becomes a focus of research in many countries, such as the Ares series and Chinese Long series launch vehicles of NASA in the United states. The launch vehicle undertakes the tasks of manned spacecraft and the like, once the launch task fails, huge economic loss is brought, and military affairs, outcrossing and the like of the whole country are influenced. Therefore, a robust and reliable flight control system is essential to ensure flight safety.
The traditional flight control method adopts a gain scheduling and proportional-integral-derivative controller, the carrier rocket has complex pneumatic environment and large interference and uncertainty, and the high-precision control of the flight process by adopting the traditional flight control method has certain difficulty. In order to solve the above problems, many scholars propose advanced control theories, such as sliding mode control, adaptive neural network control, non-parametric adaptive control and the like. The nonsingular terminal sliding mode control method has the advantages of being insensitive to parameter uncertainty and external interference, strong in fault tolerance and the like, but also has the defects. Firstly, the nonsingular terminal sliding mode control method needs to obtain an accurate mathematical model and physical parameters of a system, and certain control application capacity is reduced. Secondly, the nonsingular terminal sliding mode control method has the problem of an inherent large control buffeting phenomenon, and a switching control item caused by discontinuous large switch gain has adverse effects on a carrier rocket actuating mechanism. Furthermore, another problem with the sliding mode control method is that the switching control gain in the control law requires a priori knowledge of the upper limit of the disturbance.
Based on the nonsingular terminal sliding mode control law, the invention provides a self-adaptive neural network controller based on the nonsingular terminal sliding mode, and the self-adaptive neural network controller has the following main advantages: (1) and an accurate model of the system is not required to be obtained, and the requirement on the modeling accuracy of the system is low. (2) Aiming at the buffeting phenomenon in nonsingular terminal sliding mode control, the method provided eliminates the buffeting influence.
Disclosure of Invention
The invention aims to solve the problem of attitude control under the conditions of carrier rocket external interference, actuator failure and system model unknown.
The technical scheme adopted by the invention is as follows:
the invention provides a fault-tolerant control method of a carrier rocket attitude system based on a radial basis function neural network, which comprises the following steps:
the method comprises the following steps: establishing a dynamic model of a carrier rocket attitude control system;
step two: establishing a dynamic model of the attitude control system under the fault of the carrier rocket, establishing the dynamic model of the attitude control system under the fault by considering the fault of an actuator on the basis of the model of the attitude control system of the carrier rocket in the establishing step I, and calculating the tracking error of an attitude angle to obtain a second-order carrier rocket attitude tracking system;
step three: designing a nonsingular terminal sliding film surface, and enabling the attitude tracking error to be converged to zero in a limited time by designing a terminal sliding mode control law;
step four: based on the self-adaptive radial basis function neural network, under the condition that the rotary inertia of the carrier rocket is unknown and the terminal sliding mode control law is inapplicable to design, the radial basis function neural network is used for approaching unknown system parameters, and self-adaptive control items are added to compensate errors in disturbance and approximation processes, so that the attitude tracking error is converged to zero in limited time.
The invention has the advantages that:
(1) the control law design is directly carried out on the carrier rocket nonlinear attitude dynamics model without linearizing the model
And (6) processing.
(2) Not only unknown external disturbances and actuator faults are considered in the control law design, but also the case where the system model is unknown.
(3) The self-adaptive radial basis function neural network sliding mode nonlinear control law applied to single input and single output is expanded to a multi-input multi-output system.
Drawings
FIG. 1 is a tail view of a launch vehicle engine layout;
FIG. 2 is a diagram of a carrier rocket adaptive radial basis function neural network controller architecture;
FIG. 3 is a diagram of an attitude angle tracking error of an adaptive neural network method in an embodiment;
FIG. 4 is an attitude angle tracking error of the nonsingular terminal sliding mode method in the embodiment;
FIG. 5 is a core level engine deflection angle plot of the adaptive neural network method of an embodiment;
FIG. 6 is a graph of core-level engine deflection angles for the non-singular terminal sliding mode method in an embodiment;
FIG. 7 is a curve of a boosted engine deflection angle for the adaptive neural network method of an embodiment;
FIG. 8 is a curve of the deflection angle of the boosted engine for the nonsingular terminal sliding mode method in an embodiment;
fig. 9 is an abstract drawing.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The dynamic model of the attitude control system of the carrier rocket is established as follows:
Figure BSA0000236597380000021
in the formula: omega ═ theta, alpha, beta] T Is the attitude angle vector, theta is the roll angle, alpha is the yaw angle, and beta is the pitch angle. Omega ═ omega x ，ω y ，ω z ] T Is an angular velocity vector; j is an unknown moment of inertia matrix of the carrier rocket; d is the unknown external interference vector. S, omega × Respectively as follows:
Figure BSA0000236597380000031
Figure BSA0000236597380000032
u is a control input vector, represents an input torque, and is represented by combining the graph I:
Figure BSA0000236597380000033
the relationship between the equivalent swing angle and the swing angles of the core-level engine and the boosting engine is as follows:
Figure BSA0000236597380000034
Figure BSA0000236597380000035
in the formula, P is engine thrust; x R The distance from the engine nozzle to the top end of the rocket; x Z Is the centroid position; r and R are the distance from the engine center to the x-axis of the launch vehicle,
Figure BSA0000236597380000036
representing the engine equivalent swing angle. The control torque may be expressed as:
u＝Bδ
wherein δ is [ δ ] θ ，δ α ，δ β ] T (ii) a B is input matrix, and is obtained by sorting
Figure BSA0000236597380000037
Further, the second step is that the establishment process of the attitude control system dynamic model and the second-order carrier rocket attitude tracking system under the carrier rocket fault is as follows:
s1: attitude control system dynamics model under carrier rocket fault
Considering that a boosting engine or a core-level engine has a dead or failure fault, the fault model is as follows:
Figure BSA0000236597380000038
Figure BSA0000236597380000039
in the formula, i is 1, …, and 4 represents the ith actuator, and the number of the failed actuators does not exceed the maximum number of the failed actuators, that is, the rocket carrier can control the rest actuators to keep the system stable.
Figure BSA00002365973800000310
For the unknown failure factor of the ith actuator,
Figure BSA00002365973800000311
and
Figure BSA00002365973800000312
respectively, the upper and lower bounds of the failure factor. Sigma is the stuck value of i actuators,
Figure BSA00002365973800000313
namely when
Figure BSA00002365973800000314
No fault occurs; when in use
Figure BSA0000236597380000041
When the fault happens, the jamming fault of the ith actuator is shown; when in use
Figure BSA0000236597380000042
When, it indicates that the ith actuator section is failed.
Defining:
Figure BSA0000236597380000043
in the formula (I), the compound is shown in the specification,
Figure BSA0000236597380000044
establishing a carrier rocket dynamic model:
Figure BSA0000236597380000045
s2: second-order carrier rocket attitude tracking system
The tracking error defining the attitude angle is: e-omega r ，
Figure BSA0000236597380000046
And
Figure BSA0000236597380000047
respectively, the attitude angle tracking command and its first derivative. Order to
Figure BSA0000236597380000048
Substituting the formula (8) into the formula, and defining a carrier rocket attitude tracking system as follows:
Figure BSA0000236597380000049
wherein f (x) is ∈ R 3 ，G(x)∈R 3×3 ，d∈R 3 And is defined as follows:
Figure BSA00002365973800000410
further, the design of the terminal slide film surface and the selection of the parameters thereof in the third step are as follows:
s1: in order to ensure that the tracking error e converges to O within a limited time, the following nonsingular terminal sliding mode surfaces are designed:
s＝x 2 +c 1 x 1 +c 2 sig β (x 1 )
in the formula: s is formed by R 3 ，0＜β＜1。
S2: the parameters are selected as follows:
before controller design, 3 assumptions are given.
Assumption 1. Complex interference d in attitude tracking system is bounded and satisfied
Figure BSA00002365973800000411
Wherein
Figure BSA00002365973800000412
Is a normal number.
Suppose 2. control input vector δ (t) e L 2 The space, i.e., the integral of δ (t) over any finite time, is bounded.
Hypothesis 3. attitude angle command signal Ω r Continuous, its first two derivatives are consistently continuous and bounded.
c 1 And c 2 Positive, and satisfies c 1 ，c 2 ＝diag(c i1 ，c i2 ，c i3 )，i＝1，2。sig β (x 1 ) Is defined as follows: sig β (x 1 )＝[sig β (x 11 )，sig β (x 12 )，sig β (x 13 )] T And define sig β (x)＝|x| β sgn (x), where the sign function sgn (x) is defined as:
Figure BSA00002365973800000413
then, on the premise of assuming 1-3 are true, the slide film surface design and parameter selection are used, and the controller is designed as follows: delta is delta eq +δ d
Wherein:
Figure BSA0000236597380000051
in the formula, delta eq ，δ d ∈R 3 And k(s) are defined as follows:
Figure BSA0000236597380000052
z(x 1 )＝c 1 x 1 +c 2 sig β (x 1 ) The tracking error converges to zero within a finite time.
The proving process is as follows:
defining the Lyapunov candidate function as:
Figure BSA0000236597380000053
taking the derivative of V, we can obtain:
Figure BSA0000236597380000054
the derivative is obtained for the designed sliding mode surface and the posture tracking system is substituted into the following steps:
Figure BSA0000236597380000055
thereby:
Figure BSA0000236597380000056
Figure BSA0000236597380000057
in the formula (I), the compound is shown in the specification,
Figure BSA0000236597380000058
therefore, the attitude tracking error is converged to zero in a limited time through the designed terminal sliding mode control law.
After the syndrome is confirmed.
Further, the step four is based on the adaptive radial basis function neural network, unknown system parameters are approximated, adaptive control items are added, and the process of compensating errors in the disturbance and approximation processes is as follows:
s1: the moment of inertia J of the carrier rocket is assumed to be unknown, namely f (x) in the attitude tracking system of the carrier rocket is unknown, and the terminal sliding mode control law needs to obtain an accurate model of the system, so that the terminal sliding mode control law is not suitable for design. The process of the radial basis function neural network approaching unknown system parameters is as follows:
from the approximate characteristics of the radial basis function neural network, the unknown nonlinear function h (x) can be expressed as:
h(x)＝(W 0 ) T Ф 0 (x)+ε 0 ＝h 0 (x，c，σ)+ε 0
in the formula, W 0 The weight vector which is linearly output by the radial basis function neural network is an m multiplied by n dimensional matrix, and n is the dimension of h (x); epsilon 0 To estimate the error for the best; h is 0 (x, c, σ) is the optimal approximation function of h (x).
Figure BSA0000236597380000061
Is a vector of dimensions m in which the vector is,
Figure BSA0000236597380000062
the output of the Gaussian activation function of the hidden layer of the radial basis function is expressed as:
Figure BSA0000236597380000063
in the formula (I), the compound is shown in the specification,
Figure BSA0000236597380000064
and
Figure BSA0000236597380000065
is the optimal center point and bandwidth of the jth gaussian function.
Order to
Figure BSA0000236597380000066
F (x) can be expressed as:
F(x)＝(W 0 ) T Ф 0 (x)+ε 0 ＝F 0 (x，c，σ)+ε 0
thereby:
Figure BSA0000236597380000067
in the formula (I), the compound is shown in the specification,
Figure BSA0000236597380000068
is an optimum function F 0 (x, c, σ) and an adaptive function
Figure BSA0000236597380000069
The difference of (a).
Nonlinear function is linearized by Taylor expansion method
Figure BSA00002365973800000610
Conversion to local linearity:
Figure BSA00002365973800000611
in the formula (I), the compound is shown in the specification,
Figure BSA00002365973800000612
is an optimal weight matrix W 0 And an adaptive weight matrix
Figure BSA00002365973800000613
The difference of (a).
Figure BSA00002365973800000614
Is an optimal central vector c 0 And adaptive center vector
Figure BSA00002365973800000615
The difference of (a).
Figure BSA00002365973800000616
For an optimal bandwidth vector sigma 0 And adaptive bandwidth vector
Figure BSA00002365973800000617
The difference of (a). Epsilon 1 The residual difference value for the taylor expansion.
Figure BSA00002365973800000618
And
Figure BSA00002365973800000619
is defined as:
Figure BSA00002365973800000620
the following can be obtained:
Figure BSA00002365973800000621
external disturbances, parameter uncertainty, estimation error and linearization error are replaced by ζ:
ζ＝D+ε 1 +ε 0
then:
Figure BSA0000236597380000071
s2: the control rate is designed as follows:
u＝G -1 (x)(u tsm +u RBFNN +u ad )
in the formula u tsm A terminal sliding mode control item; u. of RBFNN Is a non-linear function f (x) approximated using a radial basis function neural network; u. of ad The adaptive control term is used for compensating disturbance and approximation process errors, enhancing the closed loop stability of the system and improving the transient performance. Three control items are defined as:
u tsm ＝-ks
Figure BSA0000236597380000072
Figure BSA0000236597380000073
in the formula (I), the compound is shown in the specification,
Figure BSA0000236597380000074
and
Figure BSA0000236597380000075
the estimated values of the unknown actual interference zeta and the adaptive gain alpha are respectively, and the adaptive updating law is designed as follows:
Figure BSA0000236597380000076
the control law is designed to make the error of the attitude tracking system of the carrier rocket converge to zero in a limited time.
The demonstration process is as follows:
defining a Lyapunov candidate function:
Figure BSA0000236597380000077
in the formula (I), the compound is shown in the specification,
Figure BSA0000236597380000078
it is not always certain about the estimation error,
Figure BSA0000236597380000079
is the difference between the adaptive gain and the fixed gain alpha. Derivation of the lyapunov function yields:
Figure BSA00002365973800000710
then:
Figure BSA00002365973800000711
and will be
Figure BSA00002365973800000712
Substituting, can obtain:
Figure BSA00002365973800000713
then:
Figure BSA0000236597380000081
and order:
Figure BSA0000236597380000082
then there are:
Figure BSA0000236597380000083
that is, in the control law design, the initial value of α is taken as a positive value, then
Figure BSA0000236597380000084
The global asymptotic stability of the system can be ensured. Therefore, the sliding mode surface can be gradually reached, and the obtained attitude tracking error can be converged to zero in a limited time by the terminal sliding mode characteristic.
After the syndrome is confirmed.
The structure diagram of the adaptive radial basis function neural network controller based on the terminal sliding mode is shown in fig. 2.
The technical effects of the present invention will be described below with reference to examples to fully understand the effects of the present invention and to demonstrate the effectiveness of the present invention. It is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and those skilled in the art can obtain other embodiments without inventive effort based on the embodiments of the present invention, and all embodiments are within the scope of the present invention.
For step one, in the embodiment, the time of flight of the launch vehicle is set to 45s, the thrust of each engine is P1200000N, and the initial attitude angle is x 1 (0)＝[-0.001 10.001 89.999] T . The attitude tracking command signal is x r ＝[10° 20° 80°] T And using filters
Figure BSA0000236597380000085
To smooth the desired gesture command signal.
For step two, the following two possible modes of the system are considered in the embodiment: and (3) a normal mode: all actuators operating normally, i.e. λ f ＝diag(1，1，…1)，η f 0. Failure mode: occurrence of stuck-in failure, i.e. lambda, of boost motor 2 f ＝0，
Figure BSA0000236597380000086
Considering the case where the system is normally operating in the first 20s, when t is 20s, the assist engine 2 has a stuck fault, and the stuck offset is σ of 3 °.
For step four, the weight matrix parameter of the radial basis function neural network in the embodiment is 19 × 3, the center of the radial basis function neural network is a 19 × 1 dimensional vector, and the bandwidth vector is 19 × 1. The input of the radial basis function neural network is a 15 multiplied by 1 dimensional vector, and the input parameters are respectively: three attitude angles, derivatives of the three attitude angles, three attitude angle error signals, angular velocity, and second derivatives of attitude angle command signals. To reduce the bandwidth, the sine and cosine values of the three attitude angles are taken as input. To ensure system convergence, the initial value of α is taken as: α is 0.4.
As can be seen from comparison between fig. 3 and fig. 4, the error convergence rate of the adaptive radial basis function neural network control law is faster than that of the terminal sliding mode control law, and when a fault occurs, the error signal can also be converged to zero rapidly. And the terminal sliding mode control law finally converges to a constant close to zero.
It can be seen from the comparison between the core-class engine and the boosted engine shown in fig. 5-8 that the buffeting characteristics based on the nonsingular terminal sliding mode control law are significantly improved by the control law based on the adaptive radial basis neural network.
The comparison result in the embodiment shows that the fault-tolerant controller adopting the adaptive neural network is obviously superior to the terminal sliding mode control method in tracking performance. From the aspect of the given control input buffeting, the controller adopting the adaptive neural network also has a better inhibiting effect on the control input buffeting.

Claims (5)

1. A fault-tolerant control method for a carrier rocket attitude system is characterized by comprising the following steps:
the method comprises the following steps: establishing a dynamic model of a carrier rocket attitude control system;
step two: establishing a dynamic model of the attitude control system under the fault of the carrier rocket, establishing the dynamic model of the attitude control system under the fault by considering the fault of an actuator on the basis of the model of the attitude control system of the carrier rocket in the establishing step I, and calculating the tracking error of an attitude angle to obtain a second-order carrier rocket attitude tracking system;
step three: designing a nonsingular terminal sliding film surface, and enabling the attitude tracking error to be converged to zero in a limited time by designing a terminal sliding mode control law;
step four: based on the self-adaptive radial basis function neural network, under the condition that the rotary inertia of the carrier rocket is unknown and the terminal sliding mode control law is inapplicable to design, the radial basis function neural network is used for approaching unknown system parameters, and self-adaptive control items are added to compensate errors in disturbance and approximation processes, so that the attitude tracking error is converged to zero in limited time.
2. The control method according to claim 1, wherein the first step of establishing the dynamic model of the attitude control system of the launch vehicle comprises:
the dynamic model of the attitude control system of the carrier rocket is established as follows:
Figure FSA0000236597370000011
in the formula: [ theta, alpha, beta ]] T Is the attitude angle vector, theta is the roll angle, alpha is the yaw angle, and beta is the pitch angle. Omega ═ omega x ，ω y ，ω z ] T Is an angular velocity vector; j is an unknown moment of inertia matrix of the carrier rocket; d is the unknown external interference vector. S, omega × Respectively as follows:
Figure FSA0000236597370000012
Figure FSA0000236597370000013
u is a control input vector, represents an input torque, and specifically comprises:
Figure FSA0000236597370000014
in the formula, P is engine thrust; x R The distance from the engine nozzle to the top end of the rocket; x Z Is the centroid position; r and R are the distance from the engine center to the x-axis of the launch vehicle,
Figure FSA0000236597370000015
representing the engine equivalent swing angle. The control torque can be expressed as:
u＝Bδ
wherein δ is [ δ ] θ ，δ α ，δ β ] T (ii) a B is input matrix, and is obtained by sorting
Figure FSA0000236597370000021
3. The control method according to claim 1, wherein the second step of establishing the attitude control system dynamics model and the second-order launch vehicle attitude tracking system under the fault of the launch vehicle comprises the following steps:
s1: attitude control system dynamics model under carrier rocket fault
Considering that a boosting engine or a core-level engine has a dead or failure fault, the fault model is as follows:
Figure FSA0000236597370000022
Figure FSA0000236597370000023
in the formula, i is 1, …, and 4 represents the ith actuator, and the number of the failed actuators does not exceed the maximum number of the failed actuators, that is, the rocket carrier can control the rest actuators to keep the system stable.
Figure FSA0000236597370000024
For the unknown failure factor of the ith actuator,
Figure FSA0000236597370000025
and
Figure FSA0000236597370000026
respectively, the upper and lower bounds of the failure factor. Sigma is the stuck value of i actuators,
Figure FSA0000236597370000027
namely when
Figure FSA0000236597370000028
No fault occurs; when in use
Figure FSA0000236597370000029
When the fault happens, the jamming fault of the ith actuator is shown; when in use
Figure FSA00002365973700000210
When, it indicates that the ith actuator is partially failed.
Defining:
Figure FSA00002365973700000211
in the formula (I), the compound is shown in the specification,
Figure FSA00002365973700000212
establishing a carrier rocket dynamic model:
Figure FSA00002365973700000213
s2: second-order carrier rocket attitude tracking system
The tracking error defining the attitude angle is: e-omega r ，
Figure FSA00002365973700000214
And
Figure FSA00002365973700000215
respectively, the attitude angle tracking command and its first derivative. Let x 1 ＝e，
Figure FSA00002365973700000216
Substituting the formula (8) into the formula, and defining a carrier rocket attitude tracking system as follows:
Figure FSA00002365973700000217
wherein f (x) is ∈ R 3 ，G(x)∈R 3×3 ，d∈R 3 And is defined as follows:
Figure FSA00002365973700000218
4. the control method according to claim 1, wherein the design of the terminal slide surface and its parameters in step three are selected as follows:
s1: in order to ensure that the tracking error e converges to 0 within a limited time, the following non-singular terminal sliding mode surfaces are designed:
s＝x 2 +c 1 x 1 +c 2 sig β (x 1 )
in the formula: s is formed by R 3 ，0＜β＜1。
S2: the parameters are selected as follows:
c 1 and c 2 Positive, and satisfies c 1 ，c 2 ＝diag(c i1 ，c i2 ，c i3 )，i＝1，2。sig β (x 1 ) Is defined as: sig β (x 1 )＝[sig β (x 11 )，sig β (x 12 )，sig β (x 13 )] T And define sig β (x)＝|x| β sgn (x), where the sign function sgn (x) is defined as:
Figure FSA0000236597370000031
adopt the synovial membrane face of above-mentioned design, and the controller design is: delta is delta eq +δ d
Wherein:
Figure FSA0000236597370000032
in the formula, delta eq ，δ d ∈R 3 And k(s) are defined as follows:
Figure FSA0000236597370000033
z(x 1 )＝c 1 x 1 +c 2 sig β (x 1 ) The tracking error converges to zero within a finite time.
5. The control method according to claim 1, wherein the step four is based on the adaptive radial basis neural network, the unknown system parameters are approximated, the adaptive control terms are added, and the process of compensating the errors in the disturbance and approximation processes is as follows:
s1: the moment of inertia J of the carrier rocket is assumed to be unknown, namely f (x) in the attitude tracking system of the carrier rocket is unknown, and the terminal sliding mode control law needs to obtain an accurate model of the system, so that the terminal sliding mode control law is not suitable for design. The process of the radial basis function neural network approaching unknown system parameters is as follows:
from the approximate characteristics of the radial basis function neural network, the unknown nonlinear function h (x) can be expressed as:
h(x)＝(W 0 ) T Φ 0 (x)+ε 0 ＝h 0 (x，c，σ)+ε 0
in the formula, W 0 The weight vector which is linearly output by the radial basis function neural network is an m multiplied by n dimensional matrix, and n is the dimension of h (x); epsilon 0 To estimate the error for the best; h is 0 (x, c, σ) is the optimal approximation function of h (x).
Figure FSA0000236597370000034
Is a vector of dimensions m in which the vector is,
Figure FSA0000236597370000035
hiding the output of the layer gaussian activation function for the radial basis function.
Order to
Figure FSA0000236597370000036
F (x) can be expressed as:
F(x)＝(W 0 ) T Φ 0 (x)+ε 0 ＝F 0 (x，c，σ)+ε 0
s2: the control rate is designed as follows:
u＝G -1 (x)(u tsm +u RBFNN +u ad )
in the formula u tsm A terminal sliding mode control item; u. of RBFNN Is a non-linear function f (x) approximated using a radial basis function neural network; u. of ad The adaptive control term is used for compensating disturbance and approximation process errors, enhancing the closed loop stability of the system and improving the transient performance. Three control items are defined as:
u tsm ＝-ks
Figure FSA0000236597370000041
Figure FSA0000236597370000042
in the formula (I), the compound is shown in the specification,
Figure FSA0000236597370000043
and
Figure FSA0000236597370000044
the estimated values of unknown actual interference zeta and adaptive gain alpha are respectively, and the adaptive update law is designed as follows:
Figure FSA0000236597370000045
the control law is designed to make the error of the attitude tracking system of the carrier rocket converge to zero in a limited time.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117085229A (en) * 2023-08-21 2023-11-21 北京理工大学 Spinning of motion feedback intervention system
CN117555227A (en) * 2023-06-05 2024-02-13 东方空间技术(山东)有限公司 Control method, computing equipment and storage medium of carrier rocket

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117555227A (en) * 2023-06-05 2024-02-13 东方空间技术(山东)有限公司 Control method, computing equipment and storage medium of carrier rocket
CN117555227B (en) * 2023-06-05 2024-03-29 东方空间技术(山东)有限公司 Control method, computing equipment and storage medium of carrier rocket
CN117085229A (en) * 2023-08-21 2023-11-21 北京理工大学 Spinning of motion feedback intervention system

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