CN110647034B - Neural network control method of pulse plasma thruster - Google Patents

Neural network control method of pulse plasma thruster Download PDF

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CN110647034B
CN110647034B CN201910830706.3A CN201910830706A CN110647034B CN 110647034 B CN110647034 B CN 110647034B CN 201910830706 A CN201910830706 A CN 201910830706A CN 110647034 B CN110647034 B CN 110647034B
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章喆
汤海滨
许舒婷
张尊
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Beihang University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03H—PRODUCING A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03H1/00—Using plasma to produce a reactive propulsive thrust
    • F03H1/0081—Electromagnetic plasma thrusters
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03H—PRODUCING A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03H1/00—Using plasma to produce a reactive propulsive thrust
    • F03H1/0087—Electro-dynamic thrusters, e.g. pulsed plasma thrusters

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Abstract

The invention discloses a neural network control method of a pulse plasma thruster, which comprises the steps of establishing a multi-input single-output single-layer neural network model for analyzing the relation between the thrust and the pulse current of the plasma thruster and establishing a multi-input single-output multi-layer neural network model, wherein an input layer is pulse current with different amplitudes and frequencies, an intermediate layer is pulse voltage, an output layer is thrust, the pulse voltage is in direct proportion to the pulse current, and the square of the pulse voltage is in direct proportion to the thrust value, so that the relation between the pulse current and the plasma thruster is determined, and the accurate value of the thrust is obtained. By the technical scheme, the relation between the pulse current and the thrust of the pulse plasma is analyzed, the convergence speed of network learning is improved and the stability of the network learning is improved by optimizing a neural network algorithm, the real-time control of the thrust of the thruster is realized, and the capability of coping with the uncertainty of the thrust is improved.

Description

Neural network control method of pulse plasma thruster
Technical Field
The invention belongs to the technical field of electric propulsion plasma control, and particularly relates to a neural network control method of a pulse plasma thruster.
Background
The electric propulsion is an advanced propulsion mode which utilizes electric energy to directly heat the propellant or utilizes electromagnetic action to ionize and accelerate the propellant so as to obtain propulsion power, has higher specific impulse, thrust and efficiency, and has wide application prospect in space tasks of orbit control, deep space exploration, interstellar navigation and the like of large-scale spacecrafts.
The pulse ion thruster is one of electromagnetic electric thrusters, and is widely applied to a main propulsion system of a satellite and a deep space probe at present.
The pulse control on the pulse plasma thruster has important significance for improving the design of the optimized engine and improving the performance of the engine. The control method of the neural network has the advantages of being suitable for nonlinear approximation, having important academic value and engineering significance for research of pulse control of the pulse plasma thruster, and no research of the neural network control method specially aiming at pulse control of the pulse plasma thruster exists at present.
Disclosure of Invention
Analyzing the uncertainty of the pulse current of the thruster by taking the pulse plasma thruster as a research object, determining an uncertain factor as the input of a neural network controller; the control parameters of the impulse current of the thruster are adjusted through the neural network, the convergence rate of network learning is improved and the stability of the network learning is improved through optimizing the neural network algorithm, the real-time control of the thrust of the thruster is realized, and therefore the capability of coping with the uncertainty of the thrust is improved.
Specifically, the technical scheme of the invention is as follows: a neural network control method of a pulsed plasma thruster is characterized by comprising the following steps of:
s1: establishing a single-layer neural network model with multiple inputs and single outputs, wherein the input layer is pulse current with different amplitudes and frequencies, the output layer is thrust, and the input layer is directly connected with the output layer and has
Figure BDA0002190596480000011
Figure BDA0002190596480000012
Wherein X is (X)1，x2......xn) For pulsed current input, xiIs a pulsed current input component; w ═ W1，w2......wn) Is a weight vector representing the influence degree of each pulse current on the thrust, wiAre weight components; b is a pulse current threshold; y is thrust output; f is the functional relation between the input layer and the output layer; n is the number of the neurons, and i is the serial number of the neurons;
s2: establishing a multi-input single-output multilayer neural network model, wherein an input layer is pulse current with different amplitudes and frequencies, an intermediate layer is pulse voltage, and an output layer is thrust; the pulse voltage is in direct proportion to the pulse current, so that the connection between the input layer and the middle layer is obtained; the square of the pulse voltage is in direct proportion to the thrust value, and then the accurate value of the thrust is determined;
s3: for the pulse current input data, 5% was randomly drawnThe data of the neural network model is used as a test group, the rest 95 percent of the data is used as a training group, the training group is used as a learning sample for learning and constructing the neural network model, and the test group is used for verifying the accuracy of the neural network model; selecting q state points to be measured, and expressing the q state points as Ii＝f(Ai，wi，bi) Wherein, I is the pulse current of different state points, a is the amplitude of the pulse current, w is the frequency of the pulse current, b is the phase of the pulse current, I is the serial number of the state point, and I is 1.. q;
s4: for the middle layer of the multi-layer neural network model with multiple inputs and single outputs, the middle layer is defined as pulse voltage, and the parameter vector U of the neural network isT＝[u1，u2，...，un]Deviation e of the network at the input of the intermediate layerT＝[e1，e2，...，em]Where n is the number of neurons, m is the number of training samples, and the loss function f is in the form of a sum-of-squares error:
Figure BDA0002190596480000021
the jacobian matrix defining the loss function is:
Figure BDA0002190596480000022
wherein, the size of the Jacobian matrix is m × n, and the Jacobian matrix consists of partial derivatives of error terms to parameters:
Figure BDA0002190596480000023
Figure BDA0002190596480000024
gradient vector of loss functionFurthermore, the Hessian matrix is H ≈ 2JTJ+λI，
In the formula, lambda is an attenuation factor to ensure that the Hessian matrix is positive; i is an identity matrix, and the parameter vector of the impulse voltage neural network is uk+1＝uk-(JTJ+λI)-1·(2JTe)，k＝1，2，...
Setting an attenuation factor lambda, training a proper pulse voltage, determining the output thrust value trained by the neural network model, wherein the square of the pulse voltage is in direct proportion to the thrust value;
s5: and calculating the relative error between the output thrust value of the neural network training and the reference thrust value obtained by experience, and evaluating the prediction performance of the neural network model.
The invention has the beneficial effects that:
1. the thrust of the pulse plasma thruster is influenced by the pulse current, the pulse current is constantly changed and has a certain threshold value and instability, and the threshold value and the dynamic and static characteristics of the pulse current can be accurately described by using a control method of a neural network;
2. according to the control characteristic analysis of the pulse, the pulse current has certain nonlinear characteristics, the neural network control method has a strong control means for representing the nonlinear problem, the mapping relation between the pulse current and the thrust can be more effectively analyzed, and the accuracy of the thrust is ensured;
3. one of the key factors for constructing the neural network is to obtain good generalization capability, wherein the generalization means that the neural network can generate reasonable output, a large number of samples are needed for experiments, and the acquisition of pulse current can generate a large number of sample data, so that the accuracy of the neural network algorithm can be ensured.
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In order to illustrate embodiments of the present invention or technical solutions in the prior art more clearly, the drawings which are needed in the embodiments will be briefly described below, so that the features and advantages of the present invention can be understood more clearly by referring to the drawings, which are schematic and should not be construed as limiting the present invention in any way, and for a person skilled in the art, other drawings can be obtained on the basis of these drawings without any inventive effort. Wherein:
FIG. 1 is a block diagram of a model of an artificial neural network of the present invention;
FIG. 2 is a diagram of a multiple-input single-output neural network of the present invention;
FIG. 3 is a flow chart of the neural network modeling of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
For a pulsed plasma thruster, the pulsed current has a certain threshold and non-linearity, the variation of which affects the final thrust output. The change process for describing the pulse current is very complicated and is difficult to describe by a linear accurate control model, so the relationship between the pulse current and the thrust of the pulse plasma is analyzed by using a control method of a neural network. The neural network control method can take pulse currents with different amplitudes and frequencies as one neuron, and corresponding thrust is obtained through a large number of calculations and processing.
The neural network control method for the pulse plasma thruster provided by the invention utilizes the pulse current to control the thrust of the pulse plasma thruster, and ensures the pulse control performance of the pulse plasma thruster. FIG. 1 is a block diagram of a model of an artificial neural network; fig. 2 is a diagram of a multi-input single-output neural network. As shown in fig. 1-2, a neural network control method of a pulsed plasma thruster includes the following steps:
s1: establishing a single-layer neural network model with multiple inputs and single outputs, wherein the input layer is pulse current with different amplitudes and frequencies, the output layer is thrust, and the input layer is directly connected with the output layer and has
Figure BDA0002190596480000041
Figure BDA0002190596480000042
Wherein X is (X)1，x2......xn) For pulsed current input, xiIs a pulsed current input component; w ═ W1，w2......wn) Is a weight vector representing the influence degree of each pulse current on the thrust, wiAre weight components; b is a pulse current threshold; y is thrust output; f is the functional relation between the input layer and the output layer; n is the number of the neurons, and i is the serial number of the neurons;
s2: establishing a multi-input single-output multilayer neural network model, wherein an input layer is pulse current with different amplitudes and frequencies, an intermediate layer is pulse voltage, and an output layer is thrust; the pulse voltage is in direct proportion to the pulse current, so that the connection between the input layer and the middle layer is obtained; the square of the pulse voltage is in direct proportion to the thrust value, and then the accurate value of the thrust is determined;
s3: for pulse current input data, randomly extracting 5% of data as a test group, taking the rest 95% of data as a training group, taking the training group as a learning sample for learning and constructing a neural network model, and using the test group for verifying the accuracy of the neural network model; selecting q state points to be measured, and expressing the q state points as Ii＝f(Ai，wi，bi) Wherein, I is the pulse current of different state points, a is the amplitude of the pulse current, w is the frequency of the pulse current, b is the phase of the pulse current, I is the serial number of the state point, and I is 1.. q;
s4: for the middle layer of the multi-layer neural network model with multiple inputs and single outputs, the middle layer is defined as pulse voltage, and the parameter vector U of the neural network isT＝[u1，u2，...，un]Deviation e of the network at the input of the intermediate layerT＝[e1，e2，...，em]Where n is the number of neurons, m is the number of training samples, and the loss function f is in the form of a sum-of-squares error:
Figure BDA0002190596480000043
the jacobian matrix defining the loss function is:
Figure BDA0002190596480000044
wherein, the size of the Jacobian matrix is m × n, and the Jacobian matrix consists of partial derivatives of error terms to parameters:
Figure BDA0002190596480000045
Figure BDA0002190596480000046
gradient vector of loss function
Figure BDA0002190596480000047
Furthermore, the Hessian matrix is H ≈ 2JTJ+λI，
In the formula, lambda is an attenuation factor to ensure that the Hessian matrix is positive; i is an identity matrix, and the parameter vector of the impulse voltage neural network is uk+1＝uk-(JTJ+λI)-1·(2JTe)，k＝1，2，...
Setting an attenuation factor lambda, training a proper pulse voltage, determining the output thrust value trained by the neural network model, wherein the square of the pulse voltage is in direct proportion to the thrust value; if the attenuation factor is 0, the attenuation speed is very fast; if the attenuation factor is set to be larger, the gradient descent method is similar to the gradient descent method with a small learning rate.
S5: and calculating the relative error between the output thrust value of the neural network training and the reference thrust value obtained by experience, and evaluating the prediction performance of the neural network model.
The neural network model of the invention needs good generalization ability, and the deficiency of the generalization ability can cause the neural network model not to fully simulate the pulse control behavior, so that a large amount of sample data of pulse current is needed, the pulse current with various frequencies and amplitudes is collected by the Rogowski coil, the accuracy of the neural network algorithm is ensured, and the most real result is approached.
Based on the neural network control theory, the nonlinear characteristic presented by the pulse current of the pulse plasma thruster is converted into mathematical calculation, and the neural network multilevel quantification and modeling of the thrust control process are realized. With the aid of the MATLAB neural network toolbox, a neural network hierarchy corresponding to the pulse current, neurons, and corresponding internal processors can be designed.
Simulation experiment the designed neural network model of the pulsed plasma thruster is simulated through Matlab and Simulink environment. And setting the reference thrust value of the pulse plasma thruster to 300uN, calculating the error between the predicted value and the reference value of the neural network model, and evaluating the prediction performance of the neural network model. Wherein the data portion of one cycle of one pulse current is intercepted as follows:
TABLE 1 data for one period of pulsed current
Figure BDA0002190596480000051
Through simulation experiments, the maximum relative error between the predicted value and the reference value of the neural network model is calculated and shown in table 2, which shows that the prediction performance of the neural network model is good.
Table 2 calculates the maximum relative error of the test results
Figure BDA0002190596480000052
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, "above" or "below" a first feature means that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact with each other via another feature therebetween. Also, a first feature being "on," "above" or "over" a second feature includes the first feature being directly on or obliquely above the second feature, or simply indicating that the first feature is at a higher level than the second feature. A first feature being "under", beneath and "under" a second feature includes the first feature being directly under and obliquely under the second feature, or simply means that the first feature is at a lesser elevation than the second feature.
In the present invention, the terms "first", "second", "third", and "fourth" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. The term "plurality" means two or more unless expressly limited otherwise.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A neural network control method of a pulsed plasma thruster is characterized by comprising the following steps of:
s1: establishing a single-layer neural network model with multiple inputs and single outputs, wherein the input layer is pulse current with different amplitudes and frequencies, the output layer is thrust, and the input layer is directly connected with the output layer and has
Figure FDA0002486310950000011
Wherein X is (X)1，x2……xn) For pulsed current input, xiIs a pulsed current input component; w ═ W1，w2……wn) Is a weight vector representing the influence degree of each pulse current on the thrust, wiAre weight components; b is a pulse current threshold;y is thrust output; f is the functional relation between the input layer and the output layer; n is the number of the neurons, and i is the serial number of the neurons;
s2: establishing a multi-input single-output multilayer neural network model, wherein an input layer is pulse current with different amplitudes and frequencies, an intermediate layer is pulse voltage, and an output layer is thrust; the pulse voltage is in direct proportion to the pulse current, so that the connection between the input layer and the middle layer is obtained; the square of the pulse voltage is in direct proportion to the thrust value, and then the accurate value of the thrust is determined;
s3: for pulse current input data, randomly extracting 5% of data as a test group, taking the rest 95% of data as a training group, taking the training group as a learning sample for learning and constructing a neural network model, and using the test group for verifying the accuracy of the neural network model; selecting q state points for measurement, and expressing the state points as
Figure FDA0002486310950000012
Wherein I is the pulse current of different state points, A is the amplitude of the pulse current, w is the frequency of the pulse current,
Figure FDA0002486310950000013
the phase of the pulse current is shown, z is a state point serial number, and z is 1 … … q;
s4: for the middle layer of the multi-layer neural network model with multiple inputs and single outputs, the middle layer is defined as pulse voltage, and the parameter vector U of the neural network isT＝[u1,u2,…,un]Deviation e of the network at the input of the intermediate layerT＝[e1,e2,…,em]Where n is the number of neurons, m is the number of training samples, and the loss function g is in the form of a sum of squares error:
Figure FDA0002486310950000014
the jacobian matrix defining the loss function is:
Figure FDA0002486310950000015
wherein, the size of the Jacobian matrix is m × n, and the Jacobian matrix consists of partial derivatives of error terms to parameters:
Figure FDA0002486310950000016
gradient vector of loss function
Figure FDA0002486310950000017
Furthermore, the Hessian matrix is H ≈ 2JTJ+λE，
In the formula, lambda is an attenuation factor to ensure that the Hessian matrix is positive; e is an identity matrix, and the parameter vector of the impulse voltage neural network is uk+1＝uk-(JTJ+λE)-1·(2JTe)，k＝1,2,…
Setting an attenuation factor lambda, training a proper pulse voltage, determining the output thrust value trained by the neural network model, wherein the square of the pulse voltage is in direct proportion to the thrust value;
s5: and calculating the relative error between the output thrust value of the neural network training and the reference thrust value obtained by experience, and evaluating the prediction performance of the neural network model.
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