CN115796021A - Adaptive PID control parameter setting method for variant aircraft based on neural network - Google Patents
Adaptive PID control parameter setting method for variant aircraft based on neural network Download PDFInfo
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Abstract
The invention discloses a self-adaptive PID control parameter setting method of a variant aircraft based on a neural network, which comprises the following specific steps: firstly, a dynamic model of the variant aircraft is established, and the moment of inertia and the position change of the mass center of the aircraft are calculated in real time according to the deformation state, so that the accuracy of the dynamic model is ensured. And then building a BP neural network, and inputting a large amount of simulated flight data for training by adopting a mode of respectively training four groups of five state parameters corresponding to one output neural network based on the dynamic model of the deformable aircraft, so as to accurately predict the flight dynamic parameters. And finally, constructing a pole configuration-based adaptive feedback control model, solving PID controller parameters, and obtaining a better control effect.
Description
Technical Field
The invention belongs to the field of flight control of aircrafts, and particularly relates to a self-adaptive PID control parameter setting method of a variant aircraft based on a neural network.
Background
The variant aircraft has key characteristics of variable configuration, repeatable flight and the like, and faces extreme flight environments such as fast time variation, strong interference, serious strong uncertainty and the like. The intelligent variant aircraft has the characteristics of wide flight range, large flight Mach number change, violent change of atmospheric density, high maneuvering performance requirement, multiple boundary limiting conditions, complex manipulation and the like, so that a great deal of problems to be solved are faced in the development of the variant aircraft technology. On the whole, flight control algorithms can be mainly divided into two major categories, one is to linearize the system under different flight states or shapes, and then design the control system based on linear control methods such as a robust control method, and the other is to complete controller design by means of nonlinear methods such as an adaptive control technology and an anti-interference theory, and both the two categories can realize aircraft control under simple deformation, but have certain requirements on the modeling accuracy of the aircraft, and are difficult to adapt to the development trend of the deformed aircraft with gradually increased complexity. For the LPV method, no matter switching or non-switching conditions, the configuration and small disturbance linearization processing needs to be carried out on the nonlinear motion model of the variant aircraft, the designed controller has a good control effect on the premise that the aircraft is simply deformed and external disturbance is small, but when the deformation is more complex or the disturbance is increased, the control performance is obviously reduced, which shows that the LPV theory is used for solving the control problem of the variant aircraft and is feasible only in a certain range, and when the nonlinear characteristic of the variant aircraft is strong, the LPV method is difficult to further apply.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects of the prior art, the invention provides a self-adaptive PID control parameter setting method of a variant aircraft based on a neural network. And (3) adopting the BP neural network, inputting and outputting data for training, and obtaining the neural network which can accurately output and quickly respond.
(II) technical scheme
In order to solve the technical purpose, the technical scheme of the invention comprises the following steps:
(1) Building a dynamic model of the variant aircraft by using the variant dynamics;
(2) Simplifying a control-oriented multimode strong coupling nonlinear time-varying model;
(3) Checking the similarity of the key features of the simplified model;
(4) And (4) self-adaptive PID flight control design of the deformable airplane.
Further, the modeling method described in step (1) includes:
based on a multi-body dynamics theory (MBD), the center of gravity, the moment of inertia and the corresponding aerodynamic characteristics at any moment in the deformation process are obtained through calculation, and the accuracy of the aircraft model is guaranteed.
Further, the simplified design method described in step (2) includes:
and constructing a BP neural network training model, and explaining a forward signal propagation process and an error backward propagation process of the neural network.
Further, the method for verifying the similarity of the key features of the simplified model described in the step (3) comprises the following steps:
selecting key features of the simplified model. And determining the input and the output of the model, and establishing a model capable of predicting the dynamic parameters of the aircraft by combining the research object.
Further, the flight control design method described in step (4) is:
flight control is considered to be a multiple-input multiple-output system. And selecting a proper pole position, solving the controller parameters and controlling distribution by adopting a pole distribution mode and through overshoot and adjusting time. The position of an expected pole in the deformation process of the aircraft is unchanged by adjusting the parameters of the controller, and self-adaptive PID control is realized.
The beneficial effects brought by adopting the technical scheme are as follows: the BP neural network is a multilayer forward neural network, adopts a signal forward propagation algorithm and an error backward propagation algorithm, has good autonomous learning capacity, can accurately fit any complex continuous function curve, does not need to manually set a weight value for a certain input factor, avoids errors caused by personal subjective factors, and has better fault-tolerant capability.
Drawings
FIG. 1 is a topological structure diagram of a neural network constructed by the invention
FIG. 2 is a BP neural network algorithm flow of the present invention
FIG. 3 shows the result of neural network training
FIG. 4 is a graph of the effect of angle of attack on thrust coefficient
FIG. 5 is a graph illustrating the effect of fuel equivalence ratio on thrust coefficient
FIG. 6 is a graph of the effect of angle of attack on lift coefficient
FIG. 7 is a graph of the effect of height on lift coefficient
FIG. 8 is a graph illustrating the effect of Mach number on lift coefficient
FIG. 9 is a graph of the effect of angle of attack on drag coefficient
FIG. 10 is a control logic diagram
FIG. 11 comparison of lift + -10% deviation angle of attack and elevator variation
FIG. 12 lift + -10% yaw rate/pitch variation comparison
FIG. 13 is a flow chart of the method of the present invention
Detailed Description
The technical scheme of the invention is explained in detail below with reference to the attached drawings:
step 1: building a dynamic model of the variant aircraft by using the variant dynamics;
step 2: simplifying a control-oriented multimode strong coupling nonlinear time-varying model;
and 3, step 3: checking the similarity of the key features of the simplified model;
and 4, step 4: and (4) self-adaptive PID flight control design of the deformable airplane.
In this embodiment, the step 1 is implemented by the following preferred scheme:
the body components of the morphing aircraft mainly comprise a fixed part and a part capable of deflecting and moving, the fixed part and the movable part are regarded as mutually independent rigid bodies, if the values of the moment of inertia and the static moment of the component in an original coordinate system are known, the values of the moment of inertia and the static moment in a new coordinate system can be obtained through a shift axis theorem and a rotation axis theorem, and then the values of all the parts are added.
The expressions for moment of inertia and static moment are:
S＝[S x ,S y ,S z ] T (2)
wherein I denotes the tensor of moment of inertia, I ij Representing the rotational inertia value of the corresponding plane, S representing the static moment, S i Representing the value of the static moment in the corresponding coordinates. Since the aircraft is symmetrical about the longitudinal plane of the fuselage, I xy ＝∫xydm＝0，I yz =0, the above formula can be simplified to:
setting the transformation matrix from the initial coordinate system to the new coordinate system as
The motion vector translated from the initial coordinate system to the new coordinate system is r i Where g denotes a new coordinate system,/ i An initial coordinate system defining the moment of inertia and the static moment of the ith rigid body part is represented.
Representing the moment of inertia of the rigid body in the initial coordinate system,
representing the static moment of the rigid body in the initial coordinate system,
representing the moment of inertia of the rigid body in the new coordinate system,
representing the static moment, m, of the rigid body in a new coordinate system i Representing the mass of the rigid body. Through rotation and translation changes, the calculation formulas of the moment of inertia and the static moment under the new coordinate system are as follows:
after transformation, the expression of the total moment of inertia and static moment of the morphing aircraft in the new coordinate system is:
according to the theorem of momentum and the theorem of moment of momentum:
wherein F represents the external force to which the morphing aircraft is subjected as a whole,
the derivative of the momentum of the aircraft, M the external moment to which the aircraft is subjected as a whole,
representing the derivative of the external moment to which the aircraft as a whole is subjected over time,
the time derivative of the static moment about the longitudinal axis of the aircraft is indicated and V indicates the flight speed of the aircraft.
And decomposing each vector into a ground coordinate system according to the relation between the absolute derivative and the relative derivative, wherein the nonlinear dynamical equation of the aircraft variant process is as follows:
from (9), (10), it can be seen that, unlike fixed wing aircraft, the dynamic equation of a morphing aircraft adds a static moment S and corresponding derivative terms. This is caused by the change in the position of the centre of mass of the morphing aircraft. In the formula S x ,S y ,S z Representing the additional force generated by the movement of the aircraft centroid position,
representing the additional force due to the speed of movement of the center of mass;
representing the additional force due to the acceleration of the centroid movement. In the formula S x ,S y ,S z Representing the additional moment generated by the movement of the aircraft centroid position,
representing an additional moment due to the moving speed of the center of mass;
representing additional moment due to acceleration of movement of the centre of mass. The first derivative of the parameter is represented by adding one point to the above character, and the second derivative of the parameter is represented by adding two points to the alphabetic sign. And F x ,F y ,F z Respectively representing the external forces, M, to which the aircraft is subjected in the x, y and z directions x ,M y ,M z The method comprises the following steps of (1) representing external moments borne by an aircraft in three directions, wherein m represents the overall mass of the aircraft, p, q and r represent the angular velocities of a ballistic coordinate system relative to the ground coordinate system in the three directions, and u, v and w represent the angular velocities of the ballistic coordinate system relative to the ground coordinate system in the three directions; I.C. A ix ,I iy ,I iz Denotes the moment of inertia, ω, of the ith wing relative to the entire machine ix ,ω iy ,ω iz The moment of inertia of the ith wing relative to the complete machine is indicated.
In this embodiment, the step 2 is implemented by the following preferred scheme:
the topology structure of the BP neural network is shown in fig. 1, and is generally a three-layer structure: the method comprises an input layer, a hidden layer and an output layer, wherein neurons of the same layer are only connected with the next layer and the previous layer, for example, a certain neuron of the hidden layer can establish connection with all the neurons of the input layer and the output layer, but can not be connected with the neurons of the same hidden layer. Signal forward propagation refers to samples coming from the input layer, passing through the hidden layer and the output layer in sequence. The error back propagation means that the error generated after the output of the neural network is compared with the expected output reaches the input layer through the hidden layer from the output layer, and the weight and the threshold of the neuron are adjusted in the propagation process, so that the actual output of the neural network is continuously close to the expected output.
FIG. 1 is a BP neural network topology diagram with only one hidden layer, assuming that the number of neurons in the input layer is n, the number of neurons in the hidden layer is q, the number of neurons in the output layer is m, and the input of the ith neuron in the input layer is x i I =1 \ 8230n, and the weight value of the connection between the jth neuron of the hidden layer and the ith neuron of the input layer is omega ij The j-th neuron of the hidden layer is connected with the k-th neuron of the output layer by a weight omega jk The threshold value of the jth neuron of the hidden layer is theta j The excitation function of the hidden layer is
The k-th neuron threshold of the output layer is a k The output is Y i K =1 \ 8230m, the excitation function adopted by the output layer is psi, and the output of the kth neuron of the output layer is o k 。
(1) The signal forward propagation process:
input net of the jth neuron of the hidden layer j Comprises the following steps:
output y of the jth neuron of the hidden layer j Comprises the following steps:
input net of k node of output layer k Comprises the following steps:
the output of the kth node of the output layer is:
(2) error back propagation process
The error for a certain sample p can be expressed as:
wherein, T k The standard value at time k is indicated.
Assuming a total of P samples, the overall error criterion function for these samples is:
the adjustment method of the neural network is a gradient descent method, and the adjustment quantity from the hidden layer to the output layer weight is assumed to be delta omega jk The adjustment amount of the k-th neuron threshold of the output layer is delta a k The adjustment of the weight from the input layer to the hidden layer is delta omega ij The adjustment amount of the jth neuron threshold of the hidden layer threshold is delta theta j The following formula is given:
where η represents the learning efficiency of neurons.
The formula for adjusting the weight between the hidden layer and the output layer is as follows:
the adjustment formula of the output layer threshold is as follows:
the adjustment formula of the weight between the input layer and the hidden layer is as follows:
adjustment formula of hidden layer threshold:
and due to
Substitution of formulae (21) to (25) for formulae (17) to (20), respectively, gives the following results:
(3) algorithm flow of BP neural network
As shown in figure 2
In this embodiment, the step 2 is implemented by the following preferred scheme:
the fitting of the BP neural network is realized based on a large amount of data, and before the related research of the neural network, an achievable flight envelope curve can be obtained by applying the normal flight state boundary of the hypersonic aircraft to the flight dynamics parameterized model simulation. The flight envelope is essentially made up of a dense series of state data points, which together with the calculated kinetic parameters are the basis for generating training data.
For a BP neural network model, training requires determining the input and output of the model, and in combination with the study object, what needs to be established is a model for predicting aircraft dynamics: the resistance coefficient CD, the lift coefficient CL, the pitching moment coefficient CM and the thrust coefficient CT are output models. After the output is determined, all variables affecting the output are considered as inputs. The invention only considers the longitudinal movement of the aircraft and combines the previous section of parametric modeling research. The state variables influencing the output, including the angle of attack a, the height H and the elevator deflection delta, can be directly deduced z Fuel equivalence ratio
It should be noted that, because there is a strong coupling relationship between each part of the hypersonic aircraft, and the linear degree of influence of some flight state variables on the output is very weak, the training point set required for obtaining an accurate result is very large in scale, and the training rate is influenced, so that the method of training a neural network with five state parameters corresponding to four outputs is abandoned, and a mode of respectively training four groups of five state parameters corresponding to one output neural network is changed. In addition, although strong coupling exists among subsystems of the hypersonic aircraft, a special flight state does not have relation with input, so that specific problem specific analysis is needed when state variables influencing output are judged, and the training process of the neural network can be increased or decreased on the basis of the five states mentioned above.
Through data requirement analysis, the input and output dimensions of the training data can be preliminarily determined. In four neural networks, input data are five-dimensional and include an attack angle a, a height H and an elevator deflection delta z Mach number, mach number, fuel equivalence ratio
The four output data are one-dimensional and respectively comprise a resistance coefficient CD, a lift coefficient CL, a pitching moment coefficient CM and a thrust coefficient CT. Defining a set matrix containing all state data points of the input and output states as a reference ballistic state data matrix I 0 。
For the initially selected input and output variables, training can be performed after expansion is performed, but the independent expansion causes the data volume to be too large and complicated and the utilization efficiency to be low. Therefore, it is necessary to perform the influence characteristic analysis of the output variable for each input variable. The normal cruise state envelope curve of the hypersonic aircraft is set to be 18000-32000 m in height, minus 1-8 degrees in attack angle, minus 20-20 degrees in elevator rudder, 4-7 degrees in Mach number and 0.1-0.7 in fuel equivalent ratio. The training sampling points of the four groups of neural networks are determined according to the linear strength of the input state parameters on the output influence and the accuracy of the neural network output in the experiment.
Through input and output influence analysis, the influence relation of input on output can be divided into three types, and different sampling point-taking strategies are correspondingly adopted:
no influence: the input-output images are in horizontal lines parallel to the x-axis; the input is directly deleted.
Linear influence: i.e. the input-output image is in a slanted straight line; a three-point expansion is performed.
Non-linear effects: selecting an expansion mode according to the non-linear degree; for example, if the input-output image is a quadratic curve, five-point expansion can be adopted, and if the degree of nonlinearity is large, the number of points to be taken is further increased.
N-point expansion (including three-point expansion and five-point expansion): the number of data points after expansion; for N-point expansion, if the expansion amplitude is A, the expansion interval of the N-point expansion is A/(N-2).
The analysis of the influence characteristics of each input on the output is already performed in the previous section, so that the key feature similarity check is directly performed.
The Neural Network model was trained with Neural Network Toolbox in Matlab. The BP neural network has good nonlinear fitting performance, so the structure is adopted. In view of the complexity of project data fitting, deep networks are used for training instead of single-layer networks. The model training method comprises the following steps:
the code interface of the BP neural network mainly relates to the reading of data, the setting of input/output dimensions, the setting of training set and test set scale and the setting of training related parameters. The training set and validation set scale settings and training related parameter settings are mainly presented here.
Generally, the data used for training is divided into three blocks, namely a training set, a validation set, and a test set. The definition is as follows:
training set: the name implies a set of samples for training, primarily to train parameters in a neural network.
And (4) verification set: a sample set for verifying model performance. And after the training of different neural networks on the training set is finished, comparing and judging the performance of each model through the verification set.
And (3) test set: for the trained neural network, the test set is used for objectively evaluating the performance of the neural network.
The validation set comes from the subdivision of the training set, which is done autonomously by default by the toolbox, thus essentially requiring only two parts of the training set and the test set to be artificially divided. The data points of this study are not specific, but for the purpose of adjusting the comparison conveniently, 15% of the input data is extracted in a fixed manner as a training set, and the rest is a test set.
The training related parameters mainly comprise:
number of net hidden layers: the number of layers of the hidden layer is set, the more the number of layers is in a certain range, the better the fitting effect is generally, and the number of layers of the hidden layer determines the depth of the network. The specific number of hidden layers and the number of hidden neurons of each network are shown in the next section.
An Epoch: when a complete data set passes through the neural network once and back once, the process is called epoch. In short, an Epoch is the process of training all training samples once. The Epoch for the four neural networks is set to 1000.
Lr: the learning rate, if too small, the gradient decreases slowly, and if too large, the gradient decreases too large, possibly crossing the optimum. The neural network learning rates were all set to 0.1 in this study.
The Goal: the model accuracy required by training is set to 0.000005.
max _ fail: the maximum number of failures to continue validation checks is allowed. This is a training termination condition set to avoid overfitting. The Epoch for the four neural networks is set to 10.
And training the neural network by using the training data matrix.
Firstly, a thrust coefficient is verified, and main factors influencing the thrust are an attack angle and a fuel equivalence ratio. The neural network training results are shown in fig. 3.
And verifying the characteristic similarity of the attack angle and the thrust coefficient of the parameterized model by the neural network under the flight conditions of 30000 m height, mach 6 height, 0 elevator and 0.7 fuel equivalence ratio. The verification result is shown in fig. 4.
And verifying the fuel equivalence ratio and the thrust coefficient characteristic similarity of the parameterized model by the neural network under the flight conditions of 30000 m height, mach 6 height, 0 elevator and 3-degree attack angle. The verification result is shown in fig. 5.
And (3) verifying the lift coefficient, wherein the main factors influencing the pitching moment coefficient are an attack angle and elevator deflection. The verification results are shown in fig. 6, 7, and 8.
And (4) verifying the resistance coefficient, wherein the main factors influencing the resistance coefficient are an attack angle, a height and a Mach number. The verification result is shown in fig. 9.
In this embodiment, the step 4 is implemented by using the following preferred scheme:
control logic is shown in fig. 10, according to the logic of controlling the fuel equivalence ratio by controlling the attack angle and the accelerator coefficient of the elevator, a fourth-order control system expressed by a state space equation is decomposed into a third-order control system and a first-order control system, and the corresponding control quantities are the attack angle and the accelerator. Generally, a three-order control system has two dominant poles and one non-dominant pole, and the dynamic index of the system is determined by the two dominant poles; the position of the dominant pole has a significant influence on the performance index of the corresponding system, and the dominant pole can be determined by calculating the damping ratio and the natural frequency, wherein the calculation formula is as follows:
wherein λ is 1,2 Two dominant poles, xi is the system damping ratio, omega n Is the natural frequency of the system, t s To adjust the time, σ is the system overshoot.
After determining the two dominant poles, based on the real part of the determined dominant pole, the non-dominant pole is selected, i.e.: lambda 3 ＝-nξω n N is selected multiple which can be adjusted according to actual control effect, and n =5 is selected in the invention
The first order system has only one pole, noted as: lambda 4 ＝-1/λ
Where T is the first order system time constant and the first order system settling time is typically 4T, so the pole of the first order system is selected by the settling time required.
Up to this point, the four desired poles may all be determined. The controller is in the form of:
U＝U c -KΔX
wherein, U c Is the input at equilibrium. Resolving a control matrix K by adopting a matrix variation method:
in the formula, a i Are the coefficients of the a matrix eigenpolynomial. The characteristic equation of the feedback control system A-BK at the selected desired pole is:
(s-λ 1 )(s-λ 2 )(s-λ 3 )(s-λ 4 )＝s 4 +α 1 s 3 +α 2 s 2 +α 3 s+α 4 (33)
wherein, a i (i =1,2,3,4) represents a characteristic polynomial coefficient, and s is an unknown quantity.
The control matrix K can be written as:
the control matrix K is a 2-row and 4-column matrix, and the first row controls the quantity delta z Calculating the deflection angle of the elevator; second row pair control quantity
And calculating the accelerator coefficient. The two control quantities are determined by the fuel equivalence ratio and the deviation of four physical quantities, namely the angular velocity, the pitch angle and the attack angle, so that the self-adaptive feedback control is realized. And the lift force is simulated by plus or minus 10 percent of pulling deviation, the simulation conditions are shown in the following table, and the results are shown in example graphs 11 and 12.
TABLE 1 simulation initial condition settings
Claims (9)
1. A self-adaptive PID control parameter setting method of a variant aircraft based on a neural network is characterized by comprising the following steps:
(1) Building a dynamic model of the variant aircraft by using the variant dynamics;
(2) Simplifying a control-oriented multimode strong coupling nonlinear time-varying model;
(3) Checking the similarity of the key features of the simplified model;
(4) And (4) self-adaptive PID flight control design of the deformable airplane.
2. The adaptive PID control parameter setting method based on the neural network as claimed in claim 1, wherein in step (1), the dynamic model design method of the morphing aircraft comprises:
based on a multi-body dynamics theory, the gravity center and the moment of inertia at any moment in the deformation process and the pneumatic characteristics of the corresponding moment can be obtained, and the accuracy of the aircraft dynamics model is ensured.
3. The method for tuning the adaptive PID control parameters of the variant aircraft based on the neural network as claimed in claim 1, wherein in the step (2), the method for designing the control-oriented multimode strongly-coupled nonlinear time-varying model comprises:
and constructing a BP neural network training model, and explaining a forward signal propagation process and an error backward propagation process of the neural network.
4. The adaptive PID control parameter tuning method based on the neural network as claimed in claim 1, wherein in step (3), the similarity check method for the key features of the simplified model comprises:
selecting key characteristics of the simplified model; and determining the input and the output of the model, and establishing a model capable of predicting the dynamic parameters of the aircraft by combining the research object.
5. The method for tuning the adaptive PID control parameters of the morphing aircraft based on the neural network according to claim 1, wherein in step (4), the adaptive PID flight design control of the morphing aircraft comprises:
regarding flight control as a multiple-input multiple-output system; selecting proper pole positions and solving and controlling distribution of controller parameters by adopting a pole distribution mode and through overshoot and adjusting time; the position of an expected pole in the deformation process of the aircraft is unchanged by adjusting parameters of the controller, and self-adaptive PID control is realized.
6. The adaptive PID control parameter tuning method for the neural network-based variant aircraft is characterized in that in the step (1), the dynamic model design method for the variant aircraft comprises the following steps:
the variant airplane body component comprises a fixed part and a part capable of deflecting and moving, the fixed part and the part capable of deflecting and moving are regarded as mutually independent rigid bodies, if the values of the moment of inertia and the static moment of a part under an original coordinate system are known, the values of the moment of inertia and the static moment in a new coordinate system are obtained through a shift axis theorem and a rotation axis theorem, and then the values of all the parts are added;
the expressions for moment of inertia and static moment are:
S＝[S x ,S y ,S z ] T (2)
wherein I represents the tensor of moment of inertia, I ij Representing the rotational inertia value of the corresponding plane, S representing the static moment, S i A value representing the static moment in the corresponding coordinate; since the aircraft is symmetrical about the longitudinal plane of the fuselage, I xy ＝∫xydm＝0，I yz =0, the above formula can be simplified to:
setting the transformation matrix from the initial coordinate system to the new coordinate system as
The translation vector from the initial coordinate system to the new coordinate system is r i Where g denotes a new coordinate system, l i Representing an initial coordinate system defining the moment of inertia and static moment of the ith rigid body part;
representing the moment of inertia of the rigid body in the initial coordinate system,
representing the static moment of the rigid body in the initial coordinate system,
representing the moment of inertia of the rigid body in the new coordinate system,
representing the static moment, m, of the rigid body in a new coordinate system i Representing the mass of the rigid body; through rotation and translation changes, the calculation formulas of the moment of inertia and the static moment under the new coordinate system are as follows:
after transformation, the expression of the total moment of inertia and static moment of the morphing aircraft in the new coordinate system is:
according to the theorem of momentum and the theorem of moment of momentum:
wherein F represents the external force to which the morphing aircraft is subjected as a whole,
the derivative of the momentum of the aircraft, M the external moment to which the aircraft is subjected as a whole,
representing the derivative of the external moment to which the aircraft as a whole is subjected with respect to time,
represents the time derivative of the static moment about the longitudinal axis of the aircraft, V represents the flight speed of the aircraft;
and decomposing each vector into a ground coordinate system according to the relation between the absolute derivative and the relative derivative, wherein the nonlinear dynamical equation of the aircraft variant process is as follows:
from (9) and (10), different from a fixed wing aircraft, the dynamic equation of the deformable aircraft is added with the static moment S and the corresponding derivative terms; this is due to the change in the position of the centre of mass of the morphing aircraft; in the formula S x ,S y ,S z Representing the additional force generated by the movement of the aircraft centroid position,
centroid of expressionAdditional force generated by the moving speed;
representing an additional force due to the acceleration of the centroid movement; in the formula S x ,S y ,S z Representing the additional moment generated by the movement of the aircraft centroid position,
representing an additional moment due to the moving speed of the center of mass;
representing an additional moment due to the acceleration of the movement of the center of mass; adding one point to the characters to represent the first derivative of the parameter, and adding two points to the letter symbols to represent the second derivative of the parameter; and F x 、F y 、F z Respectively representing the external forces, M, to which the aircraft is subjected in the x, y and z directions x ,M y ,M z The method comprises the following steps of (1) representing external moments borne by an aircraft in three directions, wherein m represents the overall mass of the aircraft, p, q and r represent the angular velocities of a ballistic coordinate system relative to the ground coordinate system in the three directions, and u, v and w represent the angular velocities of the ballistic coordinate system relative to the ground coordinate system in the three directions; i is ix 、I iy 、I iz Denotes the moment of inertia, ω, of the ith wing relative to the entire machine ix 、ω iy 、ω iz Representing the moment of inertia of the ith wing relative to the whole machine.
7. The adaptive PID control parameter tuning method for the neural network-based variant aircraft is characterized in that in the step (2), the design method for the control-oriented multi-modal strongly-coupled nonlinear time-varying model comprises the following steps:
the topological structure of the BP neural network is a three-layer structure: the neuron of the same layer is only connected with the next layer and the previous layer, and the signal forward propagation refers to that a sample entering from the input layer sequentially passes through the hidden layer and the output layer; the error back propagation means that the error generated after the output of the neural network is compared with the expected output reaches the input layer from the output layer through the hidden layer, and the weight and the threshold value of the neuron are adjusted in the propagation process, so that the actual output of the neural network is continuously close to the expected output;
for a BP neural network topology with only one hidden layer: let n be the number of neurons in the input layer, q be the number of neurons in the hidden layer, m be the number of neurons in the output layer, and x be the input of the ith neuron in the input layer i I =1 \8230n, the weight value of the connection between the jth neuron of the hidden layer and the ith neuron of the input layer is omega ij The j-th neuron of the hidden layer is connected with the k-th neuron of the output layer by a weight omega jk The threshold value of the jth neuron of the hidden layer is theta j The excitation function of the hidden layer is
The k-th neuron threshold of the output layer is a k The output is Y i K =1 \ 8230m, the excitation function adopted by the output layer is psi, and the output of the kth neuron of the output layer is o k ；
(1) The signal forward propagation process:
input net of j-th neuron of hidden layer j Comprises the following steps:
output y of the jth neuron of the hidden layer j Comprises the following steps:
input net of k node of output layer k Comprises the following steps:
the output of the kth node of the output layer is:
(2) error back propagation process
The error for a certain sample p can be expressed as:
wherein, T k A standard value indicating a time k;
assuming a total of P samples, the overall error criterion function for these samples is:
the adjustment method of the neural network is a gradient descent method, and the adjustment quantity from the hidden layer to the output layer weight is assumed to be delta omega jk The adjustment amount of the k-th neuron threshold of the output layer is delta a k The adjustment of the weight from the input layer to the hidden layer is delta omega ij The adjustment amount of the jth neuron threshold of the hidden layer threshold is delta theta j The following formula is given:
wherein η represents the learning efficiency of the neuron;
the formula for adjusting the weight between the hidden layer and the output layer is as follows:
the adjustment formula of the output layer threshold is as follows:
the formula for adjusting the weight between the input layer and the hidden layer is as follows:
adjustment formula of hidden layer threshold:
and due to
Substituting formulae (21) to (25) for formulae (17) to (20), respectively, yields the following results:
8. the adaptive PID control parameter tuning method based on the neural network is characterized in that in the step (3), the similarity checking method for the key features of the simplified model comprises the following steps:
applying the normal flight state boundary of the hypersonic aircraft to flight dynamics parametric model simulation to obtain an achievable flight envelope curve; the flight envelope curve is composed of a series of dense state data points, and the state data points and the calculated dynamic parameters are the basis for generating training data;
for a BP neural network model, training requires determining the input and output of the model, and in combination with the study object, a model for predicting the aircraft dynamics parameters is established: the resistance coefficient CD, the lift coefficient CL, the pitching moment coefficient CM and the thrust coefficient CT are output models; after determining the output, considering all variables affecting the output as inputs; state variables affecting the output, including angle of attack a, height H, elevator yaw delta z Fuel equivalence ratio
The method of training four groups of five state parameters corresponding to one output neural network is adopted to pass through data requirementsAnalyzing, and preliminarily determining input and output dimensions of the training data; in the four neural networks, input data are five dimensions including an attack angle a, a height H and an elevator deflection delta z Mach number, mach number, fuel equivalence ratio
The four output data are one-dimensional and respectively comprise a resistance coefficient CD, a lift coefficient CL, a pitching moment coefficient CM and a thrust coefficient CT; defining a set matrix containing all state data points of the input and output states as a reference ballistic state data matrix I 0 (ii) a For the preliminarily selected input variables and output variables, training is carried out after expansion, and influence characteristics of the output variables are analyzed aiming at each input variable; training sampling points of the four groups of neural networks are determined according to the linear strength of the input state parameters on the output influence and the accuracy of the neural network output in the experiment;
through input and output influence analysis, the influence relation of input on output can be divided into three types, and different sampling point-taking strategies are correspondingly adopted:
no influence: the input-output images are in horizontal straight lines parallel to the x-axis; the input is directly deleted;
linear influence: i.e. the input-output image is in a slanted straight line; performing three-point expansion;
non-linear effects: selecting an expansion mode according to the non-linear degree;
and (3) expanding points N: the number of data points after expansion is referred to; for N-point expansion, if the expansion amplitude is A, the expansion interval of the N-point expansion is A/(N-2);
based on the analysis of the influence characteristics of each input on the output, the similarity of key features is directly checked;
a Neural Network Toolbox in Matlab is used for training a Neural Network model, and the model training method comprises the following steps:
the data used for training is divided into three blocks, namely a training set, a verification set and a test set;
the training related parameters include: the net hiding layer number, epoch, learning rate Lr, model precision Goal required to be achieved by training, and maximum number of failures allowed to continuously perform validation checks, max _ fail;
and training the neural network by using the training data matrix.
9. The adaptive PID control parameter tuning method for the neural network-based morphing aircraft according to claim 1 or 5, wherein in step (4), the adaptive PID flight design control for the morphing aircraft comprises:
according to the logic of controlling the fuel equivalence ratio by controlling the attack angle and the accelerator coefficient by the elevator, a fourth-order control system expressed by a state space equation is decomposed into a third-order control system and a first-order control system, and the corresponding control quantities are the attack angle and the accelerator; the three-order control system is provided with two leading poles and a non-leading pole, and the dynamic index of the system is determined by the two leading poles; the position of the dominant pole has a significant influence on the performance index of the corresponding system, the dominant pole is determined by calculating the damping ratio and the natural frequency, and the calculation formula is as follows:
wherein λ is 1,2 Two dominant poles, xi is the system damping ratio, omega n Is the natural frequency of the system, t s To adjust time, σ is the system overshoot;
after determining the two dominant poles, based on the real part of the determined dominant pole, the non-dominant pole is selected, i.e.: lambda [ alpha ] 3 ＝-nξω n N is a selected multiple which can be adjusted according to the actual control effect;
the first order system has only one pole, noted as: lambda 4 ＝-1/λ
Wherein, T is a first-order system time constant, and the first-order system adjusting time is generally 4T, so the pole of the first-order system is selected by the required adjusting time;
up to this point, the four desired poles may all be determined; the controller is of the form:
U＝U c -KΔX
wherein, U c Is an input in equilibrium; resolving a control matrix K by adopting a matrix variation method:
in the formula, a i Is the coefficient of the characteristic polynomial of the A matrix; the characteristic equation of the feedback control system A-BK at the selected desired pole is as follows:
(s-λ 1 )(s-λ 2 )(s-λ 3 )(s-λ 4 )＝s 4 +α 1 s 3 +α 2 s 2 +α 3 s+α 4 (33)
wherein, a i Representing characteristic polynomial coefficients, i =1,2,3,4, s being an unknown quantity;
the control matrix K can be written as:
the control matrix K is a 2-row and 4-column matrix, and the first row controls the quantity delta z Calculating the deflection angle of the elevator; second row pair control quantity
Calculating an accelerator coefficient; the two control quantities are determined by the fuel equivalence ratio and the deviation of four physical quantities, namely the angular velocity, the pitch angle and the attack angle, so that the self-adaptive feedback control is realized.
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