Backstepping control method for variable-shape aircraft

Abstract

The invention discloses a variable-shape aircraft backstepping control method, and belongs to the field of aircraft control. The implementation method comprises the following steps: establishing a variable shape aircraft system model; and setting a high-order fixed time disturbance observer. And estimating the state and disturbance of the variable shape aircraft system model. And establishing a controller comprising an attitude angle control loop and an attitude angular velocity control loop, and obtaining a control instruction based on an estimation result. And substituting the control instruction into the shape-variable aircraft model to obtain the attitude change of the aircraft. According to the high-order fixed time disturbance observer, auxiliary variables are introduced to carry out high-order differential expansion on disturbance estimation, so that the estimation precision of uncertain disturbance is improved; under the condition of not depending on the initial state of the system, it is ensured that the tracking error converges to any small field of zero within fixed time; according to the backstepping control method based on the fixed-time high-order disturbance observer, effective observation and estimation of multi-source uncertain time-varying disturbance existing in a control system can be achieved.

Description

TECHNICAL FIELD

[0001] The application relates to a backstepping control method of a morphing aircraft, in particular to a morphing aircraft control method based on a fixed-time high-order disturbance observer, and belongs to the field of aircraft control. BACKGROUND

[0002] The morphing aircraft has the advantages that the aerodynamic shape can be autonomously adjusted according to flight conditions and task requirements, so that the aerodynamic characteristics are optimized and the flight performance is improved. However, because the aerodynamic shape is changed, a series of influences are also generated. The highly nonlinear and time-varying characteristics make it difficult for traditional linear control methods to meet the control requirements. At the same time, the deformation of the aircraft structure causes the change of the aerodynamic parameters, which further increases the complexity of modeling and control. In addition, the aircraft forms a strong aerodynamic heat effect and the wind field changes when flying at high speed, which has a large uncertainty influence on the aircraft control system. Therefore, it is necessary to design a controller with strong robustness, which can identify disturbances and quickly converge for the morphing aircraft. SUMMARY

[0003] The purpose of the application is to provide a backstepping control method of a morphing aircraft. By designing the backstepping control method of the morphing aircraft, accurate estimation of uncertain complex disturbances faced by the aircraft in a complex flight environment can be realized, so that the aircraft always maintains a stable attitude during the morphing process, and the risk of attitude imbalance caused by shape change is avoided. At the same time, when receiving an attitude command, the aircraft can quickly and accurately respond, greatly improving the efficiency and reliability of attitude control, and greatly expanding the application range and task adaptability of the morphing aircraft.

[0004] The purpose of the application is realized by the following technical scheme:

[0005] The backstepping control method of the morphing aircraft disclosed by the application comprises the following steps:

[0006] S1, based on the influences of the morphing mechanism, aerodynamic heat effect and external disturbance on the morphing aircraft, the disturbances caused by external disturbances, model uncertainties and deformation modeling errors are comprehensively considered as total disturbances, and a morphing aircraft system state equation considering disturbances is established;

[0007] S2, in order to improve the observation accuracy of the system disturbance, a differential expansion term is designed to approximate the estimation error, and a high-order fixed-time disturbance observer is set for a general system state equation;

[0008] S3, estimating the state and disturbance of the variable configuration aircraft system model of S1 by using a high-order fixed-time disturbance observer; obtaining the estimated values of the state and disturbance of the attitude angle control loop, and designing a virtual control law, regarding the inner loop attitude angle velocity tracking error as the state of the observer, regarding the sum of the attitude angle velocity system comprehensive disturbance and the differential of the outer loop virtual control law as the disturbance of the observer, establishing a controller including the attitude angle control loop and the attitude angle velocity control loop, and obtaining the control command based on the estimated results;

[0009] S4, using the control command obtained by S3 into the variable configuration aircraft model in S1, and obtaining the attitude change of the aircraft combined with the accurate aerodynamic parameters obtained online.

[0010] Further, the variable configuration aircraft system state equation in S1 is:

[0011]

[0012]

[0013] In the formula, x1 = [a, b, g] T And x2 = [w x , w y , w z ] T are system state variables. u = [d x , d y , d z ] T are system control variables, roll rudder deflection angle, yaw rudder deflection angle and pitch rudder deflection angle. d1 and d2 are disturbances. The symbols a, b and g respectively represent the three attitude angles of the aircraft, i.e. the attack angle, the sideslip angle and the velocity inclination angle. m, g, V and q respectively represent the mass, the gravity coefficient, the speed and the ballistic inclination angle of the aircraft. w x , w y , w z are the roll angle velocity, the yaw angle velocity and the pitch angle velocity of the aircraft. J x , J y , J z are the principal moments of inertia of the aircraft around the x, y and z axes. J xy is the inertia product of the aircraft to the x and y axes. The aircraft is a plane-symmetric configuration, so the inertia product of the aircraft to the x and z axes and the inertia product of the aircraft to the y and z axes are zero, i.e. J xz = J yz = 0. L and N are the aerodynamic lift and drag, where is the dynamic pressure, p is the atmospheric density, and S ref is the characteristic area of the aircraft. L refis the characteristic length of the aircraft. max and min are the maximum and minimum allowed rudder deflection angles of the aircraft. L , C N , C mx , C my and C mz are the lift coefficient, drag coefficient, roll moment coefficient, yaw moment coefficient and pitch moment coefficient, respectively. The subscripts in C represent the corresponding aerodynamic moment coefficient, and the superscripts represent the derivative with respect to the corresponding rudder deflection angle. For example, C

[0014] Further, the fixed-time high-order disturbance observer in S2 is:

[0015] For the aircraft system state equation:

[0016]

[0017] sig(σ) = sign(σ). |σ|

[0018] wherein: represents the estimation of the system state x, represents the estimation of the disturbance d, is the state observation error. By introducing Δ1, Δ2 as auxiliary variables, λ i and q i are settable parameters.

[0019] In S2, the gain coefficients satisfy:

[0020] The relationship between each gain coefficient is represented as λ p = λ p+1 , p = 1, 3, 5, 7, while satisfying:

[0021] (s + ω) 4 = s 4 + λ1s 3 + λ3s 2 + λ5s + λ7

[0022] wherein ω represents the bandwidth of the high-order fixed-time disturbance observer.

[0023] wherein ι1 and ι2 are small normal numbers.

[0024] Further, the specific implementation method of S3 is:

[0025] The attitude angle and attitude angular velocity tracking error is defined as

[0026]

[0027] Where: x 1d =[α d β d γ d ] T is the attitude angle tracking instruction. 2d It is the inner loop attitude angular velocity tracking instruction. 2d =x 2c The virtual control law generated for the outer loop control system.

[0028] The virtual control law for the attitude angle control system is designed as follows:

[0029]

[0030] Where a1 and b1 are diagonal matrices whose elements are positive numbers, r1 and r2 are positive constants, and 0<r1<1, r2>1. It is the estimation of the comprehensive disturbance of the attitude angle system.

[0031] According to the fixed-time high-order disturbance observer, the disturbance observation in the outer attitude angle control loop is expressed as:

[0032]

[0033] Where: is the estimation error of the disturbance observer state quantity.

[0034] Will It is regarded as a synthetic disturbance, and the synthetic disturbance is observed by a high-order fixed-time disturbance observer and compensated in the control law, which is expressed as:

[0035]

[0036] Where a2 and b2 are diagonal matrices whose elements are positive numbers. It is an estimate of the comprehensive disturbance of the attitude angular velocity system.

[0037] According to the high-order fixed-time disturbance observer, the estimation of the differential difference between the inner loop attitude angular velocity loop disturbance and the outer loop virtual control law is expressed as

[0038]

[0039] Where: is the estimation error of the disturbance observer state quantity.

[0040] According to the control law u, the control instruction u is obtained s

[0041]

[0042] Further, the aerodynamic parameters C L , C N , C mx , C my , and C mz are obtained by the following method,

[0043] S1.1, a three-layer BP neural network is established based on the nonlinear mapping relationship between the input and output parameters of the aircraft aerodynamic model.

[0044] S1.2, the weight matrix and threshold matrix of the BP neural network are selected and rearranged as a vector to serve as a system state variable, and a state equation is constructed.

[0045] S1.3, a 6-DOF aircraft motion model is established.

[0046] S1.4, the angle of attack, sideslip angle, velocity inclination angle, and angular velocities of the three channels of pitch, yaw, and roll of the aircraft in the S1.3 model are taken as the observation values of the extended Kalman filter.

[0047] S1.5, an observation equation containing observation noise is established according to the observation values of S1.4.

[0048] S1.6, based on the state equation of S1.2 and the observation equation of S1.5, the state prediction at time t k -t k+1 is performed using the extended Kalman filter method, and the measurement update is performed according to the prediction result to obtain the updated state variable.

[0049] S1.7, the state variable obtained by S1.6 is combined with the aircraft state result to obtain new aerodynamic parameters C L , C N , C mx , C my , and C mz , which are the lift coefficient, drag coefficient, roll moment coefficient, yaw moment coefficient, and pitch moment coefficient, respectively.

[0050] Further, the input-output relationship of the three-layer BP neural network established in S1.1 is:

[0051]

[0052] where H is the hidden layer neuron, g(·) is the activation function which is the sigmoid function, I is the input layer neuron, is the weight matrix from the input layer to the hidden layer, B [1] is the threshold matrix of the hidden layer. Y is the output layer neuron, B is the threshold matrix of the output layer. [2] B is the threshold matrix of the output layer.

[0053] Further, the system state variable X in S1.2 is expressed as:

[0054] X = [W1, W2, B1, B2] T

[0055] where W1, W2, B1, B2 represent as follows:

[0056]

[0057] The superscript represents the value in the weight matrix of the corresponding layer, and the subscript represents the corresponding neuron position of the front and rear layers. The superscript represents the value in the threshold matrix of the corresponding layer, and the subscript represents the corresponding neuron position of the layer

[0058] The system state equation in S1.2 is:

[0059]

[0060] where W t is the system noise vector, and if the neural network parameters tend to be stable, f(X, t) = 0.

[0061] Further, the 6-DOF aircraft motion model in S1.3 is:

[0062]

[0063] where,

[0064]

[0065] In the formula: α, β, γ are the attack angle, sideslip angle and speed inclination angle of the aircraft respectively. m, g, V, θ are the mass, gravitational coefficient, speed and ballistic inclination angle of the aircraft respectively. ω x , ω y , ω z are the roll, yaw and pitch angular velocities of the aircraft respectively. J x , J y , J z are the principal moments of inertia of the aircraft around the x, y, z axes respectively. J xy is the inertia product of the aircraft to the x, y axes. The aircraft is a plane-symmetric configuration, so the inertia product of the aircraft to the x, z axes and to the y, z axes is zero, that is, J xz = J yz = 0. L, N are the aerodynamic lift and drag respectively, where ρ is the air density, S ref is the characteristic area of the aircraft. M x is the Mach number, and y is the angle of attack, and z is the angle of sideslip, and is the characteristic length of the aircraft. C ref is the roll moment, and L is the yaw moment, and N is the pitch moment, and mx is the roll damping, and my is the yaw damping, and mz is the pitch damping.

[0066] Further, the observation equation in S1.5 is

[0067] Z = h(X, t) + V t

[0068] where V t is the observation noise vector. h(X, t) is the calculation function of the observation value at time t through the state variable.

[0069] Further, the implementation method in S1.6 is,

[0070] the state prediction at time t k ~ t k+1 is expressed as:

[0071]

[0072] The subscript k / k of the variable in the above formula indicates the final calculated value at time t k , k+1 / k indicates the value at time t k predicted by using the value at time t k+1 , and only one subscript indicates that the variable is the value at the corresponding time.

[0073] The variance matrix prediction is expressed as:

[0074]

[0075] where the state transition matrix from time t k ~ t k+1 is:

[0076]

[0077] where Δt is the filtering step length. Q k is the system process noise variance matrix. I is the unit matrix, and the Jacobian matrix of the state equation is:

[0078]

[0079] Measurement update:

[0080] State estimation:

[0081]

[0082] Variance matrix estimation:

[0083]

[0084] Filter gain matrix:

[0085]

[0086] where R k+1 is the observation noise variance matrix, and the Jacobian matrix of the observation equation is:

[0087]

[0088] Beneficial effects:

[0089] 1. The variable shape aircraft backstepping control method disclosed in the application, a high-order fixed-time disturbance observer, by introducing an auxiliary variable, carries out high-order differential expansion on disturbance estimation, uses the differential expansion term to approximate the estimation error, and improves the estimation accuracy of the uncertain disturbance.

[0090] 2. The variable shape aircraft backstepping control method disclosed in the application, the disturbance caused by external disturbance, model uncertainty and deformation modeling error is considered as a total disturbance, which greatly simplifies the estimation of the disturbance of the aircraft and the design of the disturbance observer, and improves the estimation efficiency of the uncertain disturbance.

[0091] 3. The variable shape aircraft backstepping control method disclosed in the application, a high-order fixed-time disturbance observer is used to obtain the estimated value of the state and disturbance of the attitude angle control loop, and a virtual control law is designed, in order to avoid the "calculation explosion" problem caused by continuous differentiation of the virtual control law, the sum of the differential of the virtual control law and the external disturbance is considered as a comprehensive disturbance for estimation, and the comprehensive disturbance estimated value is compensated to the control law. This method greatly simplifies the steps of controller stability proof.

[0092] 4. The variable shape aircraft backstepping control method disclosed in the application, by using the extended Kalman filter algorithm instead of the process of correcting the parameters by neural network back calculation, by adjusting the real-time neural network model and predicting and adjusting the model, compared with the single Kalman filter method, the aerodynamic parameter identification value with higher precision can be obtained.

[0093] 5. The variable geometry aircraft backstepping control method disclosed in the application uses observable flight data of the aircraft to correct the BP neural network weight and threshold value, so that the BP neural network model can approach the actual aerodynamic model in real time, and a more accurate aerodynamic model that can replace the original interpolation aerodynamic model of the aircraft is obtained. BRIEF DESCRIPTION OF DRAWINGS

[0094] Figure 1 A variable geometry aircraft backstepping control method flowchart showing a preferred embodiment of the application is shown.

[0095] Figure 2 A back sweep angle change curve in the example is shown.

[0096] Figure 3 Attack angle, sideslip angle and speed inclination angle tracking curves of the control command in Example 1 and Comparative Examples 1 and 2 are shown.

[0097] Figure 4 Attitude angle tracking error curves in Example 1 and Comparative Examples 1 and 2 are shown.

[0098] Figure 5 Attitude angle velocity curves in Example 2 and Comparative Examples 1 and 2 are shown.

[0099] Figure 6 Attitude angle state estimation value curves in Example 2 and Comparative Examples 1 and 2 are shown.

[0100] Figure 7 Attitude angle disturbance estimation value curves in Example 2 and Comparative Examples 1 and 2 are shown.

[0101] Figure 8 Attitude angle velocity state estimation value curves in Example 2 and Comparative Examples 1 and 2 are shown.

[0102] Figure 9 Attitude angle velocity disturbance estimation value curves in Example 2 and Comparative Examples 1 and 2 are shown.

[0103] Figure 10 Aerodynamic force parameter identification effect curves in the aircraft attitude control process of Example 1 are shown.

[0104] Figure 11 Aerodynamic moment parameter identification effect curves in the aircraft attitude control process of Example 1 are shown. DETAILED DESCRIPTION

[0105] Example 1

[0106] A simulation experiment is performed to achieve attitude control of the variable geometry aircraft. The initial attitude angle of the attitude control simulation is [α0, β0, γ0] T=[15°, 2°, 0°] T The initial attitude angular velocity is all 0° / s, and the sweepback angle of the morphing aircraft changes with time. In order to simulate the change of the sweepback angle of the morphing aircraft in the flight process, the sweepback angle is set to change from 30° to 90° in the first 15s of the flight time and then remain unchanged. The sweepback angle change curve is as shown in Figure 2 The attitude angle tracking instruction is designed as x 1d =[10°, 0, 10°] T In the case of introducing external disturbance,

[0107]

[0108] As shown in Figure 1 , the morphing aircraft backstepping control method disclosed in the embodiment is implemented as follows:

[0109] The morphing aircraft model in S1 is:

[0110]

[0111]

[0112] In the formula, x1=[α, β, γ] T and x2=[ω x , ω y , ω z ] T are system state quantities; u=[δ x , δ y , δ z ] T are system control quantities, roll rudder deflection angle, yaw rudder deflection angle and pitch rudder deflection angle; d1 and d2 are disturbances; the symbols α, β and γ respectively represent three attitude angles of the aircraft, i.e. attack angle, sideslip angle and velocity inclination angle; m, g, V and θ respectively represent the mass, gravitational coefficient, speed and ballistic inclination angle of the aircraft; ω x , ω y , ω z are roll angular velocity, yaw angular velocity and pitch angular velocity of the aircraft; J x , J y , J z are principal moments of inertia of the aircraft around the x, y and z axes; J xy is the inertia product of the aircraft to the x and y axes; the aircraft is a plane-symmetric configuration, so the inertia products of the aircraft to the x and z axes and to the y and z axes are zero, i.e. J xz = J yz = 0; L and N respectively represent aerodynamic lift and drag, wherein is the dynamic pressure, ρ is the atmospheric density, and Sref A is the characteristic area of the aircraft; L ref L is the characteristic length of the aircraft; u max and u min and u are the maximum and minimum rudder deflection angles allowed for the aircraft; C L , C N , C mx , C my and C mz are the lift coefficient, drag coefficient, roll moment coefficient, yaw moment coefficient and pitch moment coefficient respectively. The subscripts in C indicate the corresponding aerodynamic moment coefficient, and the superscripts indicate the derivative with respect to the corresponding rudder deflection angle, i.e. is an example of the derivative of the roll moment coefficient with respect to the roll rudder deflection angle.

[0113] The fixed-time high-order disturbance observer in S2 is:

[0114] For a general form of state equation:

[0115]

[0116] sig(σ) = sign(σ). |σ|

[0117] In the formula: x is the estimation of the system state x, d is the estimation of the disturbance d, is the state observation error; by introducing Δ1, Δ2 as auxiliary variables, λ i and q i are settable parameters;

[0118] In a preferred embodiment, in S2, the gain coefficients satisfy:

[0119] The relationship between each gain coefficient can be expressed as λ p = λ p+1 , p = 1, 3, 5, 7, while satisfying:

[0120] (s + ω) 4 = s 4 + λ1s 3 + λ3s 2 + λ5s + λ7

[0121] In the formula: ω represents the bandwidth of the high-order fixed-time disturbance observer;

[0122] where ι1 and ι2 are small normal numbers.

[0123] The specific implementation method of S3 is:

[0124] The attitude angle and attitude angular velocity tracking error is defined as

[0125]

[0126] Where: x 1d =[α d β d γ d ] T is the attitude angle tracking instruction; x 2d x is the inner loop attitude angular velocity tracking instruction; 2d =x 2c The virtual control law generated for the outer loop control system.

[0127] The virtual control law for the attitude angle control system is designed as follows:

[0128]

[0129] Where a1 and b1 are diagonal matrices whose elements are positive numbers, r1 and r2 are positive constants, and 0<r1<1, r2>1. is the estimation of the comprehensive disturbance of the attitude angle system; the controller parameters are designed as a1=b1=diag(1,1,1);

[0130] According to the fixed-time high-order disturbance observer, the disturbance observation in the outer attitude angle control loop is expressed as:

[0131]

[0132] Where: is the estimation error of the disturbance observer state quantity; the bandwidth of the outer loop attitude angle high-order fixed-time disturbance observer is ω1=4, and the observer power term parameters are: p1=0.8, p2=0.6, p3=0.4, p4=0.2, q1=1.2, q2=1.4, q3=1.6, q4=1.8.

[0133] Will It is regarded as a synthetic disturbance, and the synthetic disturbance is observed by a high-order fixed-time disturbance observer and compensated in the control law, which is expressed as:

[0134]

[0135] Where a2 and b2 are diagonal matrices whose elements are positive numbers. To estimate the comprehensive disturbance of the attitude angular velocity system; the controller parameters are designed as a2=b2=diag(3,3,5);

[0136] According to the high-order fixed-time disturbance observer, the estimation of the differential difference between the inner loop attitude angular velocity loop disturbance and the outer loop virtual control law is expressed as

[0137]

[0138] wherein: is the estimation error of the disturbance observer state quantity. The inner loop attitude angular velocity high-order fixed time disturbance observer bandwidth ω2=10, the observer power term parameters are: p1=0.8, p2=0.6, p3=0.4, p4=0.2, q1=1.2, q2=1.4, q3=1.6, q4=1.8.

[0139] Finally, the control command u is obtained for the control law u s

[0140]

[0141] S1. The aerodynamic parameters C L , C N , C mx , C my and C mz N is obtained by the following method,

[0142] S1.1, based on the nonlinear mapping relationship between the input and output parameters of the aircraft aerodynamic model, a three-layer BP neural network is established;

[0143] S1.2, the weight matrix and threshold matrix of the BP neural network are selected and rearranged as a vector to be used as a system state variable to construct a state equation;

[0144] S1.3, an aircraft 6-degree-of-freedom aircraft motion model is established;

[0145] S1.4, the aircraft angle of attack, sideslip angle, velocity inclination angle, and angular velocities of the three channels of pitch, yaw, and roll in the S1.3 model are used as observation values for the extended Kalman filter;

[0146] S1.5, an observation equation containing observation noise is established according to the observation values of S1.4;

[0147] S1.6, based on the state equation of S1.2 and the observation equation of S1.5, the state prediction at time t k ~t k+1 is performed using the extended Kalman filter method, and the measurement update is performed according to the prediction result; the updated state variable is obtained;

[0148] S1.7, the state variable obtained by S1.6 is combined with the aircraft state result to obtain new aerodynamic parameters C L , C N , C mx , C my and C mzThe aerodynamic parameters are identified, including the lift coefficient, the drag coefficient, the roll moment coefficient, the yaw moment coefficient and the pitch moment coefficient.

[0149] The input-output relationship of the three-layer BP neural network established in S1.1 is as follows:

[0150]

[0151] where H is the hidden layer neuron, g(·) is the activation function, I is the input layer neuron, is the weight matrix from the input layer to the hidden layer, B [1] is the threshold matrix of the hidden layer. Y is the output layer neuron, is the weight matrix from the hidden layer to the output layer, B [2] is the threshold matrix of the output layer.

[0152] Further, the system state variable X in S1.2 is expressed as:

[0153] X = [W1, W2, B1, B2] T

[0154] where W1, W2, B1, B2 are expressed as follows:

[0155]

[0156] The superscript indicates the value in the weight matrix of the corresponding layer, and the subscript indicates the corresponding neuron position of the front and rear layers. The superscript indicates the value in the threshold matrix of the corresponding layer, and the subscript indicates the corresponding neuron position of the layer

[0157] The system state equation in S1.2 is as follows:

[0158]

[0159] where W t is the system noise vector, and if the neural network parameters tend to be stable, f(X, t) = 0.

[0160] Further, the 6-DOF aircraft motion model in S1.3 is as follows:

[0161]

[0162] where,

[0163]

[0164] where a, b, g are the angle of attack, the angle of sideslip and the angle of velocity of the aircraft, m, g, V, g are the mass, the gravity coefficient, the velocity and the angle of trajectory of the aircraft, w x , w y , w z are the roll, the yaw and the pitch angular velocity of the aircraft, J x , J y , J z are the principal moments of inertia of the aircraft about the x, y, z axes, respectively. xy J xz , J yz are the products of inertia of the aircraft about the x, y axes. The aircraft is of plane-symmetrical configuration, so the products of inertia of the aircraft about the x, z axes and about the y, z axes are zero, i.e. J ref , J x are the aerodynamic lift and drag forces, respectively, where is the dynamic pressure, p is the air density, S y is the characteristic area of the aircraft, M z , M ref , M L are the roll, the yaw and the pitch moments, respectively, and are expressed as where L N is the characteristic length of the aircraft. C mx , C my , C mz , C t and C t are functions related to the Mach number Ma, the angle of attack a, the angle of sideslip b and the equivalent rudder deflection.

[0165] Further, the observation equation in S1.5 is

[0166] Z = h(X, t) + V k

[0167] where V k+1 is the observation noise vector. h(X, t) is the calculation function of the observation value at time t through the state variable.

[0168] Further, the implementation method in S1.6 is,

[0169] The state prediction at time t k ~ t k is expressed as:

[0170]

[0171] The subscript k / k of the variable in the above formula indicates the final calculated value at time t k+1The value of the time, only one subscript indicates that the variable is the value of the corresponding time.

[0172] The variance matrix prediction is expressed as:

[0173]

[0174] Where t k ~t k+1 The state transition matrix is:

[0175]

[0176] Where Δt is the filter step size. Q k is the system process noise variance matrix. I is the unit matrix, and the Jacobian matrix of the state equation is:

[0177]

[0178] Measurement update:

[0179] State estimation:

[0180]

[0181] Variance matrix estimation:

[0182]

[0183] Filter gain matrix:

[0184]

[0185] Where R k+1 is the observation noise variance matrix, and the Jacobian matrix of the observation equation is:

[0186]

[0187] Comparative Example 1

[0188] The same experiment as Example 1 was performed, except that the fixed-time disturbance observer designed in Zhao J Q, Feng D Z, Cui J S, et al. Finite-time extended state observer-based fixed-time attitude control for hypersonic vehicles [J]. Mathematics, 2022, 10(17): 3162. was used.

[0189] Comparative Example 2

[0190] The same experiment as example 1 was carried out, except that a traditional backstepping control method was used.

[0191] The simulation results are shown in Figures 3-9

[0192] From Figures 3-9 It can be obtained that, considering the uncertain external disturbance, compared with comparative example 1, example 1 has obvious advantages in tracking accuracy and error convergence speed because of the existence of the disturbance observer. Compared with comparative example 1, the state and disturbance value estimation is more rapid and accurate. Figures 3-4 It can be obtained that example 1 can realize stable tracking of the control instruction, and from the partial enlarged view, it can be seen that the steady-state error of example 1 is smaller. Figure 5 For the attitude angular velocity curve, it can be known that example 1 and comparative example 1 can both realize convergence of the angular velocity, so it is proved that the observer has a certain inhibitory effect on the disturbance but the convergence speed is slow.

[0193] Figures 6-9 For the state and disturbance observation values of the attitude angle and angular velocity, it can be obtained from the figure that example 1 can realize accurate estimation of the state and disturbance. From the partial enlarged view, it can be obviously seen that the estimation accuracy of the high-order fixed-time disturbance observer of example 1 on the comprehensive disturbance quantity is higher than that of comparative example 1.

[0194] Figures 10-11 The real-time identification effect of the aerodynamic parameters in the flight process.

[0195] The above specific description further details the purpose, technical scheme and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the application should be included in the protection scope of the application.​

Claims

1. A backstepping control method for a shape-shifting aircraft, characterized by: The steps include: S1. Based on the fact that the shape-shifting aircraft is affected by deformation mechanism, aerodynamic thermal effect and external disturbance, the disturbance caused by external disturbance, model uncertainty and deformation modeling error is considered as a total disturbance, and the state equation of the shape-shifting aircraft system considering the disturbance is established. S2. To improve the observation accuracy of system disturbances, a differential expansion term is designed to approximate the estimation error, and a high-order fixed-time disturbance observer is set for the general system state equation; S3. Use a high-order fixed-time disturbance observer to estimate the state and disturbance of the deformable aircraft system model of S1; obtain estimated values ​​of the loop state and disturbance for the attitude angle control loop, and simultaneously design a virtual control law. For the attitude angular velocity control loop, treat the inner loop attitude angular velocity tracking error as the observer state quantity, and treat the sum of the attitude angular velocity system comprehensive disturbance and the differential of the outer loop virtual control law as the observer disturbance quantity. Establish a controller including the attitude angle control loop and the attitude angular velocity control loop, and obtain control instructions based on the estimation results; S4. Substitute the control instructions obtained in S3 into the shape-shifting aircraft model described in S1, and combine the accurate aerodynamic parameters obtained by the aircraft online to obtain the attitude change of the aircraft.

2. The backstepping control method for a shape-shifting aircraft according to claim 1, wherein: The variable shape aircraft model described in S1 is: Where: x1 = [α, β, γ] T and x2=[ω x ,ω y ,ω z ] T is the system state quantity; u=[δ x ,δ y ,δ z ] T are the system control variables roll, yaw and pitch rudder angles; d1 and d2 are disturbances; symbol explanation: α, β and γ are the three attitude angles of the aircraft, namely the angle of attack, sideslip angle and velocity inclination; m, g, V and θ are the mass, gravity coefficient, velocity and ballistic inclination of the aircraft respectively; ω x 、ω y 、ω z are the aircraft's roll angular velocity, aircraft's yaw angular velocity, and aircraft's pitch angular velocity, J x 、J y 、J z is the main moment of inertia of the aircraft around the x, y, and z axes; J xy is the inertia product of the aircraft about the x and y axes; the aircraft is a plane-symmetrical configuration, so the inertia product of the aircraft about the x and z axes and the inertia product about the y and z axes are zero, that is, J xz =J yz =0; L and N are aerodynamic lift and drag respectively, in is the dynamic pressure, ρ is the atmospheric density, S ref is the characteristic area of ​​the aircraft; L ref is the characteristic length of the aircraft; u max and u min The maximum and minimum rudder angles allowed by the aircraft; aerodynamic parameters C L 、C N 、C mx 、C my and C mz They are lift coefficient, drag coefficient, rolling moment coefficient, yaw moment coefficient and pitching moment coefficient respectively. The subscripts in C represent the corresponding aerodynamic moment coefficients, and the superscripts represent the derivatives of the corresponding rudder deflection angles. For example, the derivative of the rolling moment coefficient with respect to the rolling rudder angle is represented.

3. The backstepping control method for a shape-shifting aircraft according to claim 2, wherein: The fixed-time high-order disturbance observer described in S2 is: The system state equation for the aircraft is: sig(σ)=sign(σ).|σ| Where: represents the estimate of the system state x, represents the estimate of the disturbance d, is the state observation error; by introducing Δ1 and Δ2 as auxiliary variables, λ i With q i All are configurable parameters; In S2, the gain coefficients satisfy: The relationship between the gain coefficients is expressed as λ p =λ p+1 , p=1,3,5,7, and satisfy: (s+ω) 4 =s 4 +λ1s 3 +λ3s 2 +λ5s+λ7 Where: ω represents the bandwidth of the high-order fixed-time disturbance observer; where ι1 and ι2 are small positive constants.

4. The backstepping control method for a shape-shifting aircraft according to claim 3, wherein: The specific implementation method of S3 is: The attitude angle and attitude angular velocity tracking error are defined as Where: x 1d =[α d β d γ d ] T is the attitude angle tracking instruction; x 2d x is the inner loop attitude angular velocity tracking instruction; 2d =x 2c The virtual control law generated for the outer loop control system. The virtual control law for the attitude angle control system is designed as follows: Where a1 and b1 are diagonal matrices whose elements are positive numbers, r1 and r2 are positive constants, and 0<r1<1, r2>1. is the estimation of the comprehensive disturbance of the attitude angle system; According to the fixed-time high-order disturbance observer, the disturbance observation in the outer attitude angle control loop is expressed as: Where: is the estimation error of the disturbance observer state quantity; Will It is regarded as a synthetic disturbance, and the synthetic disturbance is observed by a high-order fixed-time disturbance observer and compensated in the control law, which is expressed as: Where a2 and b2 are diagonal matrices whose elements are positive numbers. is the estimation of the comprehensive disturbance of the attitude angular velocity system; According to the high-order fixed-time disturbance observer, the estimation of the differential difference between the inner loop attitude angular velocity loop disturbance and the outer loop virtual control law is expressed as Where: is the estimation error of the disturbance observer state quantity. Get the control instruction u according to the control law u s 5. The backstepping control method for a shape-shifting aircraft according to claim 4, wherein: S1 aerodynamic parameters C L 、C N 、C mx 、C my and C mz N is obtained by the following method, S1.

1. Based on the nonlinear mapping relationship between the input and output parameters of the aircraft aerodynamic model, a three-layer BP neural network is established; S1.

2. Select the weight matrix and threshold matrix of the BP neural network, rearrange them into vectors as system state variables, and construct the state equation; S1.3, establish a 6-DOF aircraft motion model; S1.

4. Use the aircraft's angle of attack, sideslip angle, velocity inclination, and the angular velocity of the three channels of pitch, yaw, and roll in the S1.3 model as observation values ​​for the extended Kalman filter; S1.

5. Establish the observation equation containing observation noise based on the observation values ​​in S1.4; S1.6, based on the state equation of S1.2 and the observation equation of S1.5, the extended Kalman filter method is used to perform t k ~t k+1 The state prediction at the moment is performed, and the measurement is updated according to the prediction result; the updated state variables are obtained; S1.

7. Use the state variables obtained in S1.6 and combine them with the aircraft state results to obtain the new aerodynamic parameters C L 、C N 、C mx 、C my and C mz Complete the aerodynamic parameter identification, where the parameters are lift coefficient, drag coefficient, rolling moment coefficient, yaw moment coefficient and pitching moment coefficient.

6. The backstepping control method for a shape-shifting aircraft according to claim 5, characterized in that: The input-output relationship of the three-layer BP neural network established in S1.1 is: Among them, H is the hidden layer neuron, g(·) is the activation function which is the sigmoid function, I is the input layer neuron, is the weight matrix from the input layer to the hidden layer, B [1] is the threshold matrix of the hidden layer; Y is the output layer neuron, is the weight matrix from the hidden layer to the output layer, B [2] is the threshold matrix of the output layer.

7. The backstepping control method for a shape-shifting aircraft according to claim 6, wherein: The system state variable X described in S1.2 is expressed as, X=[W1,W2,B1,B2] T Where W1, W2, B1, and B2 are represented as follows: The superscript indicates the value in the weight matrix of the corresponding layer, and the subscript indicates the corresponding neuron position in the previous and next layers; The superscript represents the value in the threshold matrix of the corresponding layer, and the subscript represents the corresponding neuron position of the layer. The system state equation described in S1.2 is: Where W t is the system noise vector. If the neural network parameters tend to be stable, then f(X,t)=0.

8. The backstepping control method for a shape-shifting aircraft according to claim 7, wherein: The 6-DOF aircraft motion model described in S1.3 is, in, Where: α, β, γ are the aircraft's angle of attack, sideslip angle, and velocity inclination, respectively; m, g, V, θ are the aircraft's mass, gravity coefficient, velocity, and trajectory inclination, respectively; ω x 、ω y 、ω z are the roll, yaw and pitch angular velocities of the aircraft, J x 、J y 、J z are the principal moments of inertia of the aircraft around the x, y, and z axes respectively; J xy is the inertia product of the aircraft about the x and y axes; the aircraft is a plane-symmetrical configuration, so the inertia product of the aircraft about the x and z axes and the inertia product about the y and z axes are zero, that is, J xz =J yz =0; L and N are aerodynamic lift and drag respectively, in is the dynamic pressure, ρ is the atmospheric density, S ref is the characteristic area of ​​the aircraft; M x 、M y 、M z are the rolling moment, yaw moment and pitching moment respectively, expressed as Among them L ref is the characteristic length of the aircraft; C L 、C N 、C mx 、C my and C mz It is a function related to the Mach number Ma, angle of attack α, sideslip angle β and equivalent rudder deflection angle.

9. The backstepping control method for a shape-shifting aircraft according to claim 8, wherein: The observation equation described in S1.5 is, Z=h(X,t)+V t Where V t is the observation noise vector; h(X,t) is the calculation function for obtaining the observation value through the state variable at time t.

10. The backstepping control method for a shape-shifting aircraft according to claim 9, characterized in that: The implementation method in S1.6 is, The t k ~t k+1 The state prediction at the moment is expressed as: The subscript k / k of the variables in the above formula represents t k The final calculated value at time k+1 / k represents the value obtained by using t k The value of t predicted by k+1 The value at a moment, if there is only one subscript, it means that the variable takes the value at the corresponding moment; The variance matrix prediction is expressed as: Among them, t k ~t k+1 The state transition matrix is: Among them, Δt is the filtering step size; Q k is the system process noise variance matrix; I is the identity matrix, and the Jacobian matrix of the state equation is: Measurement Update: State Estimation: Variance matrix estimation: Filter gain matrix: where R k+1 is the observation noise variance matrix, and the Jacobian matrix of the observation equation is:

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