Vertical tail hinge moment load shedding method for high-speed variable vertical tail aircraft
The AMTHR method addresses the hinge torque challenge in high-speed variable vertical tail aircrafts by minimizing torque through adaptive control of deformation coefficients and rudder angles, ensuring safety and reliability under diverse flight conditions.
Patent Information
- Application Number
- CN202411206581.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-30
- Publication Date
- 2024-12-10
AI Technical Summary
The challenge of reducing hinge torque at the root of the vertical tail in high-speed variable vertical tail aircrafts, which increases with flight speed, is critical for ensuring flight safety and preventing structural failure due to limited capacity of the variable vertical tail drive motor.
An adaptive morphing tail hinge moment reduction (AMTHR) method using extreme value optimization control to minimize hinge torque by adjusting the deformation coefficient and rudder deflection angle, employing a tail allosteric model, torque characteristic analysis, and an extreme value optimization control framework to adaptively reduce hinge torque.
The method effectively maintains hinge torque at the minimum level during continuous deformation, enhancing flight safety and reliability under varying flight conditions, including gust disturbances.
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Figure CN119099844A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of flight system control, and in particular relates to a method for reducing load on a vertical tail hinge moment of a high-speed variable vertical tail aircraft. Background Art
[0002] The tailless wing-body fusion layout aircraft has the characteristics of high aerodynamic lift efficiency and good stealth performance. In addition, the omnidirectional extremely low radar reflection area and penetrating counter-air (PCA) capability of the high-speed tailless aircraft will bring about a further leap in combat effectiveness, and will play an important role in the battlefield environment of "anti-access / area denial". However, for the deformation stage of the vertical tail, there is a unique problem that the morphing aircraft needs to deal with, that is, the problem of reducing the hinge torque of the aerodynamic load attached to the root of the vertical tail. Since the hinge torque at the root of the vertical tail will increase with the increase of flight speed, how to meet the hinge torque requirements under the condition of limited capacity of the variable vertical tail drive motor is a prerequisite for realizing the flight of the variable vertical tail and ensuring flight safety. In order to prevent the failure of the tailless / vertical tail conversion caused by excessive hinge torque, the hinge torque characteristics of the variable vertical tail structure in high-speed flight are analyzed, and the idea of extreme value optimization control is borrowed to propose an adaptive morphing tail hinge moment reduction method (adaptive morphing tail hinge moment reduction, AMTHR).
[0003] The present invention proposes a method for reducing the hinge torque of the tail of a high-speed variable tail aircraft. This method draws on the idea of extreme value optimization control to control the hinge torque at the root of the tail wing to always remain at the minimum when the deformation coefficient changes continuously between 0 and 1. First, the hinge torque characteristics of the variable tail structure in high-speed flight are analyzed to obtain the parameters that have a greater impact on the hinge torque. Then, based on the idea of extreme value optimization control, the deformation coefficient is used as the scheduling parameter, the rudder deflection angle is used as the independent variable, and the control target is the hinge torque amplitude at the root of the tail wing, so that it always remains at the minimum when the deformation coefficient changes continuously between 0 and 1. Finally, the AMTHR method (adaptive morphing tail hinge moment reduction, AMTHR) is formed. Summary of the invention
[0004] In order to prevent the failure of tailless / vertical tail conversion caused by excessive hinge torque and improve the safety and reliability of high-speed aircraft structure deformation, the present invention provides a method for reducing the hinge torque of the vertical tail of a high-speed variable vertical tail aircraft. This method draws on the idea of extreme value optimization control to control the hinge torque at the root of the vertical tail to always keep it at the minimum when the deformation coefficient changes continuously. First, the hinge torque characteristics of the variable vertical tail structure in high-speed flight are analyzed to obtain the parameters that have a greater impact on the hinge torque. Then, based on the idea of extreme value optimization control, the deformation coefficient is used as the scheduling parameter, the rudder deflection angle is used as the independent variable, and the control target is the hinge torque amplitude at the root of the vertical tail, so that it always keeps the minimum when the deformation coefficient changes continuously between 0 and 1, and finally constitutes the AMTHR method. The vertical tail hinge torque is reduced in the absence of wind and in the presence of gust disturbances.
[0005] The technical solution of the present invention:
[0006] The method for reducing the torque of the tail hinge of a high-speed variable tail aircraft includes the following parts:
[0007] Step S1, establishing a tail allosteric model;
[0008] Step S2, analyzing the torque characteristics of the vertical tail hinge;
[0009] Step S3, building an extreme value optimization control framework;
[0010] Step S4: Establish an AMTHR scheme to complete adaptive load shedding.
[0011] Furthermore, in step S1, establishing a vertical tail allosteric model comprises the following steps:
[0012] The left and right vertical tails of the aircraft are symmetrically deformed. The rudder is hinged on the vertical tail and moves with the vertical tail. The variable vertical tail structure is simplified to a combination of a rod system and a hinged structure. There are two rotational degrees of freedom. The vertical tail and the rudder are simplified to a rod system. The support seat and the vertical tail, and the vertical tail and the rudder are all hinged. Set the vertical tail rotation angle value to δ vt , and its deflection range is [δ vt，min ,δ vt，max ], δ vt The range is 0~65°; the vertical tail deformation coefficient is defined as ξ vt , whose expression is:
[0013]
[0014] Furthermore, in step S2, the torque characteristics of the vertical tail hinge are analyzed, and then a hinge torque calculation formula is established; based on this, step S2 includes the following steps:
[0015] During the process of changing the vertical tail, the connecting shaft between the vertical tail and the fuselage support seat generates a hinge torque to overcome the aerodynamic load, which directly affects the success of the vertical tail change. By calculating the rudder trimming angle of the hinge torque under different angles of attack and vertical tail deformation coefficients, it is found that the increase of the vertical tail deformation coefficient will increase the rudder deflection of the trimming rudder. This shows that within the allowable range, the rudder and the vertical tail can be used to follow the movement to offset the hinge torque generated by the aerodynamic load at the root of the vertical tail, thereby reducing the demand for the vertical tail drive motor.
[0016] According to the trim analysis results, the calculation formula of the single-side vertical tail hinge moment is summarized as follows:
[0017] H dvt =QS vt c vt C hvt (α,δ r ,ξ vt ) (2)
[0018] Among them, S vt and c vt are the reference area and reference length of the vertical tail, C hvt (α,δ r ,ξ vt ) is the hinge moment coefficient, and is affected by the angle of attack α and the rudder deflection angle δ r and the tail deformation coefficient ξ vt The comprehensive influence of, Q is the dynamic pressure.
[0019] Furthermore, in step S3, an extreme value optimization control framework is constructed; by adding periodic perturbations to the system, the control input is adjusted according to the influence of the perturbations on the system output, so that the output tends to an extreme value point; based on this, step S3 includes the following specific steps:
[0020] Step S3.1 Stimulus input design
[0021] By injecting a periodic sinusoidal signal into the input u of the physical system, the input expression of the system with sinusoidal perturbation is obtained as follows:
[0022]
[0023] Where w is the sinusoidal perturbation frequency, a is the perturbation amplitude, and t is the time. is the benchmark control quantity;
[0024] Step S3.2 Estimate the optimal control quantity u *
[0025] Under the sinusoidal input shown in formula (3), the cost function J composed of the output y also shows a sinusoidal change trend at the mean; the low-frequency part of the signal J is filtered out by a high-pass filter to obtain the oscillation signal ρ, as shown in formula (4):
[0026]
[0027] Among them, ω h is the filtering frequency of the high-pass filter, s is the Laplace operator;
[0028] The signal asin(wt-φ is obtained by phase shifting the oscillation signal ρ and the input signal s ) to obtain the demodulated signal ξ:
[0029] ξ=[asin(wt-φ s )]ρ (5)
[0030] where φ s is the phase;
[0031] By integrating ξ, we can get the optimal control quantity u * Estimated value:
[0032]
[0033] Among them, k is the integral gain, which represents the learning rate. The larger k is, the more the gradient value of J is affected. The more dramatic the impact of the change;
[0034] Step S3.3 Objective function design
[0035] Assuming the physical system is a unit constant of 1, and the objective function J is a simple function of u, J can be expressed as:
[0036]
[0037] For formula (7), Perform a first-order Taylor series expansion at , and we get:
[0038]
[0039] Combined with formula (8), the approximate calculation result of signal ρ can be obtained as:
[0040]
[0041] Combining equations (5) and (9), we can calculate the mean value of ξ in one period as follows:
[0042]
[0043] It can be seen that avgProportional to the derivative of the objective function J with respect to u.
[0044] Furthermore, in step S4, establishing an AMTHR scheme to complete adaptive load shedding includes the following steps:
[0045] Step S4.1 constructs the cost function: The adaptive variable vertical tail hinge moment load reduction cost function is:
[0046] J(δ r )=-H dvt (α,ξ vt ,δ r )| (11)
[0047] By finding the maximum value of the cost function shown in equation (11), we can obtain the rudder deflection corresponding to the minimum moment of the variable tail hinge.
[0048] Step S4.2 Input signal modulation: inject a sinusoidal perturbation with a perturbation amplitude a and a sinusoidal perturbation frequency w into the control input signal, thereby modulating the rudder deflection angle δ r Modulation
[0049] Step S4.3 Input signal demodulation: Use a cutoff frequency of ω h The high-pass filter calculates the gradient of the calculated cost function J and then compares it with the phase-shifted signal asin(wt-φ s ) are multiplied to perform demodulation;
[0050] Step S4.4 solves the optimal rudder angle: Integrate the demodulated signal and multiply it by the learning rate k to obtain the estimated value of the optimal rudder angle after parameter update
[0051] Compared with the prior art, the present invention has the following beneficial effects:
[0052] The present invention explores the influence of the vertical tail rudder on the hinge torque at the root of the vertical tail, and achieves the purpose of reducing the hinge torque at the root of the vertical tail by rudder deflection. Based on the idea of extreme value optimization control, the deformation coefficient is used as the scheduling parameter and the rudder deflection angle is used as the independent variable. The rudder deflection is adaptively adjusted under different flight environments, so that the hinge torque amplitude at the root of the vertical tail is always kept at the minimum when the deformation coefficient changes continuously between 0 and 1. In addition, the invention also has good robustness under gust disturbances. BRIEF DESCRIPTION OF THE DRAWINGS
[0053] Figure 1 It is a schematic diagram of a variable tail aircraft;
[0054] Figure 2 It is a simplified schematic diagram of the deformation of the vertical tail structure;
[0055] Figure 3 It is the diagram of the change of hinge torque during the tail-changing process;
[0056] Figure 4 It is the extreme value optimization control block diagram;
[0057] Figure 5 It is the principle diagram of extreme value search;
[0058] Figure 6 It is the block diagram of the AMTHR scheme;
[0059] Figure 7 The simulation results of the adaptive tail-changing process in no wind, (a) is the deformation coefficient, (b) is the objective function, (c) is the hinge torque of the tail-changing process, and (d) is the rudder deflection angle;
[0060] Figure 8 These are the simulation results of the adaptive tail-adaptive variable vertical tail process under gusts, (a) is the deformation coefficient, (b) is the objective function, (c) is the variable vertical tail hinge torque, (d) is the rudder deflection angle, (e) is the angle of attack response, and (f) is the speed response. DETAILED DESCRIPTION
[0061] The present invention will be further described below in conjunction with the embodiments.
[0062] The present invention is aimed at a high-speed variable vertical tail aircraft system, and proposes a method for reducing the hinge torque of the vertical tail of a high-speed variable vertical tail aircraft. This method draws on the idea of extreme value optimization control to control the hinge torque at the root of the vertical tail to always remain at the minimum when the deformation coefficient changes continuously. First, the hinge torque characteristics of the variable vertical tail structure in high-speed flight are analyzed to obtain the parameters that have a greater impact on the hinge torque. Then, based on the idea of extreme value optimization control, the deformation coefficient is used as the scheduling parameter, the rudder deflection angle is used as the independent variable, and the control target is the hinge torque amplitude at the root of the vertical tail, so that it always remains at the minimum when the deformation coefficient changes continuously between 0 and 1, and finally constitutes the AMTHR method. The vertical tail hinge torque reduction is achieved in the absence of wind and in the presence of gust disturbances.
[0063] Example 1
[0064] Step S1, establish the vertical tail allosteric model:
[0065] Establish Figure 1 The high-speed variable tail vertical aircraft model shown. When the tail is fully lowered, the aircraft is in a tailless stealth configuration; when the tail is fully erected, it is in a tailed maneuvering configuration.
[0066] like Figure 1As shown in the figure, the left and right vertical tails are symmetrically deformed, and the rudder is hinged on the vertical tail and moves with the vertical tail. The variable vertical tail structure can be simplified as a combination of a rod system and a hinged structure, with two rotational degrees of freedom. The vertical tail and the rudder are simplified as a rod system, and the support seat and the vertical tail, as well as the vertical tail and the rudder are all hinged, as shown in the figure. Figure 2 shown. Figure 2 In the example, the rudder surface deflection angle is δ r The values of the torque provided by the rotation axis c and the rotation axis b to overcome the pneumatic hinge torque are τ vt and τ r The deformation coefficient of the vertical tail is ξ vt , defined as follows:
[0067]
[0068] where δ vt The range is 0~65°. From formula (12), we can get the deformation coefficient ξ vt ∈[0,1].
[0069] Step S2, analysis of the torque characteristics of the tail hinge:
[0070] The deformation process of the vertical tail studied in this paper is a continuous and slow process, so the influence of the deformation rate of the vertical tail on aerodynamics is not considered. During the process of changing the vertical tail, the connecting axis between the vertical tail and the fuselage support seat generates a hinge torque to overcome the aerodynamic load. This hinge torque directly affects the success of the vertical tail change, so it is necessary to analyze the hinge torque at the vertical tail rotation axis. The calculation formula of the hinge torque of the single-sided vertical tail is as follows:
[0071] H dvt =QS vt c vt C hvt (α,δ r ,ξ vt ) (13)
[0072] Among them, S vt and c vt are the reference area and reference length of the vertical tail, C hvt (α,δ r ,ξ vt ) is the hinge moment coefficient, and is affected by the angle of attack α and the rudder deflection angle δ r and the tail deformation coefficient ξ vt The combined effect of
[0073] Figure 3The calculation results of the hinge moment at the root of the left vertical tail during the continuous deformation process at 0.8Ma and 10000m are given. From the figure, it can be concluded that the rudder follow-up deflection can effectively reduce the hinge moment in the process of changing the vertical tail. However, there is an uncertainty problem in the way of interpolating the rudder deformation coefficient and the angle of attack. Therefore, in order to reduce the hinge moment load at the root of the vertical tail, achieve the effect of "loose floating" of the vertical tail during the entire process of changing the vertical tail, and finally achieve the goal of adaptively changing the vertical tail, a control strategy that does not rely on the model and meets the requirements of real-time calculation is needed.
[0074] Step S3, build an extreme value optimization control framework:
[0075] Step S3.1 Stimulus input design
[0076] according to Figure 5 , injecting a periodic sinusoidal signal into the input u of the physical system, the resulting system input expression with sinusoidal perturbation is:
[0077]
[0078] Where w is the sinusoidal perturbation frequency, a is the perturbation amplitude, and t is the time. is the benchmark control quantity.
[0079] Step S3.2 Estimate the optimal control quantity u *
[0080] from Figure 6 It can be seen that under the sinusoidal input shown in formula (14), the cost function J composed of the output y also shows a sinusoidal change trend at the mean. The low-frequency part of the signal J is filtered out by a high-pass filter to obtain the oscillation signal ρ, as shown in formula (15):
[0081]
[0082] Among them, ω h is the high-pass filter filtering frequency, and s is the Laplace operator.
[0083] The signal a sin(wt-φ is obtained by phase shifting the oscillation signal ρ and the input signal s ) to obtain the demodulated signal ξ:
[0084] ξ=[a sin(wt-φ s )]ρ (16)
[0085] where φ s is the phase;
[0086] By integrating ξ, we can get the optimal control quantity u * Estimated value:
[0087]
[0088] Among them, k is the integral gain, which represents the learning rate. The larger k is, the more the gradient value of J is affected. The more dramatic the impact of the change.
[0089] Step S3.3 Objective function design
[0090] Assuming that the physical system is a unit constant of 1 and the objective function J is a simple function of u, J can be expressed as:
[0091]
[0092] For formula (18), Perform a first-order Taylor series expansion at , and we get:
[0093]
[0094] Combined with formula (19), the approximate calculation result of signal ρ can be obtained as:
[0095]
[0096] Combining equations (16) and (20), we can calculate the mean value of ξ in one period as:
[0097]
[0098] It can be seen that avg Proportional to the derivative of the objective function J with respect to u.
[0099] Step S4, establish the AMTHR scheme to complete adaptive load shedding:
[0100] Step S4.1 constructs a cost function: The adaptive variable tail hinge moment load reduction cost function is:
[0101] J(δ r )=-|H dvt (α,ξ vt ,δ r )| (22)
[0102] By finding the maximum value of the cost function shown in equation (22), we can obtain the rudder deflection corresponding to the minimum moment of the variable tail hinge.
[0103] Step S4.2 Input signal modulation: inject a sinusoidal perturbation with a perturbation amplitude a and a sinusoidal perturbation frequency w into the control input signal, thereby modulating the rudder deflection angle δ r Modulate.
[0104] Step S4.3 Input signal demodulation: Use a cutoff frequency of ωh The high-pass filter calculates the gradient of the calculated cost function J and then compares it with the phase-shifted signal asin(wt-φ s ) for demodulation.
[0105] Step S4.4 solves the optimal rudder angle: Integrate the demodulated signal and multiply it by the learning rate k to obtain the estimated value of the optimal rudder angle after parameter update Figure 6 The AMTHR algorithm framework is presented.
[0106] Firstly, the adaptive variable tail hinge moment load reduction method is applied to Figure 3 Under the same simulation conditions, Figure 3 The simulation results are shown in Figure 2. Figure 7 The simulation results of adaptive tail change are given. Figure 7 (a) and Figure 7 It can be seen from (c) that during the entire tail-changing process, the hinge moment H dvt Most of them are between -15 and 15Nm. Figure 4 Simulation results without introducing rudder deflection, H dvt Reduced by 95%. Figure 7 In (c), it can be found that when the deformation coefficient of the variable tail vehicle ξ vt When it starts to change from 0 or changes to 0, H dvt A spike appears, but the initial transient impact quickly converges within 1 s, proving the adaptive ability of the method. Figure 7 (d) compares the rudder interpolation result δ obtained by the model trim relationship r and the rudder command value δ output by AMTHR r-vt It can be seen that the adaptive variable tail hinge moment load reduction method has a good estimation result for the optimal rudder deflection angle, δ r and δ r-vt The two are almost consistent in trend and value, reflecting the effectiveness of the adaptive variable tail hinge moment load reduction method.
[0107] exist Figure 6 The model of vertical gusts is introduced into the adaptive variable tail simulation model shown in the figure. The vertical gusts can be expressed as:
[0108]
[0109] In formula (23), χ represents the integral of velocity over time; d z is the wind farm length; w m is the gust amplitude. At an altitude of 10,000 m, medium turbulence (10 -3 ) case, select d z and wm 424m and 4m / s respectively. Figure 8 The deformation coefficient ξ is given at 20s. vt = 1, when the aircraft is in a tail configuration, the simulation results of adding a half-wave gust are shown. Figure 8 (e) and Figure 8 As can be seen from (f) in the figure, the 4m / s gust brings about a 1° angle of attack increase. To overcome the impact of gust disturbances, Figure 8 (d) in Figure 2 shows that the absolute value of the rudder command under AMTHR control increases by 1° and converges within 2 seconds. In addition, under gust disturbances, AMTHR achieves a good estimate of the optimal rudder trim value. Figure 8 As shown in (c) in the figure, under gust disturbance, the hinge torque does not undergo a large mutation, and the steady-state response always remains within the range of ±15Nm.
[0110] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.
Claims
1. A method for reducing the load on the hinge moment of a high-speed variable tail aircraft, characterized in that: Includes the following sections: Step S1, establishing a tail allosteric model; Step S2, analyzing the torque characteristics of the vertical tail hinge; Step S3, building an extreme value optimization control framework; Step S4: Establish an AMTHR scheme to complete adaptive load shedding.
2. The method for reducing the load on the vertical tail hinge moment of a high-speed variable vertical tail aircraft according to claim 1, characterized in that: In step S1, establishing a vertical tail allosteric model comprises the following steps: The left and right vertical tails of the aircraft are symmetrically deformed. The rudder is hinged on the vertical tail and moves with the vertical tail. The variable vertical tail structure is simplified to a combination of a rod system and a hinged structure. There are two rotational degrees of freedom. The vertical tail and the rudder are simplified to a rod system. The support seat and the vertical tail, and the vertical tail and the rudder are all hinged. Set the vertical tail rotation angle value to δ vt , and its deflection range is [δ vt，min ,δ vt，max ], δ vt The range is 0~65°; the vertical tail deformation coefficient is defined as ξ vt , whose expression is:
3. The method for reducing the load on the vertical tail hinge moment of a high-speed variable vertical tail aircraft according to claim 1, characterized in that: In the step S2, the torque characteristics of the vertical tail hinge are analyzed, and then a hinge torque calculation formula is established; based on this, the step S2 includes the following steps: During the process of changing the vertical tail, the connecting shaft between the vertical tail and the fuselage support seat generates a hinge torque to overcome the aerodynamic load, which directly affects the success of the vertical tail change. By calculating the rudder trimming angle of the hinge torque under different angles of attack and vertical tail deformation coefficients, it is found that the increase of the vertical tail deformation coefficient will increase the rudder deflection of the trimming rudder. This shows that within the allowable range, the rudder and the vertical tail can be used to follow the movement to offset the hinge torque generated by the aerodynamic load at the root of the vertical tail, thereby reducing the demand for the vertical tail drive motor. According to the trim analysis results, the calculation formula of the single-side vertical tail hinge moment is summarized as follows: H dvt =QS vt c vt C hvt (α,δ r ,ξ vt ) (2) Among them, S vt and c vt are the reference area and reference length of the vertical tail, C hvt (α,δ r ,ξ vt ) is the hinge moment coefficient, and is affected by the angle of attack α and the rudder deflection angle δ r and the tail deformation coefficient ξ vt The comprehensive influence of, Q is the dynamic pressure.
4. The method for reducing load on the vertical tail hinge moment of a high-speed variable vertical tail aircraft according to claim 1, characterized in that: In step S3, an extreme value optimization control framework is constructed; by adding periodic perturbations to the system, the control input is adjusted according to the influence of the perturbations on the system output, so that the output tends to an extreme value point; based on this, step S3 includes the following specific steps: Step S3.1 Stimulus input design By injecting a periodic sinusoidal signal into the input u of the physical system, the input expression of the system with sinusoidal perturbation is obtained as follows: Where w is the sinusoidal perturbation frequency, a is the perturbation amplitude, and t is the time. is the benchmark control quantity; Step S3.2 Estimate the optimal control quantity u * Under the sinusoidal input shown in formula (3), the cost function J composed of the output y also shows a sinusoidal change trend at the mean; the low-frequency part of the signal J is filtered out by a high-pass filter to obtain the oscillation signal ρ, as shown in formula (4): Among them, ω h is the filtering frequency of the high-pass filter, s is the Laplace operator; The signal asin(wt-φ is obtained by phase shifting the oscillation signal ρ and the input signal s ) to obtain the demodulated signal ξ: ξ=[asin(wt-φ s )]p (5) where φ s is the phase; By integrating ξ, we can get the optimal control quantity u * Estimated value: Among them, k is the integral gain, which represents the learning rate. The larger k is, the more the gradient value of J is affected. The more dramatic the impact of the change; Step S3.3 Objective function design Assuming the physical system is a unit constant of 1, and the objective function J is a simple function of u, J can be expressed as: For formula (7), Perform a first-order Taylor series expansion at , and we get: Combined with formula (8), the approximate calculation result of signal ρ can be obtained as: Combining equations (5) and (9), we can calculate the mean value of ξ in one period as follows: It can be seen that avg Proportional to the derivative of the objective function J with respect to u.
5. The method for reducing load on the vertical tail hinge moment of a high-speed variable vertical tail aircraft according to claim 1, characterized in that: In step S4, an AMTHR scheme is established to complete adaptive load shedding, including the following steps: Step S4.1 constructs the cost function: The adaptive variable vertical tail hinge moment load reduction cost function is: J(d r )=-H dvt (a,x) vt ,d r )| (11) By finding the maximum value of the cost function shown in equation (11), we can obtain the rudder deflection corresponding to the minimum moment of the variable tail hinge. Step S4.2 Input signal modulation: inject a sinusoidal perturbation with a perturbation amplitude a and a sinusoidal perturbation frequency w into the control input signal, thereby modulating the rudder deflection angle δ r Modulation is performed; Step S4.3 Input signal demodulation: Use a cutoff frequency of ω h The high-pass filter calculates the gradient of the calculated cost function J and then compares it with the phase-shifted signal asin(wt-φ s ) are multiplied to perform demodulation; Step S4.4 solves the optimal rudder angle: Integrate the demodulated signal and multiply it by the learning rate k to obtain the estimated value of the optimal rudder angle after parameter update