Helicopter adaptive command filtering backstepping tracking control law design method

Abstract

The invention belongs to the field of aircraft control, and particularly relates to a helicopter adaptive command filtering backstepping tracking control law design method, which comprises the following steps: firstly, decomposing a helicopter kinetic model into a plurality of strict feedback systems with uncertainty, and then designing a controller by using a backstepping method; a hybrid command filter is adopted to solve the problem of calculation explosion of backstepping, and a filtering compensation mechanism is introduced. In addition, an uncertain part in the model is approximated by adopting a neural network, and network parameters are updated online by adopting an adaptive law. And finally, designing a Lyapunov function to prove the effectiveness of the method.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft control, and in particular relates to a method for designing a helicopter adaptive command filtering backstepping tracking control law. Background Art

[0002] Helicopters have many advantages such as vertical take-off and landing, hovering and ultra-low-altitude flight capabilities, but due to their complex aerodynamic characteristics, severe model coupling, high nonlinearity and other properties, designing a high-performance and robust flight controller is a very challenging task. In order to reduce the difficulty of controller design caused by the complex model of helicopters, in recent years, more and more scholars have introduced Backstepping into the helicopter flight control design process. Backstepping, also known as the inversion method or the backstepping method, was proposed by Krstic, Kokotovic and others. Backstepping has attracted widespread attention for its easy handling of nonlinear control problems, especially when the system does not meet the matching conditions. Backstepping is a recursive method based on Lyapunov proposed for a class of strict feedback systems. When the controlled system can be transformed into a class of strict feedback system forms, this method can ensure the global or local convergence of the system.

[0003] However, a major drawback of backstepping is that repeated derivation of virtual control items will produce a "computational explosion" problem. In order to overcome this problem, Swaroop D proposed the Dynamic Surface Control (DSC) technology, but the dynamic surface control technology did not take into account the impact of filtering errors. In view of this, Jay A. Farrell proposed a command filtering technology based on a second-order system for a class of strict feedback systems. While eliminating computational explosion, it also avoids the filtering error caused by the filter. However, the filter proposed by Jay A. Farrell is limited by frequency and damping parameters, and not only has a slow convergence speed, but also cannot achieve finite time convergence. At the same time, this command filtering method is not suitable for multi-input and multi-output systems such as helicopters. Summary of the invention

[0004] The purpose of the present invention is: the present invention decomposes a helicopter model into multiple strict feedback subsystems, adopts the backstepping method to design a controller for each subsystem, combines a hybrid differential tracker formed by a second-order tracking-differentiator and a nonlinear tracking-differentiator to solve the computational explosion problem in the backstepping method, and designs an adaptive neural network for approximation of the uncertain parts in the model, thereby solving the helicopter tracking flight control problem with uncertainty.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A method for designing a helicopter adaptive command filtering backstepping tracking control law, the method comprising the following steps:

[0007] Step 1: Build a helicopter model;

[0008] Step 2: Design the control law using the backstepping method.

[0009] Furthermore, in the step 1, the helicopter model includes: a dynamic model under the fuselage and a main rotor flapping dynamic model;

[0010] The dynamic model of the body is expressed as follows:

[0011]

[0012] in, represents the ground coordinate system, is the body coordinate system, a s , b s Swing horizontally and vertically respectively, P = [x, y, z] T represents the position vector, F f represents the resultant moment, m represents the mass of the body, H represents the attitude matrix, V = [v x ,v y ,v z ] T represents the velocity vector, g represents the acceleration due to gravity, e3 = [0,0,1] T , Θ=[φ,θ,ψ] T is the attitude vector (φ is the roll angle, θ is the pitch angle, ψ is the yaw angle), I = diag (I x ,I y ,I z ) Moment of inertia matrix, ω=[p,q,r] T Indicates in b is the angular acceleration in the coordinate system, and τ is the torque.

[0013] R is the rotation matrix, which represents the rotation from Ξ b To e Conversion:

[0014]

[0015] The posture matrix H is:

[0016]

[0017] Among them, S = sin(·), C = cos(·), T = tan(·);

[0018] The resultant moment is:

[0019]

[0020] Torque τ = τ γ +Δ τ =τ A γ+τ B +Δ τ , and there is

[0021]

[0022]

[0023]

[0024] Where: T m represents the thrust generated by the main rotor, T t Represents the reactive torque, L b and M a are the longitudinal and transverse coefficients respectively. m , l m are the horizontal and vertical positions of the main rotor relative to the center of gravity, h t , l t are the horizontal and vertical positions of the tail rotor relative to the center of gravity, respectively.

[0025] The main rotor flapping dynamics equation is:

[0026]

[0027] Among them, τ e is the swinging time constant, A lon and A lat Longitudinal periodic pitch and lateral periodic pitch gain.

[0028] Furthermore, in step 2, the control law includes: a position control law, a speed control law, a posture control law and an angular velocity control law.

[0029] Furthermore, in step 2, the position control law design process is as follows:

[0030] Step 2A: Design the Lyapunov function of the position loop, the formula is as follows:

[0031]

[0032] where v p =e p -ξ p is the error compensation information, e p Defined as e p =PP d ;

[0033] Step 2B: Design the command filter of the position loop in the following form:

[0034]

[0035] Where R 11 , R 12 , R 21 , R 22 , β represents the design parameters, i i，1 , and is the intermediate variable, a i Represents a virtual input signal.

[0036] Step 2C: Derive the virtual control law of the position loop based on the derivative of the Lyapunov function of the position loop; Derive the derivative of the Lyapunov function The formula is as follows:

[0037]

[0038] where v v =e v -ξ v ,e v =Va p，c ,a p，c is the output of the mixed command filter;

[0039] Position loop virtual control law a p Designed for:

[0040]

[0041] in

[0042] Step 2D: Design the position loop filter error compensation equation; compensation signal ξ p It is expressed as follows:

[0043]

[0044] Substituting the position loop filter error compensation equation into the position loop Lyapunov derivative term, we can get:

[0045]

[0046] Further, in step 2, the speed control law design process is as follows:

[0047] Step 2E: Design the Lyapunov function of the velocity loop. The formula is as follows:

[0048]

[0049] Step 2F: Design the command filter of the speed loop to be the same as the command filter of the position loop;

[0050] Step 2G: Derive the virtual control law of the speed loop according to the derivative of the Lyapunov function of the speed loop;

[0051] The derivative of the Lyapunov function of the velocity loop is derived as follows:

[0052]

[0053] in

[0054] d f For unknown interference, the neural network is used to approximate the formula as follows:

[0055]

[0056] in represents the approximation error, and

[0057] According to Young's inequality, the multiplication of two terms can be written as follows:

[0058]

[0059] The virtual control law of the speed loop is designed as:

[0060]

[0061] in Represents W p An estimated value of

[0062] Step 2H: Design the speed loop filter error compensation equation ξ v , of the following form:

[0063]

[0064] Substituting the velocity loop filter error compensation equation into the velocity loop Lyapunov derivative term, we can get:

[0065]

[0066] in

[0067] Step 2I: Design the adaptive law of the estimation term in the virtual control law of the speed loop;

[0068] Choose the velocity loop Lyapunov function taking into account the estimation error:

[0069]

[0070] Where Q p satisfy

[0071] It can be written as

[0072]

[0073] The adaptive law of the estimation term in the virtual control law of the speed loop is designed as:

[0074]

[0075] Where m p >0;

[0076] Therefore, the derivative of the velocity loop Lyapunov function considering the estimation error is expressed as:

[0077]

[0078] make Then the virtual control law of the speed loop is transformed into:

[0079]

[0080] where φ d and θ d represents the expected values ​​of φ and θ.

[0081] Furthermore, in step 2, the attitude control law design process is as follows:

[0082] Step 2J: Design the Lyapunov function of the attitude loop;

[0083] Define the posture tracking error e Θ =Θ-Θ d , where Θ d =[φ d ,θ d , ψ d ] T ; Therefore, the compensated posture tracking error v Θ Defined as

[0084] v Θ =e Θ -ξ Θ

[0085] Among them, ξ Θ To compensate the attitude error;

[0086] The Lyapunov function of the attitude loop is expressed as follows:

[0087]

[0088] Step 2K: Design the command filter of the attitude loop to be the same as the command filter of the position loop;

[0089] Step 2: Derive the virtual control law of the attitude loop according to the derivative of the Lyapunov function of the attitude loop;

[0090] The derivative of the Lyapunov function of the attitude loop is expressed as follows:

[0091]

[0092] Then, the attitude loop virtual control law a ω It is expressed as:

[0093]

[0094] in,

[0095] Step 2M: Design the attitude loop filter error compensation equation in the following form:

[0096]

[0097] where a ω，c is the virtual signal a ω The filter value of

[0098] Substituting the attitude loop filter error compensation equation into the attitude loop Lyapunov derivative term, we can get

[0099]

[0100] where v w =e ω -ξ ω =ω-a ω，c -ξ ω .

[0101] Furthermore, in step 2, the angular velocity control law design process is as follows:

[0102] Step 2: Design the Lyapunov function of the angular velocity loop in the following form:

[0103]

[0104] Step 20: Design the command filter of the angular velocity loop to be the same as the command filter of the position loop;

[0105] Step 2P: Derive the virtual control law of the angular velocity loop according to the derivative of the Lyapunov function of the angular velocity loop;

[0106] The derivative form of the Lyapunov function of the angular velocity loop is as follows:

[0107]

[0108] The unknown dynamic behavior Further described as:

[0109] According to Young's inequality,

[0110]

[0111] The virtual control law of the angular velocity loop is designed as:

[0112]

[0113] in W Θ An estimated value of

[0114] Step 2Q: Design the angular velocity loop filter error compensation equation in the following form:

[0115]

[0116] Substituting the angular velocity loop filter error compensation equation into the angular velocity loop Lyapunov derivative, we can get:

[0117]

[0118] Step 2 R: Design the adaptive law of the estimation term in the virtual control law of the angular velocity loop;

[0119] Choose the Lyapunov function of the angular velocity loop taking into account the estimation error:

[0120]

[0121] Where Q Θ Positive and satisfying

[0122] The derivative of the Lyapunov function of the angular velocity loop considering the estimation error is expressed as follows:

[0123]

[0124] The adaptive law of the estimation term in the virtual control law of the angular velocity loop is designed as:

[0125]

[0126] Among them, m Θ >0;

[0127] Therefore, the derivative of the angular velocity loop Lyapunov function considering the estimation error is expressed as:

[0128]

[0129] make Then the virtual control law of the angular velocity loop is transformed into:

[0130]

[0131] According to the main rotor flapping dynamics model, the flapping dynamics behavior is described as:

[0132]

[0133] Therefore, the longitudinal and transverse periodic pitch variation is obtained:

[0134]

[0135] Among them: a sd and b sd They are respectively s and b s The given value of .

[0136] Furthermore, the method further includes: step three, analyzing the stability of the closed-loop system, the closed-loop system including: a position loop, a velocity loop, a posture loop and an angular velocity loop; the process is as follows:

[0137] Design the total Lyapunov function V;

[0138] V=V P +V Θ

[0139] Derivative the total Lyapunov function V;

[0140]

[0141] in

[0142] Determine the supremum of the total Lyapunov function V changing with time; thereby analyzing the boundedness of all signals in the closed-loop system. If all signals are bounded, the closed-loop system is stable, otherwise it is unstable.

[0143] The above inequality shows that:

[0144]

[0145] For t≥t0, it is satisfied. Therefore, the variable v p ,v v ,v Θ ,v ω , and All included in the compact set Due to e i(i=p,v,Θ,ω) satisfies e i =v i +ξ i And i is bounded, so e i is bounded, and μρ represents the upper bound of the filtering error. Therefore, it is proved that all signals in the closed-loop system are bounded, and the bounded range can be adjusted by adjusting the size of the parameter k.

[0146] Beneficial effects:

[0147] The present invention combines adaptation, neural network, hybrid differential tracker, and filter error compensation mechanism to solve the helicopter tracking control problem with uncertainty interference. Among them, the hybrid differential tracker solves the calculation explosion problem in the backstepping method, the adaptive neural network solves the model uncertainty problem, and the filter error improves the tracking control accuracy. The entire controller makes the helicopter flight control more robust and accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0148] Figure 1 This is the structure diagram of the RBF neural network. DETAILED DESCRIPTION

[0149] Aiming at the problem of helicopter position tracking flight control, the present invention combines hybrid differential tracker, adaptation, filtering error compensation and neural network technology to propose a helicopter adaptive command filtering backstepping tracking control method. First, the helicopter dynamics model is decomposed into multiple strict feedback systems with uncertainty, and then the controller is designed using the backstepping method. A hybrid command filter is used to solve the computational explosion problem of backstepping, and a filtering compensation mechanism is introduced. In addition, the uncertain parts in the model are approximated by a neural network, and the network parameters are updated online using an adaptive law. Finally, a Lyapunov function is designed to prove the effectiveness of the method. The specific method includes the following steps:

[0150] Step 1: Build a helicopter model;

[0151] The dynamic model of the body is expressed as follows:

[0152]

[0153] in, represents the ground coordinate system, is the body coordinate system, a s , b s Swing horizontally and vertically respectively, P = [x, y, z] T represents the position vector, F f represents the resultant moment, m represents the mass of the body, H represents the attitude matrix, V = [v x,v y ,v z ] T represents the velocity vector, g represents the acceleration due to gravity, e3 = [0,0,1] T , Θ=[φ,θ,ψ] T is the attitude vector (φ is the roll angle, θ is the pitch angle, ψ is the yaw angle), I = diag (I x ,I y ,I z ) Moment of inertia matrix, ω=[p,q,r] T Indicates in b Angular acceleration in the coordinate system; τ is the torque.

[0154] R is the rotation matrix, which represents the rotation from Ξ b To e Conversion:

[0155]

[0156] The posture matrix H is:

[0157]

[0158] Among them, S = sin(·), C = cos(·), T = tan(·);

[0159] The resultant moment is:

[0160]

[0161] Torque τ = τ γ +Δ τ =τ A Υ+τ B +Δ τ , and there is

[0162]

[0163]

[0164]

[0165] Where: T m represents the thrust generated by the main rotor, T t Represents the reactive torque, L b and M a are the longitudinal and transverse coefficients respectively. m , l m are the horizontal and vertical positions of the main rotor relative to the center of gravity, h t , l t are the horizontal and vertical positions of the tail rotor relative to the center of gravity, respectively.

[0166] The main rotor flapping dynamics equation is:

[0167]

[0168] Among them, τ e is the swinging time constant, A lon and A lat Longitudinal periodic pitch and lateral periodic pitch gain.

[0169] Step 2: Describe the unknown quantities in the helicopter model;

[0170] Due to a s ,b s and T t The value of is very small, the moment F f It can be written as F f =T m e3+Δ f , where Δ f satisfy

[0171]

[0172] Therefore, the position and velocity subsystems are described as

[0173]

[0174]

[0175] in Indicates the unknown part.

[0176] The attitude and angular velocity subsystem is described as

[0177]

[0178]

[0179] Where Δ τ Indicates unknown part.

[0180] Neural networks can be used to approximate the unknown parts of the model. The specific principles are as follows:

[0181] if is a definition on a compact set If it is a continuous function on , then there exists an RBF NNφ T P(z) makes

[0182]

[0183] Among them, ε>0, the ideal weight vector φ satisfies

[0184]

[0185] Among them, δ(z) represents the approximation error, represents the weight vector, m>1 is the number of nodes, is the basis function vector

[0186]

[0187] Among them, c i =[c i1 , …, c in ] T and q i Represent the center and width of the Gaussian function respectively.

[0188] Step 3: Design the controller using backstepping method.

[0189] Step 1. Design the Lyapunov function of the position loop. The formula is as follows:

[0190]

[0191] where v p =e p -ξ p is the error compensation information, e p Defined as e p =PP d . Compensation signal ξ p It will be given in the formula below.

[0192] Derived as

[0193]

[0194] where v v =e v -ξ v ,e v =Va p，c ,a p，c is the output of the hybrid command filter. The command filter design of the position loop is as follows:

[0195]

[0196] Where R 11 , R 12 , R 21 , R 22 , β represents the design parameters, ι i，1 , and is the intermediate variable, a i Represents a virtual input signal.

[0197] Therefore, the virtual control law of the position loop is a p Designed for

[0198]

[0199] in

[0200] Position loop filter error compensation signal ξ p It can be derived from the following formula

[0201]

[0202] To guide it, for

[0203]

[0204] Step 2. Design the Lyapunov function of the velocity loop. The formula is as follows:

[0205]

[0206] The derivative of

[0207]

[0208] in

[0209] d f Neural network can be used to approximate

[0210]

[0211] in represents the approximation error, and

[0212] According to Young's inequality, the multiplication of two terms can be written as follows:

[0213] The speed loop virtual control law is designed as

[0214]

[0215] in Represents W p The estimated value of .

[0216] Speed ​​loop filter error compensation signal ξ v for

[0217]

[0218] The compensation signal ξ v Substituting the Lyapunov derivative term of the velocity loop, we get

[0219]

[0220] in

[0221] Selecting the velocity loop Lyapunov function considering the estimation error

[0222] The positive definite matrix Q p satisfy

[0223] but It can be written as

[0224]

[0225] The adaptive law of the estimation term in the virtual control law of the speed loop is designed as follows:

[0226]

[0227] Where m p >0.

[0228] Thus there is

[0229]

[0230] make Then the virtual control law of the speed loop is transformed into:

[0231]

[0232] where φ d and θ d represents the expected values ​​of φ and θ.

[0233] Step 3. Define the posture tracking error as e Θ =Θ-Θ d , where Θ d =[φ d ,θ d , ψ d ] T represents the expected value of the posture. Therefore, v Θ Defined as

[0234] v Θ =e Θ -ξ Θ (32)

[0235] where ξ Θ It will be given in the formula later.

[0236] The Lyapunov function of the attitude loop is selected as

[0237]

[0238] but for

[0239]

[0240] Attitude loop virtual control lawa ω It can be written as

[0241]

[0242] in

[0243] Attitude loop filtering error compensation signal ξ Θ It can be defined as

[0244]

[0245] where a ω，c is the virtual signal a ω The filter value of .

[0246] Substituting the attitude loop filter error compensation equation into the attitude loop Lyapunov derivative term, we can get

[0247]

[0248] where v w =e ω -ξ ω =ω-a ω,c -ξ ω .

[0249] Step 4. Consider the angular velocity loop Lyapunov function as follows

[0250]

[0251] but It can be calculated as

[0252]

[0253] in The unknown dynamic behavior can be described as

[0254]

[0255] According to Young's inequality

[0256]

[0257] Combining the above formulas, the virtual control law of the angular velocity loop is designed as

[0258]

[0259] in W Θ The estimated value of .

[0260] Angular velocity loop filtering error compensation signal ξ ω for

[0261]

[0262] Substituting the angular velocity loop filter error compensation equation into the angular velocity loop Lyapunov derivative, we can get:

[0263]

[0264] Design the following Lyapunov function

[0265]

[0266] Where Q Θ Positive and satisfying

[0267] Calculated as

[0268]

[0269] The adaptive law of the estimation term in the virtual control law of the angular velocity loop is designed as:

[0270]

[0271] Where m Θ >0.

[0272] Therefore, the derivative of the angular velocity loop Lyapunov function considering the estimation error is expressed as:

[0273]

[0274] The control law can be adopted Replace it, then there is

[0275]

[0276] Since τ e is very small, the swinging dynamics behavior can be described as

[0277]

[0278] Therefore, the longitudinal and transverse periodic pitch variations are obtained:

[0279]

[0280] Among them: a sd and b sd They are respectively s and b s The given value of .

[0281] Next, the correctness and effectiveness of the control law design are proved through theoretical derivation.

[0282] The total Lyapunov function V of the entire closed-loop system is designed as

[0283] V=V P +V Θ (52)

[0284] Taking the derivative of V, we get

[0285]

[0286] Determine the supremum of the total Lyapunov function changing with time; thereby analyzing the boundedness of all signals in the closed-loop system. If all signals are bounded, the closed-loop system is stable, otherwise it is unstable.

[0287] The above inequality shows that

[0288]

[0289] Where t0 is the initial time. The above inequality is satisfied for t≥t0. Therefore, the variable v p ,v v ,v Θ ,v ω , and All included in the compact set Due to e i (i=p,v,Θ,ω) satisfies e i =v i +ξ i And i is bounded, so e i is bounded, and μρ represents the upper bound of the filtering error. Therefore, it is proved that all signals in the closed-loop system are bounded, and the bounded range can be adjusted by adjusting the size of the parameter k.

Claims

1. A method for designing a helicopter adaptive command filtering backstepping tracking control law, characterized in that: The method comprises the following steps: Step 1: Build a helicopter model; Step 2: Design the control law using the backstepping method.

2. The method according to claim 1, characterized in that: In the step 1, the helicopter model includes: a dynamic model under the fuselage and a main rotor flapping dynamic model; The dynamic model of the body is expressed as follows: in, represents the ground coordinate system, is the body coordinate system, a s 、b s Swing horizontally and vertically respectively, P = [x, y, z] T represents the position vector, F f represents the resultant moment, m represents the mass of the body, H represents the attitude matrix, V = [v x ,v y ,v z ] T represents the velocity vector, g represents the acceleration due to gravity, e3 = [0,0,1] T , Θ=[φ,θ,ψ] T is the attitude vector (φ is the roll angle, θ is the pitch angle, ψ is the yaw angle), I = diag (I x ,I y ,I z ) Moment of inertia matrix, ω=[p,q,r] T Indicates in b is the angular acceleration in the coordinate system, and τ is the torque. R is the rotation matrix, which represents the rotation from Ξ b To e Conversion: The posture matrix H is: Among them, S = sin(·), C = cos(·), T = tan(·); The resultant moment is: The torque τ = τ γ + Δ τ = τ A Υ + τ B + Δ τ and there is Where: T m represents the thrust generated by the main rotor, T t Represents the reactive torque, L b and M a are the longitudinal and transverse coefficients respectively. m , l m are the horizontal and vertical positions of the main rotor relative to the center of gravity, h t , l t are the horizontal and vertical positions of the tail rotor relative to the center of gravity, respectively. The main rotor flapping dynamics equation is: Among them, τ e is the swing time constant, A lon and A lat Longitudinal periodic pitch and lateral periodic pitch gain.

3. The method according to claim 2, characterized in that: In the step 2, the control laws include: position control law, speed control law, attitude control law and angular velocity control law.

4. The method according to claim 3, characterized in that: In step 2, the position control law design process is as follows: Step 2A: Design the Lyapunov function of the position loop, the formula is as follows: where v p =e p -ξ p is the error compensation information, e p Defined as e p =PP d ; Step 2B: Design the command filter of the position loop in the following form: Where R 11 , R 12 , R 21 , R 22 , β represents the design parameters, l i，1 , and is the intermediate variable, a t Represents a virtual input signal. Step 2C: Derive the virtual control law of the position loop based on the derivative of the Lyapunov function of the position loop; Derive the derivative of the Lyapunov function The formula is as follows: where v v =e v -ξ v ,e v =Va p，c ,a p，c is the output of the mixed command filter; Position loop virtual control law a p Designed for: in Step 2D: Design the position loop filter error compensation equation; compensation signal ξ p It is expressed as follows: Substituting the position loop filter error compensation equation into the position loop Lyapunov derivative term, we can get:

5. The method according to claim 4, characterized in that: In step 2, the speed control law design process is as follows: Step 2E: Design the Lyapunov function of the velocity loop. The formula is as follows: Step 2F: Design the command filter of the speed loop to be the same as the command filter of the position loop; Step 2G: Derive the virtual control law of the speed loop based on the derivative of the Lyapunov function of the speed loop; Derive the derivative of the Lyapunov function of the speed loop, the formula is as follows: in d f For unknown interference, the neural network is used to approximate the formula as follows: in represents the approximation error, and According to Young's inequality, the multiplication of two terms can be written as follows: The virtual control law of the speed loop is designed as: in Represents W p An estimated value of Step 2H: Design the speed loop filter error compensation equation ξ v , of the following form: Substituting the velocity loop filter error compensation equation into the velocity loop Lyapunov derivative term, we can get: in Step 2I: Design the adaptive law of the estimation term in the virtual control law of the speed loop; Choose the velocity loop Lyapunov function taking into account the estimation error: Where Q p satisfy It can be written as The adaptive law of the estimation term in the virtual control law of the speed loop is designed as: Where m p >0; Therefore, the derivative of the velocity loop Lyapunov function considering the estimation error is expressed as: make Then the virtual control law of the speed loop is transformed into: where φ d and θ d represents the expected values ​​of φ and θ.

6. The method according to claim 5, characterized in that: In step 2, the attitude control law design process is as follows: Step 2J: Design the Lyapunov function of the attitude loop; Define the posture tracking error e Θ =Θ-Θ d , where Θ d =[φ d ,θ d , ψ d ] T ; Therefore, the compensated posture tracking error v Θ Defined as v Θ =e Θ -x Θ Among them, ξ Θ To compensate the attitude error; The Lyapunov function of the attitude loop is expressed as follows: Step 2K: Design the command filter of the attitude loop to be the same as the command filter of the position loop; Step 2: Derive the virtual control law of the attitude loop according to the derivative of the Lyapunov function of the attitude loop; The derivative of the Lyapunov function of the attitude loop is expressed as follows: Then, the attitude loop virtual control law a ω It is expressed as: in, Step 2M: Design the attitude loop filter error compensation equation in the following form: where a ω，c is the virtual signal a ω The filter value of Substituting the attitude loop filter error compensation equation into the attitude loop Lyapunov derivative term, we can get among themv w =e ω -x ω =ω-a ω，c -x ω 。 7. The method according to claim 6, characterized in that: In step 2, the angular velocity control law design process is as follows: Step 2: Design the Lyapunov function of the angular velocity loop in the following form: Step 20: Design the command filter of the angular velocity loop to be the same as the command filter of the position loop; Step 2P: Derive the virtual control law of the angular velocity loop according to the derivative of the Lyapunov function of the angular velocity loop; The derivative form of the Lyapunov function of the angular velocity loop is as follows: The unknown dynamic behavior Further described as: According to Young's inequality, The virtual control law of the angular velocity loop is designed as: in W Θ An estimated value of Step 2Q: Design the angular velocity loop filter error compensation equation in the following form: Substituting the angular velocity loop filter error compensation equation into the angular velocity loop Lyapunov derivative, we can get: Step 2 R: Design the adaptive law of the estimation term in the virtual control law of the angular velocity loop; Choose the Lyapunov function of the angular velocity loop taking into account the estimation error: Where Q Θ Positive and satisfying The derivative of the Lyapunov function of the angular velocity loop considering the estimation error is expressed as follows: The adaptive law of the estimation term in the virtual control law of the angular velocity loop is designed as: Among them, m Θ >0; Therefore, the derivative of the angular velocity loop Lyapunov function considering the estimation error is expressed as: make Then the virtual control law of the angular velocity loop is transformed into: According to the main rotor flapping dynamics model, the flapping dynamics behavior is described as: Therefore, the longitudinal and transverse periodic pitch variation is obtained: Among them: a sd and b sd They are respectively s and b s The given value of .

8. The method according to claim 7, characterized in that: The method further includes: step 3, analyzing the stability of the closed-loop system, the closed-loop system including: a position loop, a velocity loop, a posture loop and an angular velocity loop; the process is as follows: Design the total Lyapunov function V; V=V P +V Θ Derivative the total Lyapunov function V; in Determine the supremum of the total Lyapunov function V changing with time; thereby analyzing the boundedness of all signals in the closed-loop system. If all signals are bounded, the closed-loop system is stable, otherwise it is unstable. The above inequality shows that: For t≥t0, it is satisfied. Therefore, the variable v p ,v v ,v Θ ,v ω , and All included in the compact set Due to e i (i=p,v,Θ,ω) satisfies e i =v i +ξ i And i is bounded, so e i is bounded, and μρ represents the upper bound of the filtering error. Therefore, it is proved that all signals in the closed-loop system are bounded, and the bounded range can be adjusted by adjusting the size of the parameter k.

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