A method and system for aircraft anti-unwinding adaptive attitude control

Abstract

The present invention discloses a method and system for aircraft anti-unwinding adaptive attitude control. The method establishes the aircraft's relative attitude kinematic and dynamic equations, defines the parameter vector of the uncertainty moment of inertia matrix, introduces a sign function, and rewrites the relative attitude kinematic and dynamic equations into the aircraft's parametric affine form. The method also defines the external form of the parameter estimate and determines the attitude tracking control law and closed-loop system equation. Based on the external form of the aircraft parameter estimate and the closed-loop system equation, the partial differential equation to be solved is obtained. A filter state is introduced to transform the partial differential equation, giving an approximate solution to the partial differential equation and the resulting error term. A dynamic scaling factor is introduced to eliminate the error term, and the internal form of the aircraft parameter estimate is determined. Finally, the complete form of the aircraft's anti-unwinding immersed and invariant adaptive attitude controller is determined. This method enables high-performance attitude tracking control of an aircraft under the coexistence of parameter uncertainty, external disturbances, and unwinding.

Description

Technical Field

[0001] The present invention relates to the technical field of rigid body aircraft control, and more specifically to an aircraft anti-unwinding adaptive attitude control method and system. Background Art

[0002] With advances in aerospace science and technology and the increasing demand for space exploration, the missions required of aircraft are becoming increasingly diverse and complex. Consequently, control systems with improved closed-loop performance, faster response, and greater reliability are required. Unit quaternions are a commonly used attitude description method. They possess the advantage of being globally singular-free, making them suitable for describing large-scale aircraft attitude motions and are widely used in aircraft attitude control. However, the use of quaternions to describe attitude has a double coverage property, which can lead to unwinding and excessive fuel consumption. Furthermore, during the execution of an aircraft's mission, factors such as fuel consumption and structural changes can cause changes in model parameters, and the complex space environment can introduce external disturbances. If these uncertainties and external disturbances are not effectively addressed, they can significantly impact control accuracy and system reliability.

[0003] Adaptive control is a commonly used solution for problems involving uncertain parameters. While traditional adaptive control methods have a simple design process and a wide range of applications, they suffer from shortcomings such as the adaptive update law not containing its own negative feedback and the direct coupling of parameter estimation with tracking error. These shortcomings lead to difficulties in regulating the dynamic process and degradation of the system's closed-loop performance. The immersion and invariant adaptive control method can fundamentally avoid the problems caused by these traditional methods, achieving high-performance adaptive control with smoother dynamic processes, greater adjustability, and lower control energy consumption. These performance improvements stem from the fact that the immersion and invariant parameter adaptive method adds a correction term regarding the system state to the parameter estimation, thereby indirectly introducing unknown parameters into the parameter estimation dynamics. However, this correction term needs to be obtained by solving partial differential equations. In the multivariable system of the aircraft attitude system, partial differential equations are often unsolvable, that is, there is an integrability barrier.

[0004] To address this problem, the common methods currently used include the filter system method and the dynamic scaling method. The filter system method significantly increases the order of the closed-loop system, increasing the online computational burden. The dynamic scaling method, on the other hand, significantly reduces the closed-loop system's dimensionality and control requirements while maintaining good closed-loop performance, offering greater practicality.

[0005] However, existing dynamic scaling methods either require prior information about model parameters or are subject to range constraints on control parameters, severely limiting their flexibility in practical applications. Furthermore, the unwinding phenomenon that quaternions can exhibit when describing attitude can lead to excessively long convergence paths and excessive fuel consumption. External disturbances caused by complex space environments can reduce control accuracy and even cause system instability.

[0006] In summary, most existing technologies focus on one or two of the following situations: model parameter uncertainty, unwinding phenomenon, and external disturbance. However, in practical applications, multiple factors often exist simultaneously and influence each other during the aircraft attitude control process, resulting in the aircraft being unable to better adapt to changes in the external environment. Summary of the Invention

[0007] In response to the problems existing in the above-mentioned fields, the present invention proposes an aircraft anti-unwinding adaptive attitude control method and system, which can solve the technical problem that most of the existing technologies focus on one or two situations among model parameter uncertainty, unwinding phenomenon and external disturbance. However, in actual applications, multiple factors often exist simultaneously and influence each other during the aircraft attitude control process, resulting in the aircraft being unable to better adapt to changes in the external environment.

[0008] To solve the above technical problems, the present invention discloses an aircraft anti-unwinding adaptive attitude control method, comprising the following steps:

[0009] Establish the kinematic and dynamic equations of the relative attitude of the aircraft;

[0010] Define the parameter vector of the uncertainty moment of inertia matrix, introduce the sign function, and rewrite the relative attitude kinematics and dynamics equations into the parametric affine form of the aircraft;

[0011] Define the external form of the aircraft parameter estimation, and determine the aircraft attitude tracking control law and closed-loop system equations based on the parameter affine form of the motion equation and the external form of the parameter estimation;

[0012] Based on the external form of the aircraft parameter estimation and the closed-loop system equation, the partial differential equation to be solved is obtained; based on the partial differential equation to be solved, a filter state is introduced to transform the non-integrable part of the partial differential equation to be solved, and the approximate solution of the partial differential equation and the error term caused by the approximate solution are given; based on the approximate solution and the error term caused by the approximate solution, a dynamic scaling factor is introduced to eliminate the influence of the error term and determine the internal form of the aircraft parameter estimation;

[0013] According to the internal form of the vehicle attitude tracking control law and parameter estimation, the complete form of the vehicle anti-unwinding immersion and invariant adaptive attitude controller without scaling factor is determined.

[0014] Preferably, the establishment of the aircraft relative attitude kinematics and dynamics equations comprises the following steps:

[0015] Define the inertial coordinate system of the aircraft as F I , the body coordinate system is F B , the expected coordinate system is F D , in the quaternion framework, the single attitude motion model of the tracking aircraft is:

[0016]

[0017] Where, q=[q0 q v ] T is the attitude quaternion of the aircraft system relative to the inertial coordinate system, q0 is the scalar part of the attitude quaternion of the aircraft system relative to the inertial coordinate system, q v is the vector part of the attitude quaternion of the aircraft system relative to the inertial coordinate system, I3 is the third-order unit matrix, ω is the body velocity, u is the control torque, d is the interference torque, and J is the uncertainty moment of inertia of the aircraft, which is defined as · × Represents the cross product matrix, for any vector a=[a1 a2a3] T , where a × is an antisymmetric matrix;

[0018] The desired motion of the aircraft satisfies the following form:

[0019]

[0020] Among them, q d =[q d0 q dv ] T is the desired attitude quaternion, q d0 is the scalar part of the desired attitude quaternion, q dv is the vector part of the desired attitude quaternion, ω d is the expected speed;

[0021] Define the attitude tracking error of the aircraft as q e and ω e for:

[0022]

[0023] ω e =ω-R e ω d

[0024] Among them, q e =[q e0 q ev ]T F B With F D The relative posture between e0 F B With F D The scalar part of the relative attitude between ev F B With F D The vector part of the relative posture between e is the relative speed, R e F D to F B The coordinate transformation matrix, Represents quaternion multiplication;

[0025] The kinematic and dynamic equations of the relative attitude of the aircraft are obtained as follows:

[0026]

[0027] Preferably, the process of obtaining the parameter affine form includes the following steps:

[0028] The parameter vector defining the uncertain moment of inertia J of the aircraft is:

[0029] θ=[J 11 J 12 J 13 J 22 J 23 J 33 ] T

[0030] For any vector x = [x1 x2 x3] T , perform the following equivalent conversion relationship:

[0031] Jx=M(x)θ

[0032] Where M(x) is defined as:

[0033]

[0034] Using this equivalent transformation relationship and considering the unwinding phenomenon of quaternions, the relative attitude dynamics equation of the aircraft is rewritten into a parametric affine form:

[0035]

[0036] Among them, k p and k d is a positive constant, sgn is a sign function, defined as W is the parameter regression matrix, which is defined as:

[0037]

[0038] Preferably, determining the aircraft attitude tracking control law and the closed-loop system equation comprises the following steps:

[0039] According to the immersion and invariance principle, the external form of the parameter estimation of the aircraft is defined as:

[0040]

[0041] Among them, υ is the dynamic update term, β is the system state correction term;

[0042] According to the affine form of the aircraft's parameters and the parameter estimation error, the adaptive attitude tracking control law of the aircraft is designed as follows:

[0043]

[0044] According to the adaptive attitude tracking control law, the closed-loop system equation of the aircraft attitude motion is obtained as follows:

[0045]

[0046] in, is the parameter estimation error.

[0047] Preferably, the introducing of the filtering state to transform the non-integrable part of the partial differential equation to be solved comprises the following steps:

[0048] According to the external form of the aircraft parameter estimation and the closed-loop system equation, υ is defined as:

[0049]

[0050] make Partial differential equations Solve and obtain the specific form of parameter estimation;

[0051] Decompose the parameter regression matrix W into integrable parts W1, W2 and W3, where:

[0052]

[0053] W2=k d M(ω)

[0054] W3=ω × M(ω)+M(ω × R e ω d )

[0055] Among them, W1 and W2 are the integrable parts, and W3 is the non-integrable part;

[0056] Introducing filter state The non-integrable part W3 is transformed into Among them, the error caused by the transformation is Among them, the dynamic equation of the filtering state is

[0057] Preferably, providing an approximate solution to the partial differential equation and an error term caused by the approximate solution comprises the following steps:

[0058] The approximate solution of the partial differential equation is β = γ (β1 + β2 + β3);

[0059] Among them, β1, β2 and β3 are:

[0060] β1=W1 T ω

[0061]

[0062] Where, γ is the adaptive gain;

[0063] and

[0064] Define the dynamic scaling factor as

[0065] Where, f(r)=1 / (1+e -r ), r is the auxiliary scaling factor, satisfying in,

[0066] Define the scaled estimation error as Design five candidate Lyapunov functions, in order:

[0067]

[0068] V e =(ak p +k d )((q e0 -sgn(q e0 (0))) 2 +q ev T q ev )+aω e T ω e +sgn(q e0 (0))q ev T ω e ,V2=cV z +V e

[0069] Among them, kp and k d is a positive constant, is the filtering error, a, b, c are sufficiently large positive numbers and satisfy

[0070] Preferably, determining the internal form of the aircraft parameter estimate comprises the following steps:

[0071] By performing a derivative analysis on the designed Lyapunov function, it is concluded that the system state will eventually enter the following set:

[0072]

[0073] in, X2=[||sgn(q e0 (0))q ev || ||ω e || ||J -1 WZ||] T , λ min (P1),λ min (P2) are the minimum eigenvalues of P1 and P2 respectively.

[0074] Preferably, the complete form of the aircraft anti-unwinding immersion and invariant adaptive attitude controller without scaling factor is:

[0075]

[0076] Among them, k p 、k d , γ and σ are positive constants, is the parameter estimation form, υ is the dynamic update term, and β is the system state correction term;

[0077] The designed controller is used in the aircraft attitude motion control system to realize anti-unwinding attitude tracking control under the coexistence of model parameter uncertainty and external disturbance.

[0078] Preferably, the system further comprises an aircraft anti-unwinding adaptive attitude control system, comprising:

[0079] The aircraft's parameter affine form acquisition module is used to establish the aircraft's relative attitude kinematics and dynamics equations; it defines the parameter vector of the uncertainty moment of inertia matrix, introduces a sign function, and rewrites the relative attitude kinematics and dynamics equations into the aircraft's parameter affine form;

[0080] The module for determining the attitude tracking control law and closed-loop system equation is used to define the external form of the aircraft parameter estimation and determine the aircraft attitude tracking control law and closed-loop system equation based on the motion equation in the parameter affine form and the external form of the parameter estimation;

[0081] The internal form acquisition module for aircraft parameter estimation is used to obtain the partial differential equation to be solved based on the external form of the aircraft parameter estimation and the closed-loop system equation; based on the partial differential equation to be solved, a filter state is introduced to transform the non-integrable part of the partial differential equation to be solved, and an approximate solution of the partial differential equation and the error term caused by the approximate solution are given; based on the approximate solution and the error term caused by the approximate solution, a dynamic scaling factor is introduced to eliminate the influence of the error term and determine the internal form of the aircraft parameter estimation;

[0082] The attitude control complete form acquisition module is used to determine the complete form of the aircraft anti-unwinding immersion and invariant adaptive attitude controller without scaling factor based on the internal form of the aircraft attitude tracking control law and parameter estimation.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] The anti-unwinding adaptive attitude control method for aircraft proposed in the present invention can overcome the technical defects in the prior art that multiple factors often exist simultaneously and influence each other during the aircraft attitude control process, resulting in the aircraft being unable to better adapt to changes in the external environment. This method introduces a sign function when defining the parameter vector, rewrites the relative attitude kinematics and dynamics equations into the parameter affine form of the aircraft, and ensures that the aircraft reaches the equilibrium point by the shortest path when performing attitude changes, effectively solves the unwinding phenomenon that may exist when the quaternion describes the attitude, and avoids excessive fuel consumption. The dynamic scaling technology is used to introduce the filter state to solve the partial differential equation, successfully overcoming the integrability obstacle, and determining the scaling estimation error by defining the dynamic scaling factor, making up for the defects of the existing dynamic scaling technology that either requires prior information on model parameters or the control parameter range is constrained, while avoiding the problems of high computational burden and high control requirements in the existing filtering system method, reducing computational complexity, improving the anti-interference performance of the system, enabling the aircraft to better adapt to changes in the external environment, and improving the flexibility of closed-loop performance regulation.

[0085] The present invention improves the practicality and flexibility of attitude adaptive control by innovating and integrating multiple control technologies, ensures performance robustness under disturbances, avoids unnecessary energy consumption, and ultimately achieves high-performance attitude tracking control of the aircraft under the coexistence of parameter uncertainty, external disturbances, and unwinding phenomena. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 Schematic diagram of the overall method steps of the present invention;

[0087] Figure 2 Schematic diagram of three coordinate systems defined in the present invention;

[0088] Figure 3 It is a closed-loop structure diagram of the aircraft relative attitude tracking control system of the present invention. DETAILED DESCRIPTION

[0089] The following is a combination of the embodiments of the present invention Figure 1-Figure 3 , the technical solutions in the embodiments of the present invention are clearly and completely described. It should be understood that the terms used in the present invention are only used to describe specific implementation methods and are not intended to limit the present invention.

[0090] Example

[0091] like Figure 1 As shown, an embodiment of the present invention provides an aircraft anti-unwinding adaptive attitude control method, comprising the following steps:

[0092] S1: Establish the kinematics and dynamics equations of the relative attitude of the aircraft;

[0093] S2: Define the parameter vector of the uncertainty moment of inertia matrix, introduce the sign function, consider the unwinding phenomenon of the quaternion, and rewrite the relative attitude dynamics equation into the parametric affine form of the aircraft;

[0094] S3: Define the external form of the aircraft parameter estimation, and determine the aircraft attitude tracking control law and closed-loop system equations based on the parameter affine form of the motion equation and the external form of the parameter estimation;

[0095] S4: Based on the external form of the aircraft parameter estimation and the closed-loop system equation, the partial differential equation to be solved is obtained; based on the partial differential equation to be solved, a filter state is introduced to transform the non-integrable part of the partial differential equation to be solved, and the approximate solution of the partial differential equation and the error term caused by the approximate solution are given; based on the approximate solution and the error term caused by the approximate solution, a dynamic scaling factor is introduced to eliminate the influence of the error term and determine the internal form of the aircraft parameter estimation;

[0096] S5: Based on the internal form of the vehicle attitude tracking control law and parameter estimation, the complete form of the vehicle anti-unwinding immersion and invariant adaptive attitude controller without scaling factor is determined.

[0097] Specifically, in step S1, the kinematic and dynamic equations of the relative attitude of the aircraft are established, including the following steps:

[0098] In order to establish the relative motion model of the aircraft, the following definitions are made: Figure 2 The three coordinate systems shown are the inertial coordinate system of the aircraft, F I, the tracking aircraft's body coordinate system is F B , the expected coordinate system is F D , in the quaternion framework, the single attitude motion model of the tracking aircraft is:

[0099]

[0100] Where, q=[q0 q v ] T is the attitude quaternion of the aircraft system relative to the inertial coordinate system, q0 is the scalar part of the attitude quaternion of the aircraft system relative to the inertial coordinate system, q v is the vector part of the attitude quaternion of the aircraft system relative to the inertial coordinate system, I3 is the third-order unit matrix, ω is the body velocity, u is the control torque, d is the interference torque, and J is the uncertainty moment of inertia of the aircraft, which is defined as · × Represents the cross product matrix, for any vector a=[a1 a2a3] T , where a × is an antisymmetric matrix;

[0101] The desired motion of the aircraft satisfies the following form:

[0102]

[0103] Among them, q d =[q d0 q dv ] T is the desired attitude quaternion of the aircraft, q d0 is the scalar part of the desired attitude quaternion, q dv is the vector part of the desired attitude quaternion, ω d is the expected speed;

[0104] Define the attitude tracking error of the aircraft as q e and ω e :

[0105]

[0106] ω e =ω-R e ω d

[0107] Among them, q e =[q e0 q ev ] T F B With F D The relative posture between e0 F BWith F D The scalar part of the relative attitude between ev F B With F D The vector part of the relative posture between e is the relative speed, R e F D to F B The coordinate transformation matrix, Represents quaternion multiplication;

[0108] Based on the above formulas, the kinematic and dynamic equations of the relative attitude of the aircraft are obtained as follows:

[0109]

[0110] Specifically, in step S2, the process of obtaining the parameter affine form includes the following steps:

[0111] In order to estimate the uncertain moment of inertia matrix J, the parameter vector of the uncertain moment of inertia J of the aircraft is defined as:

[0112] θ=[J 11 J 12 J 13 J 22 J 23 J 33 ] T

[0113] For any vector x = [x1 x2 x3] T , perform the following equivalent conversion relationship:

[0114] Jx=M(x)θ

[0115] Where M(x) is defined as:

[0116]

[0117] Using this equivalent transformation relationship and considering the possible unwinding phenomenon of quaternions, the relative attitude dynamics equation of the aircraft is rewritten into a parametric affine form:

[0118]

[0119] Among them, k p and k d is a positive constant, sgn is a sign function, defined as W is the parameter regression matrix;

[0120] Define W as:

[0121]

[0122] Specifically, in step S3, determining the aircraft attitude tracking control law and the closed-loop system equation includes the following steps:

[0123] According to the immersion and invariance principle, the external form of the parameter estimation of the aircraft is defined as:

[0124]

[0125] Among them, υ is the dynamic update term, β is the system state correction term;

[0126] The parameter estimation error of the aircraft is defined as

[0127] According to the affine form of the aircraft's parameters and the parameter estimation error, the adaptive attitude tracking control law of the aircraft is designed as follows:

[0128]

[0129] According to the adaptive attitude tracking control law, the closed-loop system equation of the aircraft attitude motion is obtained as follows:

[0130]

[0131] Specifically, in step S4, a filtering state is introduced to transform the non-integrable part of the partial differential equation to be solved, the partial differential equation is approximately solved, and the internal form of the parameter estimation is given.

[0132] According to the external form of the aircraft parameter estimation and the closed-loop system equation, υ is defined as:

[0133]

[0134] make In order to obtain the specific form of parameter estimation, it is necessary to Solve it.

[0135] Decompose the parameter regression matrix W into integrable parts W1, W2 and W3, where:

[0136]

[0137] W2=k d M(ω)

[0138] W3=ω × M(ω)+M(ω × R e ω d )

[0139] Among them, W1 and W2 are the integrable parts, and W3 is the non-integrable part.

[0140] Furthermore, it is necessary to introduce the filtering state The non-integrable part W3 is transformed into Among them, the error caused by the transformation is Among them, the dynamic equation of the filtering state is

[0141] Giving an approximate solution to a partial differential equation and the error term caused by the approximate solution includes the following steps:

[0142] The approximate solution of the partial differential equation is β = γ (β1 + β2 + β3);

[0143] Among them, β1, β2 and β3 are:

[0144] β1=W1 T ω

[0145]

[0146] Where, γ is the adaptive gain;

[0147] and

[0148] Specifically, in step S5, in order to prove the stability of the closed-loop adaptive posture tracking system, the dynamic scaling factor is defined as:

[0149]

[0150] Where, f(r)=1 / (1+e -r ), r is the auxiliary scaling factor, satisfying in,

[0151] According to the above definition, the following operational properties can be obtained:

[0152]

[0153] Using R, we define the scaled estimation error as Design five candidate Lyapunov functions, in order:

[0154]

[0155] V e =(ak p +k d )((q e0 -sgn(q e0 (0))) 2 +q ev T q ev )+aω eT ω e +sgn(q e0 (0))q ev T ω e ,V2=cV z +V e

[0156] Among them, k p and k d is a positive constant, is the filtering error, a, b, c are sufficiently large positive numbers and satisfy Therefore, a, b, and c can be set to sufficiently large positive constants.

[0157] By performing a derivative analysis on the Lyapunov function designed above, it is concluded that the system state will eventually enter the following set:

[0158]

[0159] in, X2=[||sgn(q e0 (0))q ev || ||ω e || ||J -1 WZ||] T , λ min (P1),λ min (P2) is the minimum eigenvalue of P1 and P2 respectively, and sufficiently large a, b, and c ensure the positive definiteness of P1 and P2.

[0160] In summary, it is proved that the state of the closed-loop system is ultimately bounded.

[0161] Specifically, in step S6, the complete form of the aircraft anti-unwinding immersion and invariant adaptive attitude controller without scaling factor is given as:

[0162]

[0163] The designed controller is used in the aircraft attitude motion control system to realize the anti-unwinding attitude tracking control under the coexistence of model parameter uncertainty and external disturbance. The closed-loop structure diagram of the aircraft relative attitude tracking control system is shown in the figure below. Figure 3 shown.

[0164] Based on the attitude control method, the present invention also proposes an aircraft anti-unwinding adaptive attitude control system, comprising:

[0165] The aircraft's parameter affine form acquisition module is used to establish the aircraft's relative attitude kinematics and dynamics equations; define the parameter vector of the uncertainty moment of inertia matrix, introduce symbolic functions, and rewrite the relative attitude kinematics and dynamics equations into the aircraft's parameter affine form.

[0166] The attitude tracking control law and closed-loop system equation determination module is used to define the external form of aircraft parameter estimation, and determine the aircraft attitude tracking control law and closed-loop system equation based on the motion equation in parameter affine form and the external form of parameter estimation.

[0167] The internal form acquisition module of the aircraft parameter estimation is used to obtain the partial differential equation to be solved based on the external form of the aircraft parameter estimation and the closed-loop system equation; according to the partial differential equation to be solved, a filter state is introduced to transform the non-integrable part of the partial differential equation to be solved, and the approximate solution of the partial differential equation and the error term caused by the approximate solution are given; according to the approximate solution and the error term caused by the approximate solution, a dynamic scaling factor is introduced to eliminate the influence of the error term and determine the internal form of the aircraft parameter estimation.

[0168] The attitude control complete form acquisition module is used to determine the complete form of the aircraft anti-unwinding immersion and invariant adaptive attitude controller without scaling factor based on the internal form of the aircraft attitude tracking control law and parameter estimation.

[0169] The present invention comprehensively considers three common problems in aircraft attitude tracking control: quaternion unwinding, model parameter uncertainty, and external disturbances in complex space environments.

[0170] The anti-unwinding adaptive attitude control method and system for aircraft proposed in the present invention establish the relative attitude dynamics equation of the aircraft based on quaternions, determine the uncertainty moment of inertia matrix of the aircraft, and define the parameter vector. When defining the parameter vector, the use of sign functions ensures that the aircraft reaches the equilibrium point by the shortest path when changing its attitude, effectively solving the unwinding phenomenon that may exist when the quaternion describes the attitude, and avoiding excessive fuel consumption.

[0171] The dynamic scaling technology was used to successfully overcome the integrability obstacle, and by constructing a Lyapunov function in coefficient form, it made up for the defects of existing dynamic scaling technologies, such as the need for prior information on model parameters or the constraints on the range of control parameters. At the same time, it avoided the problems of heavy computational burden and high control requirements in existing filtering system methods, reduced computational complexity, and improved the flexibility of closed-loop performance regulation. A correction term was introduced in the dynamic update term to improve the system's anti-interference performance, enabling the aircraft to better adapt to changes in the external environment.

[0172] The present invention improves the practicality and flexibility of attitude adaptive control by innovating and integrating multiple control technologies, ensures performance robustness under disturbances, avoids unnecessary energy consumption, and ultimately achieves high-performance attitude tracking control of the aircraft under the coexistence of parameter uncertainty, external disturbances, and unwinding phenomena.

[0173] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

[0174] In addition, unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those skilled in the art to which the present invention belongs. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In the event of any conflict with any incorporated document, the content of this specification shall prevail.

Claims

1. A method for anti-unwinding adaptive attitude control of an aircraft, characterized in that: The following steps are involved: Establish the kinematic and dynamic equations of the relative attitude of the aircraft; Define the parameter vector of the uncertainty moment of inertia matrix, introduce the sign function, and rewrite the relative attitude kinematics and dynamics equations into the parametric affine form of the aircraft; Define the external form of the aircraft parameter estimation, and determine the aircraft attitude tracking control law and closed-loop system equations based on the parameter affine form of the motion equation and the external form of the parameter estimation; Based on the external form of the aircraft parameter estimation and the closed-loop system equation, the partial differential equation to be solved is obtained; based on the partial differential equation to be solved, a filter state is introduced to transform the non-integrable part of the partial differential equation to be solved, and the approximate solution of the partial differential equation and the error term caused by the approximate solution are given; based on the approximate solution and the error term caused by the approximate solution, a dynamic scaling factor is introduced to eliminate the influence of the error term and determine the internal form of the aircraft parameter estimation; Based on the internal form of the vehicle attitude tracking control law and parameter estimation, the complete form of the vehicle anti-unwinding immersion and invariant adaptive attitude controller without scaling factor is determined; The step of providing an approximate solution to the partial differential equation and an error term caused by the approximate solution comprises the following steps: The approximate solution of the partial differential equation is β = γ (β1 + β2 + β3); Among them, β1, β2 and β3 are: β1=W1 T oh Where γ is the adaptive gain, k d is a positive constant, ω is the body velocity, ω1, ω2, ω3 are the three components of the body velocity ω; and Define the dynamic scaling factor as Among them, W1, W2 and W3 are the three components of the parameter regression matrix W decomposition, j m is the minimum eigenvalue of the uncertain moment of inertia J of the aircraft, f(r)=1 / (1+e -r ), r is the auxiliary scaling factor, satisfying in, Define the scaled estimation error as Design five candidate Lyapunov functions, in order: V e =(ak p +k d )((q e0 -sgn(q e0 (0))) 2 +q ev T q ev )+aω e T ω e +sgn(q e0 (0))q ev T ω e ,V2−cV z +V e Among them, q e0 is the body coordinate system F B With the expected coordinate system F D The scalar part of the relative attitude between ev F B With F D The vector part of the relative posture between e is the relative velocity, k p and k f is a positive constant, is the filtering error, a, b, c are positive numbers, and satisfy V z 、V ω , V1, V e , V2 is the candidate Lyapunov function, sgn is the sign function, q e0 (0) is q e0 The initial value of Determining the internal form of the aircraft parameter estimation includes the following steps: By performing a derivative analysis on the designed Lyapunov function, it is concluded that the system state will eventually enter the following set: Where d is the disturbance torque, J is the uncertainty moment of inertia of the aircraft, defined as θ is the parameter vector of the uncertain moment of inertia J; X2=[||sgn(q e0 (0))q ev || ||ω e || ||J -1 WZ||] T , λ min (P1),λ min (P2) are the minimum eigenvalues of P1 and P2 respectively; The complete form of the scale-free aircraft anti-unwinding immersion and invariant adaptive attitude controller is: Among them, γ and σ are positive constants, is the parameter estimation form, υ is the dynamic update term, β is the system state correction term, ω d is the desired speed; u is the control torque, R e It's F B With F D The coordinate transformation matrix between them, β1, β2, β3 are the three components of the system state correction term β, is the filtering state of the body velocity; The designed controller is used in the aircraft attitude motion control system to realize anti-unwinding attitude tracking control under the coexistence of model parameter uncertainty and external disturbance.

2. The aircraft anti-unwinding adaptive attitude control method according to claim 1, characterized in that: The establishment of the aircraft relative attitude kinematics and dynamics equations comprises the following steps: Define the inertial coordinate system of the aircraft as F I , in the quaternion framework, the single attitude motion model of the tracking aircraft is: Where, q=[q0 q v ] T is the attitude quaternion of the aircraft system relative to the inertial coordinate system, q0 is the scalar part of the attitude quaternion of the aircraft system relative to the inertial coordinate system, q v is the vector part of the attitude quaternion of the aircraft system relative to the inertial coordinate system, and I3 is the third-order unit matrix; × Represents the cross product matrix, for any vector a=[a1 a2 a3] T , where a × is an antisymmetric matrix; The desired motion of the aircraft satisfies the following form: Among them, q d =[q d0 q dv ] T is the desired attitude quaternion, q d0 is the scalar part of the desired attitude quaternion, q dv is the vector part of the desired attitude quaternion; Define the attitude tracking error of the aircraft as q e and ω e for: oh e =ω-R e oh d Among them, q e =[q e0 q ev ] T F B With F D The relative posture between Represents quaternion multiplication; The kinematic and dynamic equations of the relative attitude of the aircraft are obtained as follows:

3. The aircraft anti-unwinding adaptive attitude control method according to claim 2, characterized in that: The process of obtaining the parameter affine form includes the following steps: The parameter vector defining the uncertain moment of inertia J of the aircraft is: θ=[J 11 I 12 I 13 I 22 I 23 I 33 ] T For any vector x = [x1 x2 x3] T , perform the following equivalent conversion relationship: Jx=M(x)θ Where M(x) is defined as: Using this equivalent transformation relationship and considering the unwinding phenomenon of quaternions, the relative attitude dynamics equation of the aircraft is rewritten into a parametric affine form: Among them, it is defined as Define W as:

4. The aircraft anti-unwinding adaptive attitude control method according to claim 3, characterized in that: Determining the aircraft attitude tracking control law and the closed-loop system equation comprises the following steps: According to the immersion and invariance principle, the external form of the parameter estimation of the aircraft is defined as: According to the affine form of the aircraft's parameters and the parameter estimation error, the adaptive attitude tracking control law of the aircraft is designed as follows: According to the adaptive attitude tracking control law, the closed-loop system equation of the aircraft attitude motion is obtained as follows: in, is the parameter estimation error.

5. The aircraft anti-unwinding adaptive attitude control method according to claim 4, characterized in that: The introducing of the filtering state to transform the non-integrable part of the partial differential equation to be solved comprises the following steps: According to the external form of the aircraft parameter estimation and the closed-loop system equation, υ is defined as: make Partial differential equations Solve and obtain the specific form of parameter estimation; Decompose the parameter regression matrix W into W1, W2 and W3, where: W2=k d M(ω) W3=ω × M(ω)+M(ω × R e oh d ) Among them, W1 and W2 are the integrable parts, and W3 is the non-integrable part; Introducing filter state The non-integrable part W3 is transformed into Among them, the error caused by the transformation is Among them, the dynamic equation of the filtering state is 6. An aircraft anti-unwinding adaptive attitude control system, characterized in that: include: The aircraft's parameter affine form acquisition module is used to establish the aircraft's relative attitude kinematics and dynamics equations; it defines the parameter vector of the uncertainty moment of inertia matrix, introduces a sign function, and rewrites the relative attitude kinematics and dynamics equations into the aircraft's parameter affine form; The module for determining the attitude tracking control law and closed-loop system equation is used to define the external form of the aircraft parameter estimation and determine the aircraft attitude tracking control law and closed-loop system equation based on the motion equation in the parameter affine form and the external form of the parameter estimation; The internal form acquisition module for aircraft parameter estimation is used to obtain the partial differential equation to be solved based on the external form of the aircraft parameter estimation and the closed-loop system equation; based on the partial differential equation to be solved, a filter state is introduced to transform the non-integrable part of the partial differential equation to be solved, and an approximate solution of the partial differential equation and the error term caused by the approximate solution are given; based on the approximate solution and the error term caused by the approximate solution, a dynamic scaling factor is introduced to eliminate the influence of the error term and determine the internal form of the aircraft parameter estimation; The attitude control complete form acquisition module is used to determine the complete form of the aircraft anti-unwinding immersion and invariant adaptive attitude controller without scaling factor based on the internal form of the aircraft attitude tracking control law and parameter estimation; The step of providing an approximate solution to the partial differential equation and an error term caused by the approximate solution comprises the following steps: The approximate solution of the partial differential equation is β = γ (β1 + β2 + β3); Among them, β1, β2 and β3 are: β1=W1 T oh Where γ is the adaptive gain, k d is a positive constant, ω is the body velocity, ω1, ω2, ω3 are the three components of the body velocity ω; and Define the dynamic scaling factor as Among them, W1, W2 and W3 are the three components of the parameter regression matrix W decomposition, j m is the minimum eigenvalue of the uncertain moment of inertia J of the aircraft, f(r)=1 / (1+e -r ), r is the auxiliary scaling factor, satisfying in, Define the scaled estimation error as Design five candidate Lyapunov functions, in order: V e =(ak p +k d )((q e0 -sgn(q e0 (0))) 2 +q ev T q ev )+aω e T ω e +sgn(q e0 (0))q ev T ω e ,V2−cV z +V e Among them, q e0 F B With F D The scalar part of the relative attitude between ev F B With F D The vector part of the relative posture between e is the relative velocity, k p and k f is a positive constant, is the filtering error, a, b, c are positive numbers, and satisfy V z 、V ω , V1, V e , V2 is the candidate Lyapunov function, sgn is the sign function, q e0 (0) is q e0 The initial value of Determining the internal form of the aircraft parameter estimation includes the following steps: By performing a derivative analysis on the designed Lyapunov function, it is concluded that the system state will eventually enter the following set: Where d is the disturbance torque, J is the uncertainty moment of inertia of the aircraft, defined as θ is the parameter vector of the uncertain moment of inertia J; X2=[||sgn(q e0 (0))q ev || ||ω e || ||J -1 WZ||] T , λ min (P1),λ min (P2) are the minimum eigenvalues of P1 and P2 respectively; The complete form of the scale-free aircraft anti-unwinding immersion and invariant adaptive attitude controller is: Among them, γ and σ are positive constants, is the parameter estimation form, υ is the dynamic update term, β is the system state correction term, ω d is the desired speed; u is the control torque, R e It's F B With F D The coordinate transformation matrix between them, β1, β2, β3 are the three components of the system state correction term β, is the filtering state of the body velocity; The designed controller is used in the aircraft attitude motion control system to realize anti-unwinding attitude tracking control under the coexistence of model parameter uncertainty and external disturbance.

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