Tracking control method of electric vertical take-off and landing aircraft and high-order all-wheel-drive system

Abstract

The invention relates to the technical field of low-altitude economical electric vertical take-off and landing aircraft control, and provides a tracking control method of an electric vertical take-off and landing aircraft and a high-order all-wheel-drive system. A pose tracking kinematics model and a dynamics model of the aircraft are established, all-drive model conversion is performed on the kinematics model and the dynamics model according to a high-order all-drive system method, and a pose tracking error all-drive system model of the aircraft is obtained. Aiming at the error all-wheel-drive system model, designing a fixed time observer and a fixed time controller, rapidly observing the state of the aircraft through the fixed time observer, and estimating change disturbance generated by mass center change of the aircraft in the flight process; therefore, the fixed time controller can carry out compensation in real time according to the change disturbance estimated by the fixed time observer, stable control over the pose of the aircraft is achieved, the anti-interference capability of the aircraft in the flight process is improved, and the control speed of the fixed time controller over stable flight of the aircraft is increased.

Description

Technical Field

[0001] The present invention relates to the technical field of electric vertical take-off and landing aircraft control in the low-altitude economy, and particularly to a tracking control method and a high-order full-drive system for an electric vertical take-off and landing aircraft. Background Art

[0002] As the main transportation body of urban air mobility (UAM), the electric vertical take-off and landing aircraft (eVTOL) provides new impetus for the booming development of the low-altitude economy and future transportation. At present, the UAM scenario environment is complex, and the flight and transportation task modes of eVTOL are diverse. For the packages in eVTOL logistics transportation operations, they are often not limited to solid packages, but also involve liquid packages. When the liquid packages are placed in the cargo hold of the eVTOL, during the flight, the overall center of mass of the eVTOL will inevitably shift, resulting in the failure of the eVTOL control law, directly affecting the task completion rate, and more seriously, even leading to crash accidents.

[0003] In the prior art, aiming at the possible change of the overall center of mass of the eVTOL during flight, designers usually adopt the proportional-integral-derivative (PID) control algorithm or the linear quadratic regulator (LQR) algorithm to ensure the stable flight of the aircraft.

[0004] However, using the prior art, due to the over-reliance of the PID algorithm and the LQR algorithm on feedback information, there is a problem of low control safety for the aircraft. Summary of the Invention

[0005] Based on this, it is necessary to provide a tracking control method and a high-order full-drive system for an electric vertical take-off and landing aircraft in view of the above technical problems.

[0006] The embodiments of the present invention provide a tracking control method and a high-order full-drive system for an electric vertical take-off and landing aircraft, including:

[0007] Establish a pose tracking kinematic model and a dynamic model of the aircraft;

[0008] According to the high-order full-drive system method, perform full-drive model transformation on the kinematic model and the dynamic model to obtain the pose tracking error full-drive system model of the aircraft;

[0009] For the error full-drive system model, design a fixed-time observer, where the fixed-time observer is used to quickly observe the state of the aircraft and estimate the change disturbance of the aircraft, and the change disturbance is generated by the change of the center of mass;

[0010] For the error fully actuated system model, a fixed-time controller is designed, where the fixed-time controller is used to achieve stable control of the attitude and position of the aircraft according to the varying disturbance.

[0011] In one embodiment, the establishment of the attitude tracking kinematics and dynamics models of the aircraft includes:

[0012] Based on quaternion description, the attitude tracking kinematics model and dynamics model of the aircraft are established;

[0013] In one embodiment, the kinematics model can be defined by the following expression:

[0014]

[0015] Where, represents the spatial position coordinates of the aircraft in the inertial coordinate system; R represents the rotation matrix from the body coordinate system to the inertial coordinate system, represents the transpose of the rotation matrix; V b ∈R 3*3 , represents the particle linear velocity vector of the aircraft; ω b ∈R 3 , represents the absolute angular velocity vector of the aircraft in the body coordinate system; e × represents the skew-symmetric matrix corresponding to the vector part of the error quaternion; represents ω b corresponding skew-symmetric matrix; ω e represents the error angular velocity; e0 represents the real part of the error quaternion;

[0016] The dynamics model can be defined by the following expression:

[0017]

[0018] Where, M represents the total mass of the aircraft, and the total mass includes: the load mass of the aircraft and the mass of the aircraft; represents the first derivative of the particle linear velocity vector V b ; represents ω e first derivative of; represents ω e corresponding skew-symmetric matrix; F represents the total force received by the aircraft, and the total force includes: the total upward thrust and total hub force generated by the aircraft, the total air force, and the force received due to the change of the aircraft's center of mass; g = [0 0 g] T ∈R 3 ; J∈R 3*3 , represents the total moment of inertia of the aircraft, Js ∈R 3*3 represents the constant moment of inertia of the aircraft, J var ∈R 3*3 represents the time-varying moment of inertia of the aircraft caused by the change of the center of mass, and the total moment of inertia includes the constant moment of inertia and the time-varying moment of inertia; S bv represents the position vector from the load to the center of mass of the aircraft; T air represents the total torque acting on the aircraft; ω d represents the desired angular velocity; R e represents the error rotation matrix.

[0019] In one embodiment, the error fully actuated system model can be defined by the following expression:

[0020]

[0021] where represents the position error, p d represents the desired position trajectory, e represents the error vector based on quaternion; Γ represents the augmented first matrix, represents the augmented second matrix, represents the augmented third matrix, U represents the augmented fourth matrix, D a represents the augmented fifth matrix,

[0022] In one embodiment, for the error fully actuated system model, a fixed-time observer is designed, including:

[0023] Obtain the state vector, where the state vector is related to the nominal matrix corresponding to the third matrix and the change disturbance of the aircraft;

[0024] Substitute the state vector into the error fully actuated system model to obtain the fixed-time observer.

[0025] In one embodiment, the state vector can be defined by the following expression:

[0026]

[0027] where, Δ tol represents the change disturbance of the aircraft; represents Δtol Transpose of; Denote e ζ Transpose of; Denote Transpose of; Denote the first-order derivative of e ζ First-order derivative of;

[0028] The fixed-time observer can be defined by the following expression:

[0029]

[0030] Where, Denotes the estimated value of the state vector; x2 denotes the observation error, Denotes the parameter matrix of the fixed-time observer, Denotes the parameter of the fixed-time observer, Denotes the identity matrix of the fully actuated system model.

[0031] In one embodiment, it further includes:

[0032] According to the implicit Lyapunov method, perform fixed-time input-output stability verification on the fixed-time observer to determine whether the fixed-time observer converges to the neighborhood of the origin within a fixed time.

[0033] In one embodiment, designing a fixed-time controller for the pose tracking error fully actuated system model includes:

[0034] Design an initial controller according to the varying disturbance estimated by the fixed-time observer;

[0035] Design the fixed-time controller according to the initial controller.

[0036] In one embodiment, the initial controller can be defined by the following expression:

[0037]

[0038] Where, Denotes the nominal matrix corresponding to the third matrix; Δ obs Denotes the observation error of the varying disturbance of the aircraft; A 0～1 Denotes the identity matrix of the fully actuated system model;

[0039] The fixed-time controller can be defined by the following expression:

[0040]

[0041] wherein, ∈ represents a parameter of the fixed-time controller.

[0042] In one embodiment, it further includes:

[0043] According to the implicit Lyapunov method, perform fixed-time input-output stability verification on the fixed-time controller to determine whether the fixed-time controller converges to a neighborhood of the origin within a fixed time.

[0044] The technical solutions provided by the embodiments of the present invention have the following advantages compared with the prior art:

[0045] A tracking control method and a high-order fully actuated system for an electric vertical takeoff and landing aircraft provided by an embodiment of the present invention, by establishing a pose tracking kinematic model and a dynamic model of the aircraft, according to the high-order fully actuated system method, perform a fully actuated model transformation on the kinematic model and the dynamic model to obtain a fully actuated system model of the pose tracking error of the aircraft. For the error fully actuated system model, design a fixed-time observer and a fixed-time controller. Through the fixed-time observer, quickly observe the state of the aircraft, estimate the change disturbance generated by the change of the center of mass during the flight of the aircraft, so that the fixed-time controller can compensate in real time according to the change disturbance estimated by the fixed-time observer, realize the stable control of the pose of the aircraft, improve the anti-interference ability during the flight of the aircraft, and the control speed of the fixed-time controller for the stable flight of the aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings here are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention.

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0048] Figure 1 It is a schematic flow chart of a tracking control method and a high-order fully actuated system for an electric vertical takeoff and landing aircraft provided by an embodiment of the present invention;

[0049] Figure 2 It is a comparison diagram of simulation experiment results provided by an embodiment of the present invention;

[0050] Figure 3 It is another comparison diagram of simulation experiment results provided by an embodiment of the present invention;

[0051] Figure 4Another comparison chart of simulation experiment results provided by the embodiments of the present invention;

[0052] Figure 5 Another comparison chart of simulation experiment results provided by the embodiments of the present invention;

[0053] Figure 6 Another comparison chart of simulation experiment results provided by the embodiments of the present invention;

[0054] Figure 7 Another comparison chart of simulation experiment results provided by the embodiments of the present invention. Detailed implementation manners

[0055] In order to more clearly understand the above objects, features and advantages of the present invention, the solution of the present invention will be further described below. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0056] In the following description, many specific details are set forth to fully understand the present invention, but the present invention can also be implemented in other ways different from those described herein; obviously, the embodiments in the specification are only a part of the embodiments of the present invention, rather than all the embodiments.

[0057] As the main transportation body of urban air mobility (UAM), electric vertical take-off and landing aircraft (eVTOL) provides new impetus for the booming development of the low-altitude economy and future transportation. At present, the UAM scenario environment is complex, and the eVTOL flight and transportation task modes are diverse. For the parcels in the eVTOL logistics transportation operation, they are often not limited to solid parcels, but also involve liquid parcels. When the liquid parcels are placed in the cargo hold of the eVTOL, during the flight, the overall center of mass of the eVTOL will inevitably shift, resulting in the failure of the eVTOL control law, directly affecting the task completion rate, and more seriously, it will lead to crash accidents.

[0058] In the prior art, in view of the possible change of the overall center of mass of the eVTOL during flight, designers usually adopt a proportional-integral-derivative (PID) control algorithm or a linear quadratic regulator (LQR) algorithm to ensure the stable flight of the aircraft.

[0059] However, using the prior art, due to the over-reliance of the PID algorithm and the LQR algorithm on feedback information, there is a problem of low control safety for the aircraft.

[0060] Therefore, the present invention provides a tracking control method and a high-order full-actuation system for an electric vertical takeoff and landing aircraft. By establishing the pose tracking kinematic model and dynamic model of the aircraft, according to the high-order full-actuation system method, the full-actuation model transformation is performed on the kinematic model and dynamic model to obtain the full-actuation system model of the pose tracking error of the aircraft. For the error full-actuation system model, a fixed-time observer and a fixed-time controller are designed. The state of the aircraft is quickly observed through the fixed-time observer, and the change disturbance generated by the change of the center of mass during the flight of the aircraft is estimated, so that the fixed-time controller can compensate in real time according to the change disturbance estimated by the fixed-time observer, realize the stable control of the pose of the aircraft, improve the anti-interference ability during the flight of the aircraft, and the control speed of the fixed-time controller for the stable flight of the aircraft.

[0061] In one embodiment, as Figure 1 shown, Figure 1 is a schematic flow chart of a tracking control method and a high-order full-actuation system for an electric vertical takeoff and landing aircraft provided by an embodiment of the present invention. In the present invention, a quadrotor UAV is used as the basic model of the cargo aircraft, but it is not limited thereto. The present invention does not specifically limit, and those skilled in the art can set it according to the actual situation. The specific steps are as follows:

[0062] S10: Establish the pose tracking kinematic model and dynamic model of the aircraft.

[0063] Specifically, for the aircraft, establish the pose tracking kinematic model and dynamic model of the aircraft.

[0064] Optionally, on the basis of the above embodiment, in some embodiments of the present invention, one implementation manner of S10 may be:

[0065] S101: Based on the quaternion description, establish the pose tracking kinematic model and dynamic model of the aircraft.

[0066] Among them, the quaternion refers to a simple hypercomplex number. Let the quaternion be expressed as q0, q1, q2, q3, then the quaternion description is: Q = [q0 q T T , Q ∈ R 4 , q = [q1 q2 q3] T , q ∈ R 3 , representing the rotational motion in three-dimensional space.

[0067] Specifically, for the aircraft, by introducing the quaternion description, establish the pose tracking kinematic model and dynamic model of the aircraft.

[0068] ​Optionally, based on the above embodiments, in some embodiments of the present invention, the kinematic model may be defined by the following expression:

[0069]

[0070] Wherein, represents the spatial position coordinates of the aircraft in the inertial coordinate system; R represents the rotation matrix from the body coordinate system to the inertial coordinate system, R T represents the transpose of the rotation matrix; V b ∈R 3*3 represents the linear velocity vector of the mass point of the aircraft; ω b ∈R 3 represents the absolute angular velocity vector of the aircraft in the body coordinate system; e × represents the skew-symmetric matrix corresponding to the vector part of the error quaternion; represents ω b corresponding skew-symmetric matrix; ω e represents the error angular velocity; e0 represents the real part of the error quaternion.

[0071] Optionally, based on the above embodiments, in some embodiments of the present invention, the dynamic model may be defined by the following expression:

[0072]

[0073] Wherein, M represents the total mass of the aircraft, and the total mass includes: the load mass of the aircraft and the mass of the aircraft; represents the first derivative of the linear velocity vector V b ; represents the first derivative of ω e ; represents the skew-symmetric matrix corresponding to ω e ; F represents the total force received by the aircraft, and the total force includes: the total upward thrust and total hub force generated by the aircraft, the total air force, and the force received due to the change of the center of mass of the aircraft; g = [0 0 g] T ∈R 3 ; J ∈ R 3*3 represents the total moment of inertia of the aircraft, J s ∈R 3*3 represents the constant moment of inertia of the aircraft, J var ∈R 3*3 represents the time-varying moment of inertia caused by the change of the center of mass of the aircraft, and the total moment of inertia includes the constant moment of inertia and the time-varying moment of inertia; S bv represents the position vector from the load to the center of mass of the aircraft; T air represents the total torque received by the aircraft; ω dRepresents the desired angular velocity; R e Represents the error rotation matrix.

[0074] S11: According to the high - order fully - actuated system method, perform a fully - actuated model transformation on the kinematic model and the dynamic model to obtain the fully - actuated system model of the pose tracking error of the aircraft.

[0075] Among them, by performing a fully - actuated model transformation on the kinematic model and the dynamic model through the high - order fully - actuated system method, non - linear control of the model can be achieved.

[0076] Specifically, for the pose tracking kinematic model and the dynamic model of the aircraft, according to the high - order fully - actuated system method, perform a fully - actuated model transformation on the kinematic model and the dynamic model to obtain the fully - actuated system model of the pose tracking error of the aircraft.

[0077] Optionally, on the basis of the above - mentioned embodiments, in some embodiments of the present invention, the error fully - actuated system model can be defined by the following expression:

[0078]

[0079] Wherein, Represents the position error, p d Represents the desired position trajectory, e represents the error vector based on quaternion; Γ represents the augmented first matrix, Represents the augmented second matrix, Represents the augmented third matrix, U represents the augmented fourth matrix, D a Represents the augmented fifth matrix,

[0080] S12: Design a fixed - time observer for the error fully - actuated system model.

[0081] Among them, the fixed - time observer is used to quickly observe the state of the aircraft and estimate the change disturbance caused by the change of the center of mass of the aircraft.

[0082] Specifically, design a fixed - time observer for the error fully - actuated system model, so that the state of the aircraft can be quickly observed through the fixed - time observer, and the change disturbance caused by the change of the center of mass of the aircraft during flight can be estimated.

[0083] Optionally, on the basis of the above - mentioned embodiments, in some embodiments of the present invention, one implementation manner of S12 can be:

[0084] S121: Obtain the state vector.

[0085] Wherein, the state vector is related to the nominal matrix corresponding to the third matrix and the change perturbation of the aircraft, and is used to ensure the strong robustness of the controller that can control the aircraft to fly stably when the center of mass changes and generates perturbations during the flight of the aircraft.

[0086] Optionally, based on the above embodiments, in some embodiments of the present invention, the state vector can be defined by the following expression:

[0087]

[0088] Wherein, Δ tol The change perturbation of the aircraft; Denotes the transpose of Δ tol ; Denotes the transpose of e ζ ; Denotes The transpose of; Denotes the first derivative of e ζ ;

[0089] S121: Substitute the state vector into the error fully actuated system model to obtain a fixed-time observer.

[0090] Specifically, obtain the state vector related to the nominal matrix corresponding to the third matrix and the change perturbation of the aircraft, and substitute the state vector into the error fully actuated system model to obtain a fixed-time observer.

[0091] Optionally, based on the above embodiments, in some embodiments of the present invention, the fixed-time observer can be defined by the following expression:

[0092]

[0093] Wherein, Denotes the estimated value of the state vector; x2 denotes the observation error, Denotes the parameter matrix of the fixed-time observer, Denotes the parameter of the fixed-time observer, Denotes the identity matrix of the fully actuated system model.

[0094] Optionally, based on the above embodiments, in some embodiments of the present invention, in order to determine whether the fixed-time observer is fixed-time input-output stable and converges to a neighborhood of the origin within a fixed time, based on this, when designing the fixed-time observer, it further includes: verifying the fixed-time input-output stability of the fixed-time observer according to the implicit Lyapunov method to determine whether the fixed-time observer converges to a neighborhood of the origin within a fixed time.

[0095] Optionally, based on the above embodiments, in some embodiments of the present invention, an implementation manner of verifying the fixed-time input-output stability of the fixed-time observer to determine whether the fixed-time observer converges to a neighborhood of the origin within a fixed time may be:

[0096] Specifically, for the nonlinear system: If there exists a binary continuous function Q(V, x) that satisfies the following five preset lemmas, it indicates that the nonlinear system is fixed-time input-output stable and converges to a neighborhood of the origin within a fixed time.

[0097] Among them, the five preset lemmas include:

[0098] Preset Lemma 1: For the binary continuous function Q(V, x), it is continuously differentiable within the domain R ≥0 ×R n \{0}.

[0099] Preset Lemma 2: For the binary continuous function Q(V, x), for any x ∈ R n \{0}, there exists Q(V, x) = 0.

[0100] Preset Lemma 3: For Ω := {(V, x) ∈ R n+1 : Q(V, x) = 0}, it satisfies:

[0101]

[0102] Preset Lemma 4: For the binary continuous function Q(V, x), when V ∈ R ≥0 and x ∈ R n \{0}, it satisfies

[0103] Preset Lemma 5: For the binary continuous function Q(V, x), Q(V, x) ∈ Ω, it satisfies:

[0104] Among them, c1, c2, and c3 are all greater than 0, δ1 ∈ K ∞ , 0 < α < 1, β > 1.

[0105] Furthermore, for the nonlinear system: Before it can be stated that a nonlinear system is fixed-time input-output stable, it is necessary to further prove that the above proof method is reasonable if there exists a binary continuous function Q(V, x) that satisfies the following five preset lemmas.

[0106] Specifically, if there exists a continuously bounded function V(x): R n →R + ∪{0} that satisfies two preset conditions, then it can be stated that the nonlinear system: is fixed-time input-output stable and converges to a neighborhood of the origin within a fixed time.

[0107] Among them, preset condition 1: when the continuously bounded function V(x) = 0, there exists: x(t) = 0.

[0108] Preset condition 2: for any solution corresponding to the nonlinear system, the variable x satisfies: greater than 0, ψ belongs to 0 - 1, φ greater than 1.

[0109] The proof process is as follows:

[0110] First, referring to the related technology, it can be known that the nonlinear system converges to a neighborhood of the origin within a fixed time.

[0111] Furthermore, referring to the related technology, it can be known that for the nonlinear system, there exists an implicit Lyapunov function that is fixed-time input-output stable. When ‖x(t)‖ ≥ χ(‖d‖), it can be obtained that: and it satisfies ψ1(‖x‖) ≤ V(x) ≤ ψ2(‖x‖), ‖x‖ ≥ χ(‖d‖) → DV(x)f(x, d) ≤ -γ(‖x‖). Define the set U: U = {x: V(x) ≥ ψ2°χ(‖d‖ [0,∞) )}, for any x ∈ U, there is ψ2(‖x‖) ≥ V(x) ≥ ψ2°χ(‖d‖ [0,∞) ), then R n \U is a time-invariant attractor of x. When X(t, x0, d) ∈ U, according to the comparison lemma and direct integration, we get a function φ(r, t) such that ‖X(t, x0, d)‖ ≤ φ(‖x0‖, t) holds, and when then, there is V(x) < ψ2°χ(‖d‖) [0,∞) ), and we get ‖x‖ ≤ θ(‖d‖) [0,∞) ), where, Also, since R n \U is an invariant set, then when When there is ‖X(t,x0,d)‖≤θ(‖d‖) [0,∞) ). Based on this, it is determined that ‖X(t,x0,d)‖≤φ(‖x0‖,t)+θ(‖d‖) [0,∞) ), which satisfies the implicit fixed-time Lyapunov input-to-output stability.

[0112] According to the fixed-time observer, the fixed-time observer error model is obtained as follows:

[0113]

[0114] According to the implicit Lyapunov, the implicit Lyapunov function is determined as:

[0115]

[0116] where D r2i represents a diagonal matrix, Determine the parameters of D r2i as: where p2 is a symmetric positive definite matrix, i = 1, 2, 3.

[0117] It should be noted that the fixed-time observer error model is the above nonlinear system, and the implicit Lyapunov function is the above continuous function. Based on this, the specific proof process for verifying the fixed-time input-to-output stability of the fixed-time observer according to the above five preset lemmas, the fixed-time observer error model, and the implicit Lyapunov function is as follows:

[0118] First, according to the implicit Lyapunov function, it can be seen that it satisfies Preset Lemma 1, Preset Lemma 2, and Preset Lemma 3.

[0119] Furthermore, calculating the partial derivative of the implicit Lyapunov function Q2 with respect to V2 gives:

[0120]

[0121] where Determine When i = 1, 2, 3, V i ∈R + when, the matrix inequality has a feasible solution, then there is Then it is determined that the implicit Lyapunov function satisfies Preset Lemma 4.

[0122] Furthermore, by scaling the implicit Lyapunov function, the first inequality is obtained as:

[0123]

[0124] Based on the first inequality, the partial derivative of the implicit Lyapunov function \(Q_2\) with respect to \(x_2\) can be calculated as follows:

[0125]

[0126] After taking the partial derivative of the implicit Lyapunov function, add and subtract the first preset term from the formula after taking the partial derivative to further obtain:

[0127]

[0128] where the first preset term is: denotes a preset matrix; and \(\zeta_2\in R\) + , the matrix \(\Xi\) 2i is:

[0129]

[0130] Assume that when there is a feasible solution to the matrix inequality , according to the Schur complement theorem, determine \(\Xi\) 2i \(<0\). Further, scale according to the preset equation to obtain the second inequality as follows:

[0131]

[0132] where \(\varphi\) 2i \(>0, i = 1, 2, 3\); the preset equation can be defined by the following expression:

[0133]

[0134] Furthermore, combining the first inequality and the second inequality, the third inequality is obtained as:

[0135]

[0136]

[0137] For the third inequality, according to the Rayleigh quotient and matrix operations, when \(x_2\) satisfies the preset condition, then there is:

[0138]

[0139] where \(\mu\) 21 , \(\mu\) 22 , \(\mu\) 23 \(>0, \delta_2\in K\) ∞ , based on this, it is determined that the implicit Lyapunov function satisfies the preset Lemma 5.

[0140] The preset condition can be defined by the following expression:

[0141]

[0142] In summary, if the implicit Lyapunov function satisfies the five preset lemmas, it is determined that the fixed-time observer is fixed-time input-output stable and converges to the neighborhood of the origin within a fixed time.

[0143] Furthermore, it should be noted that the parameters of the fixed-time observer can be determined according to the preset matrix inequality. The preset matrix inequality can be defined by the following expressions:

[0144]

[0145] Specifically, when there exists , referring to the prior art, determine the matrix parameters that make the fixed-time observer stable and increase the parameter starting from 0 until the control performance of the fixed-time observer deteriorates due to actuator saturation, and then determine the value of the parameter.

[0146] S13: Design a fixed-time controller for the error fully actuated system model.

[0147] Among them, the fixed-time controller is used to achieve the attitude stabilization control of the aircraft according to the varying disturbance.

[0148] Specifically, for the error fully actuated system model, design a fixed-time controller, so that the attitude stabilization control of the aircraft can be achieved through the fixed-time controller according to the varying disturbance.

[0149] Optionally, based on the above embodiments, in some embodiments of the present invention, one implementation manner of S13 may be:

[0150] S131: Design an initial controller according to the varying disturbance estimated by the fixed-time observer.

[0151] Optionally, based on the above embodiments, in some embodiments of the present invention, the initial controller can be defined by the following expressions:

[0152]

[0153] Among them, represents the nominal matrix corresponding to the third matrix; Δ obs represents the observation error of the varying disturbance of the aircraft; A 0～1 represents the identity matrix of the fully actuated system model.

[0154] S132: Design a fixed-time controller according to the initial controller.

[0155] Specifically, after obtaining the initial controller, in order to improve the rapidity of the controller to control the stable flight of the aircraft, a fixed-time controller is designed according to the initial controller.

[0156] Optionally, on the basis of the above embodiments, in some embodiments of the present invention, the fixed-time controller can be defined by the following expression:

[0157]

[0158] Optionally, on the basis of the above embodiments, in some embodiments of the present invention, in order to determine whether the fixed-time controller converges to the neighborhood of the origin within a fixed time, so as to determine the fixed-time input-output stability of the fixed-time controller. Based on this, when designing the fixed-time controller, it further includes: verifying the fixed-time input-output stability of the fixed-time controller according to the implicit Lyapunov method.

[0159] The specific verification process is as follows:

[0160] According to the fixed-time observer, a fixed-time observer error model is obtained.

[0161] Specifically, substituting the fixed-time controller into the error fully actuated system model, a linear closed-loop time-invariant system is obtained:

[0162]

[0163] According to the introduction of the preset variable and the preset variable the linear closed-loop time-invariant system can be transformed into the following state-space form, that is, the fixed-time controller error model is obtained as:

[0164]

[0165] Among them, for the matrix ∏(X1,∈), there is

[0166] According to the implicit Lyapunov, the implicit Lyapunov function is determined as:

[0167]

[0168] Among them, D r1i represents a diagonal matrix, Determine the parameters of D r1i as: 0 < ∈ < 1, p2 is a symmetric positive definite matrix, i = 1, 2, 3.

[0169] It should be noted that the fixed-time controller error model is the above-mentioned non-linear system, and the implicit Lyapunov function is the above-mentioned continuous function. Based on this, the specific proof process for verifying the fixed-time input-output stability of the fixed-time controller according to the above five preset lemmas, the fixed-time controller error model, and the implicit Lyapunov function is as follows:

[0170] First, according to the implicit Lyapunov function, it can be known that it satisfies Preset Lemma 1, Preset Lemma 2, and Preset Lemma 3.

[0171] Furthermore, calculating the partial derivative of the implicit Lyapunov function Q1 with respect to V1 gives:

[0172]

[0173] where Determine When i = 1, 2, 3, τ i ∈R + If the matrix inequality has a feasible solution, then Then the implicit Lyapunov function satisfies Preset Lemma 4.

[0174] Furthermore, scaling the implicit Lyapunov function gives the fourth inequality:

[0175]

[0176] Based on the fourth inequality, calculating the partial derivative of the implicit Lyapunov function Q1 with respect to x1 gives:

[0177]

[0178] After taking the partial derivative of the implicit Lyapunov function, adding and subtracting the second preset term to the formula after taking the partial derivative, we further obtain:

[0179]

[0180]

[0181] where the second preset term is:

[0182] and ζ1 ∈ R + , and the matrix Ξ 1i is:

[0183]

[0184] Assuming that when the matrix inequality has a feasible solution, according to the Schur complement theorem, determine Ξ 1i< 0, and further, scaling according to a preset equation to obtain the fifth inequality as follows:

[0185]

[0186] Wherein, The preset equation can be defined by the following expression:

[0187]

[0188] Furthermore, combining the fourth inequality and the fifth inequality, the sixth inequality is obtained as:

[0189]

[0190] For the sixth inequality, according to the Rayleigh quotient and matrix operations, when x1 satisfies the preset conditions, then there is:

[0191]

[0192] Wherein, μ 11 , μ 12 , μ 13 > 0, δ1 ∈ K ∞ , based on this, it is determined that the implicit Lyapunov function satisfies the preset Lemma 5.

[0193] The preset conditions can be defined by the following expression:

[0194]

[0195] In summary, since the implicit Lyapunov function satisfies five preset lemmas, it is determined that the fixed-time controller is fixed-time input-output stable and converges to the neighborhood of the origin within a fixed time.

[0196] Furthermore, it should be noted that the parameters of the fixed-time controller can be determined according to the preset matrix inequality. The preset matrix inequality can be defined by the following expression:

[0197]

[0198] Specifically, when there is ∈ = 0, referring to the prior art, the matrix parameters that make the fixed-time controller stable are determined And the parameter ∈ is increased starting from 0 until the control performance of the fixed-time observer deteriorates due to actuator saturation, and the value of the parameter is determined.

[0199] Thus, a tracking control method and a high-order all-drive system for an electric vertical takeoff and landing aircraft provided by the present invention establish a pose tracking kinematic model and a dynamic model of the aircraft, and according to the high-order all-drive system method, perform all-drive model transformation on the kinematic model and the dynamic model to obtain a pose tracking error all-drive system model of the aircraft. For the error all-drive system model, a fixed-time observer and a fixed-time controller are designed. The state of the aircraft is quickly observed through the fixed-time observer, and the change disturbance generated by the change of the center of mass during the flight of the aircraft is estimated, so that the fixed-time controller can compensate in real time according to the change disturbance estimated by the fixed-time observer, realize the stable control of the pose of the aircraft, improve the anti-interference ability of the aircraft during the flight, and the control speed of the fixed-time controller for the stable flight of the aircraft.

[0200] Optionally, on the basis of the above embodiments, in some embodiments of the present invention, in order to verify that the present invention can improve the control of the fixed-time controller for the stable flight of the aircraft compared with the prior art. A simulation experiment comparison verification is carried out using the PID algorithm. Refer to Figures 2 to 7 As shown, the error corresponding to the algorithm adopted by the present invention can converge faster than the error corresponding to the PID algorithm, which shows that the algorithm adopted by the present invention is significantly better than the PID algorithm.

[0201] It should be understood that although Figures 1 to 7 the steps in the flowchart of Figures 1 to 7 are shown in sequence according to the indication of the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless there is a clear indication in this article, the execution of these steps has no strict order restriction, and these steps can be executed in other orders. Moreover,

[0202] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memories. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static random access memory (SRAM) and dynamic random access memory (DRAM), etc.

[0203] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0204] The above-described embodiments merely represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the invention patent should be subject to the appended claims.

Claims

1. A tracking control method and a high-order all-wheel drive system for an electric vertical takeoff and landing aircraft, characterized in that, Including: Establish a pose tracking kinematic model and a dynamic model of the aircraft; According to the high-order fully actuated system method, perform a full-actuated model transformation on the kinematic model and the dynamic model to obtain a full-actuated system model of the pose tracking error of the aircraft; For the error full-actuated system model, design a fixed-time observer, where the fixed-time observer is used to quickly observe the state of the aircraft and estimate the change disturbance of the aircraft, and the change disturbance is generated by the change of the center of mass; For the error full-actuated system model, design a fixed-time controller, where the fixed-time controller is used to achieve stable control of the pose of the aircraft according to the change disturbance.

2. The method and the high-order all-wheel drive system according to claim 1, characterized in that, The establishment of the pose tracking kinematics and dynamics model of the aircraft includes: Based on quaternion description, establish the pose tracking kinematic model and the dynamic model of the aircraft.

3. The method and the high-order all-wheel drive system according to claim 2, characterized in that, The kinematic model can be defined by the following expression: Among them, represents the spatial position coordinates of the aircraft in the inertial coordinate system; R represents the rotation matrix from the body coordinate system to the inertial coordinate system, R T represents the transpose of the rotation matrix; V b ∈R 3*3 , represents the linear velocity vector of the mass point of the aircraft; ω b ∈R 3 , represents the absolute angular velocity vector of the aircraft in the body coordinate system; e × represents the skew-symmetric matrix corresponding to the vector part of the error quaternion; represents ω b corresponding skew-symmetric matrix; ω e represents the error angular velocity; e0 represents the real part of the error quaternion; The dynamic model can be defined by the following expression: Among them, M represents the total mass of the aircraft, and the total mass includes: the payload mass of the aircraft and the mass of the aircraft; Represents the linear velocity vector V of the particle b The first derivative; Represents ω e The first derivative; Represents ω e The corresponding skew-symmetric matrix; F represents the total force received by the aircraft, and the total force includes: the total upward thrust and total hub force generated by the aircraft, the total air force, and the force received due to the change of the aircraft's center of mass; g = [0 0 g] T ∈R 3 ; J ∈ R 3*3 , represents the total moment of inertia of the aircraft, J s ∈R 3*3 , represents the constant moment of inertia of the aircraft, J var ∈R 3*3 , represents the time-varying moment of inertia caused by the change of the center of mass of the aircraft, and the total moment of inertia includes the constant moment of inertia and the time-varying moment of inertia; S bv Represents the position vector from the payload to the center of mass of the aircraft; T air Represents the total torque received by the aircraft; ω d Represents the desired angular velocity; R e Represents the error rotation matrix.

4. The method and the high-order all-wheel drive system according to claim 3, characterized in that, The error full-actuated system model can be defined by the following expression: Among them, represents the position error, p d represents the desired position trajectory, and e represents the error vector based on quaternion; Γ represents the augmented first matrix, represents the augmented second matrix, represents the augmented third matrix, U represents the augmented fourth matrix, D a represents the augmented fifth matrix, 5. The method and high-order all-wheel drive system according to claim 4, characterized in that, The design of the fixed-time observer for the error full-actuated system model includes: Obtain a state vector, where the state vector is related to the nominal matrix corresponding to the third matrix and the change disturbance of the aircraft; Substitute the state vector into the error full-actuated system model to obtain the fixed-time observer.

6. The method and high-order all-wheel drive system according to claim 5, characterized in that, The state vector can be defined by the following expression: where, Δ tol represents the change disturbance of the aircraft; represents tol transpose of Δ; represents ζ transpose of e; represents transpose of; represents the first derivative of e ζ ; The fixed-time observer can be defined by the following expression: wherein, represents the estimated value of the state vector; x2 represents the observation error, represents the parameter matrix of the fixed-time observer, represents the parameter of the fixed-time observer, represents the identity matrix of the fully actuated system model.

7. The method and the high-order all-wheel drive system according to claim 6, characterized in that, It also includes: According to the implicit Lyapunov method, perform a fixed-time input-output stability verification on the fixed-time observer to determine whether the fixed-time observer converges to a neighborhood of the origin within a fixed time.

8. The method and high-order all-wheel drive system according to claim 7, characterized in that The design of the fixed-time controller for the pose tracking error full-actuated system model includes: Design an initial controller according to the change disturbance estimated by the fixed-time observer; Design the fixed-time controller according to the initial controller.

9. The method and high-order all-wheel drive system according to claim 8, characterized in that, The initial controller can be defined by the following expression: Among them, represents the nominal matrix corresponding to the third matrix; Δ obs represents the observation error of the change disturbance of the aircraft; A 0～1 represents the identity matrix of the all-wheel drive system model; The fixed-time controller can be defined by the following expression: where ∈ represents the parameter of the fixed-time controller.

10. The method and high-order all-wheel drive system according to claim 9, characterized in that, It also includes: According to the implicit Lyapunov method, perform a fixed-time input-output stability verification on the fixed-time controller to determine whether the fixed-time controller converges to a neighborhood of the origin within a fixed time.

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