Self-adaptive robust control method for side-rotor unmanned aerial vehicle

Abstract

The invention belongs to the technical field of nonlinear position and attitude control of a side-rotor unmanned aerial vehicle, and aims to improve the strong nonlinear coupling effect, rotor slip flow interference and anti-interference capability of external unknown wind interference of the side-rotor unmanned aerial vehicle in a helicopter mode and realize high-precision position and attitude tracking control of the side-rotor unmanned aerial vehicle. Therefore, the technical scheme adopted by the invention is as follows: according to the adaptive robust control method for the side-rotor unmanned aerial vehicle, a nonlinear control strategy under a three-dimensional track of the side-rotor unmanned aerial vehicle is constructed by utilizing an adaptive backstepping method and robust integral symbol error control, and the nonlinear control strategy is divided into a position loop control strategy and an attitude loop control strategy; wherein a position loop control strategy is constructed by using an adaptive backstepping method, and an attitude loop control strategy is constructed by using robust integral symbol error control. The method is mainly applied to the manufacturing occasion of the side rotor unmanned aerial vehicle.

Description

Technical Field

[0001] The present invention belongs to the technical field of nonlinear attitude control of side-rotor unmanned aerial vehicles. Specifically, it relates to an adaptive robust control method for side-rotor unmanned aerial vehicles. Background Technique

[0002] The side rotor is a multi-layer flow high-speed transport aircraft (such as attached Figure 1As shown in [reference], it has demonstrated great value in the fields of military transportation, disaster relief, logistics delivery, urban transportation, etc. (Journal: IEEE Transactions on Intelligent Vehicles; Authors: Jiangcheng Su, Hailong Huang, Hong Zhang, Yutong Wang, and Fei-Yue Wang; Publication Date: 2024; Article Title: eVTOL Performance Analysis: A Review From Control Perspectives; Pages: 4877–4889). It combines the advantages of fixed-wing aircraft and rotorcraft, and exhibits different flight characteristics by switching between different flight modes. The tiltrotor requires less landing space than fixed-wing aircraft and has a faster cruising speed and longer range than conventional helicopters (Conference: 2016 IEEE International Conference on Information and Automation (ICIA); Authors: Chao Chen, Lincheng Shen, Daibing Zhang, and Jiyang Zhang; Publication Date: 2016; Article Title: Mathematical modeling and control of a tiltrotor UAV; Pages: 2016–2021). Compared with helicopters and fixed-wing aircraft, the tiltrotor has a wider flight envelope and redundant actuator mechanisms (Book: The History of the XV-15 Tilt Rotor Research Aircraft: From Concept to Flight; Authors: Martin D. Maisel, Demo J. Giulianetti, and Daniel C. Dugan; Publication Date: 2001). However, the strong nonlinearity and high coupling characteristics brought about by the redundant mechanisms pose significant challenges to tiltrotor control.Especially in the helicopter mode, the interaction between the rotor slipstream and the wing aerodynamics, as well as the coupling effects between the blade flapping dynamics and the airframe flexibility and rigidity, jointly result in strong nonlinear and time-varying characteristics of the system (Conference: 2016 Chinese Control and Decision Conference (CCDC); Authors: Ke Lu, Chunsheng Liu, Zhengzhong Wang, and Weihong Wang; Publication Date: 2016; Article Title: Modeling and control of tilt-rotor aircraft; Pages: 550–553), which poses a severe challenge to the robustness of the flight control system.

[0003] In 2020, L. Bauersfeld proposed a side-rotor control scheme based on switched hybrid proportional-integral-derivative control (FPID) (Conference: 2020 28th Mediterranean Conference on Control and Automation (MED); Authors: L. Bauersfeld and G. Ducard; Publication Date: 2020; Article Title: Fused-PID Control for Tilt-Rotor VTOL Aircraft; Pages: 703–708), where the FPID control scheme generates corresponding attitude expected values according to the pilot's speed command. The FPID control algorithm consists of two independent and uncorrelated proportional-integral-derivative control algorithms (PID), one for handling fixed-wing aircraft and the other designed specifically for multi-rotor aircraft. The outputs of the two control algorithms are fused for the control surface control value according to the airspeed to obtain the attitude set value and the swashplate tilt angle of the side-rotor aircraft. When the uncertainty of the aircraft mechanical model is large, the PID control has certain limitations. In response to this, in 2017, Tingting Liang proposed an adaptive backstepping control algorithm using a dynamic surface (Conference: 2017 29th Chinese Control And Decision Conference (CCDC); Authors: Tingting Liang, Weihong Wang, Sentang Wu, and Ke Lu; Publication Date: 2017; Article Title: Nonlinear attitude control of tiltrotor aircraft based on dynamic surface adaptive backstepping; Pages: 603–608). This control algorithm designs the control algorithm of the side-rotor aircraft in the fixed-wing mode using the design method of the dynamic surface. This method comprehensively considers the problem of uncertainty encountered by the side-rotor aircraft during flight, including the linear parameterization part and the unmodeled characteristics of the dynamics.A hybrid control method based on model predictive control (MPC) was proposed by L. Bauersfeld et al. (Journal: IEEE Transactions on Aerospace and Electronic Systems; Authors: Leonard Bauersfeld, Lukas Spannagl, Guillaume J. J. Ducard, and Christopher H. Onder; Publication Date: 2021; Article Title: MPC Flight Control for a Tilt-Rotor VTOL Aircraft; Pages: 2395–2409). The developed MPC control algorithm obtains speed commands from the pilot, then calculates the optimal attitude setpoint and propeller tilt angle, and provides them to the internal attitude control algorithm. However, the performance of MPC is affected by the model accuracy, which is usually unavailable during the transition process. A sliding mode control algorithm based on the appointed time prescribed performance function (ATPPF) was proposed (Journal: Aerospace Science and Technology; Authors: Danyu Li, Liang Zhang, Chongsen Mo, and Naigang Cui; Publication Date: 2024; Article Title: Application of improved appointed time control in helicopter mode of a tilt-rotor eVTOL aircraft; Pages: 109447). By setting the time parameters of the ATPPF and the predefined time control algorithm to the same value, the actual error will converge to near zero at the appointed time. However, for different systems, this algorithm needs to be adapted by modifying different parameters, making it difficult to be universal and put into practical use.

[0004] Although the above studies have made significant progress in the field of tilt-rotor aircraft control, it should be noted that the existing methods are generally based on two types of key assumptions: the dynamics model of the tilt-rotor aircraft is relatively simplified through small perturbation linearization or actuator decoupling processing; the nonlinear coupling effect between the rotor tilting mechanism and aerodynamic interference is limited within a specific operating condition range. Such assumptions have good engineering applicability in low-speed and small-angle maneuvering scenarios. However, it still poses certain challenges when facing three-dimensional trajectories and strongly nonlinear coupled tilt-rotor systems. Therefore, it is necessary to design a nonlinear control method for the problems of strong nonlinear coupling effects, model uncertainties caused by rotor slipstream interference, and unmodeled dynamics caused by unknown external wind disturbances in the low-altitude dense atmosphere environment of tilt-rotor unmanned aircraft, in order to ensure high-precision agile tracking control of tilt-rotor unmanned aircraft. Summary of the Invention

[0005] To overcome the deficiencies of the prior art, the present invention aims to improve the anti-interference ability of a side-rotor unmanned aerial vehicle (UAV) under the helicopter mode against strong non-linear coupling effects, rotor slipstream interference, and external unknown wind disturbances, and to achieve high-precision position and attitude tracking control of the side-rotor UAV. To this end, the technical solution adopted by the present invention is an adaptive robust control method for a side-rotor UAV, which constructs a non-linear control strategy for the three-dimensional trajectory of the side-rotor UAV by using adaptive backstepping and robust integral sign error control. The non-linear control strategy is divided into a position loop control strategy and an attitude loop control strategy. Among them, the position loop control strategy is constructed by using adaptive backstepping, and the attitude loop control strategy is constructed by using robust integral sign error control.

[0006] The specific steps are as follows:

[0007] 1) Establish the dynamic model of the side-rotor UAV

[0008] Define the inertial coordinate system {I} and the body coordinate system {B} as right-handed orthogonal inertial coordinate systems. The origin of the inertial coordinate system {I} is located at a point on the ground, I x points to the due north direction, I z is parallel to the gravity direction downward. The origin of the body coordinate system {B} is located at the mass center of the side-rotor UAV, B x points to the forward direction of the body, B z is perpendicular to the wing downward. Based on the Newton-Euler method, the dynamic model of the side-rotor UAV is derived as follows:

[0009]

[0010] Among them, the vector represents the position vector, the vector represents the velocity vector, m and g respectively represent the body mass and the gravitational acceleration, the matrix represents the attitude rotation from the coordinate system {B} to the coordinate system {I}, the matrix vector represents the attitude angle vector, represents the angular velocity vector, the matrix represents the inertia matrix of the side-rotor UAV, the matrix S represents the skew-symmetric matrix expanded from the vector η(t), the vector and the vector respectively represent the total body thrust and the control input torque vector in the body coordinate system, and respectively represent the external disturbances of the position loop and the attitude loop;

[0011] External disturbance is continuously differentiable and the upper bound of its second-order time derivative is bounded, At the same time, ||dp || ≤ ∈1, ||d τ || ≤ ∈2, where ∈1 and ∈2 are positive constants;

[0012] When constructing the dynamic model of the side-rotor UAV, it is considered that the total thrust T of the airframe B and torque τ are composed of six parts: the left rotor (lr), right rotor (rr), wing (w), fuselage (b), horizontal tail (h), and vertical tail (v) of the side-rotor UAV, and are expressed as:

[0013]

[0014] Among them, the forces and moments generated by the rotor parts (lr, rr) are obtained by solving through the Pitt-Peters dynamic inflow theory (Pitt-Peters) and the blade flapping motion model. The forces and moments generated by the wing (w) are solved by dividing the slipstream area. The fuselage (b) and the tail fins (h, v) are obtained by using empirical formulas and interpolation methods;

[0015] 2) Pose tracking control design

[0016] Decouple the dynamic model of the side-rotor UAV into an attitude control model and a position control model, and conduct control design respectively:

[0017] 2.1 Position loop control law design

[0018] Define the position tracking error of the side-rotor UAV Linear velocity tracking error Auxiliary vector as:

[0019] e p = p d - p, (3)

[0020] e v = v d - v, (4)

[0021]

[0022] where is a positive definite gain matrix. Take the first derivative of e v (t) with respect to time, and substitute the second equation in Equation (1) into the equation to obtain the open-loop dynamic equation of e v (t):

[0023]

[0024] Based on the open-loop dynamic equation in Equation (6) , design the non-linear robust control input of the side-rotor UAV position loop as:

[0025]

[0026] Consider the external disturbance d p (t) cannot be directly measured, and design the variable error of the external disturbance estimator and the velocity of the external disturbance estimator variable as

[0027]

[0028] where is a positive definite gain matrix;

[0029] 2.2 Attitude loop control law design

[0030] Define the attitude tracking error of the side rotor UAV and the angular velocity tracking error as follows:

[0031]

[0032] where represents the desired attitude angle, represents the desired angular velocity, and define the auxiliary filtering error function and as:

[0033] r1 = e ω + λ1e η (11)

[0034]

[0035] where and are both positive definite gain matrices. Take the derivative of r2(t) with respect to time and multiply both sides of the formula on the left by the inertia matrix J of the side rotor UAV to obtain the open-loop dynamic equation of the auxiliary filtering error function Jr2(t):

[0036]

[0037] where the auxiliary vector function and the auxiliary vector function are defined as follows:

[0038]

[0039] The upper bound of

[0040]

[0041] where ρ represents a globally invertible non-decreasing function, z = [eη r1 r2];

[0042] Based on the open-loop dynamic equation of r2(t) in Equation (15), the attitude non-linear robust control input of the side-rotor UAV is designed as:

[0043]

[0044] where represents the positive gain coefficient matrix, r1(0) represents the initial value of r1(t), and sgn(·) represents the standard sign function. Taking the first derivative of Equation (20) with respect to time gives:

[0045]

[0046] Substituting Equation (21) into Equation (15), the closed-loop dynamic equation of r2(t) is obtained as:

[0047]

[0048] Design the auxiliary functions L(t) and Q(t) as follows:

[0049] L = r2 T (M d -β η sgn(r1)) (21)

[0050]

[0051] When the control gain β η and the auxiliary variable ζ satisfy the following sufficient conditions, it can be guaranteed that Q(t) ≥ 0, holds:

[0052] ζ := β η |r1(0)| - r1(0)M d (0) (23)

[0053]

[0054] Under the following sufficient conditions, the non-linear robust control method can guarantee that the closed-loop position tracking error converges exponentially to zero:

[0055]

[0056] where is the diagonal gain matrix.

[0057] The verification steps for the position loop stability proof are as follows:

[0058] Select the Lyapunov candidate function V p (t) as follows:

[0059]

[0060] Derive and simplify the derivative of V p (t) to obtain:

[0061]

[0062] Based on Equation (11) is negative semi - definite. Based on Barbalat's lemma, it can be proved that the described adaptive backstepping position control method is uniformly globally stable;

[0063] The verification steps for the attitude loop stability proof are as follows:

[0064] Design the Lyapunov candidate function V η (t) as follows:

[0065]

[0066] By taking the first - order time derivative of V η (t), we get:

[0067]

[0068] By applying the inequality to scale Equation (29), we obtain:

[0069]

[0070] where k η is the minimum eigenvalue of the diagonal positive gain coefficient matrix K η of. λ imin is the minimum eigenvalue that satisfies the matrix λ i . When and only when it is greater than , Equation (30) is rewritten as:

[0071]

[0072] where γ ≥ 0. Therefore, it is proved that the attitude control method based on the error sign function is stable under the Lyapunov condition, and the attitude error converges to zero over time.

[0073] The features and beneficial effects of the present invention are:

[0074] The present invention proposes a novel composite adaptive control strategy for a side-rotor unmanned aerial vehicle (UAV). Due to factors such as its strong coupling characteristics, high nonlinear behavior, and unknown external disturbances, the side-rotor UAV poses a great challenge to flight control. The present invention combines the adaptive backstepping method with the RISE (Robust Integral of the Signum of the Error) method to formulate a set of efficient flight control laws for the side-rotor UAV in the helicopter mode. Among them, a position control loop is constructed through the adaptive backstepping technique, and an attitude control loop is constructed using the RISE method, thereby achieving precise three-dimensional trajectory tracking control of the side-rotor UAV. The stability analysis based on Lyapunov theory shows that under the developed nonlinear control framework, both the attitude and position tracking errors can achieve asymptotic convergence. The numerical simulation results further verify that the control scheme can not only achieve excellent trajectory tracking performance but also has strong anti-interference ability, demonstrating its significant advantages in complex flight environments. Description of the Drawings:

[0075] Figure 1 It is a schematic diagram of the coordinate system in the helicopter mode of the side-rotor UAV adopted in the present invention;

[0076] Figure 2 It is a control block diagram adopting the adaptive robust control strategy;

[0077] Figure 3 It is a graph of the circular position tracking error of the UAV after adopting the adaptive robust control strategy;

[0078] Figure 4 It is a graph of the circular attitude tracking error of the UAV after adopting the adaptive robust control strategy;

[0079] Figure 5 It is an image of the control input 1 of the UAV after adopting the adaptive robust control strategy;

[0080] Figure 6 It is an image of the control input 2 of the UAV after adopting the adaptive robust control strategy;

[0081] Figure 7 It is an image of the control input 3 of the UAV after adopting the adaptive robust control strategy;

[0082] Figure 8 It is an image of the control input 4 of the UAV after adopting the adaptive robust control strategy; Detailed Implementation Manner

[0083] The present invention belongs to the technical field of non - linear pose control for side - rotor unmanned aerial vehicles. Aiming at the problems of strong non - linear coupling effects existing in side - rotor unmanned aerial vehicles in the low - altitude dense atmosphere environment, model uncertainties caused by rotor slip - stream interference, and unmodeled dynamics caused by unknown external wind disturbances, a control strategy based on adaptive backstepping and robust integral sign error is proposed. This invention combines adaptive backstepping control and robust integral sign error strategy to achieve global asymptotic tracking of the six - degree - of - freedom pose of the helicopter. Compared with existing control methods such as proportional - integral - derivative control (PID), linear quadratic regulator (LQR), and sliding - mode control (SMC), this method has significant advantages in suppressing unmodeled high - frequency dynamic disturbances, can effectively cope with the problem of control performance decay caused by the coupling of rotor flapping dynamics and gust disturbances, and is applicable to high - precision flight control tasks in complex disturbance environments such as urban logistics and low - altitude inspection. Specifically, it involves the application of a control method based on adaptive backstepping and robust integral sign error in the pose tracking control of the helicopter mode of side - rotor unmanned aerial vehicles. Specifically: 1) A non - linear control strategy for three - dimensional trajectories of the helicopter mode of side - rotor unmanned aerial vehicles is proposed, effectively solving the problems of multivariable coupling and strong non - linearity of side - rotor unmanned aerial vehicles. 2) The robust flight control design of adaptive backstepping and RISE is adopted to construct a double - loop robust control structure, enabling the side - rotor unmanned aerial vehicle to have a certain resistance to modeling uncertainties and unknown external disturbances. 3) The asymptotic convergence of the error is proved through Lyapunov stability analysis, and the proposed control method is verified in the simulation software Simulink, verifying the effectiveness of the proposed control method.

[0084] The following further details the present invention in conjunction with the accompanying drawings and specific embodiments.

[0085] The present invention proposes a non - linear control method for three - dimensional trajectories of the helicopter mode of side - rotor unmanned aerial vehicles, effectively solving the problems of multivariable coupling and strong non - linearity of side - rotor unmanned aerial vehicles. It mainly adopts the robust flight control design of adaptive backstepping and RISE to construct a double - loop robust control structure, enabling the side - rotor unmanned aerial vehicle to have a certain resistance to modeling uncertainties and unknown external disturbances. The control block diagram of the present invention is as shown in the appendix Figure 2 and a specific example is as follows:

[0086] 1) Establish the dynamic model of the side - rotor unmanned aerial vehicle

[0087] The reference coordinate system of the side - rotor unmanned aerial vehicle is as shown in the appendix Figure 1 Define both the inertial coordinate system {I} and the body coordinate system {B} as right - hand orthogonal inertial coordinate systems. The origin of the inertial coordinate system {I} is located at a point on the ground, I x points to the due north direction, I zParallel to the downward direction of gravity. The origin of the body coordinate system {B} is located at the center of mass of the side-rotor unmanned aerial vehicle, and B x points in the forward direction of the body, and B z is perpendicular to the wing and downward.

[0088] Based on the Newton-Euler method, the dynamic model of the side-rotor unmanned aerial vehicle can be derived as follows:

[0089]

[0090] Among them, the vector represents the position vector, and the vector represents the velocity vector. m and g represent the body mass and the gravitational acceleration respectively. The matrix represents the attitude rotation matrix from the coordinate system {B} to the coordinate system {I}. The vector represents the attitude angle vector, represents the angular velocity vector. The matrix represents the inertia matrix of the side-rotor unmanned aerial vehicle. The matrix S represents the skew-symmetric matrix expanded from the vector η(t). The vectors and the vector represent the total body thrust and the control input torque vector in the body coordinate system respectively. and represent the external disturbances of the position loop and the attitude loop respectively.

[0091] Here, it is considered that the external disturbance is continuously differentiable and its second-order time derivative is bounded, and at the same time ||d p ||≤∈1, ||d τ ||≤∈2. Where ∈1 and ∈2 are positive constants.

[0092] When constructing the dynamic model of the side-rotor unmanned aerial vehicle, it is considered that the total body thrust T B and the torque τ are composed of six parts: the left rotor (lr), the right rotor (rr), the wing (w), the fuselage (b), the horizontal tail (h), and the vertical tail (v) of the side-rotor unmanned aerial vehicle, and can be expressed as:

[0093]

[0094] Among them, the forces and torques generated by the rotor parts (lr, rr) are obtained by solving through the Pitt-Peters dynamic inflow theory and the blade flapping motion model. The forces and torques generated by the wing (w) are solved by dividing the slipstream region. The fuselage (b) and the tail fins (h, v) are obtained by using empirical formulas and interpolation methods.

[0095] 2) Pose tracking control design

[0096] To better carry out control design, the dynamic model of the side-rotor UAV is decoupled into an attitude control model and a position control model, and control design is carried out separately.

[0097] 2.1 Position Loop Control Law Design

[0098] To facilitate the subsequent control method design, define the position tracking error of the side-rotor UAV Linear velocity tracking error Auxiliary vector as:

[0099] e p = pd - p, (34)

[0100] e v = v d - v, (35)

[0101]

[0102] where is a positive definite gain matrix. Take the first derivative of e v (t) with respect to time, and substitute the second equation in Equation (1) into the equation to obtain the open-loop dynamic equation of e v (t):

[0103]

[0104] Based on the open-loop dynamic equation in Equation (6) , the non-linear robust control input of the position loop of the side-rotor UAV can be designed as:

[0105]

[0106] Considering that the external disturbance d p (t) cannot be directly measured, design the external disturbance estimation variable error and the external disturbance estimation variable velocity as

[0107]

[0108] where is a positive definite gain matrix.

[0109] The steps to prove the stability of the position loop are as follows:

[0110] Select the Lyapunov candidate function V p (t) as follows:

[0111]

[0112] Take the derivative of V p(t) Derivation and simplification yield:

[0113]

[0114] That is is negative semi - definite. Based on Barbalat's lemma, it can be proved that the adaptive backstepping position control method proposed in this paper is uniformly globally stable.

[0115] 2.2 Design of Attitude Loop Control Law

[0116] To facilitate the subsequent design of the control method, the attitude tracking error of the side - rotor UAV is defined as and the angular velocity tracking error as as follows:

[0117]

[0118] where represents the desired attitude angle, and represents the desired angular velocity. Define the auxiliary filtering error functions and as:

[0119] r1 = e ω +λ1e η (44)

[0120]

[0121] where and are both positive - definite gain matrices. Take the derivative of r2(t) with respect to time and multiply both sides of the formula on the left by the inertia matrix J of the side - rotor UAV to obtain the open - loop dynamic equation of the auxiliary filtering error function Jr2(t):

[0122]

[0123] where the auxiliary vector function and the auxiliary vector function are defined as follows:

[0124]

[0125] The upper bound of

[0126]

[0127] can be expressed in the following form: where ρ represents a globally invertible non - decreasing function, and z = [e η r1 r2].

[0128] Based on the open-loop dynamic equation of \(r_2(t)\) in Equation (15), the attitude non-linear robust control input of the side rotor UAV can be designed as follows:

[0129]

[0130] where represents the positive gain coefficient matrix, \(r_1(0)\) represents the initial value of \(r_1(t)\), and \(sgn(·)\) represents the standard sign function. Taking the first derivative of Equation (20) with respect to time gives:

[0131]

[0132] Substituting Equation (21) into Equation (15), the closed-loop dynamic equation of \(r_2(t)\) can be obtained as:

[0133]

[0134] Design the auxiliary functions \(L(t)\) and \(Q(t)\) as follows:

[0135] \(L = r_2\) T (M d -\(\beta\) η \(sgn(r_1)) (54)\)

[0136]

[0137] When the control gain \(\beta\) η and the auxiliary variable \(\zeta\) satisfy the following sufficient conditions, it can be guaranteed that \(Q(t)\geq0\), holds:

[0138] \(\zeta := \beta\) η \(|r_1(0)| - r_1(0)M\) d (0) (56)\)

[0139]

[0140] Under the following sufficient conditions, the non-linear robust control method proposed in this section can guarantee that the closed-loop position tracking error converges exponentially to zero:

[0141]

[0142] where is the diagonal gain matrix.

[0143] The verification steps for the attitude loop stability proof are as follows:

[0144] Design the Lyapunov candidate function \(V\) η (t) as follows:

[0145]

[0146] By taking the first-order time derivative of V η (t), we can obtain:

[0147]

[0148] By applying the inequality to scale Equation (29), we can get:

[0149]

[0150] where k η is the minimum eigenvalue of the diagonal positive gain coefficient matrix K η . λ imin is the minimum eigenvalue that satisfies the matrix λ i . When and only when it is greater than , Equation (30) can be rewritten as:

[0151]

[0152] where γ ≥ 0. Therefore, it can be concluded that the attitude control method based on the error sign function proposed in this paper is stable under the Lyapunov condition, and the attitude error converges to zero over time.

[0153] II. Simulation Results

[0154] To further verify the effectiveness of the trajectory tracking nonlinear control algorithm based on the adaptive backstepping method and the robust integral of the error signal proposed in this paper, a simulation verification is carried out in the MATLAB / Simulink simulation software. The overall simulation design parameters are as follows: the simulation time T = 200 s, the total mass of the machine m = 5897 kg, the inertia matrix J = [I xx , 0, -I xz ; 0, I yy , 0; -I xz , 0, I zz , I xx = 71579 kg·m 2 , I yy = 28960 kg·m 2 I zz = 89937 kg·m 2 , I xz = 1673 kg·m 2 .

[0155] The desired trajectory is given as follows:

[0156]

[0157] The parameters are as follows: A = 200 (m), B = 200 (m), C = -3 (m), is a circular spiral. During the simulation experiment, the control gain parameters are selected as follows: K1 = diag([2, 2, 2]), K2 = diag([2, 2, 2]), λ1 = diag([2, 2, 2]), λ2 = diag([2, 2, 2]), K η = diag([8×10 5 , 4×10 5 , 8×10 5 ), β η = [6×10 6 ; 4×10 6 ; 6×10 6 .

[0158] The simulation results are as shown in the attached figure Figures 3 to 8 . Figure 3 is the position error of the side-rotor UAV. It can be seen from the figure that the entire control system stabilizes within 5 seconds. Moreover, the errors in the x, y, and z directions are all less than 0.1 m, ensuring the safety and accurate trajectory tracking of the helicopter. Figure 4 is the attitude tracking error of the small unmanned helicopter. It can be seen from the figure that the attitude of the side-rotor UAV can quickly track the desired attitude angle, reaching stability within 2 seconds, and finally the tracking errors in the roll and yaw directions are both less than 1 degree, and the tracking error in the pitch direction is less than 1.5 degrees.

[0159] Figures 5 to 8 is the change of the control input quantity. It can be seen from the figure that the control quantity changes rapidly, compensating the system, enabling the system to quickly and accurately track the given trajectory even in the presence of disturbances.

[0160] In summary, the three-dimensional trajectory nonlinear control strategy for the helicopter mode of the side-rotor UAV proposed by the present invention has high control accuracy, and can preferably solve problems such as the strong nonlinear coupling effect of the side-rotor UAV, the rotor slipstream interference, and the anti-interference ability of external unknown wind disturbances.

[0161] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. An adaptive robust control method for a side-rotor UAV, characterized in that, An adaptive backstepping method and a robust integral sign error control are used to construct a nonlinear control strategy for a side-rotor UAV under a three-dimensional trajectory. The nonlinear control strategy is divided into a position loop control strategy and an attitude loop control strategy. Among them, the adaptive backstepping method is used to construct the position loop control strategy, and the robust integral sign error control is used to construct the attitude loop control strategy.

2. The adaptive robust control method for a side-rotor UAV according to claim 1, characterized in that, The specific steps are as follows: 1) Establish the dynamic model of the side-rotor UAV Define the inertial coordinate system {I} and the body coordinate system {B} as right-handed orthogonal inertial coordinate systems. The origin of the inertial coordinate system {I} is located at a point on the ground. I x points due north. I z is parallel to the direction of gravity and points downward. The origin of the body coordinate system {B} is located at the center of mass of the side rotor UAV. B x points in the forward direction of the body. B z is perpendicular to the wing and points downward. Based on the Newton-Euler method, the dynamic model of the side rotor UAV is derived as follows: where the vector represents the position vector, and the vector represents the velocity vector. m and g respectively represent the mass of the body and the acceleration due to gravity. The matrix Represents the attitude rotation from coordinate system {B} to coordinate system {I}, matrix vector Represents the attitude angle vector, Represents the angular velocity vector, matrix Denote the inertial matrix of the side-rotor UAV, and matrix S represents the skew-symmetric matrix expanded by vector η(t). The vector and the vector represent the total body thrust and the control input torque vector in the body coordinate system respectively. and represent the external disturbances of the position loop and the attitude loop respectively. External disturbance is continuously differentiable and its second-order time derivative is bounded above, while ||d p || ≤ ∈1, ||d τ || ≤ ∈2, where ∈1, 2 are positive constants; When constructing the dynamic model of the side-rotor UAV, it is considered that the total thrust T of the airframe B and the torque τ are composed of six parts: the left rotor (lr), the right rotor (rr), the wing (w), the fuselage (b), the horizontal tail (h), and the vertical tail (v) of the side-rotor UAV, and are expressed as: Among them, the forces and moments generated by the rotor part (lr, rr) are obtained by solving through the Pitt-Peters dynamic inflow theory and the blade flapping motion model. The forces and moments generated by the wing (w) are solved by dividing the slip flow area. The fuselage (b) and the tail fins (h, v) are obtained by empirical formulas and interpolation methods; 2) Design of pose tracking control The dynamic model of the side-rotor UAV is decoupled into an attitude control model and a position control model, and control designs are carried out respectively: 2.1 Design of the position loop control law Define the position tracking error of the side rotor UAV Linear velocity tracking error Auxiliary vector is defined as: e p = p d -p, (3) e v = v d -v, (4) where is a positive definite gain matrix, take e v (t) and take the first derivative with respect to time. Substitute the second equation in Equation (1) into the equation to obtain the open-loop dynamic equation of e v (t): Based on the open-loop dynamic equation in Equation (6), the nonlinear robust control input of the lateral rotor UAV position loop is designed as: Consider the external disturbance d p (t) cannot be directly measured, and design the variable error of the external disturbance estimator and the velocity of the external disturbance estimator variable as wherein is a positive definite gain matrix; 2.2 Design of the attitude loop control law Define the attitude tracking error of the side-rotor UAV and the angular velocity tracking error as follows: Among them represents the desired attitude angle, represents the desired angular velocity, and define the auxiliary filtering error function and as follows: r1 = e ω + λ1e η (11) Among them and are both positive definite gain matrices. Take the derivative of r2(t) with respect to time, and left-multiply the inertial matrix J of the side rotor UAV on both sides of the formula to obtain the open-loop dynamic equation of the auxiliary filtering error function Jr2(t): where the auxiliary vector function and the auxiliary vector function are defined as follows: The upper bound is expressed in the following form: where ρ represents a globally invertible non-decreasing function, z = [e η r1 r2]; Based on the open-loop dynamic equation of r2(t) in Equation (15), the attitude nonlinear robust control input of the side-rotor UAV is designed as: where represents the positive gain coefficient matrix, r1(0) represents the initial value of r1(t), and sgn(·) represents the standard sign function. Taking the first derivative of Equation (20) with respect to time gives: Substituting Equation (21) into Equation (15), the closed-loop dynamic equation of r2(t) is obtained as: Design the auxiliary functions L(t) and Q(t) as follows: L = r2 T (M d -β η sgn(r1)) (21) When the control gain β η and the auxiliary variable ζ satisfy the following sufficient conditions, it can be ensured that Q(t) ≥ 0, Established: ζ := β η |r1(0)| - r1(0)M d (0) (23) Under the following sufficient conditions, the non-linear robust control method can ensure that the closed-loop position tracking error converges exponentially to zero: Among them is the diagonal gain matrix.

3. The adaptive robust control method for a side-rotor UAV according to claim 2, characterized in that, The verification steps for the stability proof of the position loop are as follows: Select the Lyapunov candidate function V p (t) as follows: Derive V p with respect to (t) and simplify to obtain: Based on Equation (11) is negative semi-definite. Based on Barbalat's lemma, it can be proved that the adaptive backstepping position control method is uniformly globally stable; The verification steps for the stability proof of the attitude loop are as follows: Design the Lyapunov candidate function V η (t) as follows: By taking the first-order time derivative of V η (t), we obtain: By applying the inequality the following is obtained by scaling Equation (29): where k η is the minimum eigenvalue of the diagonal positive gain coefficient matrix K η . λ imin is the minimum eigenvalue that satisfies the matrix λ i , and when and only when it is greater than , Equation (30) is rewritten as: where γ≥0, so it is proved that the attitude control method based on the error sign function is stable under the Lyapunov condition, and the attitude error converges to zero over time.

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