All-wheel-drive finite-time fault-tolerant control method for time-varying load quad-rotor unmanned aerial vehicle

Abstract

The invention relates to the technical field of unmanned aerial vehicle flight control, in particular to an all-wheel-drive finite-time fault-tolerant control method for a time-varying load quadrotor unmanned aerial vehicle, and aims at the quadrotor unmanned aerial vehicle carrying the time-varying load in an actuator failure scene and considering partial failure of an actuator, the time-varying load and external interference. A precise dynamic model is established and converted into a control-oriented design model, an all-drive system, finite time, preset performance and a fault-tolerant control design algorithm are combined, and based on a Lyapunov stability theory, it is proved that signals of a closed-loop system are consistent and finally bounded, and tracking errors of all subsystems are converged to be within preset precision within the finite time. Finally, the effectiveness of the designed method is verified through a simulation experiment. According to the all-drive finite time fault-tolerant control method for the time-varying load quadrotor unmanned aerial vehicle, the unmanned aerial vehicle can output a stable tracking reference instruction, the tracking error finite time is converged to a preset steady-state error range, and finally the feasibility of the method is proved through a simulation experiment.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) flight control technology, specifically a finite-time fault-tolerant control method for a time-varying load quadrotor UAV. Background Technology

[0002] Quadrotor drones, with their simple structure, vertical takeoff and landing capabilities, hovering ability, and high maneuverability, are widely used for various flight missions such as aerial photography, exploration, transportation, and rescue. A quadrotor drone system is a multivariable coupled nonlinear system, inevitably affected by parameter uncertainties and external disturbances, making drone system control design challenging. Most existing research on drone systems considers the system parameters as steady. However, in many practical applications, such as drone spraying of pesticides, seed sowing, and firefighting, the system parameters become time-varying. Therefore, considering the control problem of quadrotor drone systems with time-varying loads has significant theoretical and practical implications.

[0003] To establish a mathematical model for a quadrotor UAV system with time-varying loads, existing technologies employ a simplified approach, treating terms containing the derivative of rotational inertia as a global disturbance to establish a model of a quadrotor UAV carrying time-varying loads. Furthermore, the designed model is a finite-time tracking control algorithm for the time-varying load quadrotor UAV, without considering finite-time control and fault-tolerant control algorithms. Existing technologies also propose a finite-time fault-tolerant control method for quadrotor UAVs with actuator failures, but do not consider the case of the UAV carrying time-varying loads. The all-drive system method, proposed by Professor Duan Guangren, an academician of the Chinese Academy of Sciences, is a novel control system analysis and design method based on a high-order all-drive model. Compared to designs based on first-order systems, this method has many unique advantages: 1) it simplifies the control design process; 2) it gives the system a clearer physical meaning; 3) it retains the original all-drive characteristics of the system; 4) it allows more systems to possess global stability; and 5) it provides a reasonable controllability framework for nonlinear systems. In recent years, control based on high-order all-drive systems has attracted widespread attention from scholars, yielding fruitful results.

[0004] Therefore, in view of the above situation, there is an urgent need to develop a fully driven finite-time fault-tolerant control method for time-varying load quadrotor UAVs to overcome the shortcomings in current practical applications. Summary of the Invention

[0005] The purpose of this invention is to provide a finite-time fault-tolerant control method for all-drive quadrotor unmanned aerial vehicles with time-varying loads, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A finite-time fault-tolerant control method for all-drive quadrotor unmanned aerial vehicles with time-varying loads includes the following steps:

[0008] 1. Establish a mathematical model of a quadcopter unmanned aerial vehicle (UAV) system with time-varying load and actuator failure. The model considers partial actuator failure, time-varying load and external disturbance. The partial actuator failure is described by the failure coefficient and input uncertainty. The time-varying load is reflected in the time-varying mass and moment of inertia of the UAV system.

[0009] 2. Simplify and transform the mathematical model of the system, define position reference signal and attitude reference signal, and use the transformed model as the control design model;

[0010] 3. Based on the all-drive system method, fault-tolerant control technology, finite-time control technology and preset performance control method, design control laws and adaptive laws. The preset performance control method quantitatively describes the expected performance index through a preset performance function and limits the transient and steady-state range of the system tracking error.

[0011] Furthermore, the mathematical model of the quadcopter unmanned aerial vehicle system with time-varying load and actuator failure is shown in the following equation:

[0012]

[0013] Where M is the total mass of the loaded UAV system; F is the net external force; V = [xyz] T For translational velocity; I(t) = diag[I x (t)I y (t)I z (t)] T The inertial matrix of a loaded unmanned aerial vehicle (UAV) system; This represents the torque vector acting on the entire system, derived from the air drag torque. External unknown disturbance torque Control torque generated by the interaction between the rotor and the rotor It consists of three parts; ω = [p, q, r] T This represents the angular velocity vector of the drone. i ′=κ i u i +Δ ui i = 1, 2, 3, 4, u i ′ represents the control input after a fault occurs, κ represents the input after a fault occurs. i (i = 1, 2, 3, 4), 0 < κ i <1 Failure coefficient, Δ i For inputting uncertain terms.

[0014] in,

[0015] Furthermore, the control-oriented design model is as follows:

[0016]

[0017] in:

[0018]

[0019] Assumption 1: Time-varying parameter a x,1 (t), a y,1 (t), a z,1 (t), a φ,1 (t), a θ,1 (t), a φ,2 (t), a θ,2 (t), The upper and lower bounds are unknown.

[0020] Assumption 2: Time-varying parameters The upper bound of all is D, where D > 0, and is a known constant.

[0021] Assumption 3: Time-varying parameters satisfy

[0022] Define error signal

[0023]

[0024] Take a smooth decreasing positive function As a performance function, δ i0 δ i∞ h i μ is a pre-given positive constant. i0 δ represents the preset lower limit of steady-state error. i∞ h represents the upper limit of steady-state error. i Limit the minimum convergence rate of the system; and consider performance constraints. in, m i >0, The overshoot suppression parameter takes values ​​that satisfy... To handle time-varying performance constraints, let ε i (t)=e i (t) / δ i (t), and introduce error transformation Then we can conclude in, Based on the above transformation, we can obtain...

[0025] in:

[0026]

[0027]

[0028] Design an adaptive controller as follows:

[0029]

[0030] Where, 0 < ρ i <1, Yes The estimate. The adaptive law is:

[0031]

[0032] in,

[0033] Lemma 1: For any scalar positive function σ(t): R ≥0 →R + For any variable z∈R, the following inequality holds:

[0034] Lemma 2: Suppose that matrix A satisfies:

[0035] Then for μ > 0, there exists a positive definite matrix. Satisfy: A T P+PA≤-μP;

[0036] Lemma 3: Under the condition that Lemma 2 holds, for μ > 0, there exists a positive definite matrix. satisfy:

[0037] Then there exists a positive definite matrix. This can make:

[0038] Φ(A 0～n-1 ) T P(A 0～n-1 )+P(A 0～n-1 )Φ(A 0～n-1 )≤-μP(A 0～n-1 ); established.

[0039] Lemmas 2 and 3 are necessary conditions for the all-drive system approach, used to ensure that the controller designed based on the all-drive system meets the stability requirements.

[0040] Lemma 4: For a continuous system There exists a positive definite function V(x) such that b1, b2, b3 > 0, 0 < p < 1, and satisfies the inequality Then we can conclude that the trajectory of the closed-loop system is bounded within a finite time T, and its range is... θ0 is a positive constant satisfying 0 < θ0 < 1, and

[0041]

[0042] Choosing the Lyapunov function, it is represented as:

[0043]

[0044] Where, 0 < b i ≤|b i (t)|;then V i The time derivative is:

[0045]

[0046] Substituting equation (19) into the above equation and according to Lemma 1-3, we can obtain:

[0047]

[0048] because:

[0049]

[0050] but It can be further transformed into:

[0051]

[0052] Redefining a Lyapunov function It can be seen that V j It is V i The first term, therefore, we first consider V. i Let's analyze it. First, based on... V can be obtained i The time derivative is and if Then there exists a finite time T * , making For t≥T * This holds true. Then we obtain that when t ≥ T... * hour, This holds true. Therefore, we can conclude that t ≥ T. * hour, Therefore, for all t≥T, the following condition is satisfied: hour, and e i Consistency is ultimately bounded. It is to satisfy . a normal number.

[0053] According to Lemma 4, for V i When t≥T r ,and hour, and e i Uniformity is eventually bounded, and the following conclusion is proved:

[0054] (1) All signals in the closed-loop system (s) i u i (etc.) are uniformly bounded;

[0055] (2) Tracking error e i (t) can be achieved in a finite time T r The convergence is within the preset performance constraint range.

[0056] (3) When t≥T, and e i The uniform eventual boundedness means that the UAV output signal can stably track the reference command and the tracking error converges to the preset performance constraint range within a finite time.

[0057] Compared with the prior art, the beneficial effects of the present invention are:

[0058] 1. Compared with the existing time-varying load quadrotor UAV system model, this application focuses on studying a more accurate mathematical model of the quadrotor UAV system under time-varying moment of inertia, which can more accurately describe the dynamic characteristics of the UAV in practical applications. This model is based on the rotational dynamics principle of the UAV and derives a specific mathematical expression for the derivative of the moment of inertia, which is more in line with the essential laws of physical systems.

[0059] 2. Compared with the existing proposed finite-time fault-tolerant control method for quadrotor UAVs with actuator failure, this application introduces a finite-time fault-tolerant control method for quadrotor UAVs based on time-varying load. This method considers the effects of partial actuator failure, time-varying load, and external disturbances, and is closer to the actual operation scenarios of UAVs such as spraying pesticides and sowing seeds, and therefore has greater practical application value.

[0060] 3. The control algorithm designed in this invention is based on the all-drive system method. Compared with the state-space method based on the first-order system, the all-drive system method has advantages such as simplifying the control design process, giving the system a clearer physical meaning, preserving the original all-drive characteristics of the system, enabling more systems to have global stability, and providing a reasonable controllability system for nonlinear systems. Therefore, it is more novel than the state-space method. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the coordinate system and structure of a loaded quadcopter UAV in an embodiment of the present invention.

[0062] Figure 2 This is a flowchart of the closed-loop control system for a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0063] Figure 3 This is a three-dimensional trajectory tracking curve of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0064] Figure 4 This is a position tracking curve in the x-direction of a quadcopter UAV with time-varying load in an embodiment of the present invention.

[0065] Figure 5 This is a convergence curve of the x-direction position tracking error of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0066] Figure 6 This is a position tracking curve in the y-direction of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0067] Figure 7 This is a convergence curve of the position tracking error in the y-direction of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0068] Figure 8 This is a position tracking curve in the z-direction of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0069] Figure 9 This is the convergence curve of the z-direction position tracking error of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0070] Figure 10 The yaw angle of the time-varying load quadcopter UAV in this embodiment of the invention. Tracking curve graph.

[0071] Figure 11 The yaw angle of the time-varying load quadcopter UAV in this embodiment of the invention. Tracking error convergence curve.

[0072] Figure 12 This is a convergence curve of the pitch angle θ tracking error of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0073] Figure 13 This is a convergence curve of the tracking error of the roll angle φ of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0074] Figure 14 This is a comparison curve of the roll angle x-direction tracking of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0075] Figure 15This is a comparison curve of the roll angle y-direction tracking of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0076] Figure 16 This is a comparison curve of the roll angle z-direction tracking of a quadrotor UAV with time-varying load in an embodiment of the present invention.

[0077] Figure 17 The roll angle of the time-varying load quadcopter drone in this embodiment of the invention. Directional tracking comparison curve.

[0078] Figure 18 This is a comparison curve of the input u1 of the controller of a quadcopter drone with time-varying load in an embodiment of the present invention.

[0079] Figure 19 This is a comparison curve of the input u2 of the controller of a quadcopter drone with time-varying load in an embodiment of the present invention.

[0080] Figure 20 This is a comparison curve of the input u3 of the controller of a quadcopter drone with time-varying load in an embodiment of the present invention.

[0081] Figure 21 This is a comparison curve of the input u4 of the controller of a quadrotor UAV with time-varying load in an embodiment of the present invention. Detailed Implementation

[0082] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0083] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0084] Please see Figures 1-21 The present invention provides a finite-time fault-tolerant control method for all-drive quadrotor unmanned aerial vehicles with time-varying loads, which specifically includes the following:

[0085] I. System Model;

[0086] 1. Basic mathematical model of UAV with time-varying load;

[0087] Describe the kinematics and dynamics of the quadrotor UAV in Earth coordinate system and body coordinate system. Wherein, O E -X E Y E Z E For the Earth inertial coordinate system, O B-X B Y B Z B A fixed coordinate system is used for the aircraft. The vector is [x, y, z]. T This indicates the position of the loaded unmanned aerial vehicle (UAV) system in the Earth's inertial coordinate system. This indicates the roll, pitch, and yaw angles of a loaded unmanned aerial vehicle (UAV) system in the Earth's inertial coordinate system. For example... Figure 1 As shown.

[0088] The dynamic equations under time-varying mass and time-varying moment of inertia are:

[0089]

[0090] Where M is the total mass of the loaded UAV system; F is the net external force; V = [xyz] T For translational velocity; I(t) = diag[I x (t)I y (t)I z (t)] T The inertial matrix of a loaded unmanned aerial vehicle (UAV) system; This represents the torque vector acting on the entire system, derived from the air drag torque. External unknown disturbance torque Control torque generated by the interaction between the rotor and the rotor It consists of three parts; ω = [p, q, r] T The vector representing the angular velocity of the drone.

[0091] When the attitude angles φ and θ, When smaller, Based on (1)-(2), the mathematical model of the UAV system carrying time-varying load can be derived as follows:

[0092]

[0093] Where, d i (t)(i=1,2,...6) represents external disturbance, and |d i (t)|≤D i g is the acceleration due to gravity; k fi (i = 1, 2, ... 6) represents the air resistance coefficient; u1 is the position subsystem control input, representing the total lift generated by the four rotors of the quadcopter UAV;

[0094] u2, u3, and u4 are the attitude subsystem control inputs, representing the resultant torque that generates the roll angle, pitch angle, and yaw angle.

[0095] Considering the case of partial actuator failure, the actuator fault model adopts the following general form:

[0096] u i ′=κ i u i +Δ ui i = 1, 2, 3, 4(4);

[0097] Among them, u i ′ represents the control input after a fault occurs, κ represents the input after a fault occurs. i (i = 1, 2, 3, 4), 0 < κ i <1 Failure coefficient, Δ i To introduce the uncertainties, substitute equation (4) into equation (3) to obtain the model of a UAV system with time-varying load and actuator failure:

[0098]

[0099] in,

[0100] 2. Model simplification;

[0101] To facilitate subsequent controller design, model (5) is simplified first. First, we define:

[0102] Then model (5) is transformed into:

[0103]

[0104] Based on the transformed model described above, the following assumptions are proposed:

[0105] Assumption 1: Time-varying parameter a x,1 (t), a y,1 (t), a z,1 (t), a φ,1 (t), a θ,1 (t), a φ,2 (t), a θ,2 (t), The upper and lower bounds are unknown.

[0106] Assumption 2: Time-varying parameters The upper bound of all is D, where D > 0, and is an unknown constant.

[0107] Assumption 3: Time-varying parameters satisfy

[0108] For subsequent control design, define the coordinate transformation:

[0109]

[0110] In the formula, [xd y d z d [This is a position reference signal.] This is the attitude reference signal.

[0111] 3. Inner and outer loop control;

[0112] Quadrone UAVs are typical underactuated systems (four inputs, six outputs), therefore an inner-loop-outer-loop control structure is adopted to solve the underactuation problem: the position subsystem is designed as the outer loop, the attitude subsystem as the inner loop, and the connection between the inner and outer loops is achieved through an intermediate controller. For example... Figure 2 As shown.

[0113] Let the intermediate controller be u x u y u z The control inputs u1, u2, u3, u4 and the intermediate controller satisfy the following relationship:

[0114]

[0115] Based on the above relationships, the desired attitude φ can be obtained by solving the position subsystem controller. d ,θ d The specific relationship is as follows:

[0116]

[0117] The workflow of the inner and outer loop control is as follows: In the outer loop subsystem, the control input u1 is designed to make the position signal [x,y,z] of the loaded UAV... T Able to track a given reference signal [x] d ,y d ,z d ] T The intermediate controller generates u for the outer loop. x ,u y ,u z and externally input reference signal Perform the inverse solution to calculate φ. d ,θ d And input to the inner loop subsystem. In the inner loop subsystem, control inputs u2, u3, and u4 are designed to control the attitude signals of the loaded quadcopter UAV. Able to track reference signal like Figure 2 As shown.

[0118] 4. Control design objectives;

[0119] Design the control law u = [u1, u2, u3, u4] T The following two objectives must be met:

[0120] (1) System tracking error e of UAV with time-varying load x ,e y ,e z ,e φ ,e θ , Converges to within a specified error range within a finite time;

[0121] (2) All signals in the closed-loop system (including position, attitude, speed and control inputs) remain bounded.

[0122] 5. Necessary lemmas;

[0123] To achieve the above control objectives, control design and stability analysis must be carried out based on the following lemma:

[0124] Lemma 1: For any scalar positive function σ(t): R ≥0 →R + For any variable z∈R, the following inequality holds:

[0125] Lemma 2: Suppose that matrix A satisfies:

[0126] Then for μ > 0, there exists a positive definite matrix. Satisfy: A T P+PA≤-μP;

[0127] Lemma 3: Under the condition that Lemma 2 holds, for μ > 0, there exists a positive definite matrix. satisfy:

[0128] Then there exists a positive definite matrix. This can make:

[0129] Φ(A 0～n-1 ) T P(A 0～n-1 )+P(A 0～n-1 )Φ(A 0～n-1 )≤-μP(A 0～n-1 ); established.

[0130] Lemmas 2 and 3 are necessary conditions for the all-drive system approach, used to ensure that the controller designed based on the all-drive system meets the stability requirements.

[0131] Lemma 4: For a continuous system There exists a positive definite function V(x) such that b1, b2, b3 > 0, 0 < p < 1, and satisfies the inequality Then we can conclude that the trajectory of the closed-loop system is bounded within a finite time T, and its range is... θ0 is a positive constant satisfying 0 < θ0 < 1, and

[0132]

[0133] Lemma 4 is a necessary condition for realizing finite-time control techniques, and is used to prove that the system tracking error can converge in finite time.

[0134] In this invention, for ease of explanation, the following symbols are provided:

[0135]

[0136] A 0～n-1 =[A0,A1,...,A n-1 ];

[0137]

[0138] in, Φ(A 0～n-1 ) is the Herwitz matrix. It is the identity matrix. Furthermore, L is defined as [0 … I r ] r Then the following formula holds:

[0139] P L =PL;

[0140] Where P is a real symmetric matrix.

[0141] 6. Preset performance;

[0142] The core idea of ​​the pre-defined performance control method is to first use a performance function to quantitatively describe the desired performance index, and then design a controller to ensure that the performance constraints are met throughout the entire time domain.

[0143] This embodiment selects a smoothly decreasing positive function. As a performance function, δ i0 δ i∞ h i μ is a pre-given positive constant. i0 δ represents the preset lower limit of steady-state error. i∞ h represents the upper limit of steady-state error. i Limit the minimum convergence rate of the system; and consider the following performance constraints:

[0144]

[0145] in, m i >0, The overshoot suppression parameter takes values ​​that satisfy...

[0146] To handle time-varying performance constraints, let ε i (t)=e i (t) / δ i (t), and introduce error transformation:

[0147]

[0148] Then we have:

[0149]

[0150] in,

[0151]

[0152] Substituting the above error transformation and performance constraints into equation (7), we can obtain the transformed time-varying load quadrotor UAV model:

[0153]

[0154] To simplify the model representation, we define the time-varying parameter vector and the regression vector:

[0155]

[0156] Equation (17) can be further described as follows:

[0157]

[0158] In the formula, f i Given a function term, the specific expression is:

[0159]

[0160] The following are prerequisites for all-wheel drive systems:

[0161] Consider the following nth-order system:

[0162] Ex n =f(x) (0～n-1) ,t)+B(x (0～n-1) ,t)u;

[0163] Where n is an integer greater than 1, For state vectors, For the input vector, It is a constant matrix (usually an identity matrix). For continuous vector functions, Let be the coefficient matrix. Then, according to the control theory of all-drive systems, we can obtain:

[0164] (1) Definition: For any If the coefficient matrix If all functions are reversible, then the system is called a fully driven system.

[0165] (2) Conclusion: For the above-mentioned all-drive system, the controller can be used to:

[0166] u = -B -1 (x (0～n-1) ,t)[A 0～n-1 x (0～n-1) +f(x (0～n-1) ,t)-v];

[0167] The following linear time-invariant closed-loop system is obtained:

[0168] Ex n +A 0～n-1 x (0～n-1) =v.

[0169] In the formula, v is the intermediate control law to be designed to handle certain nonlinear problems, and A 0～n-1 Is it such that Φ(A) 0～n-1 Stable arbitrary matrix.

[0170] II. Controller Design;

[0171] Based on the transformed system model (Equation 21) described above, and combining the all-drive system method, finite-time control technology, and adaptive control technology, a finite-time fault-tolerant controller with preset performance is designed.

[0172] 1. Controller and adaptive law design;

[0173] The system model is as follows:

[0174]

[0175] r here i It is reversible, b i (t)>0 is an unknown parameter, therefore equation (22) belongs to a pseudo-high-order all-drive system form. The robust control method adopted in this application excludes b i The influence of (t) allows this model to be used for control design based on the all-drive system approach. Definition Yes Based on the estimation, the controller is designed as follows:

[0176]

[0177] Where 0 < ρ i <1, design The adaptive law is:

[0178]

[0179] 2. Stability analysis of the closed-loop system;

[0180] Substituting the controller (Equation 23) and the adaptive law (Equation 24) into the system model (Equation 22), we can obtain the error dynamic equation of the closed-loop system:

[0181]

[0182] To analyze the stability of a closed-loop system, the Lyapunov function is defined as follows:

[0183]

[0184] Where, 0 < b i ≤|b i (t)|;then V i The time derivative is:

[0185]

[0186] Substituting equation (25) into the above equation and according to Lemma 1-3, we can obtain:

[0187]

[0188] because:

[0189]

[0190] Equation (28) can then be further transformed into:

[0191]

[0192] Redefining a Lyapunov function It can be seen that V j It is V i The first term, therefore, we first consider V. i Let's analyze it. First, based on... V can be obtained i The time derivative is and if Then there exists a finite time T * , making For t≥T * This holds true. Then we obtain that when t ≥ T... * hour, Therefore, we can conclude that t≥T * hour, Therefore, for all t≥T, the following condition is satisfied: At that time, there exists and e i Consistency is ultimately bounded. It is to satisfy . a normal number.

[0193] According to Lemma 4, for V i When t≥T r , and e i =0 is uniformly bounded, and the following conclusion is proved:

[0194] (1) All signals in the closed-loop system (s) i u i (etc.) are uniformly bounded;

[0195] (2) Tracking error e i (t) can be achieved in a finite time T r It converges to within the preset performance constraints, and (V(0) is the initial value of the Lyapunov function);

[0196] (3) When t≥T, e i The uniform eventual boundedness means that the UAV output signal can stably track the reference command, and the tracking error converges to the preset performance constraint range within a finite time.

[0197] III. Simulation Experiment Verification;

[0198] To verify the feasibility and effectiveness of the proposed control method, a simulation experiment was conducted using Matlab 2023b, ode4, with a fixed step size of 0.01s. Specific parameter settings and simulation results analysis are as follows:

[0199] 1. Simulation parameter settings;

[0200] 1.1 UAV Body and Environmental Parameters

[0201] Initial state: x(0)=y(0)=0.2, z(0)=0.2, φ(0)=θ(0)=0,

[0202] Inertia matrix: I x =I y =0.1+0.05sin(t), I z =0.2+0.1sin(t);

[0203] Total mass of the system: M = 1 + 0.6sin(t);

[0204] Air drag coefficient: External disturbance; d i (t) = 0.01sin(t).

[0205] 1.2 Actuator fault parameters;

[0206] Failure coefficients: κ1 = 0.95, κ2 = 0.90, κ3 = 0.88, κ4 = 0.85;

[0207] Input uncertain items:

[0208] 1.3 Reference trajectory parameters;

[0209] Expected trajectory: x d =sin(πt / 5), y d =cos(πt / 5), z d =t,

[0210] 1.4 Control and preset performance parameters;

[0211] Control parameters: A1 = [5 5], A2 = [10 10], A3 = [25 30], A4 = A5 = [50 3], A6 = [5 10], ρ1~ρ6 = 0.9, μ i =2, i = 1~6, P L1 =10 -3 [1 1] T ,P L2 =10 -3 [3 2] T ,P L3 =10 -3 [5 3] T ,

[0212] P L4 =P L5 =P L6 =10 -2 [twenty one] T ;

[0213] Adaptive parameters: γ1~γ6=0.01;

[0214] Preset performance function: δ x (t)=δ y (t)=δ z (t)=(3-0.05)e -1.5t +0.05;

[0215]

[0216] Simulation effect as Figures 3-13 As shown, Figure 3 This is a diagram showing the effect of 3D trajectory tracking. Figure 4 , Figure 6 , Figure 8 and Figure 10 For x, y, z, Tracking effect curve, Figure 5 , Figure 7 , Figure 9 , Figure 11 , Figure 12 and Figure 13 For x, y, z, φ, θ, The tracking error convergence curve is shown. Simulation results demonstrate that the controller designed in this application can asymptotically track the desired trajectory using the system output signal, and all closed-loop system signals are bounded.

[0217] 2. Simulation results analysis;

[0218] The simulation results are illustrated by the tracking effect curve and the tracking error convergence curve. The specific conclusions are as follows:

[0219] Position tracking performance: The UAV's position signals x, y, z can accurately track the reference trajectory x. d ,y d ,z d ,like Figure 5 , Figure 7 , Figure 9 As shown, the tracking error e x ,e y ,e z It converges quickly to within the preset performance function boundary (satisfying the preset performance constraints);

[0220] Attitude tracking performance: UAV attitude signals φ, θ, Able to stably track the reference trajectory φ d ,θ d , like Figure 9 , Figure 11 and Figure 13 As shown, the tracking error e φ ,e θ , It converges quickly to the preset performance function boundary (satisfying the preset performance constraints) without significant overshoot;

[0221] Boundedness of closed-loop signals: The control inputs u1, u2, u3, u4 and the adaptive parameters all remain within a reasonable range without divergence, verifying the stability of the closed-loop system.

[0222] 3. Comparison of experimental parameter settings

[0223] To demonstrate the novelty of this invention, the control effects of the proposed method and the sliding mode fault-tolerant controller and backstepping fault-tolerant controller based on the "variable freezing method" under the state-space method are compared to highlight the advantages of this invention. (Note: Hereinafter, these two methods will be referred to as "sliding mode fault-tolerant control algorithm" and "backstepping fault-tolerant control algorithm" respectively.)

[0224] 3.1 UAV Body and Environmental Parameters

[0225] Initial state: x(0) = y(0) = 0.2, z(0) = -0.3,

[0226] Inertia matrix: I x =I y =0.045+0.01sin(πt / 15), I z =0.083 + 0.01sin(πt / 15);

[0227] Total mass of the system: M = 1 + 0.1sin(πt / 15);

[0228] Air drag coefficient: External disturbance: d i (t)=0.01sin(t)+0.01.

[0229] 3.2 Actuator fault parameters;

[0230] Failure coefficients: κ1 = 0.95, κ2 = 0.90, κ3 = 0.88, κ4 = 0.85;

[0231] Input uncertain items:

[0232] 3.3 Reference trajectory parameters;

[0233] Expected trajectory: x d =sin(πt / 5), y d =sin(πt / 5)cos(πt / 5), z d =cos(πt / 5),

[0234] 3.4 Control and preset performance parameters;

[0235] Control parameters: A1 = [5 5], A2 = [10 10], A3 = [25 30], A4 = A5 = [50 3], A6 = [5 10], ρ1~ρ6 = 0.9, μ i =2, i = 1~6, P L1 =10 -3 [1 1] T ,P L2 =10 -3 [3 2] T ,P L3 =10 -3 [5 3] T ,

[0236] PL4 =P L5 =P L6 =10 -2 [twenty one] T ;

[0237] Adaptive parameters: γ1~γ6=0.01;

[0238] Preset performance function: δ x (t)=δ y (t)=δ z (t)=(3-0.01)e -1.5t +0.01;

[0239]

[0240] Simulation effect as Figures 14-21 As shown, Figure 14 , Figure 15 , Figure 16 and Figure 17 The curves show a comparison of position and pose tracking performance. Figure 18 , Figure 19 , Figure 20 and Figure 21 Comparison curves for the control inputs of each actuator. For example... Figure 14-21 As shown, the controller designed in this application achieves high-precision trajectory tracking while maintaining the control input amplitude within a reasonable range. This indicates that the method, while ensuring performance, has low energy consumption requirements for the actuator and possesses good potential for engineering applications.

[0241] In summary, simulation experiments have demonstrated the feasibility of the proposed finite-time fault-tolerant control method based on the all-drive system, which can achieve stable tracking control of quadcopter UAVs under the combined influence of actuator failure, time-varying load, and external disturbances.

[0242] Therefore, the finite-time fault-tolerant control method for time-varying load quadrotor UAVs under all-drive systems proposed in this application has the following effects:

[0243] Higher model accuracy: Compared with existing simplified models, this application is based on the principle of UAV rotational dynamics, and derives a specific mathematical expression for the derivative of the moment of inertia. The established mathematical model more completely describes the time-varying dynamic characteristics of the system, thus more accurately describing the dynamic characteristics of UAVs in practical applications.

[0244] Wider range of applications: Compared with the finite-time fault-tolerant control method that only considers actuator failure, this application considers the combined effects of partial actuator failure, time-varying load and external disturbances. The designed control method is closer to actual operation scenarios such as pesticide spraying, seed sowing, fire fighting and disaster relief, and has higher practical application value.

[0245] The control method is more innovative: the control algorithm is designed based on the all-drive system method. Compared with the traditional state-space method, it simplifies the control design process, retains the original all-drive characteristics of the system, and makes the system have a clearer physical meaning and global stability. At the same time, it combines preset performance control and finite time control technology to ensure that the tracking error converges to the preset range within a finite time, thereby improving the control performance.

[0246] It should be noted that, in this application, although this specification describes the embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A finite-time fault-tolerant control method for a time-varying load quadrotor unmanned aerial vehicle, comprising the following steps: A mathematical model of a quadrotor unmanned aerial vehicle (UAV) system with time-varying load and actuator failure is established. The model considers partial actuator failure, time-varying load, and external disturbances. The partial actuator failure is described by a failure coefficient and input uncertainties. The time-varying load is represented by the time-varying mass and moment of inertia of the UAV system. The mathematical model is simplified and transformed using coordinates, and position and attitude reference signals are defined. The transformed model is then used as the control design model. Control laws and adaptive laws are designed based on the all-drive system approach, fault-tolerant control technology, finite-time control technology, and a preset performance control method. The preset performance control method quantitatively describes the desired performance index through a preset performance function and pre-sets the transient and steady-state performance of the system. Based on Lyapunov stability theory, it is proved that all signals in the closed-loop system are uniformly and eventually bounded, and that the system tracking error can converge to a preset error range within a finite time. The mathematical model of the UAV system with time-varying load is established as follows: Where, d i (t)(i=1,2,...6) represents external disturbance; g is gravitational acceleration; k fi (i = 1, 2, ... 6) represents the air resistance coefficient; u1 is the position subsystem control input, representing the total lift generated by the four rotors of the quadcopter UAV; u2, u3, u4 are the attitude subsystem control inputs, representing the resultant torque that generates the roll angle, pitch angle, and yaw angle. Considering the case of partial actuator failure, the actuator fault model adopts the following general form: you i ′=k i you i +D ui ,i=1,2,3,4 (2); Among them, u i ′ represents the control input after a fault occurs, κ represents the input after a fault occurs. i (i = 1, 2, 3, 4), 0 < κ i <1 Failure coefficient, Δ i To introduce uncertainties, substitute equation (2) into equation (1) to obtain the model of a UAV system with time-varying load and actuator failure: in, 2. The all-drive finite-time fault-tolerant control method for a time-varying load quadrotor UAV according to claim 1, characterized in that, New state variables are defined to transform the original system mathematical model into a form that is convenient for controller design; assumptions are proposed, such as upper and lower bounds or upper bound characteristics of time-varying parameters, including time-varying mass, moment of inertia and its derivatives and other related parameters; coordinate transformation relationships are defined, and the actual position and attitude signals are subtracted from the corresponding reference signals to obtain position tracking error and attitude tracking error as the core variables of control design. Step 1: Transform the system mathematical model into a control-oriented design model, and define... Then model (3) is transformed into: Step 2: Define coordinate transformations for subsequent control design: In the formula, [x d y d z d [This is a position reference signal.] This is the attitude reference signal. Based on the transformed model described above, the following assumptions are proposed: Assumption 1: Time-varying parameter a x,1 (t), a y,1 (t), a z,1 (t), a φ,1 (t), a θ,1 (t), a φ,2 (t), a θ,2 (t), The upper and lower bounds are unknown. Assumption 2: Time-varying parameters The upper bound of all is D, where D > 0, and is an unknown constant. Assumption 3: Time-varying parameters satisfy 3. The all-drive finite-time fault-tolerant control method for a time-varying load quadrotor UAV according to claim 1, characterized in that, The preset performance function is a smoothly decreasing positive function. The preset performance function includes a preset lower limit of steady-state error, an upper limit of steady-state error, and a minimum convergence rate parameter. The preset performance function constrains the system tracking error within a specified range. Choose a smooth decreasing positive function As a performance function, δ i0 δ i∞ h i μ is a pre-given positive constant. i0 δ represents the preset lower limit of steady-state error. i∞ h represents the upper limit of steady-state error. i Limit the minimum convergence rate of the system; and consider the following performance constraints: in, m i >0, The overshoot suppression parameter takes values ​​that satisfy... To handle time-varying performance constraints, let ε i (t)=e i (t) / δ i (t), and introduce error transformation: Then we have: in, Substituting the above error transformation and performance constraints into equation (5), we can obtain the transformed time-varying load quadrotor UAV model: in f i Given a function term, the specific expression is:

4. The all-drive finite-time fault-tolerant control method for a time-varying load quadrotor UAV according to claim 1, characterized in that, Based on the all-drive system approach, fault-tolerant control technology, finite-time control technology, and preset performance control method, control laws and adaptive laws are designed. The adaptive law is used to estimate the bounds of unknown time-varying parameters in the system. The unknown time-varying parameters include time-varying mass, moment of inertia, and external disturbances. The design of the adaptive law is based on Lyapunov stability theory to ensure that the system output signal converges to a preset accuracy range within a finite time, and that all signals of the closed-loop system are bounded. Step 1: Design control laws and adaptive laws based on the all-drive system approach, fault-tolerant control technology, finite-time control technology, and preset performance control methods: (from b) i (t) > 0 represents an unknown parameter, r i It is reversible. Model (13) belongs to a pseudo-high-order all-drive system form. Because the robust control method used excludes b i The influence of (t) allows this model to be used for controller design based on the all-drive system approach. Definition Yes Based on the estimation, the controller is designed as follows: Where 0 < ρ i <1, design The adaptive law is: Substituting the controller equation (17) and the adaptive law equation (18) into the system model equation (13), we can obtain the closed-loop system error dynamic equation: Lemma 1: For any scalar positive function σ(t): R ≥0 →R + For any variable z∈R, the following inequality holds: Lemma 2: Suppose that matrix A satisfies: Then for μ > 0, there exists a positive definite matrix. Satisfy: A T P+PA≤-μP; Lemma 3: Under the condition that Lemma 2 holds, for μ > 0, there exists a positive definite matrix. satisfy: Then there exists a positive definite matrix. This can make: Φ(A 0～n-1 ) T P(A 0～n-1 )+P(A 0～n-1 )Φ(A 0～n-1 )≤-μP(A 0～n-1 ); set up. Lemmas 2 and 3 are necessary conditions for the all-drive system approach, used to ensure that the controller designed based on the all-drive system meets the stability requirements. Lemma 4: For a continuous system There exists a positive definite function V(x) such that b1, b2, b3 > 0, 0 < p < 1, and satisfies the inequality Then we can conclude that the trajectory of the closed-loop system is bounded within a finite time T, and its range is... θ0 is a positive constant satisfying 0 < θ0 < 1, and Step 2: To analyze the stability of the closed-loop system, define the Lyapunov function: in, 0 < b i ≤|b i (t)|;then V i The time derivative is: Substituting equation (19) into the above equation and according to Lemma 1-3, we can obtain: because: Equation (22) can then be further transformed into: Redefining a Lyapunov function It can be seen that V j It is V i The first term, therefore, we first consider V. i Let's analyze it. First, based on... V can be obtained i The time derivative is And according to equation (18), it can be seen that if Then there exists a finite time T * , making For t≥T * This holds true. Then we obtain that when t ≥ T... * hour, Therefore, it can be concluded that when t≥T * hour, This holds true. Therefore, for all t ≥ T, the following condition is satisfied: when hour, and e i Consistent is ultimately bounded, in which It is to satisfy . a normal number. According to Lemma 4, for V i When t≥T r , hour, and e i Consistent is ultimately bounded, in which It is to satisfy The positive constant is . And the following conclusion is proved: (1) All signals in the closed-loop system (s) i u i (etc.) are uniformly bounded; (2) Tracking error e i (t) can be achieved in a finite time T r The convergence is within the preset performance constraint range. (3) When t≥T, and e i The uniform eventual boundedness means that the UAV output signal can stably track the reference command and the tracking error converges to the preset performance constraint range within a finite time.

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