A Time-Sliding Mode Control Method and Device for Quadrotor UAVs Based on Actuator Fault

Abstract

This invention provides a time-sliding mode control method and device for quadrotor unmanned aerial vehicles (UAVs) based on actuator failure, relating to the field of UAV flight control technology. Based on the structural characteristics of the X-shaped quadrotor UAV, this invention establishes the body coordinate system and inertial coordinate system of the quadrotor UAV. Considering the influence of partial actuator failure and bias faults, a dynamic model of the quadrotor UAV is constructed that treats uncertain external disturbances and actuator failures as lumped disturbances. An auxiliary equation is introduced to design a predefined time disturbance observer. Non-singular predefined time-sliding mode controllers based on the position subsystem and attitude subsystem are designed to segment the sliding surface. Based on the sliding mode controller and combined with the disturbance observer, coordinated control of the inner and outer loops of the quadrotor UAV is achieved. This invention can effectively cope with unknown disturbances and actuator failures, significantly improving the system's response speed, robustness, and fault tolerance, and is suitable for high-precision flight missions in complex environments.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) flight control technology, and more specifically, to a time sliding mode control method and device for quadrotor UAVs based on actuator failure. Background Technology

[0002] Quadrotor UAVs have been widely used in military, agricultural, forestry, and civilian fields due to their advantages such as vertical takeoff and landing, good stability, and simple structure. However, due to their underactuated and strongly coupled characteristics, achieving high-precision flight control presents certain challenges. Traditional linear control algorithms such as PID control and LQR control can meet control requirements to a certain extent, but they often exhibit insufficient control accuracy and stability issues when facing complex control targets and external disturbances. To address this, researchers have proposed nonlinear control methods such as adaptive control and sliding mode control. These methods are adaptable to model uncertainties and unknown disturbances, thereby improving the robustness of the system. However, most existing research focuses on improving tracking performance, neglecting the potential impact of inherent faults on quadrotor UAVs in practical applications, such as actuator failures, sensor failures, and component failures. The probability of these failures increases significantly due to harsh operating environments and mechanical wear, thus threatening flight safety.

[0003] To address the aforementioned issues, scholars both domestically and internationally have conducted research on fault-tolerant control for unmanned aerial vehicles (UAVs). For example, some studies have proposed methods based on active fault-tolerant control strategies to diagnose sensor faults and eliminate the influence of external disturbances through disturbance observers; others have designed composite adaptive fault-tolerant control strategies that utilize neural networks to estimate actuator faults and compensate for external disturbances. Furthermore, fault-tolerant control methods based on nonlinear extended state observers and fast nonsingular terminal sliding mode controllers have also been proposed to improve control accuracy. However, current research largely focuses on partial actuator failures, neglecting the impact of bias faults, and still has shortcomings in handling the combined effects of external disturbances, uncertainties, and actuator faults. Therefore, how to comprehensively consider partial actuator failures and bias faults, external disturbances, and uncertainties, and design an efficient fault-tolerant control method, has become an urgent technical challenge.

[0004] In view of the above, this application is hereby submitted. Summary of the Invention

[0005] The present invention aims to provide a time sliding mode control method and device for quadrotor UAVs based on actuator failure, so as to solve the problems of insufficient control accuracy, poor stability and weak robustness of existing quadrotor UAVs due to unknown disturbances and actuator failures during flight.

[0006] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0007] A time-sliding mode control method for a quadrotor unmanned aerial vehicle based on actuator failure includes:

[0008] S1. Based on the structural characteristics of the X-shaped layout of the quadrotor UAV, establish the body coordinate system and inertial coordinate system of the quadrotor UAV, and assume that the attitude angle of the quadrotor UAV is bounded.

[0009] S2. Based on the impact of actuator partial failure and bias fault, a dynamic model of a quadcopter UAV is constructed that treats uncertain external disturbances and actuator faults as lumped disturbances.

[0010] S3. Based on the aforementioned quadcopter UAV dynamics model, an auxiliary equation is introduced to design a predefined time disturbance observer;

[0011] S4. Based on the quadcopter UAV dynamics model and the predefined time disturbance observer, design non-singular predefined time sliding mode controllers based on the position subsystem and attitude subsystem respectively to segment the sliding surface;

[0012] S5, based on the non-singular predefined time sliding mode controller of the position subsystem and attitude subsystem, combined with the estimated value of the predefined time disturbance observer, realizes the inner and outer loop coordinated control of the quadcopter UAV.

[0013] Preferably, the body coordinate system is defined as follows: The inertial coordinate system is Furthermore, the attitude angles of the quadcopter drone satisfy:

[0014] , , ;

[0015] in, For the body to circle The roll angle of the shaft rotation, For the body to circle The pitch angle of the axis of rotation. For the body to circle Yaw angle of shaft rotation.

[0016] Preferably, the construction process of the quadcopter UAV dynamic model is as follows:

[0017] Based on the impact of partial actuator failure and bias fault, an actuator fault model is established, which is expressed as:

[0018] ;

[0019] in, To control the input as desired; For actual control input; Indicates an actuator bias fault; when , When the drone is in normal condition, it indicates that the drone is in a normal state; when , When, it indicates that the drone only has a failure in the actuator part; when , When, it indicates that the drone only has an actuator bias fault; when , This indicates that the drone simultaneously suffers from both partial failure and offset faults.

[0020] The dynamic model of a quadcopter UAV with actuator failure is as follows:

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] in, , , The position in inertial coordinates; , , This is the corresponding first derivative; , , This is the corresponding second derivative; , , respectively roll angle Pitch angle Yaw angle The first derivative; , , These are the second derivatives of the roll angle, pitch angle, and yaw angle, respectively. Represents the gravitational constant; This indicates the total mass of the quadcopter drone; , , These represent the air friction drag coefficients; For propeller speed margin, For the propeller's inertial constant; , , , For actual control input; External interference;

[0028] Let be the moment of inertia of the quadcopter. Assuming the quadcopter of the UAV is symmetrical, then... The moment of inertia of the asymmetric part is 0, that is... , They are respectively around , , Moment of inertia of the three axes;

[0029] Based on the actuator failure model, the dynamic model of the quadcopter UAV is simplified as follows:

[0030] ; ; ;

[0031] ; ; ;

[0032] in: ;

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] in, , , For the introduction of virtual control variables; , which is a lumped disturbance consisting of external disturbances, uncertainties, and actuator failures; The actuator failure factor corresponding to the lumped disturbance;

[0042] The expressions for the target roll angle, target pitch angle, and lift are then obtained as follows:

[0043] ;

[0044] ;

[0045] ;

[0046] in, The target location coordinates are set. , , These are the target yaw angle, target roll angle, and target pitch angle, respectively. For lift.

[0047] Preferably, the design process of the predefined time disturbance observer is as follows:

[0048] The simplified quadcopter UAV dynamics model is converted into vector form:

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] in, , State variables for a quadcopter drone; This is the lumped perturbation vector for position and attitude; for The second derivative;

[0054] The expression for the auxiliary equation is:

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] in, Let be the state variable of the auxiliary equation. for The second derivative; It is a vector of positive constants; This is the error vector between the state variables of the quadcopter UAV and the state variables of the auxiliary equations; It is the transpose symbol;

[0060] Therefore, the predefined time perturbation observer is constructed based on the auxiliary equation as follows:

[0061] ;

[0062] ;

[0063] , ;

[0064] ;

[0065] in, This is an estimate of the lumped disturbance vector D; Error vector The estimated value; for The second derivative; for The first derivative; These are the adjustment parameters for the disturbance observer; For predefined time parameters of the disturbance observer; , For the parameter factors of the disturbance observer; , ; This is the difference between the error vector and the estimated value.

[0066] Preferably, by incorporating a Lyapunov function, the predefined time-perturbation observer can converge within a predefined time; wherein the Lyapunov function is selected as follows: ;

[0067] in, It is a Lyapunov function; Error vector Compared with the estimated value The difference; It is the transpose symbol;

[0068] right Taking the time derivative yields:

[0069] ;

[0070] in, for The first derivative; These are the adjustment parameters for the disturbance observer; For predefined time parameters of the disturbance observer; , For the parameter factors of the disturbance observer;

[0071] Then the estimation error of lumped disturbance for:

[0072] ;

[0073] in, This is an estimate of the lumped disturbance vector D; The state variables of the auxiliary equation The second derivative; It is a vector of positive constants; State variables of a quadcopter drone The second derivative;

[0074] Then, when When predefined time convergence is satisfied, It also satisfies the predefined time convergence requirement.

[0075] Preferably, the non-singular predefined time sliding mode controller of the position subsystem is used to control the movement position of the quadcopter UAV in space, and the non-singular predefined time sliding mode controller of the attitude subsystem is used to maintain the attitude stability of the quadcopter UAV; by comparing the tracking error with a preset threshold, the sliding surface is segmented to avoid singularity problems.

[0076] Preferably, the expression for the non-singular predefined time sliding surface of the position subsystem is:

[0077] ;

[0078] in, This represents a non-singular predefined time sliding surface of the position subsystem. , , , These correspond to the values ​​on the x, y, and z axes, respectively.

[0079] ; ; ; ;

[0080] , , , These are all adjustable parameters of the sliding surface of the position subsystem; Predefined time parameters for the sliding surface of the position subsystem;

[0081] in, It is a very small positive number in the positional subsystem. ; , which represent the position tracking error of the quadcopter UAV along the x, y, and z axes, respectively; For the position tracking error of the quadcopter drone, ; The actual location of the quadcopter drone; For the target location; for The first derivative; when At that time, the position tracking error under the action of the sliding surface At a predefined time Converging inward to a small region approaching zero; when When the sliding surface is switched, the position tracking error gradually converges to the origin;

[0082] Therefore, the position controller based on the position subsystem is designed as follows:

[0083] ;

[0084] ;

[0085] in, Non-singular predefined time sliding surfaces for position subsystems The first derivative; For position controller; This is an estimate of the lumped disturbance of the location subsystem; It is a positive number; These are adjustable parameters for the position subsystem controller; For the adjustable time parameters of the position subsystem controller; Hyperbolic tangent function to suppress position controller Boom;

[0086] In the position controller Under the influence exist It approaches zero within a certain time.

[0087] Preferably, the attitude subsystem uses a non-singular predefined time sliding surface. The expression is:

[0088] ;

[0089] in, It is a very small positive constant in the attitude subsystem. ; , , , Corresponding to roll angles Pitch angle Yaw angle The value;

[0090] ; ; ; ;

[0091] , , , These are all adjustable parameters of the sliding surface of the attitude subsystem; Predefined time parameters for the sliding surface of the attitude subsystem; For the attitude tracking error of the quadcopter drone, ;

[0092] attitude angle The actual location of the quadcopter drone; The target attitude angle; for The first derivative; when At that time, the attitude tracking error under the action of the sliding surface At a predefined time Converging inward to a small region approaching zero; when At that time, the sliding surface will be switched, and the attitude tracking error will be reduced. It gradually converges to the origin.

[0093] The attitude controller based on the attitude subsystem is designed as follows:

[0094] ;

[0095] ;

[0096] in, Non-singular predefined time sliding surfaces for attitude subsystems The first derivative;

[0097] For attitude controller; This is an estimate of the lumped disturbance of the attitude subsystem; It is a positive number; These are adjustable parameters for the attitude controller; These are the adjustable time parameters for the attitude controller; for The second derivative;

[0098] In attitude controller Under the influence exist It approaches zero within a certain time.

[0099] Preferably, in the coordinated control of the inner and outer loops of a quadcopter UAV:

[0100] The virtual control quantity is calculated by the position controller, and then the desired lift, as well as the desired target roll angle and target pitch angle, are calculated.

[0101] The target roll angle, target pitch angle, and preset target yaw angle are used as the tracking targets of the attitude controller;

[0102] The attitude controller calculates the control torque based on the error between the actual attitude angle and the target attitude angle, thereby driving the UAV to track the desired attitude and completing the coordinated control of the inner and outer loops.

[0103] The present invention also provides a time sliding mode control device for a quadcopter unmanned aerial vehicle based on actuator failure, comprising:

[0104] The coordinate system establishment unit is used to establish the body coordinate system and inertial coordinate system of the quadrotor UAV based on the structural characteristics of the X-shaped layout, and assumes that the attitude angles of the quadrotor UAV are bounded.

[0105] The dynamic model building unit is used to construct a dynamic model of a quadcopter UAV that treats uncertain external disturbances and actuator faults as lumped disturbances based on the effects of actuator partial failure and bias faults.

[0106] The disturbance observer establishment unit is used to design a predefined time disturbance observer based on the dynamic model of the quadcopter UAV and by introducing auxiliary equations.

[0107] The sliding mode controller establishment unit is used to design non-singular predefined time sliding mode controllers based on the position subsystem and attitude subsystem respectively to segment the sliding surface based on the dynamic model of the quadrotor UAV and the predefined time disturbance observer.

[0108] The inner and outer loop coordination control unit is used to achieve inner and outer loop coordinated control of the quadrotor UAV based on the non-singular predefined time sliding mode controller of the position subsystem and attitude subsystem, combined with the estimated value of the predefined time disturbance observer.

[0109] The present invention also provides a time sliding mode control device for a quadcopter UAV based on actuator failure, including a processor and a memory. The memory stores a computer program that can be executed by the processor to implement the time sliding mode control method for a quadcopter UAV based on actuator failure as described above.

[0110] The present invention also provides a computer-readable storage medium storing computer-readable instructions, which, when executed by a processor of the device on which the computer-readable storage medium is located, implement the time sliding mode control method for a quadcopter UAV based on actuator failure as described above.

[0111] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0112] This invention treats actuator failures, uncertainties, and external disturbances as lumped disturbances and designs a predefined time disturbance observer to estimate and compensate for the lumped disturbances within a preset time. Simultaneously, addressing the singularity problem inherent in traditional predefined time sliding mode control, a non-singular predefined time sliding surface is designed based on the position and attitude subsystems respectively by segmenting the sliding surface, effectively avoiding singular values ​​in the controller. This method not only achieves rapid convergence within the predefined time but also exhibits strong robustness, effectively coping with the effects of actuator failures, external disturbances, and uncertainties, thereby significantly improving the control performance and fault tolerance of quadcopter UAVs.

[0113] By introducing a predefined time stability theory, the controller designed in this application can complete target tracking within a user-defined time, thereby improving the system's response speed. It is suitable for quadcopter UAV control tasks in complex environments, such as military reconnaissance, agricultural plant protection, and logistics transportation, and has significant engineering application prospects.

[0114] This invention provides an innovative time sliding mode control method for quadrotor UAVs based on actuator failure, which overcomes the shortcomings of existing technologies in terms of convergence speed, robustness, and singularity issues, and provides a new solution for high-performance control of quadrotor UAVs. Attached Figure Description

[0115] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0116] Figure 1 This is a schematic diagram of a non-singular sliding mode control method for a quadcopter unmanned aerial vehicle provided in Embodiment 1.

[0117] Figure 2 This is a schematic diagram of the quadcopter UAV provided in Example 1 in both the inertial coordinate system and the body coordinate system.

[0118] Figure 3 Figures a, b, and c in the middle represent the estimated values ​​of three different perturbations in the location lumped perturbation provided in Example 1, respectively. ) and actual value The tracking curve comparison chart.

[0119] Figure 4 Figures a, b, and c in the middle represent the estimated values ​​of three different perturbations in the attitude lumped perturbation provided in Example 1, respectively. ) and actual value The tracking curve comparison chart.

[0120] Figure 5 Figures a, b, and c in the middle are comparison diagrams of the position tracking curves of the desired trajectory during actuator failure, respectively, between the method of the present invention (NPTSM) provided in Example 1 and the existing sliding mode control methods (PTSM) and (NTSMC).

[0121] Figure 6 Figures a, b, and c in the middle are comparison diagrams of the attitude angle (roll / pitch / yaw) tracking curves of the method of the present invention (NPTSM) provided in Example 1, and the existing sliding mode control methods (PTSM) and (NTSMC), respectively, during the actuator failure.

[0122] Figure 7 Figures a, b, and c in the middle are comparison diagrams of the position tracking error curves of the method of the present invention (NPTSM) provided in Example 1 and the existing sliding mode control methods (PTSM) and (NTSMC) during actuator failure.

[0123] Figure 8 Figures a, b, and c in the middle are comparison diagrams of the attitude tracking error curves of the method of the present invention (NPTSM) provided in Example 1 and the existing sliding mode control methods (PTSM) and (NTSMC) during actuator failure.

[0124] Figure 9 Figures a, b, c, and d show four desired control inputs during actuator failure for the method of the present invention (NPTSM) provided in Example 1 and the existing sliding mode control methods (PTSM) and (NTSMC). A comparison chart of the curves.

[0125] Figure 10 This is a schematic diagram of a non-singular sliding mode control device for a quadcopter unmanned aerial vehicle (UAV) according to Embodiment 2. The invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Detailed Implementation

[0126] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 a part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0127] Example 1

[0128] Embodiment 1 of the present invention provides a time sliding mode control method for a quadrotor UAV based on actuator failure, which can be implemented by a time sliding mode control device for a quadrotor UAV based on actuator failure (hereinafter referred to as the control device), specifically, executed by one or more processors within the control device.

[0129] In this embodiment, the control device may be an electronic device equipped with a processor, which carries a computer program for the non-singular sliding mode control method of the quadcopter UAV and the computer program can be executed, such as a computer, smartphone, smart tablet, workstation, etc., which are not limited here.

[0130] like Figure 1 As shown, a time sliding mode control method for a quadcopter UAV based on actuator failure includes steps S1 to S5.

[0131] S1. Based on the structural characteristics of the X-shaped layout of the quadrotor UAV, establish the body coordinate system and inertial coordinate system of the quadrotor UAV, and assume that the attitude angle of the quadrotor UAV is bounded.

[0132] like Figure 2 As shown, the quadcopter drone in this embodiment adopts an "X" shaped layout. The propellers f1 and f3 of the quadcopter drone rotate clockwise, while the propellers f2 and f4 rotate counterclockwise.

[0133] To accurately describe the structure and motion principles of the UAV, the body coordinate system is defined as follows: The inertial coordinate system is .

[0134] To accurately establish the dynamic model of the quadrotor UAV and subsequently design the observer and controller, the following assumptions are made before modeling the quadrotor UAV:

[0135] Assumption 1: The structure of the quadcopter UAV is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coincides with the geometric center of gravity.

[0136] Assumption 2: The mass and moment of inertia of the quadcopter drone do not change over time.

[0137] Assumption 3: The attitude angles of the quadcopter UAV satisfy the following conditions:

[0138] , , ;

[0139] in, For the body to circle The roll angle of the shaft rotation, For the body to circle The pitch angle of the axis of rotation. For the body to circle Yaw angle of shaft rotation.

[0140] The lemma used in this embodiment: For nonlinear systems If there exists a radially unbounded Lyapunov function Satisfy the following formula: ;Formula (1)

[0141] in, Lyapunov function The first derivative, For preset time parameters, If the parameter is adjustable, then the above nonlinear system The state variables are predefined time-stable, where, Indicates time, Indicates input variables, Let represent a nonlinear function. The proof is as follows:

[0142] ;Formula (2)

[0143] in, The initial value is ,and It eventually converges to zero. Indicates to Differentiate, Indicates to Differentiate, Let be the convergence time function. for The initial value of the system is given by equation (2). Analysis shows that the convergence time of the system is less than the time parameter. .

[0144] S2. Based on the effects of actuator partial failure and bias fault, a dynamic model of a quadcopter UAV is constructed that treats uncertain external disturbances and actuator faults as lumped disturbances.

[0145] Specifically, considering that the quadcopter UAV is simultaneously affected by partial failure and bias fault, an actuator fault model is established, which is expressed as: ;Formula (3)

[0146] in, To control the input as desired; For actual control input; The actuator failure factor corresponding to the lumped disturbance; This indicates an actuator bias fault.

[0147] when , When the drone is in normal condition, it indicates that the drone is in a normal state; when , When, it indicates that the drone only has a failure in the actuator part; when , When, it indicates that the drone only has an actuator bias fault; when , This indicates that the drone simultaneously suffers from both partial failure and offset failure.

[0148] Therefore, the dynamic model of a quadcopter UAV with actuator failure is as follows:

[0149] ,

[0150] ,

[0151] , ,

[0152] , ;Formula (4)

[0153] in, , , The position in inertial coordinates; , , This is the corresponding first derivative; , , This is the corresponding second derivative; , , respectively roll angle Pitch angle Yaw angle The first derivative; , , These are the second derivatives of the roll angle, pitch angle, and yaw angle, respectively. Represents the gravitational constant; This indicates the total mass of the quadcopter drone; , , These represent the air friction drag coefficients; For propeller speed margin, For the propeller's inertial constant; , , , For actual control input; External interference.

[0154] Let be the moment of inertia of the quadcopter. Assuming the quadcopter of the UAV is symmetrical, then... The moment of inertia of the asymmetric part is 0, that is... , They are respectively around , , Moment of inertia of the three axes.

[0155] Combining the actuator failure model, substituting equation (3) into equation (4), the dynamic model of the quadcopter UAV is simplified as follows:

[0156] ， ， ， ， ，

[0157] ;Formula (5)

[0158] in:

[0159] ,

[0160] ,

[0161] ;Formula (6)

[0162] ,

[0163] ,

[0164] ;Formula (7)

[0165] ,

[0166] ,

[0167] ;Formula (8)

[0168] in, , , For the introduction of virtual control variables; , which is a lumped disturbance consisting of external disturbances, uncertainties, and actuator failures; The actuator failure factor corresponding to the lumped disturbance; , , , These all indicate different actuator bias faults.

[0169] Since the quadcopter UAV is an underactuated system, it cannot set targets for all six degrees of freedom. The target roll angle, target pitch angle, and lift can be calculated using formula (6).

[0170] , ,

[0171] ;Formula (9)

[0172] in, The target location coordinates are set. , , These are the target yaw angle, target roll angle, and target pitch angle, respectively. For lift.

[0173] S3. Based on the dynamic model of the quadcopter UAV, an auxiliary equation is introduced to design a predefined time disturbance observer.

[0174] Specifically, to facilitate the design of the disturbance observer, the simplified quadcopter UAV dynamics model is rewritten in vector form:

[0175] ;Formula (10)

[0176] ; ;

[0177] ;

[0178] in, , State variables for a quadcopter drone; This is the lumped perturbation vector for position and attitude; for The second derivative of .

[0179] To reduce the impact of lumped disturbances on quadcopter UAVs, a predefined time disturbance observer is designed to observe the lumped disturbances experienced by the quadcopter UAV, and the observed values ​​are used as compensation terms for the designed controller.

[0180] Specifically, the expression for the introduced auxiliary equation is:

[0181] ;Formula (11)

[0182] ; ;

[0183] ;

[0184] in, Let be the state variable of the auxiliary equation. for The second derivative; It is a vector of positive constants; This is the error vector between the state variables of the quadcopter UAV and the state variables of the auxiliary equations; This is the transpose symbol.

[0185] Therefore, the predefined time perturbation observer is constructed based on the auxiliary equation as follows:

[0186] ;Formula (12)

[0187] ;Formula (13)

[0188] , ; ;

[0189] in, This is an estimate of the lumped disturbance vector D; Error vector The estimated value; for The second derivative; for The first derivative; These are the adjustment parameters for the disturbance observer; For predefined time parameters of the disturbance observer; , For the parameter factors of the disturbance observer, , ; This is the difference between the error vector and the estimated value.

[0190] To achieve an efficient estimation of the lumped disturbance D, the design concept of this invention is to construct an auxiliary dynamic system and design an observer to observe the state of this auxiliary system. First, an auxiliary state variable is defined. Its dynamic characteristics are described by the auxiliary equation (11). Subsequently, a state observer is designed for the system state to estimate the auxiliary state variables. By analyzing the state observation error (i.e., the error vector) With disturbance estimation error The relationship between the error vectors can be proven when the error vectors are... When convergence occurs within a predefined time... It also converges accordingly. Based on this principle, the disturbance estimate is... Designed to include The function (as shown in Equation 13) transforms the perturbation estimation problem into a state observation problem, and its convergence is proven by Lyapunov stability theory.

[0191] Under the influence of equations (11), (12), and (13), the error It can converge within a predefined time, and the proof is as follows:

[0192] Subtract the equation from both sides of equation (13) We can obtain the following formula:

[0193] ;Formula (14)

[0194] In order to analyze Based on the convergence of the Lyapunov function, the predefined time-perturbation observer can converge within a predefined time; wherein the Lyapunov function is selected as follows: ;Formula (15)

[0195] in, It is a Lyapunov function; Error vector Compared with the estimated value The difference; It is the transpose symbol;

[0196] right Taking the time derivative yields:

[0197] ;Formula (16)

[0198] in, for The first derivative; These are the adjustment parameters for the disturbance observer; For predefined time parameters of the disturbance observer; , For the parameter factors of the perturbation observer.

[0199] According to the lemma, the error is... Able to be in a predefined time Convergence.

[0200] The estimation error of the lumped disturbance can be obtained through equations (11), (12), and (13). for:

[0201] ;Formula (17)

[0202] in, This is an estimate of the lumped disturbance vector D; The state variables of the auxiliary equation The second derivative; It is a vector of positive constants; State variables of a quadcopter drone The second derivative of .

[0203] Then, from equations (16) and (17), we know that when When predefined time convergence is satisfied, It also satisfies the predefined time convergence requirement.

[0204] S4. Based on the quadcopter UAV dynamics model and the predefined time disturbance observer, non-singular predefined time sliding mode controllers based on the position subsystem and attitude subsystem are designed to segment the sliding surface.

[0205] The quadcopter UAV system consists of inner and outer rings. The outer ring is a position subsystem, and the inner ring is an attitude subsystem. The non-singular predefined time sliding mode controller of the position subsystem is used to control the movement position of the quadcopter UAV in space, and the non-singular predefined time sliding mode controller of the attitude subsystem is used to maintain the attitude stability of the quadcopter UAV. By comparing the tracking error with a preset threshold, the sliding surface is segmented to avoid singularity issues.

[0206] Then, the expression for the non-singular predefined time sliding surface of the position subsystem is:

[0207] ;Formula (18)

[0208] in, This represents a non-singular predefined time sliding surface of the position subsystem. , , , These correspond to the values ​​on the x, y, and z axes, respectively.

[0209] ; ; ; ;

[0210] , , , These are all adjustable parameters of the sliding surface of the position subsystem; For the predefined time parameters of the sliding surface of the position subsystem; where, It is a very small positive number in the positional subsystem. ; , , and z are the x, y, and z axis values ​​of the position tracking error of the quadcopter UAV, respectively.

[0211] For the position tracking error of the quadcopter drone, ; The actual location of the quadcopter drone; For the target location, for The first derivative.

[0212] when At that time, the position tracking error under the action of the sliding surface At a predefined time Converging inward to a small region approaching zero; when When switching the sliding surface, the position tracking error asymptotically converges to the origin. The proof is as follows:

[0213] When the sliding mode surface ,when The result is obtained from equation (18):

[0214] ;Formula (19)

[0215] Choose the Lyapunov function as Taking its time derivative, we get:

[0216] ;Formula (20)

[0217] in, for The first derivative of . Equation (20) satisfies the lemma, then able to Approaching within a time period .when Let the error at this time be... According to equation (18), the expression for the position tracking error can be calculated as follows: That is, when hour The exponent converges to zero.

[0218] The position controller of the position subsystem is designed as follows:

[0219]

[0220] ;Formula (21)

[0221] in, Non-singular predefined time sliding surfaces for position subsystems The first derivative; For position controller; This is an estimate of the lumped disturbance of the location subsystem; It is a positive number; These are adjustable parameters for the position subsystem controller; For the adjustable time parameters of the position subsystem controller; Hyperbolic tangent function to suppress position controller The vibration.

[0222] The singularity problem of traditional terminal sliding mode control stems from the power terms in the sliding surface, when When the exponent of the power is less than 1, its time derivative term will contain... The negative power term, when When the value approaches 0, this term tends to infinity, leading to singular control outputs.

[0223] According to the analysis of equation (21), we can know that Negative exponent terms are a contributing factor to singular problems. By segmenting the sliding surface, negative exponent terms can be eliminated. Position error in This avoids A strange problem has occurred.

[0224] In the position controller Under the influence exist It approaches zero over time, and its stability is proven as follows:

[0225] Taking the time derivative of the sliding surface of the position subsystem, we can obtain:

[0226] ;Formula (22)

[0227] in, It is a very small positive number in the positional subsystem.

[0228] At this point, choose the Lyapunov function. for: ;Formula (23)

[0229] Taking the time derivative of equation (23), and substituting the derivative of the sliding surface equation (22) and the control law equation (21) into the equation, we get:

[0230] ;Formula (24)

[0231] If equation (24) satisfies the lemma, then able to It converges to zero within a given time. In summary, the state variables of the position subsystem can be realized within a given time. It converges to a small region near zero within a certain time.

[0232] Similarly, in order to keep the attitude of the quadcopter drone stable, a non-singular predefined time sliding mode controller was designed for the attitude loop.

[0233] The non-singular predefined time sliding surface of the attitude subsystem The expression is:

[0234] ;Formula (25)

[0235] in, It is a very small positive constant in the attitude subsystem. ; , , , Corresponding to roll angles Pitch angle Yaw angle The value;

[0236] ； ； ； ;

[0237] 、 、 、 These are all adjustable parameters of the sliding surface of the attitude subsystem; Predefined time parameters for the sliding surface of the attitude subsystem; For the attitude tracking error of the quadcopter drone, ; state angle The actual location of the quadcopter drone; The target attitude angle; for The first derivative.

[0238] when At that time, the attitude tracking error under the action of the sliding surface At a predefined time Converging inward to a small region approaching zero; when At that time, the sliding surface will be switched, and the attitude tracking error will be reduced. It gradually converges to the origin.

[0239] The proof is as follows:

[0240] When the sliding surface of the attitude subsystem , Then, from equation (25), we get:

[0241] ;Formula (26)

[0242] Choose the Lyapunov function as Differentiating it, we get:

[0243] ;Formula (27)

[0244] If equation (27) satisfies the lemma, then able to Approaching within a time period .when Let the error at this time be... According to equation (25), the expression for attitude tracking error can be calculated as follows: That is, when hour The exponent converges to zero.

[0245] According to equation (25), the attitude controller design of the attitude subsystem is obtained as follows:

[0246]

[0247] ;Formula (28)

[0248] in, Non-singular predefined time sliding surfaces for attitude subsystems The first derivative.

[0249] For attitude controller; This is an estimate of the lumped disturbance of the attitude subsystem; It is a positive number; These are adjustable parameters for the attitude controller; These are the adjustable time parameters for the attitude controller; for The second derivative of .

[0250] According to the analysis of equation (28), we can know that Negative exponent terms are a contributing factor to singular problems. By segmenting the sliding surface, negative exponent terms can be eliminated. attitude error This avoids A strange problem has occurred.

[0251] In attitude controller Under the influence exist It approaches zero over time, and its stability is proven as follows:

[0252] Taking the time derivative of the sliding surface of the attitude subsystem, we can obtain:

[0253] ;Formula (29)

[0254] Choose the Lyapunov function for: ;Formula (30)

[0255] Taking the time derivative of equation (30), and substituting the derivative of the sliding surface equation (29) and the control law equation (28) into the equation, we get:

[0256] ;Formula (31)

[0257] If equation (31) satisfies the lemma, then able to The state variables of the attitude subsystem approach zero within a given time interval. Based on the above analysis, the state variables of the attitude subsystem can be realized within... A small region that approaches zero within a given time period.

[0258] S5, based on the non-singular predefined time sliding mode controller of the position subsystem and attitude subsystem, combined with the estimated value of the predefined time disturbance observer, realizes the inner and outer loop coordinated control of the quadcopter UAV.

[0259] Specifically, it includes:

[0260] The virtual control quantity calculated by the position controller (Formula 21) in step S4 Substitute into formula (9) and perform the inverse solution to calculate the desired total lift. And the desired attitude angle (target roll angle) and target pitch angle );

[0261] The calculated target attitude angle , and the preset target yaw angle As the tracking target of the attitude controller;

[0262] The attitude controller (Formula 28) calculates the control torque based on the error between the actual attitude angle and the target attitude angle. This drives the drone to track the desired attitude and completes the coordinated control of the inner and outer loops.

[0263] During attitude tracking, the position and attitude angles of the quadcopter UAV are made to track the desired trajectory. Then, the tracking trajectory curves of position and attitude angles are analyzed along with the tracking error curves of position and attitude angles. By adjusting the predefined time parameters, the position tracking error and attitude tracking error are controlled to converge within a predefined time to meet the different mission requirements of the UAV.

[0264] In another preferred embodiment, to verify the effectiveness of the control method proposed herein, the control method of the present invention is simulated using the MATLAB / Simulink simulation platform.

[0265] The parameters of the quadcopter UAV control system were set as follows in the simulation experiment:

[0266] The acceleration due to gravity is The total mass is The air drag coefficient is Let the rotational inertia be set as , The inertial constant of the rotor is Rotor speed margin Considering that the quadcopter UAV is affected by external disturbances, the external disturbance for its position is set as follows: The attitude external disturbance is set as , The initial values ​​of the attitude angles are... The initial value of the position is The position target and attitude target values ​​are , The predefined time-perturbation observer parameters are: , The parameters for the non-singular sliding mode predefined time controller are: , , , , .

[0267] Considering the impact of actuator failure on quadcopter drones, the quadcopter drone is set to... When an actuator failure occurs, some of its failure parameters are: 1, The bias parameter is .

[0268] To verify the tracking performance of the controller and observer designed in this invention, the tracking performance of the control system under different control schemes is discussed under the same conditions. In the simulation experiment, the control algorithm (NPTSM) of this invention is compared with the predefined time sliding mode control method (PTSM) and the fixed time sliding mode control method (NTSMC) in the prior art.

[0269] like Figures 3 to 4 As shown, the tracking curve of the disturbance observer for the lumped disturbance is represented, from... Figures 3 to 4 It can be observed that the perturbation observer can track the lumped perturbation within 1 second, and the convergence time is less than the predefined time. This verifies the effectiveness of the designed disturbance observer. Similarly, the figure shows that during the actuator failure period from 5.5s to 6.5s, the disturbance observer can estimate the abrupt lumped disturbance well, indicating that the observer can effectively reduce the impact of lumped disturbance.

[0270] Figures 5 to 8 This shows the pose tracking curves and pose tracking error curves of a quadcopter UAV under different control algorithms. From... Figures 5 to 8 The results show that under the NPTSM and PTSM control algorithms, the position tracking curves with a preset time of 6s all completed target tracking within 1.5s, and the attitude angle tracking curves with a preset time of 2s all completed target tracking within 1s. Under the NTSMC control algorithm, the convergence time of the quadcopter UAV's position tracking curve is greater than 2.5s, and the convergence time of the attitude angle tracking curve is greater than 2s. These results indicate that the NPTSM algorithm enables the quadcopter UAV to complete target tracking within a predefined time, exhibiting a faster convergence rate compared to the NTSMC algorithm. Figure 7 It can be observed that during actuator failures, the position tracking error stabilizes at zero under the NPTSM and PTSM control algorithms, while the position tracking error deviates and fluctuates around zero under the NTSMC control algorithm. Figure 8 The results show that during actuator failure, the NPTSM control algorithm exhibits smaller roll and pitch tracking errors compared to the PTSM control algorithm. Furthermore, the PTSM control algorithm shows less significant fluctuation in roll tracking error between 9.8s and 10.6s. Additionally, the NPTSM control algorithm demonstrates smaller yaw and pitch tracking errors compared to the NTSMC control algorithm. Based on these simulation results and analysis, the proposed NPTSM control algorithm demonstrates better robustness compared to the PTSM control algorithm, and faster convergence rate and better robustness compared to the NTSMC algorithm.

[0271] Figure 9Figures a / b / c / d show the control outputs of the three control algorithms, respectively. From the figures, it can be seen that compared to the control algorithm presented in this paper, the PTSM and NTSMC control algorithms exhibit longer durations and higher amplitude chattering phenomena in the control outputs corresponding to roll and pitch angles. In summary, the simulation results demonstrate that the non-singular predefined time sliding mode controller designed in this paper can track the desired value within a preset time and has a fast convergence rate. Furthermore, it exhibits strong robustness against actuator failures, external disturbances, and uncertainties.

[0272] In this embodiment, the PTSM control algorithm, or Predefined Time Sliding Mode Control, is an advanced variant of sliding mode control designed to address the singularity problem inherent in traditional sliding mode control and achieve control system convergence within a predetermined time. It adjusts the system's dynamic behavior by introducing a specific time function, achieving more flexible and smoother control performance while maintaining strong robustness. For example, in spacecraft attitude tracking control, PTSM can pre-set the attitude adjustment completion time according to mission requirements.

[0273] The NTSMC control algorithm is an improved sliding mode control strategy designed to address the singularity problem in traditional terminal sliding mode control (TSMC) while retaining its finite-time convergence characteristics. NTSMC utilizes a nonlinear sliding surface design to ensure the system state converges to zero within a finite time, making it particularly suitable for scenarios requiring rapid tracking or adjustment. It possesses a natural ability to suppress system uncertainties (such as parameter variations and external disturbances). By switching control terms on the sliding surface, the impact of uncertainties on the system can be compensated.

[0274] This embodiment addresses the vulnerability of quadrotor UAVs to disturbances and actuator failures by proposing a non-singular predefined time sliding mode control method. Through analysis of the actuator failure model and the quadrotor UAV model, faults, external disturbances, and uncertainties are treated as lumped disturbances, thus establishing a quadrotor UAV fault model. To reduce the impact of lumped disturbances on the quadrotor UAV, a predefined time disturbance observer is designed based on predefined time stability theory. Furthermore, to address the singularity problem of traditional predefined time sliding mode control, a non-singular predefined time sliding surface is designed by segmenting the sliding surface, thus avoiding singularity issues in the designed controller. The stability and convergence of the designed controller and observer are proven using Lyapunov stability theory and lemmas.

[0275] Simulation results also show that the control algorithm designed in this application has better robustness than the PTSM control algorithm, and faster convergence rate and better robustness than the NTSMC algorithm.

[0276] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0277] This invention treats actuator failures, uncertainties, and external disturbances as lumped disturbances and designs a predefined time disturbance observer to estimate these lumped disturbances, effectively addressing the impact of lumped disturbances. Unlike traditional disturbance observers, this observer can improve disturbance tracking efficiency by adjusting predefined time parameters. By compensating the controller, the impact of disturbances on quadrotor attitude tracking is reduced, and control performance is improved.

[0278] To improve the position and attitude tracking performance of a quadrotor, a non-singular predefined time sliding mode controller was designed. By segmenting the traditional predefined time sliding mode surface, a non-singular predefined time sliding mode surface was designed, thus avoiding the problem of singular values ​​in the designed controller. The algorithm converges within a predefined time, exhibiting a fast convergence rate, and demonstrates strong robustness to the influence of faults, external disturbances, and uncertainties.

[0279] Example 2

[0280] like Figure 10 As shown, the second embodiment of the present invention also provides a time sliding mode control device for a quadcopter UAV based on actuator failure, comprising:

[0281] The coordinate system establishment unit is used to establish the body coordinate system and inertial coordinate system of the quadrotor UAV based on the structural characteristics of the X-shaped layout, and assumes that the attitude angles of the quadrotor UAV are bounded.

[0282] The dynamic model building unit is used to construct a dynamic model of a quadcopter UAV that treats uncertain external disturbances and actuator faults as lumped disturbances based on the effects of actuator partial failure and bias faults.

[0283] The disturbance observer establishment unit is used to design a predefined time disturbance observer based on the dynamic model of the quadcopter UAV and by introducing auxiliary equations.

[0284] The sliding mode controller establishment unit is used to design non-singular predefined time sliding mode controllers based on the position subsystem and attitude subsystem respectively to segment the sliding surface based on the dynamic model of the quadrotor UAV and the predefined time disturbance observer.

[0285] The inner and outer loop coordination control unit is used to achieve inner and outer loop coordinated control of the quadrotor UAV based on the non-singular predefined time sliding mode controller of the position subsystem and attitude subsystem, combined with the estimated value of the predefined time disturbance observer.

[0286] Example 3

[0287] The third embodiment of the present invention also provides a time sliding mode control device for a quadcopter UAV based on actuator failure, which includes a memory and a processor. The memory stores a computer program, which can be executed by the processor to implement the time sliding mode control method for a quadcopter UAV based on actuator failure as described above.

[0288] Example 4

[0289] The fourth embodiment of the present invention also provides a computer-readable storage medium storing computer-readable instructions. When the computer-readable instructions are executed by the processor of the device where the computer-readable storage medium is located, the computer-readable instructions implement the time sliding mode control method for quadcopter UAVs based on actuator failure as described above.

[0290] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A time-sliding mode control method for quadrotor unmanned aerial vehicles based on actuator faults, characterized in that, The application relates to a method for controlling a quad-rotor unmanned aerial vehicle (UAV) with actuator faults, which comprises the following steps: Based on the structural characteristics of the quad-rotor UAV with an X-shaped layout, a body coordinate system and an inertial coordinate system of the quad-rotor UAV are established, and the attitude angle of the quad-rotor UAV is bounded; Based on the influence of partial failure faults and bias faults of actuators, a quad-rotor UAV dynamics model is constructed, in which uncertain terms, external disturbances and actuator faults are regarded as collective disturbances; Based on the quad-rotor UAV dynamics model, a pre-defined time disturbance observer is designed by introducing an auxiliary equation; Based on the quad-rotor UAV dynamics model and the pre-defined time disturbance observer, a non-singular pre-defined time sliding mode controller based on a position subsystem and an attitude subsystem is designed to segment the sliding mode surface; The non-singular pre-defined time sliding mode controller based on the position subsystem and the attitude subsystem is combined with the estimated value of the pre-defined time disturbance observer to realize the coordinated control of the inner loop and the outer loop of the quad-rotor UAV; The expression of the non-singular pre-defined time sliding mode surface of the position subsystem is: ； wherein, represents a nonsingular predefined time sliding surface of the position subsystem, , , , corresponding to the values of the x, y, z axes, respectively; ； ； ； ； , , , are adjustable parameters of the position subsystem sliding surface; a predefined time parameter for the position subsystem sliding surface; wherein, is a small positive number in the position subsystem, ; are the values of the position tracking error of the quadcopter in the x, y, z axes, respectively; a position tracking error for the quadcopter, ; an actual position of the quadcopter; a target position; For the first derivative; When the position tracking error converges to a small region tending to zero within a predefined time ; when the position tracking error is switched to the sliding mode surface, it converges to the origin gradually. The position controller based on the position subsystem is designed as: ； ； wherein, is the first derivative of the nonsingular predefined time sliding surface of the position subsystem; is the position controller; is the estimated value of the lumped disturbance of the position subsystem; is a positive constant; is an adjustable parameter of the position subsystem controller; is an adjustable time parameter of the position subsystem controller; is a hyperbolic tangent function to suppress chattering of the position controller is the second derivative of is the second derivative of​ Under the action of the position controller In time, approaches zero.​ 2. The time-sliding mode control method for quadrotor UAV based on actuator failure according to claim 1, characterized in that , the body coordinate system is defined as ; the inertial coordinate system is ; and the attitude angle of the quad-rotor unmanned aerial vehicle satisfies: ， ， ； wherein, is a roll angle of the body about axis, is a pitch angle of the body about axis, is a yaw angle of the body about axis.

3. The time-sliding mode control method for quadrotor UAV based on actuator failure according to claim 2, characterized in that The construction process of the quad-rotor UAV dynamics model is as follows: Based on the influence of partial failure faults and bias faults of actuators, an actuator fault model is established and expressed as: ； wherein, is the desired control input; is the actual control input; represents an actuator bias fault; when , represents that the UAV is in a normal state; when , represents that the UAV only has an actuator partial failure fault; when , represents that the UAV only has an actuator bias fault; when , represents that the UAV has both a partial failure fault and a bias fault. The quad-rotor UAV dynamics model with actuator faults is: ； ； ； ； ； ； wherein , , are positions in inertial coordinates; , , are corresponding first derivatives; , , are corresponding second derivatives; , , are first derivatives of roll angle , pitch angle , and yaw angle , respectively; , , are second derivatives of roll angle, pitch angle, and yaw angle, respectively; denotes a gravitational constant; denotes a total mass of the quadcopter; , , denote air friction resistance coefficients, respectively; is a propeller rotation speed margin; is a propeller inertia constant; , , , are actual control inputs; is an external disturbance, ; For the moment of inertia of the quadcopter, assume that the quadcopter is symmetric, then The moment of inertia of the asymmetric part is 0, i.e. , are the moments of inertia around , , the three axes, respectively. Combined with the actuator fault model, the quad-rotor UAV dynamics model is simplified as: ； ； ； ； ； ； wherein: ; ； ； ； ； ； ； ； ； wherein, , , is an introduced virtual control variable; is a lumped disturbance consisting of external disturbances, uncertainties, actuator faults; is an actuator fault factor corresponding to the lumped disturbance. The expression of the target roll angle, the target pitch angle and the lift is: ； ； ； wherein, is a set target position coordinate; , , are a target yaw angle, a target roll angle, and a target pitch angle, respectively; is a lift.

4. The time-sliding mode control method for quadrotor UAV based on actuator failure according to claim 3, characterized in that The design process of the pre-defined time disturbance observer is as follows: The simplified quad-rotor UAV dynamics model is converted into a vector form: ； ； ； ； wherein, , is a state quantity of the quadcopter; is a collective disturbance vector of position and attitude; is a second derivative of . The expression of the auxiliary equation is: ； ； ； ； wherein, is the state of the auxiliary equation, is second derivative of is a constant vector; is the error vector of quadcopter state and auxiliary equation state; is the transpose symbol; According to the auxiliary equation, the pre-defined time disturbance observer is constructed as: ； ； ， ； ； wherein is an estimate of the collective disturbance vector D; is an estimate of the error vector ; is a second derivative of ; is a first derivative of ; is a tuning parameter of the disturbance observer; is a predefined time parameter of the disturbance observer; , is a parameter factor of the disturbance observer; is a difference between the error vector and the estimate.

5. The actuator fault-based time-sliding mode control method for quadrotor UAV according to claim 4, wherein Combined with a Lyapunov function, the pre-defined time disturbance observer can converge within a pre-defined time; the Lyapunov function is selected as follows: ； wherein is a Lyapunov function; is an error vector is a difference between the estimate and the value; is a transpose symbol; right Taking the time derivative yields: ； wherein is a first derivative; is a tuning parameter of the disturbance observer; is a predefined time parameter of the disturbance observer; , is a parameter factor of the disturbance observer; , ; the estimated error of the lumped perturbation is: ； wherein, is an estimate of the lumped disturbance vector D; is a second derivative of the state quantity of the auxiliary equation; is a constant vector; is a second derivative of the state quantity of the quadcopter. Then, when a predefined time convergence is met, a predefined time convergence is also met.

6. The actuator fault-based time-sliding mode control method for quadrotor UAV according to claim 4, wherein The non-singular pre-defined time sliding mode controller based on the position subsystem is used to control the movement position of the quad-rotor UAV in space, and the non-singular pre-defined time sliding mode controller based on the attitude subsystem is used to keep the attitude of the quad-rotor UAV stable; the sliding mode surface is segmented by comparing the tracking error with a preset threshold value, so that the singularity problem is avoided.

7. The actuator fault-based time-sliding mode control method for quadrotor UAV according to claim 6, wherein , a non-singular predefined time sliding surface of the attitude subsystem The expression of the non-singular predefined time sliding surface of the attitude subsystem is: ； wherein is a small positive number in the attitude subsystem, ; , , , correspond respectively to the values of the roll angle , the pitch angle , the yaw angle . ； ； ； ； , , , are adjustable parameters of the attitude subsystem sliding surface; a predefined time parameter for the attitude subsystem sliding surface; for a quadcopter drone, ; attitude angle is the actual position of the quadcopter; is the target attitude angle; For the first derivative; When the attitude tracking error converges to a small region tending to zero within a predefined time ; when the attitude tracking error gradually converges to the origin; The attitude controller based on the attitude subsystem is designed as: ； ； wherein, is the first derivative of the non-singular predefined time sliding surface of the attitude subsystem; is an estimate of the collective disturbance to the attitude subsystem; is an estimate of the collective disturbance to the attitude subsystem; is a positive constant; is an adjustable parameter of the attitude controller; is an adjustable time parameter of the attitude controller; is the second derivative of is the second derivative of Under the action of the attitude controller In time approaches zero.​ 8. The actuator fault-based time-sliding mode control method for quadrotor UAV according to claim 7, wherein In the coordinated control of the inner loop and the outer loop of the quad-rotor UAV: The virtual control quantity is calculated through the position controller, and then the expected lift, the expected target roll angle and the target pitch angle are calculated; The target roll angle, the target pitch angle and a preset target yaw angle are taken as the tracking targets of the attitude controller; The attitude controller calculates the control torque according to the error between the actual attitude angle and the target attitude angle, so that the UAV tracks the expected attitude and completes the coordinated control of the inner loop and the outer loop.

9. An actuator fault-based quadrotor unmanned aerial vehicle time-sliding mode control device for implementing an actuator fault-based quadrotor unmanned aerial vehicle time-sliding mode control method according to any one of claims 1-8, characterized in that, The application relates to a method for controlling a quad-rotor unmanned aerial vehicle (UAV) with actuator faults, which comprises the following steps: A coordinate system establishing unit is used to establish a body coordinate system and an inertial coordinate system of a quad-rotor UAV based on the structural characteristics of the quad-rotor UAV with an X-shaped layout, and the attitude angle of the quad-rotor UAV is bounded; The dynamics model establishing unit is configured to construct a quadrotor unmanned aerial vehicle dynamics model by regarding uncertain external disturbances and actuator faults as collective disturbances based on influences of actuator partial failure faults and bias faults; The disturbance observer establishing unit is configured to introduce an auxiliary equation to design a predefined time disturbance observer based on the quadrotor unmanned aerial vehicle dynamics model; The sliding mode controller establishing unit is configured to design a nonsingular predefined time sliding mode controller based on position subsystems and attitude subsystems, and to perform segmented processing on a sliding mode surface based on the quadrotor unmanned aerial vehicle dynamics model and the predefined time disturbance observer; The inner-outer loop coordinated control unit is configured to realize inner-outer loop coordinated control of the quadrotor unmanned aerial vehicle by combining estimated values of the predefined time disturbance observer based on the nonsingular predefined time sliding mode controller of the position subsystems and the attitude subsystems.

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