Agricultural unmanned aerial vehicle fault-tolerant control method based on a predetermined performance function

Abstract

The application discloses a novel active fault-tolerant control method for an agricultural unmanned aerial vehicle (UAV) actuator fault. A controller based on an adaptive terminal sliding mode control and a predetermined performance function is constructed. A fault estimation observer based on a radial basis function neural network is designed for the actuator fault to approximate an accurate fault value. A non-singular fast terminal sliding mode is designed based on the fault information to replace a traditional sliding mode surface, so that the convergence speed and robustness of the system are improved. In the controller design process, a predetermined performance function is introduced, and an error conversion system is constructed to limit the flight trajectory, so that the safety problem of the UAV in a complex working environment is solved. Adaptive laws are designed for the system mass and the moment of inertia respectively according to the change of the load mass of the agricultural UAV when spraying pesticides, so that the uncertainty of the model is solved. The application is used for robust fault-tolerant control of a kind of agricultural UAV for spraying pesticides containing an actuator fault.

Description

Technical Field

[0001] This invention relates to an agricultural unmanned aerial vehicle (UAV) system with actuator failure and internal parameter perturbation, and designs an adaptive sliding mode fault-tolerant control algorithm based on a predetermined performance function, belonging to the field of robust fault-tolerant control technology for uncertain nonlinear systems. Background Technology

[0002] In recent years, with the rapid development of communication technology, artificial intelligence technology, and onboard computer technology, multi-rotor drone technology has also greatly improved. Due to its wide applicability, simple structure, low cost, and ease of use, multi-rotor drones have attracted much attention in both military and civilian fields and have been deployed in various areas such as search and rescue, surveillance, and cargo transportation. Agricultural drones used for spraying pesticides and fertilizers have become a major research focus due to their high efficiency and low labor costs. However, the special working environment and long working hours make agricultural drones prone to malfunctions. Even minor malfunctions can lead to crashes, collisions, and other serious accidents, resulting in property damage and even casualties. Therefore, fault-tolerant control of agricultural drones has become crucial and a current research focus.

[0003] Fault-tolerant control is broadly categorized into active and passive fault tolerance. Passive fault tolerance primarily involves designing specific controllers for pre-estimated types of faults to improve system robustness and ensure stability even when faults occur. Passive fault tolerance does not require fault diagnosis and system reconfiguration, and its fault-tolerance capability is limited. Active fault-tolerant control, on the other hand, acquires fault information online through a diagnostic module and then reconfigures the system based on this information, adjusting the controller's parameters and structure. Compared to passive fault tolerance, active fault tolerance has a wider range of applications and does not require reducing control performance to achieve fault tolerance. Therefore, active fault-tolerant control has more significant advantages and is currently receiving considerable attention.

[0004] Actuator failure is a common type of UAV fault. In recent years, researchers have proposed many practical fault-tolerant control algorithms for UAVs with actuator failure, such as sliding mode control, backstepping control, and model predictive control. Sliding mode control algorithms have good robustness in handling internal parameter perturbations, uncertainties, and system faults, and are therefore used in many fault-tolerant control algorithms.

[0005] However, unlike conventional aircraft, agricultural drones need to spread pesticides and fertilizers during actual flight, making changes in their total mass and moment of inertia a significant concern. To mitigate the impact of parameter perturbations and uncertainties, some researchers have introduced adaptive methods to estimate changing parameters online. Furthermore, due to the complex working environment of agricultural drones, their flight trajectory needs to be constrained to prevent collisions and friction that could damage the aircraft, ensuring the drone doesn't stray from a safe area. To address state constraints, researchers have proposed a predefined performance function approach. By constructing a predefined performance function, setting boundary conditions for variables, and performing error transformation, the constrained problem is converted into an unconstrained one. Combining the predefined performance function with sliding mode control can effectively handle actuator failures and state constraints in agricultural drones. Currently, many researchers are conducting research in this area. Summary of the Invention

[0006] Objective: To address the aforementioned research background, this invention proposes an adaptive sliding mode fault-tolerant control algorithm based on a predetermined performance function for agricultural drone systems used for pesticide spraying. An RBF neural network observer is designed to acquire accurate fault values ​​online. To ensure faster convergence and robustness, a non-singular fast terminal sliding surface is designed to replace the traditional sliding surface. Considering the parameter perturbations that occur when agricultural drones spray pesticides and fertilizers, an adaptive control approach is introduced to estimate the aircraft's mass and moment of inertia online. To ensure safety and improve control performance, a predetermined performance function is designed, and error transformation defines the constraint boundaries for the system state, preventing excessive overshoot, flight outside the safe zone, and collisions during operation.

[0007] Technical Solution: A novel adaptive sliding mode fault-tolerant control method for agricultural drones spraying pesticides with actuator failures. Its key features include: firstly, approximating accurate fault information online using an RBF neural network observer; completing system decoupling and designing a predetermined performance function and corresponding error transformation to define the state boundaries of the displacement subsystem; designing a non-singular fast terminal sliding mode based on fault information to replace the traditional sliding surface, improving the system's convergence speed and robustness; and designing an adaptive law to estimate uncertain parameters, ultimately constructing a fault-tolerant controller. The method comprises the following specific steps:

[0008] Step 1) Determine the fault model of the unmanned aerial vehicle (UAV) system, including the following steps:

[0009] Step 1.1) Determine the system model. The displacement subsystem and attitude subsystem of the system are shown in equations (1) and (2):

[0010]

[0011]

[0012] Where, x i1 = (x, y, z, φ, θ, ψ) T and x i2 = (u, v, w, p, q, r) T U represents the position and velocity state of the quadcopter UAV at time t; i (t) represents the input control quantity; d i The sum of the disturbance caused by the change in mass and the external disturbance satisfies And D(t)=[d1, d2, d3, d4, d5, d6]w, and It is a known constant; k i (i = φ, θ, ψ) are the air drag coefficients; M and J i (i = x, y, z) are continuous variables, representing the total mass and moment of inertia of the UAV and its payload, respectively.

[0013] Step 1.2) Determine the fault model, given U i (t) represents the control input for the i-th channel. When an actuator failure occurs in the i-th channel, the control input is: As shown in equation (3):

[0014]

[0015] Where, σ i Let represent the failure rate of the i-th channel, and satisfy 0 ≤ σ. i <1; when σ i When = 0, The i-th channel is working normally, when 0 < σ i When <1, the i-th channel experiences partial failure but continues to function.

[0016] Step 1.3) Determine the fault information and write the system model after the fault occurs in state-space form:

[0017]

[0018] Where F(X2) is the nonlinear part of the system, U is the control vector, B is the control coefficient matrix, D(t) is the bounded disturbance, E(t) = diag{σ1, σ2, ..., σ6} is the failure matrix, and represents the failure rate of the actuator;

[0019] The failure matrix is ​​approximated using a neural network, as shown in equation (5):

[0020] E(t)=Wσ T Φσ ( X2)+ε σ (5)

[0021] Among them, W σ ∈R q×6 Let be the weight matrix, satisfying Φ σ ∈R q Denotes the basis function, ε σ ∈R 6 Let represent the reconstruction error and q represent the number of hidden layers. Therefore, equation (4) can be written as:

[0022]

[0023] Construct the following output observer for equation (6):

[0024]

[0025] in, and X2(t), D(t), and W are respectively. σ , and ε σ The observed values; L is the Herwitz matrix; according to equations (1) and (2), a constant ξ is obtained for the UAV model, such that it satisfies the following equation:

[0026]

[0027] Based on this, a positive definite matrix Q is configured such that LQ + QL + 2ξQ < 0, and the adaptive update law and disturbance compensation term of the system observations are defined as follows:

[0028]

[0029]

[0030] in, k1, k2, k3, and k4 represent the gain, which are positive constants. and They are respectively and The upper bound of the fault information can be converged to obtain accurate fault information, thereby completing the reconstruction.

[0031] Step 2) Determine the constraints. Considering that agricultural drones operate in complex environments and are prone to collisions or friction during actual flight, it is necessary to constrain their position and state. The constraints are shown in equation (11):

[0032]

[0033] in, k i and The lower and upper bounds are respectively defined, and the tracking error is defined as:

[0034]

[0035] Where x id (i = 1, 2, 3) is the desired trajectory. According to formulas (11) and (12), the performance function designed for the tracking error is shown in formula (13):

[0036]

[0037] in, ρ i0 ρ i∞ , k i and All are positive numbers;

[0038] The following conversion settings are applied to the tracking error:

[0039]

[0040] Taking its inverse, we get:

[0041]

[0042] in

[0043] Step 3) Design the sliding surface of the displacement subsystem:

[0044] Design the sliding surface function according to requirements. To ensure that the displacement state of the agricultural drone does not violate the constraints, the transformation error η must be guaranteed. i Since the sliding surface converges, the design is as shown in equation (16):

[0045]

[0046] Where, k i1 and k i2 For positive constants, to avoid singularity, α i and β i Satisfying 1 < β i <2 and β i <α i ; sign(·) is the sign function, that is:

[0047]

[0048] Step 4) Design the fault-tolerant control law for the displacement subsystem:

[0049] An adaptive method is used to estimate the total mass of the UAV airframe and its payload. The sliding mode control law consists of two parts: an equivalent control law and a switching control law.

[0050] U i =Uieq +U isw (18)

[0051] Let the derivative of the sliding surface If the value is zero, the equivalent control law is as follows:

[0052]

[0053] The switching control law is shown in equation (20):

[0054]

[0055] Where, σ i The value is obtained from the observer; Let M represent the estimated value of the total mass M in the corresponding control law, and satisfy the following conditions: h i Defined as d i The upper bound of δ; i Indicates gain. δ i and q i All are positive numbers;

[0056] Step 5) Design the attitude subsystem controller, including the following steps:

[0057] Step 5.1) Design the sliding surface:

[0058] Similar to steps 2 and 3, the attitude subsystem error is defined as:

[0059]

[0060] Designed as a sliding mold surface:

[0061]

[0062] Where, x id (i = 4, 5, 6) represents the desired trajectory; k i1 and k i2 It is a positive constant; α i and β i Satisfying 1 < β i <2 and β i <α i ; sign(·) is the sign function;

[0063] Step 5.2) Design the fault-tolerant control law:

[0064] An adaptive method is used to estimate some parameter values. Similar to the construction method in step 4, the fault-tolerant control law is designed as shown in equation (23):

[0065]

[0066] Where τ i The definition is shown in equation (24):

[0067]

[0068] Where, σ i The value is obtained from the observer; and I i and T i The estimated value, and satisfying i, j, and k are all different (for example, when i = 4, j = 5, k = 6); d i The upper bound of δ; i and c i Indicates gain. c i δ i and q i All are positive numbers;

[0069] Step 6) Select appropriate parameters based on the operating status of the agricultural drone system spraying pesticides, and complete its fault-tolerant control.

[0070] Beneficial Effects: For agricultural drone systems experiencing actuator failure, an adaptive sliding mode fault-tolerant control method incorporating a predetermined performance function is designed. An RBF neural network observer is designed to approximate accurate fault values ​​and complete system reconfiguration. A fast terminal sliding surface is constructed to replace the traditional sliding mode, improving convergence speed and robustness. To address parameter perturbation during pesticide application, an adaptive law is designed for online parameter estimation. A predetermined performance function is designed in the displacement subsystem to define the flight trajectory boundaries, preventing the drone from veerging out of the safe zone and colliding due to excessive overshoot. Specific advantages include:

[0071] (1) The designed RBF neural network observer can accurately approximate the fault information and has good tracking performance for both constant faults and time-varying faults. Based on this, the system can be reconstructed. The sliding mode controller itself has strong robustness, which makes the system more effective in handling faults and disturbances.

[0072] (2) Based on the tracking error, the traditional sliding surface is replaced with a non-singular fast terminal sliding surface, which improves the convergence speed and robustness, and gives the controller better dynamic performance.

[0073] (3) The problem of parameter fluctuation during pesticide application was considered, and an adaptive control method was introduced to estimate the mass and moment of inertia of the UAV online, which made the controller more accurate and more in line with the actual situation.

[0074] (4) Design a predetermined performance function in the displacement subsystem to complete the error transformation, so that the displacement subsystem has a constrained boundary to prevent excessive overshoot and thus avoid the danger of collision.

[0075] The method proposed in this invention is an adaptive sliding mode fault-tolerant control method for agricultural drone systems with actuator failure. It has certain application significance, is easy to implement, has good real-time performance and high accuracy, can effectively improve the safety of the control system, is highly operable, saves time, and is more efficient. It can be widely used in the actuator failure fault-tolerant control of agricultural drone systems for spraying pesticides. Attached Figure Description

[0076] Figure 1 This is a flowchart of the method of the present invention;

[0077] Figure 2 It is the Qball-X4 quadcopter, an experimental device developed by Quanser.

[0078] Figure 3 This is a simplified schematic diagram of the Qball-X4 structure;

[0079] Figure 4 This is a tracking curve of the X-axis position error when the Qball-X4 UAV actuator fails;

[0080] Figure 5 This is a Y-axis position error tracking curve of the Qball-X4 UAV when the actuator fails;

[0081] Figure 6 This is a Z-axis position error tracking curve of the Qball-X4 UAV when the actuator fails;

[0082] Figure 7 This is a graph showing the attitude error tracking of a Qball-X4 UAV when the actuator fails. Detailed Implementation

[0083] The invention will now be further explained with reference to the accompanying drawings.

[0084] like Figure 1As shown, a sliding mode fault-tolerant control method for agricultural quadcopter drones with actuator failure is characterized by: when an actuator failure occurs in the agricultural drone system for pesticide spraying, a non-singular fast terminal sliding mode fault-tolerant control method combining a predetermined performance function is proposed, enabling the drone system to operate normally after the actuator failure and keeping the maximum overshoot within a certain range to constrain the flight trajectory and prevent collisions; then, an adaptive law is designed to estimate the mass and moment of inertia of the drone online, weakening the impact of system parameter perturbations caused by pesticide spraying, and finally constructing a fault-tolerant controller, including the following specific steps:

[0085] Step 1) Determine the fault model of the unmanned aerial vehicle (UAV) system, including the following steps:

[0086] Step 1.1) Determine the system model. The displacement subsystem and attitude subsystem of the system are shown in equations (1) and (2):

[0087]

[0088]

[0089] Where, x i1 = (x, y, z, φ, θ, ψ) T and x i2 = (u, v, w, p, q, r) T U represents the position and velocity state of the quadcopter UAV at time t; i (t) represents the input control quantity; d i The sum of the disturbance caused by the change in mass and the external disturbance satisfies And D(t)=[d1, d2, d3, d4, d5, d6] T , and It is a known constant; k i (i = φ, θ, ψ) are the air drag coefficients; M and J i (i = x, y, z) are continuous variables, representing the total mass and moment of inertia of the UAV and its payload, respectively.

[0090] Step 1.2) Determine the fault model, given U i (t) represents the control input for the i-th channel. When an actuator failure occurs in the i-th channel, the control input is: As shown in equation (3):

[0091]

[0092] Where, σ i Let represent the failure rate of the i-th channel, and satisfy 0 ≤ σ. i<1; when σ i When σ = 0, the i-th channel works normally; when 0 < σ i When <1, the i-th channel experiences partial failure but continues to function.

[0093] Step 1.3) Determine the fault information and write the system model after the fault occurs in state-space form:

[0094]

[0095] Where F(X2) is the nonlinear part of the system, U is the control vector, B is the control coefficient matrix, D(t) is the bounded disturbance, E(t) = diag{σ1, σ2, ..., σ6} is the failure matrix, and represents the failure rate of the actuator;

[0096] The failure matrix is ​​approximated using a neural network, as shown in equation (5):

[0097] E(t) = W σ T Φ σ (X2)+ε σ (5)

[0098] Among them, W σ ∈R q×6 Let be the weight matrix, satisfying Φ σ ∈R q Denotes the basis function, ε σ ∈R 6 Let represent the reconstruction error and q represent the number of hidden layers. Therefore, equation (4) can be written as:

[0099]

[0100] Construct the following output observer for equation (6):

[0101]

[0102] in, and X2(t), D(t), and W are respectively. σ , and ε σ The observed values; L is the Herwitz matrix; according to equations (1) and (2), a constant ξ is obtained for the UAV model, such that it satisfies the following equation:

[0103]

[0104] Based on this, a positive definite matrix Q is configured such that LQ + QL + 2ξQ < 0, and the adaptive update law and disturbance compensation term of the system observations are defined as follows:

[0105]

[0106]

[0107] in, k1, k2, k3, and k4 represent the gain, which are positive constants. and They are respectively and The upper bound of the fault information can be converged to obtain accurate fault information, thereby completing the reconstruction.

[0108] Step 2) Determine the constraints. Considering that agricultural drones operate in complex environments and are prone to collisions or friction during actual flight, it is necessary to constrain their position and state. The constraints are shown in equation (11):

[0109]

[0110] in, k i and The lower and upper bounds are respectively defined, and the tracking error is defined as:

[0111]

[0112] Where x id (i = 1, 2, 3) is the desired trajectory. According to formulas (11) and (12), the performance function designed for the tracking error is shown in formula (13):

[0113]

[0114] in, ρ i0 ρ i∞ h i , k i and All are positive numbers;

[0115] The following conversion settings are applied to the tracking error:

[0116]

[0117] Taking its inverse, we get:

[0118]

[0119] in

[0120] Step 3) Design the sliding surface of the displacement subsystem:

[0121] Design the sliding surface function according to requirements. To ensure that the displacement state of the agricultural drone does not violate the constraints, the transformation error η must be guaranteed.i Since the sliding surface converges, the design is as shown in equation (16):

[0122]

[0123] Where, k i1 and k i2 For positive constants, to avoid singularity, α i and β i Satisfying 1 < β i <2 and β i <α i ; sign(·) is the sign function, that is:

[0124]

[0125] Step 4) Design the fault-tolerant control law for the displacement subsystem:

[0126] An adaptive method is used to estimate the total mass of the UAV airframe and its payload. The sliding mode control law consists of two parts: an equivalent control law and a switching control law.

[0127] U i =U ieq +U isw (18)

[0128] Let the derivative of the sliding surface If the value is zero, the equivalent control law is as follows:

[0129]

[0130] The switching control law is shown in equation (20):

[0131]

[0132] Where, σ i The value is obtained from the observer; Let M represent the estimated value of the total mass M in the corresponding control law, and satisfy the following conditions: h i Defined as d i The upper bound of δ; i Indicates gain. δ i and q i All are positive numbers;

[0133] Step 5) Design the attitude subsystem controller, including the following steps:

[0134] Step 5.1) Design the sliding surface:

[0135] Similar to steps 2 and 3, the attitude subsystem error is defined as:

[0136]

[0137] Designed as a sliding mold surface:

[0138]

[0139] Where, x id (i = 4, 5, 6) represents the desired trajectory; k i1 and k i2 It is a positive constant; α i and β i Satisfying 1 < β i <2 and β i <α i ; sign(·) is the sign function;

[0140] Step 5.2) Design the fault-tolerant control law:

[0141] An adaptive method is used to estimate some parameter values. Similar to the construction method in step 4, the fault-tolerant control law is designed as shown in equation (23):

[0142]

[0143] Where τ i The definition is shown in equation (24):

[0144]

[0145] Where, σ i The value is obtained from the observer; and I i and T i The estimated value, and satisfying i, j, and k are all different (for example, when i = 4, j = 5, k = 6); d i The upper bound of δ; i and c i Indicates gain. c i δ i and q i All are positive numbers;

[0146] Step 6) Select appropriate parameters based on the operating status of the agricultural drone system spraying pesticides, and complete its fault-tolerant control.

[0147] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0148] Table 1: Qball-X4 Body Parameter Values

[0149] <![CDATA[m0]]> Body mass 2kg ω Actuator bandwidth 15 rad / s <![CDATA[I z0 ]]> Yaw moment of inertia <![CDATA[0.08kg·m 2 ]]> <![CDATA[I x0 ]]> Rolling moment of inertia <![CDATA[0.04kg·m 2 ]]> <![CDATA[I y0 ]]> Pitch moment of inertia <![CDATA[0.04kg·m 2 ]]> <![CDATA[I m ]]> propeller moment of inertia <![CDATA[0.000132kg·m 2 ]]> d Fuselage radius (half the wheelbase) 0.2m Tm Motor response time constant 0.0116s

[0150] The effectiveness of the implementation plan is illustrated below using a real-world case simulation.

[0151] To verify the effectiveness of the method, the simulation object used was the Qball-X4 quadcopter UAV controlled by Quanser Inc. of Canada. The rationality and effectiveness of the proposed method were verified on this UAV. The Qball-X4 experimental device is shown below. Figure 2 As shown in Table 1, the body parameters of Qball-X4 are as follows.

[0152] The structure of the quadcopter drone Qball-X4 is simplified as follows: Figure 3 As shown. An X-type frame is used, and a body coordinate system Q is established. b -X b Y b Z b and ground coordinates O e -X e Y e Z e Typically, a quadcopter unmanned aerial vehicle (UAV) system has six-dimensional variables: (X, Y, Z, ψ, θ, φ), where X, Y, and Z are position variables, and ψ, θ, and φ are the yaw, pitch, and roll angles, respectively. Ω = [p, q, r] T and V = [u, v, w] T These represent angular velocity and linear velocity, respectively.

[0153] According to the Newton-Euler formula, the dynamic equations of the system can be introduced:

[0154]

[0155] Where, k φ k θ k ψ is the tensile coefficient; g is the gravitational acceleration; M represents the total mass of the UAV and its payload; J i (i = x, y, z) represents the total moment of inertia; The system control variables are defined as follows:

[0156]

[0157]

[0158] Among them, f i (i=1, 2, 3, 4) and τ i (i = 1, 2, 3, 4) represent the thrust and torque of the propeller, respectively.

[0159] The initial attitude angle and position are set to Θ(0) = [0, 0, 0]. T P(0) = [-0.6, 1.2, 0] T Initial linear velocity and rotational angular velocity are both zero; expected value: [x] d y d , z d , ψ d ] T =[0.8sin(0.1πt), 0.8cos(0.1πt), 0.2t, π / 3] T Set the upper limit to The white noise is used as an external disturbance; to simulate the scenario of spraying pesticides, the mass of the drone payload is shown in equation (4):

[0160]

[0161] The total mass of the system is: M = m0 + ρ; taking the roll channel as an example, 40% of the failure faults are injected starting from the 12th second, i.e., E = diag{0, 0, 0, 0.4, 0, 0}; based on the actual working conditions of agricultural drones, the flight trajectory boundaries are set, and the parameters in the predetermined performance function are set as follows: k i =1, ρ i0 =0.71, ρ i∞ =0.18, h i =0.75; the parameters in the observer are set to: ξ = 4.35, k1 = 1, k2 = 5, k3 = 0.5, k4 = 3; the parameters in the control law are set as follows: α i =2,β i =1.67, k i1 =1,k i2 =1, p=3.5; the gain in the adaptive law is set to: [c4, c5, c6] T = [1.2, 1.2, 1] T , [δ1, δ2, δ3, δ4, δ5, δ6] T =[0.3, 0.3, 0.5, 0.6, 0.6, 0.7] T .

[0162] Simulation results in this case demonstrate that the adaptive sliding mode fault-tolerant algorithm proposed in this invention for agricultural UAV systems with actuator faults can effectively handle internal parameter perturbations and fault problems, achieving good control performance, and the control law exhibits good dynamic performance. Compared with traditional adaptive sliding mode control, the UAV airframe exhibits better controllability under the control algorithm proposed in this simulation. Figure 4-6 The displacement tracking error curves in the X, Y, and Z directions are shown under the conditions of actuator failure and quality variation. Figure 7 This is the attitude tracking error curve of the UAV under this condition.

[0163] Simulation results show that the adaptive sliding mode fault-tolerant control algorithm for agricultural UAV systems with actuator failures designed in this invention has strong robustness to internal parameter perturbations and actuator failures. The control law converges quickly and accurately, while effectively suppressing overshoot and improving dynamic control performance. As can be seen from the figures, when a fault occurs, the traditional sliding mode method can achieve convergence, but the overshoot is large and cannot be controlled within the constraints, and it cannot effectively adjust for changes in mass. The method proposed in this case study is more robust, less sensitive to changes in mass, converges faster, and can satisfy the constraints, resulting in superior performance. In summary, the fault-tolerant control method simulated in this case study is effective for agricultural UAV systems used for pesticide spraying that experience actuator failures.

Claims

1. A sliding mode fault-tolerant control method for agricultural quadcopter unmanned aerial vehicles with actuator failure, characterized in that: When an actuator failure occurs in an agricultural drone system spraying pesticides, a non-singular fast terminal sliding mode fault-tolerant control method combining a predetermined performance function is proposed. This method enables the drone system to operate normally after the actuator failure and keeps the maximum overshoot within a certain range, thereby constraining the flight trajectory to prevent collisions. Then, an adaptive law is designed to estimate the drone's mass and moment of inertia online, mitigating the impact of pesticide spraying-induced system parameter perturbations. Finally, a fault-tolerant controller is constructed, comprising the following specific steps: Step 1) Determine the fault model of the unmanned aerial vehicle (UAV) system, including the following steps: Step 1.1) Determine the system model. The displacement subsystem and attitude subsystem of the system are shown in equations (1) and (2): Where, x i1 = (x, y, z, φ, θ, ψ) T and x i2 = (u, v, w, p, q, r) T U represents the position and velocity state of the quadcopter UAV at time t; i (t) represents the input control quantity; d i The sum of the disturbance caused by the change in mass and the external disturbance satisfies And D(t)=[d1, d2, d3, d4, d5, d6] T , and It is a known constant; k i (i = φ, θ, ψ) are the air drag coefficients; M and J i (i = x, y, z) are continuous variables, representing the total mass and moment of inertia of the UAV and its payload, respectively. Step 1.2) Determine the fault model, given U i (t) represents the control input for the i-th channel. When an actuator failure occurs in the i-th channel, the control input is: As shown in equation (3); Where, σ i Let represent the failure rate of the i-th channel, and satisfy 0 ≤ σ. i <1; when σ i When = 0, The i-th channel is working normally, when 0 < σ i When <1, the i-th channel experiences partial failure but continues to function. Step 1.3) Determine the fault information and write the system model after the fault occurs in state-space form: Where F(X2) is the nonlinear part of the system, U is the control vector, B is the control coefficient matrix, D(t) is the bounded disturbance, E(t) = diag{σ1, σ2, ..., σ6} is the failure matrix, and represents the failure rate of the actuator; The failure matrix is ​​approximated using a neural network, as shown in equation (5): E(t)=W σ T F σ (X2)+e σ (5) Among them, W σ ∈R q×6 Let be the weight matrix, satisfying Φ σ ∈R q Denotes the basis function, ε σ ∈R 6 Let represent the reconstruction error and q represent the number of hidden layers. Therefore, equation (4) can be written as: Construct the following output observer for equation (6): in, and X2(t), D(t), and W are respectively. σ , and ε σ The observed values; L is the Herwitz matrix; according to equations (1) and (2), a constant ξ is obtained for the UAV model, such that it satisfies the following equation: Based on this, a positive definite matrix Q is configured such that LQ + QL + 2ξQ < 0, and the adaptive update law and disturbance compensation term of the system observations are defined as follows: in, k1, k2, k3, and k4 represent the gain, which are positive constants. and They are respectively and The upper bound of the fault information can be converged to obtain accurate fault information, thereby completing the reconstruction. Step 2) Determine the constraints. Considering that agricultural drones operate in complex environments and are prone to collisions or friction during actual flight, it is necessary to constrain their position and state. The constraints are shown in equation (11): in, k i and The lower and upper bounds are respectively defined, and the tracking error is defined as: Where x id (i = 1, 2, 3) is the desired trajectory. According to formulas (11) and (12), the performance function designed for the tracking error is shown in formula (13): in, ρ i0 ρ i∞ , κ i and All are positive numbers; The following conversion settings are applied to the tracking error: Taking its inverse, we get: in Step 3) Design the sliding surface of the displacement subsystem: Design the sliding surface function according to requirements. To ensure that the displacement state of the agricultural drone does not violate the constraints, the transformation error η must be guaranteed. i Since the sliding surface converges, the design is as shown in equation (16): Where, k i1 and k i2 For positive constants, to avoid singularity, α i and β i Satisfying 1 < β i <2 and β i <α i ; sign(·) is the sign function, that is: Step 4) Design the fault-tolerant control law for the displacement subsystem: An adaptive method is used to estimate the total mass of the UAV airframe and its payload. The sliding mode control law consists of two parts: an equivalent control law and a switching control law. IN i =U ieq +U isw (18) Let the derivative of the sliding surface If the value is zero, the equivalent control law is as follows: The switching control law is shown in equation (20): Where, σ i The value is obtained from the observer; Let M represent the estimated value of the total mass M in the corresponding control law, and satisfy the following conditions: h i Defined as d i The upper bound of δ; i Indicates gain. σ i and q i All are positive numbers; Step 5) Design the attitude subsystem controller, including the following steps: Step 5.1) Design the sliding surface: Similar to steps 2 and 3, the attitude subsystem error is defined as: Designed as a sliding mold surface: Where, x id (i = 4, 5, 6) represents the desired trajectory; k i1 and k i2 It is a positive constant; α i and β i Satisfying 1 < β i <2 and β i <α i ; sign(·) is the sign function; Step 5.2) Design the fault-tolerant control law: An adaptive method is used to estimate some parameter values. Similar to the construction method in step 4, the fault-tolerant control law is designed as shown in equation (23): Where τ i The definition is shown in equation (24): Where, σ i The value is obtained from the observer; and I i and T i The estimated value, and satisfying i, j, and k are all different; d i The upper bound of σ; i and c i Indicates gain. c i σ i and q i All are positive numbers; Step 6) Select appropriate parameters based on the operating status of the agricultural drone system spraying pesticides, and complete its fault-tolerant control.

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