CN110824925A - Adaptive robust fault-tolerant control method for tilting type three-rotor unmanned aerial vehicle - Google Patents

Abstract

The invention relates to fault-tolerant control of a tilting tri-rotor unmanned aerial vehicle. In order to propose a robust and highly feasible nonlinear fault-tolerant control algorithm that does not require fault diagnosis, the tail steering gear is blocked when the tilting tri-rotor unmanned aerial vehicle is blocked. In the event of a fault, the stable control of the attitude movement is realized. The present invention provides an adaptive robust fault-tolerant control method for a tilting tri-rotor UAV. The steps are as follows: establishing a failure model of the tilting tri-rotor UAV: controller design, adaptive law design, and the adaptive law design is based on Adaptive backstepping and terminal sliding mode control. The invention is mainly applied to the fault-tolerant control occasion of the tilting three-rotor unmanned aerial vehicle.

Description

Adaptive robust fault-tolerant control method for tilting tri-rotor UAV

technical field

The invention relates to a fault-tolerant control problem of a tilting three-rotor unmanned aerial vehicle. A robust fault-tolerant controller based on adaptive backstepping and terminal sliding mode control is proposed for a tilting tri-rotor UAV affected by external disturbances and model uncertainty when the tail steering gear is blocked and faulty. .

Background technique

In recent years, small rotary-wing UAVs have been widely used in search and rescue, power maintenance, aerial photography and logistics and transportation, so researchers have carried out a lot of related research. At present, the main types of UAVs include: the more common quad-rotor UAVs, single-rotor helicopters, and tri-rotor UAVs with special structures. Among them, the tilting tri-rotor UAV is a kind of unmanned aerial vehicle type between single-rotor and quad-rotor UAV. It not only has the advantages of strong maneuverability, vertical take-off and landing, etc. Compared with the machine, it has the characteristics of a more compact mechanism, less energy consumption and longer battery life. Correspondingly, this also produces the difference between the torque solution and the dynamic model, which increases the coupling of the system and increases the difficulty of control.

Regarding the control of tilting tri-rotor UAVs, researchers have proposed some control design strategies. The University of Technology of Compiegne (UTC) in France established a six-degree-of-freedom dynamic model for a tilting tri-rotor UAV with a tiltable steering gear at the tail, and designed a control strategy based on a saturation function. For the realization of UAV attitude and position stabilization control (Journal: IEEE Transactions on Aerospace and Electronic Systems; Authors: Sergio Salazar-Cruz, Farid Kendoul, Rogelio Lozano; Publication Year: 2008; Article title: Real-time stabilization of a small three-rotor aircraft; pp. 783-794). Ecole des Mines de Paris designed a tilting tri-rotor UAV in which each rotor can be tilted independently, and designed attitude and position controllers based on Flatness-Based Control Approach. The experimental results under the motion capture system show that the UAV can achieve translation without turning in the horizontal plane (Conference: International Conference on Unmanned AircraftSystems; Authors: Etienne Servais, Brigitte d'Andrea Novel, Hugues Mounier; Publication Year: 2015; Article title: Ground control of a hybrid tricopter; pp. 945-950).

The small rotor UAV has the characteristics of high real-time performance. Its motor and steering gear are in a high-frequency working state for a long time, which greatly increases the probability of its failure. Therefore, the fault-tolerant control for the failure of the UAV actuator has become a problem. One of the important directions in the field of UAV research. Central South University linearized the quadrotor UAV model, used a robust adaptive observer to diagnose actuator failures, used dynamic output feedback control to achieve stable attitude control, and verified the effectiveness of the algorithm through numerical simulation (Journal : International Journal of Control; Authors: XiaohongNian, Weiqiang Chen, Xiaoyan Chu; Publication Year: 2018; Article Title: Robust adaptive faultestimation and fault tolerant control for quadrotor attitude systems; Pages: 1-20). Louisiana State University used a high-order sliding mode observer to estimate the actuator failure of a quadrotor UAV, and used a control strategy based on STW (Super-Twisting) to achieve fault tolerance, and verified it through numerical simulation ( Conference: IEEE Conference on Control Technology and Applications; Authors: Seema Mallavalli, Afef Fekih; Publication Year: 2017; Article Title: A fault tolerant control approach for a quadrotor UAV subject to time varying disturbances andactuator faults; Pages: 596-601). Tianjin University uses an I&I (Immersion and Invariance)-based observer to diagnose partial failure of a quadrotor UAV motor and compensate it using sliding mode control (Journal: Nonlinear Dynamics; Authors: Wei Hao, Bin Xian; Publication Year: 2017 ; Article title: Nonlinearadaptive fault-tolerant control for a quadrotor uav based on immersion and invariance methodology; pp. 2813-2826). They also established the dynamic model of the tilting three-rotor UAV by using the unit quaternion, designed the STW-based observer and the RISE (Robust Integral of the Signum of the Error)-based controller, and realized the fault detection system. (Journal: IEEE Transactions on Industrial Informatics; Author: Bin Xian, Wei Hao; Publication Year: 2018; Title: Nonlinear robust fault tolerant control of the tilt tri-rotor uavunder rear servo′s stuck fault : Theory and experiments; pages: 1-9).

To sum up, the control problem of tri-rotor UAV has achieved certain results, but few researchers consider its fault-tolerant control problem. For the fault-tolerant control design of small rotor UAVs, there are still some limitations: 1) Some control designs simplify the UAV dynamics model into a linear model. 2) Some fault-tolerant control strategies use observer-based methods to achieve fault diagnosis, and then design dynamic control strategies to compensate. Although such methods can effectively deal with various faults, the effect of fault diagnosis will directly affect the control effect, making the controller overly dependent on the diagnostic information, and the time delay from fault occurrence to fault diagnosis may be in high real-time UAV systems. 3) There are few methods for the nonlinear model of the UAV, while considering external disturbance, model uncertainty and fault to design the controller; 4) At present, most fault-tolerant control methods only use numerical simulation for experimental verification , there are less control designs for semi-physical or full degree-of-freedom platform experiments.

SUMMARY OF THE INVENTION

In order to overcome the deficiencies of the prior art, the present invention comprehensively considers the external unknown disturbance and model uncertainty for the failure of the tail steering gear of the tilting tri-rotor unmanned aerial vehicle. A nonlinear fault-tolerant control algorithm that does not require fault diagnosis, is robust, and has high feasibility is designed to achieve stable control of attitude motion in the case of a tail servo jamming failure of a tilting tri-rotor UAV. The technical solution adopted in the present invention is to invent an adaptive robust fault-tolerant control method for a tilting tri-rotor UAV based on the adaptive backstepping method and terminal sliding mode control, and the steps are as follows:

1) Establish the failure model of the tilting tri-rotor UAV:

Define two coordinate systems, including the inertial coordinate system {E} and the body coordinate system {B}, select any point on the ground as the origin of the inertial coordinate system {E}, and select the center of mass of the drone as the origin of the body coordinate system {B}. The right-hand rule defines {E _x , E _y , E _z } and {B _x , By _y , B _z } as the reference coordinate axes in the inertial coordinate system {E} and the body coordinate system {B}, respectively, according to the Euler equation The dynamic model of the UAV attitude can be obtained as

The kinematic model is

之间的关系，R(η)的具体表达式为Among them, ω(t)=[ω _φ (t), ω _θ (t), ω _ψ (t)] ^T is the angular velocity vector of the UAV relative to {E} under {B}, η(t)= [φ(t), θ(t), ψ(t)] ^T is the attitude angle vector, J=diag{[J _x , J _y , J _z ] ^T } is the moment of inertia matrix, τ(t)=[τ _φ (t), τ _θ (t), τ _ψ (t)] ^T is the control input torque, d(t)∈R ^3×1 is the external disturbance vector, and N(ω, η)∈R ^3×1 is the model Uncertainty vector. R(η) is the angular velocity transfer matrix, which expresses the angular velocity vector ω(t) and the Euler angular velocity under {B}

The relationship between, the specific expression of R(η) is

For the convenience of analysis, formula (1) can be rewritten as

where S( ) represents an antisymmetric matrix stretched by a vector, that is, for a vector ω(t)=[ω _φ (t), ω _θ (t), ω _ψ (t)] ^T , S(ω) is

ρ(t)=d(t)+N(ω, η) is the disturbance and uncertainty term.

ρ(t) is unknown, but it satisfies the following inequality,

||ρ(t)||＜b ₀ +b ₁ ||η||+b ₂ ||ω|| ² (6)

Among them, b ₀ , b ₁ , and b ₂ are all positive numbers.

Simplify equation (4) into

where G(ω) is an auxiliary variable, and the specific expression is

The moment-lift model of the tilting tri-rotor UAV is

Among them, l ₁ , l ₂ , l ₃ are positive numbers, α(t) represents the inclination angle of the tail steering gear, f _i (t), i=1, 2, 3 are the lift forces generated by the three motors respectively, and the lift force vector is defined f(t)=[f ₁ (t), f ₂ (t), f ₃ (t)] ^T , k is the ratio between the lift coefficient and the reaction torque coefficient, which satisfies:

μ _i =kfi , _i =1, 2, 3. (10)

Wherein μ _i (t), i=1, 2, 3 are the reaction torques generated by the three motors respectively;

The variation range of the steering gear inclination α(t) is within 8°, so sinα(t)＜<cosα(t). In addition, the kf ₃ sinα term is ignored, then equation (9) can be rewritten as

τ=A(α)f (11)

where auxiliary variables

When the UAV steering gear is blocked, the steering gear will stop at a fixed position and no longer change, so consider the fault as

Among them, t _f is the fault occurrence time, α(t) represents the input angle of the steering gear before the fault occurs, α _f is the angle of the blocked position of the steering gear, which is an unknown constant. According to equations (11) and (12), the , the relationship between torque and lift is

τ=A(α _f )f (13)

where auxiliary variables

Define auxiliary variables λ ₁ =l ₃ cosα _f , λ ₂ =kcosα _f -l ₃ sinα _f , then formula (13) can be rewritten as

τ=A(λ ₁ , λ ₂ )f (14)

由于α_f为未知常数，l₃与k为已知常数，因此λ₁与λ₂也是未知常数。将式(14)代入式(7)得到发生故障后的无人机动力学方程为where auxiliary variables

Since α _f is an unknown constant, l ₃ and k are known constants, so λ ₁ and λ ₂ are also unknown constants. Substituting Equation (14) into Equation (7), the dynamic equation of the UAV after the failure is obtained as

The control objective is: for the tilting three-rotor UAV systems (15) and (2), in the case of the tail servo jamming fault and the unknown quantity ρ(t), design an appropriate control input vector f(t ), so that the UAV attitude angle η(t) converges to the target value;

2) Controller design:

In order to facilitate the design of the controller, the following definitions are made:

x ₂ =ω-ξ (17)

与

均为正常数对角阵。ξ为设计的虚拟控制信号，表达式为Among them, x ₁ and x ₁ are auxiliary variables, η _d (t)∈R ^3×1 is the target attitude angle vector,

and

All are positive diagonal matrices. ξ is the designed virtual control signal, the expression is

The non-singular terminal sliding surface s(t) is defined as follows:

Among them, β=diag{[β ₁ , β ₂ , β ₃ ] ^T } is a positive diagonal matrix, p, q are positive coprime odd integers, and satisfy:

1<p/q<2 (20)

The design control input lift vector f(t) is

为A(λ₁，λ₂)的估计，其表达式为in

is the estimation of A(λ ₁ , λ ₂ ), and its expression is

与

分别为λ₁与λ₂的估计值。In formula (22)

and

are the estimated values of λ ₁ and λ ₂ , respectively.

3) Adaptive law design:

与

的更新律为design

and

The update law of is

where σ ₁ and σ ₂ are their update gains.

的可逆性，使其的行列式不等于0，则可以得到to ensure that

The invertibility of , so that its determinant is not equal to 0, then we can get

的有界性，采用投影算子来对参数估计值的上下界进行限定，定义辅助变量和

引入投影算子如下：to ensure that and

The boundedness of and

The projection operator is introduced as follows:

分别表示

与

的下界和上界。where, λ _{_} and

Respectively

and

lower and upper bounds.

The characteristics and beneficial effects of the present invention are:

The present invention studies the fault-tolerant control problem of a tilting tri-rotor unmanned aerial vehicle affected by unknown external disturbance and model uncertainty when the tail steering gear is blocked and faulty. By analyzing the attitude dynamics characteristics of tilting tri-rotor UAV, a robust fault-tolerant control design is proposed based on adaptive backstepping method and non-singular terminal sliding mode control. When the tail steering gear of the UAV is blocked, the method achieves a better control effect on the attitude movement.

Description of drawings:

FIG. 1 is a schematic diagram of the coordinate system and the UAV of the present invention.

FIG. 2 is a flow chart of the present invention.

Fig. 3 is the experimental platform used in the present invention.

Figure 4 is the effect diagram of the attitude flight control experiment, in the figure:

a is the attitude angle change curve;

b is the control input change curve;

c is the adaptive value change curve;

d is the change curve of motor speed.

Detailed ways

In order to overcome the deficiencies of the prior art, the present invention comprehensively considers the external unknown disturbance and model uncertainty for the failure of the tail steering gear of the tilting tri-rotor unmanned aerial vehicle. A nonlinear fault-tolerant control algorithm that does not require fault diagnosis, is robust, and has high feasibility is designed to achieve stable control of attitude motion in the case of a tail servo jamming failure of a tilting tri-rotor UAV. The technical solution adopted in the present invention is to invent an adaptive robust fault-tolerant control method for a tilting tri-rotor UAV based on the adaptive backstepping method and terminal sliding mode control, and the steps are as follows:

1) Establish the failure model of the tilting tri-rotor UAV:

Define two coordinate systems, including inertial coordinate system {E} and body coordinate system {B}. Select any point on the ground as the origin of the inertial coordinate system {E}, select the center of mass of the UAV as the origin of the body coordinate system {B}, and define {E _x , E _y , E _z } and {B _x , B respectively according to the right-hand rule _y , B _z } are the reference coordinate axes in the inertial coordinate system {E} and the body coordinate system {B}. According to the Euler equation, the dynamic model of the UAV attitude can be obtained as

The kinematic model is

之间的关系，R(η)的具体表达式为Among them, ω(t)=[ω _φ (t), ω _θ (t), ω _ψ (t)] ^T is the angular velocity vector of the UAV relative to {E} under {B}, η(t)= [φ(t), θ(t), ψ(t)] ^T is the attitude angle vector, J=diag{[J _x , J _y , J _z ] ^T } is the moment of inertia matrix, τ(t)=[τ _φ (t), τ _θ (t), τ _ψ (t)] ^T is the control input torque, d(t)∈R ^3×1 is the external disturbance vector, and N(ω, η)∈R ^3×1 is the model Uncertainty vector. R(η) is the angular velocity transfer matrix, which expresses the angular velocity vector ω(t) and the Euler angular velocity under {B}

The relationship between, the specific expression of R(η) is

For the convenience of analysis, formula (1) can be rewritten as

where S( ) represents an antisymmetric matrix stretched by a vector, that is, for a vector ω(t)=[ω _φ (t), ω _θ (t), ω _ψ (t)] ^T , S(ω) is

ρ(t)=d(t)+N(ω, η) is the disturbance and uncertainty term.

Assuming the following, ρ(t) is unknown, but it satisfies the following inequality,

||ρ(t)||＜b ₀ +b ₁ ||η||+b ₂ ||ω|| ² (6)

Among them, b ₀ , b ₁ , and b ₂ are all positive numbers.

Simplify equation (4) into

where G(ω) is an auxiliary variable, and the specific expression is

The moment-lift model of the tilting tri-rotor UAV is

Among them, l ₁ , l ₂ , l ₃ are positive numbers, α(t) represents the inclination angle of the tail steering gear, f _i (t), i=1, 2, 3 are the lift forces generated by the three motors respectively, and the lift force vector is defined f(t)=[f ₁ (t), f ₂ (t), f ₃ (t)] ^T , k is the ratio between the lift coefficient and the reaction torque coefficient, which satisfies:

μ _i =kfi , _i =1, 2, 3. (10)

Where μ _i (t), i=1, 2, 3 are the counter torques generated by the three motors respectively.

The tilt angle α(t) of the steering gear of the tilting tri-rotor UAV studied in the present invention changes very little under normal conditions, and the variation range is all within 8°, so sinα(t)<<cosα(t). In addition, since the value of k is small, the -kf ₃ sinα term can be ignored, then equation (9) can be rewritten as

τ=A(α)f (11)

where auxiliary variables

When the UAV steering gear is blocked, the steering gear will stop at a fixed position and no longer change, so consider the fault as

Among them, t _f is the fault occurrence time, α(t) represents the input angle of the steering gear before the fault occurs, and α _f is the angle of the blocked position of the steering gear, which is an unknown constant. According to equations (11) and (12), the relationship between torque and lift after failure is obtained as

τ=A(α _f )f (13)

where auxiliary variables

Define auxiliary variables λ ₁ =l ₃ cosα _f , λ ₂ =kcosα _f -l ₃ sinα _f , then formula (13) can be rewritten as

τ=A(λ ₁ , λ ₂ )f (14)

由于α_f为未知常数，l₃与k为已知常数，因此λ₁与λ₂也是未知常数。将式(14)代入式(7)得到发生故障后的无人机动力学方程为where auxiliary variables

Since α _f is an unknown constant, l ₃ and k are known constants, so λ ₁ and λ ₂ are also unknown constants. Substituting Equation (14) into Equation (7), the dynamic equation of the UAV after the failure is obtained as

Based on the above analysis of the dynamic characteristics of the system and the expression of the steering gear failure, the control objectives of the present invention are: for the tilting trirotor UAV systems (15) and (2), when the tail steering gear jamming fault occurs and there is a In the case of unknown ρ(t), an appropriate control input vector f(t) is designed so that the UAV attitude angle η(t) converges to the target value.

2) Controller design:

In order to facilitate the design of the controller, the following definitions are made:

x ₂ =ω-ξ (17)

与

均为正常数对角阵。ξ为设计的虚拟控制信号，表达式为Among them, x ₁ and x ₁ are auxiliary variables, η _d (t)∈R ^3×1 is the target attitude angle vector,

and

All are positive diagonal matrices. ξ is the designed virtual control signal, the expression is

Referring to reference (19), the non-singular terminal sliding surface s(t) is defined as follows:

Among them, β=diag{[β ₁ , β ₂ , β ₃ ] ^T } is a positive diagonal matrix, p, q are positive coprime odd integers, and satisfy:

1<p/q<2 (20)

The design control input lift vector f(t) is

为A(λ₁，λ₂)的估计，其表达式为in

is the estimation of A(λ ₁ , λ ₂ ), and its expression is

与

分别为λ₁与λ₂的估计值。In formula (22)

and

are the estimated values of λ ₁ and λ ₂ , respectively.

3) Adaptive law design:

的更新律为design and

The update law of is

where σ ₁ and σ ₂ are their update gains.

的可逆性，使其的行列式不等于0，则可以得到to ensure that

The invertibility of , so that its determinant is not equal to 0, then we can get

与

的有界性，采用投影算子来对参数估计值的上下界进行限定，定义辅助变量

和

引入投影算子如下：to ensure that

and

The boundedness of

and

The projection operator is introduced as follows:

分别表示

与

的下界和上界。where, λ _i and

Respectively

and

lower and upper bounds.

The fault-tolerant control method for the blocking fault of the tail steering gear of the tilting tri-rotor UAV has been designed.

The technical problem to be solved by the present invention is to propose a robust fault-tolerant control method, which can realize the stable control of the attitude movement in the case of the tail steering gear jamming failure of the tilting trirotor UAV.

The flow chart of the present invention is shown in Figure 2, and the technical solution is as follows: establish a failure model of the tail steering gear of the tilting tri-rotor unmanned aerial vehicle, and design a robust fault tolerance based on the adaptive backstepping method and terminal sliding mode control. The controller and its adaptive law, including the following steps:

1) Establish the failure model of the tilting tri-rotor UAV:

Define two coordinate systems, including inertial coordinate system {E} and body coordinate system {B}. Select any point on the ground as the origin of the inertial coordinate system {E}, select the center of mass of the UAV as the origin of the body coordinate system {B}, and define {E _x , E _y , E _z } and {B _x , B respectively according to the right-hand rule _y , B _z } are the reference coordinate axes in the inertial coordinate system {E} and the body coordinate system {B}. According to the Euler equation, the dynamic model of the UAV attitude can be obtained as

The kinematic model is

之间的关系，R(η)的具体表达式为Among them, ω(t)=[ω _φ (t), ω _θ (t), ω _ψ (t)] ^T is the angular velocity vector of the UAV relative to {E} under {B}, η(t)= [φ(t), θ(t), ψ(t)] ^T is the attitude angle vector, J=diag{[J _x , J _y , J _z ] ^T } is the moment of inertia matrix, τ(t)=[τ _φ (t), τ _θ (t), τ _ψ (t)] ^T is the control input torque, d(t)∈R ^3×1 is the external disturbance vector, and N(ω, η)∈R ^3×1 is the model Uncertainty vector. R(η) is the angular velocity transfer matrix, which expresses the angular velocity vector ω(t) and the Euler angular velocity under {B}

The relationship between, the specific expression of R(η) is

For the convenience of analysis, formula (1) can be rewritten as

where S(.) represents an antisymmetric matrix stretched by a vector, that is, for a vector ω(t)=[ω _φ (t), ω _θ (t), ω _ψ (t)] ^T , S(ω) is

ρ(t)=d(t)+N(ω, η) is the disturbance and uncertainty term.

Assuming the following, ρ(t) is unknown, but it satisfies the following inequality,

||ρ(t)||＜b ₀ +b ₁ ||η||+b ₂ ||ω|| ² (6)

Among them, b ₀ , b ₁ , and b ₂ are all positive numbers.

Simplify equation (4) into

where G(ω) is an auxiliary variable, and the specific expression is

The moment-lift model of the tilting tri-rotor UAV is

Among them, l ₁ , l ₂ , l ₃ are positive numbers, α(t) represents the inclination angle of the tail steering gear, f _i (t), i=1, 2, 3 are the lift forces generated by the three motors respectively, and the lift force vector is defined f(t)=[f ₁ (t), f ₂ (t), f ₃ (t)] ^T , k is the ratio between the lift coefficient and the reaction torque coefficient, which satisfies:

μ _i =kfi , _i =1, 2, 3. (10)

Where μ _i (t), i=1, 2, 3 are the counter torques generated by the three motors respectively.

The tilt angle α(t) of the steering gear of the tilting tri-rotor UAV studied in the present invention changes very little under normal conditions, and the variation range is all within 8°, so sinα(t)<<cosα(t). In addition, since the value of k is small, the -kf ₃ sinα term can be ignored, then equation (9) can be rewritten as

τ=A(α)f (11)

where auxiliary variables

When the UAV steering gear is blocked, the steering gear will stop at a fixed position and no longer change, so consider the fault as

Among them, t _f is the fault occurrence time, α(t) represents the input angle of the steering gear before the fault occurs, and α _f is the angle of the blocked position of the steering gear, which is an unknown constant. According to equations (11) and (12), the relationship between torque and lift after failure is obtained as

τ=A(α _f )f (13)

where auxiliary variables

Define auxiliary variables λ ₁ =l ₃ cosα _f , λ ₂ =kcosα _f -l ₃ sinα _f , then formula (13) can be rewritten as

τ=A(λ ₁ , λ ₂ )f (14)

由于α_f为未知常数，l₃与k为已知常数，因此λ₁与λ₂也是未知常数。将式(14)代入式(7)得到发生故障后的无人机动力学方程为where auxiliary variables

Since α _f is an unknown constant, l ₃ and k are known constants, so λ ₁ and λ ₂ are also unknown constants. Substituting Equation (14) into Equation (7), the dynamic equation of the UAV after the failure is obtained as

Based on the above analysis of the dynamic characteristics of the system and the expression of the steering gear failure, the control objectives of the present invention are: for the tilting trirotor UAV systems (15) and (2), when the tail steering gear jamming fault occurs and there is a In the case of unknown ρ(t), an appropriate control input vector f(t) is designed so that the UAV attitude angle η(t) converges to the target value.

2) Controller design:

In order to facilitate the design of the controller, the following definitions are made:

x ₂ =ω-ξ (17)

与

均为正常数对角阵。ξ为设计的虚拟控制信号，表达式为Among them, x ₁ and x ₁ are auxiliary variables, η _d (t)∈R ^3×1 is the target attitude angle vector,

and

All are positive diagonal matrices. ξ is the designed virtual control signal, the expression is

Referring to reference (19), the non-singular terminal sliding surface s(t) is defined as follows:

Among them, β=diag{[β ₁ , β ₂ , β ₃ ] ^T } is a positive diagonal matrix, p, q are positive coprime odd integers, and satisfy:

1<p/q<2 (20)

The design control input lift vector f(t) is

为A(λ₁，λ₂)的估计，其表达式为in

is the estimation of A(λ ₁ , λ ₂ ), and its expression is

与

分别为λ₁与λ₂的估计值。In formula (22)

and

are the estimated values of λ ₁ and λ ₂ , respectively.

3) Adaptive law design:

与

的更新律为design

and

The update law of is

where σ ₁ and σ ₂ are their update gains.

的可逆性，使其的行列式不等于0，则可以得到to ensure that

The invertibility of , so that its determinant is not equal to 0, then we can get

与

的有界性，采用投影算子来对参数估计值的上下界进行限定，定义辅助变量

和

引入投影算子如下：to ensure that

and

The boundedness of

and

The projection operator is introduced as follows:

分别表示

与

的下界和上界。where, λ _i and

Respectively

and

lower and upper bounds.

In order to verify the effectiveness of the fault-tolerant control method designed in the present invention, the experimental verification was carried out using the tilting tri-rotor UAV platform independently developed by the research group. The present invention will describe in detail the attitude control method of the tilting three-rotor UAV with reference to experiments and accompanying drawings below.

1. Introduction to the experimental platform

The experimental platform is shown in Figure 3. The experimental platform adopts PC/104 embedded computer as simulation controller, xPC target based on Matlab RTW toolbox as real-time simulation environment, adopts self-designed inertial measurement unit as attitude sensor, and the measurement accuracy of pitch angle and roll angle is ±0.5° . The yaw angle measurement accuracy is ±2.0°. The control frequency of the whole system is 500Hz.

2. Attitude flight control experiment

The control strategy proposed by the present invention is verified by using the experimental platform as described above. The relevant parameters of the UAV and the controller are selected as follows: J=diag{[0.01, 0.015, 0.008] ^T }kg·m ² , l ₁ =0.14m, l ₂ =0.08m, l ₃ =0.2m, k=0.05 , c ₁ =diag{[1.2, 1.1, 1.0] ^T }, c ₂ =diag{[9.63, 2.64, 1.22] ^T }, β=diag{[0.1, 0.1, 0.1] ^T }, p=5, q =3, b ₀ =8, b ₁ =5, b ₂ =3, σ ₁ =0.11, σ ₂ =0.04. The target attitude angle is set as η _d = [0, 0, 0] ^T , and the steering gear tilt angle is artificially fixed at -2.5 degrees at the 30th second, simulating the jamming failure of the steering gear, that is, t _f =30s, α _f = -2.5°.

和

的曲线，均在稳定后收敛于一个常值。图4(d)为电机实际转速曲线，可以看出它们维持在一个合理的范围内。基于以上结果，证明了本发明所提出的方法具有较好的容错控制效果。Figure 4(a) shows the attitude angle curve of the UAV. It can be seen from the figure that in the first 30 seconds before the UAV fails, the attitude angle error is small, the control accuracy of roll angle and pitch angle is within ±0.5°, and the control accuracy of yaw angle is within ±1°. At the 30th second, the steering gear was blocked. Although the attitude angle fluctuated, it can be seen that the UAV could still maintain a stable flight. The control accuracy of the roll angle and pitch angle remained within ±1°, and the yaw angle The angular control accuracy is kept within ±2.5°. Figure 4(b) is the control input curve. From the lift curves of the three rotors, it can be seen that after the failure occurred in the 30th second, the control input has some corresponding changes and is maintained within a certain range after that. The inclination angle of the steering gear still participates in the control when the failure has not yet occurred, and is adjusted within a certain range. After the failure of the steering gear blockage occurs, the inclination angle remains at -2.5 degrees. Figure 4(c) is the adaptive value

and

The curves of , all converge to a constant value after stabilization. Figure 4(d) is the actual speed curve of the motor, and it can be seen that they are maintained within a reasonable range. Based on the above results, it is proved that the method proposed in the present invention has a good fault-tolerant control effect.

Claims (1)

1. A self-adaptive robust fault-tolerant control method of a tilting type three-rotor unmanned aerial vehicle is characterized by comprising the following steps:

1) establishing a fault model of the tilting three-rotor unmanned aerial vehicle:

defining two coordinate systems including an inertial coordinate system { E } and a body coordinate system { B }, selecting any point on the ground as an origin of the inertial coordinate system { E }, selecting the center of mass of the unmanned aerial vehicle as the origin of the body coordinate system { B }, and respectively defining { E } according to a right-hand rule_x,E_y,E_zAnd { B }_x,B_y,B_zThe coordinate axes are reference coordinate axes in an inertial coordinate system (E) and a body coordinate system (B), and the reference coordinate axes are determined according to the Euler equationThe dynamic model of the unmanned aerial vehicle attitude can be obtained as

The kinematic model is

Wherein ω (t) ═ ω_φ(t),ω_θ(t),ω_ψ(t)]^TFor the angular velocity vector of the drone relative to { E } under { B }, η (t) ═ phi (t), theta (t), psi (t)]^TIs an attitude angle vector, J { [ Diag { [ J { ] { [_x,J_y,J_z]^TIs the moment of inertia matrix, τ (t) ═ τ_φ(t),τ_θ(t),τ_ψ(t)]^TTo control input torque, d (t) e R^3×1For external disturbance vector, N (omega, η) is belonged to R^3×1For model uncertainty vector, R (η) is angular velocity transfer matrix, which expresses angular velocity vector ω (t) and Euler angular velocity under { B }In relation to each other, R (η) is specifically expressed as

For convenience of analysis, formula (1) is rewritten as

Where S (-) denotes an antisymmetric matrix spanned by a vector, i.e. for vector ω (t) [. omega. ]_φ(t)，ω_θ(t)，ω_ψ(t)]^TS (omega) is

ρ (t) ═ d (t) + N (ω, η) is the perturbation and uncertainty term,

ρ (t) is unknown, but it satisfies the inequality,

‖ρ(t)‖<b₀+b₁‖η‖+b₂‖ω‖²(6)

wherein b is₀，b₁，b₂Are all normal numbers, and are all positive numbers,

the formula (4) is simplified into

Wherein G (omega) is an auxiliary variable, and the specific expression is

The moment-lift model of the tilting type three-rotor unmanned aerial vehicle is

Wherein l₁，l₂，l₃Is a normal number, α (t) represents the tail steering engine inclination angle, f_i(t), i is 1, 2, 3 is the lift force generated by each of the three motors, and defines a lift vector f (t) f₁(t),f₂(t),f₃(t)]^TAnd k is the ratio between the lift coefficient and the reaction torque coefficient, and satisfies the following conditions:

μ_i＝kf_i， (10)

wherein mu_i(t) reaction torques respectively generated by the three motors;

the variation range of the steering engine inclination angle α (t) is 8^°Hence sin α (t)<<cos α (t), and kf₃sin α term is ignored, then equation (9) is rewritten as

τ＝A(α)f (11)

Wherein the auxiliary variable

When the unmanned aerial vehicle steering wheel has a blockage fault, the steering wheel can stop at a certain fixed position and is not changed any more, so that the fault is considered

Wherein, t_fα (t) represents the steering engine input angle before the fault occurred, α, as the time of the fault occurrence_fThe angle of the blocked position of the steering engine is an unknown constant, and the relation between the moment and the lift force after the fault occurs is obtained according to the formulas (11) and (12)

τ＝A(α_f)f (13)

Wherein the auxiliary variable

Defining an auxiliary variable λ₁＝l₃cosα_f，λ₂＝kcosα_f-l₃sinα_fThen, the formula (13) can be rewritten as

τ＝A(λ₁,λ₂)f (14)

Wherein the auxiliary variable

Due to α_fAs an unknown constant,/₃And k is a known constant, thus λ₁And λ₂Are also unknown constants. The formula (14) is substituted for the formula (7) to obtain the dynamic equation of the unmanned aerial vehicle after the fault occurs, wherein the dynamic equation is

For tilting type three-rotor unmanned aerial vehicle systems (15) and (2), under the condition that a tail steering engine is blocked and has an unknown quantity rho (t), designing a proper control input vector f (t) to enable an attitude angle η (t) of the unmanned aerial vehicle to converge to a target value;

2) designing a controller:

for the convenience of designing the controller, the following definitions are made:

x₂＝ω-ξ (17)

wherein x is₁And x₁As an auxiliary variable, η_d(t)∈R^3×1In order to be the target attitude angle vector,

andξ is a designed virtual control signal expressed as

Defining the nonsingular terminal sliding mode surface s (t) as follows:

wherein β { [ β { [ diag { [ 78 { ] { [₁,β₂,β₃]^TThe matrix is a normal number diagonal matrix, p and q are positive relatively prime odd integers, and satisfy:

1<p/q<2 (20)

design control input lift vector f (t) is

Wherein

Is A (lambda)₁，λ₂) Is expressed as

In formula (22)

Andare each lambda₁And λ₂An estimated value of (d);

3) and (3) self-adaptation law design:

design of

Andis updated according to the law

Wherein sigma₁And σ₂Updating the gains for them.

To ensure

So that its determinant is not equal to 0, then one can obtain

To ensure

And

the upper and lower bounds of the parameter estimation value are limited by adopting a projection operator, and auxiliary variables are defined

Andthe projection operator is introduced as follows:

wherein, _iλandrespectively represent

And

lower and upper bounds.

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