Quadrotor unmanned aerial vehicle scheduled performance sliding mode fault-tolerant control method with external disturbance and actuator failure

Abstract

The application relates to a quadrotor unmanned aerial vehicle scheduled performance sliding mode fault-tolerant control method with external disturbance and actuator failure, which designs a position loop controller and an attitude loop controller through an adaptive control method, and a disturbance observer is adopted in the attitude loop to estimate unknown external disturbance. The method can accelerate the convergence speed of the system, constrain the transient state performance of the system, effectively improve the fault-tolerant capability of the system, and has good robustness and anti-interference capability.

Description

Technical Field

[0001] This invention relates to a sliding mode fault-tolerant control method for predetermined performance of a quadcopter unmanned aerial vehicle with external disturbances and actuator failures. Background Technology

[0002] Quadcopter drones are characterized by their simple structure, convenient maintenance, easy portability, and strong stealth capabilities, and they can adapt to various complex and harsh environments. Due to their numerous advantages, quadcopter drones are widely used in various fields, such as production inspection, road monitoring, and fire rescue.

[0003] However, in actual flight, quadcopter drones may experience actuator failures. Actuator failures can affect the quadcopter drone system, leading to a decrease in the aircraft's control performance and system stability, which in turn affects the drone's normal flight and causes mission failure.

[0004] Furthermore, due to environmental changes and other factors, the drag coefficient and external disturbances of quadcopter drone systems are not known conditions and are difficult to measure accurately. Ignoring the system drag coefficient and external disturbances may reduce the stability of the quadcopter drone system. Considering practical realities, quadcopter drone systems have stringent requirements for metastable performance. Reasonably controlling the overshoot, convergence speed, and output error of the drone system can effectively prevent damage to the drone due to abnormal flight conditions.

[0005] Therefore, studying the fault-tolerant tracking control of quadcopter UAVs under predetermined performance and reasonably solving the problems of external disturbances and unknown drag coefficients has important practical significance and value. Summary of the Invention

[0006] The purpose of this invention is to provide a sliding mode fault-tolerant control method for a quadrotor UAV with predetermined performance under external disturbances and actuator failures, which can accelerate the convergence speed of the system, constrain the transient steady-state performance of the system, effectively improve the fault tolerance of the system, and have good robustness and anti-interference ability.

[0007] The present invention adopts the following technical solution:

[0008] A sliding mode fault-tolerant control method for predetermined performance of a quadrotor UAV with external disturbances and actuator failures is proposed. This method uses an adaptive control approach to design a position loop controller and an attitude loop controller. The attitude loop employs a disturbance observer to estimate unknown external disturbances.

[0009] Furthermore, the position loop controller includes a position subsystem [x1, x2]. T Controller, Position Subsystem [x3,x4] T Controller and position subsystem [x5,x6]T Controller.

[0010] Furthermore, the location subsystem [x1,x2] T The controller is:

[0011]

[0012] In the formula, k x f x It is a positive number; and β x u xf and k xx The estimated value;

[0013] Location subsystem [x1, x2] T The adaptive law is:

[0014]

[0015] In the formula, λ x1 , λ x2 , λ x3 p x1 It is a positive number.

[0016] Furthermore, the location subsystem [x3,x4] T The controller is:

[0017]

[0018] in,

[0019]

[0020] In the formula, c y f y and k y x is a positive constant; 3d This is the reference trajectory in the y-direction; β y u yf and k yy The estimated value;

[0021] Location subsystem [x3, x4] T The adaptive law is:

[0022]

[0023] In the formula, λ y1 , λ y2 , λ y3 p y1 It is a positive number.

[0024] Furthermore, the location subsystem [x5,x6] T The controller is:

[0025]

[0026] in,

[0027]

[0028] In the formula, c z f z , and k z x is a positive constant; 5d This is the reference trajectory in the z-direction; β z u zf and k zz The estimated value;

[0029] Location subsystem [x5, x6] T The adaptive law is:

[0030]

[0031] In the formula, λ z1 , λ z2 , λ z3 p z1 It is a positive number.

[0032] Furthermore, the attitude loop controller includes a roll subsystem controller, a pitch subsystem controller, and a yaw subsystem controller.

[0033] Furthermore, the roll subsystem [x7,x8] T The controller is:

[0034]

[0035] In the formula, k φ f φ It is a positive number; β φ u φf The estimated value;

[0036] The adaptive law of the roll subsystem is:

[0037]

[0038] In the formula, λ φ1 , λ φ2 It is a positive number.

[0039] Furthermore, the pitch subsystem [x9,x] 10 ] TThe controller is:

[0040]

[0041] in,

[0042]

[0043] In the formula, c θ f θ and k θ x is a positive constant; 9d Let θ be the reference trajectory; β θ u θf The estimated value;

[0044] The adaptive law of the pitch subsystem is:

[0045]

[0046] In the formula, λ θ1 , λ θ2 It is a positive number.

[0047] Furthermore, the yaw subsystem [x] 11 ,x 12 ] T The controller is:

[0048]

[0049] in,

[0050]

[0051] In the formula, c ψ f ψ and k ψ x is a positive constant; 11d Let ψ be the reference trajectory in the ψ direction; β ψ u ψf The estimated value;

[0052] The adaptive law of the yaw subsystem is:

[0053]

[0054] In the formula, λ ψ1 , λ ψ2 It is a positive number.

[0055] Furthermore, the attitude loop interference observers include interference observers for the roll subsystem, pitch subsystem, and yaw subsystem.

[0056] The interference observer for the roll subsystem is:

[0057]

[0058] In the formula, They are x8 and D respectively. φ , The estimated value;

[0059] The interference observer for the pitch subsystem is:

[0060]

[0061] In the formula, x 10 D θ , The estimated value;

[0062] The interference observer for the yaw subsystem is:

[0063]

[0064] In the formula, x 12 D ψ , The estimated value.

[0065] Furthermore, the expected roll angle x 7d And desired pitch angle x 9d for:

[0066]

[0067] The beneficial effects of this invention are as follows:

[0068] Currently, there are many designs for addressing the trajectory tracking control problem of quadrotor UAVs under actuator failure conditions. However, a solution that considers actuator failure, transient steady-state performance, unknown drag coefficients, and unknown external disturbances has not yet emerged. This invention proposes a corresponding solution to address these issues. By employing a predetermined performance sliding mode control strategy, an adaptive control strategy, and designing a disturbance observer, an inner and outer loop fault-tolerant controller is constructed, thereby solving the trajectory tracking fault-tolerant control problem of quadrotor UAVs with actuator failure, unknown drag coefficients, and unknown external disturbances.

[0069] This invention employs a control algorithm combining predetermined performance control and sliding mode control. This not only accelerates the system's convergence speed but also constrains the system's transient steady-state performance, effectively improving the system's fault tolerance and robustness. Since actuator failures are unknown and the system has an unknown drag coefficient, the controller design utilizes an adaptive control strategy, resulting in strong system robustness and better stability. For unknown external disturbances, a disturbance observer is used to estimate these disturbances, enhancing the system's anti-interference capability. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of the system control framework of the present invention.

[0071] Figure 2 This is a location tracking trajectory diagram.

[0072] Figure 3 This is the position tracking error curve.

[0073] Figure 4 For attitude tracking trajectory.

[0074] Figure 5 This is the attitude tracking error curve.

[0075] Figure 6 This is to interfere with the tracking trajectory of the observer. Detailed Implementation

[0076] The technical solution of the present invention will be described in detail below with reference to the embodiments. The following embodiments are only used to illustrate and explain the present invention, and do not constitute a limitation on the technical solution of the present invention.

[0077] 1. Dynamics model of a quadcopter UAV

[0078]

[0079] In the formula, m represents the mass of the organism; k ii (ii=xx,yy,zz) are unknown drag coefficients; g is gravitational acceleration; J p Ω represents the moment of inertia of the propeller. r Indicates the propeller speed margin; l represents the distance between the center of the quadcopter UAV and the rotor center; d i (i = φ, θ, ψ) represents the disturbance vectors in each direction of the attitude angles φ, θ, ψ; the controller input is u. i ,(i=1,2,3,4).

[0080] The position and attitude subsystems of a quadcopter UAV are represented by state equations as follows:

[0081]

[0082] In the formula, X = (x1, x2, ..., x...) 12 ) T Let X be the state variable of the quadcopter unmanned aerial vehicle system; η(X) and σ(X) are nonlinear functions of X; and the control input is U = (u1, u2, u3, u4). T .

[0083] Therefore, based on the expansion and simplification of the mathematical model (1) and state equation (2) of the quadcopter unmanned aerial vehicle system, it can be rewritten as:

[0084]

[0085]

[0086] In the formula, and u i (i = x, y, z) represents the control input signal in the position direction, where u x =(cosφsinθcosψ+sinφsinψ)u1,u y =(cosφsinθsinψ-sinφcosψ)u1,u z =(cosφcosθ)u1.

[0087] 2. Lemma 1 and Assumption 2.

[0088] Lemma 1 for nonlinear systems

[0089]

[0090] In the formula, Γ>0, ω i If >0 (i=0,1,···,n) are all constants, then system (5) is finite-time stable.

[0091] Assume 2 unknown disturbance d φ ,d θ ,d ψ satisfy and in It is a bounded constant that satisfies

[0092] 3. Controller Design

[0093] To meet the transient steady-state performance requirements of the tracking error variable, the following performance function is selected:

[0094]

[0095] In the formula, Li As a positive constant, it can adjust the system's convergence speed;

[0096] If e 1i i = x, y, z, φ, θ, ψ can satisfy:

[0097]

[0098] Then, the predetermined performance control target can be achieved. Where e 1i i = x, y, z, φ, θ, ψ represents the tracking error, and δ i , For positive integers, when e 1i The initial conditions are satisfied At this time, the following state transitions can be performed:

[0099] e 1i =u i (t)ν i (ε i (8)

[0100] in,

[0101]

[0102] ν is obtained through calculation. i (ε i The inverse function of ) is:

[0103]

[0104] In the formula,

[0105] Note 1: Through the state transformations in equations (8) and (9), the state of e can be transformed. 1i The predetermined performance control problem is transformed into ε i The stability control issue.

[0106] 4. Actuator Fault Model

[0107] The mathematical model for actuator failure is as follows:

[0108] u i =τ i u ia +u if (11)

[0109] In the formula, u i (i = x, y, z, φ, θ, ψ) represents the actual output of the actuator; u ia Indicates an actuator input with a fault; 0≤τ i ≤1 indicates an unknown constant-value actuator failure; uif This indicates an unknown constant value actuator deviation fault.

[0110] 5. Position Subsystem Controller Design

[0111] The outer ring position subsystem (3) can be considered as consisting of three parts: the x-position subsystem, the y-position subsystem, and the z-position subsystem. First, regarding the position subsystem [x1, x2]... T The design process for the controller is similar for the other subsystems.

[0112] The position tracking error is:

[0113] e 1x =x1-x 1d (12)

[0114] In the formula, x 1d This is the reference trajectory in the x-direction. The time derivative of the position tracking error is:

[0115]

[0116] The design of the sliding mold surface is as follows:

[0117]

[0118] In the formula, c x It is a positive number.

[0119] set up Choose the following Lyapunov function V x1 for:

[0120]

[0121] Differentiating equation (20) gives:

[0122]

[0123] in,

[0124]

[0125]

[0126] In the formula, x 1d This is the reference trajectory in the x-direction.

[0127] To meet control requirements, the position subsystem [x1,x2] T The controller is designed as follows:

[0128]

[0129] In the formula, kx f x It is a positive number; and β x u xf and k xx The estimated value. The adaptive law is designed as follows:

[0130]

[0131] In the formula, λ x1 , λ x2 , λ x3 p x1 It is a positive number.

[0132] To verify the position subsystem [x1, x2] T For stability, the Lyapunov function V is chosen as follows. x for:

[0133]

[0134] V x Taking the derivative with respect to time, we get:

[0135]

[0136] According to Lyapunov's stability theorem, the position subsystem [x1, x2] T To achieve eventual uniformity, bounded asymptotic stability, and to satisfy predetermined performance requirements, a similar derivation process is used for the position subsystem [x3, x4]. T Location subsystem [x5, x6] T The controllers can be designed as follows:

[0137]

[0138] in,

[0139]

[0140]

[0141] in,

[0142]

[0143] In the above formula, c y c z f y f z k y and k z x is a positive constant; 3d and x 5dThese are the reference trajectories in the y and z directions, respectively; β y u yf and k yy The estimated value, β z u zf and k zz The estimated value.

[0144] The corresponding adaptive law design is as follows:

[0145]

[0146]

[0147] In the formula, λ y1 , λ y2 , λ y3 p y1 , λ z1 , λ z2 , λ z3 p z1 It is a positive number.

[0148] 6. Interference Observer Design

[0149] Based on assumption 2 and system model (4), design the attitude subsystem [x7, x8]. T The interference observer is:

[0150]

[0151] In the formula, They are x8 and D respectively. φ , The estimated value.

[0152] Based on a similar derivation process:

[0153]

[0154]

[0155] In the formula, x 10 D θ , x 12 D ψ , The estimated value.

[0156] According to Lemma 1, we know that... At that time, it made Therefore, estimates of external disturbances can be used for controller design.

[0157] 7. Attitude Subsystem Controller Design

[0158] The inner ring attitude subsystem (4) can be considered as consisting of three parts: roll subsystem, pitch subsystem, and yaw subsystem.

[0159] First, regarding the roll subsystem [x7,x8] T The design process for the controller is similar, and the design process for the other attitude subsystems is also similar.

[0160] The attitude tracking error is:

[0161] e 1φ =x7-x 7d (32)

[0162] In the formula, x 7d Let φ be the reference trajectory in the φ direction. The time derivative of the attitude tracking error is:

[0163]

[0164] The design of the sliding mold surface is as follows:

[0165]

[0166] In the formula, c φ It is a positive number.

[0167] set up Choose the following Lyapunov function V φ1 for:

[0168]

[0169] Differentiating equation (44) gives:

[0170]

[0171] in,

[0172]

[0173]

[0174] In the formula, x 7d This is the reference trajectory in the φ direction.

[0175] To meet control requirements, the roll subsystem [x7,x8] T The controller is designed as follows:

[0176]

[0177] In the formula, k φ f φIt is a positive number; β φ u φf The estimated value. The adaptive law design is as follows,

[0178]

[0179] In the formula, λ φ1 , λ φ2 It is a positive number.

[0180] To verify the roll subsystem [x7,x8] T For stability, the Lyapunov function V is chosen as follows. φ for:

[0181]

[0182] V φ Taking the derivative with respect to time, we get:

[0183]

[0184] Because the interference observer is able to Time estimation of external disturbance D φ Therefore, we get

[0185]

[0186] According to Lyapunov's stability theorem, the roll subsystem [x7, x8] T To achieve eventual uniform bounded asymptotic stability and meet predetermined performance requirements, a similar derivation process is used for the pitch subsystem [x9, x...]. 10 ] T yaw subsystem [x 11 ,x 12 ] T The controllers can be designed as follows:

[0187]

[0188] in,

[0189]

[0190]

[0191] in,

[0192]

[0193] In the above formula, c θ , fθ f ψ k θ and k ψ x is a positive constant; 9d and x 11d These are the reference trajectories in the directions θ and ψ, respectively; β θ u θf The estimated value, β ψ u ψf The estimated value. The corresponding adaptive law design is as follows:

[0194]

[0195]

[0196] In the formula, λ θ1 , λ θ2 , λ ψ1 , λ ψ2 It is a positive number.

[0197] Note 2: The expected roll angle x in this article 7d And desired pitch angle x 9d As shown below,

[0198]

[0199] 8. Simulation Experiment

[0200] The schematic diagram of the method of this invention is as follows: Figure 1 As shown, by combining predetermined performance control and sliding mode control, along with an adaptive control algorithm and a disturbance observer, a fault-tolerant controller for the position and attitude loops of a quadrotor UAV is designed. The designed inner and outer loop controllers can improve the fault tolerance and convergence speed of the UAV system, enhance its transient steady-state performance, and strengthen its anti-interference capability. Finally, a suitable Lyapunov function is constructed, and the stability of the quadrotor UAV under the designed controller is proven.

[0201] This invention uses Matlab software for simulation, where the UAV dynamics model and related algorithms are programmed using .M files, and the UAV system model is built using the Simlink module. During the simulation, the runtime and step size of the control system are appropriately set, and the results are compared and tested with corresponding simulations.

[0202] 9. Simulation Results

[0203] The simulation results obtained by simulating a quadcopter drone using Matlab are as follows. (Observation...) Figure 2 and 4It can be observed that under the fault-tolerant controller of this invention, when the position loop and attitude loop experience actuator failure in the second second, the actual trajectory can re-track the desired trajectory in a relatively short time. Furthermore, through observation... Figure 3 and 5 It can be observed that the tracking errors of the position loop and attitude loop converge well between the upper and lower bounds of the performance function. The tracking curves of the disturbance observer for external disturbances are shown below. Figure 6 As shown, the disturbance observer can accurately estimate external disturbances within a finite time. In summary, this demonstrates that the inner and outer loop controllers are effective and reasonable.

Claims

1. A sliding mode fault-tolerant control method for predetermined performance of a quadrotor unmanned aerial vehicle (UAV) with external disturbances and actuator failures, characterized in that, Design a position loop controller using an adaptive control method; The position loop controller includes a position subsystem [x1, x2] T Controller, Position Subsystem [x3,x4] T Controller and position subsystem [x5,x6] T Controller; The location subsystem [x1, x2] T The controller is In the formula, k x f x It is a positive number; and β x u xf and k xx The estimated value; Location subsystem [x1, x2] T The adaptive law is In the formula, λ x1 , λ x2 , λ x3 p x1 It is a positive number; c x It is a positive number; k ii ,ii=xx,yy,zz, are unknown drag coefficients; in i =τ i in ia +in if In the formula, u i , i = x, y, z, φ, θ, ψ, represent the actual output of the actuator; u ia Indicates an actuator input with a fault; 0≤τ i ≤1 indicates an unknown constant-value actuator failure; u if This indicates an unknown constant-value actuator deviation fault; To meet the transient steady-state performance requirements of the tracking error variable, the following performance function is selected: In the formula, L i p is a positive constant and can be used to adjust the system's convergence speed. i0 >0, If e 1i i = x, y, z, φ, θ, ψ can satisfy: Then, the predetermined performance control target can be achieved, where e 1i i = x, y, z, φ, θ, ψ represents the tracking error. d i , For positive integers, when e 1i The initial conditions are satisfied At this time, the following state transitions can be performed: e 1i =u i (t)n i (e i ) in, ν is obtained through calculation. i (ε i The inverse function of ) is: In the formula, 2. The sliding mode fault-tolerant control method for a quadrotor unmanned aerial vehicle with predetermined performance under external disturbances and actuator failures, as described in claim 1, is characterized in that... It also includes an attitude loop controller, which employs a disturbance observer to estimate unknown external disturbances. The attitude loop controller includes a roll subsystem controller, a pitch subsystem controller, and a yaw subsystem controller. The location subsystem [x3, x4] T The controller is in, In the formula, c y f y and k y x is a positive constant; 3d This is the reference trajectory in the y-direction; β y u yf and k yy The estimated value; Location subsystem [x3, x4] T The adaptive law is: In the formula, λ y1 , λ y2 , λ y3 p y1 It is a positive number.

3. The sliding mode fault-tolerant control method for a quadrotor unmanned aerial vehicle with predetermined performance under external disturbances and actuator failures, as described in claim 2, is characterized in that... Location subsystem [x5, x6] T The controller is in, In the formula, c z f z , and k z x is a positive constant; 5d This is the reference trajectory in the z-direction; β z u zf and k zz The estimated value; Location subsystem [x5, x6] T The adaptive law is: In the formula, λ z1 , λ z2 , λ z3 p z1 It is a positive number.

4. The sliding mode fault-tolerant control method for a quadrotor UAV with predetermined performance under external disturbances and actuator failures as described in claim 3, characterized in that, The roll subsystem [x7, x8] T The controller is In the formula, k φ f φ It is a positive number; β φ u φf The estimated value; The adaptive law of the roll subsystem is In the formula, λ φ1 , λ φ2 S is a positive constant. φ For the sliding surface function.

5. A sliding mode fault-tolerant control method for a quadrotor unmanned aerial vehicle with predetermined performance under external disturbances and actuator failures, as described in claim 4, is characterized in that... Pitch subsystem [x9,x 10 ] T The controller is in, In the formula, c θ f θ and k θ x is a positive constant; 9d Let θ be the reference trajectory; β θ u θf The estimated value; The adaptive law of the pitch subsystem is In the formula, λ θ1 , λ θ2 It is a positive number.

6. The sliding mode fault-tolerant control method for a quadrotor unmanned aerial vehicle with predetermined performance under external disturbances and actuator failures, as described in claim 5, is characterized in that... The yaw subsystem [x] 11 ,x 12 ] T The controller is in, In the formula, c ψ f ψ and k ψ x is a positive constant; 11d Let ψ be the reference trajectory in the ψ direction; β ψ u ψf The estimated value; The adaptive law of the yaw subsystem is In the formula, λ ψ1 , λ ψ2 It is a positive number.

7. A sliding mode fault-tolerant control method for a quadrotor unmanned aerial vehicle with predetermined performance under external disturbances and actuator failures, as described in claim 6, is characterized in that... The attitude loop interference observers include the roll subsystem interference observer, the pitch subsystem interference observer, and the yaw subsystem interference observer. The interference observer of the roll subsystem is In the formula, They are x8 and D respectively. φ , The estimated value; The interference observer of the pitch subsystem is In the formula, x 10 D θ , The estimated value; the interference observer of the yaw subsystem is In the formula, x 12 D ψ , The estimated value.

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