Fault-tolerant control method for quadrotor drone under actuator failure and input saturation

Abstract

The present invention relates to a fault-tolerant control method for a quad-rotor drone under actuator failure and input saturation, which combines an adaptive Backsteeping controller with a command filter, and introduces a hyperbolic tangent function and an error compensation mechanism to control the position subsystem and the attitude subsystem. The present invention can track the finite time convergence of the error and improve the tracking speed of the position and attitude.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle control, and in particular to a finite-time fault-tolerant control method for an uncertain quad-rotor unmanned aerial vehicle under command filter, actuator failure and input saturation. Background Art

[0002] The quadcopter has a simple structure and strong maneuverability. It can achieve vertical take-off and landing, and hover at a fixed point. It has the characteristics of high safety, flexible operation, and easy carrying. It has gradually been used in various fields, such as aerial photography, light shows, patrols, surveying, emergency rescue and other scenarios.

[0003] Quadrotors are a type of multi-input multi-output system with six degrees of freedom and four independent inputs, which are characterized by high nonlinearity, under-actuation, and strong coupling. Since the actuators of quadrotors may be subject to external interference, such as changes in temperature and humidity, or component loss, when performing tasks, the probability of actuator failure in the actual system will increase. In addition, due to the limitation of motor speed during actual flight, the force and torque provided by the quadrotor rotor are bounded. In order to avoid the control input exceeding the execution range of the aircraft system, it is necessary to consider the input saturation.

[0004] However, most studies only consider the problem of actuator failure or input saturation, so it is more practical to consider the existence of both actuator failure and input saturation at the same time.

[0005] In addition, in the design process of quadrotor controller, there is often a problem of differential blow-up. Although in some studies, the above shortcomings have been solved by dynamic surface control technology and first-order filters, there are still errors after filtering, which may affect the control performance. Summary of the invention

[0006] The purpose of the present invention is to provide a fault-tolerant control method for a quadrotor unmanned aerial vehicle under actuator failure and input saturation, which can achieve finite-time convergence of tracking errors and improve the tracking speed of position and attitude.

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

[0008] A fault-tolerant control method for a quadrotor UAV under actuator failure and input saturation is proposed. An adaptive backsteeping controller is combined with a command filter, and a hyperbolic tangent function and an error compensation mechanism are introduced to control the position subsystem and attitude subsystem.

[0009] Furthermore, the position subsystem is shown as follows:

[0010]

[0011] The posture subsystem is shown as follows:

[0012]

[0013] Among them, η mi =1 / m i , i=x,y,z;η mj =1 / I j ,j=φ,θ,ψ;T mφ =(I y -I z ) / I x ; T mθ =(I z -I x ) / I y ; T mψ =(I x -I y ) / I z ;k i , i = x, y, z, φ, θ, ψ are the unknown aerodynamic damping coefficients of the system; J φ ,J θ is the moment of inertia; Ω r The angular velocity representing the propeller speed margin; u x =(cosφsinθcosψ+sinφsinψ)·u1;u y =(cosφsinθsinψ-sinφcosψ)·u1;u z =cosφcosθ·u1.

[0014] Furthermore, the command controller is:

[0015]

[0016] Among them, α j Command filter input signal; is the output signal of the command filter; ξ is the damping ratio; ω nj is the undamped natural frequency; define ω nj >0,ξ∈(0,1], σ is a positive constant.

[0017] Furthermore, the error compensation mechanism is:

[0018] η i =e i -k i , i=1,2,3,...,12

[0019] Among them, k i is the error compensation signal, e i is the error variable.

[0020] Furthermore, the error variable is:

[0021] e1=x1-x 1d ,e2=x2-α cx

[0022] e3=x3-x 3d ,e4=x4-α cy

[0023] e5=x5-x 5d ,e6=x6-α cz

[0024] Among them, x 1d ,x 3d ,x 5d is the reference signal; α cx ,α cy ,α cz When the input signal virtual controller is α i , the output signal of the command filter when i=x,y,z.

[0025] Furthermore, the position controller u x for:

[0026]

[0027] Position controller u y for:

[0028]

[0029] Position controller u z for:

[0030]

[0031] Furthermore, the attitude controller u φ for:

[0032] Attitude Controller θ for:

[0033]

[0034] Attitude Controller ψ for:

[0035]

[0036] Furthermore, the position subsystem and the attitude subsystem are connected to each other through the attitude extraction algorithm; the reference input of the inner loop attitude angle is:

[0037]

[0038] The beneficial effects of the present invention are:

[0039] (1) By adopting adaptive technology, the limitations of the quadrotor drone, such as the need to accurately know the system dynamic parameters, air resistance, and actuator failure, are overcome. Considering the efficiency of the actuator in the actual system, the hyperbolic tangent function is used instead of the saturation function to eliminate the impact of input saturation on system performance. The present invention solves the problems of parameter uncertainty, actuator failure, and input saturation at the same time, and has strong practicality.

[0040] (2) By introducing the command filter, the problem of differential explosion is solved, making it possible to quickly approximate the derivative of the virtual control signal within a finite time; and by introducing the error compensation mechanism, the influence of the filtering error on the system performance is effectively eliminated; and the attitude and position tracking errors can ensure the convergence of the tracking errors, as well as the boundedness of all closed-loop signals within a finite time, thereby improving the tracking speed of the position and attitude. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is the three-dimensional trajectory tracking diagram of the quadrotor drone.

[0042] Figure 2 It is the tracking error curve of the position subsystem.

[0043] Figure 3 is the tracking error curve of the attitude subsystem.

[0044] Figure 4 Enter the graph for the controller.

[0045] Figure 5 is the input constraint of the controller. DETAILED DESCRIPTION

[0046] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and 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.

[0047] 1. Mathematical model and system description of uncertain dynamics

[0048] (1) Define variables:

[0049]

[0050] Considering the influence of unknown time-varying loads and aerodynamic damping coefficients on the QUAV system, the mathematical models of the position subsystem and attitude subsystem of the quadrotor UAV are established respectively according to dynamics, physics and Euler angle description.

[0051] The mathematical model of the position subsystem can be written as formula (1a).

[0052]

[0053] The mathematical model of the attitude subsystem can be written as formula (1b).

[0054]

[0055] The following parameters are defined:

[0056] Among them, η mi =1 / m i , i=x,y,z;η mj =1 / I j ,j=φ,θ,ψ;T mφ =(I y -I z ) / I x ; T mθ =(I z -I x ) / I y ; T mψ =(I x -I y ) / I z ;k i , i = x, y, z, φ, θ, ψ are the unknown aerodynamic damping coefficients of the system; J φ ,J θ is the moment of inertia; Ω r The angular velocity representing the propeller speed margin; u x =(cosφsinθcosψ+sinφsinψ)·u1;u y =(cosφsinθsinψ-sinφcosψ)·u1;u z =cosφcosθ·u1.

[0057] Assumption 1: The quadrotor drone is a rigid body and its elastic deformation is ignored; the inertial reference system is the ground, and the center of gravity coincides with the origin of the fixed coordinate system; the flexibility of the blades is relatively small and can be ignored; the gravitational acceleration does not change with the change of position.

[0058] Assumption 2: Parameter η mx ,η my ,η mz ,η mφ ,η mθ ,η mψ is unknown, and its upper limit parameter Both are greater than 0. Aerodynamic damping coefficient k i, i=x,y,z,φ,θ,ψ are also unknown and greater than zero.

[0059] Assumption 3: Assume these inequalities hold:

[0060] η mx (△ x +δ x )|≤G x ; η my (△ y +δ y )|≤G y ; η mz (△ z +δ z )|≤G z ;

[0061] max{η mφ (△ φ +δ φ ),T mφ}≤G φ ; max{η mθ (△ θ +δ θ ),T mθ}≤G θ ; max{η mψ (△ ψ +δ ψ ),T mψ}≤G ψ ;

[0062] η mx k x |≤L x ; η my k y |≤L y ; η mz k z |≤L z ; η mφ k φ |≤L φ ; η mθ k θ |≤L θ ; η mψ k ψ |≤L ψ ;

[0063]

[0064] Parameter G i ,L i , i=x,y,z,φ,θ,ψ; The upper bound of is also unknown.

[0065] (2) Command filters are used to solve the problem of differential calculation explosion and the impact of filtering errors on system performance.

[0066]

[0067] Among them, α j Command filter input signal; is the output signal of the command filter; ξ is the damping ratio; ω nj is the undamped natural frequency; define ω nj >0,ξ∈(0,1], σ is a positive constant.

[0068] The initial value of the filter is

[0069] In order to avoid the control input exceeding the execution range of the quadrotor UAV system, the saturation function form of the control input is considered to be:

[0070]

[0071] where u i is the control input of the system; M i , i = x, y, z, φ, θ, ψ actuator input constraints.

[0072] The hyperbolic tangent function is used to approximate the saturation function, and the expression is as follows:

[0073]

[0074] The actuator fault model is:

[0075] U i =Γ i u i +δ i ,i=x,y,z,φ,θ,ψ (5)

[0076] Among them, U i Represents the actual output of the actuator; u i Indicates a faulty actuator input; unknown parameter 0 < Γ i ≤1 indicates the actuator efficiency coefficient; δ i Indicates an unknown additive fault.

[0077] Lemma 1: Assume u>0,v>0 and w(p,q)>0 is a real-valued function, the following inequality holds

[0078]

[0079] Lemma 2: For any constant υ>0 and any variable c∈R, the following relation holds

[0080]

[0081] 2. Position subsystem controller design

[0082] For the position subsystem, it can be seen as consisting of the position x subsystem, the position y subsystem, and the position z subsystem.

[0083] First, for the position x subsystem [x1,x2] T Carry out controller design, and the design process of other position subsystems is similar.

[0084]

[0085] Among them, x 1d ,x 3d ,x 5d is the reference signal; α cx ,α cy ,α cz When the input signal virtual controller is α i , the output signal of the command filter when i=x,y,z.

[0086] The introduced error compensation mechanism is:

[0087] η i =e i -k i ,i=1,2,3,...,12 (7)

[0088] where k i is the error compensation signal.

[0089] Choose a Lyapunov function of the form

[0090]

[0091] V x1 The derivative can be written as follows

[0092]

[0093] Virtual control signal α x Designed for:

[0094]

[0095] Among them, the design parameter b x1 >0,b x2 >0;u>0.

[0096] Introducing an error compensation mechanism can reduce the filtering error α cx -α x The error compensation mechanism is defined as:

[0097]

[0098] Substituting equations (10) and (11) into equation (9), we obtain

[0099]

[0100] Lyapunov function V x2 The choices are as follows

[0101]

[0102] According to Hypothesis 2 and Hypothesis 3, V x2 The time derivative of

[0103]

[0104] Design position controller u x :

[0105]

[0106] Among them, the design parameter b x4 >0,b x5 >0,b x6 >0,b x7 >0; It is c x The estimate, It's G x The estimate, YesL x The estimate, yes Estimates.

[0107] Substituting equation (15) into equation (14), we get

[0108]

[0109] Finally, the total Lyapunov function is designed as

[0110]

[0111] Among them, the design parameters are r1>0, r2>0, r3>0, r4>0;

[0112]

[0113] According to Lemma 2, the total Lyapunov function of time V x The derivative is

[0114]

[0115] The adaptive law is designed as:

[0116]

[0117] in,

[0118]

[0119] Among them, the design parameters δ1>0, δ2>0, δ3>0, δ4>0.

[0120] According to Lemma 1 and Young's inequality, substituting equations (19)-(22) into equation (18), we can obtain:

[0121]

[0122] Similarly, the controller u y and u z Designed for:

[0123]

[0124] Among them, the design parameter b y4 >0,b y5 >0,b y6 >0,b y7 >0,b z4 >0,b z5 >0,b z6 >0,b z7 >0; They are c y , c z The estimate, G y , G z The estimate, L y , L z The estimate, They are Estimates.

[0125] Virtual control signal α y , α z Designed for:

[0126]

[0127] Among them, the design parameter b y1 >0,b y2 >0; b z1 >0,b z2 >0.

[0128] The error compensation mechanism is formulated as:

[0129]

[0130] The adaptive law is designed as:

[0131]

[0132] in,

[0133]

[0134] Among them, the design parameters δ5>0, δ6>0, δ7>0, δ8>0.

[0135]

[0136] in,

[0137]

[0138] Among them, the design parameters δ9>0, δ 10 >0,δ 11 >0,δ 12 >0.

[0139] The two subsystems, the position subsystem and the attitude subsystem, are interconnected through an attitude extraction algorithm;

[0140]

[0141] The reference input of the inner ring attitude angle can be obtained as

[0142]

[0143] 3. Attitude subsystem controller design

[0144] For the attitude subsystem, it can be seen as consisting of the position φ subsystem, the position θ subsystem, and the position ψ subsystem.

[0145] First, for the position φ subsystem [x7,x8] T Carry out controller design, and the design process of other attitude subsystems is similar.

[0146] Tracking error is defined as follows:

[0147]

[0148] Among them, x 7d ,x 9d ,x 11d is the reference signal; α cφ ,α cθ ,α cψ When the input signal virtual controller is α i , the output signal of the command filter when i=φ,θ,ψ.

[0149] Choose a Lyapunov function of the form

[0150]

[0151] V φ7 The time derivative of can be written as follows

[0152]

[0153] Virtual control signal α φ Designed for

[0154]

[0155] Among them, the design parameter b φ1 >0,b φ2 >0.

[0156] Introducing an error compensation mechanism can reduce the error α cφ -α φ The error compensation mechanism is defined as

[0157]

[0158] Among them, the design parameter b φ3 >0,b φ4 >0,b φ5 >0.

[0159] Substituting equations (42) and (43) into equation (41), we obtain

[0160]

[0161] Lyapunov function V φ8 Select as follows

[0162]

[0163] Combining Hypothesis 2 and Hypothesis 3, V φ8 The time derivative of

[0164]

[0165] Controller φ Designed for:

[0166]

[0167] Among them, the design parameter b φ4 >0,b φ5 >0; yes The estimate, It's Gφ The estimate, YesL φ Estimates.

[0168] Substituting equation (47) into equation (46), we obtain

[0169]

[0170] Finally, the total Lyapunov function V φ Designed to

[0171]

[0172] Among them, the design parameter r 13 >0,r 14 >0,r 15 >0,

[0173] According to Lemma 2, V φ The derivative is

[0174]

[0175] The adaptive law is designed as:

[0176]

[0177]

[0178] Among them, the design parameter is r 13 >0,r 14 >0,r 15 >0,δ 13 >0,δ 14 >0,δ 15 >0.

[0179] According to Lemma 1 and Young's inequality, substituting equations (51)-(53) into equation (50), we can obtain:

[0180]

[0181] in,

[0182]

[0183] Similarly, the controller u θ and u ψ Designed for:

[0184]

[0185] Among them, the design parameter b θ4 >0,b θ5 >0,bθ6 >0,b θ7 >0; b ψ4 >0,b ψ5 >0,b ψ6 >0,b ψ7 >0; They are The estimate, G θ , G ψ The estimate, YesL θ , L ψ Estimates.

[0186] Virtual control signal α θ and α ψ Designed for:

[0187]

[0188]

[0189] Among them, the design parameter b θ1 >0,b θ2 >0,b ψ1 >0,b ψ2 >0.

[0190] Error compensation mechanism positioning:

[0191]

[0192] Among them, the design parameter is b θ1 >0,b θ3 >0,b ψ1 >0,b ψ3 >0.

[0193] The adaptive law is designed as:

[0194]

[0195] Among them, the design parameter is r 16 >0,r 17 >0,r 18 >0,r 19 >0,r 20 >0,r 21 >0,δ 16 >0,δ 17 >0,δ 18 >0,δ 19 >0,δ 20 >0,δ 21 >0.

[0196] 4. Simulation experiment

[0197] The present invention adopts matlab software for simulation verification. First, a program is written in a .m file according to the designed controller, and then a four-rotor unmanned aerial vehicle system model is built in Simulink. Finally, parameters are debugged for simulation verification.

[0198] 5. Simulation results

[0199] Figure 1 The 3D tracking trajectory of the method designed in this paper is shown. In order to clearly observe the tracking effect, the tracking errors of the position subsystem and the attitude subsystem are shown in Figure 2 and Figure 3 As shown, this clearly shows that it can guarantee the convergence of the tracking error and the boundedness of all closed-loop signals in finite time. Figure 4 The proposed method is shown to track the changes in the control input in the presence of input constraints and actuator faults. This shows that the designed controller can achieve stability in a finite time.

[0200] In order to clearly demonstrate the effectiveness of the design control inputs, Figure 5 The control input curves for saturated and unsaturated conditions are shown. U and U s They represent the control input under saturated input and unsaturated conditions respectively. The simulation results show that when the control quantity U s If the saturation limit is exceeded, the saturation limit will cause the control input to fall back to a safe range to achieve effective control.

Claims

1. A fault-tolerant control method for a quadrotor drone under actuator failure and input saturation, characterized in that: The adaptive backsteeping controller is combined with the command filter, and the hyperbolic tangent function and error compensation mechanism are introduced to control the position subsystem and attitude subsystem. The position subsystem is shown as follows: The attitude subsystem is shown as follows: Among them, η mi =1 / m i , i=x,y,z;η mj =1 / I j ,j=φ,θ,ψ;T mφ =(I y -I z ) / I x ; T mθ =(I z -I x ) / I y ; T mψ =(I x -I y ) / I z ;k i , i = x, y, z, φ, θ, ψ are the unknown aerodynamic damping coefficients of the system; J φ ,J θ is the moment of inertia; Ω r The angular velocity representing the propeller speed margin; u x =(cosφsinθcosψ+sinφsinψ)·u1;u y =(cosφsinθsinψ-sinφcosψ)·u1;u z =cosφcosθ·u1; The command controller is: Among them, α j Command filter input signal; is the output signal of the command filter; ξ is the damping ratio; ω nj is the undamped natural frequency; define ω nj >0,ξ∈(0,1], σ is a positive constant; The error compensation mechanism is: or i =e i -k i ,i=1,2,3,...,12 Among them, k i is the error compensation signal, e i is the error variable; The error variable is: e1=x1-x 1d ,e2=x2-α cx e3=x3-x 3d ,e4=x4-α cy e5=x5-x 5d ,e6=x6-α cz Among them, x 1d ,x 3d ,x 5d is the reference signal; α cx ,α cy ,α cz When the input signal virtual controller is α i , the output signal of the command filter when i=x,y,z; The position controller u x for: Position controller u y for: Position controller u z for: The attitude controller u φ for: Attitude Controller θ for: Attitude Controller ψ for: The position subsystem and attitude subsystem are connected to each other through the attitude extraction algorithm; the reference input of the inner loop attitude angle is:

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