CN118011833A - Fault-tolerant control method for four-rotor unmanned aerial vehicle under fault and input saturation of actuator - Google Patents
Fault-tolerant control method for four-rotor unmanned aerial vehicle under fault and input saturation of actuator Download PDFInfo
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Abstract
The invention relates to a fault-tolerant control method of a four-rotor unmanned aerial vehicle under actuator fault and input saturation, which combines a self-adaptive Backsteeping controller with a command filter, introduces a hyperbolic tangent function and an error compensation mechanism, and controls a positioning subsystem and a gesture subsystem. The invention can converge the tracking error in a limited time, and improves the tracking speed of the position and the gesture.
Description
Technical Field
The invention relates to the technical field of unmanned aerial vehicle aircraft control, in particular to a finite time fault-tolerant control method of an uncertain four-rotor unmanned aerial vehicle based on a command filter and under the conditions of actuator fault and input saturation.
Background
The four-rotor unmanned aerial vehicle has the characteristics of simple structure, strong maneuverability, capability of realizing vertical take-off and landing, fixed-point hovering, high safety, flexible operation, portability and the like, and is gradually applied to various fields, such as aerophotography, light show, patrol, measurement, emergency rescue and other scenes.
The four-rotor unmanned aerial vehicle is a multi-input multi-output system with six degrees of freedom and four independent inputs, and has the characteristics of high nonlinearity, underactuation and strong coupling. Because the four-rotor unmanned aerial vehicle may be subject to external disturbances, such as changes in temperature, humidity, or component loss, when performing tasks, the probability of the actuator failing in the actual system may increase. In addition, the forces and torques provided by the four-rotor are limited due to the limitations of motor speed during actual flight. In order to avoid that the control input exceeds the execution range of the aircraft system, it is necessary to take account of the saturation of the input.
However, most studies only consider the problem of actuator failure or input saturation, so it is of practical importance to consider both the existence of actuator failure and input saturation.
In addition, differential blasting problems often exist during the design of a quad-rotor controller. Although in some studies the above drawbacks have been solved by dynamic surface control techniques and first order filters, errors remain after filtering, which may affect the control performance.
Disclosure of Invention
The invention aims to provide a four-rotor unmanned aerial vehicle fault-tolerant control method capable of converging a tracking error in a limited time and improving the tracking speed of a position and an attitude.
The invention adopts the following technical scheme:
A four-rotor unmanned aerial vehicle fault-tolerant control method under the condition of actuator fault and input saturation combines an adaptive backsteeping controller with a command filter, introduces a hyperbolic tangent function and an error compensation mechanism, and controls a positioning subsystem and a gesture subsystem.
Further, the location subsystem is represented by the following formula;
the gesture subsystem is shown in the following formula;
Wherein ,ηmi＝1/mi,(i＝x,y,z),ηmi＝1/Ij,(j＝x,y,z),Tmφ＝(Iy-Iz)/Ix,Tmθ＝(Iz-Ix)/Iy,Tmψ＝(Ix-Iy)/Iz;ki(i＝x,y,z,φ,θ,ψ) is the unknown aerodynamic damping coefficient of the system; j φ,Jθ is the moment of inertia; omega r represents the angular velocity of the propeller speed margin ;ux＝(cosφsinθcosψ+sinφsinψ)·u1,uy＝(cosφsinθsinψ-sinφcosψ)·u1,uz＝cosφcosθ·u1.
Further, the command controller is:
Wherein α j commands the input signal of the filter; Is the output signal of the command filter; ζ is the damping ratio; omega nj is the natural frequency of undamped; define ω nj >0, ζ ε (0, 1)/(S) Sigma is a positive constant.
Further, the error compensation mechanism is as follows:
ηi＝ei-ki(i＝1,2,3,...,12)
Where k i is the error compensation signal and e i is the error variable.
Further, the error variable is:
ei＝xi-xid,ej＝xj-αck
(i＝1,3,5,7,9,11；j＝2,4,6,8,10,12；k＝x,y,z,φ,θ,ψ)
Wherein x id is a reference signal; α ck is the output signal of the command filter when the input signal virtual controller is α i (i=x, y, z).
Further, the position controller u x is:
the position controller u y is:
the position controller u z is:
Further, the gesture controller u φ is:
the gesture controller u θ is:
the gesture controller u ψ is:
Wherein the design parameters bx4>0,bx5>0,bx6>0,bx7>0,by4>0,by5>0,by6>0,by7>0,bz4>0,bz5>0,bz6>0,bz7>0,bφ4>0,bφ5>0,bφ6>0,bφ7>0,bθ4>0,bθ5>0,bθ6>0,bθ7>0,bψ4>0,bψ5>0,bψ6>0,bψ7>0; Is an estimate of χ x,/>Is an estimate of χ y,/>Is an estimate of χ z; /(I)Is an estimate of G x,/>Is an estimate of G y,/>Is an estimate of G z,/>Is an estimate of G φ,/>Is an estimate of G θ,/>Is an estimate of G ψ; /(I)Is an estimate of L x,/>Is an estimate of L y,/>Is an estimate of L z,/>Is an estimate of L φ,/>Is an estimate of L θ,/>Is an estimate of L ψ; /(I)Is/>Estimate of/>Is/>Estimate of/>Is/>Estimate of/>Is/>Estimate of/>Is/>Estimate of/>Is/>Is a function of the estimate of (2).
Further, the two subsystems of the position subsystem and the gesture subsystem are connected with each other through a gesture extraction algorithm; the reference inputs of the inner ring attitude angle are:
The invention has the beneficial effects that:
(1) By adopting the self-adaptive technology, the limitation that the dynamic parameters, the air resistance and the actuator faults of the system are required to be accurately known in the quadrotor unmanned aerial vehicle is overcome. In consideration of the efficiency of an actuator in an actual system, a hyperbolic tangent function is used instead of a saturation function to eliminate the influence of input saturation on the system performance. The invention solves the problems of parameter uncertainty, actuator fault, input saturation and the like at the same time, and has stronger practicability.
(2) By introducing a command filter, the problem of differential explosion is solved, so that the differential explosion can quickly approach the derivative of the virtual control signal in a limited time; by introducing an error compensation mechanism, the influence of the filtering error on the system performance is effectively eliminated; and ensure that the attitude and the position tracking error can ensure the convergence of the tracking error and the finite nature of all closed loop signals in a finite time, and improve the tracking speed of the position and the attitude.
Drawings
Fig. 1 is a three-dimensional trajectory tracking diagram of a quad-rotor unmanned helicopter.
Fig. 2 is a position subsystem tracking error curve.
Fig. 3 is a graph of attitude subsystem tracking error curves.
Fig. 4 is a controller input diagram.
FIG. 5 is an input constraint of the controller.
Detailed Description
The technical scheme of the present invention is described in detail below with reference to the accompanying drawings and examples. The following examples are only for the purpose of illustrating and explaining the present invention and are not to be construed as limiting the technical solution of the present invention.
1. Mathematical model and system description of uncertain dynamics
(1) Defining variables:
and respectively establishing mathematical models of a position subsystem and a posture subsystem of the quadrotor unmanned aerial vehicle according to dynamics, physics and Euler angle description by considering the influence of unknown time-varying loads and aerodynamic damping coefficients on the QUAV system.
The mathematical model of the location subsystem can be written as equation (1 a):
the mathematical model of the attitude subsystem can be written as formula (1 b):
Wherein the following parameters are defined:
ηmi＝1/mi,(i＝x,y,z);ηmi＝1/Ij,(j＝x,y,z);Tmφ＝(Iy-Iz)/Ix;Tmθ＝(Iz-Ix)/Iy;Tmψ＝(Ix-Iy)/Iz;ki(i＝x,y,z,φ,θ,ψ) Is an unknown aerodynamic damping coefficient of the system; j φ,Jθ is the moment of inertia; omega r represents the angular velocity of the propeller speed margin ;ux＝(cosφsinθcosψ+sinφsinψ)·u1;uy＝(cosφsinθsinψ-sinφcosψ)·u1,uz＝cosφcosθ·u1.
Suppose 1: the quadrotor unmanned aerial vehicle is a rigid body, and the elastic deformation of the quadrotor unmanned aerial vehicle is ignored; the inertial reference system is ground, and the gravity center coincides with the origin of the fixed coordinate system; the flexibility of the blade is relatively small and negligible; the gravitational acceleration does not change with position.
Suppose 2: the parameter η mx,ηmy,ηmz,ηmφ,ηmθ,ηmψ is unknown, its upper limit parameterAre all greater than 0. The aerodynamic damping coefficient k i (i=x, y, z, phi, theta, phi) is also unknown and is greater than zero.
Suppose 3: assuming that these inequalities hold:
|ηmx(△x+δx)|≤Gx;|ηmy(△y+δy)|≤Gy;|ηmz(△z+δz)|≤Gz;
max{ηmφ(△φ+δφ),Tmφ}≤Gφ;max{ηmθ(△θ+δθ),Tmθ}≤Gθ;max{ηmψ(△ψ+δψ),Tmψ}≤Gψ;
|ηmxkx|≤Lx;|ηmyky|≤Ly;|ηmzkz|≤Lz;|ηmφkφ|≤Lφ;|ηmθkθ|≤Lθ;|ηmψkψ|≤Lψ;
Parameters G i,Li (i=x, y, z, phi, theta, phi); the upper bound of (2) is also unknown.
(2) The problem of differential calculation explosion is solved by adopting a command filter, and the influence of filtering errors on the system performance is solved.
Wherein α j commands the input signal of the filter; Is the output signal of the command filter; ζ is the damping ratio; omega nj is the natural frequency of undamped; define ω nj >0, ζ ε (0, 1)/(S) Sigma is a positive constant. The initial value of the filter is
To avoid control inputs exceeding the execution range of the four-rotor unmanned system, the saturation function form of the control inputs is considered to be:
Where u i is the control input to the system; m i (i=x, y, z, phi, theta, phi) actuator input limits.
The hyperbolic tangent function is used to approximate the saturation function, expressed as follows:
The actuator fault model is as follows:
Ui＝Γiui+δi(i＝x,y,z,φ,θ,ψ) (5)
Wherein U i represents the actual output of the actuator; u i denotes a faulty actuator input; unknown parameters 0< Γ i.ltoreq.1 represent actuator efficiency coefficients; delta i represents an unknown additive fault.
Lemma 1: assuming u >0, v >0 and w (p, q) >0 are real valued functions, the following inequality holds true
And (4) lemma 2: for any constant v >0 and any variable χ ε R, the following relationship holds
2. Location subsystem controller design
For a location subsystem, it can be considered to consist of a location x subsystem, a location y subsystem, and a location z subsystem.
First, the controller design is performed for the location x subsystem [ x 1,x2]T ] with the rest of the location subsystem design process being similar.
Wherein x 1d,x3d,x5d is a reference signal; α cx,αcy,αcz is the output signal of the command filter when the input signal virtual controller is α i (i=x, y, z).
The introduced error compensation mechanism is:
ηi＝ei-ki(i＝1,2,3,...,12) (7)
Where k i is the error compensation signal.
Selecting the following form of Lyapunov function
The derivative of V x1 can be written as follows
The virtual control signal α x is designed to:
Wherein design parameter b x1>0,bx2 >0; u >0.
The introduction of an error compensation mechanism may reduce the effect of the filtering error α cx-αx. The error compensation mechanism is defined as:
Substituting equations (10) and (11) into equation (9) to obtain
The selection of the Lyapunov function V x2 is as follows
The time derivative of V x2 is based on hypothesis 2 and hypothesis 3
Designing a position controller u x:
Wherein design parameter b x4>0,bx5>0,bx6>0,bx7 >0; Is an estimate of χ x,/> Is an estimate of G x,/>Is an estimate of L x,/>Is/>Is a function of the estimate of (2).
Substituting formula (15) into formula (14) to obtain
Finally, the total lyapunov function is designed as
Wherein, design parameter r 1>0,r2>0,r3>0,r4 >0;
According to the lemma 2, the total Lyapunov function V x derivative of time is
The adaptive law is designed as follows:
Wherein,
Wherein design parameter delta 1>0,δ2>0,δ3>0,δ4 >0.
Substituting the formulas (19) - (22) into the formula (18) according to the index 1 and the poplar inequality can be obtained,
Similarly, the controllers u y and u z are designed to:
wherein the design parameters by4>0,by5>0,by6>0,by7>0,bz4>0,bz5>0,bz6>0,bz7>0; Are estimates of χ y,χz,/>, respectivelyAre estimates of G y,Gz,/>, respectivelyAre estimates of L y,Lz,/>, respectivelyRespectively areIs a function of the estimate of (2).
The virtual control signal α y,αz is designed to:
Wherein design parameter b y1>0,by2>0;bz1>0,bz2 >0. The error compensation machine is formulated as follows:
The adaptive law is designed as follows:
Wherein,
Wherein design parameter delta 5>0,δ6>0,δ7>0,δ8 >0.
Wherein,
Wherein design parameter delta 9>0,δ10>0,δ11>0,δ12 >0.
The position subsystem and the gesture subsystem are connected with each other through a gesture extraction algorithm;
The reference input from which the inner ring attitude angle can be obtained is
3. Gesture subsystem controller design
For the gesture subsystem, the gesture subsystem can be regarded as being composed of a position phi subsystem, a position theta subsystem and a position phi subsystem.
First, the controller design is performed for the position phi subsystem [ x 7,x8]T ] and the rest of the gesture subsystem design process is similar.
The tracking error is defined as follows
Wherein x 7d,x9d,x11d is a reference signal; α cφ,αcθ,αcψ is the output signal of the command filter when the input signal virtual controller is α i (i=Φ, θ, ψ).
Selecting the following form of Lyapunov function
The time derivative of V φ7 can be written as follows
The virtual control signal alpha φ is designed as
Wherein design parameter b φ1>0,bφ2 >0.
The introduction of an error compensation mechanism may reduce the effect of the error α cφ-αφ. The error compensation mechanism is defined as
Wherein design parameter b φ3>0,bφ4>0,bφ5 >0.
Substituting the formulas (42) and (43) into the formula (41) to obtain
The Lyapunov function V φ8 is selected as follows
Combining hypothesis 2 and hypothesis 3, V φ8 has a time derivative of
The controller u φ is designed to:
wherein design parameter b φ4>0,bφ5 >0; Is/> Estimate of/>Is an estimate of G φ,/>Is an estimate of L φ.
Substituting equation (47) into equation (46) to obtain
Finally, the total lyapunov function V φ is designed to:
wherein, the design parameter r 13>0,r14>0,r15 is more than 0,
According to the quotients 2, V φ derivatives are
The adaptive law is designed as follows:
wherein the design parameter is r 13>0,r14>0,r15>0,δ13>0,δ14>0,δ15 >0.
Substituting the formulas (51) - (53) into the formula (50) according to the index 1 and the poplar inequality can be obtained,
Wherein,
Similarly, the controllers u θ and u ψ are designed to:
Wherein the design parameters bθ4>0,bθ5>0,bθ6>0,bθ7>0;bψ4>0,bψ5>0,bψ6>0,bψ7>0; Respectively areEstimate of/>Are estimates of G θ,Gψ,/>, respectivelyIs an estimate of L θ,Lψ.
The virtual control signals α θ and α ψ are designed to:
Wherein design parameter b θ1>0,bθ2>0,bψ1>0,bψ2 >0.
Error compensation mechanism positioning:
wherein the design parameter is b θ1>0,bθ3>0,bψ1>0,bψ3 >0.
The adaptive law is designed as follows:
Wherein the design parameters are r16>0,r17>0,r18>0,r19>0,r20>0,r21>0,δ16>0,δ17>0,δ18>0,δ19>0,δ20>0,δ21>0.
4. Simulation experiment
According to the simulation verification method, matlab software is adopted for simulation verification, firstly, a program is written in a m file according to a designed controller, then a four-rotor unmanned aerial vehicle system model is built in a Simulink, and finally, debugging parameters are carried out to carry out simulation verification.
5. Simulation results
Fig. 1 shows a three-dimensional tracking trajectory of the method designed herein. In order to clearly observe the tracking effect, the tracking errors of the position subsystem and the attitude subsystem are shown in fig. 2 and 3, respectively, which clearly shows that it can guarantee the convergence of the tracking errors and the finite nature of all closed loop signals over a finite time. Fig. 4 shows the variation of the control input during tracking in the case of input constraints and actuator failures of the proposed method. This indicates that the designed controller can achieve stability in a limited time.
To clearly demonstrate the effectiveness of designing control inputs, FIG. 5 shows control input curves under saturated and unsaturated conditions. U and U s represent a saturated input and a control input under unsaturated conditions, respectively. Simulation results indicate that when the control amount U s exceeds the saturation limit, the saturation limit brings the control input back into the safe range to achieve effective control.
Claims (8)
1. A four-rotor unmanned aerial vehicle fault-tolerant control method under the condition of actuator fault and input saturation is characterized in that an adaptive backsteeping controller is combined with a command filter, and a hyperbolic tangent function and an error compensation mechanism are introduced to control a positioning subsystem and a gesture subsystem.
2. The method for fault-tolerant control of a quad-rotor unmanned helicopter with actuator failure and input saturation of claim 1, wherein said position subsystem is represented by the formula;
the gesture subsystem is shown in the following formula;
Wherein ,ηmi＝1/mi,(i＝x,y,z),ηmi＝1/Ij,(j＝x,y,z),Tmφ＝(Iy-Iz)/Ix,Tmθ＝(Iz-Ix)/Iy,Tmψ＝(Ix-Iy)/Iz;ki(i＝x,y,z,φ,θ,ψ) is the unknown aerodynamic damping coefficient of the system; j φ,Jθ is the moment of inertia; omega r represents the angular velocity of the propeller speed margin ;ux＝(cosφsinθcosψ+sinφsinψ)·u1,uy＝(cosφsinθsinψ-sinφcosψ)·u1,uz＝cosφcosθ·u1.
3. The four-rotor unmanned aerial vehicle fault-tolerant control method under actuator failure and input saturation of claim 2, wherein the command controller is:
Wherein α j commands the input signal of the filter; Is the output signal of the command filter; ζ is the damping ratio; omega nj is the natural frequency of undamped; define ω nj >0, ζ ε (0, 1)/(S) Sigma is a positive constant.
4. The four-rotor unmanned aerial vehicle fault-tolerant control method under actuator failure and input saturation of claim 3, wherein the error compensation mechanism is:
ηi＝ei-ki(i＝1,2,3,...,12)
Where k i is the error compensation signal and e i is the error variable.
5. The four-rotor unmanned aerial vehicle fault-tolerant control method under actuator failure and input saturation of claim 4, wherein the error variable is:
ei＝xi-xid,ej＝xj-αck
(i＝1,3,5,7,9,11；j＝2,4,6,8,10,12；k＝x,y,z,φ,θ,ψ)
Wherein x id is a reference signal; α ck is the output signal of the command filter when the input signal virtual controller is α i (i=x, y, z).
6. The fault tolerant control method of a quad-rotor unmanned helicopter with actuator failure and input saturation of claim 5 wherein the position controller u x is:
the position controller u y is:
the position controller u z is:
wherein the design parameters bx4>0,bx5>0,bx6>0,bx7>0,by4>0,by5>0,by6>0,by7>0,bz4>0,bz5>0,bz6>0,bz7>0; Is an estimate of c x,/>Is an estimate of c y,/>Is an estimate of c z; /(I)Is an estimate of G x,/>Is an estimate of G y,/>Is an estimate of G z; /(I)Is an estimate of L x,/>Is an estimate of L y,/>Is an estimate of L z; /(I)Is/>Estimate of/>Is/>Estimate of/>Is thatIs a function of the estimate of (2).
7. The fault tolerant control method of a four rotor unmanned aerial vehicle with actuator failure and input saturation of claim 6, wherein the attitude controller u φ is:
the gesture controller u θ is:
the gesture controller u ψ is:
Wherein the design parameters bφ4>0,bφ5>0,bφ6>0,bφ7>0,bθ4>0,bθ5>0,bθ6>0,bθ7>0,bψ4>0,bψ5>0,bψ6>0,bψ7>0; Is an estimate of G φ,/>Is an estimate of G θ,/>Is an estimate of G ψ; /(I)Is an estimate of L φ,/>Is an estimate of L θ,/>Is an estimate of L ψ; /(I)Is/>Estimate of/>Is/>Estimate of/>Is/>Is a function of the estimate of (2).
8. The four-rotor unmanned aerial vehicle fault-tolerant control method under actuator failure and input saturation of claim 7, wherein the two subsystems of the position subsystem and the attitude subsystem are connected with each other through an attitude extraction algorithm; the reference inputs of the inner ring attitude angle are:
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