CN107479370B - A kind of quadrotor drone finite time self-adaptation control method based on non-singular terminal sliding formwork - Google Patents
A kind of quadrotor drone finite time self-adaptation control method based on non-singular terminal sliding formwork Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 35
- 238000009415 formwork Methods 0.000 title claims abstract description 23
- 238000013461 design Methods 0.000 claims abstract description 24
- 238000012545 processing Methods 0.000 claims abstract description 5
- 239000011159 matrix material Substances 0.000 claims description 10
- 238000009795 derivation Methods 0.000 claims description 9
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- 230000003044 adaptive effect Effects 0.000 abstract description 10
- 238000010586 diagram Methods 0.000 description 10
- 244000145845 chattering Species 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 230000003313 weakening effect Effects 0.000 description 2
- 235000021170 buffet Nutrition 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
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- 230000006641 stabilisation Effects 0.000 description 1
- 238000011105 stabilization Methods 0.000 description 1
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- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
A kind of quadrotor drone finite time self-adaptation control method based on non-singular terminal sliding formwork, for the quadrotor drone system with inertia uncertain factor and external disturbance.According to the dynamic system of quadrotor drone, a kind of quadrotor drone self-adaptation control method based on non-singular terminal sliding formwork is designed in conjunction with self adaptive control using non-singular terminal sliding-mode control.The design of non-singular terminal sliding formwork is the finite time convergence control characteristic in order to guarantee system, and avoids singularity problem existing for TSM control, effectively weakens buffeting problem.In addition, self adaptive control is the inertia uncertainty and external disturbance for processing system.Sliding-mode surface singularity problem can be eliminated the present invention provides a kind of, and can effectively inhibit and compensation system existing for inertia is uncertain and the control method of external disturbance, guarantee the finite time convergence control characteristic of system.
Description
Technical field
The present invention relates to a kind of quadrotor drone finite time self-adaptation control method based on non-singular terminal sliding formwork,
Particular with inertia uncertain factor and the quadrotor drone system control method of external disturbance.
Background technique
The one kind of quadrotor drone as rotor craft controls energy by the flight that four rotor revolving speeds of control are realized
It is enough conveniently accomplished and takes off and the movements such as landing, be widely used in aeroplane photography, geologic prospect, rescue and relief work, environmental assessment
Equal fields.Since quadrotor drone is small in size and light-weight, in-flight vulnerable to external disturbance, how to realize to quadrotor without
Man-machine High Performance Motion Control has become a hot issue.For the control problem of quadrotor drone, exist very much
Control method, such as PID control, Active Disturbance Rejection Control, sliding formwork control etc..
Wherein sliding formwork control has been widely used for nonlinear system, and advantage includes fast response time, easy to implement, right
The uncertain robustness etc. with external disturbance of system.Traditional sliding formwork control is compared, TSM control is able to achieve finite time
Convergence, but there are singular points for system, and discontinuous switching characteristic in itself will cause the buffeting of system, to system in reality
Application in the situation of border has very big obstruction.To solve this problem, non-singular terminal sliding formwork control is suggested, and this method is in reality
The singularity problem of system is efficiently solved in the situation of border, and ensure that system finite time convergence control characteristic and stronger robust
Property.
To with the probabilistic quadrotor drone dynamic system of inertia, there are external disturbance and Parameter uncertainties
Property.The problems such as external disturbance bring aerodynamic interference, gyroscopic couple interference, Parameter Perturbation, will affect quadrotor drone flight control
The sensitivity and stability of system.Therefore, interference and system parameter can be estimated using adaptive method on the basis of sliding formwork control,
Design estimation rule is so that system has better steady-state performance.
Summary of the invention
In order to overcome external disturbance existing for quadrotor drone system and inertia uncertain problem and terminal sliding mode
The deficiency of the singularity problem of control, the present invention provides a kind of quadrotor drone non-singular terminal with self adaptive control
Sliding-mode control eliminates system singularity problem, effectively inhibits chattering phenomenon, while carrying out to disturbing existing for system
Inhibit and compensate, guarantees the finite time convergence control characteristic of system.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows:
A kind of quadrotor drone finite time self-adaptation control method based on non-singular terminal sliding formwork, including following step
It is rapid:
Step 1, the kinetic model of quadrotor drone is established, system mode, sampling time and system parameter are initialized,
Process is as follows:
1.1 hypothesis unmanned planes are that rigidity is full symmetric, and its center is overlapped with body coordinate system origin, to quadrotor without
Man-machine system carries out force analysis, establishes coordinate system, one is the inertial coodinate system based on the earth, by reference axis XE、YE、ZEReally
It is fixed, the other is the body coordinate system based on quadrotor drone, by reference axis XB、YB、ZBIt determines, from body coordinate system to used
The transfer matrix M of property coordinate system are as follows:
Wherein, ψ, θ, φ are referred to as yaw angle, pitch angle, the roll angle of unmanned plane, indicate that inertial coodinate system is each around it
The rotation angle of reference axis；
1.2 according to newton Euler's formula analytic dynamics model, has under translation state:
Wherein x, y, z respectively indicates position of the quadrotor drone under inertial coodinate system, and m is the quality of unmanned plane, UF
Indicate that the lift that four rotors generate, mg are gravity suffered by unmanned plane, g is acceleration of gravity, UFIt is acted on the sum of mg expression
Bonding force F on unmanned plane；
Formula (1) is substituted into formula (2) to obtain:
1.3 under body coordinate system, according to Euler's formula, has under rotary state:
Wherein τx、τy、τzRespectively indicate each axle power square of body coordinate system, Ixx、Iyy、IzzRespectively indicate each axis of body coordinate system
Rotary inertia, ωx、ωy、ωzEach axis attitude angular velocity on body coordinate system is respectively indicated, It respectively indicates
Each axis posture angular acceleration on body coordinate system；
It is obtained by formula (4):
Quadrotor drone is to realize flight control by adjusting the revolving speed of rotor, control moment and rotor lift with
The revolving speed of rotor has direct relation, as shown in formula (6):
Wherein L indicates distance of the mass center of quadrotor drone to each rotor axis, kFIndicate lift coefficient, kMIt indicates to turn round
Moment coefficient, ω1、ω2、ω3、ω4Respectively indicate the revolving speed of each rotor；
1.4 consider that outer bound pair system generates interference under actual environment, establish the kinetic model of quadrotor drone, four rotations
Wing unmanned plane is typically in low-speed operations or floating state, and attitude angle variation is smaller, it is believed that As shown in formula (7):
Wherein
dx、dy、dz、dφ、dθ、dψThe external disturbance of representative model；
Formula (7) belongs to second order MIMO nonlinear systems, for the design convenient for controller, formula (7) be expressed as
Lower form:
Wherein state variable X=(x, y, x, φ, θ, ψ)T,
Diagonal matrix B (X)=diag { 1,1,1, b1,b2,b3, input U=(Ux,Uy,Uz,τx,τy,τz)T, external disturbance D (t)=(dx,
dy,dz,dφ,dθ,dψ)T, and meet following condition:
||D(t)||∞≤ρ (9)
Wherein | | D (t) | |∞For the Infinite Norm of D (t), ρ is a constant greater than zero；
Step 2, calculating control system tracking error designs non-singular terminal sliding-mode surface, and process is as follows:
2.1 define system tracking error are as follows:
E=X-Xd (10)
Wherein XdFor desired signal, X can be ledd=(xd,yd,zd,φd,θd,ψd)T, xd、yd、zd、φd、θd、ψdRespectively pair
The desired value of the position and attitude angle answered；
The first differential and second-order differential of formula (10) are expressed as follows:
2.2 define non-singular terminal sliding-mode surface are as follows:
Wherein S=(s1,s2,s3,s4,s5,s6)T, β-1=diag { β1 -1, β2 -1, β3 -1, β4 -1, β5 -1, β6 -1It is positive definite square
Battle array,si、βi、eiRespectively indicate corresponding x, y, z,
The sliding variable of ψ, θ, φ, constant value coefficient, error first derivative, i=1,2,3,4,5,6, sign () are sign function, and p, q are
Positive odd number, and 1 < p/q < 2；
Step 3, controller, process are designed according to non-singular terminal sliding formwork based on the dynamic system of quadrotor drone
It is as follows:
3.1 are based on formula (8), and non-singular terminal sliding mode controller is designed to:
U=Ueq+Ure (14)
Wherein, constant η > 0,
3.2 design liapunov functions
Derivation is carried out to formula (13) to obtain
Wherein
Formula (14)~(16) are substituted into formula (18) and are obtained
Derivation is carried out to formula (17) to obtain
It is obtained by formula (20)
Formula (9) are substituted into formula (21) to obtain
Wherein η > 0, β are positive definite matrix, and p, q are positive odd number,Then obviouslyTherefore, it is determined thatSystem is stable；
Step 4, optimal controller, it is uncertain using interference present in self-adaptation control method processing system and inertia
Property, process are as follows:
4.1 assume on the boundary of external disturbance D (t) again are as follows:
Wherein, c, k1、k2It is unknown boundary, is not easy to obtain due to labyrinth probabilistic in actual control system
It takes；
4.2 are modified control law based on formula (14)~(16) are as follows:
U1=Ueq1+Ure1 (24)
Wherein, It is the estimation of γ；It is c, k respectively1、k2, ρ estimation；
The more new law of design estimation parameter is respectively as follows:
Wherein, p0> 0, p1> 0, p2> 0, ε0> 0, ε1> 0, ε2> 0 is design parameter；
4.3 design liapunov functions
Wherein
Derivation is carried out to formula (32), then substitutes into formula (18) and obtains
(24)~(26) are substituted into formula (33) to obtain
Formula (28) are substituted into formula (34) to obtain
It is obtained by formula (35)
Formula (27), (29)~(31) are substituted into formula (36) and obtained；
Formula (23) are substituted into
To meetThenThen
HaveWherein δ=ε0c2+ε1k1 2+ε2k2 2, It indicates
Take the minterm of wherein element；VsaReduction drive the track of closed-loop system to beTherefore the rail of closed-loop system
Mark is finally defined as
The present invention is based on non-singular terminal sliding formwork and self adaptive controls, design the non-singular terminal of quadrotor drone system
Sliding Mode Adaptive Control method realizes the finite time convergence control characteristic of system, eliminates the nonsingular of TSM control and asks
Topic, while the buffeting for weakening system influences, and improves the robustness of system.
Technical concept of the invention are as follows: for the dynamic system of quadrotor drone, utilize non-singular terminal sliding formwork control
It is adaptive to design a kind of quadrotor drone finite time based on non-singular terminal sliding formwork in conjunction with self adaptive control for method processed
Answer control method.The design of non-singular terminal sliding formwork is the finite time convergence control characteristic in order to guarantee system, and avoids end
Singularity problem existing for sliding formwork control is held, buffeting problem is effectively weakened.In addition, self adaptive control is for processing system
Inertia uncertainty and external disturbance.Sliding-mode surface singularity problem can be eliminated the present invention provides a kind of, and can effectively be pressed down
The control method of the uncertainty of inertia existing for system and compensation system and external disturbance guarantees that the finite time convergence control of system is special
Property.
Advantage of the present invention are as follows: solve singularity problem, weaken and buffet, inhibit uncertain with inertia existing for compensation system
And external disturbance, realize finite time convergence control.
Detailed description of the invention
Fig. 1 is position tracking effect diagram of the invention.
Fig. 2 is attitude angle tracking effect schematic diagram of the invention.
Fig. 3 is that positioner of the invention inputs schematic diagram.
Fig. 4 is that posture angle controller of the invention inputs schematic diagram.
Fig. 5 is that Position disturbance boundary parameter of the invention estimates schematic diagram.
Fig. 6 estimates boundary schematic diagram with it for Position disturbance of the invention.
Fig. 7 is that attitude angle of the invention interferes boundary parameter Estimation schematic diagram.
Fig. 8 is that attitude angle interference of the invention estimates that schematic diagram is estimated on boundary with it.
Fig. 9 is system inertia uncertainty estimation schematic diagram of the invention.
Figure 10 is control flow schematic diagram of the invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
- Figure 10 referring to Fig.1, a kind of quadrotor drone finite time self adaptive control side based on non-singular terminal sliding formwork
Method, comprising the following steps:
Step 1, the kinetic model of quadrotor drone is established, system mode, sampling time and system parameter are initialized,
Process is as follows:
1.1 hypothesis unmanned planes are that rigidity is full symmetric, and its center is overlapped with body coordinate system origin, to quadrotor without
Man-machine system carries out force analysis, establishes coordinate system, one is the inertial coodinate system based on the earth, by reference axis XE、YE、ZEReally
It is fixed, the other is the body coordinate system based on quadrotor drone, by reference axis XB、YB、ZBIt determines, from body coordinate system to used
The transfer matrix M of property coordinate system are as follows:
Wherein, ψ, θ, φ are referred to as yaw angle, pitch angle, the roll angle of unmanned plane, indicate that inertial coodinate system is each around it
The rotation angle of reference axis；
1.2 according to newton Euler's formula analytic dynamics model, has under translation state:
Wherein x, y, z respectively indicates position of the quadrotor drone under inertial coodinate system, and m is the quality of unmanned plane, UF
Indicate that the lift that four rotors generate, mg are gravity suffered by unmanned plane, g is acceleration of gravity, UFIt is acted on the sum of mg expression
Bonding force F on unmanned plane；
Formula (1) is substituted into formula (2) to obtain:
1.3 under body coordinate system, according to Euler's formula, has under rotary state:
Wherein τx、τy、τzRespectively indicate each axle power square of body coordinate system, Ixx、Iyy、IzzRespectively indicate each axis of body coordinate system
Rotary inertia, ωx、ωy、ωzEach axis attitude angular velocity on body coordinate system is respectively indicated, It respectively indicates
Each axis posture angular acceleration on body coordinate system；
It is obtained by formula (4):
Quadrotor drone is to realize flight control by adjusting the revolving speed of rotor, control moment and rotor lift with
The revolving speed of rotor has direct relation, as shown in formula (6):
Wherein L indicates distance of the mass center of quadrotor drone to each rotor axis, kFIndicate lift coefficient, kMIt indicates to turn round
Moment coefficient, ω1、ω2、ω3、ω4Respectively indicate the revolving speed of each rotor；
1.4 consider that outer bound pair system generates interference under actual environment, establish the kinetic model of quadrotor drone, four rotations
Wing unmanned plane is typically in low-speed operations or floating state, and attitude angle variation is smaller, it is believed that Such as following formula (7):
Wherein
dx、dy、dz、dφ、dθ、dψThe external disturbance of representative model；
Formula (7) belongs to second order MIMO nonlinear systems, for the design convenient for controller, formula (7) be expressed as
Lower form:
Wherein state variable X=(x, y, x, φ, θ, ψ)T,
Diagonal matrix B (X)=diag { 1,1,1, b1,b2,b3, input U=(Ux,Uy,Uz,τx,τy,τz)T, external disturbance D (t)=(dx,
dy,dz,dφ,dθ,dψ)T, and meet following condition:
||D(t)||∞≤ρ (9)
Wherein | | D (t) | |∞For the Infinite Norm of D (t), ρ is a constant greater than zero；
Step 2, calculating control system tracking error designs non-singular terminal sliding-mode surface, and process is as follows:
2.1 define system tracking error are as follows:
E=X-Xd (10)
Wherein XdFor desired signal, X can be ledd=(xd,yd,zd,φd,θd,ψd)T, xd、yd、zd、φd、θd、ψdRespectively pair
The desired value of the position and attitude angle answered；
The first differential and second-order differential of formula (10) are expressed as follows:
2.2 define non-singular terminal sliding-mode surface are as follows:
Wherein S=(s1,s2,s3,s4,s5,s6)T, β-1=diag { β1 -1, β2 -1, β3 -1, β4 -1, β5 -1, β6 -1It is positive definite square
Battle array,si、βi、eiRespectively indicate corresponding x, y, z,
The sliding variable of ψ, θ, φ, constant value coefficient, error first derivative, i=1,2,3,4,5,6, sign () are sign function, and p, q are
Positive odd number, and 1 < p/q < 2；
Step 3, controller, process are designed according to non-singular terminal sliding formwork based on the dynamic system of quadrotor drone
It is as follows:
3.1 are based on formula (8), and non-singular terminal sliding mode controller is designed to:
U=Ueq+Ure (14)
Wherein, constant η > 0,
3.2 design liapunov functions
Derivation is carried out to formula (13) to obtain
Wherein
Formula (14)~(16) are substituted into formula (18) and are obtained
Derivation is carried out to formula (17) to obtain
It is obtained by formula (20)
Formula (9) are substituted into formula (21) to obtain
Wherein η > 0, β are positive definite matrix, and p, q are positive odd number,Then obviouslyTherefore, it is determined thatSystem is stable；
Step 4, optimal controller, it is uncertain using interference present in self-adaptation control method processing system and inertia
Property, process are as follows:
4.1 assume on the boundary of external disturbance D (t) again are as follows:
Wherein, c, k1、k2It is unknown boundary, is not easy to obtain due to labyrinth probabilistic in actual control system
It takes；
4.2 are modified control law based on formula (14)~(16) are as follows:
U1=Ueq1+Ure1 (24)
Wherein, It is the estimation of γ；It is c, k respectively1、k2, ρ estimation；
The more new law of design estimation parameter is respectively as follows:
Wherein, p0> 0, p1> 0, p2> 0, ε0> 0, ε1> 0, ε2> 0 is design parameter；
4.3 design liapunov functions
Wherein
Derivation is carried out to formula (32), then substitutes into formula (18) and obtains
(24)~(26) are substituted into formula (33) to obtain
Formula (28) are substituted into formula (34) to obtain
It is obtained by formula (35)
Formula (27), (29)~(31) are substituted into formula (36) and obtained；
Formula (23) are substituted into
To meetThenThen
HaveWherein δ=ε0c2+ε1k1 2+ε2k2 2, It indicates
Take the minterm of wherein element；VsaReduction drive the track of closed-loop system to beTherefore the rail of closed-loop system
Mark is finally defined as
It can be by Ux、Uy、UzThe input for regarding positioner as, by τx、τy、τzThe input for regarding posture angle controller as, according to
Formula (24)~(27) provide the design of controller.
Position desired value xd、yd、zdAnd attitude angle desired value ψdIt is directly given by reference locus, attitude angle desired value φx、
θdIt is decoupled by position and attitude relationship, as follows:
Wherein arcsin () is arcsin function, and arctan () is arctan function.
In order to verify the feasibility of proposed method, the emulation knot that The present invention gives the control methods on MATLAB platform
Fruit:
Parameter is given below: m=0.625kg, g=10 in formula (3)；I in formula (5)xx=2.3 × 10-3kg·m2, Iyy=
2.4×10-3kg·m2, Izz=2.6 × 10-3kg·m2；K in formula (6)F=2.103 × 10-6N/(rad·s-2), kM=2.091
×10-8N/(rad·s-2), L=0.1275m；X in formula (10)d=1, yd=1, zd=1, ψd=0.5；β in formula (13)i=1 (i
=1,2,3,4,5,6), p=5, q=3；C=1, k in formula (23)1=0.1, k2=0.1；η=0.1 in formula (26)；Formula (29)~
(31) p in0=0.1, p0=0.1, p0=0.1, ε0=0.5, ε1=0.5, ε2=0.5；It is 0.01 that interference signal, which is given as intensity,
White Gaussian noise.
Since quadrotor drone system is there are six freedom degree, so we track the dynamic of three positions and three attitude angles
Step response.In order to further weaken the chattering phenomenon of system, we are replaced with saturation function sat () in formula (24)~(26)
Sign function sign ():
Wherein take μ=0.1.
From Fig. 1 and 2 as can be seen that system has good arrival performance, and equilbrium position is reached in finite time.From
Fig. 3 and 4 is it can clearly be seen that system obviously weakens chattering phenomenon.From Fig. 5~9 as can be seen that the estimation rule of system finally becomes
In stabilization, estimate that parameter finally converges to constant.
In conclusion non-singular terminal sliding formwork finite time self-adaptation control method obviously can efficiently solve nonsingular ask
Topic and the influence for weakening buffeting, guarantee system have good robustness in finite time convergence control.
Described above is the excellent effect of optimization that one embodiment that the present invention provides is shown, it is clear that the present invention is not only
It is limited to above-described embodiment, without departing from essence spirit of the present invention and without departing from the premise of range involved by substantive content of the present invention
Under it can be made it is various deformation be implemented.
Claims (1)
1. a kind of quadrotor drone finite time self-adaptation control method based on non-singular terminal sliding formwork, it is characterised in that:
The following steps are included:
Step 1, the kinetic model of quadrotor drone, initialization system mode, sampling time and system parameter, process are established
It is as follows:
1.1 hypothesis unmanned planes are that rigidity is full symmetric, and its center is overlapped with body coordinate system origin, to quadrotor nobody
Machine system carries out force analysis, establishes coordinate system, one is the inertial coodinate system based on the earth, by reference axis XE、YE、ZEIt determines,
The other is the body coordinate system based on quadrotor drone, by reference axis XB、YB、ZBIt determines, is sat from body coordinate system to inertia
Mark the transfer matrix M of system are as follows:
Wherein, ψ, θ, φ are referred to as yaw angle, pitch angle, the roll angle of unmanned plane, indicate inertial coodinate system around its each coordinate
The rotation angle of axis；
1.2 according to newton Euler's formula analytic dynamics model, has under translation state:
Wherein x, y, z respectively indicates position of the quadrotor drone under inertial coodinate system, and m is the quality of unmanned plane, UFIndicate four
The lift that a rotor generates, mg are gravity suffered by unmanned plane, and g is acceleration of gravity, UFNobody is acted on the sum of mg expression
Bonding force F on machine；
Formula (1) is substituted into formula (2) to obtain:
1.3 under body coordinate system, according to Euler's formula, has under rotary state:
Wherein τx、τy、τzRespectively indicate each axle power square of body coordinate system, Ixx、Iyy、IzzRespectively indicate each axis rotation of body coordinate system
Inertia, ωx、ωy、ωzEach axis attitude angular velocity on body coordinate system is respectively indicated, Respectively indicate body
Each axis posture angular acceleration on coordinate system；
It is obtained by formula (4):
Quadrotor drone is to realize flight control, control moment and rotor lift and rotor by adjusting the revolving speed of rotor
Revolving speed have direct relation, as shown in formula (6):
Wherein L indicates distance of the mass center of quadrotor drone to each rotor axis, kFIndicate lift coefficient, kMIndicate torque system
Number, ω1、ω2、ω3、ω4Respectively indicate the revolving speed of each rotor；
1.4 consider that outer bound pair system generates interference under actual environment, establishes the kinetic model of quadrotor drone, quadrotor
Unmanned plane is typically in low-speed operations or floating state, and attitude angle variation is smaller, it is believed that Such as following formula (7):
Wherein
dx、dy、dz、dφ、dθ、dψThe external disturbance of representative model；
Formula (7) belongs to second order MIMO nonlinear systems, and for the design convenient for controller, formula (7) is expressed as shape
Formula:
Wherein state variable X=(x, y, z, φ, θ, ψ)T,It is right
Angle matrix B (X)=diag { 1,1,1, b1,b2,b3, input U=(Ux,Uy,Uz,τx,τy,τz)T, external disturbance D (t)=(dx,
dy,dz,dφ,dθ,dψ)T, and meet following condition:
||D(t)||∞≤ρ (9)
Wherein | | D (t) | |∞For the Infinite Norm of D (t), ρ is a constant greater than zero；
Step 2, calculating control system tracking error designs non-singular terminal sliding-mode surface, and process is as follows:
2.1 define system tracking error are as follows:
E=X-Xd (10)
Wherein XdFor desired signal, X can be ledd=(xd,yd,zd,φd,θd,ψd)T, xd、yd、zd、φd、θd、ψdIt is respectively corresponding
The desired value of position and attitude angle；
The first differential and second-order differential of formula (10) are expressed as follows:
2.2 define non-singular terminal sliding-mode surface are as follows:
Wherein S=(s1,s2,s3,s4,s5,s6)T, β-1=diag { β1 -1, β2 -1, β3 -1, β4 -1, β5 -1, β6 -1It is positive definite matrix,si、βi、eiRespectively indicate corresponding x, y, z, ψ,
The sliding variable of θ, φ, constant value coefficient, error first derivative, i=1,2,3,4,5,6, sign () are sign function, and p, q are positive
Odd number, and 1 < p/q < 2；
Step 3, controller is designed, process is such as according to non-singular terminal sliding formwork based on the dynamic system of quadrotor drone
Under:
3.1 are based on formula (8), and non-singular terminal sliding mode controller is designed to:
U=Ueq+Ure (14)
Wherein, constant η > 0,
3.2 design liapunov functions
Derivation is carried out to formula (13) to obtain
Wherein
Formula (14)~(16) are substituted into formula (18) and are obtained
Derivation is carried out to formula (17) to obtain
It is obtained by formula (20)
Formula (9) are substituted into formula (21) to obtain
Wherein η > 0, β are positive definite matrix, and p, q are positive odd number,Then obviouslyTherefore, it is determined thatSystem is stable；
Step 4, optimal controller, mistake uncertain using interference present in self-adaptation control method processing system and inertia
Journey is as follows:
4.1 assume on the boundary of external disturbance D (t) again are as follows:
Wherein, c, k1、k2It is unknown boundary, is not easy to obtain due to labyrinth probabilistic in actual control system；
4.2 are modified control law based on formula (14)~(16) are as follows:
U1=Ueq1+Ure1 (24)
Wherein, It is the estimation of γ；It is c, k respectively1、k2, ρ estimation；
The more new law of design estimation parameter is respectively as follows:
Wherein, p0> 0, p1> 0, p2> 0, ε0> 0, ε1> 0, ε2> 0 is design parameter；
4.3 design liapunov functions
Wherein
Derivation is carried out to formula (32), then substitutes into formula (18) and obtains
(24)~(26) are substituted into formula (33) to obtain
Formula (28) are substituted into formula (34) to obtain
It is obtained by formula (35)
Formula (27), (29)~(31) are substituted into formula (36) and obtained；
Formula (23) are substituted into
To meetThenThen haveWherein δ=ε0c2+ε1k1 2+ε2k2 2, Expression takes
The wherein minterm of element；VsaReduction drive the track of closed-loop system to beTherefore the track of closed-loop system
Finally it is defined as
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Application publication date: 20171215 Assignee: Foshan chopsticks Technology Co.,Ltd. Assignor: JIANG University OF TECHNOLOGY Contract record no.: X2024980000084 Denomination of invention: A Finite Time Adaptive Control Method for Quadcopter Unmanned Aerial Vehicle Based on Non singular Terminal Sliding Mode Granted publication date: 20191108 License type: Common License Record date: 20240104 |