Disclosure of Invention
In order to solve the problems that the traditional sliding mode surface can not realize limited time control, further accelerate the approaching speed of an approaching law and reduce buffeting, the method adopts the rapid terminal sliding mode control and the hyperbolic sine enhanced double-power-order approaching law, avoids the singularity problem through the switching control idea, accelerates the approaching speed of a system to the sliding mode surface, reduces buffeting and realizes the limited time control. Meanwhile, interference and compensation are carried out on the interference boundary through self-adaption, and the stability of the system is improved.
The technical scheme proposed for solving the technical problems is as follows:
a self-adaptive control method of a four-rotor aircraft based on hyperbolic sine enhanced double-power approach law and a fast terminal sliding mode surface comprises the following steps:
step 1, determining a transfer matrix from a body coordinate system based on a four-rotor aircraft to an inertial coordinate system based on the earth;
where psi, theta, phi are the yaw, pitch, roll angles of the aircraft, respectively, representing the angle of rotation of the aircraft about each axis of the inertial frame in sequence, TψTransition matrix, T, representing psiθA transition matrix, T, representing thetaφA transition matrix representing phi;
step 2, analyzing a four-rotor aircraft dynamic model according to a Newton Euler formula, wherein the process is as follows:
2.1, the translation process comprises the following steps:
wherein x, y and z respectively represent the position of the four rotors under an inertial coordinate system, m represents the mass of the aircraft, g represents the gravity acceleration, mg represents the gravity borne by the four rotors, and the resultant force U generated by the four rotorsr;
2.2, the rotation process comprises the following steps:
wherein tau is
x、τ
y、τ
zRespectively representing the axial moment components, I, in the coordinate system of the machine body
xx、I
yy、I
zzRespectively representing the rotational inertia component of each axis on the coordinate system of the machine body, x represents cross product, w
p、w
q、w
rRespectively representing the attitude angular velocity components of each axis on the coordinate system of the body,
respectively represent machine coordinate systemThe attitude angular acceleration component of each axis;
considering that the aircraft is in a low-speed flight or hovering state, consider
Then the formula (3) is represented as the formula (4) in the rotation process
2.3, connecting the vertical type (1), (2) and (4), and obtaining the dynamic model of the aircraft as shown in the formula (5)
Wherein
U
x、U
y、U
zThe input quantities of the three position controllers are respectively;
according to the formula (5), decoupling calculation is carried out on the position and posture relation, and the result is as follows:
wherein phidIs the desired signal value of phi, thetadDesired signal value of theta, psidFor desired signal values of ψ, the arcsin function is an arcsine function and the arctan function is an arctangent function;
equation (5) can also be written in matrix form as follows:
wherein X
1=[x,y,z,φ,θ,ψ]
T,
B(X)=diag(1,1,1,b
1,b
2,b
3),U=[U
x,U
y,U
z,τ
x,τ
y,τ
z]
T,
Step 3, calculating a tracking error, and designing a controller according to the fast terminal sliding mode surface and the first derivative thereof, wherein the process is as follows:
3.1, defining the tracking error and its first and second differentials:
e=X1-Xd (8)
wherein, X
d=[x
d,y
d,z
d,φ
d,θ
d,ψ
d]
T,x
d,y
d,z
d,φ
d,θ
d,ψ
dThe conductive desired signals are x, y, z, phi, theta, psi, respectively,
i=1,2,3,4,5,6,D
i,c
0i,c
1i,c
2i,e
i,
respectively corresponding ith element;
3.2, designing a quick terminal sliding mode surface:
wherein, sigα(x)=|x|α·sign(x),α1>α2>1,λ1>0,λ2>0;
Derivation of equation (11) yields:
order to
Formula (12) is simplified to formula (13)
But due to the presence of alpha (e)
When α (e) is 0 and β (e) is not equal to 0, the negative power term of (a) causes a singularity problem;
consider the method of handover control:
wherein q is
i(e),α
i(e),β
i(e) Q (e), alpha (e), beta (e) respectively,
combining formula (13) and formula (14) to obtain:
conjunctive formula (7), formula (10) and formula (15) yields:
3.3 design enhanced approach law
Wherein
N
-1(X) is the inverse of N (X), k
1>0,k
2>0,β
1>1,0<β
2Less than 1, delta is more than 0 and less than 1, gamma is more than 0, mu is more than 1, and p is a positive integer;
3.4, combined vertical (16) and formula (17), to obtain a controller
Wherein B is
-1(X) is the inverse of B (X),
respectively corresponding ith element;
the adaptive law is designed as follows:
step 4, property specification, the process is as follows:
when the system moves away from the sliding mode, | s | is large, N(s) approaches δ,
the approach speed of the system is accelerated; when the system approaches the sliding mode, | s | approaches 0, N(s) approaches μ,
the buffeting of the system is reduced.
The technical conception of the invention is as follows: aiming at a four-rotor aircraft system, a self-adaptive control method of the four-rotor aircraft based on hyperbolic sine enhanced double-power approximation law and a fast terminal sliding mode surface is designed by combining double-power approximation law sliding mode control and fast terminal sliding mode control. The quick terminal sliding mode surface can realize the limited time control of the tracking error, and solves the problems that the time tends to be infinite and the error tends to be 0 in the traditional sliding mode surface. Based on a hyperbolic sine enhanced approach law, the approach speed can be increased when the system is far away from a sliding mode surface, buffeting can be reduced, the rapidness and robustness of the system are improved, and rapid and stable control is realized. Meanwhile, interference and compensation are carried out on the interference boundary through self-adaption, and the stability of the system is improved.
The invention has the beneficial effects that: compared with the traditional double-power approach law sliding mode control, the method can increase the approach speed when the system is far away from the sliding mode, reduce buffeting and shorten the arrival time of the sliding mode, thereby enabling the system to realize stable convergence more quickly. In addition, the invention utilizes the quick terminal sliding mode, solves the problems that the time tends to be infinite and the error tends to be 0 in the traditional sliding mode surface, and realizes the limited time control. Meanwhile, interference and compensation are carried out on the interference boundary through self-adaption, and the stability of the system is improved.
Drawings
Fig. 1 is a schematic diagram of a position tracking effect of a four-rotor aircraft, wherein a dotted line represents "1" type enhanced double-power-law adaptive control under a linear sliding mode surface, and a dotted line represents hyperbolic sine "mu" type enhanced double-power-law adaptive control under a fast terminal sliding mode surface.
Fig. 2 is a schematic diagram of an attitude tracking effect of a four-rotor aircraft, wherein a dotted line represents "1" type enhanced double-power-law adaptive control of a linear sliding mode surface, and a dotted line represents hyperbolic sine "mu" type enhanced double-power-law adaptive control of a fast terminal sliding mode surface.
Fig. 3 is a schematic input diagram of a position controller for enhanced double power law adaptive control of a '1' type under a linear sliding mode surface of a four-rotor aircraft.
Fig. 4 is an input schematic diagram of a position controller for a four-rotor aircraft fast terminal sliding mode surface based on hyperbolic sine 'mu' type enhanced double-power approach law adaptive control.
Fig. 5 is an input schematic diagram of an attitude controller for "1" -type enhanced double-power-law adaptive control under a linear sliding mode surface of a four-rotor aircraft.
Fig. 6 is an input schematic diagram of an attitude controller for a four-rotor aircraft fast terminal sliding mode surface based on hyperbolic sine mu-type enhanced double-power approach law adaptive control.
Fig. 7 is a schematic diagram of local amplification of input of an attitude controller for "1" -type enhanced double-power approach law adaptive control under a linear sliding mode surface of a four-rotor aircraft.
Fig. 8 is a schematic diagram of local amplification of input of an attitude controller of a four-rotor aircraft fast terminal sliding mode surface based on hyperbolic sine 'mu' type enhanced double-power approach law adaptive control.
Fig. 9 is an estimation of the boundary of the position disturbance of the four-rotor aircraft fast terminal sliding mode surface based on hyperbolic sine 'mu' type enhanced double power approach law adaptive control.
Fig. 10 is an estimation of the boundary of attitude disturbance of a four-rotor aircraft fast terminal sliding mode surface based on hyperbolic sine 'mu' type enhanced double power approach law adaptive control.
FIG. 11 is a control flow diagram of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1-11, a self-adaptive control method of a quadrotor aircraft based on hyperbolic sine enhanced double-power approach law and fast terminal sliding mode surface includes the following steps:
step 1, determining a transfer matrix from a body coordinate system based on a four-rotor aircraft to an inertial coordinate system based on the earth;
where psi, theta, phi are the yaw, pitch, roll angles of the aircraft, respectively, representing the angle of rotation of the aircraft about each axis of the inertial frame in sequence, TψTransition matrix, T, representing psiθA transition matrix, T, representing thetaφA transition matrix representing phi;
step 2, analyzing a four-rotor aircraft dynamic model according to a Newton Euler formula, wherein the process is as follows:
2.1, the translation process comprises the following steps:
wherein x, y and z respectively represent the position of the four rotors under an inertial coordinate system, m represents the mass of the aircraft, g represents the gravity acceleration, mg represents the gravity borne by the four rotors, and the resultant force U generated by the four rotorsr;
2.2, the rotation process comprises the following steps:
wherein tau is
x、τ
y、τ
zRespectively represent the moment of each axis on the coordinate system of the machine bodyAmount, I
xx、I
yy、I
zzRespectively representing the rotational inertia component of each axis on the coordinate system of the machine body, x represents cross product, w
p、w
q、w
rRespectively representing the attitude angular velocity components of each axis on the coordinate system of the body,
respectively representing the attitude angular acceleration components of all axes on the coordinate system of the machine body;
considering that the aircraft is in a low-speed flight or hovering state, consider
Then the formula (3) is represented as the formula (4) in the rotation process
2.3, connecting the vertical type (1), (2) and (4), and obtaining the dynamic model of the aircraft as shown in the formula (5)
Wherein
U
x、U
y、U
zThe input quantities of the three position controllers are respectively;
according to the formula (5), decoupling calculation is carried out on the position and posture relation, and the result is as follows:
wherein phidIs the desired signal value of phi, thetadDesired signal value of theta, psidFor desired signal values of ψ, the arcsin function is an arcsine function and the arctan function is an arctangent function;
equation (5) can also be written in matrix form as follows:
wherein X
1=[x,y,z,φ,θ,ψ]
T,
B(X)=diag(1,1,1,b
1,b
2,b
3),U=[U
x,U
y,U
z,τ
x,τ
y,τ
z]
T,
Step 3, calculating a tracking error, and designing a controller according to the fast terminal sliding mode surface and the first derivative thereof, wherein the process is as follows:
3.1, defining the tracking error and its first and second differentials:
e=X1-Xd (8)
wherein, X
d=[x
d,y
d,z
d,φ
d,θ
d,ψ
d]
T,x
d,y
d,z
d,φ
d,θ
d,ψ
dX, y, z, phi, theta, psiIt is possible to derive the desired signal or signals,
i=1,2,3,4,5,6,D
i,c
0i,c
1i,c
2i,e
i,
respectively corresponding ith element;
3.2, designing a quick terminal sliding mode surface:
wherein, sigα(x)=|x|α·sign(x),α1>α2>1,λ1>0,λ2>0;
Derivation of equation (11) yields:
order to
Formula (12) is simplified to formula (13)
But due to the presence of alpha (e)
When α (e) is 0 and β (e) is not equal to 0, the negative power term of (a) causes a singularity problem;
consider the method of handover control:
wherein q is
i(e),α
i(e),β
i(e) Q (e), alpha (e), beta (e) respectively,
combining formula (13) and formula (14) to obtain:
conjunctive formula (7), formula (10) and formula (15) yields:
3.3 design enhanced approach law
Wherein
N
-1(X) is the inverse of N (X), k
1>0,k
2>0,β
1>1,0<β
2Less than 1, delta is more than 0 and less than 1, gamma is more than 0, mu is more than 1, and p is a positive integer;
3.4, combined vertical (16) and formula (17), to obtain a controller
Wherein B is
-1(X) is the inverse of B (X),
respectively corresponding ith element;
the adaptive law is designed as follows:
step 4, property specification, the process is as follows:
when the system moves away from the sliding mode, | s | is large, N(s) approaches δ,
the approach speed of the system is accelerated; when the system approaches the sliding mode, | s | approaches 0, N(s) approaches μ,
the buffeting of the system is reduced.
In order to verify the effectiveness of the method, the invention provides a contrast of a hyperbolic sine mu-shaped enhanced double-power-law approximation sliding mode control method of a rapid terminal sliding mode surface and a 1-shaped enhanced double-power-law approximation sliding mode control method of a linear sliding mode surface;
wherein the 1-type enhanced double power approximation law is
For more efficient comparison, all parameters of the system are consistent, i.e. x
d=y
d=z
d=2、ψ
d0.5, fast terminal sliding mode surface parameters: lambda [ alpha ]
1=0.5、λ
2=2、α
1=2、α
21.1, epsilon 0.3, linear slip-form face: lambda [ alpha ]
10.5, "μ" type enhanced proximity law parameter: k is a radical of
1=1、k
2=10、δ=0.1、p=1、γ=1、μ=10,β
1=1.3、β
20.7, enhanced approximation rule parameter of "1": k is a radical of
1=1、k
2=10、δ=0.1、p=1、γ=1、β
1=1.3、β
20.7, adaptive initial value setting
p
0i=p
1i=p
2i=0.1,ε
0i=ε
1i=ε
2i0.001, 1,2,3,4,5,6, interference parameter: d
x=d
y=d
z=0.2sin(0.2t)、
Parameters of the four-rotor aircraft: 1.1 and I
xx=1.22、I
yy=1.22、I
zz2.2, g 9.81, sampling parameters: t is t
s=0.007,N=5000。
As can be seen from fig. 1 and 2, the adaptive control of the quadrotor aircraft based on the hyperbolic sine enhanced double-power approach law and the fast terminal sliding mode surface can reach the expected position faster; with reference to fig. 3-8, the self-adaptive control of the quadrotor aircraft based on the hyperbolic sine enhanced double-power approach law and the fast terminal sliding mode surface has smaller buffeting. Fig. 9 and 10 can see the effectiveness of the estimation of the adaptive epipolar.
In conclusion, the self-adaptive control of the four-rotor aircraft based on the hyperbolic sine enhanced double-power-order approach law and the fast terminal sliding mode surface can reduce the buffeting, reduce the tracking time, improve the tracking performance and enable the system to enter stable convergence more quickly.
While the foregoing has described a preferred embodiment of the invention, it will be appreciated that the invention is not limited to the embodiment described, but is capable of numerous modifications without departing from the basic spirit and scope of the invention as set out in the appended claims.