CN108628333A - Quadrotor self-adaptation control method based on hyperbolic sine enhanced double power Reaching Laws and fast terminal sliding-mode surface - Google Patents

Abstract

A kind of quadrotor self-adaptation control method based on hyperbolic sine enhanced double power Reaching Laws and fast terminal sliding-mode surface, includes the following steps：Step 1, it determines from the body coordinate system based on quadrotor to the transfer matrix of the inertial coodinate system based on the earth；Step 2, quadrotor kinetic model is analyzed according to newton Euler's formula；Step 3, tracking error is calculated, controller is designed according to fast terminal sliding-mode surface and its first derivative.The enhanced double power Reaching Law sliding formwork controls of present invention combination hyperbolic sine and fast terminal sliding formwork control, not only it can increase velocity of approach when far from sliding-mode surface, and reduce buffeting, the rapidity and robustness of raising system, realize fast and stable control, it realizes tracking error finite-time control simultaneously, solves in traditional sliding-mode surface and there was only the problem of time ought tending to be infinite, tracking error just tends to 0.Simultaneously by adaptively estimating the boundary of interference, the stability of system is improved.

Description

Four rotations based on hyperbolic sine enhanced double power Reaching Laws and fast terminal sliding-mode surface Rotor aircraft self-adaptation control method

Technical field

The present invention relates to a kind of quadrotors based on hyperbolic sine enhanced double power Reaching Laws and fast terminal sliding-mode surface Aircraft self-adaptation control method.

Background technology

Quadrotor causes domestic and foreign scholars due to the feature of simple in structure, mobility strong, flying method uniqueness And the extensive concern of scientific research institution, and rapidly become one of the hot spot studied in the world at present.Compared to Fixed Wing AirVehicle, rotation Rotor aircraft can be vertically moved up or down, low to environmental requirement, not need runway, reduce cost, there is huge commercial value.Fly The development of row device makes the working at height of many danger become light safety, causes to deter to other countries in military aspect, in the people Working efficiency is set to greatly increase with aspect.Quadrotor has stronger flexibility, can realize movement and hovering at any time Fast transition, and can be with the aerial mission of the competent more challenge of smaller damage risk.In field of scientific study, due to four Dynamic characteristic of the rotor craft with non-linear, drive lacking, close coupling, researcher is often as theoretical research, method The experimental vehicle of verification.Small-sized quadrotor is relied on, vehicle flight control system is built, carries out aircraft high-performance fortune Dynamic control research, is the hot research field of current academia.

The characteristics of Reaching Law sliding formwork control, can be achieved on discontinuous control, and sliding mode is programmable, and be System parameter and disturbance are not associated with.Reaching Law sliding formwork can not only rationally design the speed for reaching sliding-mode surface, reduce the approach stage Time, improve the robustness of system, and can effectively weaken the buffeting problem in sliding formwork control.Currently, in quadrotor control It is fewer using Reaching Law sliding formwork control in field processed.Enhanced Reaching Law is further speeded up on the basis of traditional Reaching Law System reaches the velocity of approach of sliding-mode surface simultaneously so that buffeting smaller.Since quadrotor can awing encounter outside Environmental disturbances improve the stability of system by the way that adaptively the boundary of interference is interfered and compensated.

Invention content

In order to overcome traditional sliding-mode surface to cannot achieve finite-time control and further speed up the velocity of approach of Reaching Law The problem of with buffeting is reduced, present invention employs fast terminal sliding formwork control and based on the enhanced double powers approaches of hyperbolic sine Rule, singularity problem is avoided by the thought of switching control, is accelerated the velocity of approach that system reaches sliding-mode surface, is reduced and tremble It shakes, realizes finite-time control.Simultaneously by the way that adaptively the boundary of interference is interfered and compensated, the stabilization of system is improved Property.

In order to solve the above-mentioned technical problem the technical solution proposed is as follows：

A kind of quadrotor based on the enhanced double power Reaching Laws of hyperbolic sine and fast terminal sliding-mode surface is adaptive Control method is answered, is included the following steps：

Step 1, it determines from the body coordinate system based on quadrotor to the transfer of the inertial coodinate system based on the earth Matrix；

Wherein ψ, θ, φ are yaw angle, pitch angle, the roll angle of aircraft respectively, indicate aircraft around inertial coordinate successively It is the angle of each axis rotation, T_ψIndicate the transfer matrix of ψ, T_θIndicate the transfer matrix of θ, T_φIndicate the transfer matrix of φ；

Step 2, quadrotor kinetic model is analyzed according to newton Euler's formula, process is as follows：

2.1, have during translation：

Wherein x, y, z indicates that position of the quadrotor under inertial coodinate system, m indicate that the quality of aircraft, g indicate respectively Acceleration of gravity, mg indicate gravity suffered by quadrotor, the resultant force U that four rotors generate_r；

2.2, have in rotation process：

Wherein τ_x、τ_y、τ_zRespectively represent each axis moment components on body coordinate system, I_xx、I_yy、I_zzRespectively represent body seat Each axis rotary inertia component fastened is marked, × indicate multiplication cross, w_p、w_q、w_rRespectively represent each axis attitude angle speed on body coordinate system Component is spent,Respectively represent each axis posture component of angular acceleration on body coordinate system；

In view of aircraft is under low-speed operations or floating state, it is believed that

Then rotation process Chinese style (3) is expressed as formula (4)

2.3, simultaneous formula (1), (2), (4), shown in the kinetic model such as formula (5) for obtaining aircraft

Wherein U_x、U_y、U_zThe input quantity of respectively three positioners；

According to formula (5), decoupling computation is carried out to position and attitude relationship, it is as a result as follows：

Wherein φ_dFor the expected signal value of φ, θ_dFor the expected signal value of θ, ψ_dFor the expected signal value of ψ, arcsin letters Number is arcsin function, and arctan functions are arctan functions；

Formula (5) can also be write as matrix form, as follows：

Wherein X₁=[x,y,z,φ,θ,ψ]^T, B(X) =diag (1,1,1, b₁,b₂,b₃), U=[U_x,U_y,U_z,τ_x,τ_y,τ_z]^T,

Step 3, tracking error is calculated, controller is designed according to fast terminal sliding-mode surface and its first derivative, process is such as Under：

3.1, define tracking error and its first differential and second-order differential：

E=X₁-X_d (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_dRespectively x, y, z, φ, θ, ψ's leads Desired signal,I=1,2,3,4,5,6, D_i, c_0i, c_1i, c_2i, e_i,Respectively corresponding i-th A element；

3.2, design fast terminal sliding-mode surface：

Wherein, sig^α(x)=| x |^αSign (x), α₁＞ α₂＞ 1, λ₁＞ 0, λ₂＞ 0；

Derivation is carried out to formula (11), is obtained：

It enablesFormula (12) is reduced to formula (13)

But due to existing in α (e)Negative power time item, when α (e)=0 and β (e) ≠ 0 can lead to singularity problem；

Consider the method for switching control：

Wherein q_i(e),α_i(e),β_i(e) it is respectively q (e), the corresponding element of α (e), β (e),

Simultaneous formula (13) and formula (14), obtain：

Simultaneous formula (7), formula (10) and formula (15), obtain：

3.3, design enhanced Reaching Law

WhereinN^-1(X) the inverse square for being N (X) Battle array, k₁＞ 0, k₂＞ 0, β₁1,0 ＜ β of ＞₂1,0 ＜ δ ＜ 1 of ＜, γ ＞ 0, μ ＞ 1, p are positive integer；

3.4, simultaneous formula (16) and formula (17) obtain controller

Wherein B^-1(X) inverse matrix for being B (X), Respectively corresponding i-th of element；

Adaptive law design is as follows：

Step 4, property illustrates, process is as follows：

When system is far from sliding-mode surface | s | very big, N (s) approaches δ, The velocity of approach of system is accelerated；When system is close to sliding-mode surface | s | 0, N of approach (s) approaches μ,The buffeting of system reduces.

The present invention technical concept be：For quadrotor system, in conjunction with double power Reaching Law sliding formwork controls and Fast terminal sliding formwork control, devise it is a kind of based on the enhanced double power Reaching Laws of hyperbolic sine and fast terminal sliding-mode surface four Rotor craft self-adaptation control method.Fast terminal sliding-mode surface can realize the finite-time control of tracking error, solve biography The problem of time tends to be infinite in system sliding-mode surface, and error just tends to 0.It not only can be separate based on the enhanced Reaching Law of hyperbolic sine Velocity of approach can be increased when sliding-mode surface, and buffeting can be reduced, improve the rapidity and robustness of system, realize fast and stable control System.Simultaneously by the way that adaptively the boundary of interference is interfered and compensated, the stability of system is improved.

Beneficial effects of the present invention are：The robustness for enhancing system, with traditional double power Reaching Law sliding formwork control phases Than not only velocity of approach can be increased when far from sliding-mode surface, and can reduce buffeting, when shortening the arrival of sliding mode Between, to make system quickly realize stable convergence.In addition to this, the present invention utilizes fast terminal sliding formwork, solves traditional cunning The problem of time tends to be infinite in die face, and error just tends to 0, realizes finite-time control.Simultaneously by adaptively to interference Boundary interfered and compensated, improve the stability of system.

Description of the drawings

Fig. 1 is the position tracking effect diagram of quadrotor, and dotted line represents " 1 " type under linear sliding mode face Enhanced double power Reaching Law self adaptive controls, dotted line represent enhanced based on hyperbolic sine " μ " type under fast terminal sliding-mode surface Double power Reaching Law self adaptive controls.

Fig. 2 is the Attitude Tracking effect diagram of quadrotor, and " 1 " type that dotted line represents linear sliding mode face increases The double power Reaching Law self adaptive controls of strong type, dotted line represent fast terminal sliding-mode surface and are based on the enhanced double powers of hyperbolic sine " μ " type Secondary Reaching Law self adaptive control.

Fig. 3 is the position of the enhanced double power Reaching Law self adaptive controls of " 1 " type under quadrotor linear sliding mode face Set controller input schematic diagram.

Fig. 4 is that quadrotor fast terminal sliding-mode surface is based on the enhanced double power Reaching Laws of hyperbolic sine " μ " type certainly The positioner of suitable solution inputs schematic diagram.

Fig. 5 is the appearance of the enhanced double power Reaching Law self adaptive controls of " 1 " type under quadrotor linear sliding mode face State controller inputs schematic diagram.

Fig. 6 is that quadrotor fast terminal sliding-mode surface is based on the enhanced double power Reaching Laws of hyperbolic sine " μ " type certainly The attitude controller of suitable solution inputs schematic diagram.

Fig. 7 is the appearance of the enhanced double power Reaching Law self adaptive controls of " 1 " type under quadrotor linear sliding mode face State controller inputs close-up schematic view.

Fig. 8 is that quadrotor fast terminal sliding-mode surface is based on the enhanced double power Reaching Laws of hyperbolic sine " μ " type certainly The attitude controller of suitable solution inputs close-up schematic view.

Fig. 9 is that quadrotor fast terminal sliding-mode surface is based on the enhanced double power Reaching Laws of hyperbolic sine " μ " type certainly The estimation on the boundary of the Position disturbance of suitable solution.

Figure 10 is that quadrotor fast terminal sliding-mode surface is based on the enhanced double power Reaching Laws of hyperbolic sine " μ " type certainly The estimation on the boundary of the attitude disturbance of suitable solution.

Figure 11 is the control flow schematic diagram of the present invention.

Specific implementation mode

The present invention will be further described below in conjunction with the accompanying drawings.

- Figure 11 referring to Fig.1, a kind of four rotations based on hyperbolic sine enhanced double power Reaching Laws and fast terminal sliding-mode surface Rotor aircraft self-adaptation control method, includes the following steps：

Step 1, it determines from the body coordinate system based on quadrotor to the transfer of the inertial coodinate system based on the earth Matrix；

Wherein ψ, θ, φ are yaw angle, pitch angle, the roll angle of aircraft respectively, indicate aircraft around inertial coordinate successively It is the angle of each axis rotation, T_ψIndicate the transfer matrix of ψ, T_θIndicate the transfer matrix of θ, T_φIndicate the transfer matrix of φ；

Step 2, quadrotor kinetic model is analyzed according to newton Euler's formula, process is as follows：

2.1, have during translation：

Wherein x, y, z indicates that position of the quadrotor under inertial coodinate system, m indicate that the quality of aircraft, g indicate respectively Acceleration of gravity, mg indicate gravity suffered by quadrotor, the resultant force U that four rotors generate_r；

2.2, have in rotation process：

Wherein τ_x、τ_y、τ_zRespectively represent each axis moment components on body coordinate system, I_xx、I_yy、I_zzRespectively represent body seat Each axis rotary inertia component fastened is marked, × indicate multiplication cross, w_p、w_q、w_rRespectively represent each axis attitude angle speed on body coordinate system Component is spent,Respectively represent each axis posture component of angular acceleration on body coordinate system；

In view of aircraft is under low-speed operations or floating state, it is believed that

Then rotation process Chinese style (3) is expressed as formula (4)

2.3, simultaneous formula (1), (2), (4), shown in the kinetic model such as formula (5) for obtaining aircraft

Wherein U_x、U_y、U_zThe input quantity of respectively three positioners；

According to formula (5), decoupling computation is carried out to position and attitude relationship, it is as a result as follows：

Wherein φ_dFor the expected signal value of φ, θ_dFor the expected signal value of θ, ψ_dFor the expected signal value of ψ, arcsin letters Number is arcsin function, and arctan functions are arctan functions；

Formula (5) can also be write as matrix form, as follows：

Wherein X₁=[x, y, z, φ, θ, ψ]^T, B (X)=diag (1,1,1, b₁,b₂,b₃), U=[U_x,U_y,U_z,τ_x,τ_y,τ_z]^T,

Step 3, tracking error is calculated, controller is designed according to fast terminal sliding-mode surface and its first derivative, process is such as Under：

3.1, define tracking error and its first differential and second-order differential：

E=X₁-X_d (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_dRespectively x, y, z, φ, θ, ψ's leads Desired signal,I=1,2,3,4,5,6, D_i, c_0i, c_1i, c_2i, e_i,Respectively corresponding i-th A element；

3.2, design fast terminal sliding-mode surface：

Wherein, sig^α(x)=| x |^αSign (x), α₁＞ α₂＞ 1, λ₁＞ 0, λ₂＞ 0；

Derivation is carried out to formula (11), is obtained：

It enablesFormula (12) is reduced to formula (13)

But due to existing in α (e)Negative power time item, when α (e)=0 and β (e) ≠ 0 can lead to singularity problem；

Consider the method for switching control：

Wherein q_i(e),α_i(e),β_i(e) it is respectively q (e), the corresponding element of α (e), β (e),

Simultaneous formula (13) and formula (14), obtain：

Simultaneous formula (7), formula (10) and formula (15), obtain：

3.3, design enhanced Reaching Law

WhereinN^-1(X) the inverse square for being N (X) Battle array, k₁＞ 0, k₂＞ 0, β₁1,0 ＜ β of ＞₂1,0 ＜ δ ＜ 1 of ＜, γ ＞ 0, μ ＞ 1, p are positive integer；

3.4, simultaneous formula (16) and formula (17) obtain controller

Wherein B^-1(X) inverse matrix for being B (X), Respectively corresponding i-th of element；

Adaptive law design is as follows：

Step 4, property illustrates, process is as follows：

When system is far from sliding-mode surface | s | very big, N (s) approaches δ, The velocity of approach of system is accelerated；When system is close to sliding-mode surface | s | 0, N of approach (s) approaches μ,The buffeting of system reduces.

For the validity of verification institute extracting method, The present invention gives fast terminal sliding-mode surfaces to be increased based on hyperbolic sine " μ " type The enhanced double power Reaching Law sliding-mode controls of " 1 " type of strong type double power Reaching Law sliding-mode controls and linear sliding mode face Comparison；

Wherein, the enhanced double power Reaching Laws of " 1 " type are

In order to more effectively be compared, all parameters of system are all consistent, i.e. x_d=y_d=z_d=2, ψ_d=0.5, soon Fast terminal sliding mode face parameter：λ₁=0.5, λ₂=2, α₁=2, α₂=1.1, ε=0.3, linear sliding mode face：λ₁=0.5, " μ " type increases Strong type Reaching Law parameter：k₁=1, k₂=10, δ=0.1, p=1, γ=1, μ=10, β₁=1.3, β₂=0.7, the enhancing of " 1 " type Type Reaching Law parameter：k₁=1, k₂=10, δ=0.1, p=1, γ=1, β₁=1.3, β₂=0.7, adaptive initial value design p_0i=p_1i=p_2i=0.1, ε_0i=ε_1i= ε_2i=0.001, i=1,2,3,4,5,6, interference parameter：d_x=d_y=d_z=0.2sin (0.2t),Quadrotor parameter：M=1.1, I_xx=1.22, I_yy=1.22, I_zz=2.2, g= 9.81 sampling parameter：t_s=0.007, N=5000.

From Fig. 1 and Fig. 2 as can be seen that based on the enhanced double power Reaching Laws of hyperbolic sine and fast terminal sliding-mode surface Quadrotor self adaptive control can faster reach desired location；In conjunction with Fig. 3-Fig. 8, it is based on the enhanced double powers of hyperbolic sine The quadrotor self adaptive control of Reaching Law and fast terminal sliding-mode surface has smaller buffeting.Fig. 9 and Figure 10 can be seen Go out the validity of the adaptively estimation to boundary.

In conclusion the quadrotor based on hyperbolic sine enhanced double power Reaching Laws and fast terminal sliding-mode surface Self adaptive control can reduce the tracking time reducing the while of buffeting, and improve tracking performance so that system, which quickly enters, to be stablized Convergence.

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, in the premise without departing from essence spirit of the present invention and without departing from 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 based on the enhanced double power Reaching Laws of hyperbolic sine and fast terminal sliding-mode surface is adaptive Control method, which is characterized in that the control method includes the following steps：

Step 1, it determines from the body coordinate system based on quadrotor to the transfer matrix of the inertial coodinate system based on the earth；

Wherein ψ, θ, φ are yaw angle, pitch angle, the roll angle of aircraft respectively, indicate that aircraft is each around inertial coodinate system successively The angle of axis rotation, T_ψIndicate the transfer matrix of ψ, T_θIndicate the transfer matrix of θ, T_φIndicate the transfer matrix of φ；

Step 2, quadrotor kinetic model is analyzed according to newton Euler's formula, process is as follows：

2.1, have during translation：

Wherein x, y, z indicates that position of the quadrotor under inertial coodinate system, m indicate that the quality of aircraft, g indicate that gravity adds respectively Speed, mg indicate gravity suffered by quadrotor, the resultant force U that four rotors generate_r；

2.2, have in rotation process：

Wherein τ_x、τ_y、τ_zRespectively represent each axis moment components on body coordinate system, I_xx、I_yy、I_zzRespectively represent body coordinate system On each axis rotary inertia component, × indicate multiplication cross, w_p、w_q、w_rRespectively represent each axis attitude angular velocity point on body coordinate system Amount,Respectively represent each axis posture component of angular acceleration on body coordinate system；

In view of aircraft is under low-speed operations or floating state, it is believed that

Then rotation process Chinese style (3) is expressed as formula (4)

2.3, simultaneous formula (1), (2), (4), shown in the kinetic model such as formula (5) for obtaining aircraft

Wherein U_x、U_y、U_zThe input quantity of respectively three positioners；

According to formula (5), decoupling computation is carried out to position and attitude relationship, it is as a result as follows：

Wherein φ_dFor the expected signal value of φ, θ_dFor the expected signal value of θ, ψ_dFor the expected signal value of ψ, arcsin functions are anti- SIN function, arctan functions are arctan functions；

Formula (5) can also be write as matrix form, as follows：

Wherein X₁=[x, y, z, φ, θ, ψ]^T,B(X) =diag (1,1,1, b₁,b₂,b₃), U=[U_x,U_y,U_z,τ_x,τ_y,τ_z]^T,

Step 3, tracking error is calculated, controller is designed according to fast terminal sliding-mode surface and its first derivative, process is as follows：

3.1, define tracking error and its first differential and second-order differential：

E=X₁-X_d (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_dRespectively x, y, z, φ, θ, ψ's leads expectation Signal,D_i, c_0i, c_1i, c_2i, e_i,It is i-th yuan respectively corresponding Element；

3.2, design fast terminal sliding-mode surface：

Wherein, sig^α(x)=| x |^αSign (x), α₁＞ α₂＞ 1, λ₁＞ 0, λ₂＞ 0；

Derivation is carried out to formula (11), is obtained：

It enablesFormula (12) is reduced to formula (13)

But due to existing in α (e)Negative power time item, when α (e)=0 and β (e) ≠ 0 can lead to singularity problem；

Consider the method for switching control：

Wherein q_i(e),α_i(e),β_i(e) it is respectively q (e), the corresponding element of α (e), β (e),

Simultaneous formula (13) and formula (14), obtain：

Simultaneous formula (7), formula (10) and formula (15), obtain：

3.3, design enhanced Reaching Law

WhereinN^-1(X) inverse matrix for being N (X), k₁ ＞ 0, k₂＞ 0, β₁1,0 ＜ β of ＞₂1,0 ＜ δ ＜ 1 of ＜, γ ＞ 0, μ ＞ 1, p are positive integer；

3.4, simultaneous formula (16) and formula (17) obtain controller

Wherein B^-1(X) inverse matrix for being B (X), Respectively corresponding i-th of element；

Adaptive law design is as follows：

Step 4, property illustrates, process is as follows：

When system is far from sliding-mode surface | s | very big, N (s) approaches δ, The velocity of approach of system is accelerated；When system is close to sliding-mode surface | s | 0, N of approach (s) approaches μ,The buffeting of system reduces.