CN106774373A - A kind of four rotor wing unmanned aerial vehicle finite time Attitude tracking control methods - Google Patents

Abstract

A kind of four rotor wing unmanned aerial vehicle finite time Attitude tracking control methods, the present invention relates to the modeling of four rotor wing unmanned aerial vehicle attitude control systems and finite time Attitude tracking control method.The disturbance torque that four rotor wing unmanned aerial vehicles of comprehensive analysis of the present invention face, unknown rotary inertia, the factor such as controlled output saturation and Actuators Failures failure devises passive fault tolerant control device, and make it have stability in finite time energy based on parameter adaptive method.Step of the present invention is：Step one：Set up the kinematics model of four rotor wing unmanned aerial vehicle Attitude Trackings；Step 2：Set up the kinetic model of four rotor wing unmanned aerial vehicle Attitude Trackings；Step 3：Define the attitude filtering error of four rotor wing unmanned aerial vehicles；Step 4：Design finite time Integral Sliding Mode face；Step 5：Design the finite time Attitude tracking control device of four rotor wing unmanned aerial vehicles.The present invention is used for UAV Flight Control field.

Description

A kind of four rotor wing unmanned aerial vehicle finite time Attitude tracking control methods

Technical field

The present invention relates to four rotor wing unmanned aerial vehicle finite time Attitude tracking control methods.

Background technology

Four rotor wing unmanned aerial vehicles can pinpoint the small-sized unmanned aircraft for spiraling as a class with VTOL, because of its machinery knot Structure is simple, safe, the low plurality of advantages of use cost, is all obtained a wide range of applications in business and civil area, for example Federal Aviation management board approved Gas Company carries out oil field prospecting, the Bladeworx companies of Israel using four rotors Monitoring unmanned system is researched and developed to protect Jerusalem light rail damage.Additionally, four rotor wing unmanned aerial vehicles take photo by plane in video, agricultural The application aspects such as plant protection, goods carrying also achieve greatly development.

Used as a class underactuated control system, reliable gesture stability is that it completes every aerial mission to four rotor wing unmanned aerial vehicles Essential condition and guarantee.And the factor of four rotor wing unmanned aerial vehicle attitude control system stability of influence has a lot, for example system is used to Amount is uncertain, and external wind square is disturbed and the disturbance torque such as the gyroscopic couple that is caused by rotor；The execution of four rotor wing unmanned aerial vehicles Mechanism is brshless DC motor, is influenceed to be likely to occur partial failure failure by manufacturing process and high intensity task；Additionally, brushless Direct current generator has the maximum instantaneous electric current allowed, if control signal is excessive, causes the loading current of motor excessive, it is possible to Motor damage, then needs to consider the factor of controlled output saturation in control design case.Above-mentioned these factor moment affect four The control performance of rotor wing unmanned aerial vehicle attitude control system, even results in system unstable.

At present, for the gesture stability of four rotor wing unmanned aerial vehicles, in the presence of many control design case methods, such as PID control, Linear quadratic planning, adaptive robust control etc., but all come with some shortcomings and defect.On the one hand, these control design case methods Only consider above-mentioned some effects factor, such as external wind square disturbance-proof design robust controller (periodical：AIAA Infotech@Aerospace Conference；Author：Steven L.Waslander and Carlos Wang；Publication time： 2009；Title of article：Wind Disturbance Estimation and Rejection for Quadrotor Position Control；The page number：2009-1983), and for actuator failures fault-tolerant controller (periodical is designed： Journal of Guidance,Control,and Dynamics；Author：Alexander Lanzon, Alessandro Freddi and Sauro Longhi；Publication time：2014；Title of article：Flight Control of a Quadrotor Vehicle Subsequent to a Rotor Failure；The page number：580-591) etc., rarely research institution is to above-mentioned shadow The factor of sound carries out comprehensive analysis and designs control program；On the other hand, the achievement in research currently for UAV Attitude control is equal It is stabilization of asymptotic time, without reference to finite time stability, and finite-time control method is because its time optimal, Fast Convergent The superiority of property and high-precision control performance, with more preferable actual application prospect.

The content of the invention

The invention aims to solve four rotor wing unmanned aerial vehicles nothing under conditions of various factors affecting stabilities are faced Method realizes the problem of finite time Attitude Tracking, proposes a kind of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method.

A kind of four rotor wing unmanned aerial vehicle finite time Attitude tracking control methods are comprised the following steps：

Step one：Set up the kinematics model of four rotor wing unmanned aerial vehicle Attitude Trackings；

Step 2：Set up the kinetic model of four rotor wing unmanned aerial vehicle Attitude Trackings；

Step 3：The kinematics model set up according to step one defines the attitude filtering error of four rotor wing unmanned aerial vehicles；

Step 4：According to the attitude filtering error design finite time Integral Sliding Mode face that step 3 is defined；

Step 5：The finite time Integral Sliding Mode face that the kinetic model and step 4 set up according to step 2 are designed, if Count the finite time Attitude tracking control device of four rotor wing unmanned aerial vehicles.

Beneficial effects of the present invention are：

1. the present invention considers the disturbance torque that four rotor wing unmanned aerial vehicles face in Practical Project, unknown rotary inertia, control The factor of the various influence stability of system output saturation and Actuators Failures failure etc., and analyzed and modeled；

2. finite time Attitude tracking control scheme proposed by the present invention, simple structure easily realizes, and with Passive fault-tolerant control Performance, it is not necessary to detection, the separation even Controller Reconfiguration process of fault message；

3. finite time Attitude tracking control scheme proposed by the present invention, designed control is made using parameter adaptive method Device processed does not rely on the boundary of system rotary inertia information and disturbance torque, improves the robustness of UAS.

4. finite time Attitude tracking control scheme proposed by the present invention, can be realized in finite time four rotors nobody The Attitude tracking control of machine, improves the transient performance and steady-state behaviour of UAS.

Brief description of the drawings

Fig. 1 is four rotor wing unmanned aerial vehicle Attitude tracking control analysis process figures.

Fig. 2 is four rotor wing unmanned aerial vehicle attitude dynamics modeling analysis schematic diagrames.

Fig. 3 is Attitude Tracking error convergence curve map.

Fig. 4 is angular speed error convergence curve map.

Fig. 5 is the change curve of estimates of parameters.

Fig. 6 is the change curve of control moment.

Specific embodiment

Specific embodiment one：A kind of design of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method of the present invention It is：

First, kinematics model is set up in the relative motion according to four rotor wing unmanned aerial vehicle Attitude Trackings；Analyze and be modeled in reality The disturbance torque that four rotors face in the engineering of border, unknown rotary inertia, controlled output saturation and Actuators Failures failure etc. are each The factor of influence stability is planted, the kinetic model of four rotor wing unmanned aerial vehicle Attitude Trackings is set up；

Second, based on the principle of the calm attitude error of finite time, define attitude filtering error；Based on to Parameters variation and Insensitive sliding-mode control, design finite time Integral Sliding Mode face are disturbed, and suppress constant value interference by introducing integral term, Reduce steady-state error；

3rd, the design principle based on simple structure designs passive fault tolerant control device, it is not necessary to the detection of fault message, Separate even Controller Reconfiguration process；And based on the design principle of UAS robustness is improved, using parameter adaptive Method makes designed controller not rely on the boundary of system rotary inertia information and disturbance torque.

Conceive according to more than, as shown in figure 1, with reference to the embodiment of four rotor wing unmanned aerial vehicle Attitude tracking controls, illustrating A kind of four rotor wing unmanned aerial vehicle finite time Attitude tracking control methods are comprised the following steps：

Step one：Set up the kinematics model of four rotor wing unmanned aerial vehicle Attitude Trackings；

Step 2：Set up the kinetic model of four rotor wing unmanned aerial vehicle Attitude Trackings；

Step 3：The kinematics model set up according to step one defines the attitude filtering error of four rotor wing unmanned aerial vehicles；

Step 4：According to the attitude filtering error design finite time Integral Sliding Mode face that step 3 is defined；

Step 5：The finite time Integral Sliding Mode face that the kinetic model and step 4 set up according to step 2 are designed, if Count the finite time Attitude tracking control device of four rotor wing unmanned aerial vehicles.

Specific embodiment two：Present embodiment from unlike specific embodiment one：Four are set up in the step one The detailed process of the kinematics model of rotor wing unmanned aerial vehicle Attitude Tracking is：

Consider that then the relative motion of four rotor wing unmanned aerial vehicle Attitude Trackings can by the attitude of the rotor wing unmanned aerial vehicle of quaternion representation four It is expressed as：

Wherein, Represent unmanned plane body coordinate system relative to expectation coordinate system respectively Attitude Tracking error and angular speed error, and have Represent nobody respectively The body attitude and angular speed of machine； Expectation attitude and the expectation of unmanned plane are represented respectively Angular speed, and ω_d,Known and bounded；Represent that unmanned plane body coordinate system is relative In the attitude spin matrix of expectation coordinate system, and haveWith | | C | |=1；Represent quaternary number multiplication；·^TRepresent vector Or the transposition of matrix；Represent real number field；I represents three rank unit matrixs；| | | | 2 norms of representative vector or matrix；Multiplication cross Matrix

The relative motion of the UAV Attitude tracking based on the description of (1) formula, sets up the fortune of four rotor wing unmanned aerial vehicle Attitude Trackings Moving model is：

Wherein, E (e_v)=(e₀I+e^×), and have | | E (e_v) | |=1；e^×Represent the multiplication cross matrix of e；One circle in character top Point represents the first derivative to the time.

Other steps and parameter are identical with specific embodiment one.

Specific embodiment three：Present embodiment from unlike specific embodiment one or two：Built in the step 2 The detailed process of the kinetic model of vertical four rotor wing unmanned aerial vehicle Attitude Trackings is：

The executing agency of four rotor wing unmanned aerial vehicles is brshless DC motor, and it has the maximum instantaneous electric current allowed, in order to keep away Exempt from burn-down of electric motor, it is necessary to the constraint of controlled output saturation is considered in control design case；And executing agency in the progress of work by In manufacturing process and high intensity task influence it is possible that partial failure failure；Additionally, four rotor wing unmanned aerial vehicles are subjected to always The influence of the disturbance torque such as the interference of external wind square and gyroscopic couple.Above-mentioned factor is modeled in four rotor wing unmanned aerial vehicle attitude dynamicses It is required to consider in analysis, specific modeling analysis are as shown in Figure 2.

In sum, it is considered to the disturbance torque that four rotor wing unmanned aerial vehicles face, unknown rotary inertia, controlled output saturation and Actuators Failures failure, the kinetic model for setting up four rotor wing unmanned aerial vehicle Attitude Trackings is：

Wherein, symmetric positive definite matrixRepresent the unknown rotary inertia of unmanned plane；δ=diag (δ₁,δ₂,δ₃) represent The failure matrix of actuator, 0<δ_i≤ 1, i=1,2,3；Represent the control instruction produced by controller； Sat (u)=[sat (u₁),sat(u₂),sat(u₃)]^TRepresent controller output saturated characteristic, sat (u_i)=sgn (u_i)·min {|u_i|,u_imax, u_imaxI-th output maximum of control component is represented, sgn () represents sign function；It is control to define θ Beyond the part of saturation amplitude, then sat (u)=θ+u, then have θ=[θ for device output₁,θ₂,θ₃]^T, whereinI=1,2,3；(ω_e+Cω_d)^×=ω^×Represent the multiplication cross matrix of ω；Represent ω_eMultiplication cross matrix；diag(δ₁,δ₂,δ₃) represent that the elements in a main diagonal is respectively δ₁,δ₂,δ₃Diagonal matrix；

Disturbance torque, including external wind square and the gyroscopic couple that is caused by rotor are represented, disturbance torque is unknown But bounded, i.e. | | Γ | |≤d_Γ(1+ | | ω | |), d_Γ>0 is constant.

The purpose of four rotor wing unmanned aerial vehicle gesture stabilities is by designing finite time Attitude tracking control device so that nobody Machine can realize Attitude Tracking in finite time, that is, cause that the attitude error e and angular speed of UAV Attitude tracking are missed Difference ω_eLevel off to origin in finite time.

Other steps and parameter are identical with specific embodiment one or two.

Specific embodiment four：Unlike one of present embodiment and specific embodiment one to three：The step 3 The detailed process of attitude filtering error that the middle kinematics model set up according to step one defines four rotor wing unmanned aerial vehicles is：

The attitude filtering error for defining four rotor wing unmanned aerial vehicles is：

Wherein,It is Virtual Controller,^-1Representing matrix it is inverse；0<r₁<1；K₁=diag (k₁₁,k₁₂,k₁₃) it is diagonal matrix, k_1i>0, i=1,2,3；Power functionWherein

May certify that, by calm attitude filtering error z, the attitude error e that can calm is in finite time T_eInside converge to Origin.From z=0The kinematics model (2) of the four rotor wing unmanned aerial vehicle Attitude Trackings set up according to step one, in It is haveIt is V to this error dynamics system design liapunov function_e=e^TE, derivation can be obtained

It can be seen from theory according to finite-time control, attitude error e will be in finite timeInterior convergence To origin, the initial value of wherein e (0) expression attitude errors；ω is understood according to (4) formula_eAlso will be in finite time T_eInterior convergence.

Therefore, following step need to only consider the calm attitude filtering error z of design finite time Attitude tracking control device, you can Realize attitude error e and angular speed error ω simultaneously_eFinite time calm.

Other steps and parameter are identical with one of specific embodiment one to three.

Specific embodiment five：Unlike one of present embodiment and specific embodiment one to four：The step 4 The detailed process in the middle attitude filtering error design finite time Integral Sliding Mode face defined according to step 3 is：

According to Parameters variation and disturbing insensitive sliding-mode control, and missed based on the calm attitude filtering of finite time Poor thought, it is considered to design finite time Integral Sliding Mode face, and suppress constant value interference by introducing integral term, reduce stable state and miss Difference.Therefore the attitude filtering error design finite time Integral Sliding Mode face according to the definition of (4) formula is as described below：

Wherein, power function sig^p(z)=[sig^p(z₁),sig^p(z₂),sig^p(z₃)]^T, wherein sig^p(z_i)=| z_i|^psgn(z_i), i=1,2,3；τ represents integration variable；C=diag (c₁,c₂,c₃), c₁>0,c₂>0,c₃>0；0<p<1.

Sliding-mode surface for the design of (5) formula may certify that system has finite time convergence control characteristic in the sliding mode stage, I.e.：During S=0, attitude filtering error z will be in Finite-time convergence to origin.

Prove：Can be obtained by S=0Designing liapunov function isDerivation can be obtained

Wherein

It can be seen from theory according to finite-time control, attitude filtering error z will be in finite timeIt is interior Origin is converged to, wherein z (0) represents the initial value of attitude filtering error.Further combined with step 3 result understand, four rotors The attitude error e and angular speed error ω of UAV Attitude tracking_eIn finite time T_z+T_eInside converge to origin.

Other steps and parameter are identical with one of specific embodiment one to four.

Specific embodiment six：Unlike one of present embodiment and specific embodiment one to five：The step 5 The detailed process of finite time Attitude tracking control device of four rotor wing unmanned aerial vehicles of middle design is：

The finite time Integral Sliding Mode face (5) designed in the kinetic model (2) and step 4 that consider foundation in step 2, System sliding formwork dynamic can be obtained：

Wherein,Due to unmanned plane rotary inertia and The boundary of disturbance torque is unknown, and relevant parameter is required to parameter adaptive estimation, accordingly, it is considered to form every in Θ, can do Go out reasonable assumption as follows：| | Θ | |≤b Φ, Φ=(1+ | | ω | |+| | ω | |²), parameter b>0 is unknown, it is necessary to ART network.

In order to improve the transient performance and steady-state behaviour of system, the kinetic model (3) and step set up according to step 2 Four design finite time Integral Sliding Mode faces (5), design four rotor wing unmanned aerial vehicles Attitude tracking control device be：

Wherein, control gain matrix K₂=diag (k₂₁,k₂₂,k₂₃), K₃=diag (k₃₁,k₃₂,k₃₃), and k_2i>0, k_3i>0, I=1,2,3；0<r₂<1；Power functionWherein It is the estimate of parameter b, is given by parameters described below adaptive updates rule (8).

Design parameter adaptive updates are restrained：

Wherein, λ>0, η>0 is constant, and meets λ η>1.

As can be seen that the design of the fault-tolerant controller does not need the detection of any fault message, to separate even control and think highly of Structure process, and design process considers the saturation amplitude requirement of actuator；And caused using parameter adaptive method designed Finite time Attitude tracking control device (7) be not rely on the boundary of system rotary inertia information and disturbance torque, ensure that Designed controller has certain robustness for interference and systematic uncertainty.

May certify that, the parameter adaptive of finite time Attitude tracking control device and formula (8) design designed in formula (7) is more In the presence of new law, four rotor wing unmanned aerial vehicles can realize Attitude Tracking in finite time.

Prove：For the kinetic model (3) of four rotor wing unmanned aerial vehicles, it is considered to finite time Integral Sliding Mode face (5) and system Sliding formwork dynamic (6), designing liapunov function is：

Wherein, δ_minIt is the minimal eigenvalue of the matrix delta that fails.

V derivations can be obtained along system path：

Wherein, | | | |₁Represent 1 norm of vector.For any vector, set up | | | |₁>=| | | |, therefore have

In view of for any φ>0, it is total to set upWherein 0<ζ<1, therefore scalingCan obtain

Substitute the above to (9) Shi Ke get

Wherein,J_maxRepresent the maximum of rotary inertia J Characteristic value.

It can be seen from theory according to finite-time control, four rotor wing unmanned aerial vehicle Attitude tracking control systems can be in finite timeInterior completion sliding formwork convergence dynamic, wherein V₀It is the initial value of liapunov function V, 0<θ<1.Further tie The result for closing step 3 and step 4 understands that four rotor wing unmanned aerial vehicles can be in finite time T_f+T_z+T_eInside realize attitude error e and angle Velocity error ω_eWhile it is calm, realize finite time Attitude tracking control.

A kind of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method of the invention gives numerical simulation checking, says It is bright when four rotor wing unmanned aerial vehicles face various factors affecting stabilities, the control method for being proposed can realize finite time attitude Tracking, and with preferable control performance, it is specific as follows：

The model parameter of four rotor wing unmanned aerial vehicles is chosen for：

Disturbance torque Rotary inertia is uncertain

Angular speed initial value ω (0)=[0.1 0-0.1]^Trad/s；Initial attitude q_v(0)=[0.3-0.2 0.3 0.8832]^T；

Controlled output saturation amplitude u_imax=0.001Nm；；

The track for expecting tracking is：

Expect attitude initial value q_dv(0)=[0.7 0.5 0.4123 0.3]^T,

Expect angular velocity omega_d=0.05 × [sin (0.1t) 2sin (0.2t) 3sin (0.3t)]^Trad/s；

Actuators Failures failure is：

The estimation initial value of parameter adaptive more new law is all 0；

With reference to the present invention in formula (4), (5), (7), (8) for controller design and parameter adaptive more new law will Ask, parameter is taken respectively as follows：c_i=0.15, p=0.7；k_1i=0.2, r₁=0.6；k_2i=0.4, k_3i=0.1, r₂=0.75；λ =5, η=1；In order to avoid the buffeting of sign function, taken in simulating, verifyingInstead of sign function, wherein ρ is taken as 0.01。

The attitude error convergence curve figure and angular speed that Fig. 3, Fig. 4 are respectively when four rotor wing unmanned aerial vehicles carry out Attitude Tracking are missed Difference convergence curve figure, can therefrom find out, unmanned plane completes Attitude Tracking within the time of 20 seconds, and steady-state error is controllable 10^-6With 10^-5Magnitude, therefore with tracking accuracy higher；Fig. 5 is the change curve of estimates of parameters, shows parameter Estimate finally converges to 0；Fig. 6 is the change curve of control moment, can therefrom be found out, due to controlled output saturation amplitude Limitation, control moment is constrained in the range of 0.001Nm, and at 10 seconds, the curve bur phenomenon occurred at 15 seconds and 20 seconds The generation of failure of removal is correspond to, but designed controller can overcome, and illustrate there is good failure tolerant ability.

Other steps and parameter are identical with one of specific embodiment one to five.

The present invention can also have other various embodiments, in the case of without departing substantially from spirit of the invention and its essence, this area Technical staff works as can make various corresponding changes and deformation according to the present invention, but these corresponding changes and deformation should all belong to The protection domain of appended claims of the invention.

Claims (6)

1. a kind of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method, it is characterised in that：Four rotor wing unmanned aerial vehicle has Attitude tracking control method is comprised the following steps between in limited time：

Step one：Set up the kinematics model of four rotor wing unmanned aerial vehicle Attitude Trackings；

Step 2：Set up the kinetic model of four rotor wing unmanned aerial vehicle Attitude Trackings；

Step 3：The kinematics model set up according to step one defines the attitude filtering error of four rotor wing unmanned aerial vehicles；

Step 4：According to the attitude filtering error design finite time Integral Sliding Mode face that step 3 is defined；

Step 5：The finite time Integral Sliding Mode face that the kinetic model and step 4 set up according to step 2 are designed, design four The finite time Attitude tracking control device of rotor wing unmanned aerial vehicle.

2. a kind of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method according to claim 1, it is characterised in that： The detailed process that the kinematics model of four rotor wing unmanned aerial vehicle Attitude Trackings is set up in the step one is：

By the attitude of the rotor wing unmanned aerial vehicle of quaternion representation four, the relative motion for representing four rotor wing unmanned aerial vehicle Attitude Trackings is：

$\begin{array}{c}{e}_v=\left[\begin{array}{c}{e}_0\\ e\end{array}\right]=q_{dv}^{-1}\&CircleTimes;q_v=\left[\begin{array}{c}{q}_v^T{q}_{dv}\\ q_{d0}q-q_0{q}_d+q^{\&times;}{q}_d\end{array}\right]\\ {\mathrm{\&omega;}}_e=\mathrm{\&omega;}-{\mathrm{C\&omega;}}_d\end{array}---\left(1\right)$

Wherein, e_v, ω_eRepresent unmanned plane body coordinate system relative to the Attitude Tracking error and angular speed for expecting coordinate system respectively Error, e₀, attitude error e be respectively e_vScalar sum vector；q_v, ω represents the body attitude and angular speed of unmanned plane respectively, q₀, q be respectively q_vScalar sum vector；q_dv, ω_dThe expectation attitude of unmanned plane is represented respectively and expects angular speed, q_d0、q_dRespectively It is q_dvScalar sum vector；C represents unmanned plane body coordinate system relative to the attitude spin matrix for expecting coordinate system,Represent four First number multiplication；q^×It is the multiplication cross matrix of q；

The relative motion of the UAV Attitude tracking based on the description of (1) formula, sets up the kinematics of four rotor wing unmanned aerial vehicle Attitude Trackings Model is：

${\stackrel{\&CenterDot;}{e}}_0=-\frac{1}{2}{e}^T{\mathrm{\&omega;}}_e,\stackrel{\&CenterDot;}{e}=\frac{1}{2}E\left(e_v\right){\mathrm{\&omega;}}_e---\left(2\right)$

Wherein, E (e_v)=(e₀I+e^×), and | | E (e_v) | |=1, e^×Represent the multiplication cross matrix of e；I represents three rank unit matrixs.

3. a kind of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method according to claim 2, it is characterised in that： The detailed process that the kinetic model of four rotor wing unmanned aerial vehicle Attitude Trackings is set up in the step 2 is：

The kinetic model for setting up four rotor wing unmanned aerial vehicle Attitude Trackings is：

$J{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_e=-{({\mathrm{\&omega;}}_e+{\mathrm{C\&omega;}}_d)}^{\&times;}J({\mathrm{\&omega;}}_e+{\mathrm{C\&omega;}}_d)+J({\mathrm{\&omega;}}_e^{\&times;}{\mathrm{C\&omega;}}_d-C{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d)+\mathrm{\&delta;}sat\left(u\right)+\mathrm{\&Gamma;}---\left(3\right)$

Wherein, J represents the unknown rotary inertia of unmanned plane；δ=diag (δ₁,δ₂,δ₃) represent actuator failure matrix, 0<δ_i≤ 1, i=1,2,3；U=[u₁,u₂,u₃]^TRepresent the control instruction produced by controller；Sat (u)=[sat (u₁),sat(u₂), sat(u₃)]^TRepresent controller output saturated characteristic, sat (u_i)=sgn (u_i)·min{|u_i|,u_imax, u_imaxRepresent i-th The output maximum of component is controlled, sgn () represents sign function；It is the part that controller output exceeds saturation amplitude to define θ, Then sat (u)=θ+u, then have θ=[θ₁,θ₂,θ₃]^T, whereinI=1,2,3；(ω_e+C ω_d)^×=ω^×Represent the multiplication cross matrix of ω；It is ω_eMultiplication cross matrix；

Γ represents disturbance torque, including external wind square and the gyroscopic couple that is caused by rotor, | | Γ | |≤d_Γ(1+||ω| |), d_Γ>0 is constant.

4. a kind of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method according to claim 3, it is characterised in that： The kinematics model set up according to step one in the step 3 defines the specific mistake of the attitude filtering error of four rotor wing unmanned aerial vehicles Cheng Wei：

The attitude filtering error for defining four rotor wing unmanned aerial vehicles is：

Wherein,It is Virtual Controller；·^-1Representing matrix it is inverse；0<r₁<1；K₁=diag (k₁₁, k₁₂,k₁₃) it is diagonal matrix, k_1i>0, i=1,2,3；Power functionWherein

By calm attitude filtering error z, the attitude error e that calms is in finite time T_eInside converge to origin；Obtained by z=0The kinematics model (2) of the four rotor wing unmanned aerial vehicle Attitude Trackings set up according to step one, then It is V to this error dynamics system design liapunov function_e=e^TE, derivation can be obtained：

${\stackrel{\&CenterDot;}{V}}_e=2e^T\stackrel{\&CenterDot;}{e}=-e^T{K}_1{\mathrm{sig}}^{r_1}\left(e\right)\&le;-min\left\{k_{1i}\right\}{\left(e^{T}e\right)}^{\frac{1+r_1}{2}}$

Attitude error e will be in finite timeOrigin is inside converged to, wherein e (0) represents the first of attitude error Initial value；ω is understood according to (4) formula_eWill be in finite time T_eInterior convergence.

5. a kind of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method according to claim 4, it is characterised in that： The detailed process in the attitude filtering error design finite time Integral Sliding Mode face defined according to step 3 in the step 4 is：

It is as described below according to the attitude filtering error design finite time Integral Sliding Mode face that (4) formula is defined：

$S=z+c{\&Integral;}_0^t{\mathrm{sig}}^p\left(z\right)d\mathrm{\&tau;}---\left(5\right)$

Wherein, power function sig^p(z)=[sig^p(z₁),sig^p(z₂),sig^p(z₃)]^T, wherein sig^p(z_i)=| z_i|^psgn (z_i), i=1,2,3；τ represents integration variable；C=diag (c₁,c₂,c₃), c₁>0,c₂>0,c₃>0；0<p<1；

System has finite time convergence control characteristic in the sliding mode stage, i.e.,：During S=0, attitude filtering error z is in finite time T_z Inside converge to origin；

Can be obtained by S=0Designing liapunov function isDerivation can be obtained：

${\stackrel{\&CenterDot;}{V}}_S=z^T\stackrel{\&CenterDot;}{z}=-z^T{\mathrm{csig}}^p\left(z\right)=-\underset{i=1}{\overset{3}{\&Sigma;}}{c}_i|z_i{|}^{1+p}\&le;-2^{\frac{1+p}{2}}min\{c_i\}{V}_S^{\frac{1+p}{2}}$

Wherein

Attitude filtering error z is in finite timeOrigin is inside converged to, wherein z (0) represents that attitude filtering is missed Poor initial value；Understood with reference to the result of step 3, the attitude error e and angular speed error of four rotor wing unmanned aerial vehicle Attitude Trackings ω_eIn T_z+T_eOrigin is converged in time.

6. a kind of four rotor wing unmanned aerial vehicles finite time Attitude tracking control method according to claim 5, it is characterised in that： The detailed process that the finite time Attitude tracking control device of four rotor wing unmanned aerial vehicles is designed in the step 5 is：

System sliding formwork dynamic：

Wherein,Assuming that as follows：

| | Θ | |≤b Φ, Φ=(1+ | | ω | |+| | ω | |²), b>0；

The finite time Integral Sliding Mode face (5) that the kinetic model (3) and step 4 set up according to step 2 are designed, design four is revolved The Attitude tracking control device of wing unmanned plane is：

$u\left(t\right)=-K_{2}S-K_3{\mathrm{sig}}^{r_2}\left(S\right)-\hat{b}\mathrm{\&Phi;}sgn\left(S\right)---\left(7\right)$

Wherein, control gain matrix K₂=diag (k₂₁,k₂₂,k₂₃), K₃=diag (k₃₁,k₃₂,k₃₃), and k_2i>0, k_3i>0, i= 1,2,3；0<r₂<1；Power functionWhereinI= 1,2,3；It is the estimate of b, is given by formula (8)；

Design parameter adaptive updates are restrained：

$\stackrel{\&CenterDot;}{\hat{b}}=-\mathrm{\&lambda;}\mathrm{\&eta;}\hat{b}+\mathrm{\&eta;}\left|\right|S\left|\right|\mathrm{\&Phi;}---\left(8\right)$

Wherein, λ>0, η>0 is constant, and meets λ η>1；

In the presence of the finite time Attitude tracking control device of formula (7) design and the parameter adaptive more new law of formula (8) design, Four rotor wing unmanned aerial vehicles realize Attitude Tracking in finite time；

For the kinetic model (3) of four rotor wing unmanned aerial vehicles, it is considered to finite time Integral Sliding Mode face (5) and system sliding formwork dynamic (6), design liapunov function is：

$V=\frac{1}{2}{S}^{T}JS+\frac{1}{2{\mathrm{\&eta;\&delta;}}_{\min }}{(b-{\mathrm{\&delta;}}_{\min }\hat{b})}^2$

Wherein, δ_minIt is the minimal eigenvalue of the matrix delta that fails；

V derivations can be obtained along system path：

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=\frac{1}{2}{S}^{T}J\stackrel{\&CenterDot;}{S}-\frac{1}{\mathrm{\&eta;}}(b-{\mathrm{\&delta;}}_{\min }\hat{b})\stackrel{\&CenterDot;}{\hat{b}}=S^T(\mathrm{\&Theta;}+\mathrm{\&delta;}u)-(b-{\mathrm{\&delta;}}_{\min }\hat{b})(-\mathrm{\&lambda;}\hat{b}+|\left|S\right|\left|\mathrm{\&Phi;}\right)\\ \&le;b\left|\right|S\left|\right|\mathrm{\&Phi;}-{\mathrm{\&delta;}}_{\min }\hat{b}\mathrm{\&Phi;}\left|\right|S|{|}_1-S^T{\mathrm{\&delta;K}}_{2}S-S^T{\mathrm{\&delta;K}}_3{\mathrm{sig}}^{r_2}\left(S\right)-(b-{\mathrm{\&delta;}}_{\min }\hat{b})(-\mathrm{\&lambda;}\hat{b}+|\left|S\right|\left|\mathrm{\&Phi;}\right)\end{array}$

Wherein, | | | |₁Represent 1 norm of vector；For any vector, | | | |₁>=| | | | set up, then have：

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\&le;-{\mathrm{\&delta;}}_{\min }{S}^T{K}_{2}S-{\mathrm{\&delta;}}_{\min }{S}^T{K}_3{\mathrm{sig}}^{r_2}\left(S\right)+\mathrm{\&lambda;}\hat{b}(b-{\mathrm{\&delta;}}_{\min }\hat{b})\\ \&le;-{\mathrm{\&delta;}}_{\min }\min \left\{k_{3i}\right\}{\left(S^{T}S\right)}^{\frac{1+r_2}{2}}+\mathrm{\&lambda;}\hat{b}(b-{\mathrm{\&delta;}}_{\min }\hat{b})\end{array}---\left(9\right)$

For any φ>0,Set up, wherein 0<ζ<1, therefore scalingCan obtain：

$\begin{array}{c}\mathrm{\&lambda;}\hat{b}(b-{\mathrm{\&delta;}}_{\min }\hat{b})\&le;-\frac{\mathrm{\&lambda;}}{2{\mathrm{\&delta;}}_{\min }}{(b-{\mathrm{\&delta;}}_{\min }\hat{b})}^2+\frac{\mathrm{\&lambda;}}{2{\mathrm{\&delta;}}_{\min }}{b}^2\\ \&le;-\frac{1}{2{\mathrm{\&eta;\&delta;}}_{\min }}{(b-{\mathrm{\&delta;}}_{\min }\hat{b})}^2+\frac{\mathrm{\&lambda;}}{2{\mathrm{\&delta;}}_{\min }}{b}^2\\ \&le;-{\left(\frac{1}{2{\mathrm{\&eta;\&delta;}}_{\min }}{(b-{\mathrm{\&delta;}}_{\min }\hat{b})}^2\right)}^{\frac{1+r_2}{2}}+\mathrm{\&zeta;}+\frac{\mathrm{\&lambda;}}{2{\mathrm{\&delta;}}_{\min }}{b}^2\end{array}$

Substitute the above to (9) Shi Ke get：

Wherein,J_maxRepresent the maximum feature of rotary inertia J Value；

Four rotor wing unmanned aerial vehicle Attitude tracking control systems are in finite timeInterior completion sliding formwork convergence dynamic, wherein V₀ It is the initial value of liapunov function V, 0<θ<1；With reference to step 3 and the result of step 4, four rotor wing unmanned aerial vehicles are in T_f+T_z+ T_eAttitude error e and angular speed error ω is realized in time_eWhile it is calm, realize Attitude tracking control.