CN108681327A - Quadrotor flight control method based on fractional order saturation function switching law - Google Patents
Quadrotor flight control method based on fractional order saturation function switching law Download PDFInfo
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Abstract
The invention discloses a kind of quadrotor flight control methods based on fractional order saturation function switching law, system is split as two subsystems using Reverse Step Control method, then meets the sub- control law of Liapunov theorem to two subsystems design with traditional backstepping control method and sliding-mode control respectively；Specifically, Reverse Step Control method is to inherit its integrality and uniformity, and sliding-mode control is to improve robustness and anti-interference ability；The present invention introduces fractional order saturation function power switching law again when using sliding-mode control, to improve controller performance, and inhibit to shiver, ensure the quick response of the flight control of quadrotor drone in this way, meanwhile by adjusting saturation function parameter, moreover it is possible to improve the nonlinear characteristic of controller, filter out shivering in controller output, the flatness of lifting controller.
Description
Technical field
The invention belongs to quadrotor drone technical fields, more specifically, are related to a kind of based on fractional order saturation letter
The quadrotor drone flight control method of number switching law.
Background technology
Demand with people to intelligent equipment is increasing and the fast development of aeronautical and space technology, unmanned plane
From initial military affairs, production activity, start to come into people’s lives.Wherein quadrotor drone is simple in structure, and flight is flexible,
Cost is relatively low, receives the favor of ruck, also complies with the consumption level of average family.And quadrotor drone, which has, hangs down
The function of straight landing largely reduced aircraft takeoff drop, fall the harsh demand to place.Therefore, quadrotor drone becomes
A big hot spot in unmanned plane research field, has attracted the attention of large quantities of researchers, is dedicated to improving its flight
Performance, and expand its application range.
Quadrotor drone is drive lacking nonlinear system, although mechanical structure is relatively easy, due to each state variable
Between stronger coupling and dynamical system outbound course the reasons such as fix, keep its control method relative complex.With quadrotor without
A period of time has been developed in man-machine relevant control technology, and the control method of proposition is varied, and control effect is different.But it is every
Kind control method, which all certainly exists, limits its bottleneck further increased, such as patent《Quadrotor based on Fractional Control Algorithm
UAV Flight Control method》(the patent No.：201711432615.1) in, although the introducing of fractional calculus theory makes control
The control speed of device becomes faster, but becoming larger with controller mid-score rank parameter, and the output of controller can shiver phenomenon.
This root shivered is the sign function of sliding-mode control, but fractional order parameter can be amplified, and be made to controller
At great burden, very important counter productive is generated, the stability of controller is influenced.This problem is to quadrotor drone
The research of control method leaves the space of promotion, and saturation function is such as added in the controller.
Saturation function is a kind of piecewise function, and the mechanism of action is to adjust output valve according to input.And reach in input value
After specified value, output valve no longer changes.Saturation function does not fix expression formula, needs specifically to be designed according to demand.It is full
It is the common tool for improving mission nonlinear characteristic with function, itself and fractional order theory are conjointly employed in raising by the present invention
UAV Flight Control device performance.
Invention content
It is an object of the invention to overcome the deficiencies of the prior art and provide one kind being based on fractional order saturation function switching control
The quadrotor flight control method of rule, by designing three attitude angles and height controller, to improve integer rank contragradience sliding formwork control
The performance of device processed.
For achieving the above object, a kind of quadrotor flight based on fractional order saturation function switching law of the present invention
Control method, which is characterized in that include the following steps：
(1), it is based on Newton-Euller method and dynamic analysis is carried out to unmanned plane, and establish corresponding kinetic model.Nothing
Man-machine dynamics model includes translational motion model and rotary motion model, wherein translational motion model is：
Wherein, (x, y, z) is position coordinates of the unmanned plane under ground coordinate system,The second order of respectively x, y, z are led,
γ, μ, ρ are that three attitude angles for describing unmanned plane, i.e. roll angle, pitch angle and yaw angle are united to facilitate description in Fig. 1 respectively
One is indicated with A [γ, μ, ρ], FTIt is the total life that rotor generates, m is unmanned plane gross mass, and g is acceleration of gravity；
Rotary motion model is：
Wherein, Ix,Iy,IzIt is rotary inertia of the unmanned plane on x, tri- directions y, z, Nx,Ny,NzIt is three axis of unmanned plane
The torque in direction；
(2), the corresponding controller of three attitude angles is separately designed
(2.1), error analysis is carried out to roll angle γ：If practical roll angle γ and desired value γdError be：Eγ1=
γ-γd；By Eγ1Compared with roll angle error threshold ζ, if Eγ1Less than threshold value ζ, then it represents that quadrotor drone flight system is steady
It is fixed, and terminate；It is on the contrary then enter step (2.2)；
(2.2), Equivalent control law is designed
Take virtual controlling variableWherein,It is the derivative of roll angle desired value, c1For normal number；
Define error signalAnd design the sliding-mode surface of sliding formwork control：Sγ(t)=k1Eγ1+Eγ2,
In, k1＞ 0；
To sliding-mode surface Sγ(t) derivation obtains：
According to sliding formwork control Theory of Stability, enableObtain Equivalent control law：
(2.3), the switching law based on fractional order saturation function is designed
Wherein, εγ＞ 0, kγ＞ 0,0≤q ＜ 1, δ ∈ R,Γ(·)
It is gamma function, f (t) refers to function, saturation functionAnd
(2.4), the switching law design roll angle γ according to Equivalent control law and based on fractional order saturation function is corresponded to
Controller Uγ
(2.5), similarly, according to step (2.1)-(2.4) the method design pitch angle and the corresponding controller of yaw angle
UμAnd Uρ
(3), design height direction controller
(3.1), error analysis is carried out to height z：If actual height z and desired value zdError be：Ez1=z-zd；By Ez1
With height error threshold valueCompare, if Ez1Less than threshold valueIt then indicates that quadrotor drone flight system is stablized, and terminates；It is on the contrary
It then enters step (3.2)；
(3.2), Equivalent control law is designed
Take virtual controlling variableWherein,It is the derivative of high expectations value, c4For normal number；Definition
Error signalDesign the sliding-mode surface of sliding formwork control：Sz(t)=k4Ez1+Ez2, wherein k4＞ 0；
To sliding-mode surface Sz(t) derivation obtains：
According to sliding formwork control Theory of Stability, enableObtain Equivalent control law：
(3.3), the switching law based on fractional order saturation function is designed
Wherein, εγ＞ 0, kγ＞ 0,0≤q ＜ 1, δ ∈ R,Γ(·)
It is gamma function, f (t) refers to function, saturation functionAnd
(3.4), according to Equivalent control law with based on the corresponding controls of the switching law design height z of fractional order saturation function
Device U processedz
(4) using after design three attitude angles and the corresponding controller of height track roll angle, pitch angle, posture again
Angle and height show that quadrotor drone has been enter into stabilized flight condition, are used in combination if error is respectively less than its corresponding threshold value
The controller of above-mentioned design carries out flight control to quadrotor drone, ensures unmanned plane normal operation；On the contrary then return to step
(2)。
What the goal of the invention of the present invention was realized in：
The present invention is based on the quadrotor flight control method of fractional order saturation function switching law, controller overall structures
Based on backstepping control method.System is split as two subsystems by backstepping control method, then, respectively with traditional Reverse Step Control
Method and sliding-mode control meet two subsystems design the sub- control law of Liapunov theorem.Overall architecture is based on anti-
Step control method be in order to inherit its integrality and uniformity, in the second secondary design subsystem using sliding-mode control be for
Raising robustness and anti-interference ability.And the present invention also using sliding-mode control design second subsystem when,
Fractional order saturation function is introduced, to improve controller performance, and inhibits to shiver.New fractional-order system has broader stable region
And more parameter Choices, make system when iteration is debugged, most suitable parameter can be chosen, make switching law
Transition effect --- when controlled state does not reach sliding-mode surface also, or deviates sliding-mode surface because of factors such as external interferences, control
The involvement level and control dynamics of device will directly proportional to the distance between state and sliding-mode surface, i.e., remoter from sliding-mode surface when state
When, the effect dynamics of controller is bigger, and involvement level is higher, and it is closer when it is then opposite --- more quickly, stablize, greatly
Ground extenuates traditional sliding formwork control and shivers characteristic, with the quick response of this flight control for ensureing unmanned plane.Meanwhile by adjusting full
And function parameter, moreover it is possible to the nonlinear characteristic for improving controller, filter out controller output in shivering, lifting controller it is smooth
Property.
Meanwhile the present invention is based on the quadrotor flight control methods of fractional order saturation function switching law also with following
Advantageous effect：
The fractional order saturation function switching law that the present invention designs can accelerate controlled device and reach cunning from original state
The convergence rate of die face, and ensure that the state is hardly happened still and shivered on sliding-mode surface.To find out its cause, having at 2 points：
(1), on the one hand, by simulation results show,With with sat (f (t)) phase
Same symbol handoff functionality, therefore ensure that basic functionality；
(2), on the other hand, at certain moment,Absolute value can obviously be more than 1, and sgn (f
(t)) it generally is only 0 or 1, it is therefore, this to design the performance for improving controller, that is, accelerate the convergence rate of controlled device
And precision, controller response speed can be adjusted neatly relatively, convenient for selected more preferably parameter.At the same time, it adjusts
Whole saturation function parameter δ, moreover it is possible to change simultaneouslyAbsolute value and linear degree.
Description of the drawings
Fig. 1 is the quadrotor flight control method flow chart the present invention is based on fractional order saturation function switching law；
Fig. 2 is response pair of the fractional order saturation function with fractional order sign function under identical input condition in the present invention
Than figure；
Fig. 3 is the arbitrary appearance that fractional order sign function is carried out with fractional order saturation function rolling angle controller under different parameters
State tracks in emulation experiment, roll angle response curve；
Fig. 4 is the arbitrary appearance that fractional order sign function is carried out with fractional order saturation function pitch controller under different parameters
State tracks in emulation experiment, pitch angle response curve；
Fig. 5 is fractional order sign function and the response pair that fractional order saturation function yaw angle controller carries out under different parameters
It is tracked in emulation experiment than figure any attitude, yaw angle response curve；
Fig. 6 is the arbitrary height that fractional order sign function is carried out with fractional order saturation function height controller under different parameters
It tracks in emulation experiment, high response curve；
Fig. 7 is the arbitrary appearance that fractional order sign function is carried out with fractional order saturation function rolling angle controller under different parameters
State tracks in emulation experiment, the sliding-mode surface change curve of roll angle；
Fig. 8 is the arbitrary appearance that fractional order sign function is carried out with fractional order saturation function pitch controller under different parameters
State tracks in emulation experiment, the sliding-mode surface change curve of pitch angle；
Fig. 9 is fractional order sign function and the arbitrary appearance that fractional order saturation function yaw angle controller carries out under different parameters
State tracks in emulation experiment, the sliding-mode surface change curve of yaw angle；
Figure 10 is the arbitrary height that fractional order sign function is carried out with fractional order saturation function height controller under different parameters
In degree tracking emulation experiment, the sliding-mode surface change curve of height；
Figure 11 is fractional order sign function carried out with fractional order saturation function rolling angle controller under different parameters it is arbitrary
In Attitude Tracking emulation experiment, rolling angle controller curve of output；
Figure 12 is fractional order sign function carried out with fractional order saturation function pitch controller under different parameters it is arbitrary
In Attitude Tracking emulation experiment, pitch controller curve of output；
Figure 13 is that fractional order sign function yaws the arbitrary of angle controller progress with fractional order saturation function under different parameters
In Attitude Tracking emulation experiment, angle controller curve of output is yawed；
Figure 14 is the arbitrary height that fractional order sign function is carried out with fractional order saturation function height controller under different parameters
In degree tracking emulation experiment, height controller curve of output；
Specific implementation mode
The specific implementation mode of the present invention is described below in conjunction with the accompanying drawings, preferably so as to those skilled in the art
Understand the present invention.Requiring particular attention is that in the following description, when known function and the detailed description of design perhaps
When can desalinate the main contents of the present invention, these descriptions will be ignored herein.
Embodiment
Fig. 1 is the quadrotor flight control method flow chart the present invention is based on fractional order saturation function switching law.
In the present embodiment, as shown in Figure 1, the present invention propose it is a kind of based on fractional order saturation function switching law four
Rotor wing unmanned aerial vehicle flight control method, includes the following steps：
S1, dynamic analysis, including mechanical analysis and torque analysis are carried out to unmanned plane based on Newton-Euler principle, built
Vertical unmanned plane kinetic model, unmanned plane kinetic model includes translational motion model and rotary motion model, wherein translation fortune
Movable model is：
Wherein, (x, y, z) is position coordinates of the unmanned plane under ground coordinate system,The second order of respectively x, y, z are led,
γ, μ, ρ are three attitude angles for describing unmanned plane, i.e. roll angle, pitch angle and yaw angle, F respectivelyTIt is total liter that rotor generates
Power, m are unmanned plane gross masses, and g is acceleration of gravity；
Rotary motion model is：
Wherein, Ix,Iy,IzIt is rotary inertia of the unmanned plane on x, tri- directions y, z, Nx,Ny,NzIt is three axis of unmanned plane
The torque in direction；
S2, the corresponding controller of three attitude angles is separately designed
In order to describe it is apparent be illustrated, the design of controller by taking roll angle γ as an example, other two attitude angle (pitch angle,
Yaw angle) it is similar；
S2.1, first step Reverse Step Control analysis is carried out to roll angle γ：If practical roll angle γ and desired value γdError
For：Eγ1=γ-γd, by Eγ1Compared with roll angle error threshold ζ, if Eγ1Less than threshold value ζ, then it represents that quadrotor drone flies
Row system is stablized, and terminates；It is on the contrary then enter step S2.2；
S2.2, design Equivalent control law
Take virtual controlling variableWherein,It is the derivative of roll angle desired value, c1For normal number；
Second step Reverse Step Control analysis is carried out to roll angle γ, defines error signalDesign sliding formwork control
The sliding-mode surface of system：Sγ(t)=k1Eγ1+Eγ2, wherein k1＞ 0；
To sliding-mode surface Sγ(t) derivation obtains：
According to sliding formwork control Theory of Stability, enableObtain Equivalent control law：
S2.3, switching law of the design based on fractional order theory
The purpose of switching law is that controlled state is made to be shaken back and forth on sliding-mode surface, or in sliding-mode surface a small range always
It swings, improved space is that state approaches the speed of sliding-mode surface and the range of concussion herein.According to fractional order theory, the invention
It is proposed that a kind of sliding formwork control switching law based on fractional order saturation function is:
Wherein, εγ＞ 0, kγ＞ 0,0≤q ＜ 1, δ ∈ R,Γ(·)
It is gamma function, f (t) refers to function, saturation functionAnd
It can obviously ensure the functionality of general switching function in the fractional order saturation function switching law, and it is different
It is,Absolute value can obviously be more than 1, and sgn (Sγ(t)) it generally is only 0 or 1, this design is
Improve controlled device convergence rate, convergence precision, and the key that suppression system is shivered；
S2.4, to sum up, Equivalent control law is added with fractional order switching law, obtains final roll angle γ controllers
UγFor
We meet Liapunov stability theory to verify the control law below.If Liapunov function is：
It can thus be concluded that its derivative is：
Apparent first itemResidual term then need to be only considered, by controller NxIt substitutes intoIt can obtain：
According in the 2.3rd stepSymbolic property known toAnd Sγ
(t)Eγ1Symbol is unknown, therefore need to reconfigure Nx, that is, design roll angle γ finally corresponding controller Uγ：
It substitutes into again at this timeTo obtain the final product
ThereforeMeet Liapunov theorem stable condition.
S2.5, similarly designs pitch angle and the corresponding controller U of yaw angle according to step S2.1-S2.4 the methodsμWith
Uρ
S3, design height direction controller, since its flow is consistent with attitude controller, the only expression of formula slightly has area
Not, therefore it is just unified by taking the roll angle in attitude angle as an example in Fig. 1.
S3.1, error analysis is carried out to height z：If actual height z and desired value zdError be：Ez1=z-zd；By Ez1
With height error threshold valueCompare, if Ez1Less than threshold valueIt then indicates that quadrotor drone flight system is stablized, and terminates；It is on the contrary
Then enter step S3.2；
S3.2, design Equivalent control law
Take virtual controlling variableWherein,It is the derivative of high expectations value, c4For normal number；Definition
Error signal EZ2=dz/dt-C4, and design the sliding-mode surface of sliding formwork control：Sz(t)=k4Ez1+Ez2, wherein k4＞ 0；
To sliding-mode surface Sz(t) derivation obtains：
According to sliding formwork control Theory of Stability, enableObtain Equivalent control law：
S3.3, switching law of the design based on fractional order saturation function
Wherein, εγ＞ 0, kγ＞ 0,0≤q ＜ 1, δ ∈ R,Γ(·)
It is gamma function, f (t) refers to function, saturation functionAnd
S3.4, according to Equivalent control law with based on the corresponding controls of the switching law design height z of fractional order saturation function
Device U processedz
Verification herein is identical as step S2.4, and details are not described herein.
S4, using after design three attitude angles and height corresponding controller flight control is carried out to quadrotor drone
System, when the error of height, roll angle, pitch angle and attitude angle is respectively less than threshold value (a minimum normal number), illustrates unmanned plane
Into stabilized flight condition；It is on the contrary then iteration carries out step S2 and S3 again.
Meanwhile can with it is seen from figure 2 that, when reference signal input be SIN function f (t)=3sin (t) when, integer exponent character
Number functionWith fractional order saturation functionResponse curve.Institute above is illustrated in figure
Two of the present invention stated are a little.One is fractional order saturation function has the function of symbol switching；The second is working as input signal
Symbol when changing, fractional order saturation function will produce a larger amplitude, i.e., previously described at certain moment point
The absolute value of number rank saturation function is much larger than 1, its control action power will be far longer than integer rank sign function at this time, keeps control fast
Degree faster, makes controlled state reach sliding-mode surface at faster speed.And over time, the response of fractional order saturation function
Curve is gradually reduced and is less than 1.Illustrate that, when state is close to sliding-mode surface, control dynamics can reduce therewith in the control later stage, ensures
System not will produce it is excessive shiver, also illustrate that this control method of fractional order saturation function switching law is more flexible.
Example
In order to from be more intuitive to see fractional order saturation function switching law introduce after, to flight controller performance
It improves, is next illustrated by taking an emulation experiment as an example.In emulation experiment, quantity of state：Highly, roll angle, pitch angle
It is 0 with yaw angle initial value, desired value is respectively then the radian of 8 meters, 0.2,0.1 and 0.3.In experimental result picture, Fig. 2-5 is
Condition responsive curve, Fig. 6-9 are the sliding-mode surface change curves of corresponding states, and Figure 10-13 is that the controller output of corresponding states is bent
Line.In every width figure, and contain curve a --- fractional order contragradience sliding mode controller (q=0.2, δ=0), curve b --- point
Number rank saturation function contragradience sliding mode controller (q=0.2, δ=0.01) and curve c --- fractional order saturation function contragradience sliding formwork control
The performance comparison of device (q=0.5, δ=0.01) processed.The curve a of wherein every width figure is in patent《Based on Fractional Control Algorithm
Quadrotor drone flight control method》(the patent No.：201711432615.1) in curve under controller action.
Fig. 3-6 is the condition responsive curve of roll angle, pitch angle, yaw angle and height respectively.From the totality of response curve
From the point of view of trend, condition responsive curve when three kinds of situation (a, b, c) can trace into expectation state in 2-3 seconds, and keep steady
It is fixed.Controller can implement effective control action to controlled state in the case of this three kinds of explanation.But from thin in each width figure
Section figure can see, and curve c overshoot smallers, more steadily, and convergence rate is always most fast, and the speed of curve b is slightly slower than song
Line a.From the comparison of this four width figure and corresponding controller parameter, can with it is concluded that, when fractional order parameter is identical, fractional order
The control speed of saturation function controller is slightly slower than fractional order sign function controller, but by improving fractional order parameter, can be with
Realize the promotion of control speed.
Fig. 7-10 is roll angle, pitch angle, yaw angle and the corresponding sliding-mode surface change curve of height respectively.Sliding-mode surface changes
Curve is to be used for judging the exclusive index that system is stablized in sliding formwork control, and when the non-timing of product of sliding-mode surface and its derivative, system is steady
It is fixed.From the point of view of the general trend of sliding-mode surface change curve, sliding-mode surface change curve when three kinds of situation (a, b, c) can be in 2-3
0 is converged in second, and keeps stable, at this point, the product certainty of sliding-mode surface and its derivative is non-just, therefore system is stablized.Meanwhile with Fig. 2-
Corresponding condition responsive curve compares one by one in 5, and 0 is converged to sliding-mode surface at the time of condition responsive curve tracks upper desired value
Time is almost consistent, and controller can make system enter stable state in the case of this three kinds of explanation.But from each width figure
Detail view can see, curve c overshoot smallers, more steadily, and the speed for making system reach stable state is always most fast,
The effect of curve a is taken second place, and curve b is slightly slower than a.Therefore, from the comparison of this four width figure, can with it is concluded that, increase fractional order
Fractional order parameter q in saturation function contragradience sliding mode controller can make system enter the speed of stable state faster, but work as score
In the case of rank parameter is identical, the control speed of fractional order saturation function contragradience sliding mode controller can be slightly slower than fractional order symbol letter
Number contragradience sliding mode controller.
Figure 11-14 is roll angle, pitch angle, yaw angle and the corresponding controller curve of output of height respectively.Controller is defeated
The reasonability for going out curve is to judge the whether rational important test stone of control system.From the general trend of controller curve of output
From the point of view of, controller curve of output when three kinds of situation (a, b, c) can enter in 2-3 seconds to be stablized or metastable control shape
State illustrates that controller has been completed the adjustment to each state and control, and system is made to enter stable state.But from each figure
Detail view in it can be clearly seen that the output of fractional order sign function contragradience sliding mode controller produce it is apparent, intensive
It shivers phenomenon, no matter the amplitude shivered is big or small, and it is so intensive to shiver in the long-play of controller, it will necessarily be to being
Robustness, the stability of system cause harmful effect, this is that cannot hold in requiring stationarity high flight control system
Bear.The difference of curve a and b are only that the latter introduces saturation function, although it is concluded that b corresponds to control in comparison before
The control speed of device is slightly slower than a, but any phenomenon of shivering hardly is generated in b, and stationarity is good.And it is full to increase fractional order
After the fractional order parameter q in function contragradience sliding mode controller, not only speed is controlled faster, and still without generating any tremble
It quivers.
To sum up, relative to fractional order sign function contragradience sliding mode controller, fractional order saturation function switching law makes
With, it can be by adjusting fractional order parameter q and saturation function parameter δ, raising controller performance, and admirably inhibit sliding formwork control
The controller brought exports problem of shivering.
Although the illustrative specific implementation mode of the present invention is described above, in order to the technology of the art
Personnel understand the present invention, it should be apparent that the present invention is not limited to the range of specific implementation mode, to the common skill of the art
For art personnel, if various change the attached claims limit and determine the spirit and scope of the present invention in, these
Variation is it will be apparent that all utilize the innovation and creation of present inventive concept in the row of protection.
Claims (1)
1. a kind of quadrotor flight control method based on fractional order saturation function switching law, which is characterized in that including with
Lower step：
(1), it is based on Newton-Euller method and dynamic analysis is carried out to unmanned plane, and establish corresponding kinetic model.Unmanned plane
Kinetic model includes translational motion model and rotary motion model, wherein translational motion model is：
Wherein, (x, y, z) is position coordinates of the unmanned plane under ground coordinate system,The second order of respectively x, y, z are led, γ, μ,
ρ is three attitude angles for describing unmanned plane, i.e. roll angle, pitch angle and yaw angle, F respectivelyTIt is the total life that rotor generates, m
It is unmanned plane gross mass, g is acceleration of gravity；
Rotary motion model is：
Wherein, Ix,Iy,IzIt is rotary inertia of the unmanned plane on x, tri- directions y, z, Nx,Ny,NzIt is three axis directions of unmanned plane
Torque；
(2), the corresponding controller of three attitude angles is separately designed
(2.1), error analysis is carried out to roll angle γ：If practical roll angle γ and desired value γdError be：Eγ1=γ-
γd；It will be compared with roll angle error threshold ζ, if Eγ1Less than threshold value ζ, then it represents that quadrotor drone flight system is stablized, and ties
Beam；It is on the contrary then enter step (2.2)；
(2.2), Equivalent control law is designed
Take virtual controlling variableWherein,It is the derivative of roll angle desired value, c1For normal number；
Define error signalAnd design the sliding-mode surface of sliding formwork control：Sγ(t)=k1Eγ1+Eγ2, wherein k1＞
0；
To sliding-mode surface Sγ(t) derivation obtains：
According to sliding formwork control Theory of Stability, enableObtain Equivalent control law：
(2.3), the switching law based on fractional order saturation function is designed
Wherein, εγ＞ 0, kγ＞ 0,0≤q ＜ 1, δ ∈ R,Γ () is gal
Agate function, f (t) refer to function, saturation functionAnd
(2.4), according to Equivalent control law control corresponding with the switching law design roll angle γ based on fractional order saturation function
Device U processedγ
(2.5), similarly, according to step (2.1)-(2.4) the method design pitch angle and the corresponding controller U of yaw angleμAnd Uρ
(3), design height direction controller
(3.1), error analysis is carried out to height z：If actual height z and desired value zdError be：Ez1=z-zd；By Ez1With height
Spend height error threshold valueCompare, if Ez1Less than threshold valueIt then indicates that quadrotor drone flight system is stablized, and terminates；It is on the contrary
It then enters step (3.2)；
(3.2), Equivalent control law is designed
Take virtual controlling variableWherein,It is the derivative of high expectations value, c4For normal number；Define error letter
NumberDesign the sliding-mode surface of sliding formwork control：Sz(t)=k4Ez1+Ez2, wherein k4＞ 0；
To sliding-mode surface Sz(t) derivation obtains：
According to sliding formwork control Theory of Stability, enableObtain Equivalent control law：
(3.3), the switching law based on fractional order saturation function is designed
Wherein, εγ＞ 0, kγ＞ 0,0≤q ＜ 1, δ ∈ R,Γ () is gal
Agate function, f (t) refer to function, saturation functionAnd
(3.4), according to Equivalent control law with based on the corresponding controllers of the switching law design height z of fractional order saturation function
Uz
(4) using after design three attitude angles and the corresponding controller of height track again roll angle, pitch angle, attitude angle and
Highly, if error is respectively less than its corresponding threshold value, show that quadrotor drone has been enter into stabilized flight condition, be used in combination above-mentioned
The controller of design carries out flight control to quadrotor drone, ensures unmanned plane normal operation；On the contrary then return to step (2).
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