CN116300668B - Layering anti-interference control method for four-rotor unmanned aerial vehicle aiming at rainfall interference - Google Patents
Layering anti-interference control method for four-rotor unmanned aerial vehicle aiming at rainfall interference Download PDFInfo
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Abstract
The invention provides a layering anti-interference control method of a four-rotor unmanned aerial vehicle aiming at rainfall interference, which aims to solve the problems of insufficient lifting force and reduced track flight precision caused by efficiency loss of an actuator of the unmanned aerial vehicle in a rainfall environment. Firstly, constructing a rainfall interference model based on an unmanned aerial vehicle aiming at impact forces of rainfall with different intensities, and then constructing a rainfall dynamics model based on the unmanned aerial vehicle by combining a basic dynamics model of the unmanned aerial vehicle on the basis. Secondly, in the aspect of unmanned aerial vehicle control, parameters of a nonlinear interference observer are reasonably selected by utilizing related concepts and experiences of an interference observer and sliding mode control, and a sliding mode control law aiming at rainfall interference is designed on the basis. The invention is based on the composite layered anti-interference control method, can obviously improve the flight quality and track flight precision of the unmanned aerial vehicle in a rainfall environment, and can be used for the operation tasks of emergency rescue, traffic guidance, aerial mapping and the like in a severe weather environment.
Description
Technical Field
The invention belongs to the field of flying robot control, and particularly relates to a layering anti-interference control method of a four-rotor unmanned aerial vehicle aiming at rainfall interference, which is suitable for an unmanned aerial vehicle control system which needs to execute high-precision flying tasks in rainy days and needs to realize stable and safe control.
Background
In recent years, small unmanned aerial vehicles with multiple rotors as driving mechanisms are widely applied in the fields of national defense, such as disaster warning, geological investigation, emergency rescue and the like, electric power, aerial photography and the like, but most unmanned aerial vehicles cannot execute tasks in rainy days, so that the application of the unmanned aerial vehicles is greatly limited. At present, along with the development of mechanical design and processing technology, components such as a motor, a circuit board and a circuit of the unmanned aerial vehicle can have certain waterproof capability, but the unmanned aerial vehicle still can be plagued in the aspects of rainfall impact, insufficient lifting force, poor aerodynamic characteristics and the like in a rainfall environment.
Because the control theory related to the rain resistance of the unmanned aerial vehicle starts later, the control method which is proved by experiments at present is few. Chinese patent application CN202111262360.5 proposes a method for controlling stable flight of unmanned aerial vehicle in consideration of rainfall effect, and chinese patent application CN202111637133.6 proposes a method for modeling unmanned aerial vehicle dynamics in consideration of rainfall effect, but these methods are directed to fixed wing unmanned aerial vehicles, not to rotary wing unmanned aerial vehicles in the present invention. The rest of scientific researchers also research the influence of rainfall on the unmanned rotorcraft from the pneumatic field or make contributions from the waterproof design aspect of the unmanned rotorcraft, but all the works fail to design the unmanned rotorcraft rain control law for rainfall interference.
Disclosure of Invention
In order to overcome the defects and shortcomings of the existing control method, the invention provides a four-rotor unmanned aerial vehicle layering anti-interference control method aiming at rainfall interference for a flying robot system based on a multi-rotor unmanned aerial vehicle, and solves the problems of insufficient lift force and reduced track flight precision caused by efficiency loss of an actuator of the unmanned aerial vehicle in a rainfall environment. Secondly, in the aspect of unmanned aerial vehicle control, parameters of a nonlinear interference observer are reasonably selected by utilizing related concepts and experiences of an interference observer and sliding mode control, and a sliding mode control law aiming at rainfall interference is designed on the basis. The high-precision flight and stability of the aircraft under rainfall interference can be ensured, so that various operation tasks can be completed.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a layering anti-interference control method for a four-rotor unmanned aerial vehicle aiming at rainfall interference comprises the following steps:
firstly, building a rain impact load model aiming at different rainfall intensities;
secondly, establishing a rainfall dynamics model based on the unmanned aerial vehicle according to the rainfall impact load model;
thirdly, generating a smooth track which can be realized by the unmanned aerial vehicle according to a differential flattening method;
fourthly, designing a position ring and attitude ring interference observer according to the established rainfall dynamics model;
fifthly, designing a sliding mode control law to suppress disturbance based on the observed disturbance value.
Further, in the first step, the following rain impact load model is constructed according to the relation of the final rainfall speed, the rain drop spectrum and the rainfall intensity and combining the rain drop movement characteristics:
(1) Assuming rainfall intensityThe unit is mm/h;
(2) The rain drop spectrum, i.e. the distribution of the number of rain drops in a unit volume of air with the size of the rain drops, i.e. the M-P distribution N (D), is calculated:
；
wherein ,individual/m 3/mm,/d.o>Is a slope factor, ++> ，D represents the diameter of raindrops, and the unit is mm;
(3) Calculating the final speed of raindrops with different diameters：
，
(4) Calculating single drop impact force of each diameter raindrop：
，
wherein ,is of raindrop density->Indicating the rainfall speed;
(5) Calculating impact force generated by impacting all raindrops in unit volume of air to plane：
，
(6) Calculating average velocity of raindrops in unit volume of air：
，
The diameter of the raindrops is 0-2.5mm;
(7) Calculating the impact force of the raindrops in unit time, and further calculating the impact of the raindropsLoad, required to calculate the impact volume flow per unit time：
，
S represents the area of an equivalent impacted plane, and the horizontal projection area of the unmanned aerial vehicle is taken;
(8) Calculating the impact force of a given impact surface in a unit time：
，
(9) Calculating the impact load of a given impact surface at a certain moment：
，
(10) And obtaining an impact load function depending on the rainfall intensity through function fitting according to the corresponding relation between different rainfall intensities and the impact load thereof.
Further, the second step includes:
the four-rotor unmanned aerial vehicle dynamics equation is known as:
，
wherein ,is the body coordinate system, is->Is a geographic coordinate system;m is unmanned aerial vehicle mass, < >>First derivative representing speed of the drone in geographical coordinate system,/->Indicating the acceleration of gravity>Representing a rotation matrix required for transforming the coordinates of the unmanned aerial vehicle body coordinate system into the coordinates of the geographical coordinate system,/->Representing the thrust force generated by the unmanned aerial vehicle under the coordinate system of the machine body,/->Represents the angular velocity of the unmanned aerial vehicle in the body coordinate system, < ->Is->Is the first derivative of (a); />To control the moment +.>The rotational inertia of the unmanned aerial vehicle is set;
in the geographic coordinate system, letRepresenting the speed of flight of a quadrotor unmanned aircraft, +.>Representation->At->Plane projection, which is associated with->The included angle of the direction is-> ， />Representation->At->Projection of a plane, which is associated with->The included angle of the direction is->； />The plane is perpendicular to +.>；
Under the influence of unmanned aerial vehicle flight speed, average speed under rainfall natural conditionThe relative speed for the unmanned aerial vehicle is decomposed into +.>Direction speed->And perpendicular to->Direction speed->：
，
，
Obtaining rainwater from rainfall interference model based on unmanned aerial vehiclePlane and->The impact load of the plane is respectively equal to-> 、/>In relation, the impact load factor is defined> 、/>Obtaining the rainfall impact load when considering the unmanned aerial vehicle flight speed +.>Relationship with impact load when unmanned aerial vehicle hovers:
，
，
wherein , indicating that rainfall is +.>Impact load on plane->Indicating that rainfall is +.>Impact load on plane->Is the impact load of the unmanned aerial vehicle when hovering;
unmanned aerial vehicle is in orderWhen flying at speed, assume roll angle of +.>Pitch angle is +.>And obtaining rainfall impact force received by the unmanned aerial vehicle in flight:
，
，
wherein ,indicating that the drone is perpendicular to +.>Impact force applied in the plane direction +.>Indicating that the drone is perpendicular to +.>Impact force applied in the plane direction +.>Representing the horizontal projection area of the unmanned aerial vehicle;
from this, obtain the unmanned aerial vehicle's that considers unmanned aerial vehicle receives rainfall impact rainfall dynamics model:
，
wherein , ，/> ，/>respectively representing the second derivative of the three-axis direction position information of the unmanned aerial vehicle under the geographic coordinate system, ，/>，/>three euler angles of the drone are shown, respectively.
Further, the third step includes:
the z-axis of the desired body coordinate system is expressed as: , wherein />Representing euclidean norms;
by means of and withRelated intermediate unit vector, ">The other two axes represent:
,
wherein , indicating the desired yaw angle +.>And->Respectively indicate->And-> ，/>，/>，/>Respectively represent +.>，/> ，/>Representation of the axis in the geographical coordinate system, +.>Representing the +.>Shaft rotation->Representation after angle;
due toThus the desired euler angle is obtained:
,
wherein , representing the three-axis coordinates of the desired body coordinate system, +.>In order to achieve a desired rotation matrix,represents->Is->Element(s)>And->Representing the desired roll angle and pitch angle, respectively.
Further, the fourth step includes:
first, the design of the position loop disturbance observer is carried out, by means of auxiliary variablesDesign of observer gain matrixI.e. generate +.>A 3 x 3 square matrix of diagonal elements:
,
wherein ,representation and->Acceleration in the geographical coordinate system concerned, +.>First derivative representing the position of the drone in the geographical coordinate system,/-> ， />Interference value representing observer estimation, +.>For the desired lift in the geographical coordinate system, +.>Is->Is the first derivative of (2), and->；
Secondly, the design of the attitude loop disturbance observer is carried out, and auxiliary variables are used for the designDesign of observer gain matrixI.e. generate +.>A 3 x 3 square matrix of diagonal elements:
,
wherein , indicating the angular velocity of the body,/-, and>representation->First derivative of>Representing unmanned aerial vehicle moment of inertia, +.>Indicating the desired moment +.>Indicating disturbance moment->Representing the disturbance moment value estimated by the observer, +.>Representation->Is a first derivative of (a).
Further, the fifth step includes: the design of the sliding mode control law is carried out and is divided into two parts, namely a position ring and an attitude ring:
for a pair ofThe axis control law is designed and the disturbance is compensated, and an axis direction dynamics equation is given first:
,
wherein , representing unmanned plane position +.>Second derivative of>Desired acceleration for control input +.>Is an interference force;
defining the amount of position errorDesign slide face->And adopts an exponential approach lawObtain->Kinematics control law in axial direction:
,
wherein , and->Respectively representing the expectations +.>Shaft position and actual position->， />，/>Are all design parameters, sgn represents a sign function, superscript ++>Represents the first derivative, superscript ++>Representing the second derivative.
Selecting Lyapunov functionWherein s is a function symbol, which proves that the method only needs to satisfyNamely, the stability of the position ring is satisfied:
,
wherein, superscriptRepresenting the first derivative. Obtained by the above formula when->When standing, the wearer is strapped with the item of clothing>The constant is established, and the unmanned plane position loop control system is stable;
design of sliding mode control law for rotary motion and definition , wherein />Indicating the rotation angle of the machine body coordinate system relative to the geographic coordinate system, < ->For its three elements-> , wherein />Is->First derivative, ->Is->Then the original kinetic equation +.>Is converted into the following form:
,
wherein ,represents->Element(s)>， ，/>，/> ，/>Three moment of inertia representing unmanned aerial vehicle, +.>Indicating moment->Is>Representation->Is>Representing the angular velocity of the unmanned aerial vehicle in a geographic coordinate system, diag representing the generation of a diagonal matrix, superscript +.>Represents the first derivative, superscript ++>Representing the second derivative.
Definition of the definition, wherein />Three elements representing the euler angles,for the three elements of the desired Euler angle, a sliding surface is designed +.>, wherein />，/>Representation ofAnd adopts the exponential approach law +.>A control law of the rotational movement is obtained:
,
wherein ,indicating the desired angle +.>Second derivative of>Representation->Is the i-th element of (a);
selecting Lyapunov functionProve that only the +.>Namely, the stability of the attitude ring is satisfied;
the sliding mode control law is adopted to eliminate the flutter phenomenonReplaced by->Wherein:
,
where k is a parameter of the desired design.
The invention has the beneficial effects that:
the unmanned aerial vehicle control system can realize high-precision flight of the unmanned aerial vehicle and simultaneously ensure that the unmanned aerial vehicle has safe and stable control capability. Compared with the traditional flight control method, the method provided by the invention has the advantages that firstly, a natural rainfall impact quantification model is provided for the disturbance of rainfall on the unmanned aerial vehicle based on key factors such as the final rainfall speed, the rain drop spectrum, the rain drop shape and the like, and the natural rainfall impact quantification model is combined with the traditional unmanned aerial vehicle dynamic model to obtain the rain-resistant dynamic model based on the four-rotor unmanned aerial vehicle. Then, on the basis, an interference observer of a position ring and an attitude ring of the unmanned aerial vehicle is respectively designed, and the interference observer is applied to the design of a sliding mode control law. The invention can be applied to most of the existing unmanned aerial vehicles with certain waterproof capability, so as to truly endow the unmanned aerial vehicles with the capability of resisting rain in a rainfall environment, and ensure that the unmanned aerial vehicles still have higher flight quality in the rain.
Drawings
FIG. 1 is a flow chart of a method of hierarchical anti-jamming control of a quad-rotor unmanned helicopter for rainfall disturbance according to the present invention;
fig. 2 is a schematic diagram of the unmanned aerial vehicle speed decomposition definition for the translational dynamics of a quad-rotor unmanned aerial vehicle according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The design of the controller of the unmanned aerial vehicle is divided into position loop control and attitude loop control of the unmanned aerial vehicle. In the actual flight process, the working frequency of the unmanned aerial vehicle attitude ring is far greater than that of the position ring, so that controllers of the unmanned aerial vehicle position ring and the attitude ring can be designed separately.
As shown in fig. 1, the layering anti-interference control method for the four-rotor unmanned aerial vehicle for rainfall interference specifically comprises the following steps:
firstly, building a rainwater impact load model aiming at different rainfall intensities:
aiming at the relation between elements such as the final rainfall speed, the raindrop spectrum and the like and rainfall intensity, the following rain impact load model can be constructed by combining the raindrop movement characteristics:
1. assuming rainfall intensity R (mm/h), the follow-up related parameters are convenient to determine;
2. the rain drop spectrum (distribution of the number of rain drops in a unit volume of air with the size of the rain drops), i.e. the M-P distribution (Marshall and Palmer) N (D):
,
wherein , individual/m 3/mm,/d.o>Is a slope factor, ++>D represents the diameter of raindrops in mm.
3. Calculating the final speed of raindrops with different diameters ：
,
4. Calculating single drop impact force of each diameter raindrop ：
wherein , the rain drop density is water density +.>， />Indicating the rainfall speed;
5. calculating impact force generated by impacting all raindrops in unit volume of air to plane：
,
6. Calculating average velocity of raindrops in unit volume of air ：
,
Only raindrops with a diameter in the range of 0-2.5mm are counted here, since the raindrops of natural rainfall are generally between 0.1-6.5mm in diameter. Wherein, the rain drops with the diameter smaller than 2.0mm account for the majority, and the deformation of the rain drops is very small in the falling process, and the ball shape is basically maintained.
7. Calculating the impact force of the raindrops in unit time, further calculating the impact load of the raindrops, and calculating the impact volume flow in unit time ：
,
S represents the area of the equivalent impacted plane and can be directly taken as the horizontal projection area of the unmanned aerial vehicle.
8. Calculating the impact force of a given impact surface in a unit time ：
9. Calculating the impact load of a given impact surface at a certain moment：
,
10. And obtaining an impact load function depending on the rainfall intensity through function fitting according to the corresponding relation between different rainfall intensities and the impact load thereof.
Secondly, building a rainfall dynamics model based on the unmanned aerial vehicle according to the rainfall impact load model:
the four-rotor unmanned aerial vehicle dynamics equation is known as:
,
wherein , is the body coordinate system, is->Is a geographic coordinate system; m is unmanned aerial vehicle mass, < >>First derivative representing speed of the drone in geographical coordinate system,/->Indicating the acceleration of gravity>Representing a rotation matrix required for transforming the coordinates of the unmanned aerial vehicle body coordinate system into the coordinates of the geographical coordinate system,/->Representing the thrust force generated by the unmanned aerial vehicle under the coordinate system of the machine body,/->Represents the angular velocity of the unmanned aerial vehicle in the body coordinate system, < ->Is->Is the first derivative of (a); />To control the moment +.>Is unmanned aerial vehicle moment of inertia.
As shown in fig. 2, for a four-rotor unmanned aerial vehicle power model considering rainfall interference, as known from the rainfall interference model, the influence of rainfall on the impact force of the unmanned aerial vehicle is related to the relative speed between the raindrops and the unmanned aerial vehicle, so that the related parameters of the speed of the unmanned aerial vehicle when in motion are necessarily considered, and the unmanned aerial vehicle is made to operate in a geographic coordinate systemRepresenting the speed of flight of a quadrotor unmanned aircraft, +.>Representation->At the position ofPlane projection, which is associated with->The included angle of the direction is->，/>Representation->At->Projection of a plane, which is associated with->The included angle of the direction is->。/>The plane is perpendicular to +.>。
Under the influence of unmanned aerial vehicle flight speed, average speed under rainfall natural conditionThe relative speed for the unmanned aerial vehicle can be decomposed into +.>Direction speed->And perpendicular to->Direction speed->，
,
,
From the rainfall interference model based on unmanned aerial vehicle, it is known that rainwater is inPlane and->The impact load of the plane is respectively equal to->、/>In relation, the impact load factor is defined>、/>The rainfall impact load is +.>Relationship with impact load when unmanned aerial vehicle hovers:
，
，
wherein , indicating that rainfall is +.>Impact load on plane->Indicating that rainfall is +.>Impact load on plane->Is the impact load of unmanned aerial vehicle when hovering.
Unmanned aerial vehicle is in orderWhen flying at speed, assume roll angle of +.>Pitch angle is +.>The rainfall impact force of the unmanned aerial vehicle during flight can be obtained:
，
，
wherein ,indicating that the drone is perpendicular to +.>Impact force applied in the plane direction +.>Indicating that the drone is perpendicular to +.>Impact force applied in the plane direction +.>Representing the horizontal projected area of the unmanned aerial vehicle.
From this, can consider unmanned aerial vehicle position kinematics model that unmanned aerial vehicle received rainfall impact to influence:
,
wherein , ，/> ，/>respectively representing the second derivative of the three-axis direction position information of the unmanned aerial vehicle under the geographic coordinate system, ，/>，/>three euler angles of the drone are shown, respectively.
Thirdly, generating a smooth track which can be realized by the unmanned aerial vehicle according to a differential flattening method:
the z-axis of the desired body coordinate system is expressed as: , wherein />Representing euclidean norms;
by means of and withRelated intermediate unit vector->(wherein->Indicating the desired yaw angle +.>And->Respectively indicate->And->) The other two axes represent:
,
wherein , ，/>，/>respectively represent +.>，/> ，/>Representation of the axis in the geographical coordinate system, +.>Representing the +.>Shaft rotation->Representation after angle;
due toThus the desired euler angle is obtained:
,
wherein ,representing the three-axis coordinates of the desired body coordinate system, +.>In order to achieve a desired rotation matrix,represents->Is->Element(s)>And->Representing the desired roll angle and pitch angle, respectively.
Fourthly, designing a position loop and attitude loop interference observer according to the established dynamic model:
first, the design of the position loop disturbance observer is carried out, by means of auxiliary variablesDesign of observer gain matrixI.e. generate +.>A 3 x 3 square matrix of diagonal elements:
,
wherein ,representation and->Acceleration in the geographical coordinate system concerned, +.>First derivative representing the position of the drone in the geographical coordinate system,/-> ，/>Interference value representing observer estimation, +.>For the desired lift in the geographical coordinate system, +.>Is->And notice +.>。
Secondly, the design of the attitude loop disturbance observer is carried out, and auxiliary variables are used for the designDesign of observer gain matrixI.e.Generate->A 3 x 3 square matrix of diagonal elements:
,
wherein , indicating the angular velocity of the body,/-, and>representation->First derivative of>Representing unmanned aerial vehicle moment of inertia, +.>Indicating the desired moment +.>Indicating disturbance moment->Representing the disturbance moment value estimated by the observer, +.>Representation->Is a first derivative of (a).
Fifthly, designing a sliding mode control law, and equally dividing the sliding mode control law into two parts, namely a position ring and an attitude ring:
due to rainfall influence, unmanned aerial vehicle is easy to have insufficient lifting force, only toThe axis control law is designed and designedInterference is compensated for by first giving +.>Axial dynamics equation:
,
wherein , representing unmanned plane position +.>Second derivative of>Desired acceleration for control input +.>Is an interference force;
defining the amount of position error （ />And->Respectively representing the expectations +.>Shaft position and actual position), design slip plane +.>And adopts the exponential approach law +.> （/> ，/>， />Are all design parameters, sgn denotes a sign function), get +.>Kinematics control law in axial direction:
,
wherein, superscriptRepresents the first derivative, superscript ++>Representing the second derivative.
Selecting Lyapunov functionWherein s is a function symbol, which proves that the method only needs to satisfyNamely, the stability of the position ring is satisfied:
,
wherein, superscriptRepresenting the first derivative. Obtained by the above formula when->When standing, the wearer is strapped with the item of clothing>The constant is established, and the unmanned plane position loop control system is stable;
slip-form control of rotary motionLaw design, definition （ />Indicating the rotation angle of the machine body coordinate system relative to the geographic coordinate system, < ->Three elements thereof), -a.about.>（ />Is->First derivative, ->Is->Three elements of (2) then the original kinetic equation +.>Is converted into the following form:
,
wherein ,represents->Element(s)>，/> ，/>，/> ，/>Three moment of inertia representing unmanned aerial vehicle, +.>Indicating moment->Is>Representation->Is>Representing the angular velocity of the unmanned aerial vehicle in a geographic coordinate system, diag representing the generation of a diagonal matrix, superscript +.>Represents the first derivative, superscript ++>Representing the second derivative.
Definition of the definition, wherein />Three elements representing the euler angles,for the three elements of the desired Euler angle, a sliding surface is designed +.>（/> ，/>Representation ofIs the first derivative of (c) and employs the exponential approach law +.>Obtaining the control law of the available rotary motion:
,
wherein ,indicating the desired angle +.>Second derivative of>Representation->Is the i-th element of (a);
selecting Lyapunov functionProve that only the +.>Namely, the stability of the attitude ring is satisfied;
the sliding mode control law is adopted to eliminate the flutter phenomenonReplaced by->Wherein:
,
where k is a parameter of the desired design.
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art.
Claims (3)
1. The layering anti-interference control method for the four-rotor unmanned aerial vehicle for rainfall interference is characterized by comprising the following steps of:
the first step, a rain impact load model aiming at different rainfall intensities is established, and the method comprises the following steps:
aiming at the relation of the final rainfall speed, the rain drop spectrum and the rainfall intensity, and combining the rain drop movement characteristics, the following rain impact load model is constructed:
(1) Assuming rainfall intensity R, wherein the unit is mm/h;
(2) The rain drop spectrum, i.e. the distribution of the number of rain drops in a unit volume of air with the size of the rain drops, i.e. the M-P distribution N (D), is calculated:
，
wherein ,individual/m 3 /mm，/>Is a slope factor, ++>D represents the diameter of raindrops, and the unit is mm;
(3) Calculating the final speed of raindrops with different diameters：
，
(4) Calculating single drop impact force of each diameter raindrop：
，
wherein ,is of raindrop density->Indicating the rainfall speed;
(5) Calculating impact force generated by impacting all raindrops in unit volume of air to plane：
，
(6) Calculating average velocity of raindrops in unit volume of air：
，
The diameter of the raindrops is 0-2.5mm;
(7) Calculating the impact force of the raindrops in unit time, further calculating the impact load of the raindrops, and calculating the impact volume flow in unit time：
，
S represents the area of an equivalent impacted plane, and the horizontal projection area of the unmanned aerial vehicle is taken;
(8) Calculating the impact force of a given impact surface in a unit time：
，
(9) Calculating the impact load of a given impact surface at a certain moment：
，
(10) Obtaining impact load functions depending on rainfall intensity through function fitting according to the corresponding relations between different rainfall intensities and impact loads of the different rainfall intensities;
the second step, a rainfall dynamics model based on the unmanned aerial vehicle is established according to the rainfall impact load model, and the second step comprises the following steps:
the four-rotor unmanned aerial vehicle dynamics equation is known as:
，
wherein ,is the body coordinate system, is->Is a geographic coordinate system; m is unmanned aerial vehicle mass, < >>First derivative representing speed of the drone in geographical coordinate system,/->Indicating the acceleration of gravity>Representing a rotation matrix required for transforming the coordinates of the unmanned aerial vehicle body coordinate system into the coordinates of the geographical coordinate system,/->Representing the thrust force generated by the unmanned aerial vehicle under the coordinate system of the machine body,/->Represents the angular velocity of the unmanned aerial vehicle in the body coordinate system, < ->Is->Is the first derivative of (a); />For unmanned aerial vehicle moment of inertia, +.>To control the moment;
in the geographic coordinate system, letRepresenting the speed of flight of a quadrotor unmanned aircraft, +.>Representation->At->Plane projection, which is associated with->The included angle of the direction is->，/>Representation->At->Projection of a plane, which is associated with->The included angle of the direction is->；The plane is perpendicular to +.>；
Under the influence of unmanned aerial vehicle flight speed, average speed under rainfall natural conditionRelative velocity resolution for unmanned aerial vehicleDirection speed->And perpendicular to->Direction speed->：
，
，
Obtaining rainwater from rainfall interference model based on unmanned aerial vehiclePlane and->The impact load of the plane is respectively equal to->、/>In relation, the impact load factor is defined>、/>Obtaining the rainfall impact load when considering the unmanned aerial vehicle flight speed +.>Relationship with impact load when unmanned aerial vehicle hovers:
，
，
wherein ,indicating that rainfall is +.>Impact load on plane->Indicating that rainfall is +.>Impact load on plane->Is the impact load of the unmanned aerial vehicle when hovering;
unmanned aerial vehicle is in orderWhen flying at speed, assume roll angle of +.>Pitch angle is +.>And obtaining rainfall impact force received by the unmanned aerial vehicle in flight:
，
，
wherein ,indicating that the drone is perpendicular to +.>Impact force applied in the plane direction +.>Indicating that the drone is perpendicular to +.>Impact force applied in the plane direction +.>Representing the horizontal projection area of the unmanned aerial vehicle;
from this, obtain the unmanned aerial vehicle's that considers unmanned aerial vehicle receives rainfall impact rainfall dynamics model:
，
wherein ,，/>，/>respectively representing the second derivative and the +.A. of the position information of the unmanned plane in the three-axis direction under the geographic coordinate system>，/>，Three Euler angles of the unmanned aerial vehicle are respectively represented;
thirdly, generating a smooth track which can be realized by the unmanned aerial vehicle according to a differential flattening method, wherein the method comprises the following steps of:
the z-axis of the desired body coordinate system is expressed as:, wherein />Representing euclidean norms;
by means of and withRelated intermediate unit vector->The other two axes represent:
，
wherein ,indicating the desired yaw angle +.>And->Respectively indicate->And->，/>，/>，/>Respectively represent +.>，/>，/>Representation of the axis in the geographical coordinate system, +.>Representing the +.>Shaft rotation->Representation after angle;
due toThus the desired euler angle is obtained:
，
wherein ,representing the three-axis coordinates of the desired body coordinate system, +.>For the desired rotation matrix, +.>Representative ofIs->Element(s)>And->Respectively representing a desired roll angle and pitch angle;
fourthly, designing a position ring and attitude ring interference observer according to the established rainfall dynamics model;
fifthly, designing a sliding mode control law to suppress disturbance based on the observed disturbance value.
2. The method for controlling layering antijamming of a four-rotor unmanned aerial vehicle for rainfall interference of claim 1, wherein the fourth step comprises:
first, the design of the position loop disturbance observer is carried out, by means of auxiliary variablesDesign of observer gain matrixI.e. generate +.>A 3 x 3 square matrix of diagonal elements:
，
wherein ,representation and->Acceleration in the geographical coordinate system concerned, +.>First derivative representing the position of the drone in the geographical coordinate system,/->，/>Interference value representing observer estimation, +.>For the desired lift in the geographical coordinate system, +.>Is->Is the first derivative of (2), and->；
Secondly, the design of the attitude loop disturbance observer is carried out, and auxiliary variables are used for the designDesign of observer gain matrixI.e. generate +.>A 3 x 3 square matrix of diagonal elements:
，
wherein ,indicating the angular velocity of the body,/-, and>representation->First derivative of>Representing unmanned aerial vehicle moment of inertia, +.>Indicating the desired moment +.>Indicating disturbance moment->Representing the disturbance moment value estimated by the observer, +.>Representation->Is a first derivative of (a).
3. The method for controlling layering antijamming of a four-rotor unmanned aerial vehicle for rainfall interference of claim 2, wherein the fifth step comprises: the design of the sliding mode control law is carried out and is divided into two parts, namely a position ring and an attitude ring:
for a pair ofThe axis control law is designed and the disturbances are compensated for by first giving +.>Axial dynamics equation:
，
wherein ,representing unmanned plane position +.>Second derivative of>Desired acceleration for control input +.>Is an interference force;
defining the amount of position errorDesign slide face->And adopts an exponential approach lawObtain->Kinematics control law in axial direction:
，
wherein ,and->Respectively representing the expectations +.>Shaft position and actual position->Are all design parameters, sgn represents a sign function, superscript ++>Represents the first derivative, superscript ++>Representing the second derivative;
selecting Lyapunov functionWherein s is a function symbol, proving that only +.>Namely, the stability of the position ring is satisfied:
，
wherein, superscriptRepresenting the first derivative; obtained by the above formula when->When standing, the wearer is strapped with the item of clothing>The constant is established, and the unmanned plane position loop control system is stable;
design of sliding mode control law for rotary motion and definition, wherein />Indicating the rotation angle of the machine body coordinate system relative to the geographic coordinate system, < ->For its three elements->, wherein />Is->First derivative, ->Is->Then the original kinetic equation +.>Is converted into the following form:
，
wherein ,represents->Element(s)>，/>，，/>，/>Three moment of inertia representing unmanned aerial vehicle, +.>Indicating moment->Is>Representation->Is>Representing the angular velocity of the unmanned aerial vehicle in a geographic coordinate system, diag representing the generation of a diagonal matrix, superscript +.>Represents the first derivative, superscript ++>Representing the second derivative;
definition of the definition, wherein />Three elements representing the euler angles,for the three elements of the desired Euler angle, a sliding surface is designed +.>, wherein />，/>Representation ofAnd adopts the exponential approach law +.>A control law of the rotational movement is obtained:
，
wherein ,indicating the desired angle +.>Second derivative of>Representation->Is the i-th element of (a);
selecting Lyapunov functionProve that only the +.>Namely, the stability of the attitude ring is satisfied;
the sliding mode control law is adopted to eliminate the flutter phenomenonReplaced by->Wherein:
，
where k is a parameter of the desired design.
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