CN103365296B - A kind of four rotor unmanned aircraft nonlinear object feedback flight control methods - Google Patents

A kind of four rotor unmanned aircraft nonlinear object feedback flight control methods Download PDF

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CN103365296B
CN103365296B CN201310272336.9A CN201310272336A CN103365296B CN 103365296 B CN103365296 B CN 103365296B CN 201310272336 A CN201310272336 A CN 201310272336A CN 103365296 B CN103365296 B CN 103365296B
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rotor unmanned
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鲜斌
刁琛
张垚
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天津大学
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Abstract

A kind of four rotor unmanned aircraft nonlinear object feedback flight control methods, comprising: 1) determine the kinematics model of four rotor unmanned aircrafts under inertial coordinates system and the kinetic model under body axis system; 2) four rotor unmanned aircraft attitude control systems are designed: the tracking error defining four rotor unmanned aircraft attitude angles and angular velocity; Designing filter carries out On-line Estimation to angular velocity signal and obtains the open loop dynamic equation of tracking error; Adopt the unknown function in neural network feedforward divided ring dynamic equation to estimate, and design four rotor unmanned aircraft attitude system control inputs; 3) four rotor unmanned aircraft Altitude control subsystems are designed: definition height tracing error and definition auxiliary filter tracking error; Height subsystem Controller gain variations.Present invention effectively prevents polarity problems, and reach the control effects of global stability, increased substantially the robust performance of system, significantly decrease the dependence of flight controller pair and airborne sensor.

Description

A kind of four rotor unmanned aircraft nonlinear object feedback flight control methods

Technical field

The present invention relates to a kind of four rotor unmanned aircraft gesture stability.Particularly relate to a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods.

Background technology

In recent years along with the development of material technology, microprocessor technology and sensor technology, four rotor unmanned aircrafts are subject to military and civilian boundary and pay close attention to widely.Have the features such as volume is little, lightweight, vertical takeoff and landing, accurately hovering due to it, four rotor unmanned aircrafts are widely used in the fields such as fire hazard monitoring, emergency response, indoor investigation.Four rotor unmanned aircrafts adopt symmetrical structure, are provided with the screw propeller of four fixing angles of attack, can be changed displacement and the attitude angle in three directions by the rotating speed of propeller blades.Reliable attitude and Altitude control can guarantee the safe flight of four rotor unmanned aircrafts, are also the bases of carrying out position of aircraft control.

Four traditional rotor unmanned aircraft gesture stability are mainly divided into two steps to complete.First, definition and description aircraft attitude in space.Then, by the method design controller of feedback of status, complete the control to four rotor unmanned aircraft attitude angle.In attitude description, generally adopt based on Eulerian angle attitude description angle method (periodical: IEEEConferenceonDecisionandControl at present; Author: TonCT, MackunisW; Publish days: 2012; Title of article: RobustAttitudeTrackingControlofaQuadrotorHelicopterinthe PresenceofUncertainty, the page number: 937-942), but there is polarity problems in this method, that is when aircraft reaches some attitude, Jacobi matrix in four rotor unmanned aircraft kinematical equations will define, and therefore said method has some limitations.In Controller gain variations, typical control algolithm mainly contains two large classes at present: overall-finished housing method and output feedack method.Wherein overall-finished housing method is according to the attitude angle of aircraft in flight course and the Real-time Feedback Design of Signal controller of angular velocity, and reaches the tracing control (periodical: TheInternationalConferenceonRecentAdvancesinSpaceTechnol ogies with reference to attitude track; Author: DikmenIC, ArisoyA, TemeltasH; Publish days: 2009; Title of article: AttitudeControlofaQuadrotor, the page number: 722-727).In actual applications, the prerequisite of these class methods is adopted to be accurately can measure four rotor unmanned aircraft angles and angular velocity.But, because the load capacity of four rotor unmanned aircraft bodies is limited, high-precision angular-rate sensor cannot be carried, to the measurement of vehicle rate, there is very large difficulty in actual applications.From the result delivered at present, the measurement major part for aircraft angle is under indoor environment, completes by vision capture systems.The shortcoming of these class methods is that cost is higher, and can only realize under indoor environment.Output feedback ontrol method be utilize four rotor unmanned aircraft output states (concerning with gesture stability, the i.e. attitude angle of four rotor unmanned aircrafts) CONTROLLER DESIGN, make aircraft follow the tracks of predetermined attitude track (periodical: IEEETransactionsonAutomaticControl; Author: SchlanbuschM, LoriaA, KristiansenR, NicklassonPJ; Publish days: 2012; Title of article: PD+BasedOutputFeedbackAttitudeControlofRigidBodies, the page number: 2146-2152; ).Because four rotor unmanned aircraft power belong to nonlinear system, be not suitable for separation principle, therefore Design of Observer and stability prove to have very high difficulty, and are difficult to the control effects reaching asymptotic tracking.

Can find based on above analysis, the subject matter that the design of four rotor unmanned aircraft attitude controllers faces comprises: the polarity problems that traditional Eulerian angle attitude description method has, and is difficult to the problem of accurately the whole system state of aircraft being carried out to Measurement accuracy.Except above 2 points, four rotor unmanned aircrafts are set up also has a lot of uncertainties in kinetic model accurately, and these uncertainties mainly come from the following aspects.The first, the non-linear resistance that aircraft is suffered in flight course and the moment of resistance, these nonlinear functions and the aircraft linear velocity in flight course is relevant with angular velocity, but is difficult to carry out accurate modeling to it.Second, parameter uncertainty is there is in four rotor unmanned aircraft kinetic models, because four rotor unmanned aircrafts are not quite similar in each load had in-flight, this change can cause the change of vehicle mass and moment of inertia, and the aerodynamics damping parameter in vehicle dynamics model is also difficult to carry out accurately identification.3rd, aircraft is easily subject to the impact of the external disturbances such as wind, system noise and ground effect in flight course, and these disturbance terms further increase the uncertainty of system.In mathematics, the feature of himself is had by these systematic uncertainties of research discovery, if On-line Estimation and compensation can be carried out by neural network algorithm and nonlinear robust control method to these uncertainties, then greatly can improve accuracy and the rapidity of controller.Be exactly utilize neural network algorithm to carry out on-line study to the non-linear resistance square in four rotor unmanned aircraft kinetic models specifically, and as feedforward part to compensating system, this can overcome the interference of system Unmarried pregnancy to system to a certain extent.Then non linear robust algorithm is utilized to compensate the external disturbances such as wind and neural network evaluated error, the final control effects improving controller.

In recent years, minority scientific research personnel starts trial and utilizes robust control method to design four rotor unmanned aircraft output feedback controllers, and achieves some initial achievements.The people such as Zou are in 2010 employing unit quaternion attitude description methods and with Chebyshev neural network for Flight Vehicle Design output feedback controller (periodical: IEEETransactionsonNeuralNetworks; Author: ZouAM, KumarKD, HouZG; Publish days: 2010; Title of article: Quaternion-BasedAdaptiveOutputFeedbackAttitudeControlofS pacecraftUsingChebyshevNeuralNetworks, the page number: 1457-1471).But these class methods can only realize tracking slash uniform bound follows the tracks of, and cannot realize large-scale Asymptotic Stability.The people such as Mayhew utilized unit quaternion attitude description method design one class output feedack attitude controller (periodical: IEEETransactionsonAutomaticControl in 2011; Author: MayhewCG, SanfeliceRG, TeelAR; Publish days: 2011; Title of article: Quaternion-BasedHybridControlforRobustGlobalAttitudeTrac king, the page number: 2555-2566).Obviously, the method can only realize the control to attitude, cannot simultaneously to highly carrying out tracing control.The technology report analyzing existing document at present can find polarity problems, modeling uncertainty and carry out Measurement accuracy to speed to be current four rotor unmanned aircraft attitudes and the main Problems existing of Altitude control.

Summary of the invention

Technical matters to be solved by this invention is, the four rotor unmanned aircraft nonlinear object feedback flight control methods providing a kind of output feedack based on hypercomplex number attitude description method to follow the tracks of.

The technical solution adopted in the present invention is: a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods, comprise the steps:

1) kinematics model of four rotor unmanned aircrafts under inertial coordinates system and the kinetic model under body axis system is determined;

2) design four rotor unmanned aircraft attitude control systems, comprising:

(1) tracking error of four rotor unmanned aircraft attitude angles and angular velocity is defined;

(2) designing filter carries out On-line Estimation to angular velocity signal and obtains the open loop dynamic equation of tracking error;

(3) adopt the unknown function in neural network feedforward divided ring dynamic equation to estimate, and design four rotor unmanned aircraft attitude system control inputs;

3) design four rotor unmanned aircraft Altitude control subsystems, comprising:

(1) height tracing error and definition auxiliary filter tracking error is defined;

(2) height subsystem Controller gain variations.

The kinematics model under inertial coordinates system described in step 1) is:

Definition effective unit hypercomplex number q (t) represents actual body axis system, and { B} is relative to the inertial coordinates system { attitude of I}.Relation between effective unit hypercomplex number q (t) and aerocraft real angular velocity omega (t) can be represented by following kinematical equation

q · = 1 2 B ( q ) ω

Wherein auxiliary function and { B} is to the inertial coordinates system { coordinate conversion matrix of I} for actual body axis system can be expressed as

R ( q ) = ( q o 2 - q v T q v ) I 3 + 2 q v q v T - 2 q o S ( q v )

Definition is with reference to body axis system { B d, corresponding reference units hypercomplex number q dt () represents with reference to body axis system { B drelative to inertial coordinates system { attitude of I}, reference angular velocities ω dt () represents with reference to reference body coordinate system { B drelative to inertial coordinates system { angular velocity of I}, reference units hypercomplex number q d(t) and aircraft reference angular velocities ω dt the relation between () can be represented by following kinematical equation

q d · = 1 2 B d ( q d ) ω d

Wherein with reference to body axis system { B dto the inertial coordinates system { coordinate conversion matrix of I} can be expressed as

R d ( q d ) = ( q od 2 - q vd T q vd ) I 3 + 2 q vd q vd T - 2 q od S ( q vd ) .

The kinetic model under body axis system described in step 1) is:

J ω · = S ( Jω ) ω + N ( ω ) + τ + D 1

Wherein angular velocity vector ω (t)=[ω 1(t) ω 2(t) ω 3(t)] tbe defined in body axis system and { in B}, represent that { angular velocity of I}, matrix J represents the moment of inertia matrix of aircraft to aircraft, and S () represents an antisymmetric matrix, and its expression is relative to inertial coordinates system

S ( ξ ) = 0 - ξ 3 ξ 2 ξ 3 0 - ξ 1 - ξ 2 ξ 1 0 ∀ ξ = ξ 1 ξ 2 ξ 3 T

Matrix N (ω) represents the non-linear unknown moment of resistance vector relevant with angular velocity omega (t) that aircraft is subject in flight course, and u (t) represents raising force, τ (t)=[τ 1(t) τ 2(t) τ 3(t)] trepresent the rotating torque in three directions, D 1(t) and D 2(t) represent aircraft be subject to unknown time become disturbance, its expression is

D 1(t)=[d 1(t)d 2(t)d 3(t)] T

D 2(t)=d 4(t)

Constant m represents vehicle mass, and z (t) represents aircraft altitude, k zrepresent aerodynamics damping parameter, g=9.81m/s 2represent acceleration of gravity, θ (t) and represent the angle of pitch and the roll angle of aircraft.Because aircraft exists modeling uncertainty, therefore the present invention supposes vehicle mass m, moment of inertia matrix J, aerodynamic coefficient k zfor unknown constant.

Step 2) described in definition four rotor unmanned aircraft attitude angle and the tracking error of angular velocity be:

e 0 = q 0 q 0 d + q v T q vd

e v=q 0dq v-q 0q vd+S(q v)q vd

At actual body coordinate system, { { B} relatively and reference body coordinate system { B to define actual body coordinate system in B} dangular velocity for

ω ~ = ω - R ~ ω d

Wherein { B} is to reference body coordinate system { B to represent actual body coordinate system dcoordinate conversion matrix, its expression formula is

R ~ = R R d T = ( e o 2 - e v T e v ) I 3 + 2 e v e v T - 2 e o S ( e v )

Tracking error with angular velocity between relation can represent with following kinematical equation

e · q = 1 2 B e ( e q ) ω ~

Wherein and

Step 2) described in designing filter On-line Estimation is carried out to angular velocity signal and the open loop dynamic equation obtaining tracking error comprises: adopt wave filter to carry out On-line Estimation to the angular velocity signal of aircraft in flight course, expression formula is

e · f = - e f + r f

r f=p-(k 2+1)e v

p · = - r f - ( k 2 + 1 ) ( e v + e f ) - e f + e v ( 1 - e v T e v ) 2

Wherein e f(t) and represent filter output signal, represent wave filter auxiliary function, represent positive ride gain, p (t) and e ft the starting condition of () is set to p (0)=0 and e respectively f(0)=0.Definition auxiliary variable there is following form

η = e v + e · v + e f

Can obtain auxiliary variable η (t) differentiate

J ev η · = - C * η - k 2 J ev η + 1 2 B d - T D 1 + N ev + f d + τ eq

Wherein auxiliary function expression formula be

N ev = C * ( e f + e v ) + J ev ( η - e v + e v ( 1 - e v T e v ) 2 )

- 2 J ev e f - N *

Wherein, auxiliary function with there is following form

J ev = B ev - T J B ev - 1

P = B ev - 1

Auxiliary function and equivalent control input be defined as

C * = - J ev P · - 1 P - 2 P T S ( JP e · v ) P

N * = - 1 2 P T J [ S ( 2 P e · v ) R ~ ω d - R ~ ω · d ] + P T S ( P e · v ) J R ~ ω d

+ 1 2 P T S ( R ~ ω d ) J R ~ ω d + P T S ( R ~ ω d ) JP e · v - 1 2 P T D 1

+ 1 2 B d - T D 1 - 1 2 P T N ( ω ) + 1 2 B d - T N ( ω d )

τ eq = 1 2 B ev - T τ = 1 2 P T τ

Continuously and the unknown function of bounded be defined as

f d = 1 2 B d - T N ( ω d ) + J ω · d + 1 2 S ( ω d ) J ω d .

Step 2) described in employing neural network feedforward divided ring dynamic equation in unknown function carry out estimation and be,

Use neural network by continuous function f dt () is expressed as

f d=W Tσ(V Tχ)+ε(χ)

Wherein bounded input with represent neural network ground floor and the second layer and the ideal weight between the second layer and third layer, σ () represents excitation function, represent approximate error;

Feedover with nerve net represent continuous function f dt the estimation of (), its expression formula is

f ^ = W ^ T σ ( V ‾ T χ )

Wherein represent the On-line Estimation to ideal weight W, for constant value matrix, excitation function σ () is chosen for renewal function be designed to

Wherein ξ 1(t) and represent auxiliary signal, with represent positive ride gain, represent that positive definite diagonal angle is with new gain matrix, for saturation function.Can be drawn by neural network expression formula and bounded.

Step 2) described in design four rotor unmanned aircraft attitude system control inputs be following form

τ eq = - K 1 sgn ( e v + e f ) + ( k 2 + 1 ) r f - f ^ - e v ( 1 - e v T e v ) 2

Wherein represent positive definite, diagonal angle gain matrix, function sgn () is defined as

sgn(α)=[sg(α 1)sgn(α 2)sgn(α 3)] T

For any vectorial α=[α 1α 2α 3] t.

Definition height tracing error described in step 3) and definition auxiliary filter tracking error are

Definition height tracing error for

e z=z d-z

Wherein represent the desired trajectory of height.The present invention adopts the linear velocity of wave filter to four rotor unmanned aircraft short transverses to carry out On-line Estimation, and designing filter has following structure

e · fz = - e fz + r fz e fz ( 0 ) = 0

r fz=p z-(k 2z+1)e z

p · z = - r fz - ( k 2 z + 1 ) ( e z + r fz ) + e z - e fz

p z(0)=(k 2z+1)e z(0)

Wherein e fz(t) and represent filter output signal, represent wave filter auxiliary function, represent positive ride gain.Design assistant signal there is following form

η z = e · z + e z + r fz .

Height subsystem Controller gain variations described in step 3) is

Four rotor unmanned aircraft height subsystem kinetic models are rewritten as

m z · · = - k z z · - mg + u eq + d 4

Wherein equivalent control input be defined as

Mapping relations between Eulerian angle and unit quaternion can be expressed as

θ=arcsin(2(q 0q 2-q 1q 3))

To auxiliary signal η z(t) differentiate, and be multiplied by vehicle mass m in both members simultaneously and can obtain

m η · z = - k 2 z m η z + N z - m ( 2 r fz + e fz ) - u eq

Wherein auxiliary function be defined as

N z = k z z · + mg + m z · · d - d 4

Design assistant function due to z d(t) and for limited function, therefore, it is possible to prove N zd(t) and it is limited function.Formula (39) can be rewritten as following form

m η · z = - k 2 z m η z + N zd + N ~ z - u eq

Wherein auxiliary function be defined as

N ~ z = N z - N zd - m ( 2 r fz + e fz )

Design four rotor unmanned aircraft height subsystem equivalent control input u eqt () has following form

u eq=k 1zsgn(e z+e fz)-(k 2z+1)r fz+e z

Wherein k 1zand k 2zrepresent positive ride gain, sgn () represents standard signum function.

Four rotor unmanned aircraft nonlinear object feedback flight control methods of the present invention, adopt unit quaternion attitude description method design controller, fundamentally solve the polarity problems that traditional Eulerian angle attitude description method has; Utilize the linear velocity of wave filter to the angular velocity of four rotor unmanned aircrafts in flight course and short transverse to carry out On-line Estimation, realize aircraft output feedback ontrol, solve the problem being difficult to speed be carried out to Measurement accuracy; 3, the control method adopting neural network algorithm to combine with nonlinear robust control algorithm, carries out on-line study and compensation for there is modeling uncertainty in four rotor unmanned aircraft kinetic models.The present invention has following features:

1, global stability.Traditional Eulerian angle controller generally carries out linearization process to system dynamics equation when designing, designed controller is linear controller, at system balancing point place, traditional linear controller has good control effects, but when system far from equilibrium point, control effects can decline to some extent, even produces wild effect.The present invention is directed to four rotor unmanned flight kinetic models and adopt unit quaternion attitude description method design gamma controller, effectively prevent polarity problems, and reach the control effects of global stability.

2, strong robustness.During traditional four rotor unmanned aircraft Controller gain variations, suppose that vehicle dynamics model is accurate known models.The present invention adopts neural network algorithm and effectively suppresses the Unmarried pregnancy existed in system dynamics model in conjunction with Robust Control Algorithm, thus has increased substantially the robust performance of system.

3, senseless control.During traditional four rotor unmanned aircraft Controller gain variations, suppose that the whole state of aircraft can Measurement accuracy, but because four rotor unmanned aircraft load capacity are limited, high-precision speed pickup cannot be carried, therefore be difficult to ensure to realize Measurement accuracy to vehicle rate and linear velocity.The present invention adopts wave filter to carry out On-line Estimation to attitude of flight vehicle angular velocity and short transverse linear velocity, does not need the feedback signal of vehicle rate and short transverse linear velocity, thus significantly decreases the dependence of flight controller pair and airborne sensor.

Accompanying drawing explanation

Fig. 1 a is four rotor unmanned aircraft quaternion components 1 tracking error curve figure;

Fig. 1 b is four rotor unmanned aircraft quaternion components 2 tracking error curve figure;

Fig. 1 c is four rotor unmanned aircraft quaternion components 3 tracking error curve figure;

Fig. 1 d is four rotor unmanned aircraft quaternion components 4 tracking error curve figure;

Fig. 2 a is four rotor unmanned aircraft quaternion components 1 curve maps;

Fig. 2 b is four rotor unmanned aircraft quaternion components 2 curve maps;

Fig. 2 c is four rotor unmanned aircraft quaternion components 3 curve maps;

Fig. 2 d is four rotor unmanned aircraft quaternion components 4 curve maps;

Fig. 3 a is four rotor unmanned aircraft roll angle curve maps;

Fig. 3 b is four rotor unmanned aircraft angle of pitch curve maps;

Fig. 3 c is four rotor unmanned aircraft crab angle curve maps;

Fig. 4 a tetra-rotor unmanned aircraft angular velocity in roll curve map;

Fig. 4 b tetra-rotor unmanned aircraft rate of pitch curve map;

Fig. 4 c tetra-rotor unmanned aircraft yaw rate curve map;

Fig. 5 a tetra-rotor unmanned aircraft elevation references geometric locus figure;

Fig. 5 b tetra-rotor unmanned aircraft height geometric locus figure;

Fig. 5 c tetra-rotor unmanned aircraft height error curve map;

Fig. 6 a is that four rotor unmanned aircraft controllers export τ 1curve map;

Fig. 6 b is that four rotor unmanned aircraft controllers export τ 2curve map;

Fig. 6 c is that four rotor unmanned aircraft controllers export τ 3curve map;

Fig. 6 d is that four rotor unmanned aircraft controllers export τ 4curve map;

Fig. 7 a is four rotor unmanned aircraft first screw propeller propelling power curve maps;

Fig. 7 b is four rotor unmanned aircraft second screw propeller propelling power curve maps;

Fig. 7 c is four rotor unmanned aircrafts the 3rd screw propeller propelling power curve map;

Fig. 7 d is four rotor unmanned aircraft quadruple screw propeller propelling power curve maps;

Fig. 8 a is four rotor unmanned aircraft first revolution speed of propeller curve maps;

Fig. 8 b is four rotor unmanned aircraft second revolution speed of propeller curve maps;

Fig. 8 c is four rotor unmanned aircrafts the 3rd revolution speed of propeller curve maps;

Fig. 8 d is four rotor unmanned aircraft quadruple screw propeller speed curves figure;

Fig. 9 a is that neural network exports curve map;

Fig. 9 b is that neural network exports curve map;

Fig. 9 c is that neural network exports curve map.

Embodiment

Below in conjunction with embodiment and accompanying drawing, four rotor unmanned aircraft nonlinear object feedback flight control methods of the present invention are described in detail.

Four rotor unmanned aircraft nonlinear object feedback flight control methods of the present invention, comprise the steps:

1) kinematics model of four rotor unmanned aircrafts under inertial coordinates system and the kinetic model under body axis system is determined:

Kinematics model under inertial coordinates system is:

Definition effective unit hypercomplex number q (t) represents actual body axis system, and { B} is relative to the inertial coordinates system { attitude of I}.Relation between effective unit hypercomplex number q (t) and aerocraft real angular velocity omega (t) can be represented by following kinematical equation

q · = 1 2 B ( q ) ω

Wherein auxiliary function and { B} is to the inertial coordinates system { coordinate conversion matrix of I} for actual body axis system can be expressed as

R ( q ) = ( q o 2 - q v T q v ) I 3 + 2 q v q v T - 2 q o S ( q v )

Definition is with reference to body axis system { B d, corresponding reference units hypercomplex number q dt () represents with reference to body axis system { B drelative to inertial coordinates system { attitude of I}, reference angular velocities ω dt () represents with reference to reference body coordinate system { B drelative to inertial coordinates system { angular velocity of I}, reference units hypercomplex number q d(t) and aircraft reference angular velocities ω dt the relation between () can be represented by following kinematical equation

q d · = 1 2 B d ( q d ) ω d

Wherein and with reference to body axis system { B dto the inertial coordinates system { coordinate conversion matrix of I} can be expressed as

R d ( q d ) = ( q od 2 - q vd T q vd ) I 3 + 2 q vd q vd T - 2 q od S ( q vd )

The described kinetic model under body axis system is:

J ω · = S ( Jω ) ω + N ( ω ) + τ + D 1

Wherein angular velocity vector ω (t)=[ω 1(t) ω 2(t) ω 3(t)] tbe defined in body axis system and { in B}, represent that { angular velocity of I}, matrix J represents the moment of inertia matrix of aircraft to aircraft, and S () represents an antisymmetric matrix, and its expression is relative to inertial coordinates system

S ( ξ ) = 0 - ξ 3 ξ 2 ξ 3 0 - ξ 1 - ξ 2 ξ 1 0 ∀ ξ = ξ 1 ξ 2 ξ 3 T .

Matrix N (ω) represents the non-linear unknown moment of resistance vector relevant with angular velocity omega (t) that aircraft is subject in flight course, and u (t) represents raising force, τ (t)=[τ 1(t) τ 2(t) τ 3(t)] trepresent the rotating torque in three directions, D 1(t) and D 2(t) represent aircraft be subject to unknown time become disturbance, its expression is

D 1(t)=[d 1(t)d 2(t)d 3(t)] T

D 2(t)=d 4(t)

Constant m represents vehicle mass, and z (t) represents aircraft altitude, k zrepresent aerodynamics damping parameter, g=9.81m/s 2represent acceleration of gravity, θ (t) and represent the angle of pitch and the roll angle of aircraft.Because aircraft exists modeling uncertainty, therefore the present invention supposes vehicle mass m, moment of inertia matrix J, aerodynamic coefficient k zfor unknown constant.

2) design four rotor unmanned aircraft attitude control systems, comprising:

(1) tracking error defining four rotor unmanned aircraft attitude angles and angular velocity is:

e 0 = q 0 q 0 d + q v T q vd

e v=q 0dq v-q 0q vd+S(q v)q vd

At actual body coordinate system, { { B} relatively and reference body coordinate system { B to define actual body coordinate system in B} dangular velocity for

ω ~ = ω - R ~ ω d

Wherein { B} is to reference body coordinate system { B to represent actual body coordinate system dcoordinate conversion matrix, its expression formula is

R ~ = R R d T = ( e o 2 - e v T e v ) I 3 + 2 e v e v T - 2 e o S ( e v )

Tracking error e q ( t ) = e o ( t ) e v T ( t ) T With angular velocity between relation can represent with following kinematical equation

e · q = 1 2 B e ( e q ) ω ~

Wherein and

(2) designing filter carries out On-line Estimation to angular velocity signal and obtains the open loop dynamic equation of tracking error, comprising:

Adopt wave filter to carry out On-line Estimation to the angular velocity signal of aircraft in flight course, expression formula is

e · f = - e f + r f

r f=p-(k 2+1)e v

p · = - r f - ( k 2 + 1 ) ( e v + e f ) - e f + e v ( 1 - e v T e v ) 2

Wherein e f(t) and represent filter output signal, represent wave filter auxiliary function, represent positive ride gain, p (t) and e ft the starting condition of () is set to p (0)=0 and e respectively f(0)=0.Definition auxiliary variable there is following form

η = e v + e · v + e f

Can obtain auxiliary variable η (t) differentiate

J ev η · = - C * η - k 2 J ev η + 1 2 B d - T D 1 + N ev + f d + τ eq

Wherein auxiliary function expression formula be

N ev = C * ( e f + e v ) + J ev ( η - e v + e v ( 1 - e v T e v ) 2 )

-2J eve f-N *

Wherein, auxiliary function with there is following form

J ev = B ev - T J B ev - 1

P = B ev - 1

Auxiliary function and equivalent control input be defined as

C * = - J ev P · - 1 P - 2 P T S ( JP e · v ) P

N * = - 1 2 P T J [ S ( 2 P e · v ) R ~ ω d - R ~ ω · d ] + P T S ( P e · v ) J R ~ ω d

+ 1 2 P T S ( R ~ ω d ) J R ~ ω d + P T S ( R ~ ω d ) JP e · v - 1 2 P T D 1

+ 1 2 B d - T D 1 - 1 2 P T N ( ω ) + 1 2 B d - T N ( ω d )

τ eq = 1 2 B ev - T τ = 1 2 P T τ

Continuously and the unknown function of bounded be defined as

f d = 1 2 B d - T N ( ω d ) + J ω · d + 1 2 S ( ω d ) J ω d .

(3) adopt the unknown function in neural network feedforward divided ring dynamic equation to estimate, and design four rotor unmanned aircraft attitude system control inputs;

It is use neural network by continuous function f that unknown function in described employing neural network feedforward divided ring dynamic equation carries out estimation dt () is expressed as

f d=W Tσ(V Tχ)+ε(χ)

Wherein bounded input χ = 1 q d T ω d T ω · d T T , with represent neural network ground floor and the second layer and the ideal weight between the second layer and third layer, σ () represents excitation function, represent approximate error;

Feedover with nerve net represent continuous function f dt the estimation of (), its expression formula is

f ^ = W ^ T σ ( V ‾ T χ )

Wherein represent the On-line Estimation to ideal weight W, for constant value matrix, excitation function σ () is chosen for renewal function be designed to

Wherein ξ 1(t) and represent auxiliary signal, with represent positive ride gain, represent that positive definite diagonal angle is with new gain matrix, for saturation function.Can be drawn by neural network expression formula and bounded;

Described design four rotor unmanned aircraft attitude system control inputs is following form

τ eq = - K 1 sgn ( e v + e f ) + ( k 2 + 1 ) r f - f ^ - e v ( 1 - e v T e v ) 2

Wherein represent positive definite, diagonal angle gain matrix, function sgn () is defined as

sgn(α)=[sgn(α 1)sgn(α 2)sgn(α 3)] T

For any vectorial α=[α 1α 2α 3] t.

3) design four rotor unmanned aircraft Altitude control subsystems, comprising:

(1) define height tracing error and define auxiliary filter tracking error and be;

Definition height tracing error for e z=z d-z

Wherein represent the desired trajectory of height.The present invention adopts the linear velocity of wave filter to four rotor unmanned aircraft short transverses to carry out On-line Estimation, and designing filter has following structure

e · fz = - e fz + r fz e fz ( 0 ) = 0

r fz=p z-(k 2z+1)e z

p · z = - r fz - ( k 2 z + 1 ) ( e z + r fz ) + e z - e fz

p z(0)=(k 2z+1)e z(0)

Wherein e fz(t) and represent filter output signal, represent wave filter auxiliary function, represent positive ride gain.Design assistant signal there is following form

η z = e · z + e z + r fz

(2) height subsystem Controller gain variations is

Four rotor unmanned aircraft height subsystem kinetic models are rewritten as

m z · · = - k z z · - mg + u eq + d 4

Wherein equivalent control input be defined as

Mapping relations between Eulerian angle and unit quaternion can be expressed as

θ=arcsin(2(q 0q 2-q 1q 3))

To auxiliary signal η z(t) differentiate, and be multiplied by vehicle mass m in both members simultaneously and can obtain

m η · z = - k 2 z m η z + N z - m ( 2 r fz + e fz ) - u eq

Wherein auxiliary function be defined as

N z = k z z · + mg + m z · · d - d 4

Design assistant function due to zd (t) and for limited function, therefore, it is possible to prove N zd(t) and it is limited function.Formula (39) can be rewritten as following form

m η · z = - k 2 z m η z + N zd + N ~ z - u eq

Wherein auxiliary function be defined as

N ~ z = N z - N zd - m ( 2 r fz + e fz )

Design four rotor unmanned aircraft height subsystem equivalent control input u eqt () has following form

u eq=k 1zsgn(e z+e fz)-(k 2z+1)r fz+e z

Wherein k 1zand k 2zrepresent positive ride gain, sgn () represents standard signum function.

For verifying that four rotor unmanned aircraft nonlinear object feedback flight control methods of the present invention are to the control effects of four rotor unmanned aircraft attitudes and height subsystem, the present invention utilizes vehicle dynamics model to carry out numerical simulation to this controller.Four rotor unmanned aircraft moment of inertia matrix are J=diag (1.25,1.25,2.5) kgm 2, vehicle mass m=2kg, Aerodynamic parameter k z=0.01Ns/m, the expression formula of non-linear resistance square N (ω) is

N ( ω ) = g 1 + g 2 | ω 1 | 0 0 0 g 3 + g 4 | ω 1 | 0 0 0 g 5 + g 6 ( ω 1 ) ω

Wherein aerodynamic coefficient g i=0.065Nms/rad, i=1 ... 6.Aircraft original state is set as

z(0)=0mq 0(0)=0.9486

q v(0)=[0.18260.18260.1826] T

Aircraft reference angular velocities ω dt () is set as

ω d=[0.3cos(t)0.3cos(t)0.3cos(t)] Trad/s

Elevation references track is set as step function z d=2m is through firstorder filter G cresponse curve after the process of (s)=1/ (s+1).Reference units hypercomplex number q dt the starting condition of () is set as

q od(0)=1q vd(0)=[000] T

In kinetic model, external disturbance is set to

d 1=d 2=d 3=0.2sin(t)Nm

d 4=4sin(t)N

Ride gain is chosen for

K 1=diag(555)k 2=20k 1z=3k 2z=15

T=diag{10010010050505050502050}

In neural network feedforward renewal function, the bound of saturation function is set as 100 and-100.

The Flutter Problem brought for avoiding sign function, in numerical simulation, adopts standard saturation function to replace sign function.Fig. 1 a, Fig. 1 b, Fig. 1 c, Fig. 1 d represent four rotor unmanned aircraft Attitude Tracking errors.Can be found out by figure, error e vt () went to zero the 10th second time.Fig. 2 a, Fig. 2 b, Fig. 2 c, Fig. 2 d represent the attitude curve adding the rear aircraft of neural network feedforward in control inputs.Because unit quaternion attitude description method is directly perceived not, therefore the present invention utilizes the transformational relation between unit quaternion and Eulerian angle to calculate the simulation curve of Eulerian angle.Fig. 3 a, Fig. 3 b, Fig. 3 c represent the attitude angle simulation curve of four rotor unmanned aircrafts.Fig. 4 a, Fig. 4 b, Fig. 4 c represent the angular velocity curve of aircraft, can be found out by curve, and four rotor unmanned aircraft angular velocity can follow the tracks of the cosine curve that amplitude is 0.3rad.Fig. 5 a, Fig. 5 b, Fig. 5 c represent the aircraft pursuit course of four rotor unmanned aircraft short transverses, can be found out by figure, and height error went to zero at about the 10th second, and tracking error remain on ± 0.5m within the scope of.Fig. 6 a, Fig. 6 b, Fig. 6 c, Fig. 6 d represent that four rotor unmanned aircraft controllers export, because aircraft is subject to the impact of resistance and the moment of resistance in flight course shown in scheming, therefore controller exports the phenomenon with fluctuation, but four control inputs all keep in the reasonable scope.Fig. 7 a, Fig. 7 b, Fig. 7 c, Fig. 7 d represent the propelling power of four rotor unmanned aircrafts, four screw propellers, the rotating speed of Fig. 8 a, Fig. 8 b, Fig. 8 c, Fig. 8 d, expression four screw propellers, can be found out by figure, four angle of rake propelling powers of aircraft and revolution speed of propeller are all in rational scope.Fig. 9 a, Fig. 9 b, Fig. 9 c represent that neural network exports, and can be found out by figure, and neural network reached stable the 5th second time.

Above simulation result shows that the nonlinear tracking control device designed by the present invention has in the probabilistic situation of modeling, still can make four rotor unmanned aircrafts, three attitude angle and the predetermined reference locus of height tracing.Can find out from control inputs curve, four angle of rake propelling powers of aircraft and revolution speed of propeller are all in rational scope, and therefore this controller has good control effects and stronger practicality.

Claims (8)

1. four rotor unmanned aircraft nonlinear object feedback flight control methods, is characterized in that, comprise the steps:
1) determine the kinematics model of four rotor unmanned aircrafts under inertial coordinates system and the kinetic model under body axis system, the described kinematics model under inertial coordinates system is:
Definition effective unit hypercomplex number q (t) represents that { { attitude of I}, the relation between effective unit hypercomplex number q (t) and aerocraft real angular velocity omega (t) can be represented by following kinematical equation B} actual body axis system relative to inertial coordinates system
q · = 1 2 B ( q ) ω
Wherein auxiliary function and { B} is to the inertial coordinates system { coordinate conversion matrix of I} for actual body axis system can be expressed as
R ( q ) = ( q o 2 - q v T q v ) I 3 + 2 q v q v T - 2 q o S ( q v )
Definition is with reference to body axis system { B d, corresponding reference units hypercomplex number q dt () represents with reference to body axis system { B drelative to inertial coordinates system { attitude of I}, reference angular velocities ω dt () represents reference body machine coordinate system { B drelative to inertial coordinates system { angular velocity of I}, reference units hypercomplex number q d(t) and aircraft reference angular velocities ω dt the relation between () can be represented by following kinematical equation
q · d = 1 2 B d ( q b ) ω d
Wherein and with reference to body axis system { B dto the inertial coordinates system { coordinate conversion matrix of I} can be expressed as
R d ( q d ) = ( q od 2 - q vd T q vd ) I 3 + 2 q vd q vd T - 2 q od S ( q vd ) ;
2) design four rotor unmanned aircraft attitude control systems, comprising:
(1) tracking error of four rotor unmanned aircraft attitude angles and angular velocity is defined;
(2) designing filter carries out On-line Estimation to angular velocity signal and obtains the open loop dynamic equation of tracking error;
(3) adopt the unknown function in neural network feedforward divided ring dynamic equation to estimate, and design four rotor unmanned aircraft attitude system control inputs;
3) design four rotor unmanned aircraft Altitude control subsystems, comprising:
(1) height tracing error and definition auxiliary filter tracking error is defined;
(2) height subsystem Controller gain variations.
2. according to claim 1 a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods, it is characterized in that, step 1) described in the kinetic model under body axis system be:
J ω . = S ( Jω ) ω + N + τ + D 1
Wherein angular velocity vector ω (t)=[ω 1(t) ω 2(t) ω 3(t)] tbe defined in actual body axis system and { in B}, represent that { angular velocity of I}, matrix J represents the moment of inertia matrix of aircraft to aircraft, and S () represents an antisymmetric matrix, and its expression is relative to inertial coordinates system
S ( ξ ) = 0 - ξ 3 ξ 2 ξ 3 0 - ξ 1 - ξ 2 ξ 1 0 ∀ ξ = ξ 1 ξ 2 ξ 3 T
Matrix N (ω) represents the non-linear unknown moment of resistance vector relevant with angular velocity omega (t) that aircraft is subject in flight course, and u (t) represents raising force, τ (t)=[τ 1(t) τ 2(t) τ 3(t)] trepresent the rotating torque in three directions, D 1(t) and D 2(t) represent aircraft be subject to unknown time become disturbance, its expression is
D 1(t)=[d 1(t)d 2(t)d 3(t)] T
D 2(t)=d 4(t)
Constant m represents vehicle mass, and z (t) represents aircraft altitude, k zrepresent aerodynamics damping parameter, g=9.81m/s 2represent acceleration of gravity, θ (t) and represent the angle of pitch and the roll angle of aircraft, because aircraft exists modeling uncertainty, therefore the present invention supposes vehicle mass m, moment of inertia matrix J, aerodynamic coefficient k zfor unknown constant.
3. a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods according to claim 1, is characterized in that, step 2) described in definition four rotor unmanned aircraft attitude angle and the tracking error of angular velocity be:
e 0 = q 0 q 0 d + q v T q vd
e v=q 0dq v-q 0q vd+S(q v)q vd
At actual body axis system, { { B} relatively and reference body machine coordinate system { B to define actual body axis system in B} dangular velocity for
ω ~ = ω - R ~ ω d
Wherein { B} is to reference body machine coordinate system { B to represent actual body axis system dcoordinate conversion matrix, its expression formula is
R ~ = R R d T = ( e o 2 - e v T e v ) I 3 + 2 e v e v T - 2 e o S ( e v )
Tracking error e q ( t ) = e o ( t ) e v T ( t ) T With angular velocity between relation can represent with following kinematical equation
e · q = 1 2 B e ( e q ) ω ~
Wherein and
4. a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods according to claim 1, it is characterized in that, step 2) described in designing filter On-line Estimation is carried out to angular velocity signal and the open loop dynamic equation obtaining tracking error comprises: adopt wave filter to carry out On-line Estimation to the angular velocity signal of aircraft in flight course, expression formula is
e · f = - e f + r f
r f=p-(k 2+1)e v
p · = - r f - ( k 2 + 1 ) ( e v + e f ) - e f + e v ( 1 + e v T e v ) 2
Wherein e f(t) and represent filter output signal, represent wave filter auxiliary function, represent positive ride gain, p (t) and e ft the starting condition of () is set to p (0)=0 and e respectively f(0)=0, definition auxiliary variable there is following form
η = e v + e · v + e f
Can obtain auxiliary variable η (t) differentiate
J ev η · = - C * η - k 2 J ev η + 1 2 B d - T D 1 + N ev + f d + τ eq
Wherein auxiliary function expression formula be
N ev = C * ( e f + e v ) + J ev ( η - e v + e v ( 1 - e v T e v ) 2 ) - 2 J ev e f - N *
Wherein, auxiliary function with there is following form
J ev = B ev - T JB ev - 1
P = B ev - 1
Auxiliary function and equivalent control input be defined as
C * = - J ev P · - 1 P - 2 P T S ( JP e · v ) P
N * = - 1 2 P T J [ S ( 2 P e · v ) R ~ ω d - R ~ ω · d ] + P T S ( P e · v ) J R ~ ω d + 1 2 P T S ( R ~ ω d ) J R ~ ω d + P T S ( R ~ ω d ) JP e · v - 1 2 P T D 1 + 1 2 B d - T D 1 - 1 2 P T N ( ω ) + 1 2 B d - T N ( ω d )
τ eq = 1 2 B ev - T τ = 1 2 P T τ
Continuously and the unknown function of bounded be defined as
f d = 1 2 B d - T N ( ω d ) + J ω · d + 1 2 S ( ω d ) J ω d .
5. a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods according to claim 1, is characterized in that, step 2) described in employing neural network feedforward divided ring dynamic equation in unknown function carry out estimation and be,
Use neural network by continuous function f dt () is expressed as
f d=W Tσ(V Tχ)+ε(χ)
Wherein bounded input χ = 1 q d T ω d T ω · d T T , with represent neural network ground floor and the second layer and the ideal weight between the second layer and third layer, σ () represents excitation function, represent approximate error;
Feedover with nerve net represent continuous function f dt the estimation of (), its expression formula is
f ^ = W ^ T σ ( V ‾ T χ )
Wherein represent the On-line Estimation to ideal weight W, for constant value matrix, excitation function σ () is chosen for renewal function be designed to
Wherein ξ 1(t) and represent auxiliary signal, with represent positive ride gain, represent that positive definite diagonal angle upgrades gain matrix, for saturation function, can be drawn by neural network expression formula and bounded.
6. according to claim 1 a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods, it is characterized in that, step 2) described in design four rotor unmanned aircraft attitude system control inputs be following form
τ eq = - K 1 sgn ( e v + e f ) + ( k 2 + 1 ) r f - f ^ - e v ( 1 - e v T e v ) 2
Wherein represent positive definite, diagonal angle gain matrix, function sgn () is defined as
sgn(α)=[sgn(α 1)sgn(α 2)sgn(α 3)] T
For any vectorial α=[α 1α 2α 3] t.
7. a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods according to claim 1, is characterized in that, step 3) described in definition height tracing error and definition auxiliary filter tracking error be
Definition height tracing error for
e z=z d-z
Wherein represent the desired trajectory of height, the present invention adopts the linear velocity of wave filter to four rotor unmanned aircraft short transverses to carry out On-line Estimation, and designing filter has following structure
e · fz = - e fz + r fz , e fz ( 0 ) = 0
r fz=p z-(k 2z+1)e z
p · z = - r fz - ( k 2 z + 1 ) ( e z + r fz ) + e z - e fz
p z(0)=(k 2z+1)e z(0)
Wherein e fz(t) and represent filter output signal, represent wave filter auxiliary function, represent positive ride gain, Design assistant signal there is following form
η z = e · z + e z + r fz .
8. according to claim 1 a kind of four rotor unmanned aircraft nonlinear object feedback flight control methods, it is characterized in that, step 3) described in height subsystem Controller gain variations be
Four rotor unmanned aircraft height subsystem kinetic models are rewritten as
m z · · = - k z z · - mg + u eq + d 4
Wherein equivalent control input be defined as
Mapping relations between Eulerian angle and unit quaternion can be expressed as
θ = arcsin ( 2 ( q 0 q 2 - q 1 q 3 ) )
To auxiliary signal η z(t) differentiate, and be multiplied by vehicle mass m in both members simultaneously and can obtain
m η · z = - k 2 z m η z + N z - m ( 2 r fz + e fz ) - u eq
Wherein auxiliary function be defined as
N z = k z z · + mg + m z · · d - d 4
Design assistant function due to z d(t) and for limited function, therefore, it is possible to prove N zd(t) and limited function, formula (39) m η · z = - k 2 z m η z + N z - m ( 2 r fz + e fz ) - u eq Following form can be rewritten as
m η · z = - k 2 z m η z + N zd + N ~ z - u eq
Wherein auxiliary function be defined as
N ~ z = N z - N zd - m ( 2 r fz + e fz )
Design four rotor unmanned aircraft height subsystem equivalent control input u eqt () has following form
u eq=k 1zsgn(e z+e fz)-(k 2z+1)r fz+e z
Wherein k 1zand k 2zrepresent positive ride gain, sgn () represents standard signum function.
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