CN104571120A - Posture nonlinear self-adaptive control method of quad-rotor unmanned helicopter - Google Patents

Abstract

The invention relates to a flight control method of an unmanned helicopter and provides a posture nonlinear self-adaptive control method of a quad-rotor unmanned helicopter. Progressive tracking control over the flight posture of the helicopter can be effectively achieved under the condition that system parameters like the moment of inertia of the helicopter, the air damping coefficient and mass center offset are unknown. According to the adopted technical scheme, the method comprises the steps that a small quad-rotor unmanned helicopter control design model serves as a controlled object, online estimation is carried out on unknown system parameters through an immersion-invariant set theory, a controller is constructed by utilization of an estimated value, and progressive tracking control over the flight posture of the quad-rotor unmanned helicopter is achieved. The posture nonlinear self-adaptive control method of the quad-rotor unmanned helicopter is mainly applied to flight control of the unmanned helicopter.

Description

The attitude nonlinear autoregressive method of four rotor wing unmanned aerial vehicles

Technical field

The present invention relates to a kind of flight control method of unmanned plane, particularly relate to a kind of attitude nonlinear autoregressive method of four rotor wing unmanned aerial vehicles

Technical background

Four rotor wing unmanned aerial vehicles be a kind of can vertical takeoff and landing, many rotary wind types unmanned plane.It adopts cross structure, produces lift with four of frame terminal driven by motor rotor wing rotations, relies on the adjustment of four motor speeds to control the motion state of aircraft.Compared with other unmanned planes, four rotor wing unmanned aerial vehicle advantages are that machinery and electronic structure are more simply compact, take action more dexterous changeable, still possess good handling while mobility strong, (the periodical: IEEE Transactions on Control Systems Technology that takes off, hovers, flies and land can be realized among a small circle; Author: LeeTaeyoung; Publication time: 2013; Title of article: Robust Adaptive Attitude Tracking on SO (3) With an Application to a Quadrotor UAV; The page number: 1924-1930).

Four rotor wing unmanned aerial vehicles are particularly suitable for the task such as execution monitoring, scouting in environment near the ground, have wide military and civilian prospect.In recent years, along with the progress of microprocessor, MEMS (micro electro mechanical system), micro-inertial navigation monotechnics, and new material, electrokinetic cell performance boost, microminiature quadrotor has had and has developed rapidly, and attracted large quantities of scientific research personnel, become the study hotspot of domestic and international colleges and universities, research institution and enterprise.

But as rotary aircraft, four rotor wing unmanned aerial vehicles have quiet instability, drive lacking, strong coupling and the feature such as non-linear, higher requirement is proposed to the performance of flight controller, particularly as a rule, the kinetic parameter of aircraft is not easily measured as the side-play amount of moment of inertia, air damping coefficient and center of gravity etc. and is obtained, and adds difficulty (periodical: IEEE Transactions on Control Systems Technology to Controller gain variations; Author: DydekZachary T., AnnaswamyAnuradha M. and LavretskyEugene; Publication time: 2013; Title of article: Adaptive Control of Quadrotor UAVs:A Design Trade Study With Flight Evaluations; The page number: 1400-1406).

In the face of the problem of four rotor wing unmanned aerial vehicle Unknown Parameters, the scheme that most colleges and universities and research institution adopt is traditional model reference adaptive method, the method structure is simple, but need model structure and unknown parameter to meet linear parameterization condition, and easily introduce controller " singular point " problem (books: nonlinear system theory; Author: the brave pure and mild Lu Gui chapter in side; Time: 2009; Publishing house: publishing house of Tsing-Hua University; The page number: 65-79).

Summary of the invention

For overcoming the deficiencies in the prior art, a kind of nonlinear adaptive flight control method of four rotor wing unmanned aerial vehicles is provided, effectively can realizes the asymptotic tracking control to aircraft flight attitude when systematic parameter (as aircraft moment of inertia, air damping coefficient and centroid offset) is unknown.For this reason, the technical scheme that the present invention takes is, the attitude nonlinear autoregressive method of four rotor wing unmanned aerial vehicles, with small-sized four rotor wing unmanned aerial vehicle control design case models for controlled device, by immersion-invariant set theory, On-line Estimation is done to unknown system parameter, and utilize estimated value orecontrolling factor device, realize the attitude asymptotic tracking control of four rotor wing unmanned aerial vehicles.

Comprise the steps: further

1) the attitude dynamics model of four rotor wing unmanned aerial vehicles is determined

The attitude dynamics model of four described rotor wing unmanned aerial vehicles is:

Wherein, be the attitude Eulerian angle of four rotor wing unmanned aerial vehicles, represent the roll angle of unmanned plane, the angle of pitch and crab angle respectively, one, character top, two round dots represent single order, second derivative to time t respectively; ^tsymbol is transpose of a matrix operational symbol, represent that vectorial dimension is 3, be respectively four rotor wing unmanned aerial vehicles along the moment of inertia on matrix coordinate axis three directions, represent that vectorial dimension is 1, for the air damping coefficient on matrix change in coordinate axis direction, for the impact that aircraft brings along the centre-of gravity shift on matrix coordinate axis three directions, for half wheelbase of aircraft, for lift moment coefficient, u ₁, u ₂, u ₃for along the control inputs on matrix coordinate axis three directions, in the present invention, J ₁, J ₂, J ₃, K ₁, K ₂, K ₃, δ ₁, δ ₂, δ ₃, l, c are all unknown constant;

Because of J ₁, J ₂, J ₃≠ 0, then the model in formula (1) can be reduced to following form:

$\stackrel{\·\·}{\mathrm{\η}}=\mathrm{Au}-B\stackrel{\·}{\mathrm{\η}}-\mathrm{\Δ}---\left(2\right)$

Wherein be the second derivative of attitude Eulerian angle η about time t of four rotor wing unmanned aerial vehicles, for the matrix of characterization system inertia, diag{} is unit diagonal matrix structure symbol, the dimension of representing matrix is 3 × 3 the matrix of characterization system damping, the matrix of characterization system centre-of gravity shift, for the control inputs vector of system;

2) error signal of the gesture stability of four rotor wing unmanned aerial vehicles is defined

First the attitude angle η that four rotor wing unmanned aerial vehicles are expected to follow the tracks of is defined _d:

Wherein represent the expectation roll angle of four rotor wing unmanned aerial vehicles respectively, expect the angle of pitch and expect crab angle;

Define the tracking error e of attitude angle below ₁with the filtering error e of attitude angle ₂:

Wherein, for positive definite gain diagonal matrix, α ₁, α ₂, α ₃for 3 elements on diagonal line in this positive definite gain diagonal matrix;

3) the error dynamics equation of four rotor wing unmanned aerial vehicles is given expression to

Derivative about time t is asked to formula (3) and formula (4), obtains following equation:

$\begin{array}{c}{\stackrel{\·}{e}}_1=-\mathrm{\α}{e}_1+e_2\\ {\stackrel{\·}{e}}_2=\mathrm{Au}-B(e_2-\mathrm{\α}{e}_1+{\stackrel{\·}{\mathrm{\η}}}_d)-\mathrm{\Δ}+\mathrm{\α}(e_2-\mathrm{\α}{e}_1)\end{array}---\left(5\right)$

Wherein for tracking error e ₁about the derivative of time t, for filtering error e ₂about the derivative of time t;

Definition for system damping parameter vector, for system gravity migration parameter vector, for system inertia parameter vector, for systematic parameter vector; By s ₁, s ₂and A=diag{s ₂substitute into formula (5) obtain following equation:

Wherein for error vector, for comprising the auxiliary vector of error and desired trajectory, for comprising the companion matrix of error and desired trajectory, its concrete form is as follows:

Wherein I ^{3 × 3}be 3 × 3 unit matrixs;

4) the parameter estimating error kinetics equation of four rotor wing unmanned aerial vehicles is given expression to

The evaluated error of definition unknown parameter for following form:

$\begin{array}{c}{\mathrm{\ζ}}_1={\hat{s}}_1-s_1+{\mathrm{\β}}_1\\ {\mathrm{\ζ}}_2={\hat{s}}_2-s_2^{*}+{\mathrm{\β}}_2\end{array}---\left(8\right)$

Wherein, with for to parameter vector s ₁and s ₂estimation, for by s ₂the vector of the inverse composition of every element; be respectively evaluated error ζ ₁, ζ ₂auxiliary function, for about e and continuous function, ζ ₁for to parameter vector s ₁evaluated error, ζ ₂for to parameter vector s ₂evaluated error;

Definition for the evaluated error vector of systematic parameter, for the parameter estimation vector of system, for systematic parameter estimates auxiliary function, then parameter estimating error kinetics equation can be expressed as following form:

Wherein for evaluated error vector ζ is about the derivative of time t;

5) adaptive controller of four rotor wing unmanned aerial vehicles and the more new law of parameter estimation is designed

Based on formula (9), design the adaptive controller u of four rotor wing unmanned aerial vehicles and the more new law of parameter estimation for following form:

For i=1,2,3,4,5,6 and j=1,2,3 have

Wherein β _1irepresent vectorial β ₁the i-th row element, β _2jrepresent vectorial β ₂jth row element, e _2irepresent e ₂the i-th row element, e _2jrepresent e ₂jth row element, represent vector the i-th row element, represent vector jth row element, k > 0 is regulating error e ₂ride gain, ε > 0 is regulating error e ₁and e ₂the ride gain of product, γ ₁> 0 is for affect β ₁the ride gain of change, γ ₂> 0 is for affect β ₂ride gain, σ is integration metasymbol.

Under proving the effect of the four rotor wing unmanned aerial vehicle systems controller of design and more new law of parameter estimation in formula (10), closed-loop system is at equilibrium point place's Existence of Global Stable, and have

Prove:

Formula (10) and formula (11) are substituted in formula (9), obtain following equation:

Wherein for comprising the intermediate variable of error;

Known by formula (11), can be expressed as following equation:

$\frac{\∂\mathrm{\β}}{\∂e_2^T}=\left[\begin{array}{c}{\mathrm{\γ}}_1\mathrm{\φ}\\ \·\·\·\·\·\·\·\·\·\·\·\·\\ \mathrm{diag}\left\{{\mathrm{\γ}}_2\mathrm{\κ}\right\}\end{array}\right]---\left(13\right)$

Formula (12) can be expressed as following equation:

$\stackrel{\·}{\mathrm{\ζ}}=-\mathrm{\Γ\Φ}{\mathrm{\Φ}}^T\mathrm{\ζ},---\left(14\right)$

Wherein, the companion matrix of evaluated error kinetics equation with intermediate variable matrix be defined as follows:

$\begin{array}{c}\mathrm{\Γ}=\left[\begin{array}{cc}{\mathrm{\γ}}_1{I}^{3\×3}& 0\\ 0& {\mathrm{\γ}}_2{A}^{-1}\end{array}\right]\\ \mathrm{\Φ}=\left[\begin{array}{c}\mathrm{\φ}\\ \·\·\·\\ \mathrm{A\; diag}\left\{\mathrm{\κ}\right\}\end{array}\right]\end{array}---\left(15\right)$

The nonnegative function that definition evaluated error is relevant for following form:

V _ζ(ζ)＝ζ ^TΓ ^-1ζ(16)

Derivative about time t is asked to formula (16), and will try, in the result after (14) substitution differentiate, can obtain:

${\stackrel{\·}{V}}_{\mathrm{\ζ}}\left(\mathrm{\ζ}\right)=-2{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\≤0---\left(17\right)$

Wherein for nonnegative function V _ζ(ζ) about the derivative of time t;

From the conclusion in (17), ζ bounded, Φ ^tζ square integrable;

Expression formula in formula (10) and (14) substituted in (6), the closed loop equation obtaining four rotor wing unmanned aerial vehicles is following form:

$\begin{array}{c}{\stackrel{\·}{e}}_1=-\mathrm{\α}{e}_1+e_2\\ {\stackrel{\·}{e}}_2=-k{e}_2-\mathrm{\ϵ}{e}_1-{\mathrm{\Φ}}^T\mathrm{\ζ}\end{array}---\left(18\right)$

The nonnegative function that definition tracking error is relevant for following form:

$V(e,\mathrm{\ζ})=\mathrm{\ϵ}{e}_1^T{e}_1+e_2^T{e}_2+\frac{1}{k}{\mathrm{\ζ}}^T{\mathrm{\Γ}}^{-1}\mathrm{\ζ}---\left(19\right)$

Derivative about time t is asked to formula (19), can obtain:

$\begin{array}{c}\stackrel{\·}{V}(e,\mathrm{\ζ})=2\mathrm{\ϵ}{\stackrel{\·}{e}}_1^T{e}_1+2{\stackrel{\·}{e}}_2^T{e}_2-\frac{2}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\\ =-2\mathrm{\α}{e}_1^T{e}_1-2k{e}_2^T{e}_2-2{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T{e}_2-\frac{2}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\\ =-2\mathrm{\ϵ\α}{e}_1^T{e}_1-k{e}_2^T{e}_2-\frac{1}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)-\frac{1}{k}{({\mathrm{ke}}_2+{\mathrm{\Φ}}^T\mathrm{\ζ})}^T({\mathrm{ke}}_2+{\mathrm{\Φ}}^T\mathrm{\ζ})\\ \≤0\end{array}---\left(20\right)$

Wherein for nonnegative function V (e, ζ) is about the derivative of time t

From the conclusion in (20), to the closed-loop system of four rotor wing unmanned aerial vehicles at equilibrium point place's Existence of Global Stable, and system signal converges in following set:

M＝{(e,ζ)|e＝0,Φ ^Tζ＝0} (21)

According to Russell's invariant set theorems,

Compared with the prior art, technical characterstic of the present invention and effect:

1. the present invention can realize the asymptotic tracking control of attitude when dummy vehicle unknown parameters.

2. the present invention realizes simply, and the calculated amount of needs is little.

3. ride gain flexible adjustment of the present invention, can meet most of flight progress.

Accompanying drawing explanation

The actual roll angle φ of Fig. 1 tetra-rotor wing unmanned aerial vehicle, expectation roll angle φ _dwith roll angle tracking error e _φcurve map.

The actual roll angle θ of Fig. 2 tetra-rotor wing unmanned aerial vehicle, expectation roll angle θ _dwith roll angle tracking error e _θcurve map.

The actual roll angle ψ of Fig. 3 tetra-rotor wing unmanned aerial vehicle, expectation roll angle ψ _dwith roll angle tracking error e _ψcurve map.

The attitude angular velocity of Fig. 4 tetra-rotor wing unmanned aerial vehicle with curve map.

The control inputs u of Fig. 5 tetra-rotor wing unmanned aerial vehicle ₁, u ₂and u ₃curve map.

The control flow block diagram of Fig. 6 the method for the invention.

Embodiment

A kind of four rotor wing unmanned aerial vehicle attitude control methods based on immersion-invariant set theory of the present invention, with small-sized four rotor wing unmanned aerial vehicle control design case models for controlled device, by immersion-invariant set theory, On-line Estimation is done to unknown system parameter, and utilize estimated value orecontrolling factor device, the attitude asymptotic tracking control of four rotor wing unmanned aerial vehicles can be realized.

Below in conjunction with embodiment and accompanying drawing, a kind of four rotor wing unmanned aerial vehicle attitude-adaptive control methods based on immersion-invariant set theory of the present invention are described in detail.

A kind of four rotor wing unmanned aerial vehicle attitude-adaptive control methods theoretical based on immersion-invariant set of the present invention, comprise the steps:

1) the attitude dynamics model of four rotor wing unmanned aerial vehicles is determined.

The attitude dynamics model of four described rotor wing unmanned aerial vehicles is:

Wherein, be the attitude Eulerian angle of four rotor wing unmanned aerial vehicles, represent the roll angle of unmanned plane, the angle of pitch and crab angle respectively, ^tsymbol is transpose of a matrix operational symbol, represent that vectorial dimension is 3, be respectively four rotor wing unmanned aerial vehicles along the moment of inertia on matrix coordinate axis three directions, represent that vectorial dimension is 1, for the air damping coefficient on matrix change in coordinate axis direction, for the impact that aircraft brings along the centre-of gravity shift on matrix coordinate axis three directions, for half wheelbase of aircraft, for lift moment coefficient, u ₁, u ₂, u ₃for along the control inputs on matrix coordinate axis three directions.In the present invention, J ₁, J ₂, J ₃, K ₁, K ₂, K ₃, δ ₁, δ ₂, δ ₃, l, c are all unknown constant.

Because of J ₁, J ₂, J ₃≠ 0, then the model in formula (1) can be reduced to following form:

$\stackrel{\·\·}{\mathrm{\η}}=\mathrm{Au}-B\stackrel{\·}{\mathrm{\η}}-\mathrm{\Δ}---\left(2\right)$

Wherein be the second derivative of attitude Eulerian angle η about time t of four rotor wing unmanned aerial vehicles, for the matrix of characterization system inertia, diag{} is unit diagonal matrix structure symbol, the dimension of representing matrix is 3 × 3 the matrix of characterization system damping, the matrix of characterization system centre-of gravity shift, for the control inputs vector of system.

2) error signal of the gesture stability of four rotor wing unmanned aerial vehicles is defined.

First the attitude angle η that four rotor wing unmanned aerial vehicles are expected to follow the tracks of is defined _d:

Wherein represent the expectation roll angle of four rotor wing unmanned aerial vehicles respectively, expect the angle of pitch and expect crab angle.

Define the tracking error e of attitude angle below ₁with the filtering error e of attitude angle ₂:

Wherein, for positive definite gain diagonal matrix, α ₁, α ₂, α ₃for 3 elements on diagonal line in this positive definite gain diagonal matrix.

3) the error dynamics equation of four rotor wing unmanned aerial vehicles is given expression to.

Derivative about time t is asked to formula (3) and formula (4), obtains following equation:

$\begin{array}{c}{\stackrel{\·}{e}}_1=-\mathrm{\α}{e}_1+e_2\\ {\stackrel{\·}{e}}_2=\mathrm{Au}-B(e_2-\mathrm{\α}{e}_1+{\stackrel{\·}{\mathrm{\η}}}_d)-\mathrm{\Δ}+\mathrm{\α}(e_2-\mathrm{\α}{e}_1)\end{array}---\left(5\right)$

Wherein for tracking error e ₁about the derivative of time t, for filtering error e ₂about the derivative of time t.

Definition for system damping parameter vector, for system gravity migration parameter vector, for system inertia parameter vector, for systematic parameter vector.By s ₁, s ₂and A=diag{s ₂substitute into formula (5) obtain following equation:

Wherein for error vector, for comprising the auxiliary vector of error and desired trajectory, for comprising the companion matrix of error and desired trajectory, its concrete form is as follows:

Wherein I ^{3 × 3}be 3 × 3 unit matrixs.

4) the parameter estimating error kinetics equation of four rotor wing unmanned aerial vehicles is given expression to.

The evaluated error of definition unknown parameter for following form:

$\begin{array}{c}{\mathrm{\ζ}}_1={\hat{s}}_1-s_1+{\mathrm{\β}}_1\\ {\mathrm{\ζ}}_2={\hat{s}}_2-s_2^{*}+{\mathrm{\β}}_2\end{array}---\left(8\right)$

Wherein, with for to parameter vector s ₁and s ₂estimation, be respectively evaluated error ζ ₁, ζ ₂auxiliary function, for about e and continuous function, ζ ₁for to parameter vector s ₁evaluated error, ζ ₂for to parameter vector s ₂evaluated error.

Definition for the evaluated error vector of systematic parameter, for the parameter estimation vector of system, for systematic parameter estimates auxiliary function, then parameter estimating error kinetics equation can be expressed as following form:

Wherein for evaluated error vector ζ is about the derivative of time t,

5) adaptive controller of four rotor wing unmanned aerial vehicles and the more new law of parameter estimation is designed.

Based on formula (9), design the adaptive controller u of four rotor wing unmanned aerial vehicles and the more new law of parameter estimation for following form:

For i=1,2,3,4,5,6 and j=1,2,3 have

Wherein β _1irepresent vectorial β ₁the i-th row element, β _2jrepresent vectorial β ₂jth row element, e _2irepresent e ₂the i-th row element, e _2jrepresent e ₂jth row element, represent vector the i-th row element, represent vector jth row element, k > 0 is regulating error e ₂ride gain, ε > 0 is regulating error e ₁and e ₂the ride gain of product, γ ₁> 0 is for affect β ₁the ride gain of change, γ ₂> 0 is for affect β ₂ride gain, σ is integration metasymbol.

6), under proving the effect of the four rotor wing unmanned aerial vehicle systems controller of design and more new law of parameter estimation in formula (10), closed-loop system is at equilibrium point place's Existence of Global Stable, and have

Prove:

Formula (10) and formula (11) are substituted in formula (9), obtain following equation:

Wherein for comprising the intermediate variable of error.

Known by formula (11), can be expressed as following equation:

$\frac{\∂\mathrm{\β}}{\∂e_2^T}=\left[\begin{array}{c}{\mathrm{\γ}}_1\mathrm{\φ}\\ \·\·\·\·\·\·\·\·\·\·\·\·\\ \mathrm{diag}\left\{{\mathrm{\γ}}_2\mathrm{\κ}\right\}\end{array}\right]---\left(13\right)$

Formula (12) can be expressed as following equation:

$\stackrel{\·}{\mathrm{\ζ}}=-\mathrm{\Γ\Φ}{\mathrm{\Φ}}^T\mathrm{\ζ},---\left(14\right)$

Wherein, the companion matrix of evaluated error kinetics equation with intermediate variable matrix be defined as follows:

$\begin{array}{c}\mathrm{\Γ}=\left[\begin{array}{cc}{\mathrm{\γ}}_1{I}^{3\×3}& 0\\ 0& {\mathrm{\γ}}_2{A}^{-1}\end{array}\right]\\ \mathrm{\Φ}=\left[\begin{array}{c}\mathrm{\φ}\\ \·\·\·\\ \mathrm{A\; diag}\left\{\mathrm{\κ}\right\}\end{array}\right]\end{array}---\left(15\right)$

The nonnegative function that definition evaluated error is relevant for following form:

V _ζ(ζ)＝ζ ^TΓ ^-1ζ(16)

Derivative about time t is asked to formula (16), and will try, in the result after (14) substitution differentiate, can obtain:

${\stackrel{\·}{V}}_{\mathrm{\ζ}}\left(\mathrm{\ζ}\right)=-2{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\≤0---\left(17\right)$

Wherein for nonnegative function V _ζ(ζ) about the derivative of time t.

From the conclusion in (17), ζ bounded, Φ ^tζ square integrable.

Expression formula in formula (10) and (14) substituted in (6), the closed loop equation obtaining four rotor wing unmanned aerial vehicles is following form:

$\begin{array}{c}{\stackrel{\·}{e}}_1=-\mathrm{\α}{e}_1+e_2\\ {\stackrel{\·}{e}}_2=-k{e}_2-\mathrm{\ϵ}{e}_1-{\mathrm{\Φ}}^T\mathrm{\ζ}\end{array}---\left(18\right)$

The nonnegative function that definition tracking error is relevant for following form:

$V(e,\mathrm{\ζ})=\mathrm{\ϵ}{e}_1^T{e}_1+e_2^T{e}_2+\frac{1}{k}{\mathrm{\ζ}}^T{\mathrm{\Γ}}^{-1}\mathrm{\ζ}---\left(19\right)$

Derivative about time t is asked to formula (19), can obtain:

$\begin{array}{c}\stackrel{\·}{V}(e,\mathrm{\ζ})=2\mathrm{\ϵ}{\stackrel{\·}{e}}_1^T{e}_1+2{\stackrel{\·}{e}}_2^T{e}_2-\frac{2}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\\ =-2\mathrm{\α}{e}_1^T{e}_1-2k{e}_2^T{e}_2-2{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T{e}_2-\frac{2}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\\ =-2\mathrm{\ϵ\α}{e}_1^T{e}_1-k{e}_2^T{e}_2-\frac{1}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)-\frac{1}{k}{({\mathrm{ke}}_2+{\mathrm{\Φ}}^T\mathrm{\ζ})}^T({\mathrm{ke}}_2+{\mathrm{\Φ}}^T\mathrm{\ζ})\\ \≤0\end{array}---\left(20\right)$

Wherein for nonnegative function V (e, ζ) is about the derivative of time t.

From the conclusion in (20), to the closed-loop system of four rotor wing unmanned aerial vehicles at equilibrium point place's Existence of Global Stable, and system signal converges in following set:

M＝{(e,ζ)|e＝0,Φ ^Tζ＝0} (21)

According to Russell's invariant set theorems,

It is as follows that a kind of four rotor wing unmanned aerial vehicle attitude control methods based on immersion-invariant set theory of the present invention give Numerical Simulation Results, illustrates that proposed Control System Design method has good tracking performance.

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

J ₁＝J ₂＝1.25kgm ²,J ₃＝2.5kgm ²,

K ₁＝K ₂＝K ₃＝0.012Ns/rad, (22)

δ ₁＝δ ₂＝δ ₃＝0.125Nm,

l＝0.25m,c＝0.25

Four rotor wing unmanned aerial vehicles expect the attitude angle φ followed the tracks of _dand θ _dchoose as follows:

$\begin{array}{c}{\mathrm{\φ}}_d=\frac{\mathrm{\π}}{18}\sin \left(\frac{2\mathrm{\π}}{5}t\right)\mathrm{rad}\\ {\mathrm{\θ}}_d=\frac{\mathrm{\π}}{36}\cos \left(\frac{3\mathrm{\π}}{5}t\right)\mathrm{rad}\end{array}---\left(23\right)$

ψ _dfor low-pass first order filter step signal ψ under effect _d=45 (deg).

Four rotor wing unmanned aerial vehicle state initial values and all parameter estimation initial values are all 0, and ride gain is chosen as follows:

The actual attitude angle of Fig. 1-Figure 3 shows that four rotor wing unmanned aerial vehicles, expect attitude angle and Attitude Tracking error, can therefrom find out, actual attitude angle has just followed the tracks of expectation attitude angle within a short period of time, and namely Attitude Tracking error is tending towards 0 very soon.Simulation result shows that control algolithm proposed by the invention can meet good attitude angle tracking performance when there being unknown parameters.Figure 4 shows that the attitude angular velocity of four rotor wing unmanned aerial vehicles, therefrom can find out that angular velocity signal is stablized and do not disperse.Figure 5 shows that the control inputs amount of four rotor wing unmanned aerial vehicles, can therefrom find out control inputs continuous and derivable, within the zone of reasonableness remaining on permission, make easily to realize in actual applications.

Claims (3)

1. the attitude nonlinear autoregressive method of a rotor wing unmanned aerial vehicle, it is characterized in that, with small-sized four rotor wing unmanned aerial vehicle control design case models for controlled device, by immersion-invariant set theory, On-line Estimation is done to unknown system parameter, and utilize estimated value orecontrolling factor device, realize the attitude asymptotic tracking control of four rotor wing unmanned aerial vehicles.

2. the attitude nonlinear autoregressive method of four rotor wing unmanned aerial vehicles as claimed in claim 1, is characterized in that, does On-line Estimation, and utilizes estimated value orecontrolling factor device, be further refined as by immersion-invariant set theory to unknown system parameter:

1) the attitude dynamics model of four rotor wing unmanned aerial vehicles is determined

The attitude dynamics model of four described rotor wing unmanned aerial vehicles is:

$J_2\stackrel{..}{\mathrm{\θ}}+K_{2}l\stackrel{.}{\mathrm{\θ}}+{\mathrm{\δ}}_2=l{u}_2$

$J_3\stackrel{..}{\mathrm{\ψ}}+K_3\stackrel{.}{\mathrm{\ψ}}+{\mathrm{\δ}}_3={\mathrm{cu}}_3$ (1)

Wherein, be the attitude Eulerian angle of four rotor wing unmanned aerial vehicles, represent the roll angle of unmanned plane, the angle of pitch and crab angle respectively, one, character top, two round dots represent single order, second derivative to time t respectively; ^tsymbol is transpose of a matrix operational symbol, represent that vectorial dimension is 3, be respectively four rotor wing unmanned aerial vehicles along the moment of inertia on matrix coordinate axis three directions, represent that vectorial dimension is 1, for the air damping coefficient on matrix change in coordinate axis direction, for the impact that aircraft brings along the centre-of gravity shift on matrix coordinate axis three directions, for half wheelbase of aircraft, for lift moment coefficient, u ₁, u ₂, u ₃for along the control inputs on matrix coordinate axis three directions, in the present invention, J ₁, J ₂, J ₃, K ₁, K ₂, K ₃, δ ₁, δ ₂, δ ₃, l, c are all unknown constant;

Because of J ₁, J ₂, J ₃≠ 0, then the model in formula (1) can be reduced to following form:

$\stackrel{..}{\mathrm{\η}}=\mathrm{Au}-B\stackrel{.}{\mathrm{\η}}-\mathrm{\Δ}$ (2)

Wherein be the second derivative of attitude Eulerian angle η about time t of four rotor wing unmanned aerial vehicles, for the matrix of characterization system inertia, diag{} is unit diagonal matrix structure symbol, the dimension of representing matrix is the matrix of characterization system damping, the matrix of characterization system centre-of gravity shift, for the control inputs vector of system;

2) error signal of the gesture stability of four rotor wing unmanned aerial vehicles is defined

First the attitude angle η that four rotor wing unmanned aerial vehicles are expected to follow the tracks of is defined _d:

(3)

Wherein represent the expectation roll angle of four rotor wing unmanned aerial vehicles respectively, expect the angle of pitch and expect crab angle;

Define the tracking error e of attitude angle below ₁with the filtering error e of attitude angle ₂:

(4)

Wherein, for positive definite gain diagonal matrix, α ₁, α ₂, α ₃for 3 elements on diagonal line in this positive definite gain diagonal matrix;

3) the error dynamics equation of four rotor wing unmanned aerial vehicles is given expression to

Derivative about time t is asked to formula (3) and formula (4), obtains following equation:

${\stackrel{.}{e}}_1=-\mathrm{\α}{e}_1+e_2$ (5)

${\stackrel{.}{e}}_2=\mathrm{Au}-B(e_2-\mathrm{\α}{e}_1+{\stackrel{.}{\mathrm{\η}}}_d)-\mathrm{\Δ}+\mathrm{\α}(e_2-\mathrm{\α}{e}_1)$

Wherein for tracking error e ₁about the derivative of time t, for filtering error e ₂about the derivative of time t;

Definition for system damping parameter vector, for system gravity migration parameter vector, for system inertia parameter vector, for systematic parameter vector; By s ₁, s ₂and A=diag{s ₂substitute into formula (5) obtain following equation:

${\stackrel{.}{e}}_1=-\mathrm{\α}{e}_1+e_2$ (6)

Wherein for error vector, for comprising the auxiliary vector of error and desired trajectory, for comprising the companion matrix of error and desired trajectory, its concrete form is as follows:

(7)

Wherein I ^{3 × 3}be 3 × 3 unit matrixs;

4) the parameter estimating error kinetics equation of four rotor wing unmanned aerial vehicles is given expression to

The evaluated error of definition unknown parameter for following form:

${\mathrm{\ζ}}_1={\hat{s}}_1-s_1+{\mathrm{\β}}_1$ (8)

${\mathrm{\ζ}}_2={\hat{s}}_2-s_2^{*}+{\mathrm{\β}}_2$

Wherein, with for to parameter vector s ₁and s ₂estimation, for by s ₂the vector of the inverse composition of every element; be respectively evaluated error ζ ₁, ζ ₂auxiliary function, for about e and continuous function, ζ ₁for to parameter vector s ₁evaluated error, ζ ₂for to parameter vector s ₂evaluated error;

Definition for the evaluated error vector of systematic parameter, for the parameter estimation vector of system, for systematic parameter estimates auxiliary function, then parameter estimating error kinetics equation can be expressed as following form:

(9)

Wherein for evaluated error vector ζ is about the derivative of time t;

5) adaptive controller of four rotor wing unmanned aerial vehicles and the more new law of parameter estimation is designed

Based on formula (9), design the adaptive controller u of four rotor wing unmanned aerial vehicles and the more new law of parameter estimation for following form:

$\stackrel{\stackrel{.}{^}}{s}=-{(1+\frac{\∂\mathrm{\β}}{\∂{\hat{s}}^T})}^{-1}(\frac{\∂\mathrm{\β}}{\∂e_1^T}(-\mathrm{\α}{e}_1+e_2)+\frac{\∂\mathrm{\β}}{\∂e_2^T}(-k{e}_2+\mathrm{\ϵ}{e}_1))$ (10)

For i=1,2,3,4,5,6 and j=1,2,3 have

(11)

Wherein β _1irepresent vectorial β ₁the i-th row element, β _2jrepresent vectorial β ₂jth row element, e _2irepresent e ₂the i-th row element, e _2jrepresent e ₂jth row element, represent vector the i-th row element, represent vector jth row element, k > 0 is regulating error e ₂ride gain, ε > 0 is regulating error e ₁and e ₂the ride gain of product, γ ₁> 0 is for affect β ₁the ride gain of change, γ ₂> 0 is for affect β ₂ride gain, σ is integration metasymbol.

3. the attitude nonlinear autoregressive method of four rotor wing unmanned aerial vehicles as claimed in claim 2, it is characterized in that, also comprise verification step, under proving the effect of the four rotor wing unmanned aerial vehicle systems controller of design and more new law of parameter estimation in formula (10), closed-loop system is at equilibrium point place's Existence of Global Stable, and have be specially:

Formula (10) and formula (11) are substituted in formula (9), obtain following equation:

(12)

Wherein for comprising the intermediate variable of error;

Known by formula (11), can be expressed as following equation

$\frac{\∂\mathrm{\β}}{\∂e_2^T}=\left[\begin{array}{c}{\mathrm{\γ}}_1\mathrm{\φ}\\ ............\\ \mathrm{diag}\left\{{\mathrm{\γ}}_2\mathrm{\κ}\right\}\end{array}\right]$ (13)

Formula (12) can be expressed as following equation:

$\stackrel{.}{\mathrm{\ζ}}=-\mathrm{\Γ\Φ}{\mathrm{\Φ}}^T\mathrm{\ζ}$ (14)

Wherein, the companion matrix of evaluated error kinetics equation with intermediate variable matrix be defined as follows:

$\mathrm{\Γ}=\left[\begin{array}{cc}{\mathrm{\γ}}_1{I}^{3\×3}& 0\\ 0& {\mathrm{\γ}}_2{A}^{-1}\end{array}\right]$

$\mathrm{\Φ}=\left[\begin{array}{c}\mathrm{\φ}\\ ...\\ \mathrm{Adiag}\left\{\mathrm{\κ}\right\}\end{array}\right]$ (15)

The nonnegative function that definition evaluated error is relevant for following form:

V _ζ(ζ)＝ζ ^TΓ ^-1ζ (16)

Derivative about time t is asked to formula (16), and will try, in the result after (14) substitution differentiate, can obtain:

${\stackrel{.}{V}}_{\mathrm{\ζ}}\left(\mathrm{\ζ}\right)=-2{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\≤0$ (17)

Wherein for nonnegative function V _ζ(ζ) about the derivative of time t;

From the conclusion in (17), ζ bounded, Φ ^tζ square integrable;

Expression formula in formula (10) and (14) substituted in (6), the closed loop equation obtaining four rotor wing unmanned aerial vehicles is following form:

${\stackrel{.}{e}}_1=-\mathrm{\α}{e}_1+e_2$ (18) ${\stackrel{.}{e}}_2=-{\mathrm{ke}}_2-{\mathrm{\ϵe}}_1-{\mathrm{\Φ}}^T\mathrm{\ζ}$

The nonnegative function that definition tracking error is relevant for following form:

$V(e,\mathrm{\ζ})={\mathrm{\ϵe}}_1^T{e}_1+e_2^T{e}_2+\frac{1}{k}{\mathrm{\ζ}}^T{\mathrm{\Γ}}^{-1}\mathrm{\ζ}$ (19)

Derivative about time t is asked to formula (19), can obtain:

$\begin{array}{c}\stackrel{.}{V}(e,\mathrm{\ζ})=2\mathrm{\ϵ}{\stackrel{.}{e}}_1^T{e}_1+2{\stackrel{.}{e}}_2^T{e}_2-\frac{2}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\\ =-2\mathrm{\ϵ\α}{e}_1^T{e}_1-2k{e}_2^T{e}_2-2{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T{e}_2-\frac{2}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)\\ =-2\mathrm{\ϵ\α}{e}_1^T{e}_1-{\mathrm{ke}}_2^T{e}_2-\frac{1}{k}{\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)}^T\left({\mathrm{\Φ}}^T\mathrm{\ζ}\right)-\frac{1}{k}{({\mathrm{ke}}_2+{\mathrm{\Φ}}^T\mathrm{\ζ})}^T({\mathrm{ke}}_2+{\mathrm{\Φ}}^T\mathrm{\ζ})\\ \≤0\end{array},$ (20)

Wherein for nonnegative function V (e, ζ) is about the derivative of time t;

From the conclusion in (20), to the closed-loop system of four rotor wing unmanned aerial vehicles at equilibrium point place's Existence of Global Stable, and system signal converges in following set:

M＝{(e,ζ)|e＝0,Φ ^Tζ＝0} (21)

According to Russell's invariant set theorems,