CN105676641A - Nonlinear robust controller design method based on back-stepping and sliding mode control technologies and aimed at nonlinear model of quad-rotor unmanned plane - Google Patents

Abstract

The invention discloses a nonlinear robust controller design method based on back-stepping and sliding mode control technologies and aimed at a nonlinear model of a quad-rotor unmanned plane. A sliding mode controller of a speed-constant reaching law is designed to an attitude angle system of the quad-rotor unmanned plane, and rapid tracking for the attitude angle is ensured. To realize track tracking for the spatial position of the quad-rotor unmanned plane, a sliding mode surface and a virtual control quantity are constructed according to a stepping back control idea to realize nonlinear control law design and system stability design from the kernel to the external layer of a system. After an equation of the related virtual control quantity is obtained, an expected track value of the attitude angle is obtained by solving the equation via arithmetic inverse operation, and a design method of the speed-constant reaching law is used to determine a final input control law of the quad-rotor unmanned plane system. According to the method of the invention, the characteristic that sliding mode control is uncertain for the model and insensitive to external interference is utilized, robust trace tracking for the nonlinear quad-rotor unmanned plane can be controlled under interference.

Description

For four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques

Technical field

The present invention relates to a kind of based on the control method followed the tracks of for four rotor wing unmanned aerial vehicle location track of sliding mould control and non-linear Reverse Step Control, belong to unmanned aerial vehicle (UAV) control technical field.

Background technology

As the newborn member without man-machine family, four rotor wing unmanned aerial vehicles with its important in practical application area and widely purposes and receive the concern of many scholars and researchist, cause their very big interest. Four rotor wing unmanned aerial vehicles play more and more important effect in military reconnaissance, natural disaster monitoring, agricultural imaging and rescue task. This kind is VTOL without man-machine main advantage, determines higher suspension and any direction flight. Although there is so many application advantages, but the Some features of four rotor wing unmanned aerial vehicles itself, such as non-linear, tight coupling and drive lacking etc. so that flight high-quality and maneuvering ability are difficult to effectively be ensured. The conventional control method of current some is the linear model on each trim point after linear mainly, has the shortcomings such as dynamicrange is little, model out of true, poor anti jamming capability. Other control method, such as, based on the neural network control method of artificial intelligence, fuzzy control method etc., has only verified, it is achieved property and popularization on a large scale also take long enough at present on software emulation platform. Control method based on non-linear Reverse Step Control and the control of sliding mould is had clear superiority and show one's talent in numerous control method with it in freedom from jamming, accuracy, robustness, realisation and dynamicrange, is of great significance by the Trajectory Tracking Control tool realizing four rotor wing unmanned aerial vehicles.

Backstepping control method is a kind of method carrying out point stabilization design for nonlinear dynamic system proposed about nineteen ninety by people such as PetarV.Kokotovic, very effective when carrying out Controller gain variations for a quasi-nonlinear system. This quasi-nonlinear system is generally based upon on some subsystem, and these subsystems itself can realize calm by other control method. Usually, non-linear system that can be just complicated resolves into the subsystem being no more than systematic education, then from kernel, Li Yapunuofu function and intermediate virtual manipulated variable is designed for each subsystem partitions, and always by this process " retrogressing " to whole system, finally the Li Yapunuofu function of each subsystem is integrated the stability ensureing whole system. This kind designs from the kernel of Complex Nonlinear System, realizes in feedback fashion, and from inside to outside by layer design until obtain the control law of final form, and the process ensureing the stability of system is exactly typical Reverse Step Control process. Needing to design virtual controlling amount to ensure the stable of subsystem in contragradience process, the design of these virtual amounts simultaneously also to be met the ability regulating or following the tracks of of system as far as possible, makes system reach the performance index of expectation. The process of this kind of progressive alternate can be realized by symbol algebraically software, convenient and swift, further promotes Reverse Step Control in the widespread use of non-linear field.

Sliding mould control is a kind of nonlinear control method utilizing discontinuous control signal to change non-linear system kinetic characteristic.This kind of discontinuous control signal forces system to be slided near the lineoid of normality behavior, so that system has the dynamic property of expectation. Sliding mould control is a kind of control method of structure changes, and system architecture always switches between different structures according to current state position information, and uses the state feedback control law that sliding-mode control designs generally neither the continuous function of time. The principle of Sliding mode variable structure control is the tangential-hoop method that the kinetic characteristic desired by system designs system, by sliding mode control, system state is collected from the extroversion tangential-hoop method of lineoid. System is once arrival tangential-hoop method, and guarantee system is arrived system origin along tangential-hoop method by control action kou, and this process slided along tangential-hoop method to initial point is called that sliding mould controls. In sliding mould controls, the kinetic characteristic of system and lineoid choose and the nearly rule that becomes of sliding mode controller closely related, do not affect by external interference, model parameter changed insensitive, so that Sliding mode variable structure control has very strong robustness. On the other hand, sliding mould control does not need online identification, and control law is all generally realized by state or output feedack, so that sliding mould control has the advantage of fast response time.

Summary of the invention

Goal of the invention: in order to overcome the deficiencies in the prior art, the present invention provide a kind of for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, the method is for complex nonlinear model, it is possible to effectively avoid the inaccuracy that local linearization is brought; Responding range is big, overcomes linear differential integral control in the dynamic restriction among a small circle of trim point; Give overall unified nonlinear Control device, avoid the negative effect switching between controller and bringing.

Technical scheme: for achieving the above object, the technical solution used in the present invention is:

For four rotor wing unmanned aerial vehicle nonlinear models based on a method of design for contragradience and the nonlinear robust control device of sliding mould control techniques, comprise the following steps:

Step 1, obtains the physical location track of four rotor wing unmanned aerial vehicles, reference by location track and yawing angle reference locus; The tracking errors dynamic subsystem about each state variables is set up successively, all tracking errors dynamic subsystem composition tracking errors dynamic systems according to physical location track and reference by location track; Described state variables comprises attitude angle and first order derivative, position and first order derivative thereof.

Step 2, according to the tracking errors dynamic system that step 1 is set up, design can ensure the contragradience sliding mode controller of the feedback asymptotic tracking that error system is stable and restrains; Described contragradience sliding mode controller utilizes each tracking errors dynamic subsystem that the thought of Reverse Step Control is tracking errors dynamic system to design corresponding virtual controlling amount and sliding-mode surface, the tracking errors dynamic subsystem stability ensured by layer and dynamic property, until obtaining the virtual controlling amount that can ensure location track tracking power and input about attitude angle state and reality.

Step 3, virtual controlling amount step 2 obtained carries out arithmetic and inverts, and asks for four rotor wing unmanned aerial vehicle attitude angle expected values, and this attitude angle expected value comprises the 4th control component of rolling angle desired trajectory, angle of pitch desired trajectory and four rotor wing unmanned aerial vehicles.

Step 4, the yawing angle reference locus that rolling angle desired trajectory, angle of pitch desired trajectory and the step 1 obtained for step 3 obtains designs based on the conventional sliding mode tracking control device of attitude angle that constant speed becomes near respectively, obtain the sliding mould control law of four rotor wing unmanned aerial vehicles according to the conventional sliding mode tracking control device of this attitude angle, described sliding mould control law comprises the first control component, the 2nd control component and the 3rd control component.

Step 5, follows the tracks of reference locus under the effect of sliding mould control law that four rotor wing unmanned aerial vehicles obtain at the 4th control component obtained according to step 3 and step 4, and then the robust trajectory tracking control of non-linear four rotor wing unmanned aerial vehicles realized under disturbing.

Preferred: the nonlinear model of four rotor wing unmanned aerial vehicles in described step 1 is:

Wherein,It it is the state variables of system; Its physical meaning is attitude angle (φ, θ, ψ) and first order derivative thereof successivelyPosition (x, y, z) and first order derivative thereofCan entirety be expressed as followsφ is rolling angle, and θ is the angle of pitch, and ψ is yawing angle, a_i, i=1,2 ... 11 is the known constant value parameter of standardization;Being online identifier, g is universal gravity constant, U_i, i=1,2,3,4 is the working control input of system, U_i, i=1,2,3,4 is followed successively by the first control component, the 2nd control component, the 3rd control component and the 4th control component in order, S_(·)And C_(·)Represent trigonometric sine and cosine function respectively.

Preferred: the virtual controlling amount in described step 2 is:

$v_2={\stackrel{\·}{v}}_1+z_7+a_9{x}_8+{\mathrm{\ρ}}_2{s}_{p1}$

$v_4={\stackrel{\·}{v}}_3+z_9+a_{10}{x}_{10}+{\mathrm{\ρ}}_4{s}_{p2}$

$v_6={\stackrel{\·}{v}}_5+z_{11}+g+a_{11}{x}_{12}+{\mathrm{\ρ}}_6{s}_{p3};$

Wherein, v_2i, i=1,2,3 is virtual controlling amount, v_2i-1At acquisition v_2iBetween it has been determined that and its first order derivativeCan by v_2i-1Carry out first differential filtering acquisition, z₇、z₉、z₁₁It is the tracking errors of position (x, y, z) respectively, and z₇=x_7r-x₇, z₉=x_9r-x₉, z₁₁=x_11r-x₁₁; x_7r、x_9r、x_11rIt is the reference locus of position (x, y, z) respectively, ρ₂、ρ₄、ρ₆It is the optional constant value arithmetic number of position (x, y, z), s_p1、s_p2、s_p2It is the sliding-mode surface for position variable respectively.

Preferred: described step 3 carrying out the virtual controlling amount equation that arithmetic inverts is:

$v_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4$

$v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4$

$v_6=\left(C_{x_1}{C}_{x_3}\right)U_4;$

Wherein, v_2i, i=1,2,3 is virtual controlling amount, S_(·)And C_(·)Represent trigonometric sine and cosine function, U respectively₄Represent the 4th control component, x₁,x₃,x₅Represent rolling angle φ, pitching angle theta, yaw angle ψ respectively.

Preferred: the attitude angle desired trajectory and the 4th in described step 3 controls component and is:

$\{\begin{array}{c}{x}_{1d}=\arctan \left(\frac{{\mathrm{acv}}_6-{\mathrm{lv}}_4}{{\mathrm{av}}_6\sqrt{c^2+l^2}}\right)\\ x_{3d}=\arctan \left(\frac{c}{l}\right)\\ U_4=\frac{a^2(c^2+l^2){v_6}^2+{({\mathrm{acv}}_6+{\mathrm{lv}}_4)}^2}{al}\end{array};$

Wherein, x_1dRepresent rolling angle desired trajectory, x_3dRepresent angle of pitch desired trajectory, U₄Represent the 4th control component, a=cos (x_5r), b=sin (x_5r), c=(v₂+v₄)/v₆, l=a+b.

Preferred: the sliding mould control law obtained in described step 4 is:

Wherein, U_i, i=1,2,3 is the first control component, the 2nd control component, the 3rd control component respectively, z₁,z₃,z₅It is about location track (x, y, z) tracking errors respectively, and z₁=x_7r-x₇, z₃=x_9r-x₉, z₅=x_11r-x₁₁, wherein x_7r、x_9r、x_11rThe reference locus being respectively position (x, y, z), s₁(z₁)、s₃(z₃)、s₅(z₅) it is the sliding-mode surface for tracing positional respectively.

Preferred: described sliding-mode surface is chosen as follows:

$\{\begin{array}{c}{s}_1={\stackrel{\·}{\mathrm{\ϵ}}}_1+c_1{\mathrm{\ϵ}}_1\\ s_2={\stackrel{\·}{\mathrm{\ϵ}}}_2+c_2{\mathrm{\ϵ}}_2\\ s_3={\stackrel{\·}{\mathrm{\ϵ}}}_3+c_3{\mathrm{\ϵ}}_3\end{array};$

Wherein, s₁(z₁),s₃(z₃),s₅(z₅) it is the sliding-mode surface for tracing positional respectively, ε_i=η_id-η_i, i=1,3,5 is corresponding attitude angle tracking errors, c_i, i=1,2,3 is optional arithmetic number and velocity of approach with control law has related parameter.

In described step 2, virtual controlling amount choosing method is as follows:

The first step, for the follow-up control of position x selects the first error metrics V₁As follows:

$V_1=\frac{1}{2}{z_7}^2;$

Wherein, V₁Represent that the follow-up control of position x selects the first error metrics, z₇=x_7r-x₇Represent the tracking errors of position x and its desired trajectory, x₇Represent level attitude x, x_7rRepresent level attitude x desired trajectory.

Select the first virtual controlling amount v₁As follows:

$v_1={\stackrel{\·}{x}}_{7r}+{\mathrm{\ρ}}_1{z}_7;$

To the tracking errors z of position x and its desired trajectory₇Ask first order derivative also s_p1And v₁Substituting into asks the expression formula after leading to obtain:

${\stackrel{\·}{V}}_1=-{\mathrm{\ρ}}_1{z_7}^2+z_7{s}_{p1};$

s_p1The sliding-mode surface chosen for position x track following; ρ₁、ρ₂It it is optional adjustable arithmetic number.

2nd step: choose the 2nd virtual controlling amountAnd the 2nd error metrics V₂Augmentation becomes following form:

$V_2=\frac{1}{2}({z_1}^2+{s_{p1}}^2);$

To the 2nd error metrics V after augmentation₂Seek first order derivative and handleAnd v₂Substituting into asks the expression formula after leading to obtain:

${\stackrel{\·}{V}}_2=-{\mathrm{\ρ}}_1{z_7}^2+s_{p1}({\stackrel{\·}{v}}_1+z_7+a_9{x}_8-v_2).$

In order to ensureNegative qualitative, the 2nd virtual controlling amount v chosen₂As follows;

$v_2={\stackrel{\·}{v}}_1+z_7+a_9{x}_8+{\mathrm{\ρ}}_2{s}_{p1}.$

It has been determined that v₂Substitute intoIn, can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_2=-{\mathrm{\ρ}}_1{z_7}^2-{\mathrm{\ρ}}_2{s_{p1}}^2\\ \≤0\end{array}.$

3rd step: for the follow-up control of level attitude y selects the 3rd error metrics V₃As follows:

$V_3=\frac{1}{2}{z_9}^2;$

Wherein, z₉=x_9r-x₉Represent the tracking errors of position y and its desired trajectory, the 3rd virtual controlling amount v₃Select as follows:

$v_3={\stackrel{\·}{x}}_{9r}+{\mathrm{\ρ}}_3{z}_9;$

To V₃Ask first order derivative also s_p2And v₃Substituting into asks the expression formula after leading can obtain V₃Derivative as follows:

$\begin{array}{c}{\stackrel{\·}{V}}_3=z_9{\stackrel{\·}{z}}_9=z_9({\stackrel{\·}{x}}_{9r}-x_{10})=z_9({\stackrel{\·}{x}}_{9r}-v_3+s_{p2})\\ =z_9({\stackrel{\·}{x}}_{9r}-v_3+s_{p2})\\ =-{\mathrm{\ρ}}_3{z_9}^2+z_9{s}_{p2}\end{array}.$

4th step: choose the 4th virtual controlling amountThe error metrics of first three step is included in the error metrics of this step, then the 4th error metrics V after augmentation₄As follows:

$V_4=\frac{1}{2}({z_7}^2+{s_{p1}}^2+{z_9}^2+{s_{p2}}^2);$

To V₄Seek first order derivative, and the respective fictional amount designed substituted into and asks the expression formula after leading to obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_4=z_7{\stackrel{\·}{z}}_7+s_{p1}{\stackrel{\·}{s}}_{p1}+z_9{\stackrel{\·}{z}}_9+s_{p2}{\stackrel{\·}{s}}_{p2}\\ ={\stackrel{\·}{V}}_2+z_9(-{\mathrm{\ρ}}_3{z}_9+s_{p2})+s_2({\stackrel{\·}{v}}_3-{\stackrel{\·}{x}}_{10})\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}(z_9+{\stackrel{\·}{v}}_3-(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4+a_{10}{x}_{10})\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}(z_9+{\stackrel{\·}{v}}_3-v_4+a_{10}{x}_{10})\end{array};$

In this step, the 4th selected virtual controlling amount v₄Design as follows:

$v_4={\stackrel{\·}{v}}_3+z_9+a_{10}{x}_{10}+{\mathrm{\ρ}}_4{s}_{p2};$

The v designed₄Substitute intoIn, can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_4={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}(z_9+{\stackrel{\·}{v}}_3-v_4+a_{10}{x}_{10})\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2-{\mathrm{\ρ}}_4{s_{p2}}^2\≤0\end{array}.$

5th step: for the follow-up control of height z selects the 5th error metrics V₅As follows:

$V_5=\frac{1}{2}{z_{11}}^2;$

Wherein, z₁₁=x_11r-x₁₁Represent tracking errors the 5th virtual controlling amount v of height z and its desired trajectory₅Choose as follows:

$v_5={\stackrel{\·}{x}}_{11r}+{\mathrm{\ρ}}_5{z}_{11};$

To V₅Seek first order derivative, and s_p3And v₅Substituting into asks the expression formula after leading to obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_5=z_{11}{\stackrel{\·}{z}}_{11}=z_{11}({\stackrel{\·}{x}}_{11r}-x_{12})\\ =z_{11}({\stackrel{\·}{x}}_{11r}-v_5+s_{p3})\\ =-{\mathrm{\ρ}}_5{z_{11}}^2+z_{11}{s}_{p3}\end{array}.$

6th step: choose the 6th virtual controlling amountSimultaneously for meeting the requirement of system stability, the error metrics that the first five is walked is included in the 6th error metrics V after augmentation₆Among, as follows:

$V_6=\frac{1}{2}({z_7}^2+{s_{p1}}^2+{z_9}^2+{s_{p2}}^2+{z_{11}}^2+{s_{p3}}^2);$

By the 6th virtual controlling amount v₆It is designed toAnd substitute into V₆Ask in the expression formula after leading and can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_6=z_7{\stackrel{\·}{z}}_7+s_{p1}{\stackrel{\·}{s}}_{p1}+z_9{\stackrel{\·}{z}}_9+s_{p2}+z_{11}{\stackrel{\·}{z}}_{11}+s_{p3}{\stackrel{\·}{s}}_{p3}\\ ={\stackrel{\·}{V}}_4+z_{11}(-{\mathrm{\ρ}}_5{z}_{11}+s_3)+s_3({\stackrel{\·}{v}}_5-{\stackrel{\·}{x}}_{12})\\ ={\stackrel{\·}{V}}_4-{\mathrm{\ρ}}_5{z_{11}}^2+s_3(z_{11}+{\stackrel{\·}{v}}_5+g+a_{12}{x}_{12}-v_6)\\ ={\stackrel{\·}{V}}_4-{\mathrm{\ρ}}_5{z_{11}}^2-{\mathrm{\ρ}}_6{s_{p3}}^2\≤0\end{array};$

Wherein, relevant to attitude angle manipulated variable it is only:

$\{\begin{array}{c}{v}_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4\\ v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4\\ v_6=\left(C_{x_1}{C}_{x_3}\right)U_4\end{array}.$

Preferred: the first control component, the 2nd control component, the 3rd control component and the 4th control component are as follows respectively:

Wherein, U_iI=1,2,3,4 is the first control component, the 2nd control component, the 3rd control component and the 4th control component respectively, and the first control representation in components rolling angle control law, the 2nd control representation in components angle of pitch control law, the 3rd control representation in components yawing angle control law, 4th control representation in components Position Tracking Control rule, x_1d,x_3dIt is rolling angle expected value, angle of pitch expected value, x_5dIt is the reference locus of yawing angle, k_i,c_i, i=1,2,3 is optional arithmetic number and velocity of approach with control law has related parameter, a_i, i=1,2 ... 11 is the known constant value parameter of standardization,It is online identifier, x₂,x₄,x₆Be respectively rolling angle, the angle of pitch, yawing angle rank partially lead; A=cos (x_5r), b=sin (x_5r), c=(v₂+v₄)/v₆, l=a+b; v₂,v₄,v₆For being respectively the 2nd, the 4th, the 6th virtual controlling amount.

Useful effect: provided by the invention a kind of for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, compared with prior art, there is following obvious technique effect: for complex nonlinear model, it is possible to effectively avoid the inaccuracy that local linearization is brought; Responding range is big, overcomes linear differential integral control in the dynamic restriction among a small circle of trim point; Adopt constant speed to become to closely restraining sliding-mode surface, make system have very strong immunity from interference; Give overall unified nonlinear Control device, avoid the negative effect switching between controller and bringing.

Accompanying drawing explanation

Fig. 1 is the skeleton diagram of control program in the present invention.

The method that Fig. 2 provides in this patent for utilizing carries out locus and the yawing angle tracking effect figure of Trajectory Tracking Control.

The method that Fig. 3 provides in this patent for utilizing under noise jamming carries out locus and the yawing angle tracking effect figure of Trajectory Tracking Control.

Embodiment

Below in conjunction with the drawings and specific embodiments, illustrate the present invention further, these examples should be understood only be not used in for illustration of the present invention and limit the scope of the invention, after having read the present invention, the amendment of the various equivalent form of values of the present invention is all fallen within the application's claims limited range by those skilled in the art.

Embodiment

A kind of for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, as shown in Figure 1, first attitude angle subsystem for four rotor wing unmanned aerial vehicle systems carries out sliding mode controller design, by choosing of the nearly rule that becomes, ensure that attitude angle is to the quick tracking expecting attitude angle track. On this basis, from system outer shroud performance index, utilize the method for non-linear Reverse Step Control that four rotor wing unmanned aerial vehicle systems are carried out location track follow-up control, design the actual input control law meeting performance requriements.

As shown in Figure 1, specifically comprise the following steps:

Step 1, obtains the physical location track of four rotor wing unmanned aerial vehicles, reference by location track and yawing angle reference locus; For ensureing the physical location track (acturaltrajectory) of four rotor wing unmanned aerial vehicles) track can effective track reference position (referencetrajectory), set up the tracking errors dynamic subsystem about each state variables successively, all tracking errors dynamic subsystem composition tracking errors dynamic systems; Described state variables comprises attitude angle and first order derivative, position and first order derivative thereof.

The attitude angle subsystem dynamic equation of four rotor wing unmanned aerial vehicles is as follows:

Whereinφ,It is rolling angle and rolling angular derivative respectively, θ,It is the angle of pitch and angle of pitch derivative respectively, ψ,It is yawing angle and yawing angle derivative respectively, U_si, i=1,2,3 is the control law followed the tracks of and design for meeting attitude angle respectively.

Sliding mode control algorithm design for four rotor wing unmanned aerial vehicle attitude angle follow-up control is as follows:

Wherein, η_1d,η_3d,η_5dIt is the desired trajectory of rolling angle, the angle of pitch and yawing angle respectively, k_i,c_i, i=1,2,3 is optional arithmetic number and relevant with the velocity of approach of control law, ε_i=η_id-η_i, i=1,3,5 is tracking errors, sign () is-symbol function, a_i, i=1,2 ... 11 is the known constant value parameter of standardization,It is online identifier and can easily obtain.

The nonlinear model of four rotor wing unmanned aerial vehicles is:

Wherein,It it is the state variables of system; Its physical meaning is attitude angle (φ, θ, ψ) and first order derivative thereof successivelyPosition (x, y, z) and first order derivative thereofCan entirety be expressed as followsφ is rolling angle, and θ is the angle of pitch, and ψ is yawing angle, a_i, i=1,2 ... 11 is the known constant value parameter of standardization;Being online identifier, g is universal gravity constant, U_i, i=1,2,3,4 is the working control input of system, U_i, i=1,2,3,4 is followed successively by the first control component, the 2nd control component, the 3rd control component and the 4th control component in order, S_(·)And C_(·)Represent trigonometric sine and cosine function respectively.

Being typical under-actuated systems by Ore-controlling Role, namely the actual input number of system is less than system work output number, and in the four rotor mathematical models that this patent relates to, actual input has 4, i.e. U_i, i=1,2,3,4, work output has 12, i.e. x₁,x₂,x₃,x₄,x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁,x₁₂. The characteristics determined of under-actuated systems controller can not realize the follow-up control to all work outpuies simultaneously, thus selects yawing angle and the four rotors position under inertial coordinates system in this patent, i.e. x₅,x₇,x₉,x₁₁As needing the work output realizing track following.

Controller gain variations process will from the performance index requirement of system, and the performance index from outer shroud to inner ring to be met one by one, then realizes the Controller gain variations from inner ring to outer shroud according to the inverse process of said process. Concrete feature is as follows: first, and in design, ring controller realizes the follow-up control to attitude angle, is also exactly to x₁,x₃,x₅Rapid track and control so that x₁,x₃,x₅Expected value can be reached fast.Then, design outer ring controller on this basis, indirectly realize the follow-up control to outer shroud variable, be also exactly the follow-up control of location track, thus realize by the over-all properties index of Ore-controlling Role.

The design of interior ring controller is realized by the control method of sliding moding structure, it is inner ring controlled variable (attitude angle) to choose suitable sliding mould surface and choose and suitable become to closely restraining parameter, then for the sliding mould control law that the design of each controlled variable is suitable, ensure sliding-mode surface accessibility (reachability) and by the stability (stability) of control subsystem, and realize the rapid track and control of inner ring variable (attitude angle) on this basis.

In order to ensure that, to outer shroud controlled variable, namely locus is to the follow-up control of input trajectory, it is necessary to assume that virtual controlling amount, it is then determined that the value of virtual controlling amount. The value of virtual controlling amount to be combined with Backstepping techniques, ensures system stability from inside to outside and performance index. When carrying out the design of current virtual controlling amount, it is assumed that the value of virtual controlling amount designed before this is it has been determined that and be known.

Step 2, according to the tracking errors dynamic system that step 1 is set up, design can ensure the contragradience sliding mode controller of the feedback asymptotic tracking that error system is stable and restrains; Described contragradience sliding mode controller utilizes each tracking errors dynamic subsystem that the thought of Reverse Step Control is tracking errors dynamic system to design corresponding virtual controlling amount and sliding-mode surface, the tracking errors dynamic subsystem stability ensured by layer and dynamic property, until obtaining the virtual controlling amount that can ensure location track tracking power and input about attitude angle state and reality.

In order to ensure outer shroud controlled variable, i.e. the follow-up control of locus track, it is necessary to assume that virtual controlling amount, it is then determined that the value of virtual controlling amount. The value of virtual controlling amount to be combined with Backstepping techniques, ensures system stability from inside to outside and performance index. When carrying out the design of current virtual controlling amount, it is assumed that the value of virtual controlling amount designed before this is it has been determined that and be known. The virtual controlling amount that input actual in system used in this patent is associated is selected as follows respectively.

The attitude angle state of virtual controlling amount and system and working control amount U₄Relation as follows:

$v_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4$

$v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4$

$v_6=\left(C_{x_1}{C}_{x_3}\right)U_4;$

Wherein, v_2i, i=1,2,3 is the virtual controlling amount of track reference track, S_(·)And C_(·)Represent trigonometric sine and cosine function, U respectively₄For Position Tracking Control rule, x₁、x₃、x₅φ is rolling angle respectively, and θ is the angle of pitch, and ψ is yawing angle.

In this patent, the value of above-mentioned virtual controlling amount is determined according to mode below:

$v_2={\stackrel{\·}{v}}_1+z_7+a_9{x}_8+{\mathrm{\ρ}}_2{s}_{p1}$

$v_4={\stackrel{\·}{v}}_3+z_9+a_{10}{x}_{10}+{\mathrm{\ρ}}_4{s}_{p2}$

$v_6={\stackrel{\·}{v}}_5+z_{11}+g+a_{11}{x}_{12}+{\mathrm{\ρ}}_6{s}_{p3}$

Wherein, v_2i, i=1,2,3 is virtual controlling amount, v_2i-1At acquisition v_2iBetween it has been determined that and its first order derivativeCan by v_2i-1Carry out first differential filtering acquisition, z₇、z₉、z₁₁It is the tracking errors of position (x, y, z) respectively, and z₇=x_7r-x₇, z₉=x_9r-x₉, z₁₁=x_11r-x₁₁; x_7r、x_9r、x_11rIt is the reference locus of position (x, y, z) respectively, ρ₂、ρ₄、ρ₆It is the optional constant value arithmetic number of position (x, y, z), s_p1、s_p2、s_p2It is the sliding-mode surface for position variable respectively. At design v₂Time, according to ' virtual controlling amount designed before this be in current step it has been determined that and be known ' principle, v₁Determine and it is known, then its derivativeAlso it is known. z₇=x_7r-x₇It is tracking errors, x_7rIt is input reference locus, ρ₂It is optional adjustable arithmetic number, s_p1Be can real-time online obtain parameter, all the other symbols are consistent with the description in feature 1.Therefore, v₂Design complete in this step. v₄, v₆Design process and v₂Identical, each involved meaning of parameters is also similar.

For the sliding mode control algorithm of attitude angle subsystem, the guarantee of attitude angle tracking performance can be obtained by it by following method of proof:

First, for rolling angle follow-up control designed by sliding-mode surface as follows:

$s_1={\stackrel{\·}{\mathrm{\ϵ}}}_1+c_1{\mathrm{\ϵ}}_1$

It is as follows to the first order derivative of time:

For sliding-mode surface s₁The constant speed of the design nearly rule that becomes is as follows:

Similarly, sliding-mode surface designed by the follow-up control of the angle of pitch and yawing angle is respectively s₂And s₃:

$\left\{\begin{array}{c}{s}_2={\stackrel{\·}{\mathrm{\ϵ}}}_2+c_2{\mathrm{\ϵ}}_2\\ s_3={\stackrel{\·}{\mathrm{\ϵ}}}_3+c_3{\mathrm{\ϵ}}_3\end{array}\right.$

The constant speed designed respectively for above two sliding-mode surfaces nearly rule that becomes is as follows:

It is as follows to be that four rotor attitude angle subsystems choose Li Yapunuofu function:

$V_s=\frac{1}{2}({s_1}^2+{s_2}^2+{s_3}^2)\≥0$

It is sought first order derivative and sliding for the constant speed designed mould is become to closely restraining U_si, after i=1,2,3 substitutes into, the first order derivative of closed loop system Li Yapunuofu function is as follows:

$\begin{array}{c}{\stackrel{\·}{V}}_s=s_1{\stackrel{\·}{s}}_1+s_2{\stackrel{\·}{s}}_2+s_3{\stackrel{\·}{s}}_3\\ ={\Σ}_{i=1}^3{s}_i({\stackrel{\·\·}{\mathrm{\η}}}_{2i-1,d}+c_i{\stackrel{\·}{\mathrm{\ϵ}}}_{2i-1}-{\stackrel{\·}{\mathrm{\η}}}_{2i}-U_{si})\\ =-{\Σ}_{i=1}^3{s}_i*k_{i}sign\left(s_i\right)=-{\Σ}_{i=1}^3{k}_i\left|s_i\right|\\ \≤0\end{array}$

Above two formulas describe V_sJust qualitative andNegative qualitative, be stable according to the theoretical closed loop control system of Lyapunov stability. Meanwhile, above two formulas also demonstrate the accessibility of sliding-mode surface, thus ensure that the track following performance of attitude angle subsystem. Broadly, can ensure that attitude angle traces into the track of expectation fast by designing suitable sliding mould control law. Like this, when carrying out four rotor wing unmanned aerial vehicle location track follow-up control, it is possible to ensured the final tracking of location track as intermediate steps by the quick tracking of guarantee attitude angle.

Its virtual controlling amount choosing method is as follows:

The first step, for the follow-up control of position x selects the first error metrics V₁As follows:

$V_1=\frac{1}{2}{z_7}^2;$

Wherein, V₁Represent that the follow-up control of position x selects the first error metrics, z₇=x_7r-x₇Represent the tracking errors of position x and its desired trajectory, x₇Represent level attitude x, x_7rRepresent level attitude x desired trajectory.

Select the first virtual controlling amount v₁As follows:

$v_1={\stackrel{\·}{x}}_{7r}+{\mathrm{\ρ}}_1{z}_7;$

To the tracking errors z of position x and its desired trajectory₇Ask first order derivative also s_p1And v₁Substituting into asks the expression formula after leading to obtain:

${\stackrel{\·}{V}}_1=-{\mathrm{\ρ}}_1{z_7}^2+z_7{s}_{p1};$

s_p1The sliding-mode surface chosen for position x track following; ρ₁、ρ₂It it is optional adjustable arithmetic number.

Due to z₇s_p1Positive negativity is uncertain, and this step cannot ensureNegative fixed, therefore also just cannot ensure the convergence of tracking errors, contragradience process needs to continue.

2nd step: choose the 2nd virtual controlling amountAnd the 2nd error metrics V₂Augmentation becomes following form:

$V_2=\frac{1}{2}({z_1}^2+{s_{p1}}^2);$

To the 2nd error metrics V after augmentation₂Seek first order derivative and handleAnd v₂Substituting into asks the expression formula after leading to obtain:

${\stackrel{\·}{V}}_2=-{\mathrm{\ρ}}_1{z_7}^2+s_{p1}({\stackrel{\·}{v}}_1+z_7+a_9{x}_8-v_2).$

In order to ensureNegative qualitative, the 2nd virtual controlling amount v chosen₂As follows;

$v_2={\stackrel{\·}{v}}_1+z_7+a_9{x}_8+{\mathrm{\ρ}}_2{s}_{p1}.$

It has been determined that v₂Substitute intoIn, can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_2=-{\mathrm{\ρ}}_1{z_7}^2-{\mathrm{\ρ}}_2{s_{p1}}^2\\ \≤0\end{array}.$

Like this, by choosing and virtual controlling amount v reasonable in design₁,v₂Just can ensure the track following of level attitude x. But, it is to be noted that virtual controlling amount is not the actual input control of four rotor systems, and it is only a middle variable relevant to system state amount and actual input control, in order to obtain the actual input control of final form, it is necessary to Reverse Step Control step is continued.

3rd step: for the follow-up control of level attitude y selects the 3rd error metrics V₃As follows:

$V_3=\frac{1}{2}{z_9}^2;$

Wherein, z₉=x_9r-x₉Represent the tracking errors of position y and its desired trajectory, the 3rd virtual controlling amount v₃Select as follows:

$v_3={\stackrel{\·}{x}}_{9r}+{\mathrm{\ρ}}_3{z}_9;$

To V₃Ask first order derivative also s_p2And v₃Substituting into asks the expression formula after leading can obtain V₃Derivative as follows:

$\begin{array}{c}{\stackrel{\·}{V}}_3=z_9{\stackrel{\·}{z}}_9=z_9({\stackrel{\·}{x}}_{9r}-x_{10})=z_9({\stackrel{\·}{x}}_{9r}-v_3+s_{p2})\\ =z_9({\stackrel{\·}{x}}_{9r}-v_3+s_{p2})\\ =-{\mathrm{\ρ}}_3{z_9}^2+z_9{s}_{p2}\end{array}.$

Due to z₉s_p2Positive negativity be can not determine, thus cannot ensureNegative qualitative, thus also just cannot ensure the convergence of tracking errors, contragradience process also needs to continue.

4th step: choose the 4th virtual controlling amountAccording to the requirement of Reverse Step Control antithetical phrase system stability, the error metrics of first three step is included in the error metrics of this step, then the 4th error metrics V after augmentation₄As follows:

$V_4=\frac{1}{2}({z_7}^2+{s_{p1}}^2+{z_9}^2+{s_{p2}}^2);$

To V₄Seek first order derivative, and the respective fictional amount designed substituted into and asks the expression formula after leading to obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_4=z_7{\stackrel{\·}{z}}_7+s_{p1}{\stackrel{\·}{s}}_{p1}+z_9{\stackrel{\·}{z}}_9+s_{p2}{\stackrel{\·}{s}}_{p2}\\ ={\stackrel{\·}{V}}_2+z_9(-{\mathrm{\ρ}}_3{z}_9+s_{p2})+s_2({\stackrel{\·}{v}}_3-{\stackrel{\·}{x}}_{10})\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}(z_9+{\stackrel{\·}{v}}_3-(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4+a_{10}{x}_{10})\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}(z_9+{\stackrel{\·}{v}}_3-v_4+a_{10}{x}_{10})\end{array};$

In this step, the 4th selected virtual controlling amount v₄Design as follows:

$v_4={\stackrel{\·}{v}}_3+z_9+a_{10}{x}_{10}+{\mathrm{\ρ}}_4{s}_{p2};$

The v designed₄Substitute intoIn, can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_4={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}(z_9+{\stackrel{\·}{v}}_3-v_4+a_{10}{x}_{10})\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2-{\mathrm{\ρ}}_4{s_{p2}}^2\≤0\end{array}.$

Like this, by respective fictional amount v in first, second, third and fourth step₁,v₂,v₃,v₄Choose and design, just ensure that four rotor wing unmanned aerial vehicle level attitude x, the Trajectory Tracking Control on y. It is noted that virtual controlling amount v₁,v₃Only relevant to the quantity of state of reference locus and system and do not associate with the working control amount of system. v₂,v₄Except with reference locus and system state amount mutually outside the Pass, also with the input U of the reality of system₄Relevant. Up to the present, still cannot obtaining the working control rule of system, contragradience process should continue.

5th step: for the follow-up control of level attitude (highly) z selects the 5th error metrics V₅As follows:

$V_5=\frac{1}{2}{z_{11}}^2;$

Wherein, z₁₁=x_11r-x₁₁Represent tracking errors the 5th virtual controlling amount v of height z and its desired trajectory₅Choose as follows:

$v_5={\stackrel{\·}{x}}_{11r}+{\mathrm{\ρ}}_5{z}_{11};$

To V₅Seek first order derivative, and s_p3And v₅Substituting into asks the expression formula after leading to obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_5=z_{11}{\stackrel{\·}{z}}_{11}=z_{11}({\stackrel{\·}{x}}_{11r}-x_{12})\\ =z_{11}({\stackrel{\·}{x}}_{11r}-v_5+s_{p3})\\ =-{\mathrm{\ρ}}_5{z_{11}}^2+z_{11}{s}_{p3}\end{array}.$

Due to z₁₁s_p3Positive negativity be can not determine, thus this step cannot ensureNegative qualitative, thus also just cannot ensure the convergence of tracking errors, contragradience process still needs to continue.

6th step: for realizing the follow-up control of location track, this step chooses the 6th virtual controlling amountSimultaneously for meeting the requirement of system stability, the error metrics that the first five is walked is included in the 6th error metrics V after augmentation₆Among, as follows:

$V_6=\frac{1}{2}({z_7}^2+{s_{p1}}^2+{z_9}^2+{s_{p2}}^2+{z_{11}}^2+{s_{p3}}^2);$

By the 6th virtual controlling amount v₆It is designed toAnd substitute into V₆Ask in the expression formula after leading and can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_6=z_7{\stackrel{\·}{z}}_7+s_{p1}{\stackrel{\·}{s}}_{p1}+z_9{\stackrel{\·}{z}}_9+s_{p2}{\stackrel{\·}{s}}_{p2}+z_{11}{\stackrel{\·}{z}}_{11}+s_{p3}{\stackrel{\·}{s}}_{p3}\\ ={\stackrel{\·}{V}}_4+z_{11}(-{\mathrm{\ρ}}_5{z}_{11}+s_3)+s_3({\stackrel{\·}{v}}_5-{\stackrel{\·}{x}}_{12})\\ ={\stackrel{\·}{V}}_4-{\mathrm{\ρ}}_5{z_{11}}^2+s_3(z_{11}+{\stackrel{\·}{v}}_5+g+a_{12}{x}_{12}-v_6)\\ ={\stackrel{\·}{V}}_4-{\mathrm{\ρ}}_5{z_{11}}^2-{\mathrm{\ρ}}_6{s_{p3}}^2\≤0\end{array};$

Due to V₆Be positive definite andIt is negative fixed, theoretical it will be seen that system is stable according to Lyapunov stability, and tracking errors convergence. Comprehensive above six steps are it can be seen that the follow-up control being realized location track must be chosen and virtual controlling amount v reasonable in design_i, i=1,2...6. Wherein, relevant being only of manipulated variable is inputted to reality:

$\{\begin{array}{c}{v}_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4\\ v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4\\ v_6=\left(C_{x_1}{C}_{x_3}\right)U_4\end{array}.$

Due to v₂,v₄,v₆Value directly known relevant to quantity of state and other, therefore can be considered as known. Thus, equation above has x₁,x₃,x₅,U₄Four degree of freedom, such that it is able to solve and solving result is not unique.

Realizing in process above-mentioned, it is as follows respectively that the involved sliding-mode surface about position variable is the sliding-mode surface designed by Position Tracking Control:

$\left\{\begin{array}{c}{s}_{p1}=v_1-x_8\\ s_{p2}=v_3-x_{10}\\ s_{p3}=v_5-x_{12}\end{array}\right.$

Wherein, v₁,v₃,v₅Being virtual controlling amount, they are closely related with the expectation performance index of system, progressively determine, s in contragradience process_p1,s_p2,s_p3It is the locus x for realizing four rotor wing unmanned aerial vehicles, the track following of y, z and the relevant sliding-mode surface chosen, x₈,x₁₀,x₁₂Actual physics meaning be the first order derivative of x, y, z respectively.

Four rotor wing unmanned aerial vehicle attitude angle subsystem sliding mode controller design are as follows:

Wherein, U_si, i=1,2,3 is the control law designed respectively for realizing three attitude angle follow-up control, and it is respectively rolling angle control law, angle of pitch control law and yawing angle control law, is also exactly first, second, third control component, η_i, i=1,3,5 is attitude angle φ, θ, ψ respectively in attitude angle subsystem, wherein rolling angle φ, pitching angle theta, yaw angle ψ, η_id, i=1,3,5 is the desired trajectory of attitude angle respectively,It is the first order derivative of attitude angle respectively, k_i,c_i, i=1,2,3 is optional arithmetic number and relevant with the velocity of approach of control law, ε_i=η_id-η_i, i=1,3,5 is corresponding attitude angle tracking errors, identical in sign () is-symbol function, the implication of all the other symbols and claim book, therefore does not repeat.

The design of the sliding-mode surface about attitude angle used in above-mentioned Controller gain variations process is as follows:

$\{\begin{array}{c}{s}_1={\stackrel{\·}{\mathrm{\ϵ}}}_1+c_1{\mathrm{\ϵ}}_1\\ s_2={\stackrel{\·}{\mathrm{\ϵ}}}_2+c_2{\mathrm{\ϵ}}_2\\ s_3={\stackrel{\·}{\mathrm{\ϵ}}}_3+c_3{\mathrm{\ϵ}}_3\end{array};$

Wherein, s₁(z₁),s₃(z₃),s₅(z₅) it is the sliding-mode surface for tracing positional respectively, ε_i=η_id-η_i, i=1,3,5 is corresponding attitude angle tracking errors, c_i, i=1,2,3 is optional arithmetic number and velocity of approach with control law has related parameter.

Step 3, virtual controlling amount step 2 obtained carries out arithmetic and inverts, and asks for four rotor wing unmanned aerial vehicle attitude angle expected values, and this attitude angle expected value comprises the 4th control component of rolling angle desired trajectory, angle of pitch desired trajectory and four rotor wing unmanned aerial vehicles. The location track tracking performance of four rotor wing unmanned aerial vehicles under the effect expecting attitude angle can be ensured.

Controller gain variations process will from the performance index requirement of system, and the performance index from outer shroud to inner ring to be met one by one, then realizes the Controller gain variations from inner ring to outer shroud according to the inverse process of said process. Concrete feature is as follows: first, and in design, ring controller realizes the follow-up control to attitude angle, is also exactly to x₁,x₃,x₅Rapid track and control so that x₁,x₃,x₅Expected value can be reached fast. Then, design outer ring controller on this basis, indirectly realize the follow-up control to outer shroud variable, be also exactly the follow-up control of location track, thus realize by the over-all properties index of Ore-controlling Role.

Step 3 carrying out the virtual controlling amount equation that arithmetic inverts is:

$v_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4$

$v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4$

$v_6=\left(C_{x_1}{C}_{x_3}\right)U_4;$

Wherein, v_2i, i=1,2,3 is virtual controlling amount, S_(·)And C_(·)Represent trigonometric sine and cosine function, U respectively₄Represent the 4th control component, x₁,x₃,x₅Represent rolling angle φ, pitching angle theta, yaw angle ψ respectively.

The value of above-mentioned virtual controlling amount is determined according to mode below:

$v_2={\stackrel{\·}{v}}_1+z_7+a_9{x}_8+{\mathrm{\ρ}}_2{s}_{p1}$

$v_4={\stackrel{\·}{v}}_3+z_9+a_{10}{x}_{10}+{\mathrm{\ρ}}_4{s}_{p2}$

$v_6={\stackrel{\·}{v}}_5+z_{11}+g+a_{11}{x}_{12}+{\mathrm{\ρ}}_6{s}_{p3}$

Wherein, at design v₂Time, according to ' virtual controlling amount designed before this be in current step it has been determined that and be known ' principle, v₁Determine and it is known, then its derivativeAlso it is known. z₇=x_7r-x₇It is tracking errors, x_7rIt is input reference locus, ρ₂It is optional adjustable arithmetic number, s_p1Be can real-time online obtain parameter, all the other symbols are consistent with the description in feature 1. Therefore, v₂Design complete in this step. v₄, v₆Design process and v₂Identical, each involved meaning of parameters is also similar.

Namely the expected value of attitude angle can obtain by solving following equation:

$v_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4={\stackrel{\·}{v}}_1+z_7+a_9{x}_8+{\mathrm{\ρ}}_2{s}_{p1}$

$v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4={\stackrel{\·}{v}}_3+z_9+a_{10}{x}_{10}+{\mathrm{\ρ}}_4{s}_{p2}$

$v_6=\left(C_{x_1}{C}_{x_3}\right)U_4={\stackrel{\·}{v}}_5+z_{11}+g+a_{11}{x}_{12}+{\mathrm{\ρ}}_6{s}_{p3}.$

So just can obtain attitude angle and the 4th control component of expectation:

$\{\begin{array}{c}{x}_{1d}=\arctan \left(\frac{{\mathrm{acv}}_6-{\mathrm{lv}}_4}{{\mathrm{av}}_6\sqrt{c^2+l^2}}\right)\\ x_{3d}=\arctan \left(\frac{c}{l}\right)\\ U_4=\frac{a^2(c^2+l^2){v_6}^2+{({\mathrm{acv}}_6+{\mathrm{lv}}_4)}^2}{al}\end{array};$

Wherein, x_1dRepresent rolling angle desired trajectory, x_3dRepresent angle of pitch desired trajectory, U₄Represent the 4th control component, a=cos (x_5r), b=sin (x_5r), c=(v₂+v₄)/v₆, l=a+b.

Step 4, the yawing angle reference locus that rolling angle desired trajectory, angle of pitch desired trajectory and the step 1 obtained for step 3 obtains designs based on the conventional sliding mode tracking control device of attitude angle that constant speed becomes near respectively, obtain the sliding mould control law of four rotor wing unmanned aerial vehicles according to the conventional sliding mode tracking control device of this attitude angle, described sliding mould control law comprises the first control component, the 2nd control component and the 3rd control component.

The sliding mould control law of the attitude angle obtained in step 4 is:

Wherein, U_i, i=1,2,3 is the first control component, the 2nd control component, the 3rd control component respectively, z₁,z₃,z₅It is about location track (x, y, z) tracking errors respectively, and z₁=x_7r-x₇, z₃=x_9r-x₉, z₅=x_11r-x₁₁, wherein x_7r、x_9r、x_11rThe reference locus being respectively position (x, y, z), s₁(z₁)、s₃(z₃)、s₅(z₅) it is the sliding-mode surface for tracing positional respectively.

Location track follow-up control for four rotor wing unmanned aerial vehicles designs following Nonlinear control law, and namely the first control component, the 2nd control component, the 3rd control component and the 4th control component are as follows respectively:

Wherein, U_iI=1,2,3,4 is the first control component, the 2nd control component, the 3rd control component and the 4th control component respectively, and the first control representation in components rolling angle control law, the 2nd control representation in components angle of pitch control law, the 3rd control representation in components yawing angle control law, 4th control representation in components Position Tracking Control rule, x_1d,x_3dIt is rolling angle expected value, angle of pitch expected value, x_5dIt is the reference locus of yawing angle, k_i,c_i, i=1,2,3 is optional arithmetic number and velocity of approach with control law has related parameter, a_i, i=1,2 ... 11 is the known constant value parameter of standardization,It is online identifier, x₂,x₄,x₆Be respectively rolling angle, the angle of pitch, yawing angle rank partially lead;A=cos (x_5r), b=sin (x_5r), c=(v₂+v₄)/v₆, d=a+b; v₂,v₄,v₆For being respectively the 2nd, the 4th, the 6th virtual controlling amount. x_1d,x_3dIt is the expected value of the inner ring attitude angle for ensureing outer shroud location tracking performance calculated by non-linear Reverse Step Control method, it is necessary to ensure by designing actual input further, x_5rIt is the reference locus of yawing angle, z₁,z₃,z₅Outer ring position x respectively, the tracking errors of y, z, is defined as follows: z₁=x_7r-x₇,z₃=x_9r-x₉,z₅=x_11r-x₁₁, s₁(z₁),s₃(z₃),s₅(z₅) it is for z respectively₁,z₃,z₅The sliding-mode surface of design, is used for ensureing z₁,z₃,z₅Converging to trim point, other symbol is all mentioned in the preceding article, therefore repeats no more.

Step 5, follows the tracks of reference locus under the effect of sliding mould control law that four rotor wing unmanned aerial vehicles obtain at the 4th control component obtained according to step 3 and step 4, and then the robust trajectory tracking control of non-linear four rotor wing unmanned aerial vehicles realized under disturbing.

Using yawing angle also as the controlled amount needing to follow the tracks of, then the present embodiment both can realize the follow-up control that Position Tracking Control can also realize yawing angle. Control thinking is as follows:

1) location track of given expectation and yawing angle track { x_r(t),y_r(t),z_r(t),Ψ_r(t) };

2) for realizing Ψ_rT the Trajectory Tracking Control of (), takes the sliding mould control law U of sliding-mode control design₃As follows:

$U_3={\stackrel{\·\·}{x}}_{5r}+c_3{\stackrel{\·}{z}}_5-(a_7{x}_2{x}_4-a_8{x}_6)+k_{3}sign\left(s_3\right(z_5\left)\right)$

Wherein, x_5rIt is exactly Ψ_r, also it is exactly the reference locus of yawing angle, remaining symbol implication is identical with front literary composition. According to front literary composition to the known U of the stability analysis of sliding mode controller₃X can be ensured₅To x_5rQuick tracking. Thus in Controller gain variations process, x is needed₅Ground can use x_5rEffectively replace, like this, four the degree of freedom x mentioned in front literary composition₁,x₃,x₅,U₄It is reduced to three x₁,x₃,U₄。

3) according to 2) hypothesis, equation $\left\{\begin{array}{c}{v}_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4\\ v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4\\ v_6=\left(C_{x_1}{C}_{x_3}\right)U_4\end{array}\right.$ Free variable be x₁,x₃,U₄, this equation is solved as follows:

$\left\{\begin{array}{c}{x}_{1d}=l/{(c^2+l^2)}^{1/2}\\ x_{3d}=b(a-b)/(a+b)\left(v_{2}l\right)/{\left({v_6}^2\right(c^2+l^2)+b^2{\left(a-b\right)}^2)}^{1/2}\\ U_4=v_6/bl(a-b)/{({\left(a+b\right)}^2{\left(v_{2}l\right)}^2+{\left({\mathrm{bv}}_6\right)}^2{\left(a-b\right)}^2)}^{1/2}\end{array}\right.$

Wherein, x_1d,x_3dIt is x₁,x₃Solve value, be also exactly the track of attitude angle expected for ensureing location tracking, U₄It is the working control input after solving, a=cos (x_5r), b=sin (x_5r), c=(v₂+v₄)/v₆, l=a+b.

4) for 3) in the attitude angle track x of expectation that provides_1d,x_3d, the sliding mode controller design method of the attitude angle subsystem that literary composition provides before utilizing, it is possible to the working control input obtaining system is as follows:

Wherein, U₁,U₂It is the actual input of system, x_1d,x_3dNamely be 3) in the expected value of attitude angle that provides, the implication of all the other symbols is identical with in front literary composition. So far, we just obtain the working control input that can ensure location track and yawing angle Trajectory Tracking Control:

The parameter of the four rotor wing unmanned aerial vehicle models used in the present embodiment is as shown in table 1:

The present embodiment is carried out simulating, verifying below.

Table 1 four rotor wing unmanned aerial vehicle model parameter table

Here the reference locus considered is: { cos (t), sin (t), 0.5t, sin (0.5t) }. M is quality, and L is distance, and κ is resistance coefficient, and τ is moment of torsion, (d_φ, d_θ, d_ψ) it is the resistance coefficient about fuselage coordinate axis, (J_x, J_y, J_z) it is the inertial coefficient about fuselage coordinate axis, utilize the method provided in the present embodiment to provide Trajectory Tracking Control rule, location tracking effect and yawing angle tracking effect are as shown in Figure 2. There are being the location tracking effect under noise jamming and yawing angle tracking effect as shown in Figure 3.

The present embodiment is for complex nonlinear model, it is possible to effectively avoid the inaccuracy that local linearization is brought; Responding range is big, overcomes linear differential integral control in the dynamic restriction among a small circle of trim point; Adopt constant speed to become to closely restraining sliding-mode surface, make system have very strong immunity from interference; Give overall unified nonlinear Control device, avoid the negative effect switching between controller and bringing.

The above is only the preferred embodiment of the present invention; it is noted that, for those skilled in the art; under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (9)

1. one kind for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that, comprise the following steps:

Step 1, obtains the physical location track of four rotor wing unmanned aerial vehicles, reference by location track and yawing angle reference locus; The tracking errors dynamic subsystem about each state variables is set up successively, all tracking errors dynamic subsystem composition tracking errors dynamic systems according to physical location track and reference by location track; Described state variables comprises attitude angle and first order derivative, position and first order derivative thereof;

Step 2, according to the tracking errors dynamic system that step 1 is set up, design can ensure the contragradience sliding mode controller of the feedback asymptotic tracking that error system is stable and restrains; Described contragradience sliding mode controller utilizes each tracking errors dynamic subsystem that the thought of Reverse Step Control is tracking errors dynamic system to design corresponding virtual controlling amount and sliding-mode surface, the tracking errors dynamic subsystem stability ensured by layer and dynamic property, until obtaining the virtual controlling amount that can ensure location track tracking power and input about attitude angle state and reality;

Step 3, virtual controlling amount step 2 obtained carries out arithmetic and inverts, and asks for four rotor wing unmanned aerial vehicle attitude angle expected values, and this attitude angle expected value comprises the 4th control component of rolling angle desired trajectory, angle of pitch desired trajectory and four rotor wing unmanned aerial vehicles;

Step 4, the yawing angle reference locus that rolling angle desired trajectory, angle of pitch desired trajectory and the step 1 obtained for step 3 obtains designs based on the conventional sliding mode tracking control device of attitude angle that constant speed becomes near respectively, obtain the sliding mould control law of four rotor wing unmanned aerial vehicles according to the conventional sliding mode tracking control device of this attitude angle, described sliding mould control law comprises the first control component, the 2nd control component and the 3rd control component;

Step 5, under the effect of sliding mould control law that four rotor wing unmanned aerial vehicles obtain at the 4th control component obtained according to step 3 and step 4, position reference locus and yawing angle reference locus are followed the tracks of, and then the robust trajectory tracking control of non-linear four rotor wing unmanned aerial vehicles realized under disturbing.

2. according to claim 1 for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that: the nonlinear model of four rotor wing unmanned aerial vehicles in described step 1 is:

Wherein,It it is the state variables of system; Its physical meaning is attitude angle (φ, θ, ψ) and first order derivative thereof successivelyPosition (x, y, z) and first order derivative thereofCan entirety be expressed as followsφ is rolling angle, and θ is the angle of pitch, and ψ is yawing angle, a_i, i=1,2 ... 11 is the known constant value parameter of standardization;Being online identifier, g is universal gravity constant, U_i, i=1,2,3,4 is the working control input of system, U_i, i=1,2,3,4 is followed successively by the first control component, the 2nd control component, the 3rd control component and the 4th control component in order, S_(·)And C_(·)Represent trigonometric sine and cosine function respectively.

3. according to claim 1 for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that: the virtual controlling amount in described step 2 is:

$v_2={\stackrel{\·}{v}}_1+z_7+a_9{x}_8+{\mathrm{\ρ}}_2{s}_{p1}$

$v_4={\stackrel{\·}{v}}_3+z_9+a_{10}{x}_{10}+{\mathrm{\ρ}}_4{s}_{p2}$

$v_6={\stackrel{\·}{v}}_5+z_{11}+g+a_{11}{x}_{12}+{\mathrm{\ρ}}_6{s}_{p3};$

Wherein, v_2i, i=1,2,3 is virtual controlling amount, v_2i-1At acquisition v_2iBetween it has been determined that and its first order derivativeCan by v_2i-1Carry out first differential filtering acquisition, z₇、z₉、z₁₁It is the tracking errors of position (x, y, z) respectively, and z₇=x_7r-x₇, z₉=x_9r-x₉, z₁₁=x_11r-x₁₁;X_7r、x_9r、x_11rIt is the reference locus of position (x, y, z) respectively, ρ₂、ρ₄、ρ₆It is the optional constant value arithmetic number of position (x, y, z), s_p1、s_p2、s_p2Being sliding-mode surface respectively, wherein the expression sliding-mode surface of subscript p is the sliding-mode surface designed for the tracking of position quantity of state.

4. according to claim 1 for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that: described step 3 carrying out the virtual controlling amount equation that arithmetic inverts is:

$v_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4$

$v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4$

$v_6=\left(C_{x_1}{C}_{x_3}\right)U_4;$

Wherein, v_2i, i=1,2,3 is virtual controlling amount, S_(·)And C_(·)Represent trigonometric sine and cosine function, U respectively₄Represent the 4th control component, x₁,x₃,x₅Represent rolling angle φ, pitching angle theta, yaw angle ψ respectively.

5. according to claim 1 for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that: attitude angle desired trajectory and the 4th control component in described step 3 be:

$\left\{\begin{array}{c}{x}_{1d}=\arctan \left(\frac{ac{v}_6-{\mathrm{lv}}_4}{{\mathrm{av}}_6\sqrt{c^2+l^2}}\right)\\ x_{3d}=\arctan \left(\frac{c}{l}\right)\\ U_4=\frac{a^2(c^2+l^2){v_6}^2+{(ac{v}_6-{\mathrm{lv}}_4)}^2}{al}\end{array}\right.;$

Wherein, x_1dRepresent rolling angle desired trajectory, x_3dRepresent angle of pitch desired trajectory, U₄Represent the 4th control component, a=cos (x_5r), b=sin (x_5r), c=(v₂+v₄)/v₆, l=a+b.

6. according to claim 1 for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that: the sliding mould control law obtained in described step 4 is:

Wherein, U_i, i=1,2,3 is the first control component, the 2nd control component, the 3rd control component respectively, z₁,z₃,z₅It is about location track (x, y, z) tracking errors respectively, and z₁=x_7r-x₇, z₃=x_9r-x₉, z₅=x_11r-x₁₁, wherein x_7r、x_9r、x_11rThe reference locus being respectively position (x, y, z), s₁(z₁)、s₃(z₃)、s₅(z₅) it is the sliding-mode surface for attitude angle control design case respectively, k₁,k₂,k₃It is other one group of optional constant value arithmetic number respectively.

7. according to claim 6 for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that: described sliding-mode surface is chosen as follows:

$\left\{\begin{array}{c}{s}_1={\stackrel{\·}{\mathrm{\ϵ}}}_1+c_1{\mathrm{\ϵ}}_1\\ s_2={\stackrel{\·}{\mathrm{\ϵ}}}_2+c_2{\mathrm{\ϵ}}_2\\ s_3={\stackrel{\·}{\mathrm{\ϵ}}}_3+c_3{\mathrm{\ϵ}}_3\end{array}\right.;$

Wherein, s₁(z₁),s₃(z₃),s₅(z₅) it is the sliding-mode surface for tracing positional respectively, ε_i=η_id-η_i, i=1,3,5 is corresponding attitude angle tracking errors, c_i, i=1,2,3 is optional arithmetic number and velocity of approach with control law has related parameter.

8. according to claim 1 for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that: in described step 2, virtual controlling amount choosing method is as follows:

The first step, for the follow-up control of position x selects the first error metrics V₁As follows:

$V_1=\frac{1}{2}{z_7}^2;$

Wherein, V₁Represent that the follow-up control of position x selects the first error metrics, z₇=x_7r-x₇Represent the tracking errors of position x and its desired trajectory, x₇Represent level attitude x, x_7rRepresent level attitude x desired trajectory;

Select the first virtual controlling amount v₁As follows:

$v_1={\stackrel{\·}{x}}_{7r}+{\mathrm{\ρ}}_1{z}_7;$

To the tracking errors z of position x and its desired trajectory₇Ask first order derivative also s_p1And v₁Substituting into asks the expression formula after leading to obtain:

${\stackrel{\·}{V}}_1=-{\mathrm{\ρ}}_1{z_7}^2+z_7{s}_{p1};$

s_p1The sliding-mode surface chosen for position x track following; ρ₁、ρ₂It it is optional adjustable arithmetic number;

2nd step: choose the 2nd virtual controlling amountAnd the 2nd error metrics V₂Augmentation becomes following form:

$V_2=\frac{1}{2}({z_1}^2+{s_{p1}}^2);$

To the 2nd error metrics V after augmentation₂Seek first order derivative and handleAnd v₂Substituting into asks the expression formula after leading to obtain:

${\stackrel{\·}{V}}_2=-{\mathrm{\ρ}}_1{z_7}^2+s_{p1}({\stackrel{\·}{v}}_1+z_7+a_9{x}_8-v_2);$

In order to ensureNegative qualitative, the 2nd virtual controlling amount v chosen₂As follows;

$v_2={\stackrel{\·}{v}}_1+z_7+a_9{x}_8+{\mathrm{\ρ}}_2{s}_{p1};$

It has been determined that v₂Substitute intoIn, can obtain:

${\stackrel{\·}{V}}_2=-{\mathrm{\ρ}}_1{z_7}^2-{\mathrm{\ρ}}_2{s_{p1}}^2$

≤ 0;

3rd step: for the follow-up control of level attitude y selects the 3rd error metrics V₃As follows:

$V_3=\frac{1}{2}{z_9}^2;$

Wherein, z₉=x_9r-x₉Represent the tracking errors of position y and its desired trajectory, the 3rd virtual controlling amount v₃Select as follows:

$v_3={\stackrel{\·}{x}}_{9r}+{\mathrm{\ρ}}_3{z}_9;$

To V₃Ask first order derivative also s_p2And v₃Substituting into asks the expression formula after leading can obtain V₃Derivative as follows:

$\begin{array}{c}{\stackrel{\·}{V}}_3=z_9{\stackrel{\·}{z}}_9=z_9\left({\stackrel{\·}{x}}_{9r}-x_{10}\right)=z_9\left({\stackrel{\·}{x}}_{9r}-v_3+s_{p2}\right)\\ =z_9\left({\stackrel{\·}{x}}_{9r}-v_3+s_{p2}\right)\\ =-{\mathrm{\ρ}}_3{z_9}^2+z_9{s}_{p2}\end{array};$

4th step: choose the 4th virtual controlling amountThe error metrics of first three step is included in the error metrics of this step, then the 4th error metrics V after augmentation₄As follows:

$V_4=\frac{1}{2}({z_7}^2+{s_{p1}}^2+{z_9}^2+{s_{p2}}^2);$

To V₄Seek first order derivative, and the respective fictional amount designed substituted into and asks the expression formula after leading to obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_4=z_7{\stackrel{\·}{z}}_7+s_{p1}{\stackrel{\·}{s}}_{p1}+z_9{\stackrel{\·}{z}}_9+s_{p2}{\stackrel{\·}{s}}_{p2}\\ ={\stackrel{\·}{V}}_2+z_9\left(-{\mathrm{\ρ}}_3{z}_9+s_{p2}\right)+s_2\left({\stackrel{\·}{v}}_3-{\stackrel{\·}{x}}_{10}\right)\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}\left(z_9+{\stackrel{\·}{v}}_3-\left(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5}\right)U_4+a_{10}{x}_{10}\right)\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}\left(z_9+{\stackrel{\·}{v}}_3-v_4+a_{10}{x}_{10}\right)\end{array};$

In this step, the 4th selected virtual controlling amount v₄Design as follows:

$v_4={\stackrel{\·}{v}}_3+z_9+a_{10}{x}_{10}+{\mathrm{\ρ}}_4{s}_{p2};$

The v designed₄Substitute intoIn, can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_4={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2+s_{p2}(z_9+{\stackrel{\·}{v}}_3-v_4+a_{10}{x}_{10})\\ ={\stackrel{\·}{V}}_2-{\mathrm{\ρ}}_3{z_9}^2-{\mathrm{\ρ}}_4{s_{p2}}^2\≤0\end{array};$

5th step: for the follow-up control of height z selects the 5th error metrics V₅As follows:

$V_5=\frac{1}{2}{z_{11}}^2;$

Wherein, z₁₁=x_11r-x₁₁Represent tracking errors the 5th virtual controlling amount v of height z and its desired trajectory₅Choose as follows:

$v_5={\stackrel{\·}{x}}_{11r}+{\mathrm{\ρ}}_5{z}_{11};$

To V₅Seek first order derivative, and s_p3And v₅Substituting into asks the expression formula after leading to obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_5=z_{11}{\stackrel{\·}{z}}_{11}=z_{11}\left({\stackrel{\·}{x}}_{11r}-x_{12}\right)\\ =z_{11}\left({\stackrel{\·}{x}}_{11r}-v_5+s_{p3}\right)\\ =-{\mathrm{\ρ}}_5{z_{11}}^2+z_{11}{s}_{p3}\end{array};$

6th step: choose the 6th virtual controlling amountSimultaneously for meeting the requirement of system stability, the error metrics that the first five is walked is included in the 6th error metrics V after augmentation₆Among, as follows:

$V_6=\frac{1}{2}({z_7}^2+{s_{p1}}^2+{z_9}^2+{s_{p2}}^2+{z_{11}}^2+{s_{p3}}^2);$

By the 6th virtual controlling amount v₆It is designed toAnd substitute into V₆Ask in the expression formula after leading and can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_6=z_7{\stackrel{\·}{z}}_7+s_{p1}{\stackrel{\·}{s}}_{p1}+z_9{\stackrel{\·}{z}}_9+s_{p2}{\stackrel{\·}{s}}_{p2}+z_{11}{\stackrel{\·}{z}}_{11}+s_{p3}{\stackrel{\·}{s}}_{p3}\\ ={\stackrel{\·}{V}}_4+z_{11}\left(-{\mathrm{\ρ}}_5{z}_{11}+s_3\right)+s_3\left({\stackrel{\·}{v}}_5-{\stackrel{\·}{x}}_{12}\right)\\ ={\stackrel{\·}{V}}_4-{\mathrm{\ρ}}_5{z_{11}}^2+s_3\left(z_{11}+{\stackrel{\·}{v}}_5+g+a_{12}{x}_{12}-v_6\right)\\ ={\stackrel{\·}{V}}_4-{\mathrm{\ρ}}_5{z_{11}}^2-{\mathrm{\ρ}}_6{s_{p3}}^2\≤0\end{array};$

Wherein, relevant to attitude angle manipulated variable it is only:

$\left\{\begin{array}{c}{v}_2=(C_{x_1}{S}_{x_3}{C}_{x_5}+S_{x_1}{S}_{x_5})U_4\\ v_4=(C_{x_1}{S}_{x_3}{S}_{x_5}-S_{x_1}{S}_{x_5})U_4\\ v_6=\left(C_{x_1}{C}_{x_3}\right)U_4\end{array}\right..$

9. according to claim 1 for four rotor wing unmanned aerial vehicle nonlinear models based on the method for design of contragradience and the nonlinear robust control device of sliding mould control techniques, it is characterised in that: the first control component, the 2nd control component, the 3rd control component and the 4th control component are as follows respectively:

Wherein, U_iI=1,2,3,4 is the first control component, the 2nd control component, the 3rd control component and the 4th control component respectively, and the first control representation in components rolling angle control law, the 2nd control representation in components angle of pitch control law, the 3rd control representation in components yawing angle control law, 4th control representation in components Position Tracking Control rule, x_1d,x_3dIt is rolling angle expected value, angle of pitch expected value, x_5dIt is the reference locus of yawing angle, k_i,c_i, i=1,2,3 is optional arithmetic number and velocity of approach with control law has related parameter, a_i, i=1,2 ... 11 is the known constant value parameter of standardization,It is online identifier, x₂,x₄,x₆Be respectively rolling angle, the angle of pitch, yawing angle rank partially lead; A=cos (x_5r), b=sin (x_5r), c=(v₂+v₄)/v₆, d=a+b; v₂,v₄,v₆For being respectively the 2nd, the 4th, the 6th virtual controlling amount.