CN105759832A - Four-rotor aircraft sliding mode variable structure control method based on inversion method - Google Patents

Abstract

The invention discloses a four-rotor aircraft sliding mode variable structure control method based on an inversion method. The four-rotor aircraft sliding mode variable structure control method comprises the steps that firstly, a four-rotor aircraft kinetic model is analyzed and simplified and is systematically decomposed into an all-wheel-drive subsystem and an under-actuation subsystem; further, the inversion control method is utilized to derive a sliding mode control face with a sliding mode variable structure control theory as a basis, control laws are designed for the two subsystems, and the system stability is verified through a Lyapunov stability theory; finally, a controller of a four-rotor aircraft is designed out. The four-rotor aircraft sliding mode variable structure control method is integrated with the inversion method, is used for controlling spot hover and trajectory tracking control of the aircraft, analyzes the dynamic nature and the stability of the aircraft, effectively improves the response speed and control accuracy of the four-rotor aircraft and improves anti-interference performance of a system.

Description

Four-rotor aircraft sliding mode variable structure control method based on inversion method

Technical Field

The invention relates to a four-rotor aircraft sliding mode variable structure control method based on an inversion method, and belongs to the technical field of aircraft control.

Background

In recent years, four-rotor aircraft gradually becomes a research hotspot of researchers in the field of aviation, and as an unmanned aircraft, the unmanned aircraft has unique advantages and has low requirements on environment and places, so that the unmanned aircraft is more and more widely applied in the military and civil fields, including investigation, environment monitoring, power inspection, aerial photography, disaster rescue and the like. The rotating speeds of four propellers of the four-rotor aircraft are changed, various flight attitudes can be changed, and six-degree-of-freedom motions such as vertical lifting, fixed-point hovering and trajectory tracking are realized. At present, scholars have achieved a lot of achievements on an aircraft, however, the aircraft has the characteristics of nonlinearity, strong coupling, underactuation and the like, so that the dynamic model of the aircraft is very complex and the design of a controller is very complicated, and therefore a better control method is needed to ensure the flight quality of the four-rotor aircraft, wherein attitude control is the basic requirement of stable flight of the aircraft.

The method for controlling the four-rotor aircraft has various methods, including PID control, LQ control, DI control and the like, the PID control is the most common, although the method has certain robustness, the control effect is not ideal when the method is interfered by the outside, the method cannot adapt to a complex and variable environment, meanwhile, the PID control and the LQ control ignore nonlinear factors of a model, the precision of the model is poor, and the control precision is influenced. Sliding mode variable structure control is a strategy of a variable structure control system, and the fundamental difference of the control strategy from the conventional control lies in the discontinuity of control, namely, a switch characteristic which makes the system 'structure' change along with time. The design of an independent sliding mode controller is carried out on the aircraft, the attitude angle needs to be derived by high-order nonlinear constraint, the parameter uncertainty of the system is increased, the control effect is poor, and even the instability of the four-rotor aircraft is caused.

Disclosure of Invention

Aiming at the problems of the prior art, the technical problems to be solved by the invention are as follows: the method for controlling the sliding mode variable structure of the four-rotor aircraft based on the inversion method is provided, so that the controller of the aircraft has strong robustness to external interference and more stable performance.

In order to solve the technical problems, the invention adopts the following technical scheme:

a four-rotor aircraft sliding mode variable structure control method based on an inversion method is characterized by comprising the following steps: the expected track of the four-rotor aircraft is given, then the roll angle and the pitch angle which need to rotate are calculated by an inversion control method, the current control law obtained by a sliding mode control method is sent to a four-rotor aircraft dynamics model by combining three attitude angles of the aircraft, and the hovering and track tracking motions of the aircraft are effectively controlled.

In the above technical scheme, the method specifically comprises the following steps:

step S1: establishing a four-rotor aircraft dynamic model, and determining the relation between the angular speed input of four motors of the aircraft and the attitude and position, and the relation between the expected track and the attitude angle:

step S2: designing a four-rotor aircraft controller: according to the dynamics characteristics of the four-rotor aircraft, dividing the dynamics model established in the step S1 into a full-drive subsystem and an under-drive subsystem, and designing a sliding mode controller by adopting a sliding mode variable structure control method based on an inversion method;

step S3: and (4) after the design of the controller is finished, obtaining a current control law through a sliding mode control method, sending the current control law into the four-rotor aircraft dynamic model in the step S1, and feeding the generated state variables back to the position ring and the attitude ring so as to control the four-rotor aircraft to stably fly and effectively control the hovering and track tracking motions of the aircraft.

In the above technical solution, step S1 is to establish a four-rotor aircraft dynamics model as shown in formula (1):

in the formula: theta is a pitch angle, gamma is a roll angle,is a yaw angle and is three attitude angles; j. the design is a square_x、J_y、J_zRespectively the rotational inertia of the four-rotor aircraft body around three axes of a body coordinate system; l is the distance from the center of a propeller of the four-rotor aircraft to the origin of a coordinate system of the aircraft body; g is the acceleration of gravity; m is the mass of the quad-rotor aircraft; x, y and z are position quantities of the four-rotor aircraft in a navigation coordinate system respectively; omega₁，ω₂，ω₃，ω₄The input angular speeds of four motors of the four-rotor aircraft are respectively; equation (1) is self for 6 directionsEquations after degree decoupling; the degrees of freedom in the 6 directions comprise a degree of freedom of movement in the directions of three rectangular coordinate axes of x, y and z and a degree of freedom of rotation around the three rectangular coordinate axes;

the flight state of the four-rotor aircraft is divided into four independent flight channels: an upper channel, a lower channel, a left channel, a right channel, a front channel, a rear channel and a yaw channel; definition of

$\left\{\begin{array}{c}{U}_1=b({\mathrm{\ω}}_1^2+{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_3^2+{\mathrm{\ω}}_4^2)\\ U_2=b({\mathrm{\ω}}_1^2-{\mathrm{\ω}}_3^2)\\ U_3=b({\mathrm{\ω}}_2^2-{\mathrm{\ω}}_4^2)\\ U_4=d({\mathrm{\ω}}_1^2+{\mathrm{\ω}}_3^2-{\mathrm{\ω}}_2^2-{\mathrm{\ω}}_4^2)\end{array}\right.---\left(2\right)$

In the formula: b is the lift coefficient of the rotor, d is the drag coefficient of the rotor;

U₁、U₂、U₃、U₄for the system control law determined by the angular velocities of the 4 propellers: in particular U₁For the control law of the upper and lower channels, U₂For control law of front and rear channels and pitch angle, U₃Control law for left and right channels and roll angle, U₄A yaw angle control law; substituting formula (2) into formula (1) results in a four-rotor aircraft dynamics model that combines four flight paths, as shown in formula (3):

equation (3) is expressed in state space form:

$\stackrel{\·}{X}=f(X,U)$

wherein,is the state quantity of the system, U ═ U₁U₂U₃U₄]For the control law of the system, the f function is a function for solving the system state quantity at the next moment from the current system state quantity, and is specifically represented as:

then, combining equation (3) and equation (4), a final four-rotor aircraft dynamics model can be obtained, as equation (5):

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=\frac{(J_y-J_z)}{J_x}{x}_4{x}_6+\frac{l}{J_x}{U}_2\\ {\stackrel{\·}{x}}_3=x_4\\ {\stackrel{\·}{x}}_4=\frac{(J_z-J_x)}{J_y}{x}_2{x}_6+\frac{l}{J_y}{U}_3\\ {\stackrel{\·}{x}}_5=x_6\\ {\stackrel{\·}{x}}_6=\frac{(J_x-J_y)}{J_z}{x}_2{x}_4+\frac{1}{J_z}{U}_4\\ {\stackrel{\·}{x}}_7=x_8\\ {\stackrel{\·}{x}}_8=\frac{U_1}{m}\left(\cos x_1\cos x_3\right)-g\\ {\stackrel{\·}{x}}_9=x_{10}\\ {\stackrel{\·}{x}}_{10}=\frac{U_1}{m}(\cos x_1\sin x_3\cos x_5+\sin x_1\sin x_5)\\ {\stackrel{\·}{x}}_{11}=x_{12}\\ {\stackrel{\·}{x}}_{12}=\frac{U_1}{m}(\sin x_5\sin x_3\cos x_1-\cos x_5\sin x_1)\end{array}\right.---\left(5\right)$

in the above technical solution, the step S2 of designing a quad-rotor aircraft controller includes the following steps:

step S21: dividing the four-rotor aircraft dynamics model established in the step S1 into a full-drive channel and an under-drive channel, and respectively designing the channels;

firstly, designing a full-drive channel controller: the full driving channel comprises an upper channel, a lower channel and a yaw angleTwo channels, upper and lower channel z and yaw angleThe kinetic equations for the two channels are:

directly using a sliding mode variable structure control method to obtain a control law, firstly calculating the control law of an upper channel z and a lower channel z:

the state variables of the upper and lower channels z are:

$\left\{\begin{array}{c}{x}_7=z\\ x_8=\stackrel{\·}{z}\end{array}\right.---\left(7\right)$

defining an error variable:

e₇＝x₇-x_7d

wherein x is₇Is the current height; x is the number of_7dIs at a desired height; e.g. of the type₇Is the current and desired height difference.

Designing a sliding mode function as follows:

$s_z=c_7{e}_7+{\stackrel{\·}{e}}_7$

wherein, c₇Is a system parameter;is the derivative of the height difference; s_zA sliding mode surface function for the z-axis;

the Lyapunov function defining channel z isThen

${\stackrel{\·}{s}}_z=c_7{\stackrel{\·}{e}}_7+{\stackrel{\·\·}{e}}_7=c_7(x_8-{\stackrel{\·}{x}}_{7d})+({\stackrel{\·\·}{x}}_7-{\stackrel{\·\·}{x}}_{7d})$

And is

$s_z{\stackrel{\·}{s}}_z=s_z\left(c_7\right(x_8-{\stackrel{\·}{x}}_{7d})+\frac{U_1}{m}(\cos x_1\cos x_3)-g-{\stackrel{\·\·}{x}}_{7d})$

To ensureControl law U for designing upper and lower channels z₁

$U_1=(-\mathrm{\ϵ}\mathrm{sgn}(s_z)-{\mathrm{ks}}_z+c_7({\stackrel{\·}{x}}_{7d}-x_8)+g+{\stackrel{\·\·}{x}}_{7d})\frac{m}{\cos x_1\cos x_3}---\left(8\right)$

Then

$s_z{\stackrel{\·}{s}}_z=-\mathrm{\ϵ}\left|s_z\right|-{\mathrm{ks}}_z^2\≤0$

Thereby to obtain

$\stackrel{\·}{V}\≤0$

In the formula, the sum k is a constant of an approach law in sliding mode control; sgn(s)_z) Is a slip form surface s_zThe sign function of (a);

the same method is used to determine the yaw angleControl law U of channels₄：

Wherein,is a slip form surfaceThe sign function of (a); c. C₅Is a system parameter;

step S22: designing an under-actuated channel controller for the dynamic model of the four-rotor aircraft established in the step S1: the underactuated channels comprise an x-gamma channel and a y-theta channel, and the kinetic equation is as follows:

firstly, obtaining attitude information by inversion of position information through an inversion algorithm, and then defining a sliding mode surface of a coupling channel on the basis;

the control law of the x-gamma channel is firstly designed as follows:

when the four-rotor aircraft moves on the x axis, although the pitch angle theta has an influence on the movement on the x axis, the influence can be ignored, and a small angle is assumed for the pitch angle theta, so that the dynamic model of the corresponding x-gamma channel at this time is as follows:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_9=x_{10}\\ x_{10}=\cos x_5\sin x_3\frac{U_1}{m}\\ {\stackrel{\·}{x}}_3=x_4\\ {\stackrel{\·}{x}}_4=\frac{J_z-J_x}{J_y}{x}_2{x}_6+\frac{{\mathrm{lU}}_3}{J_y}\end{array}\right.---\left(12\right)$

defining an error variable:

e₉＝x₉-x_9d(13)

wherein x is₉Is the current x position quantity; x is the number of_9dIs the desired x position quantity; e.g. of the type₉Is the difference between the current and desired x position quantities.

The specific design process is as follows:

(1) the Lyapunov function defining the state variable x is

$V_9=\frac{1}{2}{e}_9^2---\left(14\right)$

Then

${\stackrel{\·}{V}}_9=e_9{\stackrel{\·}{e}}_9=e_9(x_{10}-{\stackrel{\·}{x}}_{9d})$

GetWherein c is₉>0, is a system parameter; e.g. of the type₁₀The error variable, and also the virtual control quantity,

$e_{10}=x_{10}+c_9{e}_9-{\stackrel{\·}{x}}_{9d}---\left(15\right)$

then

${\stackrel{\·}{V}}_9=-c_9{e}_9^2+e_9{e}_{10}---\left(16\right)$

If e₁₀When the value is equal to 0, thenTherefore, the coupling term must be eliminated, and for this reason, the next design is required;

(2) defining state variablesLyapunov function of

$V_{10}=V_9+\frac{1}{2}{e}_{10}^2---\left(17\right)$

Then

${\stackrel{\·}{V}}_{10}={\stackrel{\·}{V}}_9+e_{10}{\stackrel{\·}{e}}_{10}=-c_9{e}_9^2+e_9{e}_{10}+e_{10}{\stackrel{\·}{e}}_{10}$

GetWherein c is₁₀>0, is a system parameter; e.g. of the type₃The error variable, and also the virtual control quantity,

$e_3={\stackrel{\·}{e}}_{10}+c_{10}{e}_{10}+e_9---\left(18\right)$

then

$\begin{array}{c}{\stackrel{\·}{V}}_{10}=-c_9{e}_9^2+e_9{e}_{10}+e_{10}(-c_{10}{e}_{10}-e_9+e_3)\\ =-c_9{e}_9^2-c_{10}{e}_{10}^2+e_{10}{e}_3\end{array}---\left(19\right)$

If e₃When the value is equal to 0, thenTherefore, the coupling term must be eliminated, and for this reason, the next design is required;

(3) lyapunov function defining a state variable gamma

$V_3=V_{10}+\frac{1}{2}{e}_3^2---\left(20\right)$

Then

${\stackrel{\·}{V}}_3={\stackrel{\·}{V}}_{1\stackrel{\·}{0}}+e_3{\stackrel{\·}{e}}_3=-c_9{e}_9^2-c_{10}{e}_{10}^2+e_{10}{e}_3+e_3{\stackrel{\·}{e}}_3$

GetWherein c is₃>0, is a system parameter; e.g. of the type₄The error variable, and also the virtual control quantity,

$e_4=c_3{e}_3+e_{10}+{\stackrel{\·}{e}}_3---\left(21\right)$

then

$\begin{array}{c}{\stackrel{\·}{V}}_3=-c_9{e}_9^2+e_{10}{e}_{10}^2+e_3{e}_{10}+e_3(-c_3{e}_3-e_{10}+e_4)\\ =-c_9{e}_9^2-c_{10}{e}_{10}^2-c_3{e}_3^2+e_4{e}_3\end{array}---\left(22\right)$

At this time, the process of the present invention,in which there is a coupling term e₄e₃If this is eliminated, it can be concluded that the system is stable;

designing the sliding mode surface of the channel;

(4) in the process, the displacement speed difference e of the x-gamma channel is obtained₃And angular velocity difference e₄The attitude controller is thus designed:

is obtained by the formula (18)

$\begin{array}{c}{e}_3=(1+c_9{c}_{10})(x_9-x_{9d})+(c_9+c_{10})x_{10}\\ -(c_9+c_{10}){\stackrel{\·}{x}}_{9d}+{\stackrel{\·}{x}}_{\mathrm{10}}-{\stackrel{\·}{x}}_{9d}\end{array}---\left(23\right)$

The variable structure of the sliding mode is combined to define the sliding mode surface on the x axis as

s_x＝e₄(24)

(5) Defining state variablesLyapunov function of

$V_4=V_3+\frac{1}{2}{s}_x^2---\left(25\right)$

Then

${\stackrel{\·}{V}}_4=-c_9{e}_9^2-c_{10}{e}_{10}^2-c_3{e}_3^2+s_x{e}_3+s_x{\stackrel{\·}{s}}_x---\left(26\right)$

To make it possible toThe design controller is

$\begin{array}{c}{U}_3=\left(\right(-\mathrm{\ϵ}\mathrm{sgn}\left(s_x\right)-{\mathrm{ks}}_x-(c_9+c_3+c_9{c}_{10}{c}_3)({\stackrel{\·}{x}}_9-{\stackrel{\·}{x}}_{9d})\\ -(2+c_9{c}_{10}+c_9{c}_3+c_3{c}_{10})\cos x_5\sin x_3\frac{U_1}{m}\\ +(c_9+c_{10}+c_3)x_6\sin x_5\sin x_3\frac{U_1}{m}\\ -(c_9+c_{10}+c_3)x_4\cos x_5\cos x_3\frac{U_1}{m}\\ +x_6^2\cos x_5\sin x_3\frac{U_1}{m}+2x_4{x}_6\sin x_5\cos x_3\frac{U_1}{m}\\ +x_4^2\cos x_5\sin x_3\frac{U_1}{m}-(c_9+c_{10}){\stackrel{\·}{x}}_{9d}\\ +(1+c_9{c}_{10})(x_9-x_{9d})+(c_9+c_{10})x_{10}+{\stackrel{\·}{x}}_{10}\\ -{\stackrel{\·\·}{x}}_{9d}+(2+c_9{c}_{10}+c_9{c}_3+c_3{c}_{10}){\stackrel{\·\·}{x}}_{9d}\\ +(c_3+c_9+c_{10}){\stackrel{\·\·\·}{x}}_{9d}+{\stackrel{\·\·\·\·}{x}}_{9d})/\left(\cos x_5\cos x_3\frac{U_1}{m}\right)\\ -\frac{J_z-J_x}{J_y}{x}_2{x}_6)\frac{J_y}{l}\end{array}---\left(27\right)$

Wherein,>0,k>0, is a system parameter; sgn(s)_x) Is a sliding mode surface function s_xThe sign function of (a); then

${\stackrel{\·}{V}}_4=-c_9{e}_9^2-c_{\mathrm{10}}{e}_{10}^2-c_3{e}_3^2-{\mathrm{ks}}_x^2-\mathrm{\ϵ}\left|s_x\right|\≤0---\left(28\right)$

ByThe system is known to be stable;

the y-theta channel control law is designed the same as the above method,

$\begin{array}{c}{U}_2=(-(c_{11}+c_1+c_{11}{c}_{12}{c}_1)({\stackrel{\·}{x}}_{11}-{\stackrel{\·}{x}}_{11d})\\ +(2+c_{11}{c}_{12}+c_{11}{c}_1+c_{12}{c}_1)\cos x_5\sin x_1\frac{U_1}{m}\\ -(c_{11}+c_{12}+c_1)x_6\sin x_5\sin x_1\frac{U_1}{m}-(-\mathrm{\ϵ}\mathrm{sgn}(s_y)\\ +(c_{11}+c_{12}+c_1)x_2\cos x_5\cos x_1\frac{U_1}{m}-{\mathrm{ks}}_y\\ -x_6^2\cos x_5\sin x_1\frac{U_1}{m}-2x_4{x}_6\sin x_5\cos x_1\frac{U_1}{m}\\ -x_2^2\cos x_5\sin x_1\frac{U_1}{m}-(c_{11}+c_{12}){\stackrel{\·}{x}}_{11d}\\ +(1+c_{11}{c}_{12})(x_{11}-x_{11d})+(c_{11}+c_{12})x_{12}+{\stackrel{\·}{x}}_{12}\\ -{\stackrel{\·\·}{x}}_{11d}+(2+c_{11}{c}_{12}+c_{11}{c}_1+c_{12}{c}_1){\stackrel{\·\·}{x}}_{11d}\\ +(c_1+c_{11}+c_{12}){\stackrel{\·\·\·}{x}}_{11d}+{\stackrel{\·\·\·\·}{x}}_{11d})/\left(\cos x_5\cos x_1\frac{U_1}{m}\right)\\ -\frac{J_y-J_z}{J_x}{x}_4{x}_6)\frac{J_x}{l}\end{array}---\left(29\right)$

wherein,>0,k>0, is a system parameter; sgn(s)_y) Is a sliding mode surface function s_yThe sign function of (a);

at this moment, the control laws of the four channels are respectively solved;

the sign function sgn(s) in the control law obtained above is replaced by a saturation function sat(s) to suppress the chattering phenomenon caused by the sign function term,

$sat\left(s\right)=\left\{\begin{array}{cc}\begin{array}{cc}1,& s>\mathrm{\&Delta;}\\ ky,& \left|s\right|\&le;\mathrm{\&Delta;}\\ -1,& s<-\mathrm{\&Delta;}\end{array}& k=\frac{1}{\mathrm{\&Delta;}}\end{array}\right.---\left(30\right)$

in the formula, Δ is referred to as a boundary layer. Switching control is adopted outside the boundary layer, and linear feedback control is adopted in the boundary layer;

in the above technical solution, step S3 specifically includes: after the controller design is finished, the four control laws U obtained in step S2 are set₁、U₂、U₃、U₄And (5) substituting the four-rotor aircraft dynamic model formula (5) derived in the step S1, the hovering and track tracking motion of the aircraft can be effectively controlled.

The invention relates to a sliding mode variable structure control method of a four-rotor aircraft based on an inversion method, which is characterized in that a basic idea of an inversion design method is to decompose a complex nonlinear system into subsystems not exceeding the order of the system, then respectively design a Lyapunov function and an intermediate virtual control quantity for each subsystem, and retreat to the whole system until the design of the whole control law is completed. Compared with the prior art, the method has the advantages that:

(1) the system model is divided into a full-drive subsystem and an under-drive subsystem, and the controller design is respectively carried out on the full-drive subsystem and the under-drive subsystem, so that the pertinence is strong;

(2) the method combines an inversion method and a sliding mode variable structure control method, has strong decoupling performance, and improves the dynamic property and the stability of the system;

(3) the controller designed by the invention can improve the performance of the system by adjusting parameters, and can accurately hover and follow a specified track.

Therefore, the sliding mode variable structure control method of the four-rotor aircraft based on the inversion method can be applied to the field of aircraft.

Drawings

FIG. 1 is a block diagram of a control system for a quad-rotor aircraft according to the present invention;

FIG. 2 is a diagram of a structural model of a quad-rotor aircraft of the present invention;

FIG. 3 is a graphical illustration of a four-rotor aircraft position control according to the present invention;

FIG. 4 is a graphical illustration of attitude control for a quad-rotor aircraft in accordance with the present invention;

FIG. 5 is a graph of linear velocity control for a quad-rotor aircraft according to the present invention;

FIG. 6 is a graph of attitude angular velocity control for a quad-rotor aircraft according to the present invention;

FIG. 7 is a graph of the hover control law for a quad-rotor aircraft according to the present invention;

FIG. 8 is a graph of the trajectory tracking of a quad-rotor aircraft of the present invention;

figure 9 is a graph of the trajectory tracking error of a quad-rotor aircraft according to the present invention.

Detailed Description

The invention is further described below with reference to the figures and examples.

A method for controlling a sliding mode variable structure of a four-rotor aircraft based on an inversion method is disclosed, as shown in figure 1, a controller adopts double closed-loop control, namely an inner attitude loop and an outer position loop respectively, and gives an expected track of the four-rotor aircraftThen calculating the roll angle gamma of the required rotation by an inversion control algorithm_dAnd a pitch angle theta_dAnd combining three attitude angles of the aircraft, obtaining a current control law through a sliding mode control algorithm, sending the current control law into a four-rotor aircraft dynamics model, and feeding the generated state variables back to the position ring and the attitude ring so as to control the four-rotor aircraft to stably fly. Figure 2 is a schematic view of a quad-rotor aircraft.

In the above technical scheme, the method specifically comprises the following steps:

step S1: establishing a four-rotor aircraft dynamics model, determining the relation between the angular speed input and the attitude and the position of four motors of the aircraft, and the relation between the expected track and the attitude angle, as shown in formula (1):

in the formula: parameter J_x＝0.05887kg·m²，J_y＝0.05887kg·m²，J_z＝0.13151kg·m²，l＝0.3875m，m＝2.467kg,g＝9.81m/s²。

Formula (1) is the equation after decoupling the degrees of freedom (including the degrees of freedom of movement in the directions of three orthogonal axes x, y, z and the degrees of freedom of rotation around the three axes) of the four-rotor aircraft in 6 directions, and divides the flight state of the four-rotor aircraft into four independent channels: upper and lower channels, left and right channels, front and rear channels, yaw channel, defining

$\left\{\begin{array}{c}{U}_1=b({\mathrm{\&omega;}}_1^2+{\mathrm{\&omega;}}_2^2+{\mathrm{\&omega;}}_3^2+{\mathrm{\&omega;}}_4^2)\\ U_2=b({\mathrm{\&omega;}}_1^2-{\mathrm{\&omega;}}_3^2)\\ U_3=b({\mathrm{\&omega;}}_2^2-{\mathrm{\&omega;}}_4^2)\\ U_4=d({\mathrm{\&omega;}}_1^2+{\mathrm{\&omega;}}_3^2-{\mathrm{\&omega;}}_2^2-{\mathrm{\&omega;}}_4^2)\end{array}\right.---\left(2\right)$

Wherein, the parameter b is 2.2893 × 10^-5N·s²，d＝1.1897×10^-6N·ms²。

U₁、U₂、U₃、U₄Is the angular velocity (omega) of 4 propellers₁，ω₂，ω₃，ω₄) System control law determined: to express U specifically₁For the control law of the upper and lower channels, U₂For control law of front and rear channels and pitch angle, U₃Control law for left and right channels and roll angle, U₄Is a yaw angle control law. Substituting formula (2) into formula (1) results in a four-rotor aircraft dynamics model that combines four flight paths, as shown in formula (3):

expressing the established mathematical model (3) in a state space form:

$\stackrel{\&CenterDot;}{X}=f(X,U)$

wherein,is the state quantity of the system, U ═ U₁U₂U₃U₄]The f function is a function for solving the system state quantity at the next moment from the current system state quantity, and is specifically expressed as

Then, combining equation (3) and equation (4), a final four-rotor aircraft dynamics model can be obtained, as equation (5):

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=\frac{(J_y-J_z)}{J_x}{x}_4{x}_6+\frac{l}{J_x}{U}_2\\ {\stackrel{\&CenterDot;}{x}}_3=x_4\\ {\stackrel{\&CenterDot;}{x}}_4=\frac{(J_z-J_x)}{J_y}{x}_2{x}_6+\frac{l}{J_y}{U}_3\\ {\stackrel{\&CenterDot;}{x}}_5=x_6\\ {\stackrel{\&CenterDot;}{x}}_6=\frac{(J_x-J_y)}{J_z}{x}_2{x}_4+\frac{1}{J_z}{U}_4\\ {\stackrel{\&CenterDot;}{x}}_7=x_8\\ {\stackrel{\&CenterDot;}{x}}_8=\frac{U_1}{m}\left(\cos x_1\cos x_3\right)-g\\ {\stackrel{\&CenterDot;}{x}}_9=x_{10}\\ {\stackrel{\&CenterDot;}{x}}_{10}=\frac{U_1}{m}(\cos x_1\sin x_3\cos x_5+\sin x_1\sin x_5)\\ {\stackrel{\&CenterDot;}{x}}_{11}=x_{12}\\ {\stackrel{\&CenterDot;}{x}}_{12}=\frac{U_1}{m}(\sin x_5\sin x_3\cos x_1-\cos x_5\sin x_1)\end{array}\right.---\left(5\right)$

step S2: four-rotor aircraft controller design. The four-rotor aircraft moves in the front and back direction according to the roll angle in pitching, the two degrees of freedom are coupled channels, the input of a power source generates two degrees of freedom in two directions, the four-rotor aircraft is an under-actuated system, the instability of four axes is realized, and the left channel, the right channel and the roll angle are also coupled channels; the upper and lower channels and the yaw are two completely independent channels, and the channels are not coupled and are a fully-driven subsystem. According to the dynamics characteristics and characteristics of the four-rotor aircraft, the four-rotor aircraft dynamics model (formula 5) established in the step S1 is divided into a full-drive subsystem and an under-drive subsystem, and controller design is respectively carried out on the channels by adopting a sliding mode variable structure control method based on an inversion method.

Step S21: and designing a full-drive channel controller. The full driving channel comprises an upper channel, a lower channel and a yaw angleTwo channels, upper and lower channel z and yaw angleThe kinetic equations for the two channels are:

because coupling does not exist between all driving channels, a sliding mode variable structure control method can be directly used for solving a control law, and the control law of an upper channel z and a lower channel z is firstly calculated.

The state variables for the z-channel are:

$\left\{\begin{array}{c}{x}_7=z\\ x_8=\stackrel{\&CenterDot;}{z}\end{array}\right.---\left(7\right)$

defining an error variable:

e₇＝x₇-x_7d

wherein x is₇Is the current height; x is the number of_7dIs at a desired height; e.g. of the type₇Is the current and desired height difference.

Designing a sliding mode function as follows:

$s_z=c_7{e}_7+{\stackrel{\&CenterDot;}{e}}_7$

wherein, c₇Is a system parameter;is the derivative of the height difference; s_zIs a sliding mode surface function of the z-axis.

The Lyapunov function defining the z-channel isThen

${\stackrel{\&CenterDot;}{s}}_z=c_7{\stackrel{\&CenterDot;}{e}}_7+{\stackrel{\&CenterDot;\&CenterDot;}{e}}_7=c_7(x_8-{\stackrel{\&CenterDot;}{x}}_{7d})+({\stackrel{\&CenterDot;\&CenterDot;}{x}}_7-{\stackrel{\&CenterDot;\&CenterDot;}{x}}_{7d})$

And is

$s_z{\stackrel{\&CenterDot;}{s}}_z=s_z\left(c_7\right(x_8-{\stackrel{\&CenterDot;}{x}}_{7d})+\frac{U_1}{m}(\cos x_1\cos x_3)-g-{\stackrel{\&CenterDot;\&CenterDot;}{x}}_{7d})$

To ensureThe sliding mode control law is designed as

$U_1=(-\mathrm{\&epsiv;}\mathrm{sgn}(s_z)-{\mathrm{ks}}_z+c_7({\stackrel{\&CenterDot;}{x}}_{7d}-x_8)+g+{\stackrel{\&CenterDot;\&CenterDot;}{x}}_{7d})\frac{m}{\cos x_1\cos x_3}---\left(8\right)$

Then

$s_z{\stackrel{\&CenterDot;}{s}}_z=-\mathrm{\&epsiv;}\left|s_z\right|-{\mathrm{ks}}_z^2\&le;0$

Thereby to obtain

$\stackrel{\&CenterDot;}{V}\&le;0$

In the formula, the sum k is a constant of an approach law in sliding mode control; sgn(s)_z) Is a slip form surface s_zThe sign function of (a);

control law U₁Ensure thatThe resulting system is stable.

Thus, a control law U of an upper channel z and a lower channel z is obtained₁。

But yaw angleControl law U of channels₄The following can be obtained by the same method:

wherein,is a slip form surfaceThe sign function of (a); c. C₅Is a system parameter.

Step S22: designing an under-actuated channel controller for the dynamic model of the four-rotor aircraft established in the step S1: the underactuated channels comprise an x-gamma channel and a y-theta channel, and the kinetic equation is as follows:

for the design of the under-actuated channel control law, firstly obtaining attitude information by inversion of position information through an inversion algorithm, and then defining a sliding mode surface of a coupling channel on the basis;

the control law of the x-gamma channel is firstly designed as follows:

when the four-rotor aircraft moves on the x axis, although the pitch angle theta has an influence on the movement on the x axis, the influence can be ignored, and a small angle is assumed for the pitch angle theta, so that the dynamic model of the corresponding x-gamma channel at this time is as follows:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_9=x_{10}\\ x_{10}=\cos x_5\sin x_3\frac{U_1}{m}\\ {\stackrel{\&CenterDot;}{x}}_3=x_4\\ {\stackrel{\&CenterDot;}{x}}_4=\frac{J_z-J_x}{J_y}{x}_2{x}_6+\frac{{\mathrm{lU}}_3}{J_y}\end{array}\right.---\left(12\right)$

defining an error variable:

e₉＝x₉-x_9d(13)

wherein x is₉Is the current x position quantity; x is the number of_9dIs the desired x position quantity; e.g. of the type₉Is the difference between the current and desired x position quantities.

The specific design process is as follows:

(6) the Lyapunov function defining the state variable x is

$V_9=\frac{1}{2}{e}_9^2---\left(14\right)$

Then

${\stackrel{\&CenterDot;}{V}}_9=e_9{\stackrel{\&CenterDot;}{e}}_9=e_9(x_{10}-{\stackrel{\&CenterDot;}{x}}_{9d})$

GetWherein c is₉>0, is a system parameter; e.g. of the type₁₀The error variable, and also the virtual control quantity,

$e_{10}=x_{10}+c_9{e}_9-{\stackrel{\&CenterDot;}{x}}_{9d}---\left(15\right)$

then

${\stackrel{\&CenterDot;}{V}}_9=-c_9{e}_9^2+e_9{e}_{10}---\left(16\right)$

If e₁₀When the value is equal to 0, thenThe coupling term must be eliminated and for this reason, the next design step is required.

(7) Defining state variablesLyapunov function of

$V_{10}=V_9+\frac{1}{2}{e}_{10}^2---\left(17\right)$

Then

${\stackrel{\&CenterDot;}{V}}_{10}={\stackrel{\&CenterDot;}{V}}_9+e_{10}{\stackrel{\&CenterDot;}{e}}_{10}=-c_9{e}_9^2+e_9{e}_{10}+e_{10}{\stackrel{\&CenterDot;}{e}}_{10}$

GetWherein c is₁₀>0, is a system parameter; e.g. of the type₃The error variable, and also the virtual control quantity,

$e_3={\stackrel{\&CenterDot;}{e}}_{10}+c_{10}{e}_{10}+e_9---\left(18\right)$

then

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_{10}=-c_9{e}_9^2+e_9{e}_{10}+e_{10}(-c_{10}{e}_{10}-e_9+e_3)\\ =-c_9{e}_9^2-c_{10}{e}_{10}^2+e_{10}{e}_3\end{array}---\left(19\right)$

If e₃When the value is equal to 0, thenThe coupling term must be eliminated and for this reason, the next design step is required.

(8) Defining a Lyapunov function

$V_3=V_{10}+\frac{1}{2}{e}_3^2---\left(20\right)$

Then

${\stackrel{\&CenterDot;}{V}}_3={\stackrel{\&CenterDot;}{V}}_{1\stackrel{\&CenterDot;}{0}}+e_3{\stackrel{\&CenterDot;}{e}}_3=-c_9{e}_9^2-c_{10}{e}_{10}^2+e_{10}{e}_3+e_3{\stackrel{\&CenterDot;}{e}}_3$

GetWherein c is₃>0, is a system parameter; e.g. of the type₄The error variable, and also the virtual control quantity,

$e_4=c_3{e}_3+e_{10}+{\stackrel{\&CenterDot;}{e}}_3---\left(21\right)$

then

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_3=-c_9{e}_9^2-c_{10}{e}_{10}^2+e_3{e}_{10}+e_3(-c_3{e}_3-e_{10}+e_4)\\ =-c_9{e}_9^2-c_{10}{e}_{10}^2-e_3{e}_3^2+e_4{e}_3\end{array}---\left(22\right)$

At this time, the process of the present invention,in which there is a coupling term e₄e₃If this is eliminated, it is concluded that the system is stable. The next step is to design the slip-form face of the channel.

(9) In the process, the displacement speed difference e of the x-gamma channel is obtained₃And angular velocity difference e₄Thereby designing the attitude controller.

Is obtained by the formula (18)

$\begin{array}{c}{e}_3=(1+c_9{c}_{10})(x_9-x_{9d})+(c_9+c_{10})x_{10}\\ -(c_9+c_{10}){\stackrel{\&CenterDot;}{x}}_{9d}+{\stackrel{\&CenterDot;}{x}}_{\mathrm{10}}-{\stackrel{\&CenterDot;}{x}}_{9d}\end{array}---\left(23\right)$

The variable structure of the sliding mode is combined to define the sliding mode surface on the x axis as

s_x＝e₄(24)

(10) Defining state variablesLyapunov function of

$V_4=V_3+\frac{1}{2}{s}_x^2---\left(25\right)$

Then

${\stackrel{\&CenterDot;}{V}}_4=-c_9{e}_9^2-c_{10}{e}_{10}^2-c_3{e}_3^2+s_x{e}_3+s_x{\stackrel{\&CenterDot;}{s}}_x---\left(26\right)$

To make it possible toThe design controller is

$\begin{array}{c}{U}_3=\left(\right(-\mathrm{\&epsiv;}\mathrm{sgn}\left(s_x\right)-{\mathrm{ks}}_x-(c_9+c_3+c_9{c}_{10}{c}_3)({\stackrel{\&CenterDot;}{x}}_9-{\stackrel{\&CenterDot;}{x}}_{9d})\\ -(2+c_9{c}_{10}+c_9{c}_3+c_3{c}_{10})\cos x_5\sin x_3\frac{U_1}{m}\\ +(c_9+c_{10}+c_3)x_6\sin x_5\sin x_3\frac{U_1}{m}\\ -(c_9+c_{10}+c_3)x_4\cos x_5\cos x_3\frac{U_1}{m}\\ +x_6^2\cos x_5\sin x_3\frac{U_1}{m}+2x_4{x}_6\sin x_5\cos x_3\frac{U_1}{m}\\ +x_4^2\cos x_5\sin x_3\frac{U_1}{m}-(c_9+c_{10}){\stackrel{\&CenterDot;}{x}}_{9d}\\ +(1+c_9{c}_{10})(x_9-x_{9d})+(c_9+c_{10})x_{10}+{\stackrel{\&CenterDot;}{x}}_{10}\\ -{\stackrel{\&CenterDot;\&CenterDot;}{x}}_{9d}+(2+c_9{c}_{10}+c_9{c}_3+c_3{c}_{10}){\stackrel{\&CenterDot;\&CenterDot;}{x}}_{9d}\\ +(c_3+c_9+c_{10}){\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_{9d}+{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_{9d})/\left(\cos x_5\cos x_3\frac{U_1}{m}\right)\\ -\frac{J_z-J_x}{J_y}{x}_2{x}_6)\frac{J_y}{l}\end{array}---\left(27\right)$

Wherein,>0,k>0, is a system parameter; sgn(s)_x) Is a sliding mode surface function s_xThe sign function of (a); then

${\stackrel{\&CenterDot;}{V}}_4=-c_9{e}_9^2-c_{10}{e}_{10}^2-c_3{e}_3^2-{\mathrm{ks}}_x^2-\mathrm{\&epsiv;}\left|s_x\right|\&le;0---\left(28\right)$

ByThe system is known to be stable.

The y-theta channel control law is designed the same as the above method,

$\begin{array}{c}{U}_2=(-(c_{11}+c_1+c_{11}{c}_{12}{c}_1)({\stackrel{\&CenterDot;}{x}}_{11}-{\stackrel{\&CenterDot;}{x}}_{11d}))\\ +(2+c_{11}{c}_{12}+c_{11}{c}_1+c_{12}{c}_1)\cos x_5\sin x_1\frac{U_1}{m}\\ -(c_{11}+c_{12}+c_1)x_6\sin x_5\sin x_1\frac{U_1}{m}-(-\mathrm{\&epsiv;}\mathrm{sgn}(s_y))\\ +(c_{11}+c_{12}+c_1)x_2\cos x_5\cos x_1\frac{U_1}{m}-{\mathrm{ks}}_y\\ -x_6^2\cos x_5\sin x_1\frac{U_1}{m}-2x_4{x}_6\sin x_5\cos x_1\frac{U_1}{m}\\ -x_2^2\cos x_5\sin x_1\frac{U_1}{m}-(c_{11}+c_{12}){\stackrel{\&CenterDot;}{x}}_{11d}\\ +(1+c_{11}{c}_{12})(x_{11}-x_{11d})+(c_{11}+c_{12})x_{12}+{\stackrel{\&CenterDot;}{x}}_{12}\\ -{\stackrel{\&CenterDot;\&CenterDot;}{x}}_{11d}+(2+c_{11}{c}_{12}+c_{11}{c}_1+c_{12}{c}_1){\stackrel{\&CenterDot;\&CenterDot;}{x}}_{11d}\\ +(c_1+c_{11}+c_{12}){\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_{11d}+{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_{11d})/\left(\cos x_5\cos x_1\frac{U_1}{m}\right)\\ -\frac{J_y-J_z}{J_x}{x}_4{x}_6)\frac{J_x}{l}\end{array}---\left(29\right)$

wherein,>0,k>0, is a system parameter; sgn(s)_y) Is a sliding mode surface function s_yThe sign function of (2).

So far, the control laws of the four channels are respectively obtained.

The sign function sgn(s) in the control law obtained above is replaced by a saturation function sat(s) to suppress the chattering phenomenon caused by the sign function term,

$sat\left(s\right)=\left\{\begin{array}{cc}\begin{array}{cc}1,& s>\mathrm{\&Delta;}\\ ky,& \left|s\right|\&le;\mathrm{\&Delta;}\\ -1,& s<-\mathrm{\&Delta;}\end{array}& k=\frac{1}{\mathrm{\&Delta;}}\end{array}\right.---\left(30\right)$

in the formula, Δ is referred to as a boundary layer. Outside the boundary layer, switching control is adopted, and within the boundary layer, linear feedback control is adopted.

Step S3: after the controller design is finished, the four control laws U obtained in step S2 are set₁、U₂、U₃、U₄The four-rotor aircraft dynamics model (formula 5) derived in step S1 is substituted, so that the hovering and track following motions of the aircraft can be effectively controlled

Simulation verification is carried out on a four-rotor aircraft sliding mode variable structure control method based on an inversion method, and an aircraft is firstly arranged to hover at one point, such as:and assume its initial state to be:meanwhile, the related parameters of the sliding mode controller are set as follows: c. C₁＝c₃＝c₇＝c₉＝c₁₀＝c₁₁＝c₁₂＝1.8，c₅＝3.2，＝1.4，k＝6.2。

FIGS. 3-6 are graphs of a position ring and an attitude ring of a quad-rotor aircraft, the curves indicating that the aircraft can reach a target position and maintain a steady state within 4s soon, and FIG. 7 is a graph of a hover control law of the quad-rotor aircraft, the curves indicating that U is in a steady state for fixed-point hover of the aircraft₂,U₃,U₄Control law U of upper and lower channels being 0₁There is a numerical output that is required to offset the weight of the aircraft itself when it is suspended.

And moreover, the x axis and the y axis of the aircraft are respectively set to track sinusoidal motion, the target height of the z axis is 2m, and the track tracking curve graph and the track tracking error curve graph of the aircraft are respectively shown in the figures 8 and 9, so that the result shows that the expected track motion can be well tracked, the error is small, the maximum error is not more than 5cm, and the control effect is good.

In conclusion, the control method provided by the invention has the advantages that the controller design is respectively carried out on the subsystem, the pertinence is strong, the related parameters of the sliding mode controller are adjusted in real time, the sliding mode controller is accurately controlled in hovering and target track tracking, the dynamic response and the steady-state characteristic are greatly improved, and the engineering practical value is high.

The scope of the present invention is not limited to the preferred embodiments described above, and any modification or modification based on the same principle as the present invention should be included in the scope of the present invention.

Claims (5)

1. A four-rotor aircraft sliding mode variable structure control method based on an inversion method is characterized by comprising the following steps: the expected track of the four-rotor aircraft is given, then the roll angle and the pitch angle which need to rotate are calculated by an inversion control method, the current control law obtained by a sliding mode control method is sent to a four-rotor aircraft dynamics model by combining three attitude angles of the aircraft, and the hovering and track tracking motions of the aircraft are effectively controlled.

2. The inversion-based sliding mode variable structure control method for the quadrotor aircraft according to claim 1, wherein the method comprises the following steps: the method specifically comprises the following steps:

step S1: establishing a four-rotor aircraft dynamic model, and determining the relation between the angular speed input of four motors of the aircraft and the attitude and position, and the relation between the expected track and the attitude angle:

step S2: designing a four-rotor aircraft controller: according to the dynamics characteristics of the four-rotor aircraft, dividing the dynamics model established in the step S1 into a full-drive subsystem and an under-drive subsystem, and designing a sliding mode controller by adopting a sliding mode variable structure control method based on an inversion method;

step S3: and (4) after the design of the controller is finished, obtaining a current control law through a sliding mode control method, sending the current control law into the four-rotor aircraft dynamic model in the step S1, and feeding the generated state variables back to the position ring and the attitude ring so as to control the four-rotor aircraft to stably fly and effectively control the hovering and track tracking motions of the aircraft.

3. The inversion-based sliding mode variable structure control method for the quadrotor aircraft according to claim 2, wherein the method comprises the following steps: step S1 is to establish a four-rotor aircraft dynamics model as shown in equation (1):

in the formula: theta is a pitch angle, gamma is a roll angle,is a yaw angle and is three attitude angles; j. the design is a square_x、J_y、J_zRespectively the rotational inertia of the four-rotor aircraft body around three axes of a body coordinate system; l is the distance from the center of a propeller of the four-rotor aircraft to the origin of a coordinate system of the aircraft body; g is the acceleration of gravity; m is the mass of the quad-rotor aircraft; x, y and z are position quantities of the four-rotor aircraft in a navigation coordinate system respectively; omega₁，ω₂，ω₃，ω₄Are respectively four rotor wingsInput angular velocities of four motors of the traveling device; the formula (1) is an equation after the freedom degrees in 6 directions are decoupled; the degrees of freedom in the 6 directions comprise a degree of freedom of movement in the directions of three rectangular coordinate axes of x, y and z and a degree of freedom of rotation around the three rectangular coordinate axes;

the flight state of the four-rotor aircraft is divided into four independent flight channels: an upper channel, a lower channel, a left channel, a right channel, a front channel, a rear channel and a yaw channel; definition of

In the formula: b is the lift coefficient of the rotor, d is the drag coefficient of the rotor;

U₁、U₂、U₃、U₄for the system control law determined by the angular velocities of the 4 propellers: in particular U₁For the control law of the upper and lower channels, U₂For control law of front and rear channels and pitch angle, U₃Control law for left and right channels and roll angle, U₄A yaw angle control law; substituting formula (2) into formula (1) results in a four-rotor aircraft dynamics model that combines four flight paths, as shown in formula (3):

equation (3) is expressed in state space form:

wherein,is the state quantity of the system, U ═ U₁U₂U₃U₄]For the control law of the system, the f function is a function for solving the system state quantity at the next moment from the current system state quantity, and is specifically represented as:

then, combining equation (3) and equation (4), a final four-rotor aircraft dynamics model can be obtained, as equation (5):

4. the inversion-based sliding mode variable structure control method for the quadrotor aircraft according to claim 3, wherein the method comprises the following steps: step S2 quad-rotor aircraft controller design includes the steps of:

step S21: dividing the four-rotor aircraft dynamics model established in the step S1 into a full-drive channel and an under-drive channel, and respectively designing the channels;

firstly, designing a full-drive channel controller: the full driving channel comprises an upper channel, a lower channel and a yaw angleTwo channels, upper and lower channel z and yaw angleThe kinetic equations for the two channels are:

directly using a sliding mode variable structure control method to obtain a control law, firstly calculating the control law of an upper channel z and a lower channel z:

the state variables of the upper and lower channels z are:

defining an error variable:

e₇＝x₇-x_7d

wherein x is₇Is the current height; x is the number of_7dIs at a desired height; e.g. of the type₇Is the current and desired height difference.

Designing a sliding mode function as follows:

wherein, c₇Is a system parameter;is the derivative of the height difference; s_zA sliding mode surface function for the z-axis;

the Lyapunov function defining channel z isThen

And is

To ensureControl law U for designing upper and lower channels z₁

Then

Thereby to obtain

In the formula, the sum k is a constant of an approach law in sliding mode control; sgn(s)_z) Is a slip form surface s_zThe sign function of (a);

the same method is used to determine the yaw angleControl law U of channels₄：

Wherein,is a slip form surfaceThe sign function of (a); c. C₅Is a system parameter;

step S22: designing an under-actuated channel controller for the dynamic model of the four-rotor aircraft established in the step S1: the underactuated channels comprise an x-gamma channel and a y-theta channel, and the kinetic equation is as follows:

firstly, obtaining attitude information by inversion of position information through an inversion algorithm, and then defining a sliding mode surface of a coupling channel on the basis;

the control law of the x-gamma channel is firstly designed as follows:

when the four-rotor aircraft moves on the x axis, although the pitch angle theta has an influence on the movement on the x axis, the influence can be ignored, and a small angle is assumed for the pitch angle theta, so that the dynamic model of the corresponding x-gamma channel at this time is as follows:

defining an error variable:

e₉＝x₉-x_9d(13)

wherein x is₉Is the current x position quantity; x is the number of_9dIs the desired x position quantity; e.g. of the type₉Is the difference between the current and desired x position quantities.

The specific design process is as follows:

(1) the Lyapunov function defining the state variable x is

Then

GetWherein c is₉>0, is a system parameter; e.g. of the type₁₀The error variable, and also the virtual control quantity,

then

If e₁₀When the value is equal to 0, thenTherefore, the coupling term must be eliminated, and for this reason, the next design is required;

(2) defining state variablesLyapunov function of

Then

GetWherein c is₁₀>0, is a system parameter; e.g. of the type₃The error variable, and also the virtual control quantity,

then

If e₃When the value is equal to 0, thenTherefore, the coupling term must be eliminated, and for this reason, the next design is required;

(3) lyapunov function defining a state variable gamma

Then

GetWherein c is₃>0, is a system parameter; e.g. of the type₄The error variable, and also the virtual control quantity,

then

At this time, the process of the present invention,in which there is a coupling term e₄e₃If this is eliminated, it can be concluded that the system is stable;

designing the sliding mode surface of the channel;

(4) in the process, the displacement speed difference e of the x-gamma channel is obtained₃And angular velocity difference e₄Thereby designing

An attitude controller:

is obtained by the formula (18)

The variable structure of the sliding mode is combined to define the sliding mode surface on the x axis as

s_x＝e₄(24)

(5) Defining state variablesLyapunov function of

Then

To make it possible toThe design controller is

Wherein,>0,k>0, is a system parameter; sgn(s)_x) Is a sliding mode surface function s_xThe sign function of (a); then

ByThe system is known to be stable;

the y-theta channel control law is designed the same as the above method,

wherein,>0,k>0, is a system parameter; sgn(s)_y) Is a sliding mode surface function s_yThe sign function of (a);

at this moment, the control laws of the four channels are respectively solved;

the sign function sgn(s) in the control law obtained above is replaced by a saturation function sat(s) to suppress the chattering phenomenon caused by the sign function term,

in the formula, Δ is referred to as a boundary layer. Outside the boundary layer, switching control is adopted, and within the boundary layer, linear feedback control is adopted.

5. The inversion-based sliding mode variable structure control method for the quadrotor aircraft according to claim 4, wherein the method comprises the following steps: step S3 specifically includes: after the controller design is finished, the four control laws U obtained in step S2 are set₁、U₂、U₃、U₄And (5) substituting the four-rotor aircraft dynamics model formula (5) in the step S1, the hovering and track tracking motion of the aircraft can be effectively controlled.