CN114019997A - Finite time control method under position tracking deviation constraint of fixed-wing unmanned aerial vehicle - Google Patents
Finite time control method under position tracking deviation constraint of fixed-wing unmanned aerial vehicle Download PDFInfo
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Abstract
The invention discloses a finite time control method under the constraint of position tracking deviation of a fixed-wing unmanned aerial vehicle, which is used for the finite time constraint control under the position tracking deviation of the fixed-wing unmanned aerial vehicle. Firstly, converting a kinematics and three-degree-of-freedom dynamics model of a fixed wing unmanned aerial vehicle in an inertial coordinate system into an affine form, and establishing a fixed wing unmanned aerial vehicle outer ring position tracking control model by considering uncertainty disturbance; secondly, designing a constraint controller based on backstepping control theory and a barrier Lyapunov function, and processing the problem of a differential algebraic ring in backstepping control by adopting a finite time filter; then, estimating uncertainty disturbance in the model by using a disturbance observer to improve the outer ring constraint control precision of the fixed wing unmanned aerial vehicle; finally, the stability of the overall closed loop system was demonstrated. The method solves the problem that the tracking precision is reduced due to the influence of nonlinear and uncertain disturbance on the unmanned aerial vehicle flight control system.
Description
Technical Field
The invention relates to a finite time control method for position tracking deviation constraint of a fixed-wing unmanned aerial vehicle, and belongs to the field of aircraft constraint control.
Technical Field
In an unmanned aerial vehicle flight system, autonomous flight of an unmanned aerial vehicle is a cross-field research subject with strong comprehensiveness, and covers a plurality of research contents such as information fusion, mission planning, navigation control and the like. In the field of flight control, factors such as complex and variable task environments, uncertain disturbance of parameters, multi-state limited conditions and the like undoubtedly bring a series of control problems to be solved urgently for autonomous flight of the unmanned aerial vehicle. In consideration of safety, physical limitations of mechanical manufacturing and execution components and other practical applications, a constraint phenomenon generally exists in a control system, and if relevant physical constraint conditions are not considered in a control design link of an unmanned aerial vehicle flight system, during a flight task executed by the system based on an unconstrained control scheme, conditions violating constraint limits may bring certain adverse effects to system performance and stability of a closed-loop system, even damage to aircraft system equipment and occurrence of dangerous accidents are caused, personal safety is threatened, and unnecessary loss of manpower, material resources and financial resources is caused. The position tracking control of the fixed-wing unmanned aerial vehicle requires that the unmanned aerial vehicle tracks any one designated flight route as much as possible so as to complete the flight task. Under the actual complex task environment, such as hills and hilly terrains in geological exploration tasks, for such nonlinear systems as fixed-wing unmanned aerial vehicles, uncertain disturbance usually causes the position tracking response speed of the unmanned aerial vehicle to become slow, precision to descend and the like, therefore, the convergence of tracking deviation completed in limited time is a necessary means for ensuring the safety and stability control of the unmanned aerial vehicle, the tracking deviation is constrained in a certain preset range to ensure the precision of the outer ring control of the unmanned aerial vehicle, the dynamic performance and the overall stability of the unmanned aerial vehicle are ensured, the unmanned aerial vehicle fully embodies the performance advantages of original maneuvering flexibility while completing the complex tasks, and the method has important practical significance for the safe flight of the fixed-wing unmanned aerial vehicle.
The finite time control under the position tracking deviation constraint of the fixed-wing unmanned aerial vehicle covers two aspects of constraint control and flight control, the constraint control can ensure that the control transient state and the dynamic performance of the unmanned aerial vehicle are kept in the predefined constraint condition, and the flight control ensures the stability and the robustness of a flight system of the fixed-wing unmanned aerial vehicle. At present, a plurality of advanced control methods are widely applied to the constraint control of the unmanned aerial vehicle, such as adaptive control, sliding mode control, backstepping control, neural network control, fuzzy control and the like. The backstepping control enables the Lyapunov stability proving function and the design process of the controller to be systematized and structured by introducing the virtual control semaphore, embodies specific advantages and is widely applied. The existing nonlinear system constraint control scheme has quite a lot of achievements, but still has the following defects:
1. most of the existing constraint control schemes are technical means for requiring the steady-state performance of a nonlinear system to reach a certain index and not for purposefully constraining the convergence rapidity of the nonlinear system, and meanwhile, most of the existing constraint control schemes are control in a robust form, so that the conservation is high, and the constraint control for the outer ring position tracking deviation of the fixed wing unmanned aerial vehicle is relatively less;
2. when the problem of 'explosion calculation' in the backstepping control theory is solved, a dynamic surface control technology based on a low-pass filter is mostly adopted, a command filter based on finite time control is rarely considered from the dynamic performance of the system, and further intensive research is needed for better embodying the advantage of backstepping control in the position tracking deviation constraint control of the fixed-wing unmanned aerial vehicle;
3. at present, in most of fixed wing unmanned aerial vehicle outer ring position tracking deviation constraint control laws, less disturbance and modeling uncertainty are subjected to bounded estimation at the same time, so that control accuracy and constraint performance are not ideal, and the bounding performance and engineering realizability of control signals cannot be guaranteed.
Disclosure of Invention
Object of the Invention
In order to solve the above technical problems, an object of the present invention is to provide a method for controlling a limited time under the constraint of a position tracking offset of a fixed-wing drone, so as to ensure that the fixed-wing drone tracks an expected position signal and simultaneously constrains the tracking offset within a predefined constraint range within a limited time.
Technical scheme
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a finite time control method under the constraint of position tracking deviation of a fixed wing unmanned aerial vehicle, which relates to backstepping control theory, disturbance observer design and finite time filter design and is realized by the following steps:
(a) establishing a dynamic model of the fixed-wing unmanned aerial vehicle:
defining the position P of the unmanned aerial vehicle in three directions of an X axis, a Y axis and an H axis of an inertial coordinate system as [ X, Y, H ═ X]TEstablishing a fixed-wing unmanned aerial vehicle kinematics model
V is the flight airspeed of the unmanned aerial vehicle, gamma and chi are the track inclination angle and the track azimuth angle of the unmanned aerial vehicle, and a three-degree-of-freedom particle model of the unmanned aerial vehicle is established:
wherein m is the mass of the unmanned aerial vehicle, g is the acceleration of gravity, TeAnd DfPhi is the thrust and the resistance of the engine, phi is the rolling angle, n is the load coefficient, namely the ratio of the lift force to the weight, and gn cos phi and gn sin phi respectively represent the pitch acceleration and the yaw acceleration of the fixed-wing unmanned aerial vehicle; d1＝[dt，dy，dp]TFor uncertain disturbance, the actual control quantity n, phi and T of the unmanned aerial vehicle are respectively controlled by the elevator, the combination of the rudder and the aileron and the accelerator, thereby introducing the pseudo control quantity of the unmanned aerial vehicle
U＝[ut，uy，up]T (3)
Wherein the relationship between each element in the pseudo controlled variable and the actual controlled variable is
uyGn sin phi and upThe actual control variables n, phi and T can be based on the designed ut，uyAnd upDeriving to obtain;
can be obtained by deriving formula (1)
Wherein the rotation matrix R is
By substituting formula (2) for formula (4)
So that the dynamics of the drone can be rewritten as
Wherein G is [0, 0, -G]T。
(b) Affine modeling of a dynamic model:
defining the flight position of the unmanned aerial vehicle as X1＝P＝[x，y，h]TUncertainty perturbation is D ═ RD1＝[d1，d2，d3]TWherein R and D1＝[dt，dy，dp]TRespectively the rotation matrix and uncertainty interference defined in the above steps; definition of
The pseudo control quantity is U ═ Ut，uy，up]TAnd transforming the three-degree-of-freedom dynamic model (6) of the fixed-wing unmanned aerial vehicle into an affine form:
(c) finite time instruction filter design:
defining a position tracking offset E1＝X1-X1dWherein X is1dFor the desired position command, the intermediate control signals are designed as follows:
wherein, K1And S1Defining a compensation tracking deviation signal Z for a positive definite parameter matrix to be designed, wherein tau is a normal number and satisfies 0 & lttau & lt 11＝E1-ξ1In which E1Compensating signals for positional tracking offsets
Wherein L is1For positively-defined parameter matrices, X, to be designed2cTo be controlled by an intermediate control signal alpha1The output signal of the first-order Levant differentiator which is input, the finite-time instruction filter is expressed as:
wherein alpha is1For the filter input signal, X2c＝Ψ11And
is a filtered output and X2cIs a designed virtual control signal.
(d) backstepping design first step:
according to the position state X of the unmanned aerial vehicle1＝[x，y，h]TAnd the expected position instruction X1d＝[xd，yd，hd]TDefining the upper and lower bounds of the tracking deviation of the unmanned aerial vehicle position in the three directions of the X axis, the Y axis and the H axis asE 1＝[E 1x，E 1y，E 1h]And
namely, it is
Then compensating the tracking offset signal needs to be satisfied
Definition Ka＝E 1Xi1And
the barrier Lyapunov function is thus designed to be:
wherein Z1i、KaiAnd KbiRespectively showing the compensation tracking deviation and the upper and lower boundaries thereof in the three directions of the X axis, the Y axis and the H axis,
definition of
And η1＝[η11，η12，η13]TWherein
(e) Designing a disturbance observer:
setting uncertainty perturbation D (t) ═ d1(t)，d2(t)，d3(t)]TIs continuously bounded to first order can and satisfy
Where δ is a bounded normal number, defining a pair of state quantities X2Filtered tracking offset E2＝X2-X2cThen, then
Introducing a new state variable S2＝D-K2E2To obtain
The disturbance observer is designed as follows:
wherein the content of the first and second substances,
is an estimate of the disturbance D, S2As an auxiliary variable of the disturbance observer, K2A positive definite diagonal parameter matrix to be designed.
(f) Second step of backstepping design
According to the filtered state quantity X2Tracking deviation E of2＝X2-X2cAnd deviation compensation signal xi2Defining the compensated tracking offset signal Z2＝E2-ξ2And designing the pseudo control quantity of the position tracking deviation constraint controller as follows:
and the deviation compensation signal is:
wherein, K3，S2And L2A positive definite parameter matrix to be designed.
(g) And returning to the outer ring model of the fixed wing unmanned aerial vehicle according to the obtained control input U, and carrying out limited time position tracking deviation constraint control on the fixed wing unmanned aerial vehicle with uncertain disturbance.
The invention has the beneficial effects that:
(1) the method considers the problem of position tracking deviation constraint control under the conditions of uncertain disturbance and modeling uncertainty of the fixed-wing unmanned aerial vehicle, and based on backstepping control theory and a disturbance observer, the designed finite time constraint control scheme not only ensures the stable flight of the fixed-wing unmanned aerial vehicle under the uncertain disturbance, but also ensures that the outer ring position tracking deviation of the fixed-wing unmanned aerial vehicle can be constrained within a predefined bounded range in finite time;
(2) in the control design, an instruction filter with a finite time convergence characteristic is adopted to solve the traditional problem of 'differential calculation algebraic loop' in the backstepping control theory, so that the filtering deviation of the virtual control quantity is converged to zero in the finite time, and the dynamic performance, namely the rapidity, of the whole outer loop control system is ensured;
(3) the method has good practical significance and application prospect in the outer ring restraint control of the fixed wing unmanned aerial vehicle.
Drawings
FIG. 1 is a flow chart of a finite time control method under the constraint of position tracking deviation of a fixed-wing drone;
FIG. 2 is a block diagram of a finite time control system under the constraint of position tracking deviation of a fixed-wing drone;
FIG. 3 is a graph of the flight trajectory of a fixed wing drone;
FIG. 4 is a graph of position tracking deviation of a fixed wing drone in the X-axis direction;
FIG. 5 is a graph of position tracking deviation in the Y-axis direction of a fixed-wing drone;
FIG. 6 is a graph of position tracking deviation in the H-axis direction of a fixed-wing drone;
FIG. 7 is a graph of finite time instruction filter bias;
FIG. 8 is a graph of estimated deviation of a disturbance observer;
fig. 9 is a graph of the actual control input of the designed fixed-wing drone.
Detailed Description
The control method of the present invention will be further explained with reference to the attached drawings.
(a) Establishing a dynamic model of the fixed-wing unmanned aerial vehicle:
defining the position P of the unmanned aerial vehicle in three directions of an X axis, a Y axis and an H axis of an inertial coordinate system as [ X, Y, H ═ X]TEstablishing a fixed-wing unmanned aerial vehicle kinematics model
V is the flight airspeed of the unmanned aerial vehicle, gamma and chi are the track inclination angle and the track azimuth angle of the unmanned aerial vehicle, and a three-degree-of-freedom particle model of the unmanned aerial vehicle is established:
wherein m is the mass of the unmanned aerial vehicle, g is the acceleration of gravity, TeAnd Df is the thrust and the resistance of the engine, phi is the roll angle, n is the load coefficient, namely the ratio of the lift force to the weight, and gn cos phi and gn sin phi respectively represent the pitch acceleration and yaw acceleration of the fixed-wing unmanned aerial vehicle; d1＝[dt，dy，dp]TFor uncertain disturbance, the actual control quantity n, phi and T of the unmanned aerial vehicle are respectively controlled by the elevator, the combination of the rudder and the aileron and the accelerator, thereby introducing the pseudo control quantity of the unmanned aerial vehicle
U＝[ut，uy，up]T (3)
Wherein the relationship between each element in the pseudo controlled variable and the actual controlled variable is
uyGn sin phi and upThe actual control variables n, phi and T can be based on the designed ut，uyAnd upDeriving to obtain;
can be obtained by deriving formula (1)
Wherein the rotation matrix R is
By substituting formula (2) for formula (4)
So that the dynamics of the drone can be rewritten as
Wherein G is [0, 0, -G]T。
(b) Affine modeling of a dynamic model:
defining the flight position of the unmanned aerial vehicle as X1＝P＝[x，y，h]TUncertainty perturbation is D ═ RD1＝[d1，d2，d3]TWherein R and D1＝[dt，dy，dp]TRespectively the rotation matrix and uncertainty interference defined in the above steps; definition of
The pseudo control quantity is U ═ Ut，uy，up]TAnd transforming the three-degree-of-freedom dynamic model (6) of the fixed-wing unmanned aerial vehicle into an affine form:
(c) finite time instruction filter design:
defining a position tracking offset E1＝X1-X1dWherein X is1dFor the desired position command, the intermediate control signals are designed as follows:
wherein, K1And S1Defining a compensation tracking deviation signal Z for a positive definite parameter matrix to be designed, wherein tau is a normal number and satisfies 0 & lttau & lt 11＝E1-ξ1In which E1Compensating signals for positional tracking offsets
Wherein L is1For positively-defined parameter matrices, X, to be designed2cTo be controlled by an intermediate control signal alpha1The output signal of the first-order Levant differentiator which is input, the finite-time instruction filter is expressed as:
wherein alpha is1For the filter input signal, X2c＝Ψ11And
is a filtered output and X2cIs a designed virtual control signal.
(d) backstepping design first step:
according to the position state X of the unmanned aerial vehicle1＝[x，y，h]TAnd the expected position instruction X1d＝[xd，yd，hd]TDefining the upper and lower bounds of the tracking deviation of the unmanned aerial vehicle position in the three directions of the X axis, the Y axis and the H axis asE 1＝[E 1x，E 1y，E 1h]And
namely, it is
Then compensating the tracking offset signal needs to be satisfied
Definition Ka＝E 1-ξ1And
the barrier Lyapunov function is thus designed to be:
wherein Z1i、KaiAnd KbiRespectively showing the compensation tracking deviation and the upper and lower boundaries thereof in the three directions of the X axis, the Y axis and the H axis,
definition of
And η1＝[η11，η12，η13]TWherein
Barrier Lyapunov function V1The derivative of (d) can be expressed as:
(e) the disturbance observer design and its bounded stability prove:
setting uncertainty perturbation D (t) ═ d1(t)，d2(t)，d3(t)]TIs continuously bounded to first order can and satisfy
Where δ is a bounded normal number. Definition of state quantity X2Filtered tracking offset E2＝X2-X2cThen, then
Introducing a new state variable S2＝D-K2E2To obtain
The disturbance observer is designed as follows:
wherein the content of the first and second substances,
is an estimate of the disturbance D, S2As an auxiliary variable of the disturbance observer, K2A positive definite diagonal parameter matrix to be designed.
Definition of
For the estimation deviation of the disturbance observer, the Lyapunov function in the step is selected as follows:
the above equation is derived and can be obtained according to the young inequality:
(f) second step of backstepping design
According to the state quantity X2Filtered tracking offset E2＝X2-X2cAnd deviation compensation signal xi2Defining the compensated tracking offset signal Z2＝E2-ξ2And designing the pseudo control quantity of the position tracking deviation constraint controller as follows:
and the deviation compensation signal is:
wherein, K3，S2And L2A positive definite parameter matrix to be designed.
The Lyapunov function of the step is selected as follows:
the above equation is derived and can be obtained according to the young inequality:
in order to analyze the stability of the whole closed-loop system, the following Lyapunov function is selected:
by deriving the above equation from equations (12), (16) and (20), it is possible to obtain:
wherein the content of the first and second substances,
from the bounded theorem in the proof of stability, the tracking offset Z1Estimated deviation of disturbance observer
And the filtered tracking offset Z2Have consistent and bounded nature, i.e., the system may asymptotically stabilize.
To analyze the finite time stability of the position tracking bias constraint control, assume that there is ═ Π1，Π2，Π3]TSo that
Next, the following Lyapunov function is selected:
wherein
According to the finite time theorem, equation (24) can be rewritten as:
wherein0 < theta < 1, when
When it is established there is
According to the finite time theorem, the design parameters in the right definite diagonal matrix satisfy
λmin(S1) If T > 0 and lambdamin(S2) When > 0, tracking offset Z1And tracking offset Z2Will be in a limited time T1＝max{T1f1，T1f2Converge to the convex set Ω -min { Ω }1，Ω2In (c) }. Wherein the content of the first and second substances,
correspond to
Correspond to
When T > T1When there is
Position tracking compensation offset signal satisfaction
That is, the position tracking offset signal will converge to a small range of neighborhood within a limited time and will not exceed the predetermined constraint region.
And because of
And
to account for the finite time stability of the position tracking bias, it is necessary to analyze the finite time convergence of the bias compensation signal, whereby the Lyapunov function is chosen as follows:
according to equations (9) and (18), and for a finite time TnInner | X2c-α1|≤ω1Further derivation can be obtained
Wherein the content of the first and second substances,
if the parameters satisfy
And λmin(L2) Is greater than 0, and can obtain deviation compensation signal xi1、ξ2In a limited time
Inner convergence to zero, i.e. xi 1，20. Definition of
T2＝max{T1，Tn，TξFrom which analysis can be inferred
(g) And returning to the outer ring model of the fixed wing unmanned aerial vehicle according to the obtained control input U, and carrying out limited time position tracking deviation constraint control on the fixed wing unmanned aerial vehicle with uncertain disturbance.
The effectiveness of the invention is verified by performing simulations as follows:
the dynamic model of the fixed-wing unmanned aerial vehicle and the definitions thereof are shown in (1) to (6), and the values of the structural parameters are that m is 25kg, and g is 9.8 m.s-2The desired position signal is set to fly horizontally with the X-axis at 28m/s, the Y-axis and the H-axis fly in a straight line from 0m and 1024m to positions of 1m and 1025.5m, respectively, in the first 10s, and then fly with a motion trajectory of 0.5sin (0.25t-2.5) +1 and sin (0.15t-1.5) +1.5, respectively; uncertainty perturbations in the model were set to [0.02sin (0.3t), 0.02sin (0.5t), 0.03sin (0.4t) at 0s to 10s]TAnd D ═ 0.1, 0.2, 0.3 at 30s to 45s]TAfter 50s, D ═ 0.2sin (0.4t), 0.2sin (0.3t), 0.3sin (0.4t)]T(ii) a Position tracking offset constraint range is set as
AndE 1＝[-0.8e-2t-0.7，-0.5e-1.5t-0.4，-0.5e-1.5t-0.3]T(ii) a The control parameter is selected to be tau-0.6, K1＝diag{126，90，90}，S1＝diag{8，8，8}，L1＝diag{7.5，7.2，7.2}， r11＝diag{14，14，14}，K2＝diag{144，108，108}，S2＝diag{15，15，15}， L2＝diag{7，7，7}，r12＝diag(8，8，8)，h1，2，3，4＝1，K3The initial state of the system is set to V (0) ═ 28m/s, χ (0) ═ 0.01 °, γ (0) ═ 0.015 ═ 0.01 ═ V (0) ·°。
The simulation result shows that the finite time control method under the constraint of the position tracking deviation of the fixed-wing unmanned aerial vehicle can better control the position tracking of the unmanned aerial vehicle and has better deviation constraint effect. FIG. 3 is a schematic diagram of a fixed-wing drone tracking a given desired position under a designed control law, wherein a curve in the diagram indicates that a real flight trajectory of the drone tends to be consistent with a desired signal; fig. 4, 5 and 6 are graphs of constraint curves of tracking deviation of fixed wing drones on X, Y and H axes respectively, and it is obvious that the position state E of the drone is seen1Can be converged in a limited time and is strictly restricted to a preset bounded restriction rangeE 1And
internal; FIG. 7 is a schematic diagram of the filter bias of the designed command filter, according to which the filter bias of the command filter can be obtained to be converged within a limited time, and a better filtering effect is obtained; from fig. 8, it can be seen that the designed disturbance observer can better estimate the external uncertainty disturbance signal, and the estimation deviation can be converged to zero within a period of time; the curve in fig. 9 shows the actual control semaphore T in the inventionePhi and n, the actual control input signal obtained by designing the control law is finally stable and bounded.
In summary, for the case that the position tracking deviation constraint is considered under the existence of uncertain disturbance of the fixed-wing drone, the method of the present invention can realize the disturbance estimation and the position tracking deviation constraint control of the fixed-wing drone within a limited time.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and adjustments can be made without departing from the principle of the present invention, and these modifications and adjustments should also be regarded as the protection scope of the present invention.
Claims (5)
1. The method for controlling the finite time under the constraint of the position tracking deviation of the fixed-wing unmanned aerial vehicle is characterized by comprising the following steps of:
establishing a three-degree-of-freedom dynamic model of a fixed-wing unmanned aerial vehicle, and transforming a dynamic secondary integral model of the fixed-wing unmanned aerial vehicle into an affine form;
designing a constraint controller based on backstepping control theory and a barrier Lyapunov function, and processing the differential algebraic ring problem in backstepping control by adopting a finite time filter;
estimating uncertainty disturbance in the model by using a disturbance observer to improve the outer ring constraint control precision of the fixed wing unmanned aerial vehicle;
and step four, returning the output result of the constraint controller to the three-degree-of-freedom model of the fixed-wing unmanned aerial vehicle, and realizing the finite time control under the constraint of the position tracking deviation of the fixed-wing unmanned aerial vehicle.
2. The method for finite time control under the constraint of position tracking deviation of fixed-wing drone according to claim 1, characterized in that said step one includes the following processes:
step 1.1 defines the position P of the unmanned aerial vehicle in three directions of the X axis, the Y axis and the H axis of the inertial coordinate system as [ X, Y, H ═ X]TEstablishing a fixed-wing unmanned aerial vehicle kinematics model
V is the flight airspeed of the unmanned aerial vehicle, gamma and chi are the track inclination angle and the track azimuth angle of the unmanned aerial vehicle, and a three-degree-of-freedom particle model of the unmanned aerial vehicle is established:
wherein m is the mass of the unmanned aerial vehicle, g is the acceleration of gravity, TeAnd DfPhi is the rolling angle, n is the load coefficient, i.e. the ratio of lift to weight, and gn cos phi and gn sin phi respectively indicate that the fixed wing has no thrust and resistancePitch acceleration and yaw acceleration of the human machine; d1＝[dt，dy，dp]TFor uncertain disturbance, the actual control quantity n, phi and T of the unmanned aerial vehicle are respectively controlled by the elevator, the combination of the rudder and the aileron and the accelerator, thereby introducing the pseudo control quantity of the unmanned aerial vehicle
U＝[ut，uy，up]T (3)
Wherein each element u in the pseudo controlled variablet，uyAnd upThe relationships with the actual control quantities n, phi and T are respectively
uyGn sin phi and upGn cos phi, the actual control quantities n, phi and T are based on the designed ut，uyAnd upDeriving to obtain;
can be obtained by deriving formula (1)
Wherein the rotation matrix R is
By substituting formula (2) for formula (4)
So that the dynamics of the drone can be rewritten as
Wherein G is [0, 0, -G]T；
Step 1.2 defining the flight position of the unmanned aerial vehicle as X1＝P＝[x，y，h]TUncertainty perturbation is D ═ RD1＝[d1，d2，d3]TWherein R and D1＝[dt，dy，dp]TRespectively the rotation matrix and uncertainty interference defined in the above steps; definition of
The pseudo control quantity is U ═ Ut，uy，up]TAnd transforming the three-degree-of-freedom dynamic model (6) of the fixed-wing unmanned aerial vehicle into an affine form:
3. the method for finite time control under the constraint of position tracking deviation of a fixed-wing drone according to claim 2, characterized in that said second step specifically comprises the following steps:
step 2.1 define position tracking offset E1＝X1-X1dWherein X is1dFor the desired position command, the intermediate control signals are designed as follows:
wherein, K1And S1Defining a compensation tracking deviation signal Z for a positive definite parameter matrix to be designed, wherein tau is a normal number and satisfies 0 & lttau & lt 11＝E1-ξ1In which E1Compensating signals for positional tracking offsets
Wherein L is1For positively-defined parameter matrices, X, to be designed2cTo be controlled by an intermediate control signal alpha1The output signal of the first-order Levant differentiator which is input, the finite-time instruction filter is expressed as:
wherein alpha is1For the filter input signal, X2c＝Ψ11And
is a filtered output and X2cIs a designed virtual control signal;
step 2.2 according to the position state X of the unmanned aerial vehicle1＝[x，y，h]TAnd the expected position instruction X1d＝[xd，yd，hd]TDefining the upper and lower bounds of the tracking deviation of the unmanned aerial vehicle position in the three directions of the X axis, the Y axis and the H axis asE 1＝[E 1x，E 1y，E 1h]And
namely, it is
Then compensating the tracking offset signal needs to be satisfied
Definition Ka＝E 1-ξ1And
the barrier Lyapunov function is thus designed to be:
wherein Z1i、KaiAnd KbiRespectively showing the compensation tracking deviation and the upper and lower boundaries thereof in the three directions of the X axis, the Y axis and the H axis,
definition of
And η1＝[η11，η12，η13]TWherein
4. The fixed-wing drone position tracking deviation under finite time control method of claim 2, wherein the third step specifically includes the following processes:
setting uncertainty perturbation D (t) ═ d1(t)，d2(t)，d3(t)]TIs continuously bounded to first order can and satisfy
Where δ is a bounded normal number, defining a pair of state quantities X2Filtered tracking offset E2＝X2-X2cThen, then
Introducing a new state variable S2＝D-K2E2To obtain
The disturbance observer is designed as follows:
wherein the content of the first and second substances,
is an estimate of the disturbance D, S2As an auxiliary variable of the disturbance observer, K2A positive definite diagonal parameter matrix to be designed.
5. The fixed-wing drone position tracking deviation under finite time control method according to claim 1, characterized in that said fourth step specifically comprises the following processes:
step 4 according to the state quantity X2Filtered tracking offset E2＝X2-X2cAnd deviation compensation signal xi2Defining the compensated tracking offset signal Z2＝E2-ξ2And designing the pseudo control quantity of the position tracking deviation constraint controller as follows:
and the deviation compensation signal is:
wherein, K3，S2And L2A positive definite parameter matrix to be designed.
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