CN114879728A - Aircraft robust formation control method based on active disturbance rejection control - Google Patents
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Abstract
An active disturbance rejection control-based robust formation control method for aircrafts belongs to the technical field of aircraft control. The method comprises the following steps: constructing an aircraft cluster formation control model; designing an aircraft position cooperative active disturbance rejection controller; and designing an aircraft speed tracking controller. The invention provides a strong-robustness and high-adaptivity aircraft formation control method based on an active disturbance rejection control theory and a leading formation control framework, which can enable an aircraft cluster to meet formation control precision under a strong-disturbance and high-uncertainty environment, effectively weakens the influence of external disturbance and model uncertainty on formation control effect, improves the robustness of a controller, and effectively improves the environment adaptability of an unmanned aerial vehicle formation controller.
Description
Technical Field
The invention relates to an active disturbance rejection control-based robust formation control method for aircrafts, and belongs to the technical field of aircraft control.
Background
The problems of high model uncertainty, complex interference and the like are faced to the problem of aircraft formation control, and the traditional formation control method is based on simplified model design and does not consider the problem of external interference compensation, so that the robustness and the environmental adaptability are poor, the requirements of practical engineering application cannot be met, and a new aircraft formation control method is urgently needed to be developed.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides an aircraft robust formation control method based on active disturbance rejection control.
The invention adopts the following technical scheme: an active disturbance rejection control-based robust formation control method for aircrafts, comprising the following steps:
s1: constructing an aircraft cluster formation control model;
s2: designing an aircraft position cooperative active disturbance rejection controller;
s3: and designing an aircraft speed tracking controller.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a strong-robustness and high-adaptivity aircraft formation control method based on an active disturbance rejection control theory and a leading formation control framework, which can enable an aircraft cluster to meet formation control precision under a strong-disturbance and high-uncertainty environment, effectively weakens the influence of external disturbance and model uncertainty on formation control effect, improves the robustness of a controller, and effectively improves the environment adaptability of an unmanned aerial vehicle formation controller.
Drawings
FIG. 1 is a design flow diagram of the present invention;
FIG. 2 is a block diagram of the location-coordinated active-disturbance-rejection control architecture of the present invention;
FIG. 3 is a schematic diagram of the relationship between the relative coordinate system and the inertial coordinate system according to the present invention.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the invention, rather than all embodiments, and all other embodiments obtained by those skilled in the art without any creative work based on the embodiments of the present invention belong to the protection scope of the present invention.
An active disturbance rejection control-based robust formation control method for aircrafts, comprising the following steps:
s1: constructing an aircraft cluster formation control model;
s101: defining a coordinate system; studying the relative motion of the aircraft, the following coordinate systems need to be defined;
emission inertial frame o I -x I y I z I : the origin of the coordinate system is located at the emission point, o I x I The axis pointing in the initial target direction, o I y I With the axis vertically upwards o I z I The shaft and the other two shafts form a right-hand system;
ballistic coordinate system o 2 -x 2 y 2 z 2 : the origin of the coordinate system is located at the center of mass, o, of the missile 2 x 2 The axis pointing in the direction of the missile speed, o 2 y 2 Perpendicular to o in the vertical plane 2 x 2 Upwards, o 2 z 2 The shaft and the other two shafts form a right-hand system;
s102: describing the relative position relationship of the aircraft and the slave aircraft;
in order to describe the position relationship of the leading aircraft and the following aircraft, the ballistic coordinate system of the leading aircraft is taken as a relative coordinate system, and the relationship between the relative coordinate system and a launching inertia coordinate system is shown in FIG. 2; because the relative coordinate system is a motion system, the leading aircraft and the trailing aircraft have the following motion relationship in the relative coordinate system:
V fr -V lr ＝V r +ω×r (1)
in formula (1):
V fr the speed of the slave aircraft under a relative coordinate system;
V lr the speed of the aircraft is taken as the relative coordinate system;
V r the relative speed of the slave aircraft and the lead aircraft under a relative coordinate system;
omega is the description of the rotation angular velocity of the relative coordinate system relative to the inertia space in the relative coordinate system;
r is a relative position vector between the slave aircraft and the leading aircraft under a relative coordinate system;
thus, it is possible to obtain:
V r ＝(V fr -V lr )-ω×r (2)
the relative motion equation of the aircraft and the slave aircraft in the three-dimensional space is developed as follows:
in formula (3):
x is the coordinate corresponding to the x axis in the three-dimensional space;
y is a y-axis corresponding coordinate in the three-dimensional space;
z is a coordinate corresponding to a z axis in a three-dimensional space;
V f is the slave aircraft speed;
V l leading the speed of the aircraft;
θ f is the angle of inclination from the aircraft trajectory;
θ l the inclination angle of the trajectory of the lead aircraft;
ψ e the difference between the deviation angle of the aircraft trajectory and the deviation angle of the aircraft trajectory;
ψ vf is the deviation angle from the aircraft trajectory;
ψ vl the trajectory deflection angle of the lead aircraft;
s103: carrying out small-disturbance linearization processing;
while the formation of the aircraft remains in flight, the angle of inclination θ from the trajectory of the aircraft is considered f Collar aircraft trajectory inclination angle theta l And the difference phi between the deviation angle of the leading aircraft trajectory and the deviation angle of the trailing aircraft trajectory e All are small quantities, and small-disturbance linearization processing is carried out on the small quantities to obtain the following results:
in formula (4):
V fb 、θ fb 、ψ vfb all are state equilibrium points taken by linearization;
s104: modeling a formation control system;
equation (4) is described as a state space form, with:
in formula (5):
X＝[x,y,z] T state variables for the formation control system;
U＝[V fc ,θ fc ,ψ vfc ] T a control variable for controlling the system for formation, wherein: v fc A desired speed for the aircraft; theta fc Anticipating a ballistic dip for the aircraft; psi vfc Anticipating a ballistic declination for the aircraft;
W＝V l is a disturbance variable;
y is an output variable;
a is the system matrix, B 1 To control the matrix, B 2 C is an output matrix, and the value of the output matrix is shown as the following formula:
deforming the model can obtain:
in formula (7):
D＝B 2 w represents the total system disturbance;
and constructing the multi-aircraft cooperative control model.
S2: designing an aircraft position cooperative active disturbance rejection controller;
the aircraft position coordinated auto-disturbance rejection controller comprises a Tracking Differentiator (Tracking Differentiator), an Extended State Observer (Extended State Observer) and a Nonlinear State Error Feedback control Law (Nonlinear State Error Feedback Law). In the figure, the extended state observer observes and compensates the total disturbance quantity and the equivalent control quantity
The nonlinear state error feedback law and the extended state observer jointly form the linear state error feedback law and the extended state observer.
S201: designing a tracking differentiator;
in order to avoid high-frequency trembling, a second-order steepest discrete tracking differentiator is derived by using a steepest control comprehensive function of a second-order pure integrator series discrete system, and the obtained three-channel tracking differentiators are all in the following forms:
in formula (8):
fhan is a function symbol;
fh is the output value of the fhan function;
k is the kth step of discrete simulation;
v 1 a transition process that is a control target;
v 2 controlling the speed of the target transition process;
v 3 controlling the acceleration of the target transition process;
h is a simulation step length;
v 0 for controlling the target, the expected relative position v of the x, y and z directions is represented 0x 、v 0y 、v 0z ；
r 0 Is a fast factor for normal numbers;
h 0 is a filtering factor;
steepest control synthesis function fhan (x) 1 ,x 2 ,x 3 R, h) is:
in formula (9):
d、a、a 0 、a 1 、a 2 y is a process variable in the function calculation process and has no actual physical meaning;
s202: designing an extended state observer;
and respectively establishing a second-order extended state observer in the following form for the three-direction channel:
in formula (10):
e ESO is the observed error of the system output variable;
z 1 is an observed value of a system output variable;
z 2 is an observed value of the rate of change of the system output variable;
β 01 、β 02 is the extended state observer gain parameter;
u is a control variable of the formation control system;
h is a simulation step length;
s203: controlling a nonlinear state error feedback control law;
defining the error signal e as
In formula (11):
x, y and z are three-axis coordinates of the aircraft;
x c 、y c 、z c is a desired position of the aircraft;
the nonlinear feedback compensation control law of the formation controller is designed as follows:
in formula (12):
alpha is a power term coefficient;
δ is the interval half-length of the linear segment;
substituting the error signal equation (11) and the control law equation (12) into the state space expression (5) can obtain
As can be seen from equation (13), the error signal e converges to 0 within a limited time, proving the feasibility of the designed control law;
and finishing the design process of the aircraft position cooperative active disturbance rejection controller.
S3: and designing an aircraft speed tracking controller.
S301: designing a speed tracking controller;
setting up
The state variable of the speed tracking controller is X 1 ＝[V f θ f ψ vf ] T ；
The control variable of the velocity tracking controller is
The state space model is established as follows:
wherein:
let the speed control error e 1 Is composed of
In formula (16):
V fc a desired speed for the aircraft;
θ fc a desired ballistic inclination for the aircraft;
ψ vfc anticipating a ballistic declination for the aircraft;
similar to the position cooperative control, the control law of the velocity tracking controller is designed to
By substituting formula (17) with formula (14) to obtain
The speed error can be seen to be converged, which shows that the speed error is converged to 0, and the designed control law has feasibility;
s302: converting an aircraft control command;
for aircraft, the control commands are derived from aircraft speed
From aircraft ballistic inclination
And deviation from aircraft trajectory
The control commands cannot be directly linked with the control variables such as the angle of attack, the roll angle or the direct force, and therefore the control commands are converted into overload forms under the trajectory system of the aircraft:
in formula (19):
n cx is overloaded in the x-direction under the ballistic system;
n cy is ballistic y-direction overload;
n cz is ballistic overload in the z-direction;
g is the acceleration of gravity;
the aircraft reversely calculates the required attack angle and the required roll angle according to the pneumatic data or the on-off time and the thrust direction of the direct force engine, so that the tracking of the expected speed can be realized, and further the position cooperative control is realized.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.
Claims (5)
1. An aircraft robust formation control method based on active disturbance rejection control is characterized in that: the method comprises the following steps:
s1: constructing an aircraft cluster formation control model;
s2: designing an aircraft position cooperative active disturbance rejection controller;
s3: and designing an aircraft speed tracking controller.
2. The robust formation control method for the aircraft based on the active disturbance rejection control as claimed in claim 1, wherein: s1, the construction of the aircraft cluster formation control model comprises the following steps:
s101: defining a coordinate system;
s102: describing the relative position relationship of the aircraft and the slave aircraft;
with the ballistic coordinate system of the leading aircraft as the relative coordinate system, the leading aircraft and the trailing aircraft have the following motion relationship in the relative coordinate system due to the relative coordinate system as the motion system:
V fr -V lr ＝V r +ω×r (1)
in formula (1):
V fr the speed of the slave aircraft under a relative coordinate system;
V lr the speed of the aircraft is taken as the relative coordinate system;
V r the relative speed of the slave aircraft and the lead aircraft under a relative coordinate system;
omega is the description of the rotation angular velocity of the relative coordinate system relative to the inertia space in the relative coordinate system;
r is a relative position vector between the slave aircraft and the leading aircraft under a relative coordinate system;
thus, it is possible to obtain:
V r ＝(V fr -V lr )-ω×r (2)
the relative motion equation of the aircraft and the slave aircraft in the three-dimensional space is developed as follows:
in formula (3):
x is the coordinate corresponding to the x axis in the three-dimensional space;
y is a y-axis corresponding coordinate in the three-dimensional space;
z is a coordinate corresponding to a z axis in a three-dimensional space;
V f is the slave aircraft speed;
V l leading the speed of the aircraft;
θ f is the angle of inclination from the aircraft trajectory;
θ l the inclination angle of the trajectory of the lead aircraft;
ψ e the difference between the deviation angle of the aircraft trajectory and the deviation angle of the aircraft trajectory;
ψ vf is the deviation angle from the aircraft trajectory;
ψ vl leading the trajectory deflection angle of the aircraft;
s103: carrying out small-disturbance linearization processing;
while the formation of the aircraft remains in flight, the angle of inclination θ from the trajectory of the aircraft is considered f Collar aircraft trajectory inclination angle theta l And the difference phi between the deviation angle of the leading aircraft trajectory and the deviation angle of the trailing aircraft trajectory e All are small quantities, and small-disturbance linearization processing is carried out on the small quantities to obtain the following results:
in formula (4):
V fb 、θ fb 、ψ vfb all are state equilibrium points taken by linearization;
s104: modeling a formation control system;
equation (4) is described as a state space form, with:
in formula (5):
X＝[x,y,z] T state variables for the formation control system;
U＝[V fc ,θ fc ,ψ vfc ] T a control variable for controlling the system for formation, wherein: v fc A desired speed for the aircraft; theta.theta. fc Anticipating a ballistic dip for the aircraft; psi vfc Anticipating a ballistic declination for the aircraft;
W＝V l is a disturbance variable;
y is an output variable;
a is the system matrix, B 1 To control the matrix, B 2 C is a disturbance matrix, and the value of C is as follows:
deforming the model can obtain:
in formula (7):
D＝B 2 w represents the total system disturbance;
and constructing the multi-aircraft cooperative control model.
3. The robust formation control method for the aircraft based on the active disturbance rejection control as claimed in claim 2, wherein: s2, the aircraft position cooperative active disturbance rejection controller comprises a tracking differentiator, an extended state observer and a nonlinear state error feedback control law.
4. The robust formation control method for the aircraft based on the active disturbance rejection control as claimed in claim 3, wherein: s2 the method for designing the aircraft position cooperative active disturbance rejection controller comprises the following steps:
s201: designing a tracking differentiator;
in order to avoid high-frequency trembling, a second-order steepest discrete tracking differentiator is derived by using a steepest control comprehensive function of a second-order pure integrator series discrete system, and the obtained three-channel tracking differentiators are all in the following forms:
in formula (8):
fhan is a function symbol;
fh is the output value of the fhan function;
k is the kth step of discrete simulation;
v 1 a transition process that is a control target;
v 2 controlling the speed of the target transition process;
v 3 controlling the acceleration of the target transition process;
h is a simulation step length;
v 0 for controlling the target, the expected relative position v of the x, y and z directions is represented 0x 、v 0y 、v 0z ；
r 0 Is a fast factor for normal numbers;
h 0 is a filter factor;
steepest control synthesis function fhan (x) 1 ,x 2 ,x 3 R, h) is:
in formula (9):
d、a、a 0 、a 1 、a 2 y is a process variable in the function calculation process and has no actual physical meaning;
s202: designing an extended state observer;
and respectively establishing a second-order extended state observer in the following form for the three-direction channel:
in formula (10):
e ESO is the observed error of the system output variable;
z 1 is an observed value of a system output variable;
z 2 is an observed value of the rate of change of the system output variable;
β 01 、β 02 is the extended state observer gain parameter;
u is a control variable of the formation control system;
h is a simulation step length;
s203: controlling a nonlinear state error feedback control law;
defining the error signal e as
In formula (11):
x, y and z are three-axis coordinates of the aircraft;
x c 、y c 、z c is a desired position of the aircraft;
the nonlinear feedback compensation control law of the formation controller is designed as follows:
in formula (12):
alpha is a power term coefficient;
δ is the interval half-length of the linear segment;
substituting the error signal equation (11) and the control law equation (12) into the state space expression (5) can obtain
As can be seen from equation (13), the error signal e converges to 0 within a limited time, proving the feasibility of the designed control law;
and finishing the design process of the aircraft position cooperative active disturbance rejection controller.
5. The robust formation control method for the aircraft based on the active disturbance rejection control as claimed in claim 4, wherein: s3 the design method of the aircraft speed tracking controller comprises the following steps:
s301: designing a speed tracking controller;
setting up
The state variable of the speed tracking controller is X 1 ＝[V f θ f ψ vf ] T ；
The control variable of the velocity tracking controller is
The state space model is established as follows:
wherein:
let the speed control error e 1 Is composed of
In formula (16):
V fc a desired speed for the aircraft;
θ fc anticipating a ballistic dip for the aircraft;
ψ vfc anticipating a ballistic declination for the aircraft;
the control law of the velocity tracking controller is designed as
By substituting formula (17) with formula (14) to obtain
The speed error can be seen to be converged, which shows that the speed error is converged to 0, and the designed control law has feasibility;
s302: converting an aircraft control command;
converting the control command into an overload form under the ballistic system of the aircraft:
in formula (19):
n cx is overloaded in the x-direction under the ballistic system;
n cy is ballistic y-direction overload;
n cz is z-direction overload under ballistic system;
g is the acceleration of gravity;
the aircraft reversely calculates the required attack angle and the required roll angle according to the pneumatic data or the on-off time and the thrust direction of the direct force engine, so that the tracking of the expected speed can be realized, and further the position cooperative control is realized.
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