CN112965510B - Full-channel active disturbance rejection control method for high-speed maneuvering of aircraft - Google Patents

Full-channel active disturbance rejection control method for high-speed maneuvering of aircraft Download PDF

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CN112965510B
CN112965510B CN202110180024.XA CN202110180024A CN112965510B CN 112965510 B CN112965510 B CN 112965510B CN 202110180024 A CN202110180024 A CN 202110180024A CN 112965510 B CN112965510 B CN 112965510B
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aircraft
control
angle
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CN112965510A (en
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黄一
薛文超
陈森
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Academy of Mathematics and Systems Science of CAS
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Academy of Mathematics and Systems Science of CAS
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/08Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G05D1/0816Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10Simultaneous control of position or course in three dimensions
    • G05D1/101Simultaneous control of position or course in three dimensions specially adapted for aircraft

Abstract

The invention provides a full-channel active disturbance rejection control method for high-speed maneuvering of an aircraft, which comprises the following 4 steps: 1. establishing a dynamic model of the high-speed maneuvering aircraft facing active disturbance rejection control; 2. designing extended state observer to estimate total disturbance
Figure DDA0002941910270000011
And
Figure DDA0002941910270000012
3. designing a high-speed maneuvering control virtual control quantity for online compensation of total disturbance; 4. and controlling the design of the distribution scheme. The method can realize the online estimation and compensation of the nonlinear uncertainty dynamic, the coupling uncertainty dynamic and the external disturbance of each channel, realize the expected dynamic performance of a closed-loop system and ensure the high-mobility control of the aircraft to have good dynamic quality.

Description

Full-channel active disturbance rejection control method for high-speed maneuvering of aircraft
Technical Field
The invention belongs to the field of control design methods of aircrafts, and relates to a control method of high-speed maneuvering of an aircraft and a decoupling control design method with pneumatic parameter nonlinear uncertainty and multichannel coupling uncertainty. The technology is an effective solution for realizing overload control in high-speed aircraft maneuvering by using an active disturbance rejection control method and ensuring the stability of a course channel and a transverse channel.
Background
High-speed maneuver is one of the necessary capabilities of a high-performance aircraft, and large overload control during the high-speed maneuver often faces strong nonlinear uncertainty of pneumatic parameters and multi-channel coupling. Therefore, how to realize the accurate control of large overload during high-speed maneuvering and ensure the stability of each channel under multi-channel coupling has great challenge. The existing methods mainly include PID (proportional-integral-derivative) control, dynamic inverse method based on model information, and the like, and have the following limitations:
1. the dynamic inverse design needs a pneumatic parameter model to be carried out, and the uncertainty considered by the existing anti-interference method is mainly external disturbance of the system and the like;
2. the normal overload change rate is not estimated in the control design, and the normal overload proportional-differential feedback control is not adopted
Therefore, it is difficult to ensure the overload control accuracy and flight stability when the aerodynamic characteristics change rapidly in high-speed maneuvers.
In order to solve the problems, the invention provides a three-channel control method based on the normal large overload control, the stable course sideslip angle and the stable transverse roll angle rate of the active disturbance rejection control aiming at the control problem of the high-speed maneuvering of the aircraft, and the method can realize the online estimation and compensation of the nonlinear uncertainty dynamic, the coupling uncertainty dynamic and the external disturbance of each channel and ensure that the high-speed maneuvering of the aircraft has good dynamic quality.
The invention content is as follows:
the technical problems solved by the invention are as follows: a three-channel control method based on active disturbance rejection control, normal large overload control, stable course sideslip angle and stable transverse roll angle rate is provided, a three-order extended state observer is utilized to estimate overload change rate and total disturbance in a normal channel, and therefore a proportional-differential feedback algorithm combining online compensation disturbance and overload is adopted; estimating the change rate of the sideslip angle and total disturbance by using a three-order extended state observer in an aeronautical direction channel, and adopting a proportional-differential feedback algorithm combining compensation disturbance and sideslip angle; estimating the roll angle rate and the total disturbance by using a second-order extended state observer in a transverse channel, and adopting a compensation disturbance and roll angle rate proportional feedback algorithm; the algorithm realizes the online estimation and compensation of the nonlinear unknown dynamics, the coupling uncertainty dynamics and the external disturbance of each channel, and realizes the expected dynamic performance of a closed-loop system.
The technical solution of the invention comprises the following 4 steps:
establishing a dynamic model of a high-speed maneuvering aircraft facing active disturbance rejection control in the first step
The high-speed maneuvering control targets are as follows: control of normal directionOverload nzSmooth trace instruction value
Figure BDA0002941910250000021
While controlling the sideslip angle β to remain at 0 and the roll angle rate p to remain at 0. For this purpose, the active disturbance rejection control design of the high-speed maneuver is performed for the following flight dynamics models:
Figure BDA0002941910250000031
wherein ω ∈ R3×1Is a three-dimensional angular rate vector of the aircraft, alpha belongs to R as an aircraft attack angle, beta belongs to R as an aircraft sideslip angle, V belongs to R as an aircraft rate, h belongs to R as an aircraft height, and delta belongs to R as an aircraft altitudeeE R is the elevator deflection angle, delta, of the aircraftaE is R is the rudder deflection angle delta of the aileron of the aircraftrE is R is the rudder deflection angle of the aircraft, FTBelongs to the range of the thrust vector of the aircraft, deltayBelongs to the field of the thrust angle 1, delta of the aircraft as RzBelongs to the field of the thrust angle 2, n of the aircraft as RzE R is the normal overload of the aircraft, p E R is the roll angle rate of the aircraft,
Figure BDA0002941910250000035
derivative of normal overload, omega, of aircraftβE R is the derivative of the sideslip angle of the aircraft,
Figure BDA0002941910250000032
a control input gain matrix for the aircraft normal to the overload channel,
Figure BDA0002941910250000033
a control input gain matrix for the aircraft sideslip angle channel,
Figure BDA0002941910250000034
a gain matrix is input for control of the aircraft roll rate channel.
In the aircraft model (1), (n)zBeta, p) is the controlled output quantity (delta)ear) For rudder deflection angle input of aircraft systems, (F)Tzy) As a thrust vector input to the aircraft system,
Figure BDA0002941910250000041
and
Figure BDA0002941910250000042
the sum effect of uncertain dynamics and external disturbances in the overload path, the sideslip angle path, and the roll rate path, respectively (hereinafter abbreviated as "roll rate path" respectively)
Figure BDA0002941910250000043
And
Figure BDA0002941910250000044
)。
the second step is that: designing extended state observer to estimate total disturbance
Figure BDA0002941910250000045
And
Figure BDA0002941910250000046
designing three parallel Extended State Observers (ESOs) to simultaneously correct total disturbance
Figure BDA0002941910250000047
And
Figure BDA0002941910250000048
and carrying out online estimation.
Overload channel ESO:
Figure BDA0002941910250000049
wherein the content of the first and second substances,
Figure BDA00029419102500000410
is nZIs determined by the estimated value of (c),
Figure BDA00029419102500000411
is that
Figure BDA00029419102500000412
Is determined by the estimated value of (c),
Figure BDA00029419102500000413
is the total disturbance of overload
Figure BDA00029419102500000414
An estimate of (d). The parameter is taken as
Figure BDA00029419102500000415
The bandwidth is estimated for the adjustable disturbance,
sideslip passage ESO:
Figure BDA00029419102500000416
wherein z isβ1Is an estimate of beta, zβ2Is omegaβEstimate of zβ3Is total disturbance of sideslip
Figure BDA0002941910250000051
An estimate of (d). The parameter is taken as
Figure BDA0002941910250000052
ωβAnd > 0 is the adjustable disturbance estimation bandwidth.
Rolling channel ESO:
Figure BDA0002941910250000053
wherein z isp1Is an estimate of p, zp2Is total perturbation of rolling
Figure BDA0002941910250000054
An estimate of (d). Taking the parameter as betap1=2ωp
Figure BDA0002941910250000055
ωpAnd > 0 is the adjustable disturbance estimation bandwidth.
The third step: designing virtual control quantity of high-speed maneuvering control for compensating total disturbance online
Obtaining total disturbance by using ESO
Figure BDA0002941910250000056
And
Figure BDA0002941910250000057
after estimation, a virtual control quantity with disturbance compensation and feedback control is designed:
Figure BDA0002941910250000058
in the formula
Figure BDA0002941910250000059
To compensate for the total disturbance of the system in the control law,
Figure BDA00029419102500000510
in order to be an overload instruction,
Figure BDA00029419102500000511
in the form of a derivative of the overload command,
Figure BDA00029419102500000512
in order to overload the channel proportional feedback gain,
Figure BDA00029419102500000513
for the overload channel differential feedback gain, kβpProportional feedback gain, k, for the sideslip angle channelβdFor the differential feedback gain, k, of the sideslip angle channelppAnd (4) proportionally feeding back the gain for the yaw rate channel.
(5) The parameters in (1) are taken as:
Figure BDA00029419102500000514
wherein
Figure BDA00029419102500000515
kβ>0 and kppAnd the adjustable parameter of the feedback law is more than 0.
The fourth step: control distribution scheme design
The virtual control quantity obtained from equation (5)
Figure BDA0002941910250000061
To assign the required rudder deflection angle input
Figure BDA0002941910250000062
And thrust vector input
Figure BDA0002941910250000063
The control action generated by the cooperation of the control device and the aircraft is enabled to be as close as possible to the virtual control quantity required by the flight control.
Virtual control quantity
Figure BDA0002941910250000064
Angle of departure from rudder input
Figure BDA0002941910250000065
And thrust vector input
Figure BDA0002941910250000066
The relationship of (1) is:
Figure BDA0002941910250000067
is provided with
Figure BDA0002941910250000068
Is composed of
Figure BDA0002941910250000069
The first three columns of (a) make up a matrix,
Figure BDA00029419102500000610
is composed of
Figure BDA00029419102500000611
The last two columns of (a) form a matrix,the control allocation scheme proceeds as follows.
(I) Solving for corresponding rudder deflection angles
The thrust vector control input maintains the value of the previous sampling moment, and the control capability of the lifting control surface is limited when high-speed maneuvering pulling is carried out, so that the control is mainly carried out by means of thrust. Therefore, the required rudder deflection angle input (δ) is obtained by the following equatione1a1r1) Comprises the following steps:
Figure BDA0002941910250000071
wherein, FT,tpE R is the thrust of the sampling moment before the moment t, deltay,tpEpsilon R is thrust angle 1, delta of sampling moment before t momentz,tpE R is the thrust angle 2 at the sampling instant before the instant t,
Figure BDA0002941910250000079
is composed of
Figure BDA00029419102500000710
The inverse matrix of (c).
Order to
Figure BDA0002941910250000072
The saturation value of the rudder deflection angle input.
Further, the rudder deflection angle input satisfying the clipping condition is obtained by the following formula:
Figure BDA0002941910250000073
(II) solving for the required thrust vector input magnitude
Solving by least squares the two-dimensional control vector that needs to be provided by thrust
Figure BDA0002941910250000074
Figure BDA0002941910250000075
Wherein
Figure BDA0002941910250000076
Is composed of
Figure BDA0002941910250000077
Is used as the rank matrix.
Then by the following equation
Figure BDA0002941910250000078
Solving for the required thrust vector control input FTAnd (delta)y,δz) The method comprises the following specific steps:
first, a required thrust vector input is determined (F)T1y1z1) The method specifically comprises the following steps:
Figure BDA0002941910250000081
note the book
Figure BDA0002941910250000082
The saturation values for two angles of the thrust vector.
If it is
Figure BDA0002941910250000083
And is
Figure BDA0002941910250000084
Then take the thrust vector input as:
[FT,δy,δz]=[FT1,δy1,δz1], (12)
if it is
Figure BDA0002941910250000085
And is
Figure BDA0002941910250000086
Then take the thrust vector input as:
Figure BDA0002941910250000087
if it is
Figure BDA0002941910250000088
And is
Figure BDA0002941910250000089
Then take the thrust vector input as:
Figure BDA00029419102500000810
if it is
Figure BDA00029419102500000811
And is
Figure BDA00029419102500000812
Then take the thrust vector as input
Figure BDA00029419102500000813
Wherein
Figure BDA00029419102500000814
Figure BDA00029419102500000815
Is DyzIs used as the rank matrix.
The rudder deflection angle and thrust vector inputs required for the high-speed maneuvering control are obtained by the above-described (8), (12) to (15).
Compared with the prior art, the invention has the advantages that:
1. the invention does not depend on the aerodynamic parameter model of the aircraft and the dynamic inverse calculation, exceptThe nominal value of the gain matrix needs to be controlled, i.e.
Figure BDA0002941910250000091
The nominal value of (2) does not need other specific model information, and the dependency on the model is greatly reduced.
2. The real-time online estimation of the normal overload change rate is realized by designing the extended state observer, and then a normal overload proportional-differential feedback loop is designed.
3. The invention fully considers the influence of nonlinear unknown dynamics, coupling uncertainty dynamics, external disturbance and the like of each channel on the flight, and can realize the consistency of dynamic response and control precision of high-speed maneuvering flight in the presence of uncertain dynamics, disturbance and the like by designing three extended state observers working in parallel to carry out real-time estimation and compensation of the disturbance.
Drawings
FIG. 1 is a block diagram of the aircraft high-speed maneuvering full-channel active disturbance rejection control provided by the invention.
FIG. 2 is a flow chart of the design of the aircraft high-speed maneuvering full-channel active disturbance rejection control provided by the invention.
FIG. 3 is a response curve for normal overload, side slip angle, and roll rate.
FIG. 4 is a graph of the variation of the aircraft control surface declination and thrust vector control input.
FIG. 5, FIG. 6 and FIG. 7 are the state and "total disturbance" estimates of the extended state observers for the normal channel, the course channel and the lateral channel, respectively.
The symbols are as follows:
t: time;
α ∈ R: angle of attack; beta epsilon R: a sideslip angle; v epsilon R: the speed of the aircraft relative to the air;
h epsilon R: the altitude of the aircraft;
p ∈ R: roll rate, q ∈ R: pitch rate, R ∈ R: yaw rate;
ω=[p,q,r]T: an angular rate vector;
δee.g. R: an elevator declination angle; deltaaE.g. R: an aileron rudder deflection angle; deltarE.g. R: rudder deflection angle;
FTe.g. R: a thrust force; deltayE.g. R: a thrust angle 1; deltazE.g. R: a thrust angle 2;
FT,tpe.g. R: thrust at a sampling moment before the moment t;
δy,tpe.g. R: a thrust angle 1 at a sampling time before the time t;
δz,tpe.g. R: a thrust angle 2 at a sampling moment before the moment t;
Figure BDA0002941910250000101
a rudder deflection angle saturation value;
Figure BDA0002941910250000102
saturation values of two angles of the thrust vector;
nze.g. R: normal overload;
Figure BDA0002941910250000103
normal overload command;
Figure BDA0002941910250000104
total disturbance of the overload channel;
Figure BDA0002941910250000105
total perturbation of the sideslip angular channel;
Figure BDA0002941910250000106
total perturbation of the roll rate channel;
Figure BDA0002941910250000107
a control input gain matrix of the normal overload channel;
Figure BDA0002941910250000108
a control input gain matrix for the sideslip angle channel;
Figure BDA0002941910250000109
a control input gain matrix of the roll rate channel;
Detailed Description
The control block diagram is shown in figure 1, and the controller design flow diagram is shown in figure 2.
In order to test the practicability of the method, a simulation experiment is carried out by taking a typical thrust vector aircraft high-speed maneuver as an example.
Simulation conditions are as follows:
the flying height of the aircraft is 1500 meters, and the flying speed is 300 meters/second. The normal overload command is:
Figure BDA0002941910250000111
the method comprises the following specific implementation steps:
1. the initial values of ESO (2) - (4) are set as follows:
Figure BDA0002941910250000112
and the bandwidth of ESOs (2) - (4) is designed as:
ωnZ=15;ωβ=15;ωp=15,
thereby calculating the output of ESO (2) - (4)
2. Substituting the outputs of ESOs (2) - (4) into equation (5) to calculate the virtual control quantity with disturbance compensation feedback control, i.e.
Figure BDA0002941910250000113
Wherein the parameters are taken as
Figure BDA0002941910250000115
kβ=1,kpp=1
3. (u) obtained in step 21,u2,u3) Bringing in (7) to obtain the required rudder deflection angle (delta)e1a1r1) Comprises the following steps:
Figure BDA0002941910250000114
and further obtaining the rudder deflection angle input meeting the amplitude limiting condition through the following formula:
Figure BDA0002941910250000121
4. solving two-dimensional control vectors that need to be provided by thrust
Figure BDA0002941910250000122
Figure BDA0002941910250000123
Then, the required thrust vector input (F) is obtained through (11)T1y1z1):
Figure BDA0002941910250000124
Finally, obtaining the thrust vector input (F) meeting the limiting condition through (12) - (15)Tyz)。
Fig. 3-7 show simulation results. As can be seen from FIG. 3, the control law proposed by the present invention can make the normal overload track its command quickly and stably in the presence of external disturbance and model uncertainty, and ensure that the sideslip angle and the roll angle rate are kept near zero, the estimation curve of FIG. 5 shows that the control method proposed by the present invention has the capability of estimating the normal overload change rate and the "total disturbance" of its channel in real time. Accordingly, FIGS. 6 and 7 show that the proposed control method of the present invention has good capability of estimating the side-slip angle change rate and the "total disturbance" of the side-slip path, and the "total disturbance" of the roll angle rate path. And these "total disturbances" are quickly compensated for by feedback.

Claims (2)

1. A full-channel active disturbance rejection control method for high-speed maneuvering of an aircraft is characterized by comprising the following steps: the method comprises the following 4 steps:
the first step is as follows: establishing high-speed maneuvering aircraft dynamic model facing active disturbance rejection control
The high-speed maneuvering control targets are as follows: controlling normal overload nzMake it track of overload instructions
Figure FDA0003409457530000011
Meanwhile, controlling the sideslip angle beta to be kept at 0, and keeping the roll angle rate p at 0; for this purpose, the active disturbance rejection control design of the high-speed maneuver is performed for the following flight dynamics models:
Figure FDA0003409457530000012
wherein ω ∈ R3×1Is a three-dimensional angular rate vector of the aircraft, alpha belongs to R as an aircraft attack angle, beta belongs to R as an aircraft sideslip angle, V belongs to R as an aircraft rate, h belongs to R as an aircraft height, and delta belongs to R as an aircraft altitudeeE R is the elevator deflection angle, delta, of the aircraftaE is R is the rudder deflection angle delta of the aileron of the aircraftrE is R is the rudder deflection angle of the aircraft, FTBelongs to the range of the thrust vector of the aircraft, deltayBelongs to the field of the thrust angle 1, delta of the aircraft as RzBelongs to the field of the thrust angle 2, n of the aircraft as RzE R is the normal overload of the aircraft, p E R is the roll angle rate of the aircraft,
Figure FDA0003409457530000021
derivative of normal overload, omega, of aircraftβE R is the derivative of the sideslip angle of the aircraft,
Figure FDA0003409457530000022
a control input gain matrix for the aircraft normal to the overload channel,
Figure FDA0003409457530000023
a control input gain matrix for the aircraft sideslip angle channel,
Figure FDA0003409457530000024
inputting a gain matrix for control of an aircraft roll rate channel;
in the formula (1), (n)zBeta, p) is the controlled output quantity (delta)ear) For rudder deflection angle input of aircraft systems, (F)Tzy) As a thrust vector input to the aircraft system,
Figure FDA0003409457530000025
and
Figure FDA0003409457530000026
the sum effect of uncertain dynamics and external disturbances in the overload path, the sideslip angle path, and the roll rate path, respectively, are hereinafter abbreviated as
Figure FDA0003409457530000027
And
Figure FDA0003409457530000028
the second step is that: designing extended state observer to estimate total disturbance
Figure FDA0003409457530000029
And
Figure FDA00034094575300000210
designing the following three parallel extended state observers ESO to simultaneously carry out total disturbance
Figure FDA00034094575300000211
And
Figure FDA00034094575300000212
carrying out online estimation;
overload channel ESO:
Figure FDA00034094575300000213
wherein the content of the first and second substances,
Figure FDA0003409457530000031
is nZIs determined by the estimated value of (c),
Figure FDA0003409457530000032
is that
Figure FDA0003409457530000033
Is determined by the estimated value of (c),
Figure FDA0003409457530000034
is the total disturbance of overload
Figure FDA0003409457530000035
An estimated value of (d); the parameter is taken as
Figure FDA0003409457530000036
Figure FDA0003409457530000037
The bandwidth is estimated for the adjustable disturbance,
sideslip passage ESO:
Figure FDA0003409457530000038
wherein z isβ1Is an estimate of beta, zβ2Is omegaβEstimate of zβ3Is total disturbance of sideslip
Figure FDA0003409457530000039
An estimated value of (d); the parameter is taken as
Figure FDA00034094575300000310
Figure FDA00034094575300000311
Estimating a bandwidth for the adjustable disturbance;
rolling channel ESO:
Figure FDA00034094575300000312
wherein z isp1Is an estimate of p, zp2Is total perturbation of rolling
Figure FDA00034094575300000313
An estimated value of (d); taking the parameter as betap1=2ωp,
Figure FDA00034094575300000314
ωpThe disturbance estimation bandwidth is adjustable when the bandwidth is more than 0;
the third step: designing virtual control quantity of high-speed maneuvering control for compensating total disturbance online
Obtaining total disturbance by using ESO
Figure FDA00034094575300000315
And
Figure FDA00034094575300000316
after estimation, a virtual control quantity with disturbance compensation and feedback control is designed:
Figure FDA0003409457530000041
in the formula
Figure FDA0003409457530000042
zβ3,zp2To compensate for the total disturbance of the system in the control law,
Figure FDA0003409457530000043
in order to be an overload instruction,
Figure FDA0003409457530000044
in the form of a derivative of the overload command,
Figure FDA0003409457530000045
in order to overload the channel proportional feedback gain,
Figure FDA0003409457530000046
for the overload channel differential feedback gain, kβpProportional feedback gain, k, for the sideslip angle channelβdFor the differential feedback gain, k, of the sideslip angle channelppProportional feedback gain for yaw rate channel;
the parameters in equation (5) are taken as:
Figure FDA0003409457530000047
Figure FDA0003409457530000048
and kβ>0 is a feedback law adjustable parameter;
the fourth step: control distribution scheme design
Obtaining the virtual control quantity according to the formula (5)
Figure FDA0003409457530000049
To assign the required rudder deflection angle input
Figure FDA00034094575300000410
And thrust vector input
Figure FDA00034094575300000411
The control action generated by the cooperation of the control device and the virtual control quantity required by the flight control is enabled to be close;
virtual control quantity
Figure FDA00034094575300000412
Angle of departure from rudder input
Figure FDA00034094575300000413
And thrust vector input
Figure FDA00034094575300000414
The relationship of (1) is:
Figure FDA00034094575300000415
2. the method for controlling full channel active disturbance rejection of an aircraft high speed maneuver according to claim 1, wherein: is provided with
Figure FDA0003409457530000051
Is composed of
Figure FDA0003409457530000052
The first three columns of (a) make up a matrix,
Figure FDA0003409457530000053
is composed of
Figure FDA0003409457530000054
The control distribution scheme of the matrix formed by the last two columns is carried out according to the following steps;
(I) solving for corresponding rudder deflection angles
The desired rudder deflection angle input (δ) is obtained bye1a1r1) Comprises the following steps:
Figure FDA0003409457530000055
wherein, FT,tpE R is the thrust of the sampling moment before the moment t, deltay,tpEpsilon R is thrust angle 1, delta of sampling moment before t momentz,tpE R is the thrust angle 2 at the sampling instant before the instant t,
Figure FDA0003409457530000056
is composed of
Figure FDA0003409457530000057
The inverse matrix of (d);
order to
Figure FDA0003409457530000058
A saturation value input for the rudder deflection angle;
further, the rudder deflection angle input satisfying the clipping condition is obtained by the following formula:
Figure FDA0003409457530000059
(II) solving for the required thrust vector input magnitude
Solving by least squares the two-dimensional control vector that needs to be provided by thrust
Figure FDA00034094575300000510
Figure FDA0003409457530000061
Wherein
Figure FDA0003409457530000062
Is composed of
Figure FDA0003409457530000063
A rank matrix of (d);
then by the following equation
Figure FDA0003409457530000064
Solving the required thrust vector control size and the thrust angle of the aircraft, and specifically comprising the following steps:
first, a required thrust vector input is determined (F)T1y1z1) The method specifically comprises the following steps:
Figure FDA0003409457530000065
note the book
Figure FDA0003409457530000066
The saturation values of two angles of the thrust vector are obtained;
if it is
Figure FDA0003409457530000067
And is
Figure FDA0003409457530000068
Then take the thrust vector input as:
[FT,δy,δz]=[FT1,δy1,δz1], (12)
if it is
Figure FDA0003409457530000069
And is
Figure FDA00034094575300000610
Then take the thrust vector input as:
Figure FDA00034094575300000611
if it is
Figure FDA00034094575300000612
And is
Figure FDA00034094575300000613
Then take the thrust vector input as:
Figure FDA0003409457530000071
if it is
Figure FDA0003409457530000072
And is
Figure FDA0003409457530000073
Then take the thrust vector as input
Figure FDA0003409457530000074
Wherein
Figure FDA0003409457530000075
Figure FDA0003409457530000076
Is DyzA rank matrix of (d);
the above-mentioned (8), (12) to (15) obtain rudder deflection angle and thrust vector inputs required for the high-speed maneuvering control.
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