CN109828602B - Track loop nonlinear model transformation method based on observation compensation technology - Google Patents

Track loop nonlinear model transformation method based on observation compensation technology Download PDF

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CN109828602B
CN109828602B CN201910047309.9A CN201910047309A CN109828602B CN 109828602 B CN109828602 B CN 109828602B CN 201910047309 A CN201910047309 A CN 201910047309A CN 109828602 B CN109828602 B CN 109828602B
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CN109828602A (en
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王宏伦
苏子康
李娜
刘一恒
吴健发
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Beihang University
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Abstract

The invention discloses a flight path loop nonlinear model transformation method based on an observation compensation technology, and belongs to the technical field of unmanned aerial vehicle navigation guidance and control. Decomposing a track loop motion model of the fixed wing unmanned aerial vehicle into a track drift angle motion model, a track inclination angle motion model, a track speed motion model and a transverse position motion model and a vertical position motion model, then respectively taking terms which are linearly independent of virtual control quantities on the right end form of the whole differential equation as total interference through the introduction of middle virtual control quantities and the equivalent transformation of the equation to obtain an affine nonlinear form of the track loop motion model, realizing the estimation of motion states of each track and the total disturbance of the model through an observation compensation technology based on a linear expansion state observer, and compensating when in a controller. The method realizes model affine processing, has clear physical significance in the processing process, is convenient for parameter setting, and is easy for engineering realization.

Description

Track loop nonlinear model transformation method based on observation compensation technology
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle navigation guidance and control, and particularly relates to a flight path loop nonlinear model transformation method based on an observation compensation technology.
Background
Unmanned aerial vehicles are also called unmanned aircrafts and are widely applied to military and civil fields; the unmanned aerial vehicle track loop model is a mathematical model for describing the track motion of the unmanned aerial vehicle. With the increasing diversity of the executing tasks of the unmanned aerial vehicle, the requirement of people on the external uncertain disturbance resistance performance of the unmanned aerial vehicle flight controller is increased day by day, the traditional method of resisting the external disturbance only by depending on the attitude loop controller cannot meet the requirement, and in addition, the non-affine nonlinear characteristic of the unmanned aerial vehicle track loop model further increases the research requirement on the disturbance resistance nonlinear control of the unmanned aerial vehicle track loop. The method for researching the affine processing of the unmanned aerial vehicle track loop model has important significance for realizing disturbance-resistant high-precision tracking control of the three-dimensional track of the unmanned aerial vehicle, and can be widely applied to special tasks such as terrain avoidance, formation flight, autonomous aerial refueling and the like of the unmanned aerial vehicle.
In the trajectory tracking control of the unmanned aerial vehicle, the realization of the unmanned aerial vehicle directly flying along the real-time given trajectory has important practical value, but because of the strong nonlinearity, strong coupling property and non-affine property of the trajectory loop motion equation of the fixed wing unmanned aerial vehicle, in addition, many nonlinear control methods are designed based on the affine nonlinear model of the controlled object, the research of the nonlinear anti-interference tracking controller of the unmanned aerial vehicle at present mainly focuses on attitude control, such as reference file 1[ Wang Geng, Zong, Tian Bai, and Normal text ], hypersonic vehicle reentry attitude control theory and application based on a quasi-continuous high-order sliding mode [ J ]. control theory and application, 2014,31 (1161161163) ], reference file 2[ Sun M, Zhang L, Wang Z, PID. pitch control for unsmooth flight in the actual sensory sender of real and analysis [ J ], 2014,351(12), 5523 and 5547, the research of designing the track control and the attitude control of the fixed-wing unmanned aerial vehicle under the same anti-interference theoretical framework directly causes the interference resistance of a track ring controller to be limited, and simultaneously restricts the application of a plurality of nonlinear control methods with better interference resistance in the aspect of unmanned aerial vehicle track control to a great extent. This situation is very disadvantageous for some drone application sites where strong and complex airflow disturbances are present.
At present, in the aspect of hose type autonomous docking control, a great deal of research work is carried out from different angles at home and abroad, and a plurality of research results with high success are obtained, but in general, the effect of autonomous docking control under the condition of multiple complex disturbances is not ideal. NASA demonstrated only 2 successes with 6 docks in 2006 in an autonomous airborne fueling demonstration in flight. Although the X-47B completes the first air refueling test of the unmanned aerial vehicle, the movement of the taper sleeve in the successfully docked video is very stable, which shows that the current airflow disturbance is very small, and obviously is the result of carefully selecting meteorological conditions. In contrast, under the condition of airflow disturbance with similar size, the aircraft is very successful in the practice of manually controlled air refueling at home and abroad, and a fighter pilot can often achieve high success rate of air refueling and docking through hard training.
Compared with the essential characteristics of the autonomous refueling control and the manual control, the following essential differences exist between the autonomous refueling control and the manual control: 1) in terms of control methods, mature linear control methods are mostly adopted for autonomous control, as described in reference documents 3 and 4, and especially, the LQR method is often used, and there are no targeted measures for uncertain disturbance. Reference 3: valasek J, Gunnam K, KimmettJ, et al, Vision-based sensor and navigation system for Autonomous air recovery [ J ]. Journal of guide, Control, and Dynamics,2005,28(5): 979-: tandale M D, Bowers R, Valasek J. custom tracking Control for vision-based probe and hydrogum automotive refiufying [ J ]. Journal of guide Control and Dynamics,2006,29(4): 846) 857. The manual control realizes the nonlinear control on the basis of stability augmentation, has higher control efficiency, and simultaneously, the pilot carries out control compensation according to the sensed condition of the joystick force, so that the influence of interference can be furthest inhibited. Therefore, it is very necessary to obtain a nonlinear model of the track loop.
Disclosure of Invention
Aiming at the existing problems: the unmanned aerial vehicle position equation and the track motion equation are in strong coupling and non-affine nonlinear forms, so that the application of a plurality of nonlinear control methods with better disturbance resistance in unmanned aerial vehicle track control is restricted, and the disturbance resistance performance of the nonlinear control methods is bound to be limited to a great extent.
The invention relates to a track loop nonlinear model transformation method based on an observation compensation technology, which comprises the following steps:
setting various wind fields in the atmosphere, synthesizing various wind field vectors to serve as a wind field of the mass center of the fixed-wing unmanned aerial vehicle, decomposing the wind field of the mass center of the fixed-wing unmanned aerial vehicle into three-axis wind speed components in an inertial system, and obtaining the three-axis wind speed components of the track speed in the inertial system.
Establishing a fixed-wing unmanned aerial vehicle track loop motion model reflecting the influence of a changing wind field on the basis of a six-degree-of-freedom rigid motion model of the fixed-wing unmanned aerial vehicle, wherein the fixed-wing unmanned aerial vehicle track loop motion model comprises a track drift angle chi, a track inclination angle gamma motion model and a track speed VkA motion model and a lateral position y and a vertical position z motion model.
Step three, sequentially aiming at the airflow angle and the track roll angle mu, defining a middle variable upsilon1And upsilon2The airflow angle includes the drone's angle of attack α and the drone's angle of sideslip β.
Step four, defining the intermediate variable upsilon defined in the step three1And upsilon2And (3) as a virtual control quantity of the attitude loop controller, changing the track drift angle x and the track dip angle gamma motion model established in the step two into an affine nonlinear model form facing the control design.
Step five, establishing the track speed V in the step twokMotion model, change to control-oriented design, with respect to control meteringTAffine non-linear model form of (1).
Step six, selecting a track angle state vector [ gamma x]TAnd changing the transverse position y and vertical position z motion models established in the step two into an affine nonlinear model form facing the control design as the virtual control quantity of the attitude loop controller.
Step seven, aiming at the affine nonlinear model forms of the three motion models respectively obtained, linearly irrelevant to the virtual control quantity in the system dynamic form
Figure GDA0002484896300000021
And (3) regarding the model total interference, estimating and compensating the affine nonlinear model state and the total interference by adopting a Linear Extended State Observer (LESO), and compensating when designing the trajectory loop controller.
Compared with the prior art, the invention has the following obvious advantages:
(1) a flight path loop nonlinear model transformation method based on an observation compensation technology can give consideration to the influence of a changing wind field on the track loop motion of an unmanned aerial vehicle.
(2) A flight path loop nonlinear model transformation method based on an observation compensation technology can simultaneously process and transform an unmanned plane position equation and a flight path motion equation into a simple affine nonlinear form convenient for control design.
(3) The method can realize model affine processing of the unmanned aerial vehicle track loop motion state equation under the condition of considering the change of the wind field, has clear physical significance in the processing process, is convenient for parameter setting, and is easy for engineering realization.
Drawings
FIG. 1 is a flow chart of a track loop nonlinear model transformation method based on an observation compensation technology;
FIG. 2 is a graph of the varying wind field disturbances acting on the vertical, lateral, and vertical axes of the drone in this example;
fig. 3A is a schematic view of the tracking effect of the lateral position y of the drone over time;
FIG. 3B is a diagram of a lateral position model disturbance FyA schematic diagram of the tracking effect over time;
fig. 3C is a schematic view of the tracking effect of the vertical position z of the drone over time;
FIG. 3D is a diagram of vertical position model interference FzA schematic diagram of the tracking effect over time;
FIG. 3E is a schematic view of the tracking error at the lateral position y;
FIG. 3F is a diagram of a lateral position model disturbance FyA schematic of the tracking error of (a);
FIG. 3G is a schematic diagram of the tracking error of the vertical position z;
FIG. 3H illustrates a vertical position model disturbance FzA schematic of the tracking error of (a);
FIG. 4A shows the track velocity V of the UAVkA schematic diagram of the tracking effect over time;
FIG. 4B illustrates unmanned aerial vehicle track velocity model interference
Figure GDA0002484896300000031
Tracking over timeThe effect schematic diagram;
FIG. 4C shows the track velocity V of the UAVkA schematic of the tracking error of (a);
FIG. 4D illustrates model interference of flight path velocity of an UAV
Figure GDA0002484896300000032
A schematic of the tracking error of (a);
fig. 5A is a schematic view of the tracking effect of the trajectory deviation angle χ of the unmanned aerial vehicle with time;
FIG. 5B shows track yaw model disturbance FχA schematic diagram of the tracking effect over time;
fig. 5C is a schematic view of the tracking effect of the track inclination γ of the drone over time;
FIG. 5D shows track dip model disturbance FγA schematic diagram of the tracking effect over time;
FIG. 5E is a schematic diagram of the tracking error of the track yaw angle χ;
FIG. 5F shows track yaw model disturbance FχA schematic of the tracking error of (a);
FIG. 5G is a schematic diagram of the tracking error of the track inclination γ;
FIG. 5H illustrates track dip model disturbance FγSchematic diagram of tracking error of (1).
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail below with reference to the accompanying drawings and examples.
In the track loop nonlinear model transformation method provided by the invention, a track loop motion model of the fixed wing unmanned aerial vehicle is decomposed into a track deflection angle chi, a track inclination angle gamma motion model and a track speed VkAnd respectively considering items which are linearly independent from the virtual control quantity on the right end form of the whole differential equation as total interference through the introduction of the middle virtual control quantity and the equivalent transformation of the equation so as to obtain an affine nonlinear form of the track loop motion model. On the basis, the sum of motion states of each track is realized by an observation compensation technology based on a Linear Extended State Observer (LESO)The estimation of the model total disturbance is carried out and compensated in the controller.
In the embodiment of the invention, the unmanned aerial vehicle flies at the ground speed of 200m/s, and the initial height is 7010 m.
As shown in fig. 1, each step is specifically described below for a process flow of the track loop nonlinear model transformation method based on the observation compensation technique of the present invention.
Step one, setting wind fields of various changes in the atmosphere, synthesizing the wind field vectors of various changes to be used as a wind field of the fixed-wing unmanned aerial vehicle centroid, and decomposing the wind field of the fixed-wing unmanned aerial vehicle centroid into component fields of three-axis wind speed components in an inertial system
Figure GDA0002484896300000041
VWIs the wind velocity vector u under the inertial systemw、vwAnd wwThe wind velocity components along the vertical, horizontal and vertical directions under the inertial system are respectively.
Obtaining three-axis component V of track speed under inertial systemK＝[ukvkwk]T，VKIs a track velocity vector u under the inertial systemk、vkAnd wkIs the track velocity component along the vertical, horizontal and vertical directions under the inertial system.
Setting simulation conditions after establishing a simulation environment in the step one, selecting moderate atmospheric turbulence, and adding vertical, horizontal and vertical triaxial step wind with the amplitude of 5m/s at the time of 10s, 20s and 30s respectively.
And step two, analyzing the essence of the influence of a changing wind field in the atmosphere on the motion of the unmanned aerial vehicle on the basis of a six-degree-of-freedom rigid motion model of the fixed-wing unmanned aerial vehicle in a quiet atmospheric environment, and establishing a track loop motion model of the fixed-wing unmanned aerial vehicle reflecting the influence of the changing wind field, as shown in formulas (1) and (2).
Wherein, unmanned aerial vehicle's position equation is:
Figure GDA0002484896300000042
wherein x, y and z are each independentlyVertical, horizontal and vertical three-dimensional position coordinates V of man-machine under inertial systemkTaking the track speed of the unmanned aerial vehicle as the target, taking x as the track deflection angle of the unmanned aerial vehicle, and taking gamma as the track inclination angle of the unmanned aerial vehicle;
Figure GDA0002484896300000043
are the differential of x, y, z, respectively.
The equation of state of the ground speed and the track angle is as follows:
Figure GDA0002484896300000044
wherein m is the mass of the unmanned aerial vehicle, g is the gravity acceleration, α is the angle of attack of the unmanned aerial vehicle, the sideslip angle of the unmanned aerial vehicle and the track rolling angle of the unmanned aerial vehicle, T, D, C and L are the engine thrust of the unmanned aerial vehicle, the resistance of the unmanned aerial vehicle, the side force of the unmanned aerial vehicle and the lift force of the unmanned aerial vehicle, sigma is the engine installation angle, and the angle of attack α caused by the change of a wind field isw≈wwV, side slip angle β caused by changing wind fieldw≈vwV is airspeed, track speed angle of attack αk≈wk/VkTrack speed sideslip angle βk≈vk/Vk，
Figure GDA0002484896300000051
Is a VkThe first order differential with respect to time is,
Figure GDA0002484896300000052
is the first differential of χ versus time,
Figure GDA0002484896300000053
is the first differential of gamma versus time.
The fixed wing unmanned aerial vehicle track loop motion model comprises a track drift angle chi, a track dip angle gamma motion model and a track speed VkA motion model and a lateral position y and a vertical position z motion model.
Wherein: and m is 11281 kg.
Transverse position y and vertical position z motion model:
Figure GDA0002484896300000054
track velocity VkAnd (3) motion model:
Figure GDA0002484896300000055
track yaw angle χ and track dip γ motion models:
Figure GDA0002484896300000056
step three, sequentially aiming at the airflow angle and the track roll angle mu, defining a middle variable upsilon1And upsilon2The airflow angle includes an angle of attack α of the drone and a sideslip angle β of the drone;
υ1＝αsinμ,υ2＝αcosμ (6)
simultaneously such that:
Figure GDA0002484896300000057
step four, selecting the intermediate variable upsilon defined in the step three based on a backstepping method design idea according to a track deflection angle x and a track inclination angle gamma motion model in the fixed wing unmanned aerial vehicle track loop motion model which is established in the step two and reflects the influence of the changing wind field1And upsilon2Will [ v [ ]1υ2]T＝[αsinμ αcosμ]TAs a virtual control quantity of the attitude loop controller, changing a strongly-coupled and non-affine nonlinear track drift angle x and track dip angle gamma motion model into an affine nonlinear model form facing a control design;
the method comprises the following specific steps:
step 401, a track drift angle x and a track inclination angle gamma motion model of the unmanned aerial vehicle comprise a track drift angle x of the unmanned aerial vehicle and a track inclination angle gamma motion nonlinear equation of the unmanned aerial vehicle;
the method comprises the following specific steps:
Figure GDA0002484896300000058
step 402, decomposing the resistance D of the drone, the lateral force C of the drone and the lift L of the drone and representing them in terms of angle of attack α and angle of sideslip β;
the decomposition process is as follows:
Figure GDA0002484896300000061
Q＝0.5ρV2(ii) a Q is dynamic pressure; ρ is the air density; s is the pneumatic sectional area of the unmanned plane, and S is 75.12m2；cD,cC,cLThe aerodynamic coefficients of the resistance D, the lateral force C and the lift L are respectively;
Figure GDA0002484896300000062
is the average aerodynamic chord length; q is the pitch angle rate; c. CL,0Is a basic coefficient of lift, cL,0＝0.062；cD,0Is a coefficient of zero resistance, cD,0＝0.023；cC,0For basic lateral force coefficient, when the profile of the unmanned aerial vehicle is bilaterally symmetrical, cC,0＝0；
Figure GDA0002484896300000063
In order to be the slope of the wing lift line,
Figure GDA0002484896300000064
Figure GDA0002484896300000065
is the partial derivative of aerodynamic lift to the square of the angle of attack,
Figure GDA0002484896300000066
Figure GDA0002484896300000067
for the pitch angle rate lift coefficient,
Figure GDA0002484896300000068
Figure GDA0002484896300000069
in order to obtain the lift coefficient of the elevator,
Figure GDA00024848963000000610
Figure GDA00024848963000000611
in order to be the derivative of the resistance,
Figure GDA00024848963000000612
Figure GDA00024848963000000613
the partial derivative of aerodynamic drag to the angle of attack bisector,
Figure GDA00024848963000000614
Figure GDA00024848963000000615
in order to be the elevator drag coefficient,
Figure GDA00024848963000000616
Figure GDA00024848963000000617
is the resistance coefficient of the elevator squared,
Figure GDA00024848963000000618
Figure GDA00024848963000000619
in order to be the derivative of the lateral force,
Figure GDA00024848963000000620
Figure GDA00024848963000000621
for the derivative of the aileron-side force,
Figure GDA00024848963000000622
Figure GDA00024848963000000623
as is the derivative of the rudder side force,
Figure GDA00024848963000000624
auxiliary wing rudder deflection angleaThe range is as follows: minus 25 degrees and lessaLess than or equal to 25 degrees, and deflection angle of elevatoreThe range is as follows: minus 25 degrees and lesseLess than or equal to 25 degrees and rudder deflection anglerThe range is as follows: minus 25 degrees and lessr≤25°；
Figure GDA00024848963000000625
Is the coefficient of lift;
Figure GDA00024848963000000626
is a coefficient of resistance;
Figure GDA00024848963000000627
the lateral force coefficient.
Step 403, substituting the expressions of the power D, C and L decomposed in the step 402 into a track drift angle x of the unmanned aerial vehicle and a track inclination angle gamma motion nonlinear equation of the unmanned aerial vehicle, and decomposing and writing the right end of the track drift angle x motion nonlinear equation of the unmanned aerial vehicle into the power D, C and L
Figure GDA00024848963000000628
Related and unrelated items of (c):
Figure GDA00024848963000000629
similarly, the right end of the flight path inclination angle gamma motion nonlinear equation of the unmanned aerial vehicle is decomposed and written into
Figure GDA00024848963000000630
Related and unrelated items of (c):
Figure GDA00024848963000000631
step 404, using the intermediate variable v1,υ2Instead of α sin μ, α cAnd os mu, writing the track drift angle chi and the track dip angle gamma motion nonlinear equation into an affine nonlinear form, and completing the transformation of the track drift angle chi and the track dip angle gamma motion model.
Figure GDA00024848963000000632
Figure GDA00024848963000000633
Figure GDA00024848963000000634
X2＝[γ χ]T,υ＝[υ1υ2]T＝[αsinμ αcosμ]T,X3＝[α β μ]T(15)
Wherein, F2Total disturbance of the track angle loop, B2Is the input matrix of the track angle loop,
Figure GDA0002484896300000071
is X2First order differential over time, X2For track angle state vector, X3Is the flow angle state vector, and upsilon is the intermediate virtual control vector.
Step five, reflecting the track speed V in the fixed wing unmanned aerial vehicle track loop motion model influenced by the changing wind field established in the step twokMotion model, change to control-oriented design, with respect to control meteringTAffine non-linear model form of (1).
The method comprises the following specific steps:
step 501, track speed V of unmanned aerial vehiclekThe motion model is written in the form of standard differential equations, as follows:
Figure GDA0002484896300000072
at step 502, engine thrust T is resolved and expressed in terms of controlling fuel meteringOpening of doorTSubstituting the form of (A) into track speed VkThe motion model is specifically as follows:
Figure GDA0002484896300000073
Tmaxis the maximum thrust of the engine; t ismax36849N, controlling the opening of the throttle valveTThe range is as follows: 0 is less than or equal toT≤1。
Step 503, the track speed V is calculatedkMotion model written about control metering gateTIn the form of affine nonlinear model, the track velocity V is completedkTransformation of motion models
Figure GDA0002484896300000074
Figure GDA0002484896300000075
Wherein the content of the first and second substances,
Figure GDA0002484896300000076
the total disturbance of the ground speed loop is represented,
Figure GDA0002484896300000077
an input matrix representing the ground speed loop.
Step six, selecting a track angle state vector [ gamma chi ] according to a transverse position y and a vertical position z motion model in the fixed wing unmanned aerial vehicle track loop motion model which is established in the step two and reflects the influence of the changing wind field, and based on a backstepping method design thought]TAnd as a virtual control quantity of the attitude loop controller, changing the motion models of the transverse position y and the vertical position z into an affine nonlinear model form facing the control design through equivalent change of the models.
The method comprises the following specific steps:
601, simultaneously increasing and decreasing the same linear term x in the motion equation of the transverse position y in the motion model of the transverse position y and the vertical position z of the unmanned aerial vehicleVkX, simultaneously increasing and decreasing the same linear term-V related to gamma in the Z motion equation of the vertical position of the unmanned aerial vehiclekγ, specifically as follows;
Figure GDA0002484896300000078
step 602, writing a transverse position y motion equation and a vertical position z motion equation of the unmanned aerial vehicle into:
Figure GDA0002484896300000079
and 603, writing the motion equation of the transverse position y and the motion equation of the vertical position z into affine nonlinear forms related to the track drift angle chi and the track inclination angle gamma, and completing affine nonlinear transformation of motion models of the transverse position y and the vertical position z.
Figure GDA0002484896300000081
Figure GDA0002484896300000082
Wherein, F1Indicating the total interference of the position loop, B1An input matrix representing a loop of positions,
Figure GDA0002484896300000083
is X1First order differential over time, X1＝[y z]T，X1Is a track position state vector.
Step seven, aiming at the affine nonlinear model forms of the three motion models which are respectively obtained and are oriented to the control design, linearly irrelevant to the virtual control quantity in the system dynamic form
Figure GDA0002484896300000084
Regarding as total interference, estimating and compensating the affine nonlinear model state and the total interference by adopting a Linear Extended State Observer (LESO), and setting a controllerThe timing is compensated.
The method comprises the following specific steps:
step 701, based on the affine nonlinear models of the three established motion models facing the control design, determining the V in the model dynamicsk,XiI 1,2 being formally linearly independent of the virtual control quantity
Figure GDA0002484896300000085
The model total interference is considered.
Step 702, taking an affine nonlinear model formed by changing a track drift angle χ and a track dip angle γ motion model as an example, designing a linear extended state observer, wherein the linear extended state observer is specifically designed as follows:
the following linear extended state observer was constructed:
Figure GDA0002484896300000086
Figure GDA0002484896300000087
wherein x is21Is X2The measured value of (a) is,
Figure GDA0002484896300000088
for linear expansion of the state observer to state X2Is estimated by the estimation of (a) a,
Figure GDA0002484896300000089
for linear extended state observer to total disturbance F2The interference estimation of (2) is performed,
Figure GDA00024848963000000810
is composed of
Figure GDA00024848963000000811
The first order differential with respect to time is,
Figure GDA00024848963000000812
is composed of
Figure GDA00024848963000000813
First order differential over time, F2Will be used in subsequent feedback control designs to compensate for model disturbances. li(i ═ 1,2) is the linear extended state observer gain to be designed, and
l1＝diag(2ω21,2ω22)，l2＝diag(ω21 2,ω22 2)
wherein, ω is21,ω22Respectively linearly expanding the bandwidth of the state observer by X and gamma channels;
step 703, adjusting and selecting a suitable bandwidth ω of the linear extended state observer21＝15,ω2215, implement state X2And total interference F2Estimating and compensating;
step 704, repeat the operation mode in steps 702 and 703, respectively for track speed VkEstimating and compensating states and total interference in the affine nonlinear model formed by the motion model change and the affine nonlinear model formed by the motion model change at the transverse position y and the vertical position z, wherein the appropriate motion model at the transverse position y and the vertical position z is selected to linearly expand the bandwidth of the state observer: omega11＝5,ω2Track speed V5kMotion model linear extended state observer bandwidth:
Figure GDA00024848963000000814
by adopting the method, under the given wind disturbance condition, the unmanned aerial vehicle track loop model conversion method is matched with the control action of the controller, and the unmanned aerial vehicle track loop state, the disturbance estimation effect and the compensation result are obtained.
As shown in FIG. 2, it is the varying wind field disturbance acting on the three vertical, horizontal and vertical axes of the unmanned plane in this example, wherein W isx，WyAnd WzThe components of the total wind disturbance in the vertical, horizontal and vertical directions under the inertial system are shown.
As shown in fig. 3A to 3H, the horizontal position y and the vertical position z of the unmanned aerial vehicle are usedThe dynamic model flight path loop state, disturbance estimation effect and estimation error-free map, and fig. 3A is a schematic view of the tracking effect of the transverse position y of the unmanned aerial vehicle along with time; FIG. 3B is a diagram of a lateral position model disturbance FyA schematic diagram of the tracking effect over time; fig. 3C is a schematic view of the tracking effect of the vertical position z of the drone over time; FIG. 3D is a diagram of vertical position model interference FzA schematic diagram of the tracking effect over time; FIG. 3E is a schematic view of the tracking error for the lateral position y, EyRepresents the tracking error of y; FIG. 3F is a diagram of a lateral position model disturbance FySchematic diagram of tracking error of (e)FyIs represented by FyThe tracking error of (2); FIG. 3G is a schematic view of the tracking error of the vertical position z, ezRepresents the tracking error of z; FIG. 3H illustrates a vertical position model disturbance FzSchematic diagram of tracking error of (e)FzIs represented by FzThe tracking error of (2). The estimation of the horizontal and vertical states of the unmanned aerial vehicle is very accurate, and the state estimation error is kept within the magnitude of 10 e-4; corresponding model interference FyAnd FzThe estimation errors are respectively within 10e-3 and 0.02, and accurate estimation of the total disturbance of the model can be realized.
As shown in fig. 4A-4D, the track velocity V of the dronekThe motion model track loop state, disturbance estimation effect and estimation error map, and FIG. 4A shows the track velocity V of the UAVkA schematic diagram of the tracking effect over time; FIG. 4B illustrates unmanned aerial vehicle track velocity model interference
Figure GDA0002484896300000091
A schematic diagram of the tracking effect over time; FIG. 4C shows the track velocity V of the UAVkIs shown in the figure of the tracking error of (1),
Figure GDA0002484896300000092
represents VkThe tracking error of (2); FIG. 4D illustrates model interference of flight path velocity of an UAV
Figure GDA0002484896300000093
Is shown in the figure of the tracking error of (1),
Figure GDA0002484896300000094
to represent
Figure GDA0002484896300000095
The tracking error of (2). The unmanned aerial vehicle track speed estimation is also very accurate, and the state estimation error is kept within 0.01 magnitude; corresponding model total interference
Figure GDA0002484896300000096
Is also within 0.4, and the accuracy is quite high at a given flight speed and altitude.
As shown in fig. 5A to 5H, the diagrams are a track loop state, a disturbance estimation effect and an estimated error-free diagram of a track bias angle χ and a track inclination γ motion model of the unmanned aerial vehicle, and fig. 5A is a schematic diagram of a tracking effect of the track bias angle χ of the unmanned aerial vehicle with time; FIG. 5B shows track yaw model disturbance FχA schematic diagram of the tracking effect over time; fig. 5C is a schematic view of the tracking effect of the track inclination γ of the drone over time; FIG. 5D shows track dip model disturbance FγA schematic diagram of the tracking effect over time; FIG. 5E is a schematic diagram of the tracking error of the track yaw angle χ; FIG. 5F shows track yaw model disturbance FχA schematic of the tracking error of (a); FIG. 5G is a schematic diagram of the tracking error of the track inclination γ; FIG. 5H illustrates track dip model disturbance FγSchematic diagram of tracking error of (1). The flight path angle state x and gamma of the unmanned aerial vehicle are estimated accurately, and the state estimation errors are respectively kept within 10e-3 and 0.05; corresponding model total interference Fχ、FγAlso within 0.05 and 2, respectively, the accuracy at a given flying speed (200m/s) and altitude (7010m) is relatively high.
By combining the mathematical analysis and the simulation verification, the effectiveness of the flight path loop nonlinear model transformation method based on the observation compensation technology in the unmanned aerial vehicle flight path loop model affine processing is fully proved.

Claims (7)

1. A flight path loop nonlinear model transformation method based on an observation compensation technology is characterized by comprising the following steps:
step one, settingDetermining various changed wind fields in the atmosphere, synthesizing various changed wind field vectors to be used as a wind field of the fixed-wing unmanned aerial vehicle mass center, and decomposing the wind field of the fixed-wing unmanned aerial vehicle mass center into three-axis wind speed component under an inertial system
Figure FDA0002592616350000011
VWIs the wind velocity vector u under the inertial systemw、vwAnd wwRespectively wind velocity components along the vertical, transverse and vertical directions under the inertial system; obtaining three-axis component V of track speed under inertial systemK＝[ukvkwk]T，VKIs a track velocity vector u under the inertial systemk、vkAnd wkThe track velocity components along the longitudinal direction, the transverse direction and the vertical direction under the inertial system;
establishing a fixed-wing unmanned aerial vehicle track loop motion model reflecting the influence of a changing wind field on the basis of a six-degree-of-freedom rigid motion model of the fixed-wing unmanned aerial vehicle, wherein the fixed-wing unmanned aerial vehicle track loop motion model comprises a track drift angle chi, a track inclination angle gamma motion model and a track speed VkA motion model and a motion model of a transverse position y and a vertical position z;
step three, sequentially aiming at the airflow angle and the track roll angle mu, defining a middle variable upsilon1And upsilon2；
Step four, defining the intermediate variable upsilon defined in the step three1And upsilon2Changing the track drift angle x and the track dip angle gamma motion model established in the step two into an affine nonlinear model form facing the control design as a virtual control quantity of the attitude loop controller;
step five, establishing the track speed V in the step twokMotion model, change to control-oriented design, with respect to control meteringTAffine nonlinear model form of (1);
step six, selecting a track angle state vector [ gamma x]TChanging the motion models of the transverse position y and the vertical position z established in the step two into affine non-lines facing the control design as virtual control quantity of the attitude loop controllerA sexual model form;
step seven, aiming at the affine nonlinear model forms of the three motion models respectively obtained, linearly irrelevant to the virtual control quantity in form
Figure FDA0002592616350000012
FiI is 1,2 is regarded as model total interference; wherein the content of the first and second substances,
Figure FDA0002592616350000013
representing the total disturbance of the ground speed loop, F1Indicating the total interference of the position loop, F2Representing the total disturbance of the track angle loop; and estimating the state and the total interference of the affine nonlinear model by adopting a linear extended state observer, and compensating when designing the trajectory loop controller.
2. The observation compensation technique-based track loop nonlinear model transformation method of claim 1, wherein in step two, the fixed-wing drone track loop motion model is shown in equations (1) and (2):
wherein, unmanned aerial vehicle's position equation is:
Figure FDA0002592616350000014
in the formula, x, y and z are respectively vertical, horizontal and vertical three-dimensional position coordinates of the unmanned aerial vehicle under an inertial system, and VkTaking the track speed of the unmanned aerial vehicle as the target, taking x as the track deflection angle of the unmanned aerial vehicle, and taking gamma as the track inclination angle of the unmanned aerial vehicle;
Figure FDA0002592616350000015
are the differential of x, y, z, respectively;
the equation of state of the ground speed and the track angle is as follows:
Figure FDA0002592616350000021
wherein m is the mass of the unmanned aerial vehicle, g isα, mu is the attack angle of the unmanned aerial vehicle, the sideslip angle of the unmanned aerial vehicle and the track rolling angle of the unmanned aerial vehicle, T, D, C and L are the engine thrust of the unmanned aerial vehicle, the resistance of the unmanned aerial vehicle, the side force of the unmanned aerial vehicle and the lift force of the unmanned aerial vehicle, sigma is the installation angle of the engine, and the attack angle α caused by changing the wind fieldw≈wwV, side slip angle β caused by changing wind fieldw≈vwV is airspeed, track speed angle of attack αk≈wk/VkTrack speed sideslip angle βk≈vk/Vk，
Figure FDA0002592616350000022
Is a VkThe first order differential with respect to time is,
Figure FDA0002592616350000023
is the first differential of χ versus time,
Figure FDA0002592616350000024
is the first differential of gamma versus time;
the motion model of the transverse position y and the vertical position z is as follows:
Figure FDA0002592616350000025
said track speed VkThe motion model is as follows:
Figure FDA0002592616350000026
the track drift angle x and the track dip angle gamma motion model are as follows:
Figure FDA0002592616350000027
3. the method as claimed in claim 2, wherein the track loop nonlinear model transformation method based on the observation compensation technique is characterized in thatIn step three, the intermediate variable v1And upsilon2As follows:
υ1＝αsinμ,υ2＝αcosμ (6)
simultaneously such that:
Figure FDA0002592616350000028
4. the track loop nonlinear model transformation method based on the observation compensation technology as claimed in claim 3, wherein the step four of changing the track drift angle χ and track dip γ motion model into the affine nonlinear model form facing the control design is specifically:
step 401, a track drift angle x and a track inclination angle gamma motion model of the unmanned aerial vehicle comprise a track drift angle x of the unmanned aerial vehicle and a track inclination angle gamma motion nonlinear equation of the unmanned aerial vehicle;
the method comprises the following specific steps:
Figure FDA0002592616350000029
step 402, decomposing the resistance D of the drone, the lateral force C of the drone and the lift L of the drone and representing them in terms of angle of attack α and angle of sideslip β;
the decomposition process is as follows:
Figure FDA0002592616350000031
q is dynamic pressure; s is the aerodynamic cross section of the unmanned aerial vehicle; c. CD,cC,cLThe aerodynamic coefficients of the resistance D, the lateral force C and the lift L are respectively; c is the average aerodynamic chord length; q is the pitch angle rate; c. CL,0Is the basic lift coefficient; c. CD,0Is a zero resistance coefficient; c. CC,0The lateral force coefficient is basic, and when the appearance of the unmanned aerial vehicle is bilaterally symmetrical;
Figure FDA0002592616350000032
is the wing lift line slope;
Figure FDA0002592616350000033
the partial derivative of the aerodynamic lift force to the square of the angle of attack;
Figure FDA0002592616350000034
is the pitch angle velocity lift coefficient;
Figure FDA0002592616350000035
is the elevator lift coefficient;
Figure FDA0002592616350000036
is the resistance derivative;
Figure FDA0002592616350000037
the partial derivative of the aerodynamic resistance to the angle of attack bisector;
Figure FDA0002592616350000038
is the elevator drag coefficient;
Figure FDA0002592616350000039
resistance coefficient as elevator squared;
Figure FDA00025926163500000310
is the lateral force derivative;
Figure FDA00025926163500000311
is the aileron side force derivative;
Figure FDA00025926163500000312
is the rudder side force derivative;athe rudder deflection angle of the aileron is adopted,ein order to raise and lower the rudder deflection angle,ris a rudder deflection angle;
Figure FDA00025926163500000313
is the coefficient of lift;
Figure FDA00025926163500000314
is a coefficient of resistance;
Figure FDA00025926163500000315
is the lateral force coefficient;
step 403, substituting the expressions of the power D, C and L decomposed in the step 402 into a track drift angle x of the unmanned aerial vehicle and a track inclination angle gamma motion nonlinear equation of the unmanned aerial vehicle, and decomposing and writing the right end of the track drift angle x motion nonlinear equation of the unmanned aerial vehicle into the power D, C and L
Figure FDA00025926163500000316
Related and unrelated items of (c):
Figure FDA00025926163500000317
the right end of the flight path inclination angle gamma motion nonlinear equation of the unmanned aerial vehicle is decomposed and written into
Figure FDA00025926163500000318
Related and unrelated items of (c):
Figure FDA00025926163500000319
step 404, using the intermediate variable v1,υ2Replacing α sin mu and α cos mu, writing a track deviation angle chi and a track dip angle gamma motion nonlinear equation into an affine nonlinear form, and completing the transformation of a track deviation angle chi and a track dip angle gamma motion model;
Figure FDA00025926163500000320
Figure FDA00025926163500000321
Figure FDA00025926163500000322
X2＝[γ χ]T,υ＝[υ1υ2]T＝[αsinμ αcosμ]T,X3＝[α β μ]T(15)
wherein, F2Total disturbance of the track angle loop, B2Is the input matrix of the track angle loop,
Figure FDA00025926163500000323
is X2First order differential over time, X2As a track angle attitude vector, X3Is the flow angle state vector, and upsilon is the intermediate virtual control vector.
5. The method as claimed in claim 4, wherein in the fifth step, the track velocity V is converted into the track loop nonlinear modelkVariation of motion model into control-oriented design with respect to control metering openingTThe affine nonlinear model form is specifically as follows:
step 501, track speed V of unmanned aerial vehiclekThe motion model is written in the form of standard differential equations, as follows:
Figure FDA0002592616350000041
step 502, decompose the engine thrust T and show it as about controlling the throttle openingTSubstituting the form of (A) into track speed VkThe motion model is as follows:
Figure FDA0002592616350000042
Tmaxis the maximum thrust of the engine;Tthe opening range of the metering valve is controlled;
step 503, calculating the track speed VkMotion model write-related controlThrottle opening of metering valveTIn the form of affine nonlinear model, the track velocity V is completedkTransformation of the motion model:
Figure FDA0002592616350000043
Figure FDA0002592616350000044
wherein the content of the first and second substances,
Figure FDA0002592616350000045
the total disturbance of the ground speed loop is represented,
Figure FDA0002592616350000046
an input matrix representing the ground speed loop.
6. The method for transforming the track loop nonlinear model based on the observation compensation technology as claimed in claim 5, wherein in the sixth step, the changing the motion model of the transverse position y and the vertical position z into the affine nonlinear model form facing the control design is specifically as follows:
601, simultaneously increasing and decreasing the same linear term V related to chi in a motion equation of the transverse position y in a motion model of the transverse position y and the vertical position z of the unmanned aerial vehiclekX, simultaneously increasing and decreasing the same linear term-V related to gamma in the Z motion equation of the vertical position of the unmanned aerial vehiclekγ, specifically as follows;
Figure FDA0002592616350000047
step 602, writing a transverse position y motion equation and a vertical position z motion equation of the unmanned aerial vehicle into:
Figure FDA0002592616350000048
step 603, writing a motion equation of the transverse position y and a motion equation of the vertical position z into affine nonlinear forms related to a track drift angle χ and a track dip angle γ, and completing affine nonlinear transformation of motion models of the transverse position y and the vertical position z;
Figure FDA0002592616350000049
Figure FDA00025926163500000410
wherein, F1Indicating the total interference of the position loop, B1An input matrix representing a loop of positions,
Figure FDA00025926163500000411
is X1First order differential over time, X1＝[y z]T，X1Is a track position state vector.
7. The method for transforming the non-linear model of the track loop based on the observation compensation technique as claimed in claim 6, wherein said seventh step comprises:
step 701, based on the established affine nonlinear model, determining V in model dynamick,XiI 1,2 being formally linearly independent of the virtual control quantity
Figure FDA0002592616350000051
FiI is 1,2 is regarded as model total interference;
step 702, designing a linear extended state observer for an affine nonlinear model formed by the changes of the track drift angle χ and the track dip angle γ motion model, wherein the linear extended state observer is specifically designed as follows:
constructed linear extended state observer:
Figure FDA0002592616350000052
wherein x is21Is X2The measured value of (a) is,
Figure FDA0002592616350000053
for linear expansion of the state observer to state X2Is estimated by the estimation of (a) a,
Figure FDA0002592616350000054
for linear extended state observer to total disturbance F2The interference estimation of (2) is performed,
Figure FDA0002592616350000055
is composed of
Figure FDA0002592616350000056
The first order differential with respect to time is,
Figure FDA0002592616350000057
is composed of
Figure FDA0002592616350000058
First order differential over time, F2Will be used in subsequent feedback control designs to compensate for model disturbances; liI 1,2 is the linear extended state observer gain to be designed, and
l1＝diag(2ω21,2ω22)，l2＝diag(ω21 2,ω22 2)
wherein, ω is21,ω22Respectively linearly expanding the bandwidth of the state observer by X and gamma channels;
step 703, adjusting and selecting a suitable bandwidth of the linear extended state observer to realize the state X2And total interference F2And estimating and compensating.
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