CN109828602A - A kind of track circuit nonlinear model transform method based on observation compensation technique - Google Patents
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Abstract
The invention discloses a kind of track circuit nonlinear model transform methods based on observation compensation technique, belong to Navigation of Pilotless Aircraft guidance and control technology field.It is track drift angle and flight path angle motion model by fixed-wing unmanned aerial vehicle flight path looping motion model decomposition, flight path velocity motion model and lateral position and vertical position motion model, then pass through the equivalent transformation of the introducing of intermediate virtual control amount and equation respectively, entire differential equation right end is regarded as always interfering with the item of virtual controlling amount linear independence in form, in the form of obtaining the affine nonlinear of track looping motion model, the estimation always disturbed to each track motion state and model is realized by the observation compensation technique based on linear extended state observer, and it is compensated by controller.The processing of the method for the present invention implementation model affineization, treatment process explicit physical meaning, parameter tuning is convenient, is easy to Project Realization.
Description
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, regarding control metering opening deltaTAffine non-linear model form of (1).
Step six, selecting a track angle vector [ chi gamma ]]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 respectivelyThe obtained affine nonlinear model forms of the three motion models are linearly independent from the virtual control quantity in the system dynamic formAnd (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 interferenceA schematic diagram of the tracking effect over time;
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 UAVA 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 estimation of the motion state of each track and the total disturbance of the model is realized by an observation compensation technology based on a Linear Extended State Observer (LESO), and the estimation is 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 various wind fields in the atmosphere, synthesizing various wind field vectors to be used as a wind field of the mass center of the fixed-wing unmanned aerial vehicle, and decomposing the wind field of the mass center of the fixed-wing unmanned aerial vehicle into a wind field under an inertial systemThree-axis wind velocity component VW＝[uwvwww]T，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:
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;are the differential of x, y, z, respectively.
The equation of state of the ground speed and the track angle is as follows:
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，Is a VkThe first order differential with respect to time is,is the first differential of χ versus time,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:
track velocity VkAnd (3) motion model:
track yaw angle χ and track dip γ motion models:
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:
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＝[αsinμαcosμ]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:
step 402, decomposing engine thrust D of the drone, resistance C of the drone and lateral force L of the drone and representing in terms of angle of attack α and angle of sideslip β;
the decomposition process is as follows:
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 thrust D, the resistance C and the side force L are respectively;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；In order to be the slope of the wing lift line,is the partial derivative of aerodynamic lift to the square of the angle of attack,for the pitch angle rate lift coefficient,in order to obtain the lift coefficient of the elevator,in order to be the derivative of the resistance,the partial derivative of aerodynamic drag to the angle of attack bisector,in order to be the elevator drag coefficient, is the resistance coefficient of the elevator squared,in order to be the derivative of the lateral force,for the derivative of the aileron-side force,as is the derivative of the rudder side force,rudder deflection angle delta of auxiliary wingaThe range is as follows: delta is more than or equal to minus 25 degreesaNot more than 25 degrees and deflection angle delta of elevatoreThe range is as follows: delta is more than or equal to minus 25 degreeseNot more than 25 degrees and rudder deflection angle deltarThe range is as follows: delta is more than or equal to minus 25 degreesr≤25°；Is the coefficient of lift;is a coefficient of resistance;the lateral force coefficient.
Step 403, substituting the expressions of the decomposed powers D, C and L 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 substituting the track drift angle x motion nonlinear equation of the unmanned aerial vehicle into the right end of the track drift angle gamma motion nonlinear equation of the unmanned aerial vehicleDecomposed intoRelated and unrelated items of (c):
similarly, the right end of the flight path inclination angle gamma motion nonlinear equation of the unmanned aerial vehicle is decomposed and written intoRelated and unrelated items of (c):
step 404, using the intermediate variable v1,υ2And replacing α sin mu and α cos mu, writing the track drift angle chi and the track dip angle gamma motion nonlinear equation into affine nonlinear form, and completing the transformation of the track drift angle chi and the track dip angle gamma motion model.
X2＝[γ χ]T,υ＝[υ1υ2]T＝[αsinμ αcosμ]T,X3＝[α β μ]T(15)
Wherein, F2Total disturbance of the track angle loop, B2To make voyageThe input matrix of the trace-angle loop,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, regarding control metering opening deltaTAffine 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:
at step 502, engine thrust T is resolved and expressed as throttle opening delta for controlTSubstituting the form of (A) into track speed VkThe motion model is specifically as follows:
Tmaxis the maximum thrust of the engine; t ismaxControl throttle opening delta 36849NTThe range is as follows: delta is not less than 0T≤1。
Step 503, the track speed V is calculatedkThe motion model is written as a function of the control metering opening deltaTIn the form of affine nonlinear model, the track velocity V is completedkTransformation of motion models
Wherein,the total disturbance of the ground speed loop is represented,an input matrix representing the ground speed loop.
Step six, selecting a track angle vector [ chi gamma ] 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 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;
step 602, writing a transverse position y motion equation and a vertical position z motion equation of the unmanned aerial vehicle into:
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.
Wherein, F1Indicating the total interference of the position loop, B1An input matrix representing a loop of positions,is X1First order differential over time, X1＝[yz]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 formRegarding as total disturbance, a Linear Extended State Observer (LESO) is used to estimate and compensate the affine nonlinear model state and the total disturbance, and the compensation is performed during the design of the controller.
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 quantityViewed as aModel total interference.
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:
wherein x is21Is X2The measured value of (a) is,for linear expansion of the state observer to state X2Is estimated by the estimation of (a) a,for linear extended state observer to total disturbance F2The interference estimation of (2) is performed,is composed ofThe first order differential with respect to time is,is composed ofFirst 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,ω21,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:
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 diagrams are track loop states, disturbance estimation effects and estimation error-free diagrams of a motion model of a horizontal position y and a vertical position z of an unmanned aerial vehicle, and fig. 3A is a schematic diagram of a tracking effect of the horizontal 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 shows the horizontal positionSet y tracking error diagram, 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 interferenceA 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),represents VkThe tracking error of (2); FIG. 4D illustrates model interference of flight path velocity of an UAVIs shown in the figure of the tracking error of (1),to representThe 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 interferenceIs 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, 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, and decomposing the wind field of the mass center of the fixed-wing unmanned aerial vehicle into three-axis wind speed components V under an inertial systemW＝[uwvwww]T，VWIs the wind velocity vector u under the inertial systemw、vwAnd wwAre respectively inertiaThe wind speed components along the vertical, horizontal and vertical directions are tied down; 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, regarding control metering opening deltaTAffine nonlinear model form of (1);
step six, selecting a track angle vector [ chi gamma ]]TChanging 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 a 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 formFiAnd i is 1 and 2, the model total interference is regarded as the model total interference, the affine nonlinear model state and the total interference are estimated by adopting a linear extended state observer, and the method is carried outThe track loop controller is designed to compensate.
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:
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;are the differential of x, y, z, respectively;
the equation of state of the ground speed and the track angle is as follows:
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，Is a VkThe first order differential with respect to time is,is the first differential of χ versus time,is the first differential of gamma versus time;
the motion model of the transverse position y and the vertical position z is as follows:
said track speed VkThe motion model is as follows:
the track drift angle x and the track dip angle gamma motion model are as follows:
3. the method for transforming track loop nonlinear model based on observation compensation technology as claimed in claim 2, characterized in that the intermediate variable v in step three is1And upsilon2As follows:
υ1＝αsinμ,υ2＝αcosμ (6)
simultaneously such that:
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:
step 402, decomposing engine thrust D of the drone, resistance C of the drone and lateral force L of the drone and representing in terms of angle of attack α and angle of sideslip β;
the decomposition process is as follows:
q is dynamic pressure; s is the aerodynamic cross section of the unmanned aerial vehicle; c. CD,cC,cLThe aerodynamic coefficients of the thrust D, the resistance C and the side force 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;is the wing lift line slope;the partial derivative of the aerodynamic lift force to the square of the angle of attack;is the pitch angle velocity lift coefficient;is the elevator lift coefficient;is resistance forceA derivative;the partial derivative of the aerodynamic resistance to the angle of attack bisector;is the elevator drag coefficient;resistance coefficient as elevator squared;is the lateral force derivative;is the aileron side force derivative;is the rudder side force derivative; deltaaFor aileron rudder angle, deltaeFor elevator rudder deflection angle, deltarIs a rudder deflection angle;is the coefficient of lift;is a coefficient of resistance;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 LAre related and unrelatedItem (1):
the right end of the flight path inclination angle gamma motion nonlinear equation of the unmanned aerial vehicle is decomposed and written intoRelated and unrelated items of (c):
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;
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,is X2First order differential over time, X2As a track angle attitude vector, X3Virtual control vector with airflow angle state vector and upsilon as middle。
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 to control-oriented design with respect to control metering opening deltaTThe 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:
step 502, decompose the engine thrust T and express it as the throttle opening delta for controlTSubstituting the form of (A) into track speed VkThe motion model is as follows:
Tmaxis the maximum thrust of the engine; deltaTThe opening range of the metering valve is controlled;
step 503, calculating the track speed VkThe motion model is written as a function of the control metering opening deltaTIn the form of affine nonlinear model, the track velocity V is completedkTransformation of the motion model:
wherein,the total disturbance of the ground speed loop is represented,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;
step 602, writing a transverse position y motion equation and a vertical position z motion equation of the unmanned aerial vehicle into:
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;
wherein, F1Indicating the total interference of the position loop, B1An input matrix representing a loop of positions,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 quantityFiI 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:
wherein x is21Is X2The measured value of (a) is,for linear expansion of the state observer to state X2Is estimated by the estimation of (a) a,for linear extended state observer to total disturbance F2The interference estimation of (2) is performed,is composed ofThe first order differential with respect to time is,is composed ofFirst 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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