CN115686041A - Parafoil system track tracking control method based on linear active disturbance rejection control and predictive control switching - Google Patents

Parafoil system track tracking control method based on linear active disturbance rejection control and predictive control switching Download PDF

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CN115686041A
CN115686041A CN202211322036.2A CN202211322036A CN115686041A CN 115686041 A CN115686041 A CN 115686041A CN 202211322036 A CN202211322036 A CN 202211322036A CN 115686041 A CN115686041 A CN 115686041A
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control
parafoil
controller
track
parafoil system
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刘蓉
王闯
王佑
杨明
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a flight path tracking control method of a parafoil system based on linear active disturbance rejection control and predictive control switching, which comprises the steps of establishing a horizontal movement and rotation six-degree-of-freedom model of the parafoil system as a flight path tracking control basis; designing a guider of the parafoil system, and eliminating the error between the actual track and the target track by tracking the course angle of the target track; designing a linear active disturbance rejection controller; designing a predictive controller; and setting switching conditions of two control methods according to the course angle deviation amount, and performing tracking control on the homing track of the parafoil system. Meanwhile, the advantages of good anti-interference capability of linear active disturbance rejection control, overcoming of time lag by predictive control and the like are exerted, so that a better control effect is achieved.

Description

Parafoil system track tracking control method based on linear active disturbance rejection control and predictive control switching
Technical Field
The invention belongs to the technical field of parafoil system track tracking control, and particularly relates to a parafoil system track tracking control method based on linear active disturbance rejection control and predictive control switching.
Background
The parafoil system is used as a special flexible-wing aircraft, adopts the flexible stamping parafoil to provide lift force, has good gliding property and controllability, and is widely applied to accurate air drop in the fields of military affairs and aerospace. The parafoil system is a very complex, strong coupling and strong nonlinear system with large time lag, so that the trajectory tracking control of the parafoil system is very necessary in the autonomous accurate homing process. The parafoil system is an under-actuated and unpowered system, and can only change aerodynamic force and aerodynamic moment of the parafoil canopy through pull-down ropes on two sides of the trailing edge of a pull-down parafoil flap so as to control the parafoil system, thereby realizing maneuvering flight and sparrow landing of the parafoil in the air.
Currently, the researches on the track tracking control of the parafoil system mainly include: the system comprises a traditional PD controller and a gain adjustment type fuzzy controller for track tracking of a parafoil system, a prediction controller for simplifying the parafoil system into a linear model, an active disturbance rejection controller designed for wind disturbance and the like.
In the above control methods, a single control method is mostly adopted to perform tracking control on the homing trajectory of the parafoil system. However, the parafoil system is a high-altitude delivery, unpowered and nonlinear system, the flight speed of the parafoil system is low, the parafoil system is easily interfered by an external wind field in the homing process, and the control rope is adopted to control the parafoil system, so that the control response of the parafoil system has a large hysteresis.
Therefore, the single control method is difficult to simultaneously and effectively solve the problems of large time lag, easy wind field interference and the like in the track tracking control process of the parafoil system.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for track tracking control of a parafoil system based on linear active disturbance rejection control and predictive control switching, to perform track tracking control on a glider section and an energy control section of the parafoil system, and simultaneously exert the advantages of good disturbance rejection capability of the linear active disturbance rejection control, overcoming time lag by the predictive control and the like, so as to achieve better control effect, have better control precision, stronger disturbance rejection capability and good dynamic performance, and solve the problems of strong nonlinearity, strong coupling, large time lag and the like in track tracking control of the parafoil system.
In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:
a parafoil system track tracking control method based on linear active disturbance rejection control and predictive control switching comprises the following steps:
step 1, carrying out stress analysis on a parafoil system, and establishing a six-degree-of-freedom model of translation and rotation of the parafoil system as a track tracking control basis according to a Newton-Euler equation;
step 2, designing a guider of the parafoil system by adopting a two-dimensional track tracking guidance strategy based on a guidance path tracking principle, calculating a forward error and a transverse error between an actual track and a target track, and eliminating the error by tracking a course angle of the target track movement;
step 3, designing a linear active disturbance rejection controller LADRC by constructing a linear extended state observer LESO and a PD controller of the system on the basis of a two-dimensional track tracking guidance strategy;
step 4, designing a predictive controller MPC by constructing a state space model of the system on the basis of a two-dimensional track tracking guidance strategy;
and 5, setting a switching condition according to the course angle deviation, receiving an instruction by the controller to adopt a linear active disturbance rejection controller for control when the course angle deviation does not meet the condition, and switching the controller to a predictive controller for control when the course angle deviation meets the condition to realize the switching control of the parafoil system.
In order to optimize the technical scheme, the specific measures adopted further comprise:
the step 1 is specifically as follows:
setting the position vector of the parafoil system under an inertial coordinate system as P I ＝[x I y I z I ] T The velocity vector of the parafoil system under the coordinate system of the object parachute body is V B ＝[u B v B w B ] T The attitude angle vector of the parafoil system in the inertial coordinate system is A I ＝[φ θ ψ] T The attitude angular velocity vector of the parafoil system under the object parachute body coordinate system is W B ＝[p q r] T ；
According to the Newton-Euler equation, a six-degree-of-freedom model of translation and rotation of the parafoil system can be obtained:
(1) Translation equation of three degrees of freedom:
Figure BDA0003910938850000021
Figure BDA0003910938850000022
(2) Equation of rotational three degrees of freedom:
Figure BDA0003910938850000023
Figure BDA0003910938850000024
wherein M is the total mass of the parafoil system, R IB A transformation matrix from the object umbrella coordinate system B to the geodetic coordinate system I, F G For the force of gravity, F, of the parafoil system in the parachute body coordinate system A For the aerodynamic force of the parafoil system in the object parachute body coordinate system, F S Is the effective resistance of the load under the coordinate system of the umbrella body of the object, F AW The additional power generated by the mass under the object umbrella body coordinate system is added to the parafoil system,
Figure BDA0003910938850000031
antisymmetric matrix, M, generated for angular velocity A For the parafoil system aerodynamic moment, M, in the parachute body coordinate system AM And adding an additional pneumatic moment generated by the mass of the parafoil system under the object parachute body coordinate system, wherein J is the rotational inertia of the parafoil system.
The step 2 is specifically:
defining a point p as a point on the actual homing track of the parafoil system, and respectively using p = [ x y ]] T And
Figure BDA0003910938850000032
representing the inertial position and velocity vector of point p, by
Figure BDA0003910938850000033
The velocity of the point p is shown by
Figure BDA0003910938850000034
Represents the direction angle of movement of point p;
defining a point p p For one point on the homing trajectory of the parafoil system, use it separately
Figure BDA0003910938850000035
And
Figure BDA0003910938850000036
represents a point p p Inertial position and velocity vector of
Figure BDA0003910938850000037
Represents a point p p The direction angle of motion;
wherein, the point p p Position of (2) as a function of scale
Figure BDA0003910938850000038
Is changed;
establishing a target track coordinate system taking the target track motion direction as an x axis, wherein a conversion matrix from an inertial coordinate system to the target track coordinate system is as follows:
Figure BDA0003910938850000039
then point p and point p p The amount of error therebetween is:
Figure BDA00039109388500000310
in the formula, s represents a forward error, and e represents a lateral error.
For the parafoil system, in the track tracking process, the forward error is determined by a target track point p p To U p And
Figure BDA00039109388500000311
is eliminated, so that only the controller needs to be set to control the heading angle chi of the parafoil system d Tracking target track motion course angle x p And (4) finishing.
The step 3 is specifically:
the current course angle of the parafoil system is as follows:
Figure BDA0003910938850000041
according to the dynamic model of the parafoil system, the second-order form of the parafoil system course angle is expressed as:
Figure BDA0003910938850000042
wherein f is the total disturbance of the parafoil system, u (t) is the parafoil system control quantity, and b is the controller gain;
assuming that f is differentiable, extending it to a new state variable, reconstructing the LESO equation yields:
Figure BDA0003910938850000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003910938850000044
is the state variable of LESO, beta 1 ，β 2 ，β 3 Is the observer gain;
performing Laplace transformation on the LESO equation and configuring the pole of the characteristic equation to the left half real axis-omega of the s plane o To thereby determine an observer gain as: beta is a 1 ＝3ω o ，
Figure BDA0003910938850000045
After the LESO estimates the disturbance and compensates, the controller is essentially a PD controller, which causes:
Figure BDA0003910938850000046
Figure BDA0003910938850000047
Figure BDA0003910938850000048
in the formula, chi p Is the azimuth angle, psi, of the target track e Is the course deviation u 0 For virtually controlling the quantity, β 01 ，β 02 Is the controller gain. Calculating controller χ according to the above formula p →u 0 The transfer function is:
Figure BDA0003910938850000049
the characteristic equation is then: c(s) = s 2 +β 02 s+β 01 Two poles of the PD controller are configured to the left half shaft-omega of the s plane c Then, C(s) = (s + omega) is obtained c ) 2
Thereby determining the PD controller gain as:
Figure BDA0003910938850000051
β 02 ＝2ω c 。
the control law of the linear active disturbance rejection controller is as follows:
Figure BDA0003910938850000052
the step 4 is specifically:
firstly, the heading angle psi of the parafoil system is given as an output, and the brake delta is pulled down on one side a For the input state space model: x is the number of k+1 ＝Ax k +Bu k ，y k ＝Cx k ；
Suppose the prediction interval is H p The direction angle of the target track is w k Then the estimation error is
Figure BDA0003910938850000053
To calculate the control input at a given time, a cost function is introduced as:
Figure BDA0003910938850000054
in the formula (I), the compound is shown in the specification,
Figure BDA0003910938850000055
for the desired value of the system to be,
Figure BDA0003910938850000056
for system prediction output, Q and R are system weight coefficient matrixes, U is a system input control sequence, and the system state equation is used for obtaining:
Figure BDA0003910938850000057
Figure BDA0003910938850000059
Figure BDA0003910938850000058
J＝(W-K CA x k -K CAB U) T Q·(W-K CA x k -K CAB U)+U T RU
by minimizing the cost function, the expression of the control quantity U is solved as:
Figure BDA0003910938850000061
the above formula represents the predictive controlMaking the optimum control quantity input in the whole control range, but only taking the first control quantity u at the moment k k 。
The above-described course angle deviation switching condition in step 5 is set to ψ e Less than or equal to pi/20, and after the parafoil system is put in, the requirements of psi are met e When the phi is less than or equal to pi/20, the controller receives the instruction and adopts a linear active disturbance rejection controller to control, when psi is greater than or equal to phi e And when the current value is less than or equal to pi/20, switching to the predictive controller for control.
The invention has the following beneficial effects:
aiming at the problems that a parafoil system is easily interfered by an external wind field, aerodynamic force of the parafoil system is inaccurate and the like, the invention adopts a control strategy of switching between linear active disturbance rejection control and predictive control, combines the advantages of strong disturbance rejection capability and high response speed of the linear active disturbance rejection control and can effectively overcome time lag and high tracking precision of the system by predictive control, adopts a two-dimensional guidance track tracking strategy to design a guidance law and track and control a homing track of the parafoil system, thereby not only improving the tracking precision of the parafoil system, but also ensuring that the parafoil system has good dynamic property and interference resistance in the track tracking process, reducing input of control quantity and avoiding instability caused by frequently pulling a control rope by the system.
Drawings
FIG. 1 is a schematic flow chart of a method for controlling the switching of a parafoil system disclosed by the invention;
FIG. 2 is a diagram of a guidance-based two-dimensional track following strategy in accordance with an embodiment of the present invention;
FIG. 3 is a diagram illustrating a process for controlling handover policy according to an embodiment of the present invention;
FIG. 4 is a target homing trajectory in accordance with an embodiment of the present invention;
FIG. 5 is a comparison effect graph of course angle tracking curves;
FIG. 6 is a graph of the comparative effect of the horizontal trace tracking curve;
FIG. 7 is a graph showing the effect of the control amount variation;
fig. 8 is a schematic diagram of a three-dimensional tracking curve under switching control.
Detailed Description
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
With reference to fig. 1, the method for track-following control of a parafoil system based on linear active disturbance rejection control and predictive control switching in the present invention includes:
step 1, carrying out stress analysis on a parafoil system, and establishing a six-degree-of-freedom model of translation and rotation of the parafoil system as a track tracking control basis according to a Newton-Euler equation;
the invention neglects the relative movement between the parachute body and the load, regards the parafoil system as a whole, and establishes the 6-degree-of-freedom nonlinear dynamical model of the parafoil system.
Setting the position vector of the parafoil system under an inertial coordinate system as P I ＝[x I y I z I ] T The velocity vector of the parafoil system under the coordinate system of the object parachute body is V B ＝[u B v B w B ] T The attitude angle vector of the parafoil system in the inertial coordinate system is A I ＝[φ θ ψ] T And the attitude angular velocity vector of the parafoil system in the parachute body coordinate system is W B ＝[p q r] T 。
The six-degree-of-freedom equation of the parafoil system can be obtained according to the Newton-Euler equation:
Figure BDA0003910938850000071
wherein M is the total mass of the parafoil system, R IB A transformation matrix from the object umbrella coordinate system B to the geodetic coordinate system I, F G For the gravity of the parafoil system in the object parachute body coordinate system, F A For the aerodynamic force of the parafoil system in the object parachute body coordinate system, F S Effective resistance of the load in an object umbrella body coordinate system, F AW The additional power generated by the mass under the object umbrella body coordinate system is added to the parafoil system,
Figure BDA0003910938850000072
an antisymmetric matrix is generated for the angular velocity. M A For the parafoil system aerodynamic moment, M, in the parachute body coordinate system AM Is a wingThe additional mass of the parachute system generates an additional aerodynamic moment under an object parachute body coordinate system, and J is the rotational inertia of the parafoil system.
Step 2, combining the graph 2, designing a guider of the parafoil system by adopting a two-dimensional track tracking guidance strategy based on a guidance path tracking principle, calculating a forward error and a transverse error between an actual track and a target track, and eliminating the error by tracking a course angle of the target track movement;
in general, the descending speed of the parafoil system in the gliding section and the energy control section is not changed, and the horizontal track error is corrected by controlling a motor to pull down the control rope at the trailing edge of the flap of the parafoil system in a single-side way. The invention adopts a two-dimensional track tracking guidance strategy to design the guidance law of the parafoil system.
Defining a point p as a point on the actual homing track of the parafoil system, and respectively using p = [ x y ]] T And
Figure BDA0003910938850000073
representing the inertial position and velocity vector of point p, using
Figure BDA0003910938850000081
The velocity of the point p is shown by
Figure BDA0003910938850000082
Representing the direction angle of movement of point p.
Defining a point p p For one point on the homing trajectory of the parafoil system, use it separately
Figure BDA0003910938850000083
And
Figure BDA0003910938850000084
representing point p p Inertial position and velocity vector of
Figure BDA0003910938850000085
Represents a point p p The direction angle of the movement. Wherein, the point p p Position of (2) as a function of scale
Figure BDA0003910938850000086
May vary.
Establishing a target track coordinate system taking the target track motion direction as an x axis, wherein a conversion matrix from an inertial coordinate system to the target track coordinate system is as follows:
Figure BDA0003910938850000087
then point p and point p p The amount of error therebetween is:
Figure BDA0003910938850000088
in the formula, s represents a forward error, and e represents a lateral error. For the parafoil system, in the track tracking process, the forward error is determined by a target track point p p To U p And
Figure BDA0003910938850000089
is eliminated, so that only the controller needs to be set to control the heading angle chi of the parafoil system d Tracking direction angle x of target track motion p And (4) finishing.
Step 3, designing a linear active disturbance rejection controller LADRC by constructing a linear extended state observer LESO and a PD controller of the system on the basis of a two-dimensional track tracking guidance strategy;
firstly, a linear active disturbance rejection controller is designed, and the heading angle chi of a parafoil system is controlled according to a guidance strategy d The transverse error between the current position and the target position of the parafoil system can be eliminated, and the current course angle of the parafoil system is as follows:
Figure BDA00039109388500000810
according to the kinetic model of the parafoil system, the second order form of the parafoil system course angle can be expressed as:
Figure BDA00039109388500000811
wherein f is the total disturbance of the parafoil system, u (t) is the parafoil system control quantity, and b is the controller gain. Assuming f is differentiable, extending it to a new state variable, we can get:
Figure BDA0003910938850000091
in the formula, chi 1 ＝y，
Figure BDA0003910938850000092
χ 3 ＝f。
The state observer theory proposed by Luenberger solves the problem of state reconstruction of a controlled system under deterministic conditions, and the LESO equation is as follows:
Figure BDA0003910938850000093
in the formula (I), the compound is shown in the specification,
Figure BDA0003910938850000094
is the state variable of LESO, beta 1 ，β 2 ，β 3 Is the observer gain.
The lagrange transformation of the LESO equation can be obtained:
Figure BDA0003910938850000095
the corresponding characteristic equation is:
L * (s)＝s 3 +β 1 s 2 +β 2 s+β 3
uniformly allocating 3 poles of the observer to the left half real axis-omega of the s plane o And (3) obtaining:
L * (s)＝(s+ω o ) 3
the observer gain can thus be determined as:
β 1 ＝3ω o ，
Figure BDA0003910938850000096
after the LESO estimates the disturbance and compensates, the controller is essentially a PD controller. Order:
Figure BDA0003910938850000097
that is to say that the first and second electrodes,
Figure BDA0003910938850000098
Figure BDA0003910938850000101
in the formula, x p Is the azimuth angle, psi, of the target track e For tracking errors, u 0 For virtually controlling the quantity, β 01 ，β 02 Is the controller gain. Calculating controller χ according to the above formula p →u 0 The transfer function is;
Figure BDA0003910938850000102
the characteristic equation is then:
C(s)＝s 2 +β 02 s+β 01
two poles of the controller are configured to the left half shaft-omega of the s plane c And (3) obtaining:
C(s)＝(s+ω c ) 2
the controller gain can thus be determined as:
Figure BDA0003910938850000103
β 02 ＝2ω c
therefore, the control law of the linear active disturbance rejection controller is as follows:
Figure BDA0003910938850000104
step 4, designing a predictive controller MPC by constructing a state space model of the system on the basis of a two-dimensional track tracking guidance strategy;
secondly, designing a predictive controller, firstly giving an output of a heading angle psi of the parafoil system, and pulling down the brake delta on one side a State space model for input:
x k+1 ＝Ax k +Bu k ，y k ＝Cx k
wherein A, B and C are system matrix, x k Is a state vector, u k For control input, y k Is the output at time k.
Suppose the prediction interval is H p The direction angle of the target track is w k Then the estimation error is
Figure BDA0003910938850000105
To calculate the control input at a given time, a cost function is introduced as:
Figure BDA0003910938850000106
in the formula (I), the compound is shown in the specification,
Figure BDA0003910938850000111
for the desired value of the system to be,
Figure BDA0003910938850000112
for system prediction output, Q and R are system weight coefficient matrixes, U is a system input control sequence, and the system state equation can be used for obtaining:
Figure BDA0003910938850000113
Figure BDA0003910938850000114
Figure BDA0003910938850000115
J＝(W-K CA x k -K CAB U) T Q·(W-K CA x k -K CAB U)+U T RU
by minimizing the cost function, the expression of the control quantity U is solved as:
Figure BDA0003910938850000116
the above equation represents the optimum control amount input of the predictive control in the entire control range, but only the first control amount u need be taken at the time k k 。
And 6, setting a course angle deviation switching condition by combining the figure 3, wherein when the course angle deviation does not meet the condition, the controller receives an instruction and adopts a linear active disturbance rejection controller for control, and after control tracking for a period of time, when the course angle deviation meets the condition, the controller is switched to a prediction controller for control, so that the switching control of the parafoil system is realized.
According to the guidance strategy, after the parafoil system is launched, the transverse error between the flight track and the target track is eliminated by controlling the course angle of the parafoil system. When the heading deviation psi e Greater than a given value psi e When the ratio is less than or equal to pi/20, the controller receives the instruction and adopts linear active disturbance rejection control. After a period of control tracking, when the heading bias psi e Less than or given value ψ e And when the target track is less than or equal to pi/20, the controller is switched to prediction control to continuously and accurately track the target track.
Example 1
Geometrical parameters, quality of parafoil systemThe quantity characteristic parameters mainly comprise: wingspan b =13.98m, chord length c =5.59m, canopy effective area S p ＝62.5m 2 Mounting angle
Figure BDA0003910938850000117
Length L =7.45m of umbrella rope and effective area S of load body s ＝1.9m 2 And the total mass of the system M =620kg.
As shown in figure 4, the initial position of the target homing track of the parafoil system is set to be x 0 ＝1000m，y 0 ＝500m，z 0 =2000m, initial motion course angle x p (= pi/3) and the termination position is x 1 ＝0m，y 1 ＝0m，z 1 ＝0m。
Setting the initial position of the parafoil system release as x =950m, y =600m, z =2000m and the initial course angle as χ = d And (= pi/2). Adding wind disturbance in the process of tracking the track of a parafoil system: 0 s-354 s, applying constant wind with the wind speed of 8m/s and the wind direction of 180; 200-300 s, applying a gust with an amplitude of 5m/s and a wind direction of 270 degrees:
Figure BDA0003910938850000121
setting parameters of the linear active disturbance rejection controller to be omega 0 ＝20,ω c ＝10,b 0 ＝5；
The parameters of the predictive controller are set as follows: sampling time T s =0.1s, prediction step H p ＝30。
Fig. 5 to 6 show the tracking effects of the predictive control and the switching control on the target direction angle and the target trajectory, respectively.
Under the prediction control, the dynamic response time of the parafoil system for tracking the target course angle is about 4s, and the final landing error is 23m.
Under the switching control, the dynamic response time of the parafoil system for tracking the target direction angle is about 2s, and the final landing error is 9m.
Meanwhile, fig. 6 shows that the switching control has a smaller steady-state error than the predictive control in the case of the transient phase and the gust disturbance.
Fig. 7 shows the homing of the parafoil system controlled by the switching controller for three-dimensional trajectory tracking under wind disturbance conditions.
Fig. 8 shows the control amount variation, and compared with the predictive control, the control amount variation of the switching control is more stable, and the driving motor is prevented from frequently pulling the control rope.
Compared with single prediction control, the switching control method has better control precision, stronger anti-interference capability and good dynamic performance.
The above are only preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples, and all technical solutions that fall under the spirit of the present invention belong to the scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (6)

1. A parafoil system track tracking control method based on linear active disturbance rejection control and predictive control switching is characterized by comprising the following steps:
step 1, carrying out stress analysis on a parafoil system, and establishing a six-degree-of-freedom model of translation and rotation of the parafoil system as a track tracking control basis according to a Newton-Euler equation;
step 2, designing a guider of the parafoil system by adopting a two-dimensional track tracking guidance strategy based on a guidance path tracking principle, calculating a forward error and a transverse error between an actual track and a target track, and eliminating the error by tracking a course angle of the target track motion;
step 3, designing a linear active disturbance rejection controller LADRC by constructing a linear extended state observer LESO and a PD controller of the system on the basis of a two-dimensional track tracking guidance strategy;
step 4, designing a predictive controller MPC by constructing a state space model of the system on the basis of a two-dimensional track tracking guidance strategy;
and 5, setting a switching condition according to the course angle deviation, receiving an instruction by the controller to adopt a linear active disturbance rejection controller for control when the course angle deviation does not meet the condition, and switching the controller to a predictive controller for control when the course angle deviation meets the condition to realize the switching control of the parafoil system.
2. The method for track following control of a parafoil system based on linear active disturbance rejection control and predictive control switching according to claim 1, wherein the step 1 specifically comprises:
setting the position vector of the parafoil system under an inertial coordinate system as P I ＝[x I y I z I ] T The velocity vector of the parafoil system under the coordinate system of the object parachute body is V B ＝[u B v B w B ] T The attitude angle vector of the parafoil system in the inertial coordinate system is A I ＝[φ θ ψ] T The attitude angular velocity vector of the parafoil system under the object parachute body coordinate system is W B ＝[p q r] T ；
According to the Newton-Euler equation, a six-degree-of-freedom model of translation and rotation of the parafoil system can be obtained:
(1) Translation equation of three degrees of freedom:
Figure FDA0003910938840000011
Figure FDA0003910938840000012
(2) Equation of rotational three degrees of freedom:
Figure FDA0003910938840000013
Figure FDA0003910938840000021
wherein M is the total mass of the parafoil system, R IB Is a transformation matrix, F, from the object umbrella coordinate system B to the geodetic coordinate system I G For the force of gravity, F, of the parafoil system in the parachute body coordinate system A Aerodynamic force, F, of parafoil system in parachute body coordinate system S Is the effective resistance of the load under the coordinate system of the umbrella body of the object, F AW The additional power generated by the mass under the object umbrella body coordinate system is added to the parafoil system,
Figure FDA0003910938840000022
generating an antisymmetric matrix for angular velocity, M A For the parafoil system aerodynamic moment, M, in the parachute body coordinate system AM And adding an additional pneumatic moment generated by the mass of the parafoil system under the object parachute body coordinate system, wherein J is the rotational inertia of the parafoil system.
3. The method for track following control of a parafoil system based on linear active disturbance rejection control and predictive control switching according to claim 1, wherein the step 2 is specifically as follows:
defining a point p as a point on the actual homing track of the parafoil system, and respectively using p = [ x y ]] T And
Figure FDA0003910938840000023
representing the inertial position and velocity vector of point p, by
Figure FDA0003910938840000024
The velocity of the point p is shown by
Figure FDA0003910938840000025
Represents the direction angle of movement of point p;
defining a point p p For one point on the homing track of the parafoil system target, respectively
Figure FDA0003910938840000026
And
Figure FDA0003910938840000027
represents a point p p Inertial position and velocity vector of
Figure FDA0003910938840000028
Represents a point p p The direction angle of motion;
wherein, the point p p Position of (2) as a function of scale
Figure FDA0003910938840000029
Is changed;
establishing a target track coordinate system taking the target track motion direction as an x axis, wherein a conversion matrix from an inertial coordinate system to the target track coordinate system is as follows:
Figure FDA00039109388400000210
then point p and point p p The amount of error therebetween is:
Figure FDA00039109388400000211
wherein s represents a forward error and e represents a lateral error;
for the parafoil system, in the track tracking process, the forward error is determined by a target track point p p To U p And
Figure FDA00039109388400000212
is eliminated, so that only the controller is required to be set to control the heading angle x of the parachute system d Tracking target track motion course angle x p And (4) finishing.
4. The method for track following control of a parafoil system based on linear active disturbance rejection control and predictive control switching according to claim 1, wherein the step 3 is specifically as follows:
from step 2, the course angle χ of the system is controlled d The transverse error between the current position and the target position of the parafoil system can be eliminated, and the current course angle of the parafoil system is as follows:
Figure FDA0003910938840000031
according to the dynamical model of the parafoil system, the second-order form of the parafoil system course angle is expressed as:
Figure FDA0003910938840000032
wherein f is the total disturbance of the parafoil system, u (t) is the parafoil system control quantity, and b is the controller gain;
assuming f is differentiable, extending it to a new state variable, and reconstructing the LESO equation can yield:
Figure FDA0003910938840000033
in the formula (I), the compound is shown in the specification,
Figure FDA0003910938840000034
is a state variable of LESO, beta 1 ，β 2 ，β 3 Is the observer gain;
performing Laplace transformation on the LESO equation and configuring the pole of the characteristic equation to the left semi-real axis-omega of the s plane o To thereby determine an observer gain as: beta is a 1 ＝3ω o ，
Figure FDA0003910938840000035
After the LESO estimates the disturbance and compensates, the controller is essentially a PD controller, which causes:
Figure FDA0003910938840000036
Figure FDA0003910938840000037
Figure FDA0003910938840000038
in the formula, x p Is the azimuth angle, psi, of the target track e Is the course deviation u 0 For virtually controlling the quantity, β 01 ，β 02 Is the controller gain. Calculating controller χ according to the above formula p →u 0 The transfer function is:
Figure FDA0003910938840000041
the characteristic equation is then: c(s) = s 2 +β 02 s+β 01
Two poles of the PD controller are configured to the left half shaft-omega of the s plane c Then, C(s) = (s + omega) is obtained c ) 2
Thereby determining the PD controller gain as:
Figure FDA0003910938840000042
β 02 ＝2ω c ；
therefore, the control law of the linear active disturbance rejection controller is as follows:
Figure FDA0003910938840000043
5. the method for track-following control of a parafoil system based on linear active disturbance rejection control and predictive control switching as claimed in claim 1, wherein said step 4 specifically comprises:
firstly, the heading angle psi of the parafoil system is given as an output, and the brake delta is pulled down on one side a For the input state space model: x is the number of k+1 ＝Ax k +Bu k ，y k ＝Cx k ；
Suppose the prediction interval is H p The direction angle of the target track is w k Then the estimation error is
Figure FDA0003910938840000044
To calculate the control input at a given time, a cost function is introduced as:
Figure FDA0003910938840000045
in the formula (I), the compound is shown in the specification,
Figure FDA0003910938840000046
for the desired value of the system to be,
Figure FDA0003910938840000047
for system prediction output, Q and R are system weight coefficient matrixes, U is a system input control sequence, and the system state equation is used for obtaining:
Figure FDA0003910938840000048
Figure FDA0003910938840000049
Figure FDA00039109388400000410
J＝(W-K CA x k -K CAB U) T Q·(W-K CA x k -K CAB U)+U T RU
by minimizing the cost function, the expression of the control quantity U is solved as follows:
Figure FDA0003910938840000051
the above expression represents the optimum control amount input of the predictive control over the entire control range, but only the first control amount u need be taken at time k k 。
6. The method for controlling track following of parafoil system based on linear active disturbance rejection control and predictive control switching as claimed in claim 1, wherein said heading angle deviation switching condition in step 6 is set to ψ e Less than or equal to pi/20, and after the parafoil system is put in, the requirements of psi are met e When the phi is less than or equal to pi/20, the controller receives the instruction and adopts a linear active disturbance rejection controller to control, when psi is greater than or equal to phi e And when the sum is less than or equal to pi/20, switching to the control of the predictive controller.
CN202211322036.2A 2022-10-27 2022-10-27 Parafoil system track tracking control method based on linear active disturbance rejection control and predictive control switching Pending CN115686041A (en)

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