CN114942649B - Airplane pitching attitude and track angle decoupling control method based on backstepping method - Google Patents
Airplane pitching attitude and track angle decoupling control method based on backstepping method Download PDFInfo
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- G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
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Abstract
The invention discloses a method for decoupling and controlling the pitching attitude and the track angle of an airplane based on a backstepping method, which comprises the following steps: establishing a mathematical model suitable for designing a backstepping control law of the aircraft attack angle according to a motion equation about the aircraft attack angle; designing an improved airplane angle of attack backstepping control law by utilizing a Lyapunov function and introducing undetermined parameters based on a mathematical model of the airplane angle of attack backstepping control law; determining the value of a parameter to be determined in the improved backstepping control law of the aircraft attack angle by optimizing the step response performance of the aircraft attack angle; designing a control law of the accelerator control track angle, optimizing track angle control law parameters by optimizing the tracking performance of the track angle on expected response, and keeping the track angle unchanged after the aircraft attack angle is adjusted. The method has high control precision, can accurately control the attack angle by adjusting the pitching attitude of the airplane, and can not change the flight path angle; the control law has the advantages of less related model information, easy acquisition and strong practicability.
Description
Technical Field
The invention relates to the technical field of control of aviation aircrafts, in particular to a method for decoupling and controlling a pitching attitude and a track angle of an airplane based on a backstepping method.
Background
In the flying process of an airplane, variables such as the attitude, the angle of attack, the track angle and the like of the airplane need to be controlled frequently, and the control effect directly influences the flying state and the feeling of passengers: the angle of attack directly affects the aerodynamic force and moment on the aircraft, the flight path angle is related to the flight height and course, and the adjustment of the attitude of the aircraft can change the angle of attack and the flight path and also can change the sight of a driver. Indeed, the control priorities and specific requirements for these variables are determined by the specific flight conditions.
These controlled variables are coupled to each other as known from the equations of motion of the aircraft. The coupling relation is often used for completing flight control tasks, such as 'head up' when an airplane climbs and 'head down' when the airplane lands; however, the coupling relationship between variables also increases the control difficulty, which brings many troubles. For example, during landing of a carrier-based aircraft operated by a pilot, 3 things need to be completed simultaneously: (1) the steering column is used for adjusting the direction of the aircraft nose so as to aim at the centerline of the bevel deck of the aircraft carrier for flight, namely 'centering'; (2) the throttle lever is used for controlling the aircraft glide track to enable the carrier-based aircraft to fly along the optical glide track, namely 'seeing light'; (3) the pitching attitude is controlled by a steering column, and the error of the attack angle is limited within +/-0.5 degrees, namely the 'angle of repose'. 3 things of 'centering, lamp watching and angle keeping' are highly coupled: the left and right control of the steering column centering can cause the loss of the height of the airplane and cause the airplane to deviate from an ideal flight path; the angle of attack can be changed when the throttle lever is adjusted to correct the deviation of the glide slope; the track can be influenced when the angle of attack is adjusted by operating the steering column to change the pitch angle. Therefore, the pilot has to coordinate and operate the double levers continuously in the landing stage, the working strength is even higher than that of an air battle, and the pilot is one of the main reasons of high incidence of the landing accidents of the carrier-based aircraft.
The analysis shows that the research on the decoupling control law of the aircraft has important practical significance. In addition, in the theoretical research and design stage of the flight control law, in order to reduce the implementation difficulty of the control law and enhance the practicability of theoretical research results, the motion model information related to the control law is hoped to be reliable, accurate and easy to obtain.
Disclosure of Invention
The invention aims to provide a decoupling control method for a pitching attitude and a track angle of an airplane based on a backstepping method, which can realize the decoupling control of the pitching attitude and the track angle of the airplane in a longitudinal motion state, so that the airplane can accurately control an attack angle by adjusting a pitch angle and simultaneously keep the flight track angle unchanged.
The purpose of the invention is realized by the following technical scheme:
a method for decoupling and controlling the pitching attitude and the track angle of an airplane based on a backstepping method comprises the following steps:
establishing a mathematical model suitable for designing a backstepping control law of the aircraft attack angle according to a motion equation about the aircraft attack angle;
designing an improved airplane angle of attack backstepping control law by utilizing a Lyapunov function and introducing undetermined parameters based on a mathematical model for designing the airplane angle of attack backstepping control law, wherein the undetermined parameters comprise undetermined parameters and functions;
determining the value of a parameter to be determined in the improved backstepping control law of the aircraft attack angle by optimizing the step response performance of the aircraft attack angle;
designing a control law of the accelerator control track angle, optimizing track angle control law parameters by optimizing the tracking performance of the track angle on expected response, and keeping the track angle unchanged after the aircraft attack angle is adjusted.
According to the technical scheme provided by the invention, the control precision is high, the attack angle can be accurately controlled by adjusting the pitching attitude of the airplane, and the track angle cannot be changed; the control law has the advantages of less related model information, easy acquisition and strong practicability.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a method for controlling decoupling of an aircraft pitch attitude and a track angle based on a back stepping method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a force analysis performed during a steady-state landing of an aircraft according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a method for verifying an improved backstepping control law for an aircraft angle of attack according to an embodiment of the present invention;
fig. 4 is a schematic diagram of parameters of an attack angle backstepping control law designed by a step response optimization tool of Matlab software according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a command response of an aircraft after optimization of parameters of an angle of attack backstepping control law provided by an embodiment of the present invention;
fig. 6 is a schematic diagram of a track angle control law parameter designed by a reference signal tracking tool of Matlab software according to an embodiment of the present invention;
fig. 7 is a schematic diagram of command response of an aircraft under the combined action of the control laws of the attack angle and the track angle according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The terms that may be used herein are first described as follows:
the terms "comprising," "including," "containing," "having," or other similar terms of meaning should be construed as non-exclusive inclusions. For example: including a feature (e.g., material, component, ingredient, carrier, formulation, material, dimension, part, component, mechanism, device, process, procedure, method, reaction condition, processing condition, parameter, algorithm, signal, data, product, or article of manufacture), is to be construed as including not only the particular feature explicitly listed but also other features not explicitly listed as such which are known in the art.
The method for controlling decoupling of the pitching attitude and the track angle of the airplane based on the backstepping method is described in detail below. Details which are not described in detail in the embodiments of the invention belong to the prior art which is known to a person skilled in the art. Those not specifically mentioned in the examples of the present invention were carried out according to the conventional conditions in the art or conditions suggested by the manufacturer. The apparatus used in the examples of the present invention is not indicated by manufacturers, and is a general product that can be obtained by commercial purchase.
As shown in fig. 1, an aircraft pitch attitude and track angle decoupling control method based on a back stepping method provided in an embodiment of the present invention mainly includes the following steps:
In an embodiment of the present invention, the equation of motion related to the aircraft angle of attack is a first order differential equation related to the aircraft angle of attack α, which is obtained by relating to the aircraft inertial angle of attack α I Is derived from the first order differential equation of (a). In a symmetric flight state in the vertical plane of the airplane and no wind, a first order differential equation about the attack angle alpha of the airplane is expressed as:
wherein m is the aircraft mass; g is the acceleration of gravity; p and L respectively represent the thrust and the aerodynamic lift force borne by the aircraft engine, the thrust acting direction is along the longitudinal axis of the aircraft body, and the thrust installation angle and the eccentricity are both zero; v represents the aircraft airspeed, equal toGround speed v of aircraft I (ii) a Gamma and q respectively represent the flight path angle and the pitch angle speed of the airplane; the first order derivative of the pitch angle velocity q is:
m represents the pitching moment applied to the aircraft, I y Representing the pitch moment of inertia.
Let variable x 1 And variable x 2 Respectively equal to the aircraft angle of attack alpha and the pitch angle speed q, and the backstepping control law u of the aircraft angle of attack is equal to M/I y (ii) a And let the function f (x) 1 Y) is equal to
The variable y represents x 1 All other variables except that, then we get:
wherein the black dots at the top of the variables are first order differential symbols.
Continuously carrying out variable substitution to make variable xi 1 、ξ 2 Sum function
Satisfies the following conditions:
where the subscript indicates the value of the respective variable in the nominal flight state, i.e. the reference value (nominal value), which is a constant. Therefore, a mathematical model suitable for designing the airplane angle of attack backstepping control law can be established, and is expressed as follows:
and 2, designing an improved airplane angle of attack backstepping control law by utilizing a Lyapunov function and introducing undetermined parameters based on a mathematical model for designing the airplane angle of attack backstepping control law.
Considering that the angle of attack control law established based on the traditional backstepping design idea contains a large amount of information of a nonlinear model and is difficult to accurately obtain in practical application, the invention designs the improved airplane angle of attack backstepping control law and furthest reduces the information of a motion model contained in the control law. The method comprises the following specific steps:
two Lyapunov functions were chosen, expressed as:
V 1 ＝0.5ξ 1 2
V 2 ＝0.5c 0 ξ 1 2 +F(ξ 1 )+0.5z 2
wherein, variable
Coefficient k 1 ＞0；c 0 Is a undetermined constant; f (xi) 1 ) Is a positive semi-definite function and it is paired with (xi) 1 ) The derivative of (b) satisfies: f' (xi) 1 )·ξ 1 ≥0；
Constructing positive semi-definite function F (xi) meeting requirements 1 ) And seeks to make a second Lyapunov function V 2 First order differentiation of
Is a negative parameter c 0 And an airplane angle of attack backstepping control law u, obtaining:
u＝-c 2 [c 1 (x 1 -x 1* )+x 2 +f(x 1* ,y * )]＝-c 2 [c 1 ·Δx 1 +x 2 ]
wherein, c 1 And c 2 Are undetermined parameters, satisfy c 2 ＞c 1 ，c 1 A, a is
Maximum value of, Δ x 1 ＝ξ 1 And Δ denotes the deviation of the corresponding physical quantity from its reference value, i.e. Δ x 1 ＝x 1 -x 1* 。
Because the improved airplane angle of attack backstepping control law is established for the nonlinear motion model, if the linear model is used as the controlled object, the control law needs to be further converted into a form suitable for the linear model, and the form is expressed as follows:
wherein, mu α 、μ q 、
μ e 、μ c Both longitudinal stability and steering derivatives are related to the aircraft pitching moment and represent M to alpha, q, respectively,
δ e 、δ c Nominal value of partial derivative and I y The ratio of (A) to (B); c. C 1 And c 2 Are all undetermined parameters; delta e And delta c Respectively, an elevator deflection angle and a canard deflection angle, and Δ represents a deviation amount between a corresponding physical quantity and a reference value thereof.
In the embodiment of the invention, the undetermined parameters mainly comprise: parameter c to be determined 1 And c 2 And a function F (ξ) 1 ) (ii) a Of course, the undetermined constant c is strictly included 0 C is given only in the derivation 0 Does not necessarily find a specific numerical value.
And 3, determining the value of the undetermined parameter in the improved airplane angle of attack backstepping control law by optimizing the step response performance of the airplane angle of attack.
In the embodiment of the invention, the step response performance of the aircraft attack angle is optimized by using a first software program, so that undetermined parameters in the backstepping control law of the aircraft attack angle are automatically optimized: setting a value range of a parameter to be determined and performance requirements of aircraft attack angle step response in a software program; and automatically optimizing the parameters through software to meet the set performance requirement, then gradually improving the performance requirement, and continuously performing parameter self-optimization until the step response performance is improved to the extent that the parameter optimization cannot be met, so that the optimal configuration condition of undetermined parameters in the aircraft angle of attack backstepping control law can be determined, and the parameter optimization work is finished.
As mentioned before, the pending parameters mainly include c 1 And c 2 However, when the airplane angle of attack backstepping control law is specifically implemented, namely a simulation verification link, in order to facilitate the realization of the airplane angle of attack backstepping control law, the delta is made c Taking undetermined constant, and then obtaining delta through optimization by utilizing a first software program c So that the undetermined parameters in the control law of the backstepping of the aircraft angle of attack in this step include c 1 、c 2 And delta c 。
Illustratively, the first software program may be a Check Step Response Characteristics module of the Matlab software Simulink module library.
And 4, designing a control law of the accelerator control track angle, and optimizing track angle control law parameters by optimizing the tracking performance of the track angle on expected response so as to keep the track angle unchanged after the aircraft incidence angle is adjusted.
In the embodiment of the invention, the control law of the throttle control track angle adopts a PID control structure, and the corresponding complex field expression is as follows:
in the formula: s is a variable in complex field space, k p 、k i 、k d Respectively representing the undetermined proportional, integral and differential gains, delta pl Indicating the deviation amount of the throttle lever from the reference value thereof; Δ γ represents the deviation of the aircraft track angle from its baseline value.
In the embodiment of the invention, the optimized and determined attack angle control law parameter value (namely c obtained by optimization) is not changed when the aircraft track angle control law parameter is optimized 1 、c 2 And delta c ) (ii) a The optimization aim is to keep the flight path angle unchanged after the system responds to the aircraft attack angle step instruction; the optimization process is carried out by causing the track angle response to track a specified reference signal, using a software programAs an aid, the reference signal is set in the software program as a function of a constant value of 0 over a set period of time.
Illustratively, the second software program may be a Check Against Reference module of Matlab software Simulink module library.
The scheme provided by the embodiment of the invention mainly has the following beneficial effects:
1) The decoupling control of the pitching attitude and the track angle of the airplane in the longitudinal motion state can be realized, so that the attack angle of the airplane is accurately controlled by adjusting the pitch angle, and the flight track angle is kept unchanged.
2) The information related to the model in the airplane attack angle backstepping control law is less and is easy to obtain, so that the method has stronger practicability.
In order to facilitate understanding and to more clearly show the technical solutions and the technical effects thereof provided by the present invention, the following describes the whole solution in more detail by combining various analysis and derivation processes performed in the design process of the present invention.
1. And establishing a mathematical model suitable for designing the backstepping control law of the aircraft attack angle according to a motion equation related to the aircraft attack angle.
The first order differential equation for the aircraft angle of attack α may be derived from the equation for the aircraft inertial angle of attack α I The first order differential equation (1) is deduced, the equation is established on the premise that the airplane does symmetrical flight in a vertical plane according to the longitudinal movement condition of the airplane, and the equation is as follows: m is the aircraft mass; g is gravity acceleration, and a constant is taken; gamma and q respectively represent the flight path angle and the pitch angle speed of the airplane; p, L and D respectively represent thrust, aerodynamic lift and resistance of the aircraft engine, the thrust acting direction is along the longitudinal axis of the aircraft body, and the thrust installation angle and the eccentricity are zero; v. of I Representing the ground speed of the aircraft. The expression of q is formula (2), where M represents the pitching moment experienced by the aircraft, I y Representing the pitch moment of inertia.
In the absence of wind, alpha and alpha I Equal, aircraft airspeeds v and v I Equal, the first order differential equation for α, i.e., equation (3), can be derived from equation (1).
Let variable x 1 And variable x 2 Is respectively equal to alpha and q, and the backstepping control law u of the aircraft angle of attack is equal to M/I y (ii) a And let the function f (x) 1 Y) is equal to formula
The variable y represents x 1 All other variables except. Equation (4) can be obtained from equations (2) and (3).
Continuously carrying out variable substitution to make variable xi 1 、ξ 2 Sum function
Formula (5) is satisfied, and the symbol with subscript in the formula represents the value of the corresponding variable in the nominal flight state, that is, the reference value (nominal value), is a constant, and the same applies below. From this, f (x) is known 1* ,y * ) If the value is constant, then equation (6) can be obtained from equations (4) and (5). The form of the formula (6) is a mathematical model form suitable for designing the backstepping control law.
2. An attack angle control law is established based on the traditional backstepping design method, and the problems existing in the traditional design method are analyzed.
The traditional backstepping method is a design method with robustness, and the basic design idea is to decompose a complex nonlinear system into subsystems with the order not exceeding the system order, and then to start the design from the last stage of subsystem to make the system reach asymptotic stability; the previous stage subsystem including the last stage subsystem is designed to reach asymptotic stability 8230, and the system is backed up until the control law design of the whole system is completed. The final Lyapunov function for proving the stability of the complete closed-loop system can be obtained by accumulating the Lyapunov functions for verifying each level of subsystem step by step, and the Lyapunov functions also determine the final implementation form of a system control law.
And (3) designing an attack angle control law according to a traditional backstepping method by taking the system corresponding to the formula (6) as a controlled object.
Firstly, selecting a 1 st Lyapunov function: v 1 ＝0.5ξ 1 2 . Then, as can be seen from equation (6), V 1 Satisfies the formula (7). Order to
Wherein the parameter k 1 When > 0, then xi 2 ＝ξ 2d When the utility model is used, the water is discharged,
formula (9) can be obtained by performing a variable substitution by formula (8).
z＝ξ 2 -ξ 2d ＝ξ 2 -φ(ξ 1 ) (8)
In the embodiment of the present invention, the first and second substrates,a series of intermediate parameters (or functions) introduced, e.g. the variable x defined previously 1 、x 2 、ξ 1 、ξ 2 Sum function
Z, φ (ξ) defined in this section 1 )、u 0 Etc., mainly to simplify the expression form of the formula.
Then, aim at xi 2 Converge to xi 2d The 2 nd Lyapunov function is selected: v 2 ＝V 1 +0.5z 2 . Then V is known from the formula (7) -the formula (9) 2 Satisfies the formula (10). If u is selected 0 ＝-ξ 1 -k 2 z, wherein the parameter k 2 If greater than 0, then
In summary, the control law of the original system is formula (11), and further formula (5) and ξ 1 ＝Δx 1 Equation (12) can be obtained.
The problems with this design approach are: the formula (12) contains a great deal of information of the nonlinear model, which is difficult to obtain accurately in practical application, especially for function derivative terms
From the function f (x) 1 Y) specific expressions in the equation of motion of the aircraft including lift, thrust, mass,The physical quantities such as the angle of attack, the flight path angle and the like are difficult to be measured and fed back and calculated accurately in the actual flight process
The difficulty will be greater; even in a numerical simulation environment, because the underlying data used to calculate aircraft lift and thrust is discrete, the calculations are performed
A large amount of data fitting processing is also required before.
3. An improved airplane attack angle backstepping control law is designed, and the information of a motion model contained in the control law is reduced to the maximum extent.
In light of the problems with the conventional design methods as indicated in the second section, the improved design method for the aircraft angle of attack backstepping control law provided by the present invention needs to be accomplished in the following two steps.
First, the 1 st Lyapunov function is still selected as V 1 ＝0.5ξ 1 2 And make an order
When the maximum value of (b) is "a", the formula (13) holds, and the formula (14) is obtained from the formula (7). If xi is taken 2d ＝-c 1 ξ 1 Wherein c is 1 If > a, it can be seen from the formula (14)
Then, taking the second-stage error function, i.e. equation (15), in combination with equation (6), equation (16) can be obtained. If the control law u is designed by the conventional backstepping method in the second part, the 2 nd control law is still adoptedThe Lyapunov function is taken as V 2 ＝V 1 +0.5z 2 Then derive the order xi 1 And z-stabilized u will contain
It is shown that the non-linear function f (x) must be precisely known in the process of implementing u 1 Y), which is difficult in practical applications.
z＝ξ 2 -ξ 2d ＝ξ 2 +c 1 ξ 1 (15)
To avoid this problem and minimize the motion model information related to the control law, the 2 nd Lyapunov function is taken as equation (17), where: c. C 0 Is a undetermined constant, F (xi) 1 ) Is a positive semi-definite function and it is vs xi 1 Derivative of F' (ξ) 1 ) Equation (18) is satisfied.
V 2 ＝0.5c 0 ξ 1 2 +F(ξ 1 )+0.5z 2 (17)
F′(ξ 1 )·ξ 1 ≥0 (18)
And (3) obtaining a derivative of the equal sign of the formula (17) with respect to time, and substituting the derivative into the formula (16) to obtain a formula (19).
Will be provided with
Is divided into two parts, one part is a xi 1 And the other part is described as
Namely, formula (20), and thus formula (21) is derived from formula (13) and formula (18). Substituting equation (20) into equation (19) yields equation (22), which is further based on equation (18), equation (21), and equations(22) Equation (23) is derived.
Let parameter c 0 And function F (ξ) 1 ) Satisfying the formula (24), F (xi) can be guaranteed 1 ) Positive semi-qualitative, and from equation (23), equation (25) results. Obviously, in order to make
Negative determination, taking u = -c 2 z and c 2 ＞c 1 And (4) finishing. For the original system represented by formula (4), the control law expression obtained from formula (5) and formula (15) is formula (26), where f (x) 1* ,y * ) The reason why =0 is that when the aircraft is in a longitudinal reference motion state (e.g., during steady-state landing), the resultant force in the direction perpendicular to the velocity thereof is 0, that is, the formula (27) is satisfied, as shown in fig. 2, a schematic diagram of a force analysis performed on the aircraft during steady-state landing, which is provided for the embodiment of the present invention, ox in fig. 2 g Axis and Oz g The axes representing the horizontal and vertical axes, ox, respectively, of a geodetic coordinate system b The axis represents the horizontal axis of the body coordinate system; according to the action direction of the aerodynamic force, the directions of the lift force L and the drag force D are respectively vertical and parallel to the speed direction of the airplane, and the airplane stress is analyzed in the direction parallel to the L to obtain a formula (27).
u＝-c 2 [c 1 (x 1 -x 1* )+x 2 +f(x 1* ,y * )]＝-c 2 [c 1 ·Δx 1 +x 2 ] (26)
P * ·sinα * +L * ＝mg·cosγ * (27)
According to the Lyapunov stability criterion, when the aircraft incidence backstepping control law u is taken as an expression (26), ξ in the formula (17) 1 And z both converge to 0 over time, so that x is known from equations (5) and (15) 1 And x 2 Respectively converge to x 1* And 0, namely the backstepping control law of the aircraft angle of attack can ensure that the aircraft angle of attack converges to a reference value and the pitch angle speed converges to 0.
Compared with the traditional angle of attack backstepping control law represented by the formula (12), the improved angle of attack backstepping control law represented by the formula (26) has the advantages that the amount of model information is obviously reduced, and only the angle of attack deviation delta alpha, the pitch angle speed q and the undetermined control parameter c are included 1 And c 2 Wherein c is 1 Should be greater than
A is a maximum value of. It can be seen that a satisfies the formula (28), and further, the formula (29) is satisfied according to the lagrangian median theorem of the continuous function. In normal flight conditions, alpha is smaller than the stall angle of attack, a nonlinear function f (x) 1 Y) is mainly influenced by the lift L, while the slope of the L-alpha curve before the stall angle of attack is positive, i.e. corresponds to
Thus, select c 1 C can be satisfied if > 0 1 ＞a。
Fig. 3 is a schematic diagram for verifying an improved aircraft angle of attack backstepping control law according to an embodiment of the present invention, and fig. 3 shows a closed-loop system established on a MATLAB software Simulink platform. A linear small disturbance model describing the approach landing motion of a certain type of airplane is used as a controlled object, the model is stored in a module named as an airplane motion model in a state space equation form, and the expression is as follows:
wherein:
the unit of v is m/s; the units of alpha, theta (aircraft pitch angle) and gamma are all rad; the unit of q is rad/s; h represents height in m; n is z Representing normal overload, taking gravity acceleration g as a unit; control vector u 1 The 3 components in the system sequentially represent deviation amounts of an elevator deflection angle, a canard deflection angle and an accelerator opening degree from a reference value, and the unit is degrees; Δ represents a deviation amount of the physical quantity from its reference value (nominal value), the same applies below; the constant value matrices A-D are represented as:
wherein, O represents a zero matrix, namely a 2-row and 3-column all 0 matrix; i represents an identity matrix, namely a 5-order identity matrix, which are both conventional expressions in linear algebra.
The model control law given by the formula (26) is established for a nonlinear motion model, wherein the aircraft attack angle backstepping control law u does not represent a control execution mechanism of a controlled object, namely, the control law is different from u in the formula (30) 1 Therefore, the formula (26) cannot be directly used as the control input of the linear model, and needs to be further converted into a form suitable for the linear model, and the specific method is as follows:
1) U equals to M/I y And M * And q is * The numerical values of (1) are all 0, and a formula (31) can be obtained by combining the formula (26);
u＝ΔM/I y ＝-c 2 (c 1 ·Δα+Δq) (31)
2) According to the disturbance linearization theory and the aerodynamic characteristics of the controlled object, Δ M can be expressed as a formula (32), in which 6 aerodynamic coefficients related to the pitching moment take values of μ v ＝0，μ α ＝0.71936，μ q ＝-0.10061，
μ e ＝-0.01993，μ c =0.00513, as shown in figure 3;
3) By combining the formula (31) and the formula (32), a control law expression (33) of the control plane input offset of the linear small perturbation model can be obtained.
When the control law (33) is realized by using the Simulink platform, delta can be controlled c The pending constant, KC in fig. 3, is taken and a step signal is added as a command, setting the step time to 0s as indicated by the step input labeled "C _ delta _ alpha" in fig. 3. Considering that "a positive rudder command produces a negative angle of attack increment", to construct a negative feedback control mode, the step command is introduced with a negative sign, and the feedback Δ α information takes a positive sign. Furthermore, the constants labeled "P _ k1" and "P _ k2" in FIG. 3 correspond to the parameter c in equation (33), respectively 1 And c 2 And requires that the gain labeled "k _ mark" in FIG. 3 take a positive value to ensure that c 2 ＞c 1 (ii) a Since the formula (33) does not contain the track angle feedback information, 3 PID parameters on the track angle feedback loop in FIG. 3 all take 0, and data 57.3 all represent the conversion proportional relation between the angle and the radian; when designing the control law, the problem of limited motion amplitude of the control surface and the throttle lever of the airplane is also considered, as shown by 3 limiting links in fig. 3.
4. And optimizing the step response performance of the aircraft angle of attack on the basis of the third part, thereby determining the value of the undetermined parameter in the improved backstepping control law of the aircraft angle of attack.
The undetermined parameter value is optimized to obtain better system response performance, and the undetermined parameter value is not only required to be stable. When the Step Response performance of the aircraft angle of attack is optimized, a 'Check Step Response Characteristics' function module in a Matlab software Simulink module library is used, the module can convert the expected Step performance index of the control system into a constraint boundary of Step Response, and undetermined parameters of the control system are automatically optimized until the system output meets the expected performance index. Considering that the value range of the parameter to be determined affects the operation efficiency and the effect of the module, and in addition, the optimal response condition of the variable to be optimized is generally difficult to pre-judge before optimization, when in actual use, the value range of the parameter to be determined is not easy to be too wide, and the performance index requirement can be gradually improved.
Fig. 4 is a schematic diagram of parameters of a pitch backstepping control law designed by a Step Response optimization tool of Matlab software according to an embodiment of the present invention, that is, an effect obtained after a "Check Step Response Characteristics" module is connected to a pitch output end of fig. 3. During specific operation, the value ranges of undetermined parameters K1, KC and K _ mark are set to be 0-100, -19-24 and 0-200 respectively, the requirement of step response is gradually improved, finally, the performance indexes of attack angle response are set to be 0.5s of rising time, 1.5s of adjusting time, 0.5% of steady state error range, 2% of overshoot and 0% of negative overshoot, the optimal response result meeting the requirement of the indexes is obtained, and the values of corresponding parameters K1, KC and K _ mark are 12.34, -19 and 16.234 respectively. Fig. 5 is a schematic diagram of an instruction response of an aircraft after optimization of parameters of an angle of attack backstepping control law provided by an embodiment of the present invention. Fig. 5 shows that the steady state is achieved less than 1s after the response command of the angle of attack and the pitch angle speed, the former is stabilized at the command value, and the latter converges to 0, which shows that the parameter optimization of the angle of attack control law is successful. Nevertheless, the overall response of the system is still not satisfactory, and fig. 5 shows that the pitch attitude and the track angle of the aircraft are greatly affected by the adjustment of the attack angle, and cannot be stabilized for a long time after the response of the attack angle converges.
5. And designing a control law of the accelerator control track angle on the basis of the fourth part, and optimizing track angle control law parameters by optimizing the tracking performance of the track angle on expected response so as to keep the track angle unchanged after the attack angle is adjusted.
The reason for controlling the aircraft track angle by the throttle is that:
on the one hand, fig. 5 fully shows that the control law of the formula (33) is only adopted and the parameters in the control law are optimized, so that the incidence angle and the pitch angle rate of the airplane can be accurately controlled, but the pitching attitude and the track angle of the airplane cannot be stabilized; considering that the pitch angle, the track angle and the 3 incidence angles of the airplane are linearly related under the longitudinal motion state of the airplane, the formula (34) is satisfied, and on the basis of ensuring the control effect of the incidence angle and the pitch angle rate of the airplane, if the track angle can be kept stable, the decoupling control of the pitching attitude and the track angle is expected to be realized, namely, the airplane can accurately adjust the incidence angles by adjusting the pitch angles without influencing the track angle;
Δθ＝Δα+Δγ (34)
on the other hand, the control law shown in the formula (33) does not contain the information of the accelerator and the track angle, which indicates that the control effect on the incidence angle and the pitch angle rate cannot be damaged only by using the accelerator to control the track angle on the basis of implementing the control law, that is, after the control law parameters shown in the formula (33) are optimized, the track angle control law parameters based on the accelerator control are further optimized, so that the comprehensive optimized control on the aircraft attitude, the incidence angle, the angular speed and the track angle can be realized.
The track angle control law adopts a PID control structure, and a complex field expression of the track angle control law is shown as a formula (35), wherein: k is a radical of p 、k i 、k d Respectively representing undetermined proportional, integral and differential gains; delta pl Indicating throttle lever, and throttle delta p The transfer function between them is 1/(s + 1), as shown in fig. 3 and 4.
The targets for optimizing the parameters of the track angle control law are as follows: the track angle converges in response to the angle of attack step command, and the steady state value is 0. Fig. 6 is a schematic diagram of a track angle control law parameter design by a Reference signal tracking tool of Matlab software according to an embodiment of the present invention, and provides a specific connection method for optimizing a track angle control law parameter by using a Check Against Reference module of a Matlab software Simulink module library. According to the convergence time of the aircraft attack angle response shown in FIG. 5, the expected track angle response (i.e., the Reference signal) in the "Check aging Reference" module is set as a constant 0 function in a time period of 1-8 s, and 3 undetermined gains (k) in formula (35) are set p 、k i 、k d ) The value range of (a). Fig. 7 is a schematic diagram of a command response of an aircraft under a combined action of an angle of attack and a track angle control law, where parameters of the angle of attack control law are optimized and determined through step 4, and are not adjusted any more when the parameters of the track angle control law are optimized. The optimization results of the flight path angle control law parameters kp, ki and kd are respectively 74.34, 4.65 and 176.43.
In fig. 3, 4, and 6: delta _ alpha is Δ α and delta _ dalpha is
delta _ q is Δ q and delta _ delete _ c is Δ δ c Delta gamma is Δ γ,30/s +30, 1/s +1 represent the dynamics of the control surface and the throttle, respectively, and the number 0 is the desired track angle convergence to 0.
Fig. 7 shows that the track angle enters a 2% error band around a steady-state value less than 1s after responding to the attack angle step command, the disturbance converges to 0 and keeps unchanged at 3s, the pitch angle converges to a command amplitude and keeps constant after responding to the attack angle command about 1s, and accurate tracking of the attack angle response is realized; meanwhile, the fluctuation range of the flight speed is very small, and the flight speed is only deviated from the reference value by 0.05m/s in a steady state, so that the flight speed can be basically kept unchanged. In addition, according to
It can be seen that when the flight path angle is small, for example, at the approach landing stage of the aircraft, the formula (36) holds, which shows that the control law shown in fig. 7 has the capability of stabilizing the altitude change rate of the aircraft.
Therefore, the decoupling control law of the pitching attitude and the track angle of the airplane based on the backstepping method, which is designed by the method provided by the embodiment of the invention, has higher control precision, can enable the airplane in a longitudinal motion state to quickly and accurately control the attack angle by adjusting the pitch angle, and keep the flight track angle unchanged.
Through the above description of the embodiments, it is clear to those skilled in the art that the above embodiments can be implemented by software, and can also be implemented by software plus a necessary general hardware platform. With this understanding, the technical solutions of the embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a usb disk, a removable hard disk, etc.), and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods according to the embodiments of the present invention.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (6)
1. A method for decoupling and controlling the pitching attitude and the track angle of an airplane based on a backstepping method is characterized by comprising the following steps of:
establishing a mathematical model suitable for designing a backstepping control law of the aircraft attack angle according to a motion equation about the aircraft attack angle;
designing an improved airplane angle of attack backstepping control law by utilizing a Lyapunov function and introducing undetermined parameters based on a mathematical model for designing the airplane angle of attack backstepping control law, wherein the undetermined parameters comprise undetermined parameters and functions;
determining the value of a parameter to be determined in the improved airplane angle of attack backstepping control law by optimizing the step response performance of the airplane angle of attack;
designing a control law of an accelerator control track angle, and optimizing track angle control law parameters by optimizing the tracking performance of the track angle on expected response to ensure that the track angle is kept unchanged after the aircraft attack angle is adjusted;
the aircraft angle of attack backstepping control law is designed and improved by utilizing a Lyapunov function and introducing undetermined parameters, and comprises the following steps of:
two Lyapunov functions were chosen, expressed as:
wherein, variable
Coefficient k 1 ＞0；c 0 Is a undetermined constant; f (xi) 1 ) Is a positive semi-definite function and it is on xi 1 The derivative of (b) satisfies: f' (xi) 1 )·ξ 1 Not less than 0; let variable xi 1 、ξ 2 Sum function
Satisfies the following conditions:
function f (x) 1 Y) is equal to formula
Variable x 1 And variable x 2 Respectively equal to the aircraft angle of attack alpha and the pitch angular rate q, the subscript indicates the value of the corresponding variable in the nominal flight state, and the variable y represents x 1 All other variables, P and L, respectively represent the thrust and the aerodynamic lift force borne by the aircraft engine, m is the mass of the aircraft, g is the gravity acceleration, v represents the airspeed of the aircraft, and gamma represents the flight path angle of the aircraft;
constructing positive semidefinite function F (xi) meeting the requirement 1 ) And seeks to make a second Lyapunov function V 2 First order differential over time
Parameter c being negative 0 And an airplane angle of attack backstepping control law u, obtaining:
u＝-c 2 [c 1 (x 1 -x 1* )+x 2 +f(x 1* ,y * )]＝-c 2 [c 1 ·Δx 1 +x 2 ]
wherein, c 1 And c 2 Are undetermined parameters, satisfy c 2 ＞c 1 ，c 1 A, a is
Maximum value of, Δ x 1 ＝ξ 1 Where Δ denotes the deviation of the respective physical quantity from its reference value, i.e. Δ x 1 ＝x 1 -x 1* ；
The control law of the throttle control track angle adopts a PID control structure, and the corresponding complex field expression is as follows:
where s is a complex-field space variable, k p 、k i 、k d Respectively representing the undetermined proportional, integral and differential gains, delta pl Indicating the deviation amount of the throttle lever from the reference value thereof; Δ γ represents the deviation of the aircraft track angle from its baseline value.
2. The method for controlling the decoupling between the pitching attitude and the track angle of an aircraft based on the backstepping method as claimed in claim 1, wherein the equation of motion related to the aircraft angle of attack is a first order differential equation related to the aircraft angle of attack α, which is obtained by relating to the aircraft inertial angle of attack α I Deriving a first order differential equation;
in a symmetric flight state in the vertical plane and no wind, the first order differential equation about the aircraft attack angle alpha is expressed as:
wherein the thrust acting direction is along the longitudinal axis of the machine body, and the thrust installation angle and the eccentricity are both zero; the airspeed v of the aircraft is equal to the ground speed v of the aircraft I (ii) a The first order differential of the pitch angle rate q is:
m represents the pitching moment applied to the aircraft, I y Representing the pitch moment of inertia.
3. The method for controlling decoupling of aircraft pitch attitude and track angle based on back stepping as claimed in claim 2, wherein said establishing a mathematical model suitable for designing a back stepping control law of aircraft angle of attack comprises:
make the reverse control law u equal to M/I y Obtaining:
wherein, the black point at the top of the variable is a first order differential symbol;
establishing a mathematical model suitable for designing a reverse control law of the aircraft attack angle, wherein the mathematical model is expressed as follows:
4. the backstepping-based aircraft pitch attitude and track angle decoupling control method as claimed in claim 1, characterized in that the method further comprises: the improved airplane angle of attack backstepping control law is converted into a form suitable for a linear model, and is expressed as follows:
wherein, mu α 、μ q 、
μ e 、μ c Both longitudinal stability and steering derivatives are related to the aircraft pitching moment; c. C 1 And c 2 Are all undetermined parameters; delta e And delta c Respectively representing an elevator deflection angle and a canard wing deflection angle; alpha is the aircraft angle of attack, the first order differential of which is
q represents a pitch angular velocity; Δ represents the deviation of the corresponding physical quantity from its reference value.
5. The method for controlling decoupling of aircraft pitch attitude and track angle based on back stepping method according to claim 1, wherein the step response performance of the aircraft angle of attack is optimized, and the determining of the value of the parameter to be determined in the improved aircraft angle of attack back stepping control law comprises:
and (3) optimizing the step response performance of the aircraft angle of attack by using a first software program so as to automatically optimize undetermined parameters in the backstepping control law of the aircraft angle of attack: setting the value range of the undetermined parameter and the performance requirement of airplane attack angle step response in a software program; and automatically optimizing the parameters through software to meet the set performance requirement, then gradually improving the performance requirement, and continuously performing parameter self-optimization until the step response performance is improved to the extent that the parameter optimization cannot be met, so that the optimal configuration condition of undetermined parameters in the aircraft angle of attack backstepping control law can be determined, and the parameter optimization work is finished.
6. The method of claim 1, wherein the optimizing the track angle control law parameters such that the track angle remains unchanged after the aircraft angle of attack is adjusted comprises:
when optimizing the flight path angle control law parameters of the airplane, the incidence angle control law parameter values which are determined by optimization before are not changed; the optimization aim is to keep the flight path angle unchanged after the system responds to the aircraft attack angle step instruction; the optimization process is achieved by having the track angle response track a specified reference signal, using a second software program as an auxiliary tool, in which the reference signal is set as a function of a constant value of 0 over a set period of time.
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