CN115859461A - Longitudinal controllable domain and stability analysis method for low-speed fixed wing unmanned aerial vehicle - Google Patents

Abstract

The invention discloses a longitudinal controllable domain and a stability analysis method of a low-speed fixed-wing unmanned aerial vehicle, including: determining the expected working range of the angle of attack and track inclination; Trim elevator deflection, trim airspeed and trim thrust; with the angle of attack as the horizontal axis and the track inclination as the vertical axis, the trim elevator deflection, trim airspeed and trim thrust are expressed in the form of contour distribution, and the full state trim equality Highline distribution diagram; introduce aircraft performance constraints and control constraints in the full-state trim equal-height distribution diagram to obtain the controllable area; select the desired operating point in the controllable area, and calculate the speed and angle of attack changes in the neighborhood of the operating point According to the trend, the phase diagram of speed angle of attack is obtained, and the stability of the working point is judged by the phase diagram of speed angle of attack. The invention is applied in the technical field of unmanned aerial vehicles, and has the advantages of low complexity in solving the balance, strong intuition of result display, high application analysis efficiency, and the like.

Description

A longitudinal controllable domain and stability analysis method for low-speed fixed-wing UAV

technical field

The invention relates to the technical field of unmanned aerial vehicles, in particular to a longitudinal controllable domain and stability analysis method of a low-speed fixed-wing unmanned aerial vehicle.

Background technique

In the field of aircraft design and application, the flight envelope represents the flight performance to a certain extent, while in the design process of the UAV control system, more attention is paid to the stability of the equilibrium state and the controllability. The calculation of the equilibrium state is usually called trimming. The current trimming method is generally to determine the flight airspeed and track inclination at the target operating point, and further calculate the corresponding trimming angle of attack, elevator deflection and thrust through an iterative method. This method has the disadvantages of severe coupling and low solution efficiency, and the stability cannot be directly judged, so it needs to further use small disturbance linearization or pole distribution methods to increase the computational complexity.

In addition, during the autonomous landing process of the UAV, it is usually divided into stages such as unpowered descent, drifting and sliding. Control objectives include altitude, speed, sink rate and aircraft attitude. Among them, the sinking rate is related to the speed, and will further affect the height change, and there is a coupling and constraint relationship between the three. In the design of conventional control methods, the focus is on whether the target state is reachable and stable, and the state transition process and the balance constraint relationship between target states are often ignored. There is a lack of intuitive formulas or charts for explicit analysis of the state transition process, which will affect the actual state. Flight control effects.

To sum up, the traditional UAV control characteristics, stability analysis and control method design process have certain defects in the application, and it is difficult to meet the actual needs.

Contents of the invention

Aiming at the technical defects in the design process of the existing UAV control method, the present invention provides a low-speed fixed-wing UAV longitudinal controllable domain and stability analysis method, which has the advantages of low coupling degree, efficient solution, and strong intuitiveness of diagrams, etc. advantage.

In order to achieve the above object, the present invention provides a low-speed fixed-wing UAV longitudinal controllable domain and stability analysis method, including the following steps:

Step 1, determine the expected working range of UAV angle of attack and track inclination state;

Step 2, traversing the expected working range of the angle of attack and track inclination, and substituting the expected value of the angle of attack and track inclination into the trim calculation to obtain the trim elevator deflection, trim airspeed and trim thrust;

Step 3, taking the angle of attack as the horizontal axis and the track inclination as the vertical axis, express the trim elevator deflection, trim airspeed and trim thrust in the form of contour distribution, and obtain the trim contour distribution diagram of the whole state;

Step 4. Introduce aircraft performance constraints and control constraints in the full-state trim contour distribution diagram to obtain the controllable domain of the UAV;

Step 5: Select the expected operating point of the UAV in the controllable area, calculate the change trend of velocity and angle of attack in the neighborhood of the expected operating point, obtain the velocity angle of attack phase diagram, and judge the expected operating point through the velocity angle of attack phase diagram Stability, specifically: in the speed angle-of-attack phase diagram, the angle of attack and speed changes near a certain trim state are represented in the form of a trend line with arrows, and the stability of the trim state can be further judged according to the trend characteristics.

Compared with the prior art, the present invention has the following beneficial technical effects:

1. In the process of fast calculation of the trim state, the present invention avoids the coupling problem of the lift coefficient, drag coefficient and pitching moment coefficient caused by the simultaneous change of the angle of attack and the elevator deflection by adjusting the calculation sequence of the trim state, greatly reducing the The complexity of solving a single trim state is reduced, and the calculation efficiency of full state trim is improved;

2. In the present invention, in the process of determining the controllable region based on the full-state trim contour distribution diagram, the trim state and distribution within the flight envelope range are displayed in a visualized form, which intuitively shows the control condition constraints of the UAV The distribution of the controllable domain under the controllable domain, by selecting the required operating point and the state of the transfer process in the controllable domain, the smooth transition of the control process can be realized, and the poor tracking accuracy and degradation caused by the instruction not satisfying the balance constraints in the actual control process can be avoided. problems such as speed and difficulty;

3. In the process of stability analysis based on the angle-of-attack-velocity phase diagram, the present invention expresses the angle-of-attack and speed changes near a certain trim state in the form of a trend line with arrows, intuitively reflecting the state of the trim state. Stability, and through the stability analysis, the control law design of the operating point can be adjusted accordingly, and finally the stable control near the equilibrium operating point can be realized.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained according to the structures shown in these drawings without creative effort.

Fig. 1 is a flow chart of the longitudinal controllable domain and stability analysis method of a low-speed fixed-wing unmanned aerial vehicle in an embodiment of the present invention;

Fig. 2 is the distribution map of the controllable domain contour obtained for the characteristics of a certain unmanned aerial vehicle in the embodiment of the present invention;

Fig. 3 is an angle-of-attack phase diagram obtained for points S1 and S2 in Fig. 2 in an embodiment of the present invention.

The realization of the purpose of the present invention, functional characteristics and advantages will be further described in conjunction with the embodiments and with reference to the accompanying drawings.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

It should be noted that all directional indications (such as up, down, left, right, front, back...) in the embodiments of the present invention are only used to explain the relationship between the components in a certain posture (as shown in the accompanying drawings). Relative positional relationship, movement conditions, etc., if the specific posture changes, the directional indication will also change accordingly.

In addition, the technical solutions of the various embodiments of the present invention can be combined with each other, but it must be based on the realization of those skilled in the art. When the combination of technical solutions is contradictory or cannot be realized, it should be considered as a combination of technical solutions. Does not exist, nor is it within the scope of protection required by the present invention.

This embodiment discloses a method for analyzing the longitudinal controllable domain and stability of a low-speed fixed-wing UAV. Referring to FIG. 1 , it specifically includes the following steps 1-5.

Step 1, according to the design flight performance of the UAV, determine the expected working range of the UAV's angle of attack and track inclination;

Step 2, traversing the expected working range of the angle of attack and track inclination, and substituting the expected value of the angle of attack and track inclination into the trim calculation to obtain the trim elevator deflection, trim airspeed and trim thrust, wherein the specific implementation of the trim calculation is:

Step 2.1, obtaining the lift coefficient, drag coefficient and pitching moment coefficient of the UAV with the angle of attack and the variation of the elevator deflection;

Step 2.2, establish the force and moment balance equations of aerodynamic force, gravity and engine thrust, which are:

In the formula, Q is the dynamic pressure, the airspeed is implied in the dynamic pressure Q, S is the wetted area of the UAV wing, γ is the track inclination, T is the thrust, C _L (α, δ _e ), C _D ( α, δ _e ), C _m (α, δ _e ) are the lift coefficient, drag coefficient, and pitch moment coefficient of the UAV determined in step 2.1, and C _L (α, δ _e ), C _D (α, δ _e ), C _m (α, δ _e ) are related to the UAV’s angle of attack α and elevator deflection δ _e ;

Step 2.3, define the angle of attack and track inclination of the trim state based on the expected working range of the UAV’s angle of attack and track inclination, and use the gradient descent method to solve the equation through the third formula of the balance equation group in formula (1). The current trim angle of attack corresponds to the elevator deflection, and the iteration formula is:

δ _e (k+1)＝δ _e (k)+μ(0-C _m (α _trim ,δ _e (k))) (2)

In the formula, δ _e (k+1) is the elevator deflection of the k+1 iteration, δ _e (k) is the elevator deflection of the k iteration, μ is the iteration coefficient, which is used to adjust the iteration convergence characteristics, and α _trim is Angle of attack in trim state;

In step 2.4, substitute the angle of attack and track inclination of the trim state and the elevator deflection obtained in step 2.3 into the second equation of the balance equation group in equation (1) to obtain the trim airspeed, which is:

In the formula, V _a,trim is the trim airspeed, θ _trim is the pitch angle of the trim state, ρ is the air density, m is the mass of the drone, g is the acceleration of gravity, C _D,trim is the drag coefficient of the trim state, C _{L, trim} is the lift coefficient in the trim state;

In step 2.5, substitute the angle of attack and track inclination in the trim state, the elevator deflection obtained in step 2.3, and the trim airspeed obtained in step 2.4 into the first equation of the balance equation group in equation (1) to obtain the trim thrust, which is:

In the formula, T _trim is the trim thrust.

Step 3, taking the angle of attack as the horizontal axis and the track inclination as the vertical axis, express the trim elevator deflection, trim airspeed, and trim thrust in the form of contour distribution, and obtain the full-state trim contour distribution map, specifically:

On the basis of the trim calculation in step 2, iteratively calculate the trim elevator deflection, airspeed and engine thrust state corresponding to different trim angles of attack and track inclination within the expected working range, and then take the angle of attack as the abscissa and the track inclination as the ordinate , draw the contour line distribution of trim airspeed, engine thrust, elevator deflection and corresponding pitch angle, that is, obtain the contour line distribution diagram of full state trim. In the full-state trim contour distribution diagram, the angle of attack, track inclination, airspeed, elevator deflection, engine thrust, and pitch angle corresponding to a certain point are in the same group of trim states.

Step 4. Introduce aircraft performance constraints and control constraints in the full-state trim contour distribution diagram to obtain the controllable domain of the UAV, specifically:

In the full-state trim contour distribution diagram, determine the area from the zero thrust contour line to the maximum thrust contour line, the elevator deflection limited area, and the non-negative airspeed area. The intersection of the three areas is the possible UAV. The control domain can further design the smooth transition process of different states in the figure.

Step 5: Select the expected operating point of the UAV in the controllable area, calculate the change trend of velocity and angle of attack in the neighborhood of the expected operating point, obtain the velocity angle of attack phase diagram, and judge the expected operating point through the velocity angle of attack phase diagram Stability, the specific implementation process is:

Step 5.1, select the expected operating point of the UAV in the full-state trim contour distribution diagram, and limit the thrust and pitch angle of the operating point;

Step 5.2, establish the dynamic differential equation of angle of attack and velocity, which is:

In the formula, V _a is the speed of the UAV, α is the angle of attack of the UAV, D is the resistance, θ _c is the pitch angle corresponding to the desired working point, T _c is the thrust corresponding to the desired working point, and L is the lift force; Substituting the thrust and the pitch angle of the expected working point of the drone into the differential equation of dynamics in step 5.1, traversing the airspeed at the expected working point of the calculation drone and the rate of change in the neighborhood of the angle of attack;

Step 5.3, obtain the angle-of-attack phase diagram according to the airspeed at the UAV's expected operating point and the rate of change in the neighborhood of the angle of attack, and judge the stability of the UAV's expected operating point in step 5.1 through the angle-of-attack phase diagram.

Figure 2 is the full-state trim contour distribution diagram calculated according to the characteristics of a UAV. In Fig. 2, the thick solid line represents the trim thrust contour distribution, the vertical dashed line represents the velocity distribution, and the vertical thin solid line represents the trim rudder deflection angle, and the oblique dotted line represents the pitch angle. The limit of control rudder deviation is plus or minus 30 degrees. In Figure 2, the rudder deviation is distributed within the limit range, so the area between the zero thrust line and the maximum thrust line is the controllable area. In Figure 2, the velocity contour distribution becomes sparse with the increase of the angle of attack, and in the Y-shaped area surrounded by the 11m/s and 10m/s velocity lines, the velocity changes little but the angle of attack changes greatly, so in this area The trim state is more sensitive to speed changes.

Select points S1 and S2 in Figure 2 as the expected operating points, that is, limit the thrust and pitch angle, calculate the change trend of velocity and angle of attack in the nearby area, and obtain the angle-of-attack-velocity phase diagram for the S1 and S2 states shown in Figure 3. The trend changes in Figure 3 can be intuitively judged that the S1 operating point is an unstable saddle point, and the S2 state is a stable focus.

The above is only a preferred embodiment of the present invention, and does not therefore limit the patent scope of the present invention. Under the inventive concept of the present invention, the equivalent structural transformation made by using the description of the present invention and the contents of the accompanying drawings, or direct/indirect use All other relevant technical fields are included in the patent protection scope of the present invention.

Claims (7)

1. A longitudinal controllable domain and stability analysis method for a low-speed fixed wing unmanned aerial vehicle is characterized by comprising the following steps:

step 1, determining expected working ranges of an attack angle and a track inclination angle state of an unmanned aerial vehicle;

step 2, traversing the expected working ranges of the states of the attack angle and the track inclination angle, and substituting the expected values of the attack angle and the track inclination angle into balancing calculation to obtain the deviation of the balancing elevator, the balancing airspeed and the balancing thrust;

step 3, with the attack angle as a horizontal axis and the track inclination angle as a vertical axis, expressing the trim elevator deflection, the trim airspeed and the trim thrust in a contour line distribution mode to obtain an all-state trim contour line distribution diagram;

step 4, introducing aircraft performance constraint and control constraint conditions into the full-state trim contour distribution map to obtain a controllable domain of the unmanned aerial vehicle;

and 5, selecting an expected working point of the unmanned aerial vehicle in the controllable domain, calculating the speed and attack angle change trend in the neighborhood of the expected working point to obtain a speed attack angle phase diagram, and judging the stability of the expected working point through the speed attack angle phase diagram.

2. The method for analyzing the longitudinal controllable domain and stability of the low-speed fixed-wing drone of claim 1, wherein in step 2, the trim calculation is specifically:

step 2.1, obtaining the change conditions of the lift coefficient, the resistance coefficient and the pitching moment coefficient of the unmanned aerial vehicle along with the change conditions of the attack angle and the elevator deviation;

step 2.2, establishing a balance equation set of force and moment of aerodynamic force, gravity and engine thrust, which comprises the following steps:

in the formula, Q is dynamic pressure, S is wing infiltration area of the unmanned aerial vehicle, gamma is track inclination angle, T is thrust, and C is _L (α，δ _e ) Lift coefficient for unmanned aerial vehicles, C _D (α，δ _e ) Coefficient of resistance for unmanned aerial vehicle, C _m (α，δ _e ) Is the pitching moment coefficient of the unmanned aerial vehicle, C _L (α，δ _e )、C _D (α，δ _e )、C _m (α，δ _e ) Are both offset by delta from the angle of attack alpha and the elevator of the unmanned aerial vehicle _e Correlation;

step 2.3, limiting the attack angle and the track inclination angle of the trim state, and obtaining the elevator deviation corresponding to the current trim attack angle by applying a gradient descent method through a third formula of the balance equation set, wherein the third formula comprises the following steps:

δ _e (k+1)＝δ _e (k)+μ(0-C _m (α _trim ,δ _e (k)))

in the formula, delta _e (k + 1) is the elevator yaw, δ, of the (k + 1) th iteration _e (k) The elevator deflection is the k iteration, mu is the iteration coefficient and is used for adjusting the iteration convergence characteristic, alpha _trim Angle of attack for trim state;

step 2.4, substituting the incidence angle, the track inclination angle and the corresponding elevator deflection in the trim state into a second formula of the balance equation set to obtain the trim airspeed;

and 2.5, substituting the incidence angle and the track inclination angle of the trim state, the corresponding elevator deflection and the trim airspeed into the first equation of the balance equation set to obtain trim thrust.

3. The method for analyzing the longitudinal controllable domain and stability of the low-speed fixed-wing drone of claim 2, wherein in step 2.4, the trim airspeed is:

in the formula, V _a,trim To trim airspeed, [ theta ] _trim For trim state pitch angle, ρ is air density, m is unmanned aerial vehicle mass, g is gravitational acceleration, C _D,trim To trim state drag coefficient, C _L,trim The lift coefficient is the trim state.

4. The method for analyzing the longitudinal controllable domain and stability of the low-speed fixed-wing drone of claim 3, wherein in step 2.5, the trim thrust is:

in the formula, T _trim To trim the thrust.

5. The method for analyzing the longitudinal controllable domain and stability of the low-speed fixed-wing unmanned aerial vehicle according to any one of claims 1 to 4, wherein the step 4 specifically comprises:

and determining the intersection part of the zero thrust contour line to the maximum thrust contour line region, the elevator deflection limiting region and the airspeed non-negative region in the all-state trim contour line distribution diagram, namely the controllable region of the unmanned aerial vehicle.

6. The method for analyzing the longitudinal controllable domain and stability of the low-speed fixed-wing unmanned aerial vehicle according to any one of claims 1 to 4, wherein the step 5 is specifically as follows:

step 5.1, selecting an expected working point of the unmanned aerial vehicle in the full-state trim contour distribution diagram, and limiting the thrust and pitch angle of the working point;

step 5.2, establishing a dynamics differential equation of an attack angle and a speed, substituting the thrust and the pitch angle of the working point expected by the unmanned aerial vehicle in the step 5.1 into the dynamics differential equation, and traversing and calculating the airspeed and the change rate in the neighborhood of the attack angle of the unmanned aerial vehicle at the expected working point;

and 5.3, obtaining an attack angle velocity phase diagram according to the airspeed at the working point expected by the unmanned aerial vehicle and the change rate in the attack angle neighborhood, and judging the stability of the working point expected by the unmanned aerial vehicle in the step 5.1 according to the attack angle velocity phase diagram.

7. The method for analyzing the longitudinal controllable domain and stability of the low-speed fixed-wing unmanned aerial vehicle according to claim 6, wherein in step 5.2, the dynamic differential equations of the attack angle and the speed are as follows:

in the formula, V _a Is the speed of the unmanned aerial vehicle, alpha is the angle of attack of the unmanned aerial vehicle, D is the resistance, theta _c Pitch angle, T, corresponding to desired operating point _c For a thrust corresponding to the desired operating point, L is the lift.

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