Fixed wing vertical hovering control method adopting longitudinal periodic excitation

Abstract

The invention discloses a fixed-wing vertical hovering control method adopting longitudinal periodic excitation. The method comprises the following steps: firstly, establishing a flight mechanical model in a longitudinal plane of a fixed-wing unmanned aerial vehicle; deducing and simplifying the established flight mechanical model in the longitudinal plane of the fixed-wing unmanned aerial vehicle to obtain a simplified new flight mechanical model in the longitudinal plane of the unmanned aerial vehicle; analyzing the stability of the new flight mechanical model in the longitudinal plane of the unmanned aerial vehicle; and verifying the new flight mechanical model in the longitudinal plane of the unmanned aerial vehicle through the periodic excitation parameters. According to the method for enhancing the attitude stability of the fixed-wing unmanned aerial vehicle in the vertical hovering state by applying longitudinal periodic excitation, a flight mechanical model in a longitudinal plane of the fixed-wing unmanned aerial vehicle is established, and the mechanical model is reasonably deduced and converted; the dynamic response of the fixed-wing unmanned aerial vehicle under longitudinal periodic excitation is analyzed, the attitude of the unmanned aerial vehicle is effectively controlled, and the operation safety and stability are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle control, and particularly relates to a fixed-wing vertical hovering control method using longitudinal periodic excitation. Background Art

[0002] During the flight of a fixed-wing unmanned aerial vehicle, if its aerodynamic center is below the center of gravity in the vertical state, it is in an unstable state, and the effect of the aerodynamic control surface is very limited during hovering or descending, and it is often affected by external disturbances such as crosswinds, resulting in difficulty in maintaining a stable attitude. Therefore, in order to improve the flight stability and safety, this problem urgently needs to be solved. Summary of the Invention

[0003] Object of the Invention: To overcome the above deficiencies, the object of the present invention is to provide a fixed-wing vertical hovering control method using longitudinal periodic excitation, a method for enhancing the attitude stability of a fixed-wing unmanned aerial vehicle in the vertical hovering state by applying longitudinal periodic excitation. This method establishes a flight mechanics model in the longitudinal plane of the fixed-wing unmanned aerial vehicle, reasonably derives and transforms the mechanics model, analyzes the dynamic response of the fixed-wing unmanned aerial vehicle when subjected to longitudinal periodic excitation, thereby realizing the effective control of the unmanned aerial vehicle attitude and improving its operation safety and stability.

[0004] Technical Solution: To achieve the above object, the present invention provides a fixed-wing vertical hovering control method using longitudinal periodic excitation, including: S1): First, establish a flight mechanics model in the longitudinal plane of the fixed-wing unmanned aerial vehicle; S2): Derive and simplify the flight mechanics model in the longitudinal plane of the fixed-wing unmanned aerial vehicle established in S1) to obtain a new simplified flight mechanics model in the longitudinal plane of the unmanned aerial vehicle; S3): Analyze the stability of the new flight mechanics model in the longitudinal plane of the unmanned aerial vehicle obtained in S2); S4): Verify the new flight mechanics model in the longitudinal plane of the unmanned aerial vehicle through the periodic excitation parameters.

[0005] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in the present invention, the establishment of the flight mechanics model in the longitudinal plane of the fixed-wing unmanned aerial vehicle in S1) is specifically as follows: Assume that the fixed-wing unmanned aerial vehicle moves in the longitudinal plane, ignoring the influence of lateral movement and roll and yaw, and only considering the following variables: : The angle of the aircraft longitudinal axis relative to the vertical plane; : Pitch angular velocity; : Pitch angular acceleration; T: Propeller thrust G: Gravity of the UAV; m: Mass of the UAV; g: Acceleration due to gravity; I: Moment of inertia of the UAV; M: Resultant moment Only considering that the UAV maintains attitude stability, that is, it does not rotate or rotates within a small angle, and not considering the linear drift of the UAV. Assuming the mechanical model of the UAV is the rotation of a rigid body around the center of mass, The flight mechanical model in the longitudinal plane of the UAV is: where I is the moment of inertia of the UAV, is the pitch angular acceleration, and M is the resultant moment; When the gravity and aerodynamic drag both pass through the center of gravity of the UAV, no pitching moment is generated. Only considering the influence of the periodic change of the propeller power, that is, the longitudinal excitation, so the control surface is forced not to deflect. At this time, the pitching moment caused by the control surface is also 0; Assuming that the propeller thrust passes through the center of gravity of the UAV, then the propeller thrust does not provide a pitching moment at this time; when the aircraft hovers in this state, the flight speed is almost 0, so there is no lift generated by the relative airflow during flight, and there is no aerodynamic moment generated by the relative airflow either: Then: where, where, is the aerodynamic moment caused by the lift generated by the wing in the slipstream area, is the moment caused by wind disturbance, is the lift generated by the wing in the slipstream area, and d is the perpendicular distance from the action line of the lift generated by the wing in the slipstream area to the center of gravity.

[0006] In the fixed-wing vertical hover control method using longitudinal periodic excitation described in the present invention, when the UAV is located in the slipstream area, the lift generated by its wing is mainly related to the propeller thrust, wetted area, propeller area and aerodynamic coefficient. For any wing, the lift L generated by the wing in the propeller slipstream area can be given by the classical formula: , where: is the air density, is the effective flow velocity on the wing, which mainly comes from the propeller slipstream here.

[0007] S is the effective wing area in the slipstream area, is the lift coefficient of the wing; The velocity model on the wing behind the propeller is: Among them, T is the propeller thrust; A is the propeller disc area; Substituting the velocity model into the lift formula and arranging, we can get: , Among them, L is the lift generated by the wing in the propeller slipstream; S is the wing area affected by the propeller slipstream; Among them, a periodic change is applied to the propeller thrust, and it is defined as: , Among them, is the basic propeller thrust, , Among them, G is the gravity of the UAV; m is the mass of the UAV; g is the acceleration due to gravity; is the pitch angular acceleration; I is the moment of inertia of the UAV; is the introduced parameter, and its physical meaning is the amplitude of the change in the propeller pull; When wind disturbance is not considered, the above formula can be transformed into: Normalize the above formula Let , , ; Then the above formula is transformed into Introduce a term with zero mean: Finally, the following equation is obtained: In the formula, and are parameters. There is theoretical research that when the parameters and take certain values, the system will be in a stable state.

[0008] In the fixed-wing vertical hover control method using longitudinal periodic excitation described in the present invention, the process of verifying the new flight mechanics model of the UAV in the longitudinal plane through the periodic excitation parameters in the S4) is as follows: The equation is solved by the singular perturbation method; According to Floquet theory, for any linear differential equation with periodic coefficients, there exists a transition curve that The plane is divided into stable and unstable regions, and the transition curve occurs when the period of the solution of the equation is or ; along the transition curve, at least one solution of the equation is periodic with period or ; Expand the solution of the equation and the parameter into power series of : Substitute them into the original equation and arrange according to the degree of to get (1) (2) (3) …… To ensure that the period is or , there can only be ; Let From the differential formula (1), it is known that it has two linearly independent particular solutions and ; Let , where is a constant. Substitute it into formula (2) to get (4) To eliminate the secular terms, it is necessary to satisfy The first-order periodic solution of formula (4) is Substitute it into formula (3) to get (5); To eliminate the secular terms, it is necessary to satisfy Therefore, the second-order periodic solution of formula (5) is Therefore, the periodic solution of the original equation is The corresponding transition curve is Therefore, the stability diagram can be drawn according to the values of , .

[0009] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in the present invention, within the system, , wherein, , For a determined unmanned aerial vehicle (UAV), the parameter can be approximately regarded as determined by the parameters of the UAV itself. At this time, When , it can be known that the variable affecting the stability of the system is mainly related to the parameter b, that is, the amplitude b of the periodic change of the thrust determines whether the system can maintain stability.

[0010] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in the present invention, according to the stability map, when is determined, the value range of that can make the system stable can always be obtained. At this time, for it can always make the UAV system maintain stability when hovering in the vertical state.

[0011] From the above technical solutions, the present invention has the following beneficial effects: A fixed-wing vertical hovering control method using longitudinal periodic excitation described in the present invention is a method for enhancing the attitude stability of a fixed-wing UAV in the vertical hovering state by applying longitudinal periodic excitation. This method establishes a flight mechanics model in the longitudinal plane of the fixed-wing UAV, and reasonably deduces and transforms the mechanics model, analyzes the dynamic response of the fixed-wing UAV when receiving longitudinal periodic excitation, so as to realize the effective control of the UAV attitude and improve the safety and stability of its operation.

[0012] 2. By making the thrust of the UAV change periodically in the present invention, a pitch restoring moment can be provided to the UAV to a certain extent, so as to offset the small disturbances in the face of gusts and other situations, and further improve its controllability, flight safety and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a schematic structural diagram of the fixed-wing vertical hovering control method using longitudinal periodic excitation described in the present invention; Figure 2 is the stability map in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0014] The present invention will be further clarified below with reference to the drawings and specific embodiments. Embodiment

[0015] Such as Figure 1 A fixed-wing vertical hovering control method using longitudinal periodic excitation as shown, comprising: S1): First, establish a flight mechanics model of the fixed-wing UAV in the longitudinal plane; S2): Derive and simplify the flight mechanics model of the fixed-wing UAV in the longitudinal plane established in S1) to obtain a new simplified flight mechanics model of the UAV in the longitudinal plane; S3): Analyze the stability of the new flight mechanics model of the UAV in the longitudinal plane obtained in S2); S4): Verify the new flight mechanics model of the UAV in the longitudinal plane through the periodic excitation parameters.

[0016] For the fixed-wing vertical hovering control method using longitudinal periodic excitation described in this embodiment, the specific method for establishing the flight mechanics model of the fixed-wing UAV in the longitudinal plane in S1) is as follows: Assume that the fixed-wing UAV moves in the longitudinal plane, ignoring the influence of lateral movement, roll, and yaw, and only considering the following variables: : The angle of the longitudinal axis of the aircraft relative to the vertical plane; : Pitch angular velocity; : Pitch angular acceleration; T: Propeller thrust; G: Gravity of the UAV; m: Mass of the UAV; g: Acceleration due to gravity; I: Moment of inertia of the UAV; M: Resultant moment Only considering that the UAV maintains attitude stability, that is, does not rotate or rotates within a small angle, and not considering the linear drift of the UAV, assume that the mechanical model of the UAV is the rotation of a rigid body around the center of mass, The flight mechanics model of the fixed-wing UAV in the longitudinal plane is: Among them, I is the moment of inertia of the UAV, is the pitch angular acceleration, and M is the resultant moment; When the gravity and aerodynamic drag both pass through the center of gravity of the UAV and do not generate a pitching moment, only considering the influence of the periodic change of the propeller power, that is, the longitudinal excitation, so the control surface is forced not to deflect, and at this time the pitching moment caused by the control surface is also 0; Assume that the propeller thrust passes through the center of gravity of the UAV. In this case, the propeller thrust does not provide pitching moment either. When the aircraft hovers in this state, the flight speed is almost zero. Therefore, there is no lift generated by the relative airflow during flight, and there is also no aerodynamic moment generated by the relative airflow. Then: Wherein, Wherein, is the aerodynamic moment caused by the lift generated by the wing in the slipstream area, is the moment caused by wind disturbance, is the lift generated by the wing in the slipstream area, and d is the perpendicular distance from the action line of the lift generated by the wing in the slipstream area to the center of gravity.

[0017] In this embodiment, when the UAV is located in the slipstream area, the lift generated by its wing is mainly related to the propeller thrust, wetted area, propeller area and aerodynamic coefficient. For any wing, the lift L generated by the wing in the propeller slipstream area can be given by the classical formula: , Wherein: is the air density, is the effective flow velocity on the wing, which mainly comes from the propeller slipstream here.

[0018] S is the effective wing area in the slipstream area, is the lift coefficient of the wing; The velocity model on the wing behind the propeller is: Wherein, T is the propeller thrust; A is the propeller disk area; Substituting the velocity model into the lift formula and sorting it out, we can get: , Wherein, L is the lift generated by the wing in the propeller slipstream area; S is the wing area affected by the propeller slipstream; Wherein, a periodic change is applied to the propeller thrust, and it is defined as: , Wherein, is the basic propeller thrust, , Wherein, G is the gravity of the UAV; m is the mass of the UAV; g is the acceleration due to gravity; is the pitch angular acceleration; I is the moment of inertia of the UAV; is the introduced parameter, and its physical meaning is the amplitude of the change in propeller pull; When wind disturbances are not considered, the above equation can be transformed into: Normalize the above equation Let , , ; Then the above equation is transformed into Introduce a term with zero mean: Finally, the following equation is obtained: In the formula, and are parameters. There is theoretical research that when the parameters and take certain values, the system will be in a stable state.

[0019] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in this embodiment, the process of verifying the new flight mechanics model of the unmanned aerial vehicle in the longitudinal plane through the periodic excitation parameters in S4) is as follows: The equation is solved using the singular perturbation method; According to Floquet theory, for any linear differential equation with periodic coefficients, there exists a transition curve that divides the plane into a stable region and an unstable region, and the transition curve is generated when the period of the solution of the equation is or ; along the transition curve, at least one solution of the equation is periodic, with a period of or ; Expand the solution of the equation and the parameter into power series of : Substitute into the original equation and organize according to the order of , and there is (1) (2) (3) ...... To ensure that the period is or , there can only be ; Let From the differential formula (1), it is known that it has two linearly independent particular solutions and ; Let , is a constant Substituting into formula (2) gives (4) To eliminate the secular term, it is necessary to satisfy The first-order periodic solution of formula (4) is Substituting into formula (3) gives (5); To eliminate the secular term, it is necessary to satisfy Therefore, the second-order periodic solution of formula (5) is Therefore, the periodic solution of the original equation is The corresponding transition curve is Therefore, it is possible to draw a stability map according to , values.

[0020] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in this embodiment, within the system, , where , For a determined unmanned aerial vehicle, the parameter can be approximately regarded as determined by the parameters of the unmanned aerial vehicle itself. At this time When , it can be seen that the variable affecting the stability of the system is mainly related to the parameter b, that is, the amplitude b of the periodic change of the thrust determines whether the system can maintain stability.

[0021] In the actual operation process, according to the value of the actual aircraft, it is possible to select a suitable - in the stability map values, and then back-calculate to determine other parameters such as amplitude to stabilize the system; similarly, the amplitude can also be selected first to obtain a set of , values, and check whether they are in the stable region by comparing them in the - stability map.

[0022] According to the stability map as shown in Figure 2 , when is determined, the value range that can stabilize the system can be obtained. At this time, for it can always keep the UAV system stable when hovering in the vertical state.

[0023] The stability map is a graphical representation of the eigenvalues of the solutions of the equations based on two parameters , . The eigenvalues under different parameters are calculated according to the perturbation method and plotted in the parameter space. Figure 2 The gray shaded part in , indicates that the solution is stable, and the non-shaded part indicates that the solution is unstable. Therefore, by the two parameter

[0024] values of the real aircraft, find the corresponding eigenvalue position on the stability map to determine whether the applied longitudinal periodic excitation can stabilize the system.

[0025] The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A method for controlling a fixed-wing vertical hovering using longitudinal periodic excitation, characterized in that: include: S1): First, establish the flight mechanics model of the fixed-wing UAV in the longitudinal plane; S2): The fixed-wing UAV longitudinal plane flight mechanics model established in S1) is derived and simplified to obtain a simplified new UAV longitudinal plane flight mechanics model; S3): Analyze the stability of the new UAV longitudinal plane flight mechanics model obtained in S2); S4): The new UAV flight mechanics model in the longitudinal plane is verified by periodic excitation parameters.

2. The method for controlling a fixed-wing vertical hovering using longitudinal periodic excitation according to claim 1, characterized in that: The flight mechanics model of the fixed-wing UAV in the longitudinal plane established in S1) is as follows: Assume that the fixed-wing UAV moves in the longitudinal plane, ignore the effects of lateral movement and roll and yaw, and only consider the following variables: : The angle of the aircraft's longitudinal axis relative to the vertical plane; : pitch angular velocity; : pitch angle acceleration; T: propeller thrust; G: drone gravity; m: mass of the drone; g: acceleration due to gravity; I: moment of inertia of the drone; M: resultant moment; When only considering the drone to maintain a stable attitude, that is, not rotating or rotating within a small angle, and not considering the drone's linear drift, it is assumed that the drone's mechanical model is the rotation of a rigid body around the center of mass. The flight mechanics model of the UAV in the longitudinal plane is: Where I is the moment of inertia of the drone, is the pitch angular acceleration, M is the resultant moment; When both gravity and aerodynamic drag pass the center of gravity of the drone, no pitching moment is generated. Only the influence of the propeller power cycle change, i.e., the longitudinal excitation, is considered. Therefore, the rudder is forced not to deflect. At this time, the pitching moment caused by the rudder is also 0. Assuming that the propeller thrust exceeds the center of gravity of the drone, the propeller thrust does not provide a pitch moment at this time; when the aircraft is hovering in this state, the flight speed is almost 0, so there is no lift generated by the relative airflow during flight, and there is also no aerodynamic torque generated by the relative airflow: Then: in, in, is the aerodynamic moment caused by the lift generated by the wing in the slipstream area, is the torque caused by wind disturbance, is the lift generated by the wing in the slipstream area, and d is the vertical distance from the line of action of the lift generated by the wing in the slipstream area to the center of gravity.

3. The method for controlling a fixed-wing vertical hovering using longitudinal periodic excitation according to claim 2, characterized in that: When the UAV is in the slipstream area, the lift generated by its wing is mainly related to the propeller thrust, wetted area, propeller area and aerodynamic coefficient. For any wing, the lift L generated by the wing in the propeller slipstream area can be given by the classic formula: ， in: is the air density, is the effective flow velocity on the wing, which mainly comes from the propeller slipstream; S is the effective wing area in the slipstream region, is the lift coefficient of the wing; The velocity model on the wing behind the propeller is: Where, T is propeller thrust; A is propeller disc area; Substituting the velocity model into the lift formula, we can get: ， Where, L is the lift generated by the wing in the propeller slipstream area; S is the wing area affected by the propeller slipstream; Among them, the propeller thrust is given a periodic change, defined as: ， in, is the propeller basic thrust, , Among them, G is the gravity of the drone; m is the mass of the drone; g is the acceleration due to gravity; is the pitch angular acceleration; I is the moment of inertia of the drone; is the introduced parameter, and its physical meaning is the amplitude of propeller thrust change; When wind disturbance is not considered, the above formula can be transformed into: Standardize the above formula make , , ; The above formula is transformed into Introduce a term with zero mean: Finally, we get the following equation: In the formula, and is a parameter. This equation has been theoretically studied. and When certain values ​​are achieved the system will be in a stable state.

4. The method for controlling a fixed-wing vertical hovering using longitudinal periodic excitation according to claim 3, characterized in that: The process of verifying the new UAV longitudinal plane flight mechanics model by periodic excitation parameters in S4) is as follows: The equation is solved by singular perturbation method; According to Floquet theory, any linear differential equation with periodic coefficients has a transition curve. The plane is divided into stable and unstable regions, and the transition curve is the period of the solution of the equation or When the transition curve is generated, at least one solution of the equation is periodic, with period or ; Solve the equation and parameters Expand into The power series of : Substitute into the original equation and press The number of times is sorted, there are （1） （2） （3） …… To ensure that the cycle is or , there can only be ; make From the differential formula (1), we know that it has two linearly independent special solutions: and ; make ,in, is a constant; Substituting into formula (2) we get （4） In order to eliminate the duration term, The first-order periodic solution of formula (4) is Substituting into formula (3) we get （5）； In order to eliminate the duration term, Therefore, the second-order periodic solution of formula (5) is: Therefore, the periodic solution of the original equation is: The corresponding transition curve is: Therefore, according to , Draw a stability diagram based on the values ​​of .

5. The method for controlling a fixed-wing vertical hovering using longitudinal periodic excitation according to claim 4, characterized in that: In the system, , in, , For a given drone, the parameters It is approximately determined by the parameters of the drone itself. when It can be seen that the variables that affect whether the system is stable are mainly related to parameter b, that is, the amplitude b of the thrust cycle change determines whether the system can remain stable.

6. The method for controlling a fixed-wing vertical hovering using longitudinal periodic excitation according to claim 5, characterized in that: According to the stability diagram, when When the system is determined, we can always get Value range, at this time for It can always keep the drone system stable when hovering in a vertical state.

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