A fixed-wing vertical hover control method using longitudinal periodic excitation

Abstract

The present invention discloses a method for controlling a fixed-wing vertical hovering aircraft using longitudinal periodic excitation, comprising: first establishing a flight mechanics model for a fixed-wing UAV in the longitudinal plane; deducing and simplifying the established flight mechanics model for the fixed-wing UAV in the longitudinal plane to obtain a simplified new flight mechanics model for the UAV in the longitudinal plane; analyzing the stability of the new flight mechanics model for the UAV in the longitudinal plane; and verifying the new flight mechanics model for the UAV in the longitudinal plane using periodic excitation parameters. The present invention enhances the attitude stability of a fixed-wing UAV in a vertical hovering state by applying longitudinal periodic excitation. The method establishes a flight mechanics model for the fixed-wing UAV in the longitudinal plane, rationally derives and transforms the mechanics model, and analyzes the dynamic response of the fixed-wing UAV when subjected to longitudinal periodic excitation, thereby achieving effective control of the UAV's attitude and improving operational safety and stability.

Description

Technical Field

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

[0002] During flight, fixed-wing drones are unstable if their aerodynamic center is below their center of gravity when in an upright position. Furthermore, the effectiveness of their aerodynamic control surfaces is very limited when hovering or descending, and they are often affected by external disturbances such as crosswinds, making it difficult for them to maintain a stable attitude. Therefore, in order to improve flight stability and safety, this problem urgently needs to be addressed. Summary of the Invention

[0003] Purpose of the invention: In order to overcome the above shortcomings, the purpose 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 UAV in a 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 derives and transforms the mechanics model, analyzes the dynamic response of the fixed-wing UAV when subjected to longitudinal periodic excitation, thereby achieving effective control of the UAV's attitude and improving its operation safety and stability.

[0004] Technical Solution: To achieve the above objectives, the present invention provides a method for controlling a fixed-wing vertical hover using longitudinal periodic excitation, comprising:

[0005] S1): First, establish a flight dynamics model of the fixed-wing UAV in the longitudinal plane;

[0006] S2): deriving and simplifying the fixed-wing UAV longitudinal plane flight dynamics model established in S1) to obtain a simplified new UAV longitudinal plane flight dynamics model;

[0007] S3): Analyze the stability of the new UAV longitudinal plane flight dynamics model obtained in S2);

[0008] S4): Verify the new UAV longitudinal plane flight dynamics model using periodic excitation parameters.

[0009] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in the present invention, the flight dynamics model of the fixed-wing UAV in the longitudinal plane established in S1) is specifically as follows:

[0010] Assuming that the fixed-wing UAV moves in the longitudinal plane, ignoring the effects of lateral motion and roll and yaw, only the following variables are considered:

[0011] θ: the angle of the aircraft's longitudinal axis relative to the vertical plane;

[0012] Pitch angular velocity;

[0013] Pitch angular acceleration;

[0014] T: propeller thrust;

[0015] G: drone gravity;

[0016] m: mass of the drone;

[0017] g: acceleration due to gravity;

[0018] I: UAV’s moment of inertia;

[0019] M: Resultant moment

[0020] Only consider the UAV to maintain a stable attitude, that is, not turning or turning within a small angle;

[0021] When the linear drift of the UAV is not considered, the mechanical model of the UAV is assumed to be the rotation of a rigid body around its center of mass;

[0022] The flight dynamics model of the UAV in the longitudinal plane is:

[0023]

[0024] Where, I is the moment of inertia of the UAV, is the pitch angular acceleration, M is the resultant moment;

[0025] When the lines of action of gravity and aerodynamic drag pass through the center of gravity of the drone, no pitching moment is generated. Only the influence of the propeller power cycle change, that is, the longitudinal excitation, is considered. Therefore, the rudder is forced not to deflect, and the pitching moment caused by the rudder is also 0.

[0026] Assuming the propeller thrust line passes through the center of gravity of the drone, the propeller thrust does not provide any pitching torque. In this state, when the aircraft is hovering, the flight speed is almost zero, so there is no lift generated by the relative airflow during flight, and there is also no aerodynamic torque generated by the relative airflow:

[0027] but:

[0028] ∑M=M 滑 +M 风

[0029] Among them, M 滑 =F 滑 ·d

[0030] Among them, M 滑 is the aerodynamic moment caused by the lift generated by the wing in the slipstream area, M 风 is the moment caused by wind disturbance, F 滑is the lift generated by the wing in the slipstream region, and d is the vertical distance from the line of action of the lift generated by the wing in the slipstream region to the center of gravity.

[0031] 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 the wing is mainly related to the propeller thrust, the wetted area, the propeller area, and the aerodynamic coefficient. For any wing, the lift L generated by the wing in the propeller slipstream area can be given by the classic formula:

[0032]

[0033] Where: ρ is the air density, V eff is the effective flow velocity on the wing, which mainly comes from the propeller slipstream.

[0034] S is the effective wing area in the slipstream region, C L is the lift coefficient of the wing;

[0035] The velocity model on the wing behind the propeller is:

[0036]

[0037] Where, T is the propeller thrust; A is the propeller disc area;

[0038] Substituting the velocity model into the lift formula, we can get:

[0039]

[0040] Where L is the lift generated by the wing in the propeller slipstream region; S is the effective wing area in the slipstream region;

[0041] Among them, the propeller thrust is given a periodic change, defined as:

[0042] T=T0(1+b cos(ωt)),

[0043] Among them, T0 is the basic thrust of the propeller, T0=G=mg,

[0044]

[0045] Where 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;

[0046] I is the moment of inertia of the UAV; b is an introduced parameter, the physical meaning of which is the amplitude of the propeller thrust change;

[0047] When wind disturbance is not considered, the above formula can be transformed into:

[0048]

[0049] Standardize the above formula

[0050]

[0051] make

[0052] The above formula is transformed into

[0053]

[0054] Introduce a term with zero mean:

[0055] Finally, we get the following equation:

[0056]

[0057] In the formula, δ and ε are parameters. Theoretical studies have shown that when the parameters δ and ε take certain values, the system will be in a stable state.

[0058] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in the present invention, the process of verifying the new UAV longitudinal plane flight mechanics model by periodic excitation parameters in S4) is as follows: The equations are solved using the singular perturbation method;

[0059] According to Floquet theory, for any linear differential equation with periodic coefficients, there exists a transition curve that divides the δ-ε plane into stable and unstable regions. The transition curve is generated when the period of the solution of the equation is π or 2π. Along the transition curve, at least one solution of the equation is periodic, with a period of π or 2π.

[0060] Expand the solution θ and the parameter δ of the equation into a power series of ε:

[0061] θ=θ0+εθ1+ε 2 θ2+…

[0062] δ=δ0+εδ1+ε 2 δ2+…

[0063] Substitute into the original equation and sort by the power of ε, we have

[0064]

[0065]

[0066] …

[0067] In order to ensure that the period is π or 2π, only δ0=n 2 ;

[0068] make From the differential formula (1), we know that it has two linearly independent special solutions: and

[0069] make a is a constant

[0070] Substituting into formula (2) we get

[0071]

[0072] In order to eliminate the duration term, The first-order periodic solution of formula (4) is

[0073]

[0074] Substituting into formula (3) we get

[0075]

[0076] In order to eliminate the duration term, Therefore, the second-order periodic solution of formula (5) is

[0077]

[0078] Therefore, the periodic solution of the original equation is

[0079]

[0080] The corresponding transition curve is

[0081]

[0082] Therefore, a stability diagram can be drawn based on the values of δ and ε.

[0083] The fixed-wing vertical hovering control method using longitudinal periodic excitation described in the present invention, within the system,

[0084] in,

[0085] For a certain UAV, the parameter δ can be approximately regarded as determined by the parameters of the UAV itself.

[0086]

[0087] when It can be seen that the variables that affect whether the system is stable are mainly related to the parameter b, that is, the amplitude b of the thrust cycle change determines whether the system can remain stable.

[0088] The method for controlling the vertical hovering of a fixed wing using longitudinal periodic excitation described in the present invention can always obtain the range of ε values that make the system stable when δ is determined according to the stability map.

[0089]

[0090] It can always keep the drone system stable when hovering in a vertical state.

[0091] It can be seen from the above technical solution that the present invention has the following beneficial effects:

[0092] The present invention discloses a method for controlling a fixed-wing vertical hovering using longitudinal periodic excitation, which enhances the attitude stability of a fixed-wing UAV in a vertical hovering state by applying longitudinal periodic excitation. The method establishes a flight mechanics model within the longitudinal plane of the fixed-wing UAV, rationally derives and transforms the mechanics model, and analyzes the dynamic response of the fixed-wing UAV when subjected to longitudinal periodic excitation, thereby achieving effective control of the UAV's attitude and improving its operational safety and stability.

[0093] 2. In the present invention, by allowing the UAV thrust to change periodically, a pitch restoring torque can be provided to the UAV to a certain extent, thereby offsetting small disturbances in the face of gusts and other situations, further improving its controllability and flight safety and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 Schematic diagram of the structure of the fixed-wing vertical hovering control method using longitudinal periodic excitation according to the present invention;

[0095] Figure 2 This is the stability map of the present invention. DETAILED DESCRIPTION

[0096] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0097] Example

[0098] like Figure 1 A method for controlling a fixed-wing vertical hovering using longitudinal periodic excitation is shown, comprising:

[0099] S1): First, establish a flight dynamics model of the fixed-wing UAV in the longitudinal plane;

[0100] S2): deriving and simplifying the fixed-wing UAV longitudinal plane flight dynamics model established in S1) to obtain a simplified new UAV longitudinal plane flight dynamics model;

[0101] S3): Analyze the stability of the new UAV longitudinal plane flight dynamics model obtained in S2);

[0102] S4): Verify the new UAV longitudinal plane flight dynamics model using periodic excitation parameters.

[0103] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in this embodiment, the flight dynamics model of the fixed-wing UAV in the longitudinal plane is established in S1) as follows:

[0104] Assuming that the fixed-wing UAV moves in the longitudinal plane, ignoring the effects of lateral motion and roll and yaw, only the following variables are considered:

[0105] θ: the angle of the aircraft's longitudinal axis relative to the vertical plane;

[0106] Pitch angular velocity;

[0107] Pitch angular acceleration;

[0108] T: propeller thrust;

[0109] G: drone gravity;

[0110] m: mass of the drone;

[0111] g: acceleration due to gravity;

[0112] I: UAV’s moment of inertia;

[0113] M: Resultant moment

[0114] Only consider the UAV to maintain a stable attitude, that is, not turning or turning within a small angle;

[0115] When the linear drift of the UAV is not considered, the mechanical model of the UAV is assumed to be the rotation of a rigid body around its center of mass;

[0116] The flight dynamics model of the UAV in the longitudinal plane is:

[0117]

[0118] Where, I is the moment of inertia of the UAV, is the pitch angular acceleration, M is the resultant moment;

[0119] When the lines of action of gravity and aerodynamic drag pass through the center of gravity of the drone, no pitching moment is generated. Only the influence of the propeller power cycle change, that is, the longitudinal excitation, is considered. Therefore, the rudder is forced not to deflect, and the pitching moment caused by the rudder is also 0.

[0120] Assuming the propeller thrust line passes through the center of gravity of the drone, the propeller thrust does not provide any pitching torque. In this state, when the aircraft is hovering, the flight speed is almost zero, so there is no lift generated by the relative airflow during flight, and there is also no aerodynamic torque generated by the relative airflow:

[0121] but:

[0122] ∑M=M 滑 +M 风

[0123] Among them, M 滑 =F 滑 ·d

[0124] Among them, M 滑 is the aerodynamic moment caused by the lift generated by the wing in the slipstream area, M 风 is the moment caused by wind disturbance, F 滑 is the lift generated by the wing in the slipstream region, and d is the vertical distance from the line of action of the lift generated by the wing in the slipstream region to the center of gravity.

[0125] In this embodiment, when the UAV is in the slipstream area, the lift generated by its wings 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:

[0126]

[0127] Where: ρ is the air density, V eff is the effective flow velocity on the wing, which mainly comes from the propeller slipstream.

[0128] S is the effective wing area in the slipstream region, C L is the lift coefficient of the wing;

[0129] The velocity model on the wing behind the propeller is:

[0130]

[0131] Where, T is the propeller thrust; A is the propeller disc area;

[0132] Substituting the velocity model into the lift formula, we can get:

[0133]

[0134] Where L is the lift generated by the wing in the propeller slipstream region; S is the effective wing area in the slipstream region;

[0135] Among them, the propeller thrust is given a periodic change, defined as:

[0136] T=T0(1+b cos(ωt)),

[0137] Among them, T0 is the basic thrust of the propeller, T0=G=mg,

[0138]

[0139] Where 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;

[0140] I is the moment of inertia of the UAV; b is an introduced parameter, the physical meaning of which is the amplitude of the propeller thrust change;

[0141] When wind disturbance is not considered, the above formula can be transformed into:

[0142]

[0143] Standardize the above formula

[0144]

[0145] make

[0146] The above formula is transformed into

[0147]

[0148] Introduce a term with zero mean:

[0149] Finally, we get the following equation:

[0150]

[0151] In the formula, δ and ε are parameters. Theoretical studies have shown that when the parameters δ and ε take certain values, the system will be in a stable state.

[0152] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in this embodiment, the process of verifying the new UAV longitudinal plane flight mechanics model by using periodic excitation parameters in S4) is as follows: The equations are solved using the singular perturbation method;

[0153] According to Floquet theory, for linear differential equations with periodic coefficients, there exists a transition curve that divides the δ-ε plane into stable and unstable regions. Moreover, the transition curve is generated when the period of the solution of the equation is π or 2π. Along the transition curve, at least one solution of the equation is periodic, with a period of π or 2π.

[0154] Expand the solution θ and the parameter δ of the equation into a power series of ε:

[0155] θ=θ0+εθ1+ε 2 θ2+…

[0156] δ=δ0+εδ1+ε 2 δ2+…

[0157] Substitute into the original equation and sort by the power of ε, we have

[0158]

[0159] …

[0160] In order to ensure that the period is π or 2π, only δ0=n 2 ;

[0161] make From the differential formula (1), we know that it has two linearly independent special solutions: and

[0162] make a is a constant

[0163] Substituting into formula (2) we get

[0164]

[0165] In order to eliminate the duration term,

[0166] The first-order periodic solution of formula (4) is

[0167]

[0168] Substituting into formula (3) we get

[0169]

[0170] In order to eliminate the duration term,

[0171] Therefore, the second-order periodic solution of formula (5) is

[0172]

[0173] Therefore, the periodic solution of the original equation is

[0174]

[0175] The corresponding transition curve is

[0176]

[0177] Therefore, a stability diagram can be drawn based on the values of δ and ε.

[0178] In the fixed-wing vertical hovering control method using longitudinal periodic excitation described in this embodiment, within the system,

[0179] in,

[0180] For a certain UAV, the parameter δ can be approximately regarded as determined by the parameters of the UAV itself.

[0181]

[0182] when It can be seen that the variables that affect whether the system is stable are mainly related to the parameter b, that is, the amplitude b of the thrust cycle change determines whether the system can remain stable.

[0183] In practice, based on the actual aircraft's δ value, a suitable ε value can be selected from the δ-ε stability map, and then other parameters such as amplitude can be determined back-translated to stabilize the system. Similarly, the amplitude can be selected first to obtain a set of δ and ε values, which can then be compared in the δ-ε stability map to see if they are in the stable area.

[0184] According to Figure 2 As shown in the stability spectrum, when δ is determined, the range of ε values that makes the system stable can be obtained.

[0185]

[0186] It can always keep the drone system stable when hovering in a vertical state.

[0187] The stability map is a graphical representation of the eigenvalues of the solution of the equation based on two parameters δ and ε. The eigenvalues under different parameters are calculated according to the perturbation method and these eigenvalues are plotted in the parameter space. Figure 2 The medium gray shaded area indicates a stable solution, while the unshaded area indicates an unstable solution. Therefore, by using the values of the two parameters δ and ε of the real aircraft, we find the corresponding eigenvalue position on the stability spectrum to determine whether the applied longitudinal periodic excitation can stabilize the system.

[0188] By changing the thrust of the drone periodically, a pitch restoring torque can be provided to the drone to a certain extent, thereby offsetting small disturbances when facing gusts of wind and other situations.

[0189] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be regarded as the scope of protection of the present invention.

Claims

1. A method for controlling a fixed-wing vertical hovering aircraft using longitudinal periodic excitation, characterized by: include: S1): First, establish the flight dynamics model of the fixed-wing UAV in the longitudinal plane; S2): derive and simplify the fixed-wing UAV longitudinal plane flight dynamics model established in S1) to obtain a simplified new UAV longitudinal plane flight dynamics model; S3): Analyze the stability of the new UAV longitudinal plane flight dynamics model obtained in S2); S4): Verify the new UAV longitudinal plane flight dynamics model through periodic excitation parameters; The flight dynamics model of the fixed-wing UAV in the longitudinal plane established in S1) is as follows: Assuming that the fixed-wing UAV moves in the longitudinal plane, ignoring the effects of lateral motion and roll and yaw, only the following variables are considered: : The angle of the aircraft's longitudinal axis relative to the vertical plane; : pitch angular velocity; : pitch angular acceleration; T: propeller thrust; G: drone gravity; m: mass of the drone; g: acceleration due to gravity; I: UAV’s moment of inertia; M: resultant moment; Only consider the UAV to maintain a stable attitude, that is, not turning or turning within a small angle; When the linear drift of the UAV is not considered, the mechanical model of the UAV is assumed to be the rotation of a rigid body around its center of mass; The flight dynamics model of the UAV in the longitudinal plane is: Where, I is the moment of inertia of the UAV, is the pitch angular acceleration, M is the resultant moment; When the lines of action of gravity and aerodynamic drag pass through the center of gravity of the drone, no pitching moment is generated. Only the influence of the propeller power cycle change, that is, the longitudinal excitation, is considered. Therefore, the rudder is forced not to deflect, and the pitching moment caused by the rudder is also 0. Assuming that the propeller thrust line passes through the center of gravity of the drone, the propeller thrust does not provide any pitching torque. In this state, when the aircraft is hovering, the flight speed is almost zero, 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 region, is the torque caused by wind disturbance, is the lift generated by the wing in the slipstream region, d is the vertical distance from the line of action of the lift generated by the wing in the slipstream region to the center of gravity; When the UAV is in the slipstream area, the lift generated by its wings is 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 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 the propeller thrust; A is the 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 region; S is the effective wing area in the slipstream region; Among them, the propeller thrust is given a periodic change, defined as: ， in, is the propeller basic thrust, , Where 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 UAV; is an 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: Where, and is a parameter. The equation has theoretical research when the parameter and When certain values are achieved, the system will be in a stable state; The process of verifying the new UAV longitudinal plane flight mechanics model by periodic excitation parameters in S4) is as follows: The equations are solved using the singular perturbation method; According to Floquet theory, there is a transition curve for linear differential equations with periodic coefficients. 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 ; The solution of the equation and parameters Expand into The power series of : Substitute into the original equation, 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 for the value of In the system, , in, , For a certain drone, the parameters Determined by the parameters of the drone itself, at this time when When , it can be seen that the variable that affects whether the system is stable is related to the parameter b, that is, the amplitude b of the thrust cycle change determines whether the system can remain stable; According to the stability diagram, when When determined, we can get the system stability Value range, at this time for It can always keep the drone system stable when hovering in a vertical state.

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