Ducted tailstock type aircraft mode conversion control method based on transition corridor planning and combination

By establishing a dynamic model and an airborne computer solution transition corridor, and combining the optimal control principle to plan the path online, the ducted tailstock aircraft realizes the combined application of multiple mode conversions, solving the problem that traditional conversion methods cannot meet the rapid multiple conversions and broadening the application scenarios.

CN120540035APending Publication Date: 2025-08-26NORTHWESTERN POLYTECHNICAL UNIV
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Patent Information

Application Number
CN202510470718.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-15
Publication Date
2025-08-26

AI Technical Summary

Technical Problem

The existing duct tailstock aircraft mode conversion method cannot meet the needs of fast multiple sag-peaceful and peaceful sag-penetrating mode conversion, and the traditional jump conversion cannot meet the requirements of minimum altitude change and minimum conversion time, which limits its application scenarios.

Method used

By establishing a dynamic model of a duct tailstock aircraft, combining airborne computers with flight mission data, solving the transition corridor of four basic conversion modes, and planning the optimal conversion path online based on the optimal control principle, selecting the optimal conversion mode, and using the flight controller to generate control instructions to achieve mode conversion.

Benefits of technology

The application scenarios of duct tailstock aircraft have been broadened, and its application flexibility has been improved. It can select the optimal conversion mode according to different mission requirements to meet the requirements of rapid multiple conversions and landings.

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Abstract

The invention discloses a ducted tailstock type aircraft mode conversion control method based on transition corridor planning and combination, and the method comprises the steps: fusing a flight task, an aircraft dynamics model and actual flight data through an airborne computer, solving transition corridors of four basic conversion modes, and selecting an optimal conversion mode; on the basis of an optimal control principle, an optimal conversion path is planned on line and transmitted to a flight controller, the flight controller generates a control instruction to achieve conversion path tracking and complete the aircraft mode conversion process, different basic conversion modes can be adopted in each mode conversion process, and combined application of jumping, diving, height fixing and sinking conversion can be achieved. According to the mode conversion control method provided by the invention, the application scene of the ducted tailstock type aircraft can be effectively widened, and the application flexibility of the ducted tailstock type aircraft can be improved.
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Description

Technical Field

[0001] The present invention belongs to the field of aviation technology, and in particular relates to a mode conversion control method for a ducted tailsitter aircraft based on transition corridor planning and combination. Background Art

[0002] Ducted tailsitter vertical take-off and landing (VTOL) aircraft combine the advantages of fixed-wing and rotary-wing UAVs, offering both hovering and high-speed cruise flight modes. They offer both the maneuverability and flexibility of vertical take-off and landing (VTOL) and are suitable for long-distance cruise missions. Compared to fixed-rotor and tilt-rotor layouts, ducted tailsitters eliminate the need for redundant drag, weight, or complex tilt-rotor mechanisms, resulting in higher flight efficiency. Most existing ducted tailsitter aircraft utilize a jump-to-transition method to transition from vertical to horizontal and horizontal to vertical modes. This is characterized by a gradual increase in altitude during the transition. During this transition, the dynamics of ducted tailsitter systems approach those of traditional fixed-wing aircraft, with sufficient control surfaces and ease of control, making them relatively easy to implement. However, the significant altitude gain and slow transition speed associated with this jump-to-transition approach may not meet the mission requirements of this type of aircraft. For example, when an aircraft needs to perform multiple vertical-to-level and level-to-vertical transitions in restricted airspace, traditional jump transitions cannot meet the minimum altitude change requirements. Alternatively, if an aircraft is required to quickly complete a vertical takeoff and transition to level flight, or quickly complete a landing after transitioning from level flight to vertical, traditional jump transitions cannot meet the minimum transition time requirements and the requirements for rapid takeoff and landing. These issues limit the application scenarios of these ducted tailsitter aircraft.

[0003] Ducted tailsitter vertical take-off and landing (VTOL) aircraft possess powerful vector power control capabilities, enabling them to perform a variety of complex maneuvers. The aircraft's mode transition process can be considered a single maneuver. In addition to traditional jump transitions, ducted tailsitter mode transitions can also be accomplished through dive transitions (exchange of kinetic and potential energy during vertical-to-horizontal transitions), constant-altitude transitions (conversions with no or a small altitude difference), and sinking transitions (mode transitions accompanied by a decrease in altitude). Jump transitions have the advantages of simplicity and reliability, dive transitions have the advantage of low energy consumption, constant-altitude transitions are suitable for rapid and multiple transitions, and sinking transitions facilitate rapid landings. Therefore, the optimal transition mode can be selected based on the requirements of different flight missions. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the present invention provides a mode conversion control method for a ducted tailsitter aircraft based on transition corridor planning and combination. The onboard computer integrates the flight mission, aircraft dynamics model, and actual flight data to solve the transition corridors of the four basic conversion modes and select the optimal conversion mode. Based on the optimal control principle, the optimal conversion path is planned online and transmitted to the flight controller. The flight controller generates control instructions to achieve conversion path tracking and complete the aircraft mode conversion process. Each mode conversion process can adopt a different basic conversion mode, which can realize the combined application of jump, dive, altitude hold, and sinking conversion. The mode conversion control method proposed by the present invention can effectively broaden the application scenarios of this type of ducted tailsitter aircraft and improve its application flexibility.

[0005] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0006] Step 1: Establish a dynamic model of the ducted tailsitter aircraft as a basis for solving the transition corridor and planning the conversion path;

[0007] Step 2: Load the flight mission data into the onboard computer, including the mission type, airspace restrictions, and flight duration, as the basis for the onboard computer to make the optimal switching mode decision;

[0008] Step 3: Before the ducted tailsitter aircraft switches from vertical to horizontal or horizontal to vertical mode, the onboard sensors collect current flight data and transmit it to the onboard computer as a basis for calculating the transition corridor;

[0009] Step 4: The onboard computer calculates the transition corridors for the four basic conversion modes: jump conversion, dive conversion, altitude conversion, and sink conversion. Based on the calculation results and the flight mission, it makes autonomous decisions and selects the optimal conversion mode.

[0010] Step 5: The onboard computer plans a feasible optimal mode transition path online based on the transition corridor of the selected optimal transition mode and the flight mission requirements, and sends the desired transition path to the flight controller;

[0011] Step 6: The ducted tailsitter aircraft performs vertical-to-horizontal or horizontal-to-vertical mode conversion.

[0012] Preferably, the step 1 is specifically:

[0013] Based on the actual ducted tailsitter aircraft, the basic dynamic model of the entire aircraft was established component by component using experimental measurement, CFD calculation, wind tunnel test, and aerodynamic estimation methods. The dynamic model was modified according to the actual payload and fuel carried, and the actual dynamic model data of the ducted tailsitter aircraft was loaded into the onboard computer.

[0014] Preferably, the flight data includes position, altitude, speed, attitude, control surface deflection angle, and propeller speed.

[0015] Preferably, the step 4 is specifically as follows:

[0016] The pitch plane motion equation of the aircraft is established and simplified; the constraints of the four basic transition modes of jump transition, dive transition, altitude conversion, and sink transition are determined, and the quantities to be solved are the horizontal velocity u and the pitch angle θ; the optimal control theory is used to solve the above constrained optimization problem and obtain the transition corridors of the ducted tailsitter aircraft in the four basic transition modes. That is, the horizontal velocity-pitch angle feasible region;

[0017] The process of autonomous decision-making by the onboard computer is as follows: Step 1, determine whether there is a feasible mode conversion channel among the four basic conversion modes, and exclude those that do not exist; Step 2, determine whether the basic conversion mode retained in the first step meets the flight mission requirements, and exclude those that do not meet the requirements; Step 3, calculate the reliability of the transition corridor of the basic conversion mode retained in the second step, and select the mode conversion method with the highest reliability; If there is no mode conversion method that meets the flight mission requirements, select the mode conversion method with the highest reliability; If there is no feasible mode conversion channel for any of the four basic conversion modes, terminate the current conversion process and wait until the conversion conditions are met before performing the mode conversion again.

[0018] Preferably, the step 5 is specifically as follows:

[0019] Taking the minimum conversion time as the first indicator, the minimum conversion time performance indicator is described as When the state quantity satisfies the initial condition x0 and the terminal constraint condition x f , transition corridor boundary conditions Under the condition of , the optimal control theory is used to solve the above constrained optimization problem so that the performance index function J reaches the minimum value, and the optimal transition trajectory that meets the minimum transition time requirement can be planned in the transition corridor.

[0020] Preferably, the flight mission requirements include minimum transition time and minimum altitude change.

[0021] Preferably, the step 6 is specifically:

[0022] The flight controller sends control instructions to the control surfaces and controls the propeller speed. The actuator drives the corresponding control surfaces to move. At the same time, the onboard sensors collect flight data during the mode conversion process and transmit it to the flight controller. The expected conversion path and the actual conversion path constitute negative feedback control to achieve aircraft mode conversion path tracking.

[0023] Preferably, the control surfaces include eight slipstream rudders and ailerons.

[0024] Preferably, the aircraft mode conversion path tracking is specifically:

[0025] The ducted tailseat aircraft adopts a cascade PID controller, including a position controller, a speed controller, an attitude angle controller, and an angular velocity controller. After receiving the optimal conversion path provided by the onboard computer, the flight controller generates an equivalent control surface deflection angle δ a , δ e , δ r and throttle δ T Control signal, and distribute it to the eight slipstream rudder deflection angles δ1~δ8, aileron deflection angle δ fy and propeller speed The actuator drives the deflection of each control surface to generate control torque and realize mode conversion path tracking.

[0026] The beneficial effects of the present invention are as follows:

[0027] The present invention proposes a mode conversion control method for a ducted tailsitter aircraft based on transition corridor planning and combination. The method can autonomously plan the transition corridors of each basic conversion mode according to the actual dynamic model of the ducted tailsitter aircraft, adaptively select feasible conversion methods according to flight mission requirements and actual flight conditions, and the four basic conversion methods can be used in combination in stages. The feasible optimal conversion path can be planned online based on the optimal control principle, which can broaden the application scenarios of the ducted tailsitter aircraft and enhance its application flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of a mode conversion control method of a ducted tailsitter aircraft based on transition corridor planning and combination according to the present invention;

[0029] Figure 2 1 is a schematic diagram of the overall structure of a ducted tailseat aircraft provided by an embodiment of the present invention;

[0030] Figure 3 Schematic diagram of the jump conversion process provided by an embodiment of the present invention;

[0031] Figure 4 is a schematic diagram of a subduction conversion process provided by an embodiment of the present invention;

[0032] Figure 5 Schematic diagram of the fixed height conversion process provided by an embodiment of the present invention;

[0033] Figure 6 This is a schematic diagram of the sinking conversion process provided by an embodiment of the present invention.

[0034] In the picture, 1-fuselage, 2-wing, 3-aileron, 4-carbon fiber support rod, 5-duct, 6-carbon fiber landing gear, 7-propeller, 8-slipstream rudder. DETAILED DESCRIPTION

[0035] The present invention will be further described below with reference to the accompanying drawings and examples.

[0036] The purpose of the present invention is to provide a mode conversion control method for a ducted tailsitter aircraft based on transition corridor planning and combination, which can broaden the application scenarios of the ducted tailsitter aircraft and improve its application flexibility.

[0037] like Figure 2 As shown, the present invention is applied to a ducted tailsitter aircraft, comprising a fuselage 1, wings 2, ailerons 3, carbon fiber support rods 4, a duct 5, carbon fiber landing gear 6, propellers 7, and slipstream fins 8. The fuselage 1 is used to carry onboard equipment, payload, and fuel; the wings 2 provide the lift required for the aircraft's flight; the ailerons 3, arranged at the trailing edge of the wings 2, provide the aircraft's rolling control torque during horizontal flight; the carbon fiber support rods 4 connect the fuselage 1 and the duct 5; the duct 5 is annular and provides lift enhancement, protection, and noise reduction; the carbon fiber landing gear 6 provides support and cushioning for the aircraft's vertical takeoff and landing; the propellers 7, located within the duct 5, provide the power required for vertical takeoff and landing and horizontal flight; and eight slipstream fins 8 are arranged behind the propellers 7. The propeller slipstream flows through each of the fins, and the combined deflection of the fins generates torque to control the aircraft's flight attitude.

[0038] like Figure 1 As shown, the present invention provides a mode conversion control method for a ducted tailsitter aircraft based on transition corridor planning and combination, comprising the following steps:

[0039] Step 1: Establish a dynamic model of the ducted tailsitter aircraft as a basis for solving the transition corridor and planning the conversion path. The specific methods include: based on the actual ducted tailsitter aircraft, using experimental measurement, CFD calculation, wind tunnel testing, aerodynamic estimation and other methods to establish the basic dynamic model of the entire aircraft component by component, modifying the dynamic model according to the actual payload and fuel carried, and loading the actual dynamic model data of the ducted tailsitter aircraft into the onboard computer.

[0040] Step 2: Load the flight mission data into the onboard computer, including the flight mission type, airspace restrictions, flight range and duration, etc., as the basis for the onboard computer to make the optimal conversion mode decision.

[0041] Step 3: Before the ducted tailsitter aircraft switches from vertical to horizontal or horizontal to vertical mode, the onboard sensors collect the current flight data (including position, altitude, speed, attitude, control surface deflection angle, propeller speed, etc.) and transmit it to the onboard computer as the basis for calculating the transition corridor.

[0042] Step 4: The onboard computer calculates the transition corridors of the four basic conversion modes, namely, jump conversion, dive conversion, constant altitude conversion, and sinking conversion, and selects the optimal conversion mode based on the calculation results and autonomous decision-making of the flight mission.

[0043] In step 5, the onboard computer plans the feasible optimal mode transition path online based on the transition corridor of the selected optimal transition mode and the flight mission requirements (such as minimum transition time, minimum altitude change, etc.), and sends the expected transition path to the flight controller.

[0044] Step 6, the ducted tailsitter aircraft performs vertical-to-horizontal or horizontal-to-vertical mode conversion. The specific method is: the flight controller sends control instructions to the control surfaces (including eight slipstream rudders and ailerons) and controls the propeller speed. The actuator drives the corresponding control surfaces to move. At the same time, the onboard sensors collect flight data during the mode conversion process and transmit it to the flight controller. The expected conversion path and the actual conversion path constitute negative feedback control to achieve tracking of the aircraft mode conversion path.

[0045] Example:

[0046] Step 1: Establish a dynamic model of the ducted tailsitter aircraft. The details are as follows:

[0047] The total force of the entire aircraft takes into account the weight of the fuselage, propeller thrust, slipstream rudder aerodynamic force, ducted aerodynamic force, and wing-fuselage aerodynamic force. The total moment of the entire aircraft takes into account the propeller torque, slipstream rudder aerodynamic moment, ducted aerodynamic moment, and wing-fuselage aerodynamic moment. By obtaining basic aircraft parameters (including overall aircraft parameters, wing parameters, fuselage parameters, propeller parameters, slipstream rudder parameters, ducted parameters, etc.) and aerodynamic derivatives (including static derivatives, dynamic derivatives, and control derivatives), a basic dynamic model of the ducted aircraft can be established. Based on the payload and fuel loading, the total weight characteristics of the aircraft are calculated, and the model is modified to obtain the actual dynamic model of the ducted tailsitter aircraft.

[0048] Step 2: Load the flight mission data into the onboard computer, including the mission type, airspace restrictions, flight range and duration, etc. In a preferred embodiment, the ducted tailsitter aircraft needs to be at the minimum flight altitude H min and maximum flight altitude H max The vertical-horizontal transition and the horizontal-vertical transition are completed in the airspace between max .

[0049] Step 3: Before the ducted tailsitter aircraft switches from vertical to horizontal or horizontal to vertical mode, the onboard sensors collect current flight data and transmit it to the onboard computer as a basis for calculating the transition corridor.

[0050] Preferably, the collected flight data include: aircraft position (including longitude Lon, latitude Lat, altitude H), speed u, v, w, attitude angle Φ, θ, ψ, angular velocity p, q, r, airspeed V a , angle of attack α, sideslip angle β, aileron deflection angle δ fy , slipstream rudder deflection angle δ1~δ8, propeller speed wait.

[0051] Step 4: The onboard computer calculates the transition corridors for the four basic conversion modes: jump conversion, dive conversion, altitude conversion, and sink conversion. Based on the calculation results and the flight mission, the optimal conversion mode is selected. The details are as follows:

[0052] The pitch plane motion equation of the aircraft is established and reasonably simplified. The constraints (including horizontal speed, pitch angle, altitude, propeller power, etc.) of the four basic transition modes, namely, jump transition, dive transition, fixed-altitude transition, and sinking transition, are determined. The quantities to be solved are the horizontal speed u and the pitch angle θ. The optimal control theory is used to solve the above constrained optimization problem and obtain the transition corridors of the ducted tailsitter aircraft in the four basic transition modes. That is the feasible range of horizontal velocity-pitch angle. Figures 3 to 6 shown.

[0053] The process of autonomous decision-making by the onboard computer is as follows: the first step is to determine whether there is a feasible mode conversion channel among the four basic conversion modes, and exclude those that do not exist; the second step is to determine whether the basic conversion mode retained in the first step meets the flight mission requirements, and exclude those that do not meet the requirements; the third step is to calculate the transition corridor reliability (i.e., the width of the transition corridor) of the basic conversion mode retained in the second step, and select the mode conversion method with the highest reliability. If there is no mode conversion method that meets the flight mission requirements, the mode conversion method with the highest reliability is selected. If there is no feasible mode conversion channel for any of the four basic conversion modes, the current conversion process is terminated, and the mode conversion is performed again when the conversion conditions (such as external environmental conditions, etc.) are met. In the above preferred embodiment, the onboard computer decides to use the fixed altitude conversion method, which has a smaller altitude change and a faster conversion time, and can meet the flight mission requirements in step 2.

[0054] Step 5: The onboard computer plans the optimal mode transition path online based on the transition corridor of the selected optimal mode and the flight mission requirements (such as minimum transition time, minimum altitude change, etc.), and sends the desired transition path to the flight controller. The details are as follows:

[0055] In a preferred embodiment, the minimum conversion time is used as the first indicator, and the minimum conversion time performance indicator is described as When the state quantity satisfies the initial condition x0 and the terminal constraint condition x f, transition corridor boundary conditions Under the condition of , the optimal control theory is used to solve the above constrained optimization problem so that the performance index function J reaches the minimum value, and the optimal transition trajectory that meets the minimum transition time requirement can be planned in the transition corridor.

[0056] Step 6, the ducted tailsitter aircraft performs vertical-to-horizontal or horizontal-to-vertical mode conversion. The specific method is: the flight controller sends control instructions to the control surfaces (including eight slipstream rudders and ailerons) and controls the propeller speed. The actuator drives the corresponding control surfaces to move. At the same time, the onboard sensors collect flight data during the mode conversion process and transmit it to the flight controller. The expected conversion path and the actual conversion path constitute negative feedback control to achieve tracking of the aircraft mode conversion path.

[0057] In a preferred embodiment, the ducted tailsitter aircraft adopts a cascade PID controller, which includes a position controller, a speed controller, an attitude angle controller, and an angular velocity controller. After receiving the optimal conversion path provided by the onboard computer, the flight controller generates an equivalent control surface deflection angle δ a , δ e , δ r and throttle δ T Control signal, and distribute it to the eight slipstream rudder deflection angles δ1~δ8, aileron deflection angle δ fy and propeller speed The actuator drives the deflection of each control surface to generate control torque and realize mode conversion trajectory tracking.

Claims

1. A mode transition control method for a ducted tailsitter aircraft based on transition corridor planning and combination, characterized in that: The steps include: Step 1: Establish a dynamic model of the ducted tailsitter aircraft as a basis for solving the transition corridor and planning the conversion path; Step 2: Load the flight mission data into the onboard computer, including the mission type, airspace restrictions, and flight duration, as the basis for the onboard computer to make the optimal switching mode decision; Step 3: Before the ducted tailsitter aircraft switches from vertical to horizontal or horizontal to vertical mode, the onboard sensors collect current flight data and transmit it to the onboard computer as a basis for calculating the transition corridor; Step 4: The onboard computer calculates the transition corridors for the four basic conversion modes: jump conversion, dive conversion, altitude conversion, and sink conversion. Based on the calculation results and the flight mission, it makes autonomous decisions and selects the optimal conversion mode. Step 5: The onboard computer plans a feasible optimal mode transition path online based on the transition corridor of the selected optimal transition mode and the flight mission requirements, and sends the desired transition path to the flight controller; Step 6: The ducted tailsitter aircraft performs vertical-to-horizontal or horizontal-to-vertical mode conversion.

2. The method for controlling mode transition of a ducted tailsitter aircraft based on transition corridor planning and combination according to claim 1, characterized in that: The step 1 is specifically as follows: Based on the actual ducted tailsitter aircraft, the basic dynamic model of the entire aircraft was established component by component using experimental measurement, CFD calculation, wind tunnel test, and aerodynamic estimation methods. The dynamic model was modified according to the actual payload and fuel carried, and the actual dynamic model data of the ducted tailsitter aircraft was loaded into the onboard computer.

3. The method for controlling mode transition of a ducted tailsitter aircraft based on transition corridor planning and combination according to claim 2, characterized in that: The flight data includes position, altitude, speed, attitude, control surface deflection angle, and propeller speed.

4. The method for controlling mode transition of a ducted tailsitter aircraft based on transition corridor planning and combination according to claim 3, characterized in that: The step 4 is specifically as follows: The pitch plane motion equation of the aircraft is established and simplified; the constraints of the four basic transition modes of jump transition, dive transition, altitude conversion, and sink transition are determined, and the quantities to be solved are the horizontal velocity u and the pitch angle θ; the optimal control theory is used to solve the above constrained optimization problem and obtain the transition corridors of the ducted tailsitter aircraft in the four basic transition modes. That is, the horizontal velocity-pitch angle feasible region; The process of autonomous decision-making by the onboard computer is as follows: Step 1, determine whether there is a feasible mode conversion channel among the four basic conversion modes, and exclude those that do not exist; Step 2, determine whether the basic conversion mode retained in the first step meets the flight mission requirements, and exclude those that do not meet the requirements; Step 3, calculate the reliability of the transition corridor of the basic conversion mode retained in the second step, and select the mode conversion method with the highest reliability; If there is no mode conversion method that meets the flight mission requirements, select the mode conversion method with the highest reliability; If there is no feasible mode conversion channel for any of the four basic conversion modes, terminate the current conversion process and wait until the conversion conditions are met before performing the mode conversion again.

5. The method for controlling mode transition of a ducted tailsitter aircraft based on transition corridor planning and combination according to claim 4, characterized in that: The step 5 is specifically as follows: Taking the minimum conversion time as the first indicator, the minimum conversion time performance indicator is described as When the state quantity satisfies the initial condition x0 and the terminal constraint condition x f , transition corridor boundary conditions Under the condition of , the optimal control theory is used to solve the above constrained optimization problem so that the performance index function J reaches the minimum value, and the optimal transition trajectory that meets the minimum transition time requirement can be planned in the transition corridor.

6. The method for controlling mode transition of a ducted tailsitter aircraft based on transition corridor planning and combination according to claim 5, characterized in that: The flight mission requirements include minimum transition time and minimum altitude change.

7. The method for controlling mode transition of a ducted tailsitter aircraft based on transition corridor planning and combination according to claim 6, characterized in that: The step 6 is specifically as follows: The flight controller sends control instructions to the control surfaces and controls the propeller speed. The actuator drives the corresponding control surfaces to move. At the same time, the onboard sensors collect flight data during the mode conversion process and transmit it to the flight controller. The expected conversion path and the actual conversion path constitute negative feedback control to achieve aircraft mode conversion path tracking.

8. The method for controlling mode transition of a ducted tailsitter aircraft based on transition corridor planning and combination according to claim 7, characterized in that: The control surfaces include eight slipstream rudders and ailerons.

9. The method for controlling mode transition of a ducted tailsitter aircraft based on transition corridor planning and combination according to claim 8, characterized in that: The aircraft mode conversion path tracking is specifically as follows: The ducted tailseat aircraft adopts a cascade PID controller, including a position controller, a speed controller, an attitude angle controller, and an angular velocity controller. After receiving the optimal conversion path provided by the onboard computer, the flight controller generates an equivalent control surface deflection angle δ a , δ e , δ r and throttle δ T Control signal, and distribute it to the eight slipstream rudder deflection angles δ1~δ8, aileron deflection angle δ fy and propeller speed The actuator drives the deflection of each control surface to generate control torque and realize mode conversion path tracking.