Electromotive aircraft reachable set evaluation method and system based on quasi-static electric quantity discretization

Abstract

The embodiment of the specification provides a kind of based on quasi-static electric quantity discrete electric aircraft reachable domain evaluation method and system, wherein, method includes: the quasi-static dimension reduction conversion of electric aircraft dynamics model, according to quasi-static hypothesis, simplify electric aircraft dynamics equation, it is decoupled as horizontal plane kinematics equation and push resistance balance and lift weight balance equation constraint, reduce state quantity dimension, obtain dimension reduction flight dynamics model;The electric quantity discrete conversion of dimension reduction flight dynamics model, the form of relative to time dynamics equation is converted into relative to electric quantity consumption value, determines simulation interval and discrete grid;Based on the dimension reduction flight dynamics model, by setting roll angle numerical sequence, numerical integration simulation is carried out on the simulation interval and discrete grid, and the horizontal plane maneuvering reachable domain boundary of electric aircraft is obtained.

Description

Technical Field

[0001] This document relates to the field of electric aircraft technology, and in particular to a method and system for evaluating the reachability of electric aircraft based on quasi-static electrical discharge discreteness. Background Technology

[0002] Medium or large electric aircraft with vertical takeoff and landing capabilities and manned flight capability, especially winged electric aircraft which can achieve efficient and high-speed flight during the cruise phase based on the aerodynamic characteristics of their wings, hold promise for future urban air mobility and low-altitude commuting. During low-altitude flight, to ensure safe flight and avoidance of buildings, other non-cooperative aircraft, and other static or dynamic no-fly zones, it is necessary to quickly assess the reachability of the electric aircraft based on its current available energy state, thus providing a reference for online replanning of flight missions. However, existing numerical simulation or optimization methods for analyzing the reachability of electric aircraft suffer from time-consuming processes and difficulty in convergence, making them unsuitable for the rapid demands of urban air mobility. Summary of the Invention

[0003] This specification provides one or more embodiments of a method for evaluating the reachability of electric aircraft based on quasi-static energy discreteness, including:

[0004] S1. Quasi-static dimensionality reduction transformation is performed on the dynamic model of electric aircraft. Based on the quasi-static assumption, the dynamic equations of electric aircraft are simplified and decoupled into kinematic equations in the horizontal plane and equation constraints for thrust balance and lift-weight balance. The dimension of state variables is reduced to obtain a dimensionality-reduced flight dynamic model.

[0005] S2. Perform energy discretization on the reduced-dimensional flight dynamics model, transforming the dynamic equations relative to time into the form relative to energy consumption values, and determine the simulation interval and discrete grid;

[0006] S3. Based on the reduced-dimensional flight dynamics model, by setting the roll angle numerical sequence, numerical integration simulation is performed on the simulation interval and discrete grid to obtain the boundary of the horizontal maneuverable domain of the electric aircraft.

[0007] Furthermore, the dynamic equations of an electric aircraft are as follows:

[0008]

[0009] Among them, the state variables include altitude h, longitudinal distance x and lateral distance y relative to the starting point, velocity V, track inclination angle γ and track deviation angle χ; the control variables and external forces include roll angle σ, thrust T, aerodynamic drag D and lift L; other parameters include gravitational acceleration g and total mass of the aircraft m;

[0010] The thrust T in the above equation is provided by the electrodynamic system, and this process is described by the following electrodynamic system equations:

[0011]

[0012] Among them, Q B Q consumes power for the battery max I represents the total capacity of a single battery cell. B U is the battery load current. B R is the battery output voltage. B U is the internal resistance of the battery. OC N is the open-circuit voltage. S and N P β1, β2, β3, β4 are the number of cells connected in series and parallel in the battery pack, respectively; SOC is the state of charge of the battery; [β1, β2, β3, β4] are all constants; I M R is the motor current, ν is the motor controller duty cycle, and R is the motor current. M K is the internal resistance of the motor. E Let L be the back electromotive force constant of the motor, ω be the rotational speed of the motor-propeller shaft, and L be the rotational speed of the propeller shaft. M K is the motor inductance. T J is the motor torque constant. M Let C be the moment of inertia of the motor shaft. Q D is the propeller torque coefficient. P J is the propeller diameter. P The moment of inertia of the propeller;

[0013] Introducing the quasi-static assumption, the electric aircraft is in a trim state at all times during flight, with constant speed and altitude, V = V0. C h = h C γ = 0, and V C h C Since all are constant values, equation (1) can be simplified as follows:

[0014]

[0015] Equation (3) can be further decoupled into two parts, which are the kinematic equations of the electric aircraft in the horizontal plane:

[0016]

[0017] And to maintain the drag balance and lift-weight balance equation constraints at a given speed and height; due to mass and speed V C Since neither of them is zero, the fourth and fifth fractions of equation (3) can be simplified as follows:

[0018]

[0019] Furthermore, the aircraft's trim drag is calculated based on the lift and drag expressions and the relationships under trim conditions:

[0020] For an electric aircraft with a wing configuration, lift and drag can be expressed as:

[0021]

[0022] Among them, S R For reference area, C L and C D These are the lift coefficient and drag coefficient, respectively, where α is the angle of attack and C is the drag coefficient. L0 C La C D0 Both k and k are constants;

[0023] Given the roll angle σ and the total mass m of the aircraft, the required lift and lift coefficient are respectively:

[0024]

[0025] Therefore, the corresponding drag coefficients and the required resistance to balance can be obtained as follows:

[0026]

[0027] Therefore, based on the thrust-resistance balance relationship in equation (5), it can be known that D in equation (8) is the total balancing thrust T.

[0028] Furthermore, the propeller equilibrium speed that satisfies the trim thrust and propeller thrust expressions is calculated:

[0029] The trim thrust T is provided by the propeller of the electric power system, and the expression for the propeller thrust is:

[0030]

[0031] Among them, C T For thrust coefficient, [C] t2 C t1 C t0 ] are all constants, and C t2 <0, C t1 >0, C t0 >0; represents the propeller advance ratio;

[0032] Substituting the balancing resistance into equation (9), we obtain the following equation regarding the required rotational speed ω:

[0033]

[0034] The simplified formula (10) yields:

[0035]

[0036] And rearranged into the following quadratic equation in ω:

[0037] a2ω 2 +a1ω+a0=0

[0038]

[0039] To ensure that the balancing speed is positive, the following solution should be taken from equation (12):

[0040]

[0041] This is the propeller balance speed that satisfies the trim flight state of an electric aircraft.

[0042] Furthermore, based on the simplified electrodynamic system model using the characteristics of the motor and battery, the duty cycle of the motor controller and the cell load current in the balanced state are obtained:

[0043] In equation (2), excluding the rate of change in battery power consumption The equations other than those in the equations simplify to:

[0044]

[0045] This can be further simplified into the following equation constraint:

[0046]

[0047] Solving equation (15) yields the motor controller duty cycle and cell load current in the balanced state:

[0048]

[0049] Thus, all state variables of the electrodynamic system can be obtained without numerical integration.

[0050] Furthermore, the reduced-dimensional flight dynamics model undergoes a power consumption discretization transformation, converting the time-dependent dynamic equations into power consumption-dependent values. The specific method for determining the simulation interval and discrete grid is as follows:

[0051] Transforming the dynamic equations relative to time into forms relative to energy consumption, for the state vector x, we have:

[0052]

[0053] Then the state derivatives in the electric aircraft motion equation of equation (4) are transformed into:

[0054]

[0055] The simulation range is set as the initial power consumption value Q0 and the final allowable value Q. f The total number of discrete grids for the electrical quantity is N. Q Then the interval ΔQ is:

[0056]

[0057] The discrete grid is:

[0058] Q0, Q0+ΔQ, Q0+2ΔQ, …, Q0+N Q ΔQ, (21).

[0059] Furthermore, based on the reduced-dimensional flight dynamics model, by setting a numerical sequence of roll angles and performing numerical integration simulations on the simulation interval and discrete grid, the specific method for obtaining the boundary of the horizontal maneuverable domain of the electric aircraft is as follows:

[0060] Within the allowable roll maneuverability of electric aircraft, from the minimum roll angle σ min to the maximum value σ max Select a series of roll angle values, and set the total number of required simulated roll angles to N. σ Then the roll angle interval Δσ is:

[0061]

[0062] The roll angle sequence is as follows:

[0063] σ min ,σ min +Δσ,σ min +2Δσ,…,σ max (twenty three);

[0064] Based on the roll angle sequence given in equation (23), numerical integration simulations are performed sequentially on the interval and discrete grid defined in equation (21), with a total number of simulations of N. σ In each simulation, the roll angle σ is fixed to the value corresponding to equation (23) and remains unchanged. The initial state variables of the electric aircraft in equation (4) are set as follows:

[0065] x(Q0)=0, y(Q0)=0, χ(Q0)=0 (24);

[0066] The constant speed and altitude of the aircraft are V0 and h0, respectively. The state variables of the electrodynamic system required for each step in the simulation can be obtained by substituting the current roll angle σ into equations (13), (16), and (17) and then by algebraic operations.

[0067] Corresponding to N σ The simulation yielded the following two matrices representing the position sequence of the electric aircraft in the horizontal plane:

[0068]

[0069] Where X and Y are the longitudinal and transverse position matrices in the horizontal plane, respectively, each row of the matrix represents the result of each simulation, and the data length of each row is N. Q All simulation results are arranged into a matrix, which has N rows. σ The data constituting the boundary of the horizontal maneuverability domain of an electric aircraft are the last columns of X and Y respectively:

[0070]

[0071] Among them, X B and Y B These are the longitudinal and lateral coordinate sequences of the horizontal maneuverable reachable domain boundary of an electric aircraft.

[0072] This specification provides one or more embodiments of an electric aircraft reachability assessment system based on quasi-static energy discreteness, including:

[0073] Model Dimensionality Reduction Module: Used to perform quasi-static dimensionality reduction transformation on the dynamics model of electric aircraft. Based on the quasi-static assumption, the dynamics equations of electric aircraft are simplified and decoupled into kinematic equations in the horizontal plane and equation constraints for thrust balance and lift-weight balance, thereby reducing the dimension of state variables and obtaining a dimensionality-reduced flight dynamics model.

[0074] Model Conversion Module: Used to perform energy discretization on the reduced-dimensional flight dynamics model, converting the dynamic equations relative to time into the form of energy consumption values, and determining the simulation interval and discrete grid.

[0075] The reachability domain assessment module is used to obtain the horizontal maneuverability domain boundary of the electric aircraft by performing numerical integration simulation on the simulation interval and discrete grid based on the reduced-dimensional flight dynamics model and by setting the roll angle numerical sequence.

[0076] This specification provides one or more embodiments of an electronic device, including:

[0077] Processor; and,

[0078] A memory is configured to store computer-executable instructions, which, when executed, cause the processor to implement the steps of the above-described method for evaluating the reachability of electric aircraft based on quasi-static energy discreteness.

[0079] This specification provides one or more embodiments of a storage medium for storing computer-executable instructions that, when executed, implement the steps of the above-described method for evaluating the reachability of electric aircraft based on quasi-static power discreteness.

[0080] By employing the embodiments of the present invention, the flight dynamics equations of the cruise flight phase of a winged electric aircraft are transformed through quasi-static transformation, which significantly reduces the system dimension and improves the numerical integration speed. By discretizing the electric charge, the original time-domain-based electric aircraft dynamics equations are transformed into those based on the electric charge dissipation domain, thereby transforming the uncertain time intervals and step sizes of the numerical simulation of the flight process into definite intervals and step size values, further improving the simulation speed.

[0081] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0082] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0083] Figure 1 A flowchart illustrating an reachability assessment method for electric aircraft based on quasi-static energy discretization, provided for one or more embodiments of this specification;

[0084] Figure 2 A schematic diagram of the reachability domain calculated at a flight altitude of 1 km for one or more embodiments of this specification, which is based on a quasi-static electric power discrete-time electric aircraft reachability domain assessment method.

[0085] Figure 3 A schematic diagram of the reachability domain calculated at a flight altitude of 2km for one or more embodiments of this specification, which is based on a quasi-static electric power discrete-time electric aircraft reachability domain assessment method.

[0086] Figure 4 A schematic diagram of the reachability domain calculated at a flight altitude of 3km for one or more embodiments of this specification, which is based on a quasi-static electric charge discreteness method for evaluating the reachability domain of an electric aircraft.

[0087] Figure 5 A schematic diagram of the reachability domain calculated at a flight altitude of 4km, provided for one or more embodiments of this specification, of an electric aircraft reachability domain assessment method based on quasi-static electric charge discreteness.

[0088] Figure 6A schematic diagram showing the reachability calculation results at four flight altitudes for an electric aircraft reachability assessment method based on quasi-static electric charge discreteness provided in one or more embodiments of this specification.

[0089] Figure 7 A schematic diagram illustrating the composition of an electric aircraft reachability assessment system based on quasi-static energy discreteness, provided for one or more embodiments of this specification;

[0090] Figure 8 This is a schematic diagram of the structure of an electronic device provided for one or more embodiments of this specification. Detailed Implementation

[0091] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0092] Method Implementation Examples

[0093] According to embodiments of the present invention, a method for evaluating the reachability domain of electric aircraft based on quasi-static energy discreteness is provided. Figure 1 A flowchart illustrating an reachability domain assessment method for electric aircraft based on quasi-static energy discretization, provided for one or more embodiments of this specification, is shown below. Figure 1 As shown, the reachability domain assessment method for electric aircraft based on quasi-static energy discreteness according to an embodiment of the present invention specifically includes:

[0094] S1. The dynamic model of the electric aircraft is transformed into a quasi-static dimension reduction model. Based on the quasi-static assumption, the dynamic equation of the electric aircraft is simplified and decoupled into kinematic equations in the horizontal plane and equation constraints for thrust balance and lift-weight balance. The dimension of the state variables is reduced, and a dimension-reduced flight dynamic model is obtained.

[0095] Electric aircraft are mainly used for low-altitude and low-velocity flight. The dynamic equations of electric aircraft are constructed as follows:

[0096]

[0097] Among them, the state variables include altitude h, longitudinal distance x and lateral distance y relative to the starting point, velocity V, track inclination angle γ and track deviation angle χ; the control variables and external forces include roll angle σ, thrust T, aerodynamic drag D and lift L; other parameters include gravitational acceleration g and total mass of the aircraft m;

[0098] The thrust T in the above equation is provided by the electrodynamic system, and this process is described by the following electrodynamic system equations:

[0099]

[0100] Among them, Q B Q consumes power for the battery max I represents the total capacity of a single battery cell. B U is the battery load current. B R is the battery output voltage. B U is the internal resistance of the battery. OC N is the open-circuit voltage. S and N P β1, β2, β3, β4 are the number of cells connected in series and parallel in the battery pack, respectively; SOC is the state of charge of the battery; [β1, β2, β3, β4] are all constants; I M R is the motor current, ν is the motor controller duty cycle, and R is the motor current. M K is the internal resistance of the motor. E Let L be the back electromotive force constant of the motor, ω be the rotational speed of the motor-propeller shaft, and L be the rotational speed of the propeller shaft. M K is the motor inductance. T J is the motor torque constant. M Let C be the moment of inertia of the motor shaft. Q D is the propeller torque coefficient. P J is the propeller diameter. P The moment of inertia of the propeller;

[0101] Compared to traditional aircraft, the dynamics system of the aforementioned electric aircraft has higher dimensionality and stronger nonlinearity, resulting in slower calculation of the reachable domain. This embodiment introduces a quasi-static assumption, meaning that the electric aircraft is in a trim state at all times during flight, with constant speed and altitude, denoted as V = V0. C h = h C γ = 0, and V C h C Since all are constant values, equation (1) can be simplified as follows:

[0102]

[0103] Equation (3) can be further decoupled into two parts, which are the kinematic equations of the electric aircraft in the horizontal plane:

[0104]

[0105] And to maintain the drag balance and lift-weight balance equation constraints at a given speed and height; due to mass and speed V C Since neither of them is zero, the fourth and fifth fractions of equation (3) can be simplified as follows:

[0106]

[0107] Calculate the aircraft trim drag based on the lift and drag expressions and the relationship under trim conditions:

[0108] For an electric aircraft with a wing configuration, lift and drag can be expressed as:

[0109]

[0110] Among them, S R For reference area, C L and C D These are the lift coefficient and drag coefficient, respectively, where α is the angle of attack and C is the drag coefficient. L0 C Lα C D0 Both k and k are constants;

[0111] Given the roll angle σ and the total mass m of the aircraft, the required lift and lift coefficient are respectively:

[0112]

[0113] Therefore, the corresponding drag coefficients and the required resistance to balance can be obtained as follows:

[0114]

[0115] Therefore, based on the thrust-resistance balance relationship in equation (5), it can be known that D in equation (8) is the total balancing thrust T.

[0116] The propeller equilibrium speed that satisfies the trim thrust and propeller thrust expressions is calculated as follows:

[0117] The trim thrust T is provided by the propeller of the electric power system, and the expression for the propeller thrust is:

[0118]

[0119] Among them, C T For thrust coefficient, [C] t2 C t1 C t0 ] are all constants, and C t2 <0, C t1 >0, C t0 >0; represents the propeller advance ratio;

[0120] Substituting the balancing resistance into equation (9), we obtain the following equation regarding the required rotational speed ω:

[0121]

[0122] The simplified formula (10) yields:

[0123]

[0124] And rearranged into the following quadratic equation in ω:

[0125] a2ω 2 +a1ω+a0=0

[0126]

[0127] To ensure that the balancing speed is positive, the following solution should be taken from equation (12):

[0128]

[0129] This is the propeller balance speed that satisfies the trim flight state of an electric aircraft.

[0130] Based on the simplified electrodynamic system model using the characteristics of the motor and battery, the duty cycle of the motor controller and the cell load current in the balanced state are obtained by solving:

[0131] In the electrodynamic system model of Equation (2), the speed and current regulation response of the motor are much faster than the rigid body motion of the electric aircraft. Therefore, it can be assumed that the motor is also at a steady-state operating point when the aircraft is in a trim state. However, the battery power consumption in Equation (2) is a slow accumulation process. The change rate of battery power consumption in Equation (2) is then reduced. The equations other than those in the equations simplify to:

[0132]

[0133] This can be further simplified into the following equation constraint:

[0134]

[0135] Solving equation (15) yields the motor controller duty cycle and cell load current in the balanced state:

[0136]

[0137] Thus, all state variables of the electrodynamic system can be obtained without numerical integration.

[0138] S2. Perform energy discretization on the reduced-dimensional flight dynamics model, transforming the dynamic equations relative to time into the form relative to energy consumption values, and determine the simulation interval and discrete grid.

[0139] The dynamic equations of the electric aircraft are simplified based on the quasi-static assumption, and the state variables involved are derivatives with respect to time t. In subsequent simulations, the total flight time t is... fSince it is an unknown quantity, it is impossible to pre-select the simulation time interval or choose an appropriate simulation time step. Transforming the dynamic equations relative to time into forms relative to power consumption, for the state vector x, we have:

[0140]

[0141] Then the state derivatives in the electric aircraft motion equation of equation (4) are transformed into:

[0142]

[0143] Among them, I B This represents the cell current.

[0144] The simulation range is set as the initial power consumption value Q0 and the final allowable value Q. f The total number of discrete grids for the electrical quantity is N. Q Then the interval ΔQ is:

[0145]

[0146] The discrete grid is:

[0147] Q0, Q0+ΔQ, Q0+2ΔQ, …, Q0+N Q ΔQ, (21).

[0148] S3. Based on the reduced-dimensional flight dynamics model, by setting the roll angle numerical sequence, numerical integration simulation is performed on the simulation interval and discrete grid to obtain the boundary of the horizontal maneuverable domain of the electric aircraft.

[0149] Within the allowable roll maneuverability of electric aircraft, from the minimum roll angle σ min to the maximum value σ max Select a series of roll angle values, and set the total number of required simulated roll angles to N. σ Then the roll angle interval Δσ is:

[0150]

[0151] The roll angle sequence is as follows:

[0152] σ min ,σ min +Δσ,σ min +2Δσ,…,σ max (twenty three);

[0153] Based on the roll angle sequence given in equation (23), numerical integration simulations are performed sequentially on the interval and discrete grid defined in equation (21), with a total number of simulations of N. σIn each simulation, the roll angle σ is fixed to the value corresponding to equation (23) and remains unchanged. The initial state variables of the electric aircraft in equation (4) are set as follows:

[0154] x(Q0)=0, y(Q0)=0, χ(Q0)=0 (24);

[0155] The constant speed and altitude of the aircraft are V0 and h0, respectively. The state variables of the electrodynamic system required for each step in the simulation can be obtained by substituting the current roll angle σ into equations (13), (16), and (17) and then by algebraic operations.

[0156] Corresponding to N σ The simulation yielded the following two matrices representing the position sequence of the electric aircraft in the horizontal plane:

[0157]

[0158] Where X and Y are the longitudinal and transverse position matrices in the horizontal plane, respectively, each row of the matrix represents the result of each simulation, and the data length of each row is N. Q All simulation results are arranged into a matrix, which has N rows. σ The data constituting the boundary of the horizontal maneuverability domain of an electric aircraft are the last columns of X and Y respectively:

[0159]

[0160] Among them, X B and Y B These are the longitudinal and lateral coordinate sequences of the horizontal maneuverable reachable domain boundary of an electric aircraft.

[0161] A specific embodiment of this method is as follows: Assuming that the starting point of the electric aircraft is located at the origin (0,0) of the coordinate system, and given four flight altitudes of 1km, 2km, 3km and 4km respectively, and a flight speed of 50m / s, the reachable domain of the aircraft is calculated using this method. Figures 2 to 5 The flight reachable domains of the example aircraft at four flight altitudes of 1km, 2km, 3km, and 4km are shown in sequence. The solid lines represent the flight trajectories of the aircraft after exhausting its available power under different roll angles, and the dotted lines represent the reachable domains determined by all flight trajectories. Figure 6 This further illustrates the impact of flight altitude on the reachable range.

[0162] The beneficial effects of this invention are as follows:

[0163] By employing the embodiments of the present invention, the flight dynamics equations of the cruise flight phase of a winged electric aircraft are transformed through quasi-static transformation, which significantly reduces the system dimension and improves the numerical integration speed. By discretizing the electric charge, the original time-domain-based electric aircraft dynamics equations are transformed into those based on the electric charge dissipation domain, thereby transforming the uncertain time intervals and step sizes of the numerical simulation of the flight process into definite intervals and step size values, further improving the simulation speed.

[0164] System Implementation Examples

[0165] According to embodiments of the present invention, an reachability domain assessment system for electric aircraft based on quasi-static energy discreteness is provided. Figure 7 A schematic diagram illustrating the composition of an electric aircraft reachability domain assessment system based on quasi-static energy discreteness, provided for one or more embodiments of this specification, is shown below. Figure 7 As shown, the reachability domain assessment system for electric aircraft based on quasi-static energy discreteness according to an embodiment of the present invention specifically includes:

[0166] Model Dimensionality Reduction Module 70: Used to perform quasi-static dimensionality reduction transformation on the dynamics model of electric aircraft. Based on the quasi-static assumption, the dynamics equations of electric aircraft are simplified and decoupled into kinematic equations in the horizontal plane and equation constraints for thrust balance and lift-weight balance, thereby reducing the dimension of state variables and obtaining a dimensionality-reduced flight dynamics model.

[0167] Model conversion module 72: used to perform power discretization on the reduced-dimensional flight dynamics model, converting the dynamic equations relative to time into the form of power consumption values, and determining the simulation interval and discrete grid;

[0168] Reachability domain assessment module 74: Based on the reduced-dimensional flight dynamics model, it performs numerical integration simulation on the simulation interval and discrete grid by setting a roll angle numerical sequence to obtain the horizontal maneuverability domain boundary of the electric aircraft.

[0169] The embodiments of the present invention are system embodiments corresponding to the above method embodiments. The specific operation of each module can be understood by referring to the description of the method embodiments, and will not be repeated here.

[0170] Device Example 1

[0171] This invention provides an electronic device, such as... Figure 8 As shown, it includes: a memory 80, a processor 82, and a computer program stored in the memory 80 and executable on the processor 82. When the computer program is executed by the processor 82, it performs the following method steps:

[0172] S1. Quasi-static dimensionality reduction transformation is performed on the dynamic model of electric aircraft. Based on the quasi-static assumption, the dynamic equations of electric aircraft are simplified and decoupled into kinematic equations in the horizontal plane and equation constraints for thrust balance and lift-weight balance. The dimension of state variables is reduced to obtain a dimensionality-reduced flight dynamic model.

[0173] S2. Perform energy discretization on the reduced-dimensional flight dynamics model, transforming the dynamic equations relative to time into the form relative to energy consumption values, and determine the simulation interval and discrete grid;

[0174] S3. Based on the reduced-dimensional flight dynamics model, by setting the roll angle numerical sequence, numerical integration simulation is performed on the simulation interval and discrete grid to obtain the boundary of the horizontal maneuverable domain of the electric aircraft.

[0175] Device Example 2

[0176] This invention provides a computer-readable storage medium storing an information transmission implementation program. When executed by a processor 82, the program performs the following method steps:

[0177] S1. Quasi-static dimensionality reduction transformation is performed on the dynamic model of electric aircraft. Based on the quasi-static assumption, the dynamic equations of electric aircraft are simplified and decoupled into kinematic equations in the horizontal plane and equation constraints for thrust balance and lift-weight balance. The dimension of state variables is reduced to obtain a dimensionality-reduced flight dynamic model.

[0178] S2. Perform energy discretization on the reduced-dimensional flight dynamics model, transforming the dynamic equations relative to time into the form relative to energy consumption values, and determine the simulation interval and discrete grid;

[0179] S3. Based on the reduced-dimensional flight dynamics model, by setting the roll angle numerical sequence, numerical integration simulation is performed on the simulation interval and discrete grid to obtain the boundary of the horizontal maneuverable domain of the electric aircraft.

[0180] The computer-readable storage media described in this embodiment include, but are not limited to, ROM, RAM, disk, or optical disk.

[0181] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the reachability region of an electric aircraft based on quasi-static charge discretization, characterized in that, include: S1. Quasi-static dimensionality reduction transformation is performed on the dynamic model of electric aircraft. Based on the quasi-static assumption, the dynamic equations of electric aircraft are simplified and decoupled into kinematic equations in the horizontal plane and equation constraints for thrust balance and lift-weight balance. The dimension of state variables is reduced to obtain a dimensionality-reduced flight dynamic model. The dynamic equations of an electric aircraft are shown below: （1）； Among them, the state quantity includes altitude. Longitudinal distance relative to the starting point and lateral distance ,speed Track inclination and track deflection Control parameters and external forces include roll angle. ,thrust Aerodynamic drag and lift Other parameters include gravitational acceleration. Total mass of aircraft ; The thrust in the above formula Powered by an electrodynamic system, this process is described by the following electrodynamic system equations: （2）； in, To consume power for the battery, This refers to the total capacity of a single battery cell. This is the battery load current. This is the battery output voltage. This refers to the battery's internal resistance. Open circuit voltage, and These represent the number of batteries connected in series and in parallel within the battery pack. The battery is in its state of charge. All are constants. This is the motor current. This refers to the duty cycle of the motor controller. The internal resistance of the motor, Let be the back electromotive force constant of the motor. The rotational speed of the motor-propeller shaft. For motor inductance, The torque constant of the motor. The moment of inertia of the motor shaft. This is the propeller torque coefficient. The diameter of the propeller. The moment of inertia of the propeller; The quasi-static assumption is introduced, meaning that the electric aircraft is in a trim state at all times during flight, and its speed and altitude are constant values, respectively. , , ,and , Since all are constant values, equation (1) can be simplified as follows: （3）； Equation (3) can be further decoupled into two parts, which are the kinematic equations of the electric aircraft in the horizontal plane: （4）； And the drag balance and lift-weight balance equation constraints to maintain a given speed and altitude; due to mass and speed Since neither of them is zero, the fourth and fifth fractions of equation (3) can be simplified as follows: （5）； S2. Perform energy discretization on the reduced-dimensional flight dynamics model, transforming the dynamic equations relative to time into the form relative to energy consumption values, and determine the simulation interval and discrete grid; S3. Based on the reduced-dimensional flight dynamics model, by setting the roll angle numerical sequence, numerical integration simulation is performed on the simulation interval and discrete grid to obtain the boundary of the horizontal maneuverable domain of the electric aircraft.

2. The evaluation method according to claim 1, characterized in that, Calculate the aircraft trim drag based on the lift and drag expressions and the relationship under trim conditions: For an electric aircraft with a wing configuration, lift and drag can be expressed as: （6）； in, For reference area, and These are the lift coefficient and drag coefficient, respectively. For the angle of attack, , , , All are constants; When a roll angle is given and the total mass of the aircraft At that time, the required lift and lift coefficient are respectively: （7）； Therefore, the corresponding drag coefficients and the required resistance to balance can be obtained as follows: （8）； Therefore, based on the deduction balance relationship in equation (5), we can know that in equation (8) For total balanced thrust .

3. The evaluation method according to claim 1, characterized in that, The propeller equilibrium speed that satisfies the trim thrust and propeller thrust expressions is calculated as follows: The balance thrust The propeller, powered by an electric propulsion system, provides the thrust, expressed as: （9）； in, For thrust coefficient, All are constants, and , , ; This refers to the propeller's forward ratio; Substituting the balancing resistance into equation (9) yields the required rotational speed. The equation is as follows: （10）； The simplified formula (10) yields: （11）； And compiled as follows about The quadratic equation of : （12）； To ensure that the balancing speed is positive, the following solution should be taken from equation (12): （13）； This is the propeller balance speed that satisfies the trim flight state of an electric aircraft.

4. The evaluation method according to claim 1, characterized in that, Based on the simplified electrodynamic system model using the characteristics of the motor and battery, the duty cycle of the motor controller and the cell load current in the balanced state are obtained by solving: Remove the battery power consumption rate from equation (2) The equations other than those in the equations simplify to: （14）； This can be further simplified into the following equation constraint: （15）； Solving equation (15) yields the motor controller duty cycle and cell load current in the balanced state: （16）； （17）； Thus, all state variables of the electrodynamic system can be obtained without numerical integration.

5. The evaluation method according to claim 1, characterized in that, The energy consumption discretization transformation is performed on the reduced-dimensional flight dynamics model, converting the dynamic equations relative to time into forms relative to energy consumption values. The specific method for determining the simulation interval and discrete grid is as follows: Transforming the dynamic equations relative to time into forms relative to energy consumption values, for the state vector... Then we have: （18）； Then the state derivatives in the electric aircraft motion equation of equation (4) are transformed into: （19）； Set the simulation range to the initial value of power consumption. and final allowable value The total number of discrete grids for electrical energy is Then the interval for: （20）； The discrete grid is: （21）。 6. The evaluation method according to claim 1, characterized in that, Based on the reduced-dimensional flight dynamics model, by setting a numerical sequence of roll angles and performing numerical integration simulations on the simulation interval and discrete grid, the specific method for obtaining the boundary of the horizontal maneuverable domain of the electric aircraft is as follows: Within the allowable roll maneuverability of electric aircraft, from the minimum roll angle... To the maximum value Select a series of roll angle values, and set the total number of simulated roll angles required to be [value missing]. Then the roll angle interval for: （22）； The roll angle sequence is as follows: （23）； Based on the roll angle sequence given in equation (23), numerical integration simulations are performed sequentially on the interval and discrete grid defined in equation (21), with a total number of simulations of [number missing]. The roll angle in each simulation The values ​​in equation (23) are fixed and remain unchanged, and the initial state quantities of the electric aircraft in equation (4) are set as follows: （24）； The aircraft's constant speed and altitude are respectively and In the simulation, the state variables of the electrodynamic system required for each step can be determined by the current roll angle. Substitute these into equations (13), (16), and (17), and then obtain the results through algebraic operations; correspond The simulation yielded the following two matrices representing the position sequence of the electric aircraft in the horizontal plane: （25）； in, , These are the vertical and horizontal position matrices within the horizontal plane, respectively. Each row of the matrix represents the result of each simulation, and the data length of each row is [data length missing]. All simulation results are arranged into a matrix, and the matrix has 100 rows. The data constituting the boundary of the horizontal maneuverable reachable domain of an electric aircraft are: , The last column for each: （26）； in, and These are the longitudinal and lateral coordinate sequences of the horizontal maneuverable reachable domain boundary of an electric aircraft.

7. A system for evaluating the reachability domain of electric aircraft based on quasi-static energy discreteness, characterized in that, include: Model Dimensionality Reduction Module: Used to perform quasi-static dimensionality reduction transformation on the dynamics model of electric aircraft. Based on the quasi-static assumption, the dynamics equations of electric aircraft are simplified and decoupled into kinematic equations in the horizontal plane and equation constraints for thrust balance and lift-weight balance, thereby reducing the dimension of state variables and obtaining a dimensionality-reduced flight dynamics model. The dynamic equations of an electric aircraft are shown below: （1）； Among them, the state quantity includes altitude. Longitudinal distance relative to the starting point and lateral distance ,speed Track inclination and track deflection Control parameters and external forces include roll angle. ,thrust Aerodynamic drag and lift Other parameters include gravitational acceleration. Total mass of aircraft ; The thrust in the above formula Powered by an electrodynamic system, this process is described by the following electrodynamic system equations: （2）； in, To consume power for the battery, This refers to the total capacity of a single battery cell. This is the battery load current. This is the battery output voltage. This refers to the battery's internal resistance. Open circuit voltage, and These represent the number of batteries connected in series and in parallel within the battery pack. The battery is in its state of charge. All are constants. This is the motor current. This refers to the duty cycle of the motor controller. The internal resistance of the motor, Let be the back electromotive force constant of the motor. The rotational speed of the motor-propeller shaft. For motor inductance, The torque constant of the motor. The moment of inertia of the motor shaft. This is the propeller torque coefficient. The diameter of the propeller. The moment of inertia of the propeller; The quasi-static assumption is introduced, meaning that the electric aircraft is in a trim state at all times during flight, and its speed and altitude are constant values, respectively. , , ,and , Since all are constant values, equation (1) can be simplified as follows: （3）； Equation (3) can be further decoupled into two parts, which are the kinematic equations of the electric aircraft in the horizontal plane: （4）； And the drag balance and lift-weight balance equation constraints to maintain a given speed and altitude; due to mass and speed Since neither of them is zero, the fourth and fifth fractions of equation (3) can be simplified as follows: （5）； Model Conversion Module: Used to perform energy discretization on the reduced-dimensional flight dynamics model, converting the dynamic equations relative to time into the form of energy consumption values, and determining the simulation interval and discrete grid. The reachability domain assessment module is used to obtain the horizontal maneuverability domain boundary of the electric aircraft by performing numerical integration simulation on the simulation interval and discrete grid based on the reduced-dimensional flight dynamics model and by setting the roll angle numerical sequence.

8. An electronic device, characterized in that, include: processor; as well as, A memory configured to store computer-executable instructions, which, when executed, cause the processor to implement the steps of the electric aircraft reachability assessment method based on quasi-static power discreteness as described in any one of claims 1 to 6.

9. A storage medium, characterized in that, Used to store computer-executable instructions, which, when executed, implement the steps of the electric aircraft reachability assessment method based on quasi-static power discreteness as described in any one of claims 1 to 6.

Images