Electric aircraft reachable domain evaluation method and system based on quasi-static electric quantity discretization

Abstract

The embodiment of the invention provides an electric aircraft reachable domain evaluation method and system based on quasi-static electric quantity discretization, and the method comprises the steps: carrying out the quasi-static dimensionality reduction conversion of an electric aircraft kinetic model, simplifying an electric aircraft kinetic equation according to a quasi-static hypothesis, and obtaining an electric aircraft reachable domain evaluation result; decoupling the model into a kinematics equation in a horizontal plane and equality constraints of thrust-drag balance and lift-weight balance, and reducing state quantity dimensions to obtain a dimension-reduced flight dynamics model; performing electric quantity discrete conversion on the dimensionality reduction flight dynamics model, converting a dynamics equation relative to time into a form relative to an electric quantity consumption value, and determining a simulation interval and a discrete grid; and on the basis of the dimension reduction flight dynamics model, numerical integration simulation is carried out on the simulation interval and the discrete grid by setting a roll angle numerical sequence, and the electric aircraft horizontal plane maneuvering reachable domain boundary is obtained.

Description

Technical Field

[0001] This document relates to the technical field of electric aircraft, and particularly to a method and system for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization. Background Art

[0002] Medium or large electric aircraft with vertical takeoff and landing characteristics and the ability to carry people. Among them, winged electric aircraft can achieve efficient and high-speed flight based on the aerodynamic characteristics of the wings during the cruise phase, and are expected to be applied to future urban air traffic to achieve low-altitude commuting. During the flight in low-altitude airspace, to ensure that the electric aircraft avoids various static or dynamic no-fly zones such as buildings and other non-cooperative aircraft and realizes safe flight, it is necessary to quickly evaluate its flight reachable domain according to the current available energy state of the electric aircraft, and then provide a reference for online re-planning of flight tasks. However, when analyzing the reachable domain of an electric aircraft using existing numerical simulation or optimization methods, there are problems such as long time consumption and difficult convergence, which are difficult to meet the rapidity requirements of urban air traffic. Summary of the Invention

[0003] One or more embodiments of this specification provide a method for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization, including:

[0004] S1. Perform quasi-static dimensionality reduction transformation on the dynamic model of the electric aircraft, simplify the dynamic equation of the electric aircraft according to the quasi-static assumption, decouple it into kinematic equations in the horizontal plane and equality constraints of thrust-drag balance and lift-weight balance, reduce the dimensionality of the state variables, and obtain a reduced-dimensional flight dynamic model;

[0005] S2. Perform power discretization transformation on the reduced-dimensional flight dynamic model, transform the dynamic equation with respect to time into a form with respect to the power consumption value, and determine the simulation interval and discrete grid;

[0006] S3. Based on the reduced-dimensional flight dynamic model, by setting a numerical sequence of roll angles, perform numerical integration simulation on the simulation interval and discrete grid to obtain the boundary of the reachable domain of the electric aircraft in the horizontal plane maneuver.

[0007] Further, the dynamic equation of the electric aircraft is as follows:

[0008]

[0009] Among them, the state variables include altitude h, longitudinal distance x and lateral distance y relative to the starting point, speed V, flight path inclination angle γ and flight path 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 m of the aircraft;

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

[0011]

[0012] Where Q B is the power consumption of the battery, Q max is the total capacity of a single battery, I B is the battery load current, U B is the battery output voltage, R B is the internal resistance of the battery, U OC is the open-circuit voltage, N S and N P are the numbers of batteries 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 is the motor current, ν is the duty ratio of the motor controller, R M is the internal resistance of the motor, K E is the back electromotive force constant of the motor, ω is the rotational speed of the motor-propeller shaft, L M is the inductance of the motor, K T is the torque constant of the motor, J M is the moment of inertia of the motor shaft, C Q is the torque coefficient of the propeller, D P is the diameter of the propeller, J P is the moment of inertia of the propeller;

[0013] Introduce the quasi-static assumption, that is, the electric aircraft is in a trimmed state at all times during flight, and the speed and altitude are both constant values, which are V = V C , h = h C , γ = 0, and V C , h C are all constant values. Thus, 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 the equality constraints of thrust-drag balance and lift-weight balance to maintain the given speed and altitude; since the mass and speed V C are both non-zero, the 4th and 5th fractions of Equation (3) can be simplified as follows:

[0018]

[0019] Furthermore, calculate the trim drag of the aircraft according to the lift, drag expressions and the relationships under the trimmed state:

[0020] For a winged configuration electric aircraft, the lift and drag can be expressed as:

[0021]

[0022] Where S R is the reference area, C L and C D are the lift coefficient and drag coefficient respectively, α is the angle of attack, C L0 , C La , C D0 , k are all constants;

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

[0024]

[0025] Furthermore, the corresponding drag coefficient and the required balanced drag can be obtained as:

[0026]

[0027] From the thrust-drag balance relationship of Equation (5), it can be known that D in Equation (8) is the total trim thrust T.

[0028] Furthermore, calculate the propeller balance rotational speed that satisfies the trimmed flight state from the trim thrust and the propeller thrust expression:

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

[0030]

[0031] Where C T is the thrust coefficient, [C t2 , C t1 , C t0 are all constants, and C t2 <0, C t1 >0, C t0 >0; is the propeller advance ratio;

[0032] Substitute the balanced drag into Equation (9) to obtain the following equation about the required rotational speed ω:

[0033]

[0034] Simplify Equation (10) to get:

[0035]

[0036] And it is arranged into the following quadratic equation of one variable about ω:

[0037] a2ω 2 + a1ω + a0 = 0

[0038]

[0039] To ensure that the trimming speed is positive, the following solution of Equation (12) should be taken:

[0040]

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

[0042] Furthermore, based on the motor and battery characteristics, simplify the electric power system model, and solve to obtain the duty ratio of the motor controller and the core load current in the trimmed state:

[0043] Simplify the equation in Equation (2) except for the battery power consumption change rate as follows:

[0044]

[0045] It can be further arranged into the following equality constraint:

[0046]

[0047] Solve Equation (15) to obtain the duty ratio of the motor controller and the core load current in the trimmed state:

[0048]

[0049] Thus, all state variables of the electric power system are obtained without numerical integration.

[0050] Furthermore, perform power discretization transformation on the reduced-order flight dynamics model, transform the dynamics equation with respect to time into the form with respect to the power consumption value, and the specific methods for determining the simulation interval and discrete grid are as follows:

[0051] Transform the dynamics equation with respect to time into the form with respect to the power consumption value. For the state variable vector x, there is:

[0052]

[0053] Then the derivative of the state variable in the motion equation of the electric aircraft in Equation (4) is transformed into:

[0054]

[0055] Set the simulation interval as the initial value Q0 and the final allowable value Q of the power consumption f , and the total number of power discrete grids 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 - order flight dynamics model, by setting the numerical sequence of the roll angle, numerical integration simulation is carried out on the simulation interval and the discrete grid to obtain the boundary of the reachable domain of the electric aircraft in the horizontal plane. The specific method is as follows:

[0060] Within the allowable range of the roll maneuverability of the electric aircraft, a series of roll angle values are selected from the minimum value σ min of the roll angle to the maximum value σ max . Set the total number of required simulation roll angles as N σ , then the roll angle interval Δσ is:

[0061]

[0062] The roll angle sequence is:

[0063] σ min , σ min +Δσ, σ min +2Δσ, …, σ max (23);

[0064] Based on the roll angle sequence given by Equation (23), numerical integration simulation is carried out on the interval and discrete grid defined by Equation (21) in turn. The total number of simulations is N σ , and the roll angle σ in each simulation is fixed as the corresponding value in Equation (23) and remains unchanged. And set the initial state variables of the electric aircraft in Equation (4) 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 electric power 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 through algebraic operations.

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

[0068]

[0069] Among them, X and Y are respectively the longitudinal and lateral position matrices in the horizontal plane. Each row of the matrix represents the result of each simulation, and the data length of each row is N Q ; All simulation results form a matrix, and the number of rows of the matrix is N σ . The data constituting the boundary of the reachable domain of the electric aircraft's horizontal plane maneuver are the last columns of X and Y respectively:

[0070]

[0071] Among them, X B and Y B are respectively the longitudinal and lateral coordinate sequences of the boundary of the reachable domain of the electric aircraft's horizontal plane maneuver.

[0072] One or more embodiments of this specification provide a reachable domain evaluation system for electric aircraft based on quasi-static power discretization, including:

[0073] Model reduction module: used to perform quasi-static reduction transformation on the dynamic model of the electric aircraft, simplify the dynamic equation of the electric aircraft according to the quasi-static assumption, decouple it into the kinematic equation in the horizontal plane and the equality constraints of thrust-drag balance and lift-weight balance, reduce the dimension of the state variables, and obtain the reduced-order flight dynamic model;

[0074] Model transformation module: used to perform power discretization transformation on the reduced-order flight dynamic model, transform the dynamic equation with respect to time into a form with respect to the power consumption value, and determine the simulation interval and discrete grid;

[0075] Reachable domain evaluation module: used to perform numerical integration simulation on the reduced-order flight dynamic model by setting a numerical sequence of roll angles in the simulation interval and discrete grid to obtain the boundary of the reachable domain of the electric aircraft's horizontal plane maneuver.

[0076] One or more embodiments of this specification provide an electronic device, including:

[0077] A processor; and,

[0078] A memory arranged to store computer-executable instructions, and the computer-executable instructions, when executed, cause the processor to implement the steps of the above-mentioned method for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization.

[0079] One or more embodiments of this specification provide a storage medium for storing computer-executable instructions, and the computer-executable instructions, when executed, implement the steps of the above-mentioned method for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization.

[0080] By adopting the embodiments of the present invention, the flight dynamics equations in the cruise flight stage of the winged electric aircraft are quasi-statically transformed, significantly reducing the system dimension and improving the numerical integration speed; through electricity quantity discretization, the original electric aircraft dynamics equations based on the time domain are transformed into those based on the electricity dissipation domain, so that the uncertain time intervals and step sizes in the numerical simulation of the flight process are transformed into definite interval and step size values, further improving the simulation speed.

[0081] The above description is only an overview of the technical solution of the present invention. In order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the specification. And in order to make the above and other purposes, features and advantages of the present invention more obvious and understandable, the specific embodiments of the present invention are specifically exemplified below. Brief Description of the Drawings

[0082] In order to more clearly illustrate the technical solutions in one or more embodiments of this specification or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in this specification. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0083] Figure 1 It is a flowchart of a method for evaluating the reachable domain of an electric aircraft based on quasi-static electricity quantity discretization provided for one or more embodiments of this specification;

[0084] Figure 2 It is a schematic diagram of the reachable domain calculated at a flight altitude of 1 km for a method for evaluating the reachable domain of an electric aircraft based on quasi-static electricity quantity discretization provided for one or more embodiments of this specification;

[0085] Figure 3 It is a schematic diagram of the reachable domain calculated at a flight altitude of 2 km for a method for evaluating the reachable domain of an electric aircraft based on quasi-static electricity quantity discretization provided for one or more embodiments of this specification;

[0086] Figure 4 It is a schematic diagram of the reachable domain calculated at a flight altitude of 3 km for a method for evaluating the reachable domain of an electric aircraft based on quasi-static electricity quantity discretization provided for one or more embodiments of this specification;

[0087] Figure 5 It is a schematic diagram of the reachable domain calculated at a flight altitude of 4 km for a method for evaluating the reachable domain of an electric aircraft based on quasi-static electricity quantity discretization provided for one or more embodiments of this specification;

[0088] Figure 6Schematic diagram of the reachable domain calculation results at 4 flight altitudes for a method for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization provided by one or more embodiments of this specification;

[0089] Figure 7 Schematic diagram of the composition of a system for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization provided by one or more embodiments of this specification;

[0090] Figure 8 Schematic diagram of the structure of an electronic device provided by one or more embodiments of this specification. Detailed implementation manners

[0091] In order to enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the following will clearly and completely describe the technical solutions in one or more embodiments of this specification with reference to the accompanying drawings in one or more embodiments of this specification. Obviously, the described embodiments are only a part of the embodiments of this specification, rather than all the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of this document.

[0092] Method embodiments

[0093] According to an embodiment of the present invention, there is provided a method for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization, Figure 1 Flowchart of a method for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization provided by one or more embodiments of this specification, as Figure 1 shown, the method for evaluating the reachable domain of an electric aircraft based on quasi-static power discretization according to an embodiment of the present invention specifically includes:

[0094] S1. Perform quasi-static dimensionality reduction transformation on the dynamic model of the electric aircraft, simplify the dynamic equation of the electric aircraft according to the quasi-static assumption, decouple it into the kinematic equation in the horizontal plane and the equality constraints of thrust-drag balance and lift-weight balance, reduce the dimensionality of the state variables, and obtain a reduced-dimensional flight dynamic model.

[0095] The electric aircraft is mainly used for low-altitude and low-speed flight. The dynamic equation of the electric aircraft is 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, speed V, flight path inclination angle γ and flight path 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 m of the aircraft;

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

[0099]

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

[0101] Compared with traditional aircraft, the above-mentioned electric aircraft dynamics system has a high dimension and strong nonlinearity, so the reachable domain calculation is slow. In this embodiment, a quasi-static assumption is introduced, that is, the electric aircraft is in a trimmed state at all times during flight, and the speed and altitude are both constant values, which are V = V C , h = h C , γ = 0, and V C , h C are both constant values. Thus, formula (1) can be simplified as follows:

[0102]

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

[0104]

[0105] and the equality constraints of thrust-drag balance and lift-weight balance to maintain the given speed and altitude; since the mass and speed V C are both non-zero, the 4th and 5th fractions of formula (3) can be simplified as follows:

[0106]

[0107] Calculate the trim drag of the aircraft according to the lift, drag expressions and the relationships under the trimmed state:

[0108] For a winged configuration electric aircraft, the lift and drag can be expressed as:

[0109]

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

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

[0112]

[0113] Furthermore, the corresponding drag coefficient and the required balanced drag can be obtained as:

[0114]

[0115] From the thrust-drag balance relationship of Equation (5), it can be known that D in Equation (8) is the total trim thrust T.

[0116] Calculate the propeller balance rotational speed that satisfies the trimmed flight state from the trim thrust and the propeller thrust expression:

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

[0118]

[0119] where C T is the thrust coefficient, [C t2 , C t1 , C t0 are all constants, and C t2 < 0, C t1 > 0, C t0 > 0; is the propeller advance ratio;

[0120] Substitute the balanced drag into Equation (9) to obtain the following equation about the required rotational speed ω:

[0121]

[0122] Simplify Equation (10) to get:

[0123]

[0124] And it is arranged into the following quadratic equation of one variable about ω:

[0125] a2ω 2 + a1ω + a0 = 0

[0126]

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

[0128]

[0129] This is the balanced rotational speed of the propeller that satisfies the trimmed flight state of the electric aircraft.

[0130] Based on the characteristics of the motor and battery, the electric power system model is simplified, and the duty ratio of the motor controller and the core load current in the trimmed state are obtained by solving:

[0131] In the electric power system model of equation (2), the speed and current regulation response speed of the motor are much faster than the rigid body motion of the electric aircraft. Therefore, it can be considered that the motor is also at the steady-state operating point when the aircraft is in the trimmed state; while the battery power consumption in equation (2) is a slow accumulation process. Excluding the battery power consumption change rate in equation (2) The equations other than are simplified to:

[0132]

[0133] It can be further arranged into the following equality constraint:

[0134]

[0135] Solving equation (15) to obtain the duty ratio of the motor controller and the core load current in the trimmed state:

[0136]

[0137] Thus, all state variables of the electric power system are obtained without numerical integration.

[0138] S2. Perform power discretization transformation on the reduced-order flight dynamics model, transform the dynamic equation with respect to time into a form with respect to the power consumption value, and determine the simulation interval and discrete grid.

[0139] Based on the quasi-static assumption, the dynamic equation of the electric aircraft is simplified. The state variables involved are the derivatives with respect to time t, and in the subsequent simulation, the total flight time t fis an unknown quantity. Therefore, it is impossible to select the simulation time interval range in advance, and it is also difficult to select an appropriate simulation time step. By transforming the dynamic equation with respect to time into a form with respect to the power consumption value, for the state quantity vector x, we have:

[0140]

[0141] Then, the derivative of the state quantity in the motion equation of the electric aircraft in Equation (4) is transformed into:

[0142]

[0143] where I B is the cell current.

[0144] Set the simulation interval as the initial value Q0 and the final allowable value Q f of the power consumption, and the total number of power discrete grids 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-order flight dynamics model, by setting a sequence of roll angle values, numerical integration simulation is performed on the simulation interval and discrete grid to obtain the boundary of the reachable domain of the electric aircraft in the horizontal plane maneuver.

[0149] Within the allowable range of the roll maneuverability of the electric aircraft, a series of roll angle values are selected from the minimum value σ min to the maximum value σ max . Set the total number of required simulation roll angles as N σ . Then the roll angle interval Δσ is:

[0150]

[0151] The roll angle sequence is:

[0152] σ min , σ min + Δσ, σ min + 2Δσ, …, σ max (23);

[0153] Based on the roll angle sequence given in Equation (23), numerical integration simulation is performed on the interval and discrete grid defined in Equation (21) in sequence, and the total number of simulations is N σ, the roll angle σ in each simulation is fixed at the corresponding value in 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 electric power 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 through algebraic operations.

[0156] Corresponding to N σ The position sequences of the electric aircraft in the horizontal plane obtained by simulation are the following two matrices:

[0157]

[0158] Among them, X and Y are the longitudinal and lateral 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 form a matrix, and the number of rows of the matrix is N σ . The data constituting the boundary of the maneuverable reachable area of the electric aircraft in the horizontal plane are the last columns of X and Y respectively:

[0159]

[0160] Among them, X B and Y B are the longitudinal and lateral coordinate sequences of the boundary of the maneuverable reachable area of the electric aircraft in the horizontal plane respectively.

[0161] A specific embodiment of the present method is as follows. Assume that the flight starting point of the electric aircraft is located at the origin (0, 0) of the coordinate system. Four flight altitudes of 1 km, 2 km, 3 km, and 4 km are given respectively, and the flight speed is 50 m / s. The reachable area of the aircraft is calculated using the present method. Figures 2 to 5 The flight reachable areas of the example aircraft at four flight altitudes of 1 km, 2 km, 3 km, and 4 km are shown in sequence. Among them, the solid line is the flight trajectory of the aircraft when the available power is exhausted under the action of different roll angles, and the dotted line is the reachable area determined by all flight trajectories; Figure 6 It further shows the influence of flight altitude on the range of the reachable area.

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

[0163] By adopting the embodiments of the present invention, the flight dynamics equations in the cruise flight stage of the winged configuration electric aircraft are transformed through quasi-static transformation, significantly reducing the system dimension and improving the numerical integration speed; through the discretization of electric quantity, the original electric aircraft dynamics equations based on the time domain are transformed into those based on the electric quantity dissipation domain, so that the uncertain time intervals and step sizes in the numerical simulation of the flight process are transformed into definite interval and step size values, further improving the simulation speed.

[0164] System embodiment

[0165] According to the embodiments of the present invention, there is provided an evaluation system for the reachable domain of an electric aircraft based on quasi-static electric quantity discretization. Figure 7 FIG. is a schematic diagram of the composition of an evaluation system for the reachable domain of an electric aircraft based on quasi-static electric quantity discretization provided for one or more embodiments of this specification. As Figure 7 shown, the evaluation system for the reachable domain of an electric aircraft based on quasi-static electric quantity discretization according to the embodiments of the present invention specifically includes:

[0166] Model dimension reduction module 70: used to perform quasi-static dimension reduction transformation on the electric aircraft dynamics model, simplify the electric aircraft dynamics equations according to the quasi-static assumption, decouple them into kinematic equations in the horizontal plane and equality constraints of thrust-drag balance and lift-weight balance, reduce the dimension of state variables, and obtain a dimension-reduced flight dynamics model;

[0167] Model transformation module 72: used to perform electric quantity discretization transformation on the dimension-reduced flight dynamics model, transform the dynamics equations with respect to time into a form with respect to the electric quantity consumption value, and determine the simulation interval and discrete grid;

[0168] Reachable domain evaluation module 74: used to perform numerical integration simulation on the simulation interval and discrete grid based on the dimension-reduced flight dynamics model by setting a numerical sequence of roll angles, and obtain the boundary of the reachable domain of the electric aircraft's horizontal plane maneuver.

[0169] The embodiments of the present invention are system embodiments corresponding to the above method embodiments. The specific operations of each module can be understood with reference to the description of the method embodiments and will not be elaborated here.

[0170] Device embodiment 1

[0171] The embodiments of the present invention provide an electronic device. As Figure 8 shown, it includes: a memory 80, a processor 82, and a computer program stored on the memory 80 and executable on the processor 82. When the computer program is executed by the processor 82, the following method steps are implemented:

[0172] S1. Perform quasi - static dimensionality reduction transformation on the dynamic model of the electric aircraft. Simplify the dynamic equations of the electric aircraft according to the quasi - static assumption, decouple them into kinematic equations in the horizontal plane and equality constraints of thrust - drag balance and lift - weight balance, reduce the dimension of the state variables, and obtain a reduced - order flight dynamic model;

[0173] S2. Perform power consumption discretization transformation on the reduced - order flight dynamic model, transform the dynamic equations with respect to time into the form with respect to the power consumption value, and determine the simulation interval and discrete grid;

[0174] S3. Based on the reduced - order flight dynamic model, by setting a numerical sequence of roll angles, perform numerical integration simulation on the simulation interval and discrete grid to obtain the boundary of the horizontal plane maneuverable reachable domain of the electric aircraft.

[0175] Device Embodiment II

[0176] An embodiment of the present invention provides a computer - readable storage medium, on which an implementation program for information transmission is stored. When the program is executed by a processor 82, the following method steps are implemented:

[0177] S1. Perform quasi - static dimensionality reduction transformation on the dynamic model of the electric aircraft. Simplify the dynamic equations of the electric aircraft according to the quasi - static assumption, decouple them into kinematic equations in the horizontal plane and equality constraints of thrust - drag balance and lift - weight balance, reduce the dimension of the state variables, and obtain a reduced - order flight dynamic model;

[0178] S2. Perform power consumption discretization transformation on the reduced - order flight dynamic model, transform the dynamic equations with respect to time into the form with respect to the power consumption value, and determine the simulation interval and discrete grid;

[0179] S3. Based on the reduced - order flight dynamic model, by setting a numerical sequence of roll angles, perform numerical integration simulation on the simulation interval and discrete grid to obtain the boundary of the horizontal plane maneuverable reachable domain of the electric aircraft.

[0180] The computer - readable storage medium described in this embodiment includes, but is not limited to: ROM, RAM, magnetic disk or optical disk, etc.

[0181] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the reachable domain of an electric aircraft based on the discretization of quasi-static electrical quantities, characterized in that, Including: S1. Perform quasi-static dimensionality reduction transformation on the dynamic model of the electric aircraft. Simplify the dynamic equation of the electric aircraft according to the quasi-static assumption, decouple it into the kinematic equation in the horizontal plane and the equality constraints of thrust-drag balance and lift-weight balance, reduce the dimensionality of the state variables, and obtain the reduced-order flight dynamic model; S2. Perform electric quantity discretization transformation on the reduced-order flight dynamic model, transform the dynamic equation with respect to time into a form with respect to the electric quantity consumption value, and determine the simulation interval and discrete grid; S3. Based on the reduced-order flight dynamic model, by setting a numerical sequence of roll angles, perform numerical integration simulation on the simulation interval and discrete grid to obtain the boundary of the maneuverable reachable domain of the electric aircraft in the horizontal plane.

2. The evaluation method according to claim 1, characterized in that, The dynamic equation of the electric aircraft is as follows: Among them, the state variables include the altitude h, the longitudinal distance x and the lateral distance y relative to the starting point, the speed V, the flight path inclination angle γ and the flight path deviation angle χ; the control variables and external forces include the roll angle σ, the thrust T, the aerodynamic drag D and the lift L; other parameters include the gravitational acceleration g and the total mass m of the aircraft; The thrust T in the above formula is provided by the electric power system, and this process is described by the following electric power system equation: Among them, Q B is the battery power consumption, Q max is the total capacity of a single battery, I B is the battery load current, U B is the battery output voltage, R B is the battery internal resistance, U OC is the open-circuit voltage, N S and N P are the number of series-connected and parallel-connected batteries in the battery pack respectively, SOC is the state of charge of the battery, [β1, β2, β3, β4] are all constants, I M is the motor current, v is the duty cycle of the motor controller, R M is the motor internal resistance, K E is the motor back electromotive force constant, ω is the rotational speed of the motor-propeller shaft, L M is the motor inductance, K T is the motor torque constant, K M is the moment of inertia of the motor shaft, C Q is the propeller torque coefficient, D P is the propeller diameter, J P is the moment of inertia of the propeller; Introduce the quasi-static assumption, that is, the electric aircraft is in a trimmed state at all times during flight, and the speed and altitude are both constant values, which are V = V C , h = h C , γ = 0, and V C , h C are both constant values. Thus, Equation (1) can be simplified as follows: Equation (3) can be further decoupled into two parts, which are the kinematic equations of the electric aircraft in the horizontal plane: and the thrust-drag balance and lift-weight balance equality constraints for maintaining a given speed and altitude; since the mass m and the velocity V C are both non-zero, the 4th and 5th fractions of Equation (3) can be simplified as follows:

3. The evaluation method according to claim 2, characterized in that Calculate the trim drag of the aircraft according to the lift and drag expressions and the relationship under the trimmed state: For a winged configuration electric aircraft, the lift and drag can be expressed as: where S R is the reference area, C L and C D are the lift coefficient and the drag coefficient respectively, α is the angle of attack, C L0 , C Lα , C D0 , and k are all constants; When the roll angle σ and the total mass m of the aircraft are given, the required lift and lift coefficient are respectively: Furthermore, the corresponding drag coefficient and the required balanced drag can be obtained: From this, according to the thrust-drag balance relationship in Equation (5), it can be known that D in Equation (8) is the total trim thrust T.

4. The evaluation method according to claim 2, wherein Calculate the balanced rotational speed of the propeller that satisfies the trimmed flight state from the trim thrust and the propeller thrust expression: The trim thrust T is provided by the propeller of the electric power system, and the propeller thrust expression is: Among them, C T is the thrust coefficient, [C t2 , C t1 , C t0 are all constants, and C t2 < 0, C t1 > 0, C t0 > 0; λ is the advance ratio of the propeller; Substitute the balanced drag into Equation (9) to obtain the following equation about the required rotational speed ω: Simplify Equation (10) to get: And organize it into the following quadratic equation about ω: a2ω 2 + a1ω + a0 = 0 To ensure that the trim rotational speed is positive, the following solution of Equation (12) should be taken: This is the balanced rotational speed of the propeller that satisfies the trimmed flight state of the electric aircraft.

5. The evaluation method according to claim 2, wherein Simplify the electric power system model based on the motor and battery characteristics, and solve to obtain the duty cycle of the motor controller and the cell load current in the trimmed state: Simplify the equation in Equation (2) except for the battery power consumption change rate to: It can be further organized into the following equality constraint: Solve Equation (15) to obtain the duty cycle of the motor controller and the cell load current in the trimmed state: Thus, all the state variables of the electric power system are obtained without numerical integration.

6. The evaluation method according to claim 2, wherein The specific method for performing electric quantity discretization transformation on the reduced-order flight dynamic model, transforming the dynamic equation with respect to time into a form with respect to the electric quantity consumption value, and determining the simulation interval and discrete grid is as follows: Transform the dynamic equation with respect to time into a form with respect to the electric quantity consumption value. For the state variable vector x, there is: Then the derivative of the state variable in the motion equation of the electric aircraft in Equation (4) is transformed into: Set the simulation interval as the initial value Q0 and the final allowable value Q of power consumption f , and the total number of power discrete grids is N Q , then the interval ΔQ is: The discrete grid is: Q0, Q0 + ΔQ, Q0 + 2ΔQ, …, Q0 + N Q ΔQ, (21).

7. The evaluation method according to claim 1, characterized in that, Based on the reduced - order flight dynamics model, by setting a sequence of roll angle values, numerical integration simulation is carried out on the simulation interval and discrete grid to obtain the boundary of the maneuverable reachable domain of the electric aircraft in the horizontal plane. The specific method is as follows: Within the allowable range of the rolling maneuverability of the electric aircraft, from the minimum value σ of the roll angle min to the maximum value σ max a series of roll angle values are selected, and the total number of simulated roll angles required is set to N σ , then the roll angle interval Δσ is: The roll angle sequence is: σ min ,σ min +Δσ,σ min +2Δσ,…,σ max (23); Numerical integration simulations are successively performed on the interval and discrete grid defined by Equation (21) based on the roll angle sequence given by Equation (23), and the total number of simulation times is N σ , the roll angle σ in each simulation is fixed at the corresponding value in Equation (23) and remains unchanged, and the initial state variables of the electric aircraft in Equation (4) are set as follows: x(Q0) = 0, y(Q0) = 0, χ(Q0) = 0 (24); The constant speed and altitude of the aircraft are V0 and h0 respectively. The state variables of the electric power 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 through algebraic operations. Corresponding to N σ The position sequences of the electric aircraft in the horizontal plane obtained by simulation are the following two matrices: Among them, X and Y are the longitudinal and lateral 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 the simulation results form a matrix, and the number of rows of the matrix is N σ . The data constituting the boundary of the reachable domain of the electric aircraft's horizontal plane maneuver are the last columns of X and Y respectively: Among them, X B and Y B are respectively the longitudinal and lateral coordinate sequences of the boundary of the reachable domain of the horizontal plane maneuver of the electric aircraft.

8. An evaluation system for the reachable domain of an electric aircraft based on the discretization of quasi-static electric quantities, characterized in that, It includes: Model reduction module: used to perform quasi - static reduction transformation on the electric aircraft dynamics model, simplify the electric aircraft dynamics equation according to the quasi - static assumption, decouple it into the kinematic equation in the horizontal plane and the equality constraints of thrust - drag balance and lift - weight balance, reduce the dimension of state variables, and obtain the reduced - order flight dynamics model; Model transformation module: used to perform discrete transformation of electric quantity on the reduced - order flight dynamics model, transform the dynamics equation with respect to time into a form with respect to the electric quantity consumption value, and determine the simulation interval and discrete grid; Reachable domain evaluation module: used to obtain the boundary of the maneuverable reachable domain of the electric aircraft in the horizontal plane based on the reduced - order flight dynamics model, by setting a sequence of roll angle values and performing numerical integration simulation on the simulation interval and discrete grid.

9. An electronic device, characterized in that, It includes: A processor; And, A memory arranged to store computer - executable instructions, which when executed cause the processor to implement the steps of the method for evaluating the reachable domain of an electric aircraft based on quasi - static electric quantity discretization as described in any one of claims 1 to 7.

10. A storage medium, characterized in that, For storing computer - executable instructions, which when executed implement the steps of the method for evaluating the reachable domain of an electric aircraft based on quasi - static electric quantity discretization as described in any one of claims 1 to 7.

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