Time-varying speed aircraft position reachable set calculation method based on simple thrust method

Abstract

The invention relates to a time-varying speed aircraft position reachable set calculation method based on a simple thrust method, and provides a position dynamic reachable set calculation method based on the simple thrust method for solving the problem of reachable set calculation of a variable speed aircraft. The method comprises the following steps: firstly, calculating a possible speed range of the aircraft under the conditions of given gravity and flight height by using pneumatic and engine model data of the aircraft, namely determining the minimum and maximum speeds of the aircraft under the model; secondly, determining possible reachable set positions of the aircraft at the minimum speed and the maximum speed by using a reachable set calculation method; and finally, calculating a position reachable set of the time-varying speed aircraft by considering the variable speed condition, namely acceleration and deceleration processes. A numerical simulation result verifies the effectiveness and superiority of the method in calculating the position reachable set of the aircraft.

Description

Technical Field

[0001] The invention belongs to the field of guidance and control of aerospace vehicles, and relates to a method for calculating a reachable set of positions of a time-varying speed aircraft based on a simple thrust method. Background Art

[0002] In the field of guidance and control of aerospace vehicles, the calculation method of the flight envelope reachability set has always been one of the focuses of attention. The flight envelope reachability set refers to a set of states that the aircraft can reach under given flight environment and control constraints, which has an important impact on the flight safety, performance and combat effectiveness of the aircraft.

[0003] Traditional reachable set calculation methods are usually oriented towards scenarios with constant speed, that is, it is assumed that the aircraft maintains a constant speed during the calculation process. However, in actual flight, especially in complex environments or in tasks that require rapid response, the speed of the aircraft may change significantly. The flight envelope mainly consists of three parts: the minimum level flight speed, the maximum level flight speed, and the static ceiling. The "simple thrust method" is a method that solves the minimum and maximum level flight speeds of an aircraft at a specific altitude based on data such as the aerodynamic parameters and engine thrust of the aircraft. The present invention derives the minimum and maximum speeds of the aircraft based on the aerodynamics and engine model of the aircraft, and designs a position reachable set calculation method under time-varying speed flight based on speed boundary constraints. Summary of the invention

[0004] Technical issues to be solved

[0005] In order to avoid the shortcomings of the prior art, the present invention proposes a method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method.

[0006] Technical Solution

[0007] A method for calculating a reachable set of positions of a time-varying speed aircraft based on a simple thrust method, characterized by the following steps:

[0008] Step 1: Establish the model of the aircraft and the engine, that is, the force equation of the aircraft, including the gravity G of the aircraft and the thrust P of the engine;

[0009] Step 2: Use the simple thrust method to find the aircraft's flight speed range, including the aircraft's minimum speed v min and the maximum speed v of the aircraft max ;

[0010] Step 3: Analyze the reachable set of the aircraft position under the limit speed state:

[0011] After determining the minimum and maximum speeds of the aircraft, the reachable range of the aircraft's position within a given time is calculated at a given altitude;

[0012] According to the reachable set space range of the aircraft's limit speed, find the front position of the reachable set at the aircraft's limit speed;

[0013] Step 4: After finding the limit speed position of the aircraft, analyze the dynamic reachable set of the aircraft position under variable speed to obtain the position coordinates (P i,x ,P i,y );

[0014] Step 5: Based on the left and right turning circles obtained when the aircraft makes a minimum turning radius turn with a fixed normal acceleration and speed, calculate the shortest time trajectory of the aircraft. The shortest time trajectory is equivalent to the Dubins shortest path trajectory of the aircraft. Use the shortest path to draw the Dubins trajectory of the aircraft at a variable speed. The set of all Dubins trajectories is the position set of the variable speed aircraft.

[0015] The gravity G and engine thrust P of the aircraft of the model of the aircraft and the engine are:

[0016]

[0017] Where: G is the gravity on the aircraft, ρ(H) is the air density related to altitude, C Lmax is the maximum allowable lift coefficient, s is the wing area, v' is the local sound speed, Ma is the Mach number, C Dmin represents the minimum drag coefficient and P is the engine thrust.

[0018] The minimum speed v of the aircraft min and the maximum speed v of the aircraft max for:

[0019] Where: G is the gravity on the aircraft, ρ(H) is the air density related to altitude, C Lmax is the maximum allowable lift coefficient, s is the wing area, v' is the local sound speed, Ma is the Mach number, and g is 9.80665m / s 2 ;

[0020]

[0021] Where: P is the available thrust of the engine, ρ(H) is the air density related to altitude, C Dmin represents the minimum drag coefficient, s represents the wing area, v' represents the local speed of sound, Ma represents the Mach number, T max is the maximum available thrust of the engine.

[0022] The reachable set describes the evolution process of the system, which is the set of all possible states that the system can reach under given initial conditions and after control input.

[0023] The frontier of the reachable set is a curve composed of the farthest distance points reached by the aircraft within a given time. The reachable set of the aircraft is obtained through the involute of the left and right turning radius circles of the aircraft; the involute is composed of all equal-length end points of the shortest path trajectories based on the Dubins curve.

[0024] The calculation of the reachable set range of the aircraft is:

[0025] First, calculate the frontier RSF of the reachable set i for:

[0026] RSF i (t,t+Δt|x i (t)) = g(V i ,a i,max ,x i (t),Δt)=RSF i,R ∪RSF i,L

[0027] RSF i,R and RSF i,L They are respectively RSF based on heading i The right and left halves are obtained by the following involute formula:

[0028]

[0029] where θ i is the velocity heading angle, and are the center coordinates of the right and left minimum radius turning circles, which are equal to and is the minimum turning radius, whose value is V i 2 / a i,max ;

[0030] Substituting the minimum speed and maximum speed into the involute formula, we can get the reachable set range when the aircraft turns at the minimum speed and maximum speed; the minimum radius turning radius at the minimum and maximum speed states is V respectively. min 2 / a i,max With V max 2 / a i,max , a i,max is the maximum normal acceleration of the vehicle turning.

[0031] The aircraft takes time t as the starting point and reaches the position coordinate (P i,x (t+Δt),P i,y (t+Δt)):

[0032]

[0033] r oi (t) = V i (t) 2 / a i,max

[0034] Where: The initial velocity is set to V i0 , the normal acceleration of the aircraft is set to a i,max , with a i The tangential acceleration is used to accelerate / decelerate the movement.

[0035] An electronic device, characterized in that it includes a processor and a memory, wherein the processor is used to implement the data migration steps of the method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method when executing a computer program stored in the memory.

[0036] A readable storage medium, characterized in that a computer program is stored on the readable storage medium, and when the computer program is executed by a processor, the steps of the method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method are implemented.

[0037] A computer program product, characterized by comprising computer executable instructions, which, when executed, are used to implement the method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method.

[0038] Beneficial Effects

[0039] The present invention proposes a method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method. Aiming at the reachable set calculation problem of a variable speed aircraft, a method for calculating the dynamic reachable set of positions based on a simple thrust method is provided. Firstly, the aerodynamic and engine model data of the aircraft are used to calculate the speed range that the aircraft may reach under given gravity and flight altitude conditions, that is, to determine the minimum and maximum speeds of the aircraft under the model. Secondly, the reachable set calculation method is used to determine the reachable set positions that the aircraft may reach at the minimum and maximum speeds. Finally, the position reachable set of the time-varying speed aircraft is calculated by considering the variable speed situation, that is, the acceleration and deceleration process. Numerical simulation results verify the effectiveness and superiority of this method in calculating the reachable set of aircraft positions. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0041] Figure 1 The figure is a flow chart of the calculation method of the present invention.

[0042] Figure 2 The figure is a schematic diagram of the motion principle of the aircraft of the present invention.

[0043] Figure 3 The figure is a schematic diagram of the position reachable set of the present invention.

[0044] Figure 4 It is a trend diagram of air density changing with altitude of the present invention.

[0045] Figure 5 The position of the maximum speed limit of the present invention can be reached.

[0046] Figure 6 It is the position reachable set of the minimum limiting speed of the present invention.

[0047] Figure 7 It is the position reachable set of the acceleration model of the present invention.

[0048] Figure 8 It is the position reachable set of the deceleration model of the present invention.

[0049] Fig. 9 It is the Dubins trajectory of the forward reachable set of the aircraft of the acceleration model of the present invention.

[0050] Fig.10 It is the aircraft Dubins trajectory of the acceleration model of the present invention.

[0051] Fig.11 It is the aircraft Dubins trajectory of the deceleration model of the present invention. DETAILED DESCRIPTION

[0052] The present invention will now be further described with reference to the embodiments and the accompanying drawings:

[0053] like Figure 1 The figure is a flow chart of the calculation method of the present invention. To achieve the above object, the present invention adopts the following technical solutions:

[0054] The method for calculating the reachable set of the position of a time-varying speed aircraft based on a simple thrust method comprises the following steps:

[0055] Step 1: Model the aircraft and engine

[0056] like Figure 2 The figure shows the force diagram of the aircraft. The aircraft is mainly subject to four forces during flight: thrust, drag, lift and gravity. When the aircraft maintains level flight in the air, the aircraft and engine models are established based on the force conditions of the aircraft. When the aircraft maintains level flight, the force equation of the aircraft is:

[0057]

[0058] G is the gravity on the aircraft, ρ(H) is the air density related to the altitude, C Lmax is the maximum allowable lift coefficient, s is the wing area, v' is the local sound speed, Ma is the Mach number, C Dmin represents the minimum drag coefficient and P is the engine thrust.

[0059] In the embodiment, the aerodynamic and engine model data of the aircraft are used to calculate the speed range that the aircraft may reach under given gravity and flight altitude conditions, that is, to determine the minimum and maximum speeds of the aircraft under the model;

[0060] Table 1 Aerodynamic and engine model data of aircraft

[0061]

[0062] Assume that the aerodynamic and engine data of the aircraft are shown in Table 1, and the air density at this time is Figure 4 shown.

[0063] The formula for air density is:

[0064] ρ(H)=ρ0×(1-0.0000225577×h) 4.2561 (3)

[0065] ρ0 represents the air density, ρ0 represents the air density at sea level (1.225kg / m 3 ), h is the altitude.

[0066] Step 2: Use the simple thrust method to find the aircraft's flight speed range

[0067] When the gravity and flight altitude of the aircraft are given, the speed range of the aircraft can be calculated by the simple thrust method. The minimum speed of the aircraft is the minimum speed at which the aircraft can maintain level flight at a certain altitude. It is the left boundary of the basic flight envelope, that is, the stall limit. The minimum speed of the aircraft can be derived from formula (1):

[0068]

[0069] G is the gravity on the aircraft, ρ(H) is the air density related to the altitude, CLmax is the maximum allowable lift coefficient, s is the wing area, v' is the local sound speed, Ma is the Mach number, and g is 9.80665m / s 2 .

[0070] The maximum speed of the aircraft is based on the level flight condition. The maximum level flight speed of the aircraft limited by thrust is obtained by assuming that the thrust required for level flight is equal to the available thrust of the engine. The maximum speed of the aircraft can be derived from formula (2):

[0071]

[0072] P is the available thrust of the engine, ρ(H) is the air density related to altitude, and C Dmin represents the minimum drag coefficient, s represents the wing area, v' represents the local speed of sound, Ma represents the Mach number, T max is the maximum available thrust of the engine.

[0073] In the embodiment, the minimum speed and maximum speed of the aircraft at a certain altitude are obtained by calculating the minimum speed and maximum speed of the aircraft.

[0074] By using formulas (3) and (4), the minimum and maximum speed ranges of the aircraft can be calculated. The left side represents the minimum speed of the aircraft, and the right side represents the maximum speed of the aircraft.

[0075] Assume that a certain aircraft is located at an altitude of 6000m. Substituting the altitude into formula (8), combining formulas (3) and (4) yields:

[0076] v min is 86.8122m / s, v m a x It is 305.8655m / s.

[0077] Step 3: Analysis of the reachable set of the aircraft position under the limit speed state

[0078] After obtaining the minimum and maximum speeds of the aircraft, the range of the aircraft's position that can be reached within a certain period of time at a given altitude can be calculated.

[0079] The concept of reachable set can be used to describe the evolution of a system, that is, the set of all possible states that a system can reach under given initial conditions and after certain control inputs. The reachable set front (RSF) is a curve consisting of the farthest distance points that can be reached within a period of time. The reachable set of an aircraft can be obtained by the involute of its left and right turning radius circles, such as Figure 3As shown in Figure 1, these involutes consist of the end points of all equal-length Dubins trajectories, represented by dotted lines in the figure. Regardless of the strategy adopted, its position point within a certain period of time is always located in the corresponding reachable set, as shown in the gray area in the figure.

[0080] Let a certain aircraft be i, then its reachable set frontier is RSF i , the calculation formula is as follows

[0081] RSF i (t,t+Δt|x i (t)) = g(V i ,a i,max ,x i (t),Δt)=RSF i,R ∪RSF i,L (6)

[0082] RSF i,R and RSF i,L They are respectively RSF based on heading i The right and left halves can be calculated using the involute formula (6):

[0083]

[0084] where θ i is the velocity heading angle, and are the center coordinates of the right and left minimum radius turning circles, which are equal to and is the minimum turning radius, whose value is V i 2 / a i,max .

[0085] Substituting the minimum speed and maximum speed into formula (7), we can obtain the reachable set range when the aircraft turns at the minimum speed and maximum speed.

[0086] At this point, we can get the minimum radius turning radius at the minimum and maximum speed states are V min 2 / a i,max With V max 2 / a i,max , a i,max is the maximum normal acceleration of the aircraft turning. According to the reachable set space range of the aircraft's limit speed, the front position of the reachable set at the aircraft's limit speed can be calculated.

[0087] In the embodiment, after the minimum speed and the maximum speed of the aircraft are obtained, the normal acceleration of the aircraft is taken as 5g, and the reachable set state space range of the aircraft in 9s at an altitude of 6000 is obtained.

[0088] Substituting the minimum speed and the maximum speed into formula (6) respectively, we can get the limit speed reachable set.

[0089] Step 4: Dynamic reachable set analysis of aircraft position under variable speed

[0090] After the limit speed position of the aircraft is obtained, the dynamic reachable set of the aircraft under variable speed can be analyzed based on the limit speed.

[0091] (P i,x ,P i,y ) is the position coordinate that the aircraft can reach within the time range. Now set the initial speed of the aircraft to V i0 , the normal acceleration of the aircraft is set to a i,max , with a i The tangential acceleration of the aircraft is used for acceleration / deceleration. The position coordinates of the aircraft at time t can be expressed by the following formula:

[0092]

[0093] In the embodiment: after obtaining the minimum speed and maximum speed of the aircraft, the normal acceleration of the aircraft is taken as 5g, and the tangential acceleration of the aircraft is calculated to be g at an altitude of 6000, and the position when accelerating from the minimum speed to the maximum speed can reach the set range.

[0094] Substituting the velocity into formula (7), we can obtain the position reachable set of the aircraft acceleration model and the dynamic reachable set of the aircraft as follows: Figure 7 Similarly, substituting the speed into formula (7) yields the dynamic reachable set of the aircraft deceleration model. The dynamic reachable set of the aircraft is as follows: Figure 8 shown.

[0095] Step 5: Based on the shortest path Dubins trajectory, find the position of the aircraft at each moment

[0096] like Figure 3 As shown in the figure, it is the reachable set range obtained within a certain time when a certain aircraft moves at a certain acceleration. The aircraft makes a minimum turning radius turn with a fixed normal acceleration and speed to obtain the left and right turning circles, and then the shortest time trajectory of the aircraft is calculated to analyze the reachable set. The shortest time trajectory is equivalent to the Dubins shortest path trajectory, which is closely related to the motion accessibility and represents the farthest position that can be reached within a given time.

[0097] Analyzing the reachable set from the perspective of the Dubins shortest path, the Dubins trajectory with the shortest distance can be divided into three categories: a straight line path, a path with the minimum turning radius, and a path with the minimum turning radius plus a straight line path.

[0098] Based on the shortest path, the Dubins trajectory of the aircraft at a variable speed can be drawn, and the set of all Dubins trajectories is the position set of the variable speed aircraft.

[0099] In the embodiment, the initial position of the aircraft is (0,0), Fig. 9 is the shortest Dubins trajectory of the aircraft acceleration model. At this time, only the part above x = 0 is taken as the forward reachable set of the aircraft, such as Fig. 9 shown. Fig.10 It is the shortest Dubins trajectory of the aircraft acceleration model.

[0100] Similarly, take the normal acceleration of the aircraft as 5g, and find the reachable set range when the aircraft decelerates from the maximum speed to the minimum speed at an altitude of 6000m with a tangential acceleration of 5g. Fig.11 It is the shortest Dubins trajectory for the aircraft deceleration model.

[0101] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method, characterized in that Here are the steps: Step 1: Establish the model of the aircraft and the engine, that is, the force equation of the aircraft, including the gravity G of the aircraft and the thrust P of the engine; Step 2: Use the simple thrust method to find the aircraft's flight speed range, including the aircraft's minimum speed v min and the maximum speed of the aircraft v max ; Step 3: Analyze the reachable set of the aircraft position under the limit speed state: After determining the minimum and maximum speeds of the aircraft, the reachable range of the aircraft's position within a given time is calculated at a given altitude; According to the reachable set space range of the aircraft's limit speed, find the front position of the reachable set at the aircraft's limit speed; Step 4: After finding the limit speed position of the aircraft, analyze the dynamic reachable set of the aircraft position under variable speed to obtain the position coordinates (P i,x ,P i,y ); Step 5: Based on the left and right turning circles obtained when the aircraft makes a minimum turning radius turn with a fixed normal acceleration and speed, calculate the shortest time trajectory of the aircraft. The shortest time trajectory is equivalent to the Dubins shortest path trajectory of the aircraft. Use the shortest path to draw the Dubins trajectory of the aircraft at a variable speed. The set of all Dubins trajectories is the position set of the variable speed aircraft.

2. The method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method according to claim 1, characterized in that: The gravity G and engine thrust P of the aircraft of the model of the aircraft and the engine are: Where: G is the gravity on the aircraft, ρ(H) is the air density related to altitude, C Lmax is the maximum allowable lift coefficient, s is the wing area, v' is the local sound speed, Ma is the Mach number, C Dmin represents the minimum drag coefficient and P is the engine thrust.

3. The method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method according to claim 1, characterized in that: The minimum speed v of the aircraft min and the maximum speed of the aircraft v max for: Where: G is the gravity on the aircraft, ρ(H) is the air density related to altitude, C Lmax is the maximum allowable lift coefficient, s is the wing area, v' is the local sound speed, Ma is the Mach number, and g is 9.80665 m / s 2 ; Where: P is the available thrust of the engine, ρ(H) is the air density related to altitude, C Dmin represents the minimum drag coefficient, s represents the wing area, v' represents the local speed of sound, Ma represents the Mach number, T max is the maximum available thrust of the engine.

4. The method for calculating the reachable set of positions of a time-varying speed aircraft based on the simple thrust method according to claim 1, characterized in that: The reachable set describes the evolution process of the system, which is the set of all possible states that the system can reach under given initial conditions and after control input.

5. The method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method according to claim 1 or 4, characterized in that: The frontier of the reachable set is a curve composed of the farthest distance points reached by the aircraft within a given time. The reachable set of the aircraft is obtained through the involute of the left and right turning radius circles of the aircraft; the involute is composed of all equal-length end points of the shortest path trajectories based on the Dubins curve.

6. The method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method according to claim 1, characterized in that: The calculation of the reachable set range of the aircraft is: First, calculate the frontier RSF of the reachable set i for: RSF i (t,t+Δt|x i (t))=g(V i ,a i,max ,x i (t),Δt)=RSF i,R ∪RSF i,L RSF i,R and RSF i,L They are respectively RSF based on heading i The right and left halves are obtained by the following involute formula: where θ i is the velocity heading angle, and are the center coordinates of the right and left minimum radius turning circles, which are equal to is the minimum turning radius, whose value is V i 2 / a i,max ; Substituting the minimum speed and maximum speed into the involute formula, we can get the reachable set range when the aircraft turns at the minimum speed and maximum speed; the minimum radius turning radius at the minimum and maximum speed states is V respectively. min 2 / a i,max With V max 2 / a i,max , a i,max is the maximum normal acceleration of the vehicle turning.

7. The method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method according to claim 1, characterized in that: The aircraft takes time t as the starting point and reaches the position coordinate (P i,x (t+Δt),P i,y (t+Δt)): r oi (t)=V i (t) 2 / a i,max Where: The initial velocity is set to V i0 , the normal acceleration of the aircraft is set to a i,max , with a i The tangential acceleration is used to accelerate / decelerate the movement.

8. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the processor is used to implement the data migration step of the method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method as claimed in any one of claims 1 to 7 when executing a computer program stored in the memory.

9. A readable storage medium, characterized in that: The readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method as described in any one of claims 1 to 7.

10. A computer program product, characterized in that The invention comprises computer executable instructions, which are used to implement the method for calculating the reachable set of positions of a time-varying speed aircraft based on a simple thrust method as described in any one of claims 1 to 7 when being executed.

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