An Online Repetitive Trajectory Replanning Method for Powered Return Based on Sliding Mode Theory

Abstract

A method for online replanning of the powered return trajectory based on the sliding mode theory belongs to the field of aircraft control technology. The method is as follows: establish a nominal altitude domain guidance model; divide the trajectory of the reusable aircraft during the powered return section into three stages according to the engine on / off state; design the form of the velocity-altitude profile; design a three-dimensional sliding mode surface vector and a second-order sliding mode guidance law based on the nominal altitude domain guidance model; generate the angle of attack command, the bank angle command, and the throttle opening command according to the current state, the terminal state, and the second-order sliding mode guidance law, and perform the flight during the return section. The present invention has a large improvement in accuracy compared with the traditional trajectory planning method, has a small algorithm calculation amount, can meet the requirements of real-time correction, and has a good application prospect.

Description

Technical Field

[0001] The present invention relates to an online replanning method for the powered return trajectory based on the sliding mode theory, belonging to the technical field of aircraft control. Background Art

[0002] When a reusable aircraft returns to the field, it may encounter situations where the airport needs to be temporarily changed, or it cannot return to the field along the predetermined trajectory due to flight deviations. During the return process, process constraints such as heat flux, overload, and dynamic pressure, as well as terminal constraints such as terminal velocity, terminal altitude, and terminal position, also need to be satisfied. The aircraft dynamics model will change suddenly due to the engine start and stop during the return section.

[0003] Traditional trajectory planning methods take a long time to calculate and cannot meet the requirements of real-time correction. Summary of the Invention

[0004] To solve the problems in the background art, the present invention provides an online replanning method for the powered return trajectory based on the sliding mode theory.

[0005] To achieve the above object, the present invention adopts the following technical solutions: An online replanning method for the powered return trajectory based on the sliding mode theory, the method comprising the following steps:

[0006] S1: Establish a nominal altitude domain guidance model;

[0007] S2: Divide the powered return section trajectory of the reusable aircraft into three stages according to the engine start and stop states;

[0008] S3: Design the speed-altitude profile form;

[0009] S4: Design the three-dimensional sliding mode surface vector s a and the second-order sliding mode guidance law u;

[0010] S5: Generate the angle of attack command, bank angle command, and throttle opening command according to the current state, terminal state, and the second-order sliding mode guidance law, and perform the flight in the return section.

[0011] Compared with the prior art, the beneficial effects of the present invention are:

[0012] The present invention designs a sliding mode guidance law based on the nominal altitude domain model, enabling the aircraft to glide from the current state to the terminal state and satisfying the process dynamic pressure constraint and the terminal constraint. Substituting the guidance law as the input into the altitude domain guidance differential equation, the initial value problem of the ordinary differential equation from the current state to the terminal state is solved using the Runge-Kutta method to obtain a discrete guidance command sequence. Inputting it into the time-domain system can obtain the flight trajectory, which has a significant improvement in accuracy compared with the traditional trajectory planning method. The algorithm has a small computational load and can meet the requirements of real-time correction, solving the problem that the traditional reusable aircraft return trajectory planning method takes a long time to calculate and cannot adapt to the needs of real-time correction under the change of the return mission, and has good application prospects. Description of the Drawings

[0013] Figure 1 is the flowchart of the present invention. Detailed Embodiments

[0014] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present invention.

[0015] An online replanning method for a powered return trajectory based on the sliding mode theory, the method includes the following steps:

[0016] S1: Considering two states of engine startup and shutdown, establish a nominal altitude domain guidance model with altitude replacing time as the independent variable;

[0017] S101: Define the altitude of the aircraft in the return section as h, the initial altitude as h0, and the monotonically increasing virtual altitude H = h0 - h;

[0018] S102: Considering that there is no time constraint for the aircraft to return at the end, using altitude to replace time as the independent variable, obtain the dynamic equation with the virtual altitude H as the independent variable and the dynamic pressure as the guidance state variable, that is: the nominal altitude domain guidance model is as follows:

[0019]

[0020] In formula (1):

[0021] x is the system state,

[0022] V is the speed of the aircraft;

[0023] γ is the flight path angle of the aircraft;

[0024] ψ is the heading angle of the aircraft;

[0025] is the x - coordinate of the airport coordinate system;

[0026] z is the z - coordinate of the airport coordinate system;

[0027] m is the mass of the aircraft;

[0028] u is the system input, u = [α, σ, η] T ;

[0029] α is the angle of attack;

[0030] σ is the bank angle;

[0031] η is the throttle opening, which affects the thrust and fuel consumption per second;

[0032] It should be noted that the guidance reference profile is designed within a fixed altitude range, and the boundary conditions can be accurately described. The time information is not lost and can still be extracted from it.

[0033] f H = [f H1 , f H2 , f H3 , f H4 , f H5 , f H6 T The specific form is:

[0034]

[0035] In Equation (2):

[0036] g is the acceleration due to gravity;

[0037] is the first derivative of m;

[0038] T L is the resultant force of the aerodynamic force in the lift direction and the thrust component, T L = L + Psinα;

[0039] T D is the resultant force of the aerodynamic force in the drag direction and the thrust component, T D = Pcosα - D;

[0040] P is the thrust;

[0041] L is the aerodynamic lift;

[0042] D is the aerodynamic drag:

[0043] And:

[0044] ​

[0045] In Equation (3):

[0046] q is the dynamic pressure, q = ρV 2 / 2, where: ρ is the air density;

[0047] S ref is the characteristic area of the aircraft;

[0048] C L is the lift coefficient, C D is the drag coefficient, both of which are obtained by interpolation of the angle of attack α and the Mach number Ma;

[0049] S103: The difference between the engine-off state and the engine-on state is the presence or absence of thrust P. Therefore, the dynamic equation in the powerless stage is:

[0050]

[0051] S104: For the convenience of writing, define the derivative of the subsequent variable a with respect to the virtual height as the derivative of the subsequent variable a with respect to time as

[0052] S2: Divide the trajectory of the powered return section of the reusable aircraft into three stages according to the engine on / off state;

[0053] When encountering a change in the return mission, the reusable aircraft turns on the turbofan engine in the return section to replenish energy and thus complete the return mission.

[0054] The trajectory of the powered return section of the reusable aircraft can be divided into three stages: the first stage is the powerless return section, and when the altitude and speed reach the engine-on state, it enters the second stage; the second stage is the engine-on energy replenishment section, where the engine is turned on to replenish energy for the aircraft; the third stage is the powerless landing section. Since it is necessary to reduce the speed of the aircraft at the end of the return to meet the landing constraints, the engine is turned off for gliding deceleration at the end of the return section.

[0055] S3: Design the speed-altitude profile form;

[0056] S301: After the reusable aircraft turns on the engine at the end of the return section, the speed will continue to increase, and it will decrease after the engine is turned off. The speed profile needs to conform to this change trend and meet the initial speed and terminal speed conditions. Therefore, the quadratic polynomial form of the designed speed-altitude profile is as follows:

[0057] V(H) = a1H 2 + a2H + a3 (5)

[0058] In Equation (5):

[0059] a1, a2, and a3 are all coefficients of the speed - altitude profile;

[0060] S302: Substitute the initial velocity V0 and its corresponding initial altitude, the intermediate velocity V mid and its corresponding intermediate altitude H mid as well as the terminal velocity V f and its corresponding terminal altitude H f , into Equation (5), we can get:

[0061]

[0062] Solve Equation (6) to obtain the coefficients a1, a2, and a3 of the speed - altitude profile.

[0063] S4: Design a three - dimensional sliding - mode surface vector s a and a second - order sliding - mode guidance law to ensure that the generated state trajectory satisfies the pre - set speed - altitude profile constraints, and at the same time satisfies the constraints of the end - point position, flight path angle, and heading angle in the return segment, and generate guidance commands;

[0064] S401: Design the three - dimensional sliding - mode surface vector as:

[0065] s a = f a (x(H), H) (7)

[0066] In Equation (7):

[0067] f a = [f a1 , f a2 , f a3 T The form is as follows:

[0068]

[0069] In Equation (8):

[0070] V d is the pre - set speed profile;

[0071] is the end - point constraint of the x - coordinate in the pre - set airport coordinate system;

[0072] z f is the end - point constraint of the z - coordinate in the pre - set airport coordinate system;

[0073] ψ f is the end - point constraint of the heading angle of the aircraft;

[0074] γf is the end constraint of the track angle of the preset aircraft;

[0075] z f , ψ f , γ f , H f are all constant values;

[0076] S402: Take the first derivative and second derivative of the three-dimensional sliding mode surface vector s a with respect to the virtual height H, and let the resultant force T of the aerodynamic force and thrust component in the drag direction D = Pcosα - D, then we can get:

[0077]

[0078]

[0079] In Equation (10):

[0080] G is the virtual control matrix;

[0081]

[0082] is the second-order sliding mode guidance law, that is: the virtual control quantity is obtained through the second-order sliding mode design;

[0083] F is the virtual state matrix;

[0084]

[0085] It can be seen from Equation (8) that if the three-dimensional sliding mode surface vector S a = 0, when H = H f , it is necessary to satisfy and z = z f ; Therefore, the three-dimensional sliding mode surface vector S a = 0 has a unique solution V = V(H), z = z f . If dS a / dH = 0, by combining the equations S a2 ′ = 0 and S a3 ′ = 0, we can get ψ = ψ f , γ = γ f , and S a1 ′ = 0 then solves for V′ = V′(H). Therefore, this trajectory planning problem becomes how to ensure S a = 0 and S a ′ = 0.

[0086] S403: Design the second-order sliding mode surface vector S b as:

[0087]

[0088] In Equation (11):

[0089] k a is the convergence coefficient;

[0090] S404: Taking the derivative of the virtual height H gives:

[0091]

[0092] In Equation (12):

[0093] A is the transfer symbol, A = (k a S a + k a S a ′(H f - H)) / (H f - H) 2 ;

[0094] S405: Considering Equation (8), design the second - order sliding - mode guidance law as:

[0095]

[0096] In Equation (13):

[0097] k is the approaching coefficient,

[0098] Under the action of the guidance law, when the virtual height H approaches the desired height H r (H r ≤ ηH f ), the second - order sliding - mode surface vector S b approaches the equilibrium point 0. Considering the dynamic system:

[0099] S a ′ = k a S a / (H f - H), k a >1 (14)

[0100] Therefore, in the interval [H r , H f , when the virtual height H approaches the terminal height H f , the three - dimensional sliding - mode surface vector S a and the dynamic system S a ′ both approach 0.

[0101] S5: Generate the angle of attack command, bank angle command, and throttle opening command according to the current state, terminal state, and second-order sliding mode guidance law, and perform the flight during the return phase.

[0102] S501: Obtain the corresponding angle of attack α from the second-order sliding mode guidance law

[0103] S502: The calculation formula for the bank angle σ is as follows:

[0104]

[0105] S503: The calculation formula for the throttle opening η is as follows:

[0106]

[0107] Thus, the sliding mode guidance law in the altitude domain is obtained. By using the Runge-Kutta method to solve the initial value problem of the ordinary differential equation from the current state to the terminal state, a discrete guidance command sequence is obtained. Taking this command as the input of the time-domain system, the flight trajectory can be obtained.

[0108] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent conditions of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0109] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.​

Claims

1. An online replanning method for the powered return trajectory based on the sliding mode theory, characterized in that: The method includes the following steps: S1: Establish a nominal altitude domain guidance model; S2: Divide the powered return flight path of the reusable vehicle into three stages according to the engine on / off state: The first stage is the unpowered return stage, and when the altitude and speed reach the on state, it enters the second stage; The second stage is the power-on energy replenishment stage, where the engine is turned on to replenish energy for the vehicle; The third stage is the unpowered landing stage, and the engine is turned off at the end of the return stage for gliding deceleration; S3: Design the speed-altitude profile form; The S3 includes the following steps: S301: Design the speed-altitude profile quadratic polynomial form as follows: V(H) = a1H 2 + a2H + a3 (5) In Equation (5): a1, a2, and a3 are all coefficients of the speed-altitude profile; S302: Substitute the initial velocity V0 and its corresponding initial height, the intermediate velocity V mid and its corresponding intermediate height H mid as well as the terminal velocity V f and its corresponding terminal height H f , and substituting these three sets of conditions into Equation (5) gives: Solving Equation (6) can obtain the coefficients a1, a2, and a3 of the speed-altitude profile; S4: Design the three-dimensional sliding-mode oriented vector s a and the second-order sliding-mode guidance law S5: Generate the angle of attack command, bank angle command, and throttle opening command according to the current state, terminal state, and second-order sliding mode guidance law, and perform the return flight.

2. The online replanning method for the powered return trajectory based on the sliding mode theory according to claim 1, characterized in that: The S1 includes the following steps: S101: Define the altitude of the vehicle in the return stage as h, the initial altitude as h0, and the monotonically increasing virtual altitude H = h0 - h; S102: Use altitude to replace time as the independent variable to obtain the dynamic equation with virtual altitude H as the independent variable and dynamic pressure as the guidance state variable, that is: The nominal altitude domain guidance model is as follows: In Equation (1): x is the system state, V is the speed of the vehicle; γ is the flight path angle of the vehicle; ψ is the heading angle of the vehicle; is the x coordinate of the airport coordinate system; z is the z coordinate of the airport coordinate system; m is the mass of the vehicle; u is the system input, u = [α, σ, η] T ; α is the angle of attack; σ is the bank angle; η is the throttle opening; f H = [f H1 , f H2 , f H3 , f H4 , f H5 , f H6 T The specific form is:​ In Equation (2): g is the acceleration due to gravity; is the first derivative of m; T L is the resultant force of the aerodynamic force in the lift direction and the thrust component, T L = L + P sin α; T D is the resultant force of the aerodynamic force in the drag direction and the thrust component, T D = Pcosα - D; P is the thrust; L is the aerodynamic lift; D is the aerodynamic drag: And: In Equation (3): q is the dynamic pressure, q = ρV 2 / 2, where: ρ is the air density; S ref is the characteristic area of the aircraft; C L is the lift coefficient, and C D is the drag coefficient, both of which are obtained by interpolation of the angle of attack α and the Mach number Ma; S103: The dynamic equation in the unpowered stage is: S104: Define the derivative of the subsequent variable a with respect to the virtual height as The derivative of the subsequent variable a with respect to time is 3. A method for online replanning of the powered return trajectory based on the sliding mode theory according to claim 2, characterized in that: The S4 includes the following steps: S401: Design the three-dimensional sliding mode facing vector It is: s a = f a (x(H), H) (7) In Equation (7): f a = [f a1 , f a2 , f a3 T is in the following form:​ In Equation (8): V d is a preset speed profile; is the end constraint of the x coordinate in the pre-set airport coordinate system; z f is the end constraint of the z coordinate in the pre-set airport coordinate system; ψ f is the end constraint of the heading angle of the preset aircraft; γ f is the end constraint of the track angle of the preset aircraft; z f , ψ f , γ f , H f are all constant values; S402: Take the first derivative and the second derivative of the three-dimensional sliding mode vector s a with respect to the virtual height H, and let the resultant force T of the aerodynamic force and the thrust component in the drag direction D = Pcosα - D, then we can obtain: In Equation (10): G is the virtual control matrix; is a second-order sliding mode guidance law, F is the virtual state matrix; S403: Design the second-order sliding mode oriented vector S b It is as follows: In Equation (11): k a is the convergence coefficient; S404: Taking the derivative of the virtual altitude H gives: In Equation (12): A is a forwarding symbol, A = (k a S a +k a S a ′(H f -H)) / (H f -H) 2 ; S405: Considering Equation (8), design a second-order sliding mode guidance law as follows: In Equation (13): k is the approaching coefficient, 4. A method for online replanning of a powered return trajectory based on the sliding mode theory according to claim 1 or 3, characterized in that: The S5 includes the following steps: S501: Obtained the corresponding angle of attack α from the second-order sliding mode guidance law ​ S502: The calculation formula for the bank angle σ is as follows: S503: The calculation formula for the throttle opening η is as follows:

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