Iterative guidance method independent of time compensation

Abstract

The present application relates to a kind of iterative guidance methods not dependent on time compensation, comprising the following steps: (1) constructing the state equation of optimal control;(2) establishing the initial state of optimal control;(3) establishing the terminal constraint condition of optimal control;(4) designing optimal control performance index function;(5) selecting optimal control quantity;(6) calculating optimal control quantity.The present application can calculate the direction of current desired thrust vector according to predetermined target orbit parameters and current motion parameters of vehicle, is very suitable for some small overload conditions with fluctuation, can reduce the influence of time-dependent correction quantity fast change caused by the violent change of overload, provide a more stable program instruction angle for the input of attitude control system, improve control quality.

Description

An iterative guidance method that does not rely on time compensation Technical Field

[0001] This invention relates to the field of iterative guidance technology for launch vehicles, and in particular to an iterative guidance method that does not rely on time compensation. Background Technology

[0002] After more than half a century of development, my country has made significant progress in space launch vehicles, especially launch vehicles, possessing multiple rocket series of large, medium, and small sizes, covering various types of orbital launch missions from near-Earth to deep space. Furthermore, heavy-lift launch vehicles with even greater carrying capacity are under development. In the diversified development of these spaceflight missions, guidance methods play a crucial role.

[0003] To date, guidance methods applied to launch vehicles mainly fall into two categories: standard trajectory tracking guidance and online flight trajectory planning. The former is typically represented by perturbation guidance, while the latter is typically represented by iterative guidance. In comparison, with the increasing diversification and complexity of space launch missions, perturbation guidance methods are becoming increasingly inadequate for the requirements of these missions, while iterative guidance, with its online planning method that does not rely on standard trajectories, is becoming more suitable.

[0004] Iterative guidance is characterized by high guidance accuracy, strong mission adaptability, and relatively low requirements for ground-based parameter preparation. It is a guidance method that calculates program angle commands in real time based on predetermined target trajectory parameters and the current motion parameters of the spacecraft. Existing iterative guidance methods all add time-dependent correction parameters to the average attitude angle. This approach can achieve good control results when overload changes are relatively stable. However, in situations with drastic overload changes, the time-dependent correction parameters are prone to rapid changes, leading to significant fluctuations in program angle commands.

[0005] To address this, an iterative guidance method independent of time compensation is proposed. This method reduces the impact of rapid changes in time-related corrections caused by drastic overload variations, providing a more stable program instruction angle for the attitude control system input and improving control quality. Summary of the Invention

[0006] The purpose of this invention is to overcome the problem that existing iterative guidance methods are prone to rapid changes in program angle commands when overload changes are drastic. This invention proposes an iterative guidance method that does not rely on time compensation. Based on parameters such as the spacecraft's current speed, position, and orbital information of the predetermined target point, the average program angle information expected to reach the target orbit is calculated, and only time-independent corrections are added to this information.

[0007] The above-mentioned objective of the present invention is achieved through the following technical solution:

[0008] An iterative guidance method that does not rely on time compensation is provided, comprising the following steps:

[0009] (1) Construct the state equation for optimal control;

[0010] (2) Establish the initial state for optimal control;

[0011] (3) Establish terminal constraints for optimal control;

[0012] (4) Design the optimal control performance index function;

[0013] (5) Select the optimal control variable;

[0014] (6) Calculate the optimal control quantity.

[0015] Preferably, step (1) can construct the following state equation:

[0016]

[0017] In the formula: v x v y v z x, y, and z represent the velocity and position of the aircraft along the three axes (x, y, and z axes) in the reference coordinate system; a represents the apparent acceleration generated by the control force. Let ψ be the angle between the projection of the desired thrust vector onto the O-XY plane and the OX axis, with counterclockwise being positive when viewed from the positive Z-axis direction; c Let be the angle between the desired thrust vector and the O-XY plane. From the positive Z-axis direction, the desired thrust vector direction is positive if it is located inside the O-XY plane. and ψ c The geometric schematic diagram is shown in Figure 2, where the dashed lines represent areas inside the screen; g x g y g z The gravitational acceleration can be calculated using the formula for gravitational acceleration. This invention takes the average of the gravitational acceleration at the target point and at the current moment. This approach has appeared in many research papers and has also been applied in engineering. Its advantage is that it can improve the efficiency of calculation while ensuring the accuracy of prediction.

[0018] Preferably, the reference coordinate system O-XYZ is an inertial system, defined as follows: the origin O is the Earth's center; the OY axis lies in the orbital plane determined by the target point and points to the ascending intersection; the OZ axis is perpendicular to the orbital plane and points in the negative direction of the orbital normal; O-XYZ is a right-handed rectangular coordinate system.

[0019] The preferred formula for calculating gravitational acceleration is:

[0020] (a) Based on the position R in the launch inertial coordinate system of the current point of the aircraft i0 Calculate its corresponding gravitational acceleration G. i0 for

[0021]

[0022] Where: R 0x R 0y and R 0z The three-axis components of the position from the Earth's center to the launch point in the launch inertial coordinate system; x g0 y g0 and z g0 The three-axis components of the launch vehicle's center of mass in the launch inertial coordinate system;

[0023]

[0024] z c =p x (R 0x +x i0 )+p y (R 0y +y i0 )+p z (R 0z +z i0 ), p x =cos(A0)cos(B0), p y =sin(B0), p z = -sin(A0)cos(B0); μ is the Earth's gravitational constant; J2 is the Earth's J2 gravitational coefficient; R e A0 is the radius of the Earth's equator; B0 is the azimuth of the launch point; and B0 is the geodetic latitude of the launch point.

[0025] Preferably, the launch inertial coordinate system O g -X g Y g Z g The coordinate system origin O is defined as follows: g For the launch point; O g X g The axis points in the aiming direction within the horizontal plane of the earth; O g Y g The axis is along the vertical line of gravity at the launch point, with upward being positive; O g -X g Y g Z gIt is a right-handed rectangular coordinate system.

[0026] (b) Based on the semi-major axis a of the target point m eccentricity e m Track inclination angle i m Longitude of the ascending node Ω m Argument of perigee ω m and true close angle f m The position R1 of the target point in the three axes of the geocentric equatorial coordinate system can be obtained as follows:

[0027] R1 = r m ·cos(f m )·P+r m ·sin(f m )·Q (3)

[0028] In the formula:

[0029]

[0030] Preferably, the geocentric equatorial coordinate system O1-X1Y1Z1 is defined as follows: the origin O1 is the geocenter; the O1X1 axis points to the zero meridian in the equatorial plane; the O1Z1 axis points to the North Pole; and O1-X1Y1Z1 is a right-handed rectangular coordinate system.

[0031] (c) Based on the target point's position R1 in the geocentric equatorial coordinate system, calculate its position R in the launch inertial coordinate system. gm The method is as follows:

[0032]

[0033] In the formula:

[0034]

[0035] λ0, A0, and B0 are the longitude, azimuth, and geodetic latitude of the launch point, respectively.

[0036] (c) Based on the position R in the launch inertial coordinate system gm The gravitational acceleration G in the launch inertial coordinate system is calculated using a formula similar to equation (2). gm .

[0037] (d) Obtain the average gravitational acceleration between the target point and the current point. And convert it into a representation in the reference coordinate system. The method is as follows:

[0038]

[0039] In the formula:

[0040]

[0041] Where: λ0, A0, and B0 are the longitude, azimuth, and geodetic latitude of the launch point, respectively; Ω m i m The longitude of the ascending node and the orbital inclination of the target point.

[0042] Preferably, the initial state in step (2) can be the velocity V0 and position R0 of the aircraft at the current moment in the reference coordinate system, as expressed below:

[0043]

[0044] Preferably, the terminal condition in step (3) can be selected as the velocity V of the target point in the reference coordinate system. m Location R m The expression is as follows:

[0045]

[0046] Preferably, in step (4), since the flow rate of the aircraft is approximately constant during stable flight, the design of the fuel-optimal control law can be equivalent to designing the control law with the shortest time. The performance index function is as follows:

[0047]

[0048] In the formula T m The time for integration.

[0049] Preferably, the control variable in step (5) can be selected as:

[0050] Preferably, step (6) can directly use the Pontryagin maximum principle from numerous documents to provide a general solution to this optimal control problem. The result is:

[0051]

[0052] make:

[0053]

[0054] Then: of The coefficients of k1 and k3 are as follows:

[0055]

[0056] A1, D1, D2, and S are integration constants. The detailed derivation process can be found in Chapter 3 of the book "Design of High-Reliability Launch Vehicle Control Systems".

[0057] Compared with the prior art, the present invention has the following advantages:

[0058] (1) This invention reduces the calculation of time-related parameters in iterative guidance calculation, making the algorithm simpler;

[0059] (2) This invention is based on the existing iterative guidance calculation, only omitting the correction amount related to the time parameter, and the algorithm has good inheritance.

[0060] (3) This invention is particularly applicable to some small overload situations with large fluctuations, and can reduce the impact of rapid changes in time-related correction due to drastic changes in overload;

[0061] (4) The present invention can effectively reduce the rapid change of program angle command, provide a more stable program command angle for the input of attitude control system, and improve control quality. Attached Figure Description

[0062] Figure 1 is a flowchart of an iterative guidance method of the present invention that does not rely on time compensation.

[0063] Figure 2 is a schematic diagram of the geometric relationship between pitch and yaw program angle commands. Detailed Implementation

[0064] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments:

[0065] Referring to Figure 1, which is a flowchart of an iterative guidance method of the present invention that does not rely on time compensation, the specific steps include:

[0066] (1) Construct the following state equations:

[0067]

[0068] In the formula: v x v y v z x, y, and z represent the velocity and position of the aircraft along the three axes (x, y, and z axes) in the reference coordinate system; a represents the apparent acceleration generated by the control force. Let ψ be the angle between the projection of the desired thrust vector onto the O-XY plane in the reference coordinate system and the OX axis, with counterclockwise being positive when viewed from the positive Z-axis direction; cLet be the angle between the desired thrust vector and the O-XY plane in the reference coordinate system. From the positive Z-axis direction, the desired thrust vector direction is positive if it is located inside the O-XY plane in the reference coordinate system. and ψ c The geometric schematic diagram is shown in Figure 2, where the dashed lines represent areas inside the screen; g x g y g z The gravitational acceleration can be calculated using the formula for gravitational acceleration. This invention takes the average of the gravitational acceleration at the target point and at the current moment. This approach has appeared in many research papers and has also been applied in engineering. Its advantage is that it can improve the efficiency of calculation while ensuring the accuracy of prediction. The reference coordinate system O-XYZ is an inertial frame, defined as follows: the origin O is the geocenter; the OY axis lies in the orbital plane determined by the target point and points to the ascending node; the OZ axis is perpendicular to the orbital plane and points in the negative direction of the orbital normal; O-XYZ is a right-handed rectangular coordinate system.

[0069] The formula for calculating gravitational acceleration is:

[0070] (a) Based on the position R in the launch inertial coordinate system of the current point of the aircraft i0 Calculate its corresponding gravitational acceleration G. i0 for

[0071]

[0072] Where: R 0x R 0y and R 0z The three-axis components of the position from the Earth's center to the launch point in the launch inertial coordinate system; x g0 y g0 and z g0 The three-axis components of the launch vehicle's center of mass in the launch inertial coordinate system;

[0073]

[0074] z c =p x (R 0x +x i0 )+p y (R 0y +y i0 )+p z (R 0z +z i0 ), p x =cos(A0)cos(B0), p y =sin(B0), pz = -sin(A0)cos(B0); μ is the Earth's gravitational constant, with a value of 3.986005 × 10⁻⁶. 14 m 3 / s 2 J2 represents the Earth's gravitational coefficient J2, with a value of 0.00108263; R e A0 is the Earth's equatorial radius, which is 6,378,140 m; B0 is the azimuth of the launch point; and B0 is the geodetic latitude of the launch point.

[0075] Launch inertial coordinate system O g -X g Y g Z g The coordinate system origin O is defined as follows: g For the launch point; O g X g The axis points in the aiming direction within the horizontal plane of the earth; O g Y g The axis is along the vertical line of gravity at the launch point, with upward being positive; O g -X g Y g Z g It is a right-handed rectangular coordinate system.

[0076] (b) Based on the semi-major axis a of the target point m eccentricity e m Track inclination angle i m Longitude of the ascending node Ω m Argument of perigee ω m and true close angle f m The position R1 of the target point in the three axes of the geocentric equatorial coordinate system can be obtained as follows:

[0077] R1 = r m ·cos(f m )·P+r m ·sin(f m )·Q (11)

[0078] In the formula:

[0079]

[0080] The geocentric equatorial coordinate system O1-X1Y1Z1 is defined as follows: the origin O1 is the Earth's center; the O1X1 axis points to the zero meridian in the equatorial plane; the O1Z1 axis points to the North Pole; O1-X1Y1Z1 is a right-handed rectangular coordinate system.

[0081] (c) Based on the target point's position R1 in the geocentric equatorial coordinate system, calculate its position R in the launch inertial coordinate system. gmThe method is as follows:

[0082]

[0083] In the formula:

[0084]

[0085] λ0, A0, and B0 are the longitude, azimuth, and geodetic latitude of the launch point, respectively.

[0086] (c) Based on the position R in the launch inertial coordinate system gm The gravitational acceleration G in the launch inertial coordinate system is calculated using a formula similar to equation (10). gm .

[0087] (d) Obtain the average gravitational acceleration between the target point and the current point. And convert it into a representation in the reference coordinate system. The method is as follows:

[0088]

[0089] In the formula:

[0090]

[0091] λ0, A0, and B0 are the longitude, azimuth, and geodetic latitude of the launch point, respectively; Ω m i m The longitude of the ascending node and the orbital inclination of the target point.

[0092] (2) The initial values ​​are selected as the velocity V0 and position R0 of the aircraft in the reference coordinate system at the current moment, and the expressions are as follows:

[0093]

[0094] (3) The terminal condition is selected as the velocity V of the target point in the reference coordinate system. m Location R m The expression is as follows:

[0095]

[0096] (4) Since the flow rate of the aircraft is approximately constant during stable flight, the design of the fuel-optimal control law can be equivalent to designing the control law with the shortest time. The performance index function is as follows:

[0097]

[0098] In the formula T m The time for integration.

[0099] (5) The control variable is selected as

[0100] (6) Calculate the magnitude of the optimal control law u using numerical optimization methods.

[0101] The Pontryagin maximum principle, which can be directly cited from numerous publications, provides a general solution to this optimal control problem. The result is:

[0102]

[0103] make:

[0104]

[0105] but: The coefficients of k1 and k3 are as follows:

[0106]

[0107] A1, D1, D2, and S are integration constants. The detailed derivation process can be found in Chapter 3 of the book "Design of High-Reliability Launch Vehicle Control Systems".

[0108] The method proposed in this invention can calculate the direction of the current desired thrust vector based on the predetermined target trajectory parameters and the current motion parameters of the spacecraft. It is very suitable for some small overload situations with large overload fluctuations. It can reduce the impact of rapid changes in time-related corrections caused by drastic changes in overload, provide a more stable program command angle for the input of the attitude control system, and improve control quality.

[0109] The above description is only the best specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the protection scope of the present invention.

[0110] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. An iterative guidance method that does not rely on time compensation, characterized in that: The process includes the following steps: (1) Constructing the state equation for optimal control; (2) Establishing the initial state for optimal control; (3) Establishing the terminal constraints for optimal control; (4) Designing the performance index function for optimal control; (5) Selecting the optimal control quantity; (6) Calculating the optimal control quantity. Step (1) can construct the following state equation: In the formula: 、 、 、 、 、 This refers to the velocity and position of the aircraft along the three axes in the reference coordinate system. The apparent acceleration generated by the control force; Let be the angle between the projection of the desired thrust vector onto the O-XY plane and the OX axis. From the positive Z-axis direction, counterclockwise is positive. Let be the angle between the desired thrust vector and the O-XY plane. From the positive Z-axis direction, the desired thrust vector direction is positive if it is located inside the O-XY plane. 、 、 For gravitational acceleration, the reference coordinate system O-XYZ is an inertial frame, defined as follows: the origin O is the Earth's center; the OY axis lies in the orbital plane determined by the target point, pointing towards the ascending node; the OZ axis is perpendicular to the orbital plane, pointing in the negative direction of the orbital normal; O-XYZ is a right-handed rectangular coordinate system; the formula for calculating gravitational acceleration is: based on the spacecraft's current position R in the launch inertial coordinate system... i0 Calculate its corresponding gravitational acceleration G. i0 for in: 、 and The three-axis components of the position from the Earth's center to the launch point in the launch inertial coordinate system; 、 and The three-axis components of the launch vehicle's center of mass in the launch inertial coordinate system; 、 、 、 、 、 、 、 ； The gravitational constant of Earth; The Earth's J2 gravitational coefficient; The radius of the Earth's equator; The azimuth angle for launch; The coordinates of the launch point are the geodetic latitude; the launch inertial coordinate system is O. g -X g Y g Z g The coordinate system origin O is defined as follows: g For the launch point; O g X g The axis points in the aiming direction within the horizontal plane of the earth; O g Y g The axis is along the vertical line of gravity at the launch point, with upward being positive; O g -X g Y g Z g It is a right-handed rectangular coordinate system; based on the semi-major axis of the target point eccentricity Track inclination Longitude of ascending node Perigeal argument And true near point angle The position of the target point in the three axes of the geocentric equatorial coordinate system can be obtained. The calculation method is as follows: In the formula: 、 、 、 、 The geocentric equatorial coordinate system O1-X1Y1Z1 is defined as follows: the origin O1 is the Earth's center; the O1X1 axis points to the zero meridian in the equatorial plane; the O1Z1 axis points to the North Pole; O1-X1Y1Z1 is a right-handed rectangular coordinate system; based on the position of the target point in the geocentric equatorial coordinate system... Calculate its position in the launch inertial coordinate system. The method is as follows: In the formula: 、 and These are the longitude, azimuth, and geodetic latitude of the launch point; based on the position in the launch inertial coordinate system. The gravitational acceleration in the launch inertial coordinate system is calculated using a formula similar to equation (2). The average gravitational acceleration between the target point and the current point is obtained. And convert it into a representation in the reference coordinate system. The method is as follows: In the formula: ;in: 、 and These are the longitude, azimuth, and geodetic latitude of the launch point, respectively. 、 Given the longitude of the ascending node and the orbital inclination of the target point; designing the fuel-optimal control law is equivalent to designing the control law with the shortest time, and the performance index function is as follows: In the formula Integral time; general solution 、 The result is: make: 、 、 、 、 but: 、 as well as and The coefficients are as follows: 、 、 、 、 、 is the integration constant.

2. The iterative guidance method according to claim 1, which does not rely on time compensation, is characterized in that: The initial state of step (2) is the velocity of the aircraft in the reference coordinate system at the current moment. ,Location The expression is as follows: 。 3. The iterative guidance method according to claim 1, which does not rely on time compensation, is characterized in that: The terminal condition in step (3) is the velocity of the target point in the reference coordinate system. ,Location The expression is as follows: 。 4. The iterative guidance method that does not rely on time compensation according to claim 1, characterized in that: Step (5) The control variable is 。

Images