Iterative guidance method independent of time compensation

Abstract

The invention relates to an iterative guidance method independent of time compensation. The method comprises the following steps: (1) constructing an optimal control state equation; (2) establishing an initial state of optimal control; (3) establishing a terminal constraint condition of optimal control; (4) designing an optimal control performance index function; (5) selecting an optimal control quantity; and (6) calculating the optimal control quantity. According to the method, the direction of the current expected thrust vector can be calculated according to the preset target orbit parameters and the current motion parameters of the aircraft, so that the method is very suitable for some small overload conditions with relatively large fluctuation, and the influence of quick change of time-related correction caused by severe change of overload can be reduced; a more stable program instruction angle is provided for input of an attitude control system, and the control quality is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of iterative guidance of carrier rockets, in particular to an iterative guidance method that does not rely on time compensation. Background Art

[0002] After more than half a century of development, my country has achieved considerable success in space launch vehicles, particularly launch vehicles. The country now boasts a diverse range of large, medium, and small rocket systems, covering launch missions from near-Earth orbits to deep space. Heavy-lift launch vehicles with even greater carrying capacity are also under development. Guidance methods have played a crucial role in the diversification of these space missions.

[0003] To date, the guidance methods used in launch vehicles primarily fall into two categories: standard trajectory tracking and online trajectory planning. The former is typified by perturbation guidance, while the latter is typified by iterative guidance. With the increasing diversity and complexity of space launch missions, perturbation guidance has become increasingly inadequate for these missions. Iterative guidance, with its independent online planning approach that doesn't rely on a standard trajectory, has become more applicable.

[0004] Iterative guidance boasts high guidance accuracy, strong mission adaptability, and relatively low ground preparation requirements. It is a guidance method that calculates program angle commands in real time based on predetermined target orbital parameters and the vehicle's current motion parameters. Existing iterative guidance methods all add time-dependent correction parameters to the average attitude angle. This approach achieves good control under conditions with relatively stable overload variations. However, under conditions with more drastic overload variations, the time-dependent corrections can change rapidly, leading to large fluctuations in the program angle commands.

[0005] To this end, an iterative guidance method that does not rely on time compensation is proposed to reduce the impact of rapid changes in time-related corrections caused by drastic changes in overload, provide a smoother program command angle for the input of the attitude control system, and improve the control quality. Summary of the Invention

[0006] The purpose of the present invention is to overcome the problem that the existing iterative guidance method is prone to rapid changes in program angle instructions in some situations where the overload changes are relatively drastic. An iterative guidance method that does not rely on time compensation is proposed. Based on parameters such as the current speed and position of the aircraft and the orbit information of the predetermined target point, the expected average program angle information for reaching the target orbit is calculated, and only a time-independent correction amount is added to this information.

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

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

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

[0010] (2) Establishing the initial state of 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 quantity;

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

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

[0016]

[0017] Where: v x 、v y 、v z , x, y, z are the velocity and position of the aircraft along the three axes (x, y, and z) in the reference coordinate system; a is the apparent acceleration generated by the control force; is the angle between the projection of the desired thrust vector on the O-XY plane and the OX axis. From the positive direction of the Z axis, counterclockwise is positive; ψ c is the angle between the desired thrust vector and the O-XY plane. From the positive direction of the Z axis, the direction of the desired thrust vector is positive if it is located inside the O-XY plane. and ψ c The geometric diagram of Figure 2 As shown, the dotted line in the figure indicates that it is inside the screen; g x 、g y 、g z It is the gravitational acceleration, which can be calculated according to the calculation formula of gravitational acceleration. The present invention takes the average value of the gravitational acceleration of the target point and the current moment. This processing method not only appears in many research literatures, but also has been applied in engineering. Its advantage is that it can improve the calculation efficiency while ensuring the prediction accuracy.

[0018] Preferably, the reference coordinate system O-XYZ is an inertial system, which is defined as follows: the origin O of the coordinate system is the center of the earth; the OY axis is in the orbital plane determined by the target point, pointing 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.

[0019] Preferably, the calculation formula of gravitational acceleration is:

[0020] (a) The position R in the inertial coordinate system is launched based on 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 is the three-axis component of the position from the center of the earth to the launch point in the launch inertial coordinate system; g0 、y g0 and z g0 are the three-axis components of the center of mass of the launch vehicle 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 is the equatorial radius of the Earth; A0 is the azimuth of the launch; 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 definition is as follows: The origin of the coordinate system O g is the launch point; O g X g The axis points in the aiming direction in the geoid plane; g Y g The axis is along the vertical line of gravity at the launch point, and is positive upwards; g -X g Y g Z g It is a right-handed rectangular coordinate system.

[0026] (b) According to the semi-major axis a of the target point m , eccentricity em , orbital inclination i m , longitude of ascending node Ω m 、Argument of perigee ω m and true close angle f m , we can get the position R1 of the target point in the three-axis direction in the geocentric equatorial coordinate system. The calculation method is as follows:

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

[0028] Where:

[0029]

[0030] Preferably, the geocentric equatorial coordinate system O1-X1Y1Z1 is defined as follows: the origin O1 of the coordinate system is the center of the earth; 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 , as follows:

[0032]

[0033] Where:

[0034]

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

[0036] (c) According to the position R in the launch inertial coordinate system gm , use a formula similar to formula (2) to calculate the gravitational acceleration G in the launch inertial coordinate system gm .

[0037] (d) Get the average value of gravitational acceleration between the target point and the current point And convert it into the representation of the reference coordinate system Here’s how:

[0038]

[0039] Where:

[0040]

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

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

[0043]

[0044] Preferably, the terminal condition of step (3) can be selected as the velocity V of the target point in the reference coordinate system. m 、Position 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 optimal fuel control law can be equivalent to how to design the shortest time control law. The performance index function is as follows:

[0047]

[0048] Where T m is the integration time.

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

[0050] Preferably, step (6) can directly refer to the Pontryagin maximum principle in many literatures for the general solution of this optimal control problem. The result is:

[0051]

[0052] make:

[0053]

[0054] Then: And the coefficients of k1 and k3 are:

[0055]

[0056] A1, D1, D2, and S are integral 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) The present invention reduces the calculation of time-related parameters in the iterative guidance calculation, and the algorithm is simpler;

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

[0060] (3) The present invention is particularly suitable for some small overload conditions with large fluctuations, and can reduce the impact of rapid changes in time-related correction values ​​caused by drastic changes in overload;

[0061] (4) The present invention can effectively reduce the rapid change of the program angle instruction, provide a more stable program instruction angle for the input of the attitude control system, and improve the control quality. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0063] Figure 2 Schematic diagram of the geometric relationship between pitch and yaw program angle commands DETAILED DESCRIPTION

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

[0065] refer to Figure 1 This is a flow chart of an iterative guidance method that does not rely on time compensation according to the present invention. The specific steps include:

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

[0067]

[0068] Where: v x 、v y 、v z , x, y, z are the velocity and position of the aircraft along the three axes (x, y, and z) in the reference coordinate system; a is the apparent acceleration generated by the control force; is the angle between the projection of the desired thrust vector on the O-XY plane in the reference coordinate system and the OX axis. From the positive direction of the Z axis, counterclockwise is positive; ψ c is the angle between the desired thrust vector and the O-XY plane in the reference coordinate system. From the positive direction of the Z axis, the direction of the desired thrust vector is positive if it is located inside the O-XY plane in the reference coordinate system. and ψ c The geometric diagram of Figure 2 As shown, the dotted line in the figure indicates that it is inside the screen; g x 、g y 、g zIt is the gravitational acceleration, which can be calculated according to the calculation formula of gravitational acceleration. The present invention takes the average value of the gravitational acceleration of the target point and the current moment. This processing method not only appears in many research documents, but also has been applied in engineering. Its advantage is that it can improve the efficiency of calculation while ensuring the prediction accuracy; the reference coordinate system O-XYZ is an inertial system, which is defined as follows: the origin O of the coordinate system is the center of the earth; the OY axis is in the orbital plane determined by the target point, pointing to the ascending node; the OZ axis is perpendicular to the orbital plane, pointing to 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) The position R in the inertial coordinate system is launched based on 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 is the three-axis component of the position from the center of the earth to the launch point in the launch inertial coordinate system; g0 、y g0 and z g0 are the three-axis components of the center of mass of the launch vehicle 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), p z =-sin(A0)cos(B0); μ is the Earth's gravitational constant, which is 3.986005×10 14 m 3 / s 2 ; J2 is the J2 gravitational coefficient of the Earth, and its value is 0.00108263; R e is the equatorial radius of the earth, which is 6378140m; A0 is the azimuth of the launch; B0 is the geodetic latitude of the launch point.

[0075] Launch inertial coordinate system O g -X g Y g Z g The definition is as follows: The origin of the coordinate system O g is the launch point; O g X g The axis points in the aiming direction in the geoid plane; g Y g The axis is along the vertical line of gravity at the launch point, and is positive upwards; g -X g Y g Z g It is a right-handed rectangular coordinate system.

[0076] (b) According to the semi-major axis a of the target point m , eccentricity e m , orbital inclination i m , longitude of ascending node Ω m 、Argument of perigee ω m and true close angle f m , we can get the position R1 of the target point in the three-axis direction in the geocentric equatorial coordinate system. The calculation method is as follows:

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

[0078] Where:

[0079]

[0080] The geocentric equatorial coordinate system O1-X1Y1Z1 is defined as follows: the origin O1 of the coordinate system is the center of the earth; 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. gm , as follows:

[0082]

[0083] Where:

[0084]

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

[0086] (c) According to the position R in the launch inertial coordinate system gm , use a formula similar to formula (10) to calculate the gravitational acceleration G in the launch inertial coordinate system gm .

[0087] (d) Get the average value of gravitational acceleration between the target point and the current point And convert it into the representation of the reference coordinate system Here’s how:

[0088]

[0089] Where:

[0090]

[0091] λ0, A0 and B0 are the longitude, azimuth and geodetic latitude of the transmitting point respectively; Ω m 、i m is the ascending node longitude and orbit inclination of the target point.

[0092] (2) The initial values ​​are the velocity V0 and position R0 of the aircraft at the current moment in the reference coordinate system, 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 、Position R m , the expression is as follows:

[0095]

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

[0097]

[0098] Where T m is the integration time.

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

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

[0101] The general solution to this optimal control problem can be directly referenced from the Pontryagin maximum principle in many literatures. The result is:

[0102]

[0103] make:

[0104]

[0105] but: And the coefficients of k1 and k3 are:

[0106]

[0107] A1, D1, D2, and S are integral 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 the present invention can calculate the direction of the current expected thrust vector based on the predetermined target orbit parameters and the current motion parameters of the aircraft. It is very suitable for some small overload situations with large overload fluctuations. It can reduce the impact of rapid changes in time-related correction amounts caused by drastic changes in overload, provide a smoother program command angle for the input of the attitude control system, and improve control quality.

[0109] The above description is only the best specific implementation method of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

[0110] The contents not described in detail in the specification of the present invention belong to the common knowledge of professionals in this field.

Claims

1. An iterative guidance method that does not rely on time compensation, characterized by: The steps include: (1) Constructing the state equation for optimal control; (2) Establishing the initial state of optimal control; (3) Establish terminal constraints for optimal control; (4) Design the optimal control performance index function; (5) Select the optimal control quantity; (6) Calculate the optimal control quantity.

2. The iterative guidance method according to claim 1, wherein: Step (1) can construct the following state equation: Where: 、 、 、 、 、 The speed and position of the aircraft along the three axes (x, y and z) in the reference coordinate system; The apparent acceleration produced by the control force; is the angle between the projection of the desired thrust vector on the O-XY plane and the OX axis, and is positive counterclockwise from the positive direction of the Z axis; is the angle between the desired thrust vector and the O-XY plane. From the positive direction of the Z axis, the direction of the desired thrust vector is positive if it is located inside the O-XY plane. and The geometric diagram of is shown in Figure 2, where the dotted line indicates that it is inside the screen; 、 、 It is the gravitational acceleration, which can be calculated according to the calculation formula of gravitational acceleration. The present invention takes the average value of the gravitational acceleration of the target point and the current moment. This processing method not only appears in many research documents, but also has been applied in engineering. Its advantage is that it can improve the efficiency of calculation while ensuring the prediction accuracy; the reference coordinate system O-XYZ is an inertial system, which is defined as follows: the origin O of the coordinate system is the center of the earth; the OY axis is in the orbital plane determined by the target point, pointing to the ascending node; the OZ axis is perpendicular to the orbital plane, pointing to the negative direction of the orbital normal; O-XYZ is a right-handed rectangular coordinate system.

3. The iterative guidance method according to claim 1, wherein: The initial state of step (2) can be the velocity of the aircraft at the current moment in the reference coordinate system ,Location , the expression is as follows:

4. The iterative guidance method according to claim 1, wherein: The terminal condition of step (3) can be selected as the velocity of the target point in the reference coordinate system ,Location , the expression is as follows:

5. The iterative guidance method according to claim 1, which is independent of time compensation, is characterized in that: Step (4) Since the flow rate of the aircraft is approximately constant during stable flight, the design of the optimal fuel control law can be equivalent to how to design the integral time The shortest control law and performance index function are as follows:

6. The iterative guidance method according to claim 1, which is independent of time compensation, is characterized in that: Step (5) The control variable can be .

7. The iterative guidance method according to claim 1, which is independent of time compensation, is characterized in that: Step (6) can directly refer to the Pontryagin maximum principle in many literatures to find a general solution to this optimal control problem. 、 The result is: ;but: 、 as well as and The coefficients are: 、 、 、 、 、 、 、 ; 、 、 、 is the integral constant. The detailed derivation process can be found in Chapter 3 of the book "Design of High Reliability Launch Vehicle Control Systems".

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