A method for reducing the nutation axis deflection and nutation angle of space spin objects based on solid rocket motors

Abstract

This invention discloses a method for reducing the nutation axis deflection and nutation angle of a space-borne spinning object based on a solid rocket motor. The method includes: real-time measurement of the pitch angle, yaw angle, and roll angular velocity of the space load; integration after coordinate transformation to obtain the attitude angles of the space load in the ECI coordinate system, obtaining the transformation matrix; calculating possible nutation axis direction vectors; averaging the results to obtain the optimal nutation axis direction vector; and calculating the plane... YOUR With plane NOZ The clockwise angle, the angle between the nutation axis and the target axis, the angle between the body axis and the target axis, and the nutation angle are calculated; it is determined whether to enter the deflection step, the delayed ignition time and the expected ignition direction of the solid rocket motor are calculated; the corresponding solid rocket motor is started for deflection; the plane is calculated. YOUR With plane NOZ The clockwise angle is used to calculate the delayed ignition timing and the expected ignition direction of the solid rocket motor. This invention improves the controllability and maneuverability of spin-stabilized space payloads, laying the technological foundation for modern deep space exploration.

Description

Technical Field

[0001] This invention belongs to the field of space load dynamics and control, specifically relating to a method for reducing the deflection of the nutation axis and the nutation angle of a space spin object based on a solid rocket motor. Background Technology

[0002] In space missions, spin stabilization technology is widely used in satellites, spacecraft, and other objects. It maintains attitude stability through the gyroscopic effect generated by high-speed rotation, ensuring precise payload pointing or orbital control. However, this stability is often affected by external disturbances (such as microgravity environments or propellant sloshing), which cause periodic motion of the spin axis, leading to energy dissipation and attitude inaccuracies, potentially resulting in mission failure. For example, early satellites like Dongfanghong-1 faced this challenge, requiring passive damping mechanisms to suppress wobbling. Simultaneously, mission requirements often necessitate dynamic adjustment of the nutation axis direction (such as orbital maneuvers or Earth observation pointing), but traditional methods are inefficient.

[0003] Solid propulsion engines have become an ideal choice for attitude control of space-spinning objects due to their advantages such as high thrust, fast response, compact structure, easy storage, and low cost. They directly act on angular momentum through thrust vector adjustment, while avoiding the sloshing caused by liquid propellants and the inefficiency of other forms of control actuators (such as dampers and moment gyroscopes), thus enabling the reliable operation of modern spin spacecraft. Summary of the Invention

[0004] The purpose of this invention is to provide an active attitude control method for reducing the nutation axis deflection and nutation angle of a spin-stabilized space payload. Utilizing the high thrust and rapid response characteristics of solid rocket motors arranged around the sidewalls of the space payload, the angular momentum of the spin-stabilized space payload is actively controlled, thereby precisely reducing the nutation angle and optimizing the nutation axis direction. This improves the controllability and maneuverability of the spin-stabilized space payload, laying a technological foundation for modern deep space exploration.

[0005] The technical solution to achieve the purpose of this invention is as follows: a method for reducing the deflection of the nutation shaft and the nutation angle of a spin-type space payload based on solid rocket motors. The spin-type space payload is equipped with an inertial measurement unit. The spin-type space payload is cylindrical in shape, with multiple solid rocket motors evenly distributed circumferentially at the upper and lower ends of the cylindrical sidewalls. The deflection and reduction method is as follows:

[0006] Step (1): Measure the pitch angular velocity of the space load in real time using an inertial measurement unit. oh y yaw rate oh x and roll angular velocity oh z ;

[0007] Step (2): Transform the angular velocity measured in step (1) from the body coordinate system to the ECI coordinate system, and integrate it to obtain the attitude angle of the space load in the ECI coordinate system, obtain the transformation matrix, and calculate the direction vector of the body axis in the ECI coordinate system. ,according to ,calculate Z n Coordinates, based on Z n Calculate the possible nutation axis direction vectors using coordinate calculations, and take the average value to obtain the optimal nutation axis direction vector. ;

[0008] Step (3): Calculate the plane TON With plane NOZ The clockwise included angle A J Nucleus shaft ON With target axis OT Angle A p Body shaft OZ With target axis OT Angle A ZT And chordal angle A N ;

[0009] Step (4): Determine whether to enter the deflection step based on the calculation result of step (3), and calculate the delayed ignition time t. d1 The expected ignition direction of the solid rocket motor is determined; the expected ignition direction of the solid rocket motor is converted to the engine system, and the corresponding solid rocket motor is started to deflect it.

[0010] Step (5): Calculate the plane TON With plane NOZ The clockwise included angle A J According to the included angle A J Calculate the delayed ignition time t d2 And the expected ignition direction of the solid rocket motor, at t d2 The corresponding solid rocket motor is activated to reduce the nutation angle.

[0011] Furthermore, step (2) specifically involves:

[0012] Determine the target orientation axis in the ECI coordinate system at time t. OT Nucleus shaft ON With the body axis OZ Vector expression:

[0013] z=[1;0;0]

[0014] in, ,

[0015] Load Euler Attitude Angle , i , ψ The initial Euler attitude angles of the load are respectively 0 , i 0 , ψ 0 With rate of change , , The rate of change is obtained by integration; it is derived from the measured angular velocity of the IMU using the following formula:

[0016] ;

[0017] Nucleus shaft ON Direction vector Depend on OZ The position of the set point on the axis in space is obtained by fitting:

[0018] Known Z 1 , Z 2 … Z n n OZ Fixed points on the shaft ;

[0019] in, X O , Y O , Z O They are respectively O The three-degree-of-freedom coordinates of a point in the ECI coordinate system; l The coefficients are constants.

[0020] Possible nutation axis direction vectors can be obtained using the cross product method:

[0021] ,

[0022] ,

[0023] …

[0024] ;

[0025] but The estimated value, i.e. the optimal nutation axis direction vector, is .

[0026] Furthermore, step (3) specifically involves:

[0027] The target axis at time t is obtained by cross product of the direction vectors of the body axis, target axis, and nutation axis. OT With nutation axis ON The plane formed TON normal vector of the equation and nutation axis ON With the body axis OZ The plane formed ZON normal vector ;

[0028] Determined by calculating the included angles of the normal vectors:

[0029] flat TON With plane NOZ The clockwise included angle A J ,

[0030] Offset angle A p ,

[0031] Angle A between the body axis and the target axis ZT ,

[0032] A p A ZT A J ∈[0°,360°);

[0033] The nutation angle A is calculated using the following formula. N :

[0034] A N = ,

[0035] in H G Angular momentum, , J z , J x , J y For the loads to be wound around Z , Y , X Three-axis rotational inertia.

[0036] Furthermore, step (4) specifically involves:

[0037] Step (41): When A N +A p When the value is greater than the threshold, the nutation axis deflection step is initiated.

[0038] Step (42): When A J When <120°, A J The value is set to the current value plus 360°;

[0039] Step (43): Calculate the delayed ignition time t from the current time t. d1 =A J / oh J -t pre ,in oh J The expression for precession angular velocity is:

[0040] ;

[0041] in oh z Let t be the rolling angular velocity. pre To account for the pulse width setting of solid rocket motors, a reserved advance ignition time is provided;

[0042] Step (44): Calculate t d1 Roll angle of time Pitch angle Yaw angle Specifically:

[0043] ,

[0044] Let be the attitude angle vector in the ECI coordinate system at the initial time t;

[0045] Step (45): Calculate t d1 Time Machine Axis OZ normal resultant angular velocity vector :

[0046] ,

[0047] The cross product of the resultant angular velocity vector and the direction vector of the body axis in the ECI coordinate system. This is converted into the load body coordinate system as the expected ignition direction of the solid rocket motor;

[0048] Step (46): Obtain t d1 lower plane of ECI coordinate system at time TON normal vector And convert it to the machine system:

[0049] ,

[0050] in for Representation in body coordinate system;

[0051] Compare The angle α between the line and the expected ignition direction, when α ≤ 90°, selects an engine that has not been ignited within the region of the engine to which the expected ignition direction line belongs or the nearest adjacent region in the machine coordinate system. At t d1 The engine should be kept running at all times.

[0052] Furthermore, step (5) specifically involves:

[0053] Step (51): When A is calculated J When <120°, A J The value is set to the current value plus 360°;

[0054] Step (52): Calculate the delayed ignition time t from the current time t. d2 ;

[0055] Step (53): Calculate t from the real-time IMU measurement. d2 Time Machine Axis OZ normal resultant angular velocity vector ,choose The opposite direction in the body coordinate system is taken as the expected ignition direction of the solid rocket motor;

[0056] Step (54): Select an engine in the area of ​​the engine whose expected ignition direction line is located in the body coordinate system that has not been ignited, or in the nearest adjacent area. d2 The engine should be kept running at all times.

[0057] Compared with the prior art, the significant advantages of this invention are:

[0058] 1. The auxiliary control system required by this solution consists of three parts: an inertial measurement unit (IMU), a control board, and a solid rocket motor unit. The load can be controlled through a closed-loop architecture of IMU perception - control board decision-engine execution.

[0059] 2. The IMU can monitor the pitch, yaw, and roll angular velocities in real time and transmit the measured parameter values ​​to the main control board.

[0060] 3. The main control board dynamically analyzes IMU data, calculates angle data theoretically, determines the nutation angle of the load and the direction of the nutation axis, selects the appropriate control torque according to the target adjustment threshold, and sends ignition commands to the solid rocket motor unit in the corresponding direction.

[0061] 4. It can achieve the dual objectives of deflecting the nutation axis of a space spin load and reducing the nutation angle. Attached Figure Description

[0062] Figure 1 shows the distribution effect of the solid rocket motor unit on the space payload body.

[0063] Figure 2 shows the circumferential distribution of the solid rocket motor units on the space payload body.

[0064] Figure 3 shows the overall architecture of the control system.

[0065] Figure 4 shows a schematic diagram of each axis and variable.

[0066] Figure 5 Pitch angle in ECI geocentric inertial coordinate system i -Yaw angle ψ Planar load rolling shaft Z Trajectory diagram.

[0067] Figure 6. Pitch angular velocity in the load body coordinate system oh x -Yaw rate oh y Coupled trajectory diagram. Detailed Implementation

[0068] The present invention will now be described in further detail with reference to the accompanying drawings.

[0069] like Figure 3 As shown, the control system of this scheme consists of three parts: an inertial measurement unit (IMU), a main control board, and a solid rocket motor unit. Through the closed-loop architecture of IMU perception - control board decision-engine execution, the dual objectives of nutation axis deflection and nutation angle reduction are achieved.

[0070] In this control system, the IMU monitors the roll, pitch, and yaw angular velocities of the payload in the body coordinate system in real time, providing high-frequency attitude perception for the control system.

[0071] The control board runs an adaptive algorithm, which integrates the measured angular velocity data from the IMU to generate attitude angle information in the inertial frame and generates key control commands based on this information, including ignition timing to match the nutation phase and thrust vector direction.

[0072] Solid engine units installed at specific load locations receive ignition commands and trigger the solid engine to achieve precise torque output.

[0073] Regulations: such as Figure 4 As shown, the body axis and ON The angle between the axes (angular momentum axis or nutation axis) is the nutation angle A. N , ON Axis and target direction axis OT The angle between the two is Ap, and the body axis is perpendicular to the target. OT The included angle of the axis is A. ZT .along Figure 3 Yaw axis X The direction is the yaw rate. oh x Along the pitch axisY The direction is the pitch angular velocity. oh y Along the roll axis Z The direction is the roll angular velocity. oh z . , i , ψ These represent the roll, pitch, and yaw angles of the load relative to the ECI coordinate system, respectively. J z , J x , J y For the loads to be wound around Z , Y , X Three-axis rotational inertia. The pulse engine nozzles are arranged at 18° intervals between their axes, with 20 nozzles per layer for each engine and 40 nozzles in the upper and lower layers.

[0074] 1. Nucleation shaft deflection

[0075] (1) Determine the target direction axis at time t. OT Nucleus shaft ON With the body axis OZ The vector expression (ECI coordinate system) where z=[1;0;0] . X O , Y O , Z O They are respectively O The three-degree-of-freedom coordinates of the point in the ECI coordinate system. , i , ψ Each is determined by its initial value. 0 , i 0 , ψ 0 With rate of change , , The rate of change is obtained by integration. It is derived from the measured angular velocity from the IMU using the formula: Obtained. Nucleus axis ON vector Depend on OZ It is obtained by fitting the position of a specific point on the axis in space. For example, given... Z 1 , Z 2 … Z n of nindivual OZ Points on the axis Possible nutation axis direction vectors can be obtained using the cross product method: , ,… .but The estimated value is ;

[0076] (2) Obtain the target direction axis at time t by vector cross product. OT With nutation axis ON The plane formed TON normal vector of the equation and nutation axis ON With the body axis body axis OZ The plane formed ZON normal vector The planes are determined by calculating the angle between the normal vectors. TON With plane NOZ The clockwise included angle A J (Real-time changes), offset angle A p (Relative invariants), Angle A between the body axis and the target axis ZT (Real-time changes). Nucleation angle A N = (Relative invariants), where H G Angular momentum, ; (A p A ZT A J ∈[0°,360°))

[0077] (3) When A N +A p When the value is greater than a certain set threshold, proceed to the next step;

[0078] (4) When A J When <120°, A J Set the value to the current value plus 360°; (allow preparation time)

[0079] (5) Calculate the delayed ignition time t from the current time t. d =A J / oh J -t pre ,in oh J Let be the precession angular velocity, and its expression is: .in oh zt represents the roll angular velocity, obtained from IMU measurements. pre The advance ignition time is reserved to account for the pulse width of solid rocket motors;

[0080] (6) The integral value of the IMU real-time measurement is used to obtain t. d Roll angle of time Pitch angle Yaw angle ,in , Let be the attitude angle vector in the ECI coordinate system at the initial time t;

[0081] (7) t is calculated from the real-time measurement value of the IMU. d Time Machine Axis OZ normal resultant angular velocity vector ,get The direction in the airframe coordinate system is taken as the expected ignition direction of the solid rocket motor. ;

[0082] (8) Obtain t d lower plane of ECI coordinate system at time TON normal vector And convert it to the machine system: ,in for Representation in body coordinate system. Comparison The angle α between the line and the expected ignition direction, when α ≤ 90°, selects an engine that has not been ignited in the region of the engine to which the expected ignition direction line belongs or the nearest adjacent region in the machine coordinate system. Figure 2 ); ( Figure 1 Solid rocket motors in the opposite direction of the upper or lower layers

[0083] (9) Finally, at t d The engine should be kept running at all times.

[0084] 2. Nucleation Angle Reduction

[0085] (1) Using part 1 of the steps (2), the plane at time t is obtained. TON With plane NOZ The clockwise included angle A J ;

[0086] (2) When A J When <120°, A J Set the value to the current value plus 360°; (allow preparation time)

[0087] (3) Calculate the delayed ignition time t from the current time t using the same method as step (5) in Part 1. d ;

[0088] (4) t is calculated from the real-time measurement value of the IMU. d Time Machine Axis OZ normal resultant angular velocity vector ,choose The opposite direction in the body coordinate system is taken as the expected ignition direction of the solid rocket motor;

[0089] (5) Select an engine that has not been ignited in the area of ​​the engine to which the expected ignition direction line is located in the body coordinate system, or in the nearest adjacent area. Figure 2 ); ( Figure 1 Solid rocket motors operating in the opposite direction in the upper or lower layers.

[0090] (6) Finally, at t d The engine should be kept running at all times.

Claims

1. A method for reducing nutation shaft deflection and nutation angle of a spin-type space load based on a solid rocket motor, characterized in that, The spin-type space payload carries an inertial measurement unit. The spin-type space payload is cylindrical in shape, with multiple solid rocket motors evenly distributed circumferentially at the upper and lower ends of the cylindrical sidewalls. The deflection and attenuation methods are as follows: Step (1): Measure the pitch angular velocity of the space load in real time using an inertial measurement unit. ω y yaw rate ω x and roll angular velocity ω z ; Step (2): Transform the angular velocity measured in step (1) from the body coordinate system to the ECI coordinate system, and integrate it to obtain the attitude angle of the space load in the ECI coordinate system, obtain the transformation matrix, and calculate the direction vector of the body axis in the ECI coordinate system. According to the direction vector ,calculate Z n Coordinates, based on Z n Calculate the possible nutation axis direction vectors using coordinate calculations, and take the average value to obtain the optimal nutation axis direction vector. ; Step (3): Calculate the plane TON With plane NOZ The clockwise included angle A J Nucleus shaft ON With target axis OT Angle A p Body shaft OZ With target axis OT Angle A ZT And chordal angle A N ; Step (4): Determine whether to enter the deflection step based on the calculation result of step (3), and calculate the delayed ignition time t. d1 The expected ignition direction of the solid rocket motor is determined; the expected ignition direction of the solid rocket motor is converted to the engine system, and the corresponding solid rocket motor is started to deflect it. Step (5): Calculate the plane TON With plane NOZ The clockwise included angle A J According to the included angle A J Calculate the delayed ignition time t d2 And the expected ignition direction of the solid rocket motor, at t d2 The corresponding solid rocket motor is activated to reduce the nutation angle.

2. The method according to claim 1, characterized in that, Step (2) is as follows: Determine the target orientation axis in the ECI coordinate system at time t. OT Nucleus shaft ON With the body axis OZ Vector expression: ，z=[1;0;0]， in, , Load Euler Attitude Angle , θ , ψ The initial Euler attitude angles of the load are respectively 0 , θ 0 , ψ 0 With rate of change , , The rate of change is obtained by integration; it is derived from the measured angular velocity of the IMU using the following formula: ； Nucleus shaft ON Direction vector Depend on OZ The position of the set point on the axis in space is obtained by fitting: Known Z 1 , Z 2 … Z n of n indivual OZ Fixed points on the shaft ; in, X O , Y O , Z O They are respectively O The three-degree-of-freedom coordinates of a point in the ECI coordinate system; λ The coefficients are constants. Possible nutation axis direction vectors can be obtained using the cross product method: ， ， … ； but The estimated value, i.e. the optimal nutation axis direction vector, is .

3. The method according to claim 2, characterized in that, Step (3) is as follows: The target axis at time t is obtained by cross product of the direction vectors of the body axis, target axis, and nutation axis. OT With nutation axis ON The plane formed TON normal vector of the equation and nutation axis ON With the body axis OZ The plane formed ZON normal vector ; Determined by calculating the included angles of the normal vectors: flat TON With plane NOZ The clockwise included angle A J , Offset angle A p , Angle A between the body axis and the target axis ZT , A p 、A ZT 、A J ∈[0°,360°); The nutation angle A is calculated using the following formula. N : A N = ， in H G Angular momentum, , J z , J x , J y For the loads to be wound around Z , Y , X Three-axis rotational inertia.

4. The method according to claim 3, characterized in that, Step (4) is as follows: Step (41): When A N +A p When the value is greater than the threshold, the nutation axis deflection step is initiated. Step (42): When A J When <120°, A J The value is set to the current value plus 360°; Step (43): Calculate the delayed ignition time t from the current time t. d1 =A J / ω J -t pre ,in ω J The expression for precession angular velocity is: ； in ω z Let t be the rolling angular velocity. pre To account for the advance ignition time in the solid rocket motor pulse width setting; Step (44): Calculate t d1 Roll angle of time Pitch angle Yaw angle Specifically: ， Let be the attitude angle vector in the ECI coordinate system at the initial time t; Step (45): Calculate t d1 Time Machine Axis OZ normal resultant angular velocity vector : ， The cross product of the resultant angular velocity vector and the direction vector of the body axis in the ECI coordinate system. This is converted to the load body coordinate system as the expected ignition direction of the solid rocket motor. Step (46): Obtain t d1 lower plane of ECI coordinate system at time TON normal vector And convert it to the machine system: ， in for Representation in body coordinate system; Compare The angle α between the line and the expected ignition direction, when α ≤ 90°, selects an engine that has not been ignited within the region of the engine to which the expected ignition direction line belongs or the nearest adjacent region in the machine coordinate system. At t d1 The engine should be kept running at all times.

5. The method according to claim 4, characterized in that, Step (5) is as follows: Step (51): When A is calculated J When <120°, A J The value is set to the current value plus 360°; Step (52): Calculate the delayed ignition time t from the current time t. d2 ; Step (53): Calculate t from the real-time IMU measurement. d2 Time Machine Axis OZ normal resultant angular velocity vector ,choose The opposite direction in the body coordinate system is taken as the expected ignition direction of the solid rocket motor; Step (54): Select an engine in the area of ​​the engine whose expected ignition direction line is located in the body coordinate system that has not been ignited, or in the nearest adjacent area. d2 The engine should be kept running at all times.

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