A Coordinate System Conversion Method and Its Control Simulation Application during the Turning Process of a Launch Vehicle

Abstract

The present invention relates to a coordinate system conversion method and its control simulation application during the turning process of a launch vehicle. The conversion moment from the secondary stage body coordinate system to the final stage body coordinate system during the flight of the rocket body is selected as the moment when the secondary stage separation command is issued. Before the separation of the secondary stage body and the final stage body, the secondary stage body coordinate system is used for navigation, guidance, attitude control calculation, and control system simulation calculation; after the secondary stage separation, starting from the coordinate system switching moment of the rocket body, the final stage body coordinate system is used for navigation, guidance, attitude control calculation, and control system simulation calculation; this reduces the computing load of the flight control computer and the simulation computer, and reduces the computational complexity of the pre-launch control software and the control system simulation model, improving the operating efficiency of the rocket flight control system.

Description

Technical Field

[0001] The present invention relates to the technical fields of aircraft navigation, guidance, control and simulation, and particularly relates to a coordinate system conversion method during the turning process of a launch vehicle and its control simulation application. Background Art

[0002] Space launch vehicles adopt a multi-stage series configuration form. After the operation of each sub-stage power system is completed, they are separated step by step according to the time sequence, and the payload carried on the last stage is sent into the predetermined orbit to complete the launch mission. Usually, in the full-arrow state, each sub-stage adopts a normal layout scheme with the engine nozzle direction arranged backward. After the separation of the previous sub-stage, the rocket body completes a small-range attitude adjustment and stabilization and can directly ignite / start the next-stage flight phase. In order to enable the rocket body to have excellent aerodynamic performance, the fairing is usually designed into a spinning body shape such as a von Kármán curve. For small launch vehicles, due to the limitations of the rocket body length and diameter, the envelope space of the internal structure in the fairing is very limited. The external envelopes of small satellite single / multi-satellite payloads are mostly in the form of a cuboid. If the normal layout form is adopted, there will be a situation where there is a lot of remaining space between the top of the payload and the inner wall of the top of the fairing, that is, the available space in the fairing is not fully utilized, and the contradiction of "excess launch capacity but insufficient payload installation space" appears. The usual solution is to increase the envelope size of the fairing to increase the available space inside the fairing. The disadvantage of this solution is that it will cause the center of pressure of the entire rocket body to move forward, resulting in a worse aerodynamic static instability characteristic of the rocket body. Without changing the external dimensions of the fairing, a general technical solution is that the last-stage rocket body adopts an overall inverted scheme, so that the last-stage liquid propulsion engine is located in the envelope space of the fairing head curve, and the protruding objects such as the nozzle are in the contraction space of the small cross-section radius at the top. The satellite payload is located in the cylindrical envelope payload compartment near the previous stage of the last stage of the rocket body. In this way, the space in the last-stage rocket body and the payload compartment is more fully utilized, and the adaptability of small launch vehicles to satellite payloads is further improved.

[0003] Taking a three-stage tandem small launch vehicle as the research object, the overall inverted installation layout scheme of the last-stage rocket body is adopted. During the gliding stage of the second stage, the rocket body completes the turning and attitude adjustment process in the yaw direction. After the separation of the second stage, the fairing separation, attitude adjustment and stabilization are completed. Then, the last-stage propulsion engine is started and enters the orbital flight stage. During the navigation, guidance and attitude control calculations of the launch vehicle control system, the second-stage body coordinate system is used during the flight stage of the second stage before separation. The positive direction of the OX axis of the body coordinate system points from the tail of the entire rocket body along the central axis to the vertex of the head fairing. The last-stage flight stage uses the last-stage body coordinate system. The positive direction of the OX axis of the body coordinate system points from the bottom propulsion engine of the last stage along the central axis to the head satellite payload direction. The OX directions of the second-stage body coordinate system and the last-stage body coordinate system are coaxial and in opposite directions. The OY axes of the second-stage body coordinate system and the last-stage body coordinate system are both located in the longitudinal symmetry plane of the rocket body and have the same direction. Taking the direction perpendicular to the OX axis and pointing upward from below in the horizontal state of the rocket body as positive, according to the right-hand rule, the positive directions of the OZ axes of the second-stage body coordinate system and the last-stage body coordinate system are in opposite directions.

[0004] The above two definitions of the body coordinate system respectively correspond to the Euler angles ψ and γ that describe the rotational azimuth relationship of the body coordinate system relative to the launch inertial coordinate system. During the flight stage of the second stage, the Euler angles defined by the second-stage body coordinate system before turning are used to describe the attitude azimuth relationship of the rocket body in the inertial space. During the flight stage of the last stage, the Euler angles defined by the last-stage body coordinate system after turning are used to describe the relative attitude azimuth relationship of the rocket body in the inertial space. The corresponding Euler angles as the calculation results of the navigation quantities can more intuitively describe the attitude information of the rocket body in the inertial space during different flight periods, bringing direct convenience to the design and calculation of the guidance system and the attitude control system. At the same time, it is more conducive to coordinating the technical index requirements with relevant subsystems as the interface parameters of the control system and interpreting the flight data.

[0005] As Figure 1 shown in the control simulation system diagram of the rocket body turning flight process, Figure 1 in it, the input quantities of the force and moment calculation model are flight state quantities (including flight speed, position, attitude angle and other state quantities) and the control signals of the side jet engines. The output quantities are the resultant force vector and the resultant moment vector acting on the rocket body. The input quantities of the attitude dynamics and kinematics calculations are the force vector and the moment vector. The output quantities are flight state quantities such as the flight speed, position, attitude angle rate, Euler angle and quaternion of the rocket body. The input quantity of the navigation calculation is the apparent acceleration and attitude angle rate of the rocket body sensed by the inertial measurement unit. The output quantity is the calculation result of the flight state parameters. The input quantity of the guidance and attitude control calculations is the calculation result of the flight state parameters obtained from the navigation calculation. The output quantity is the control signal of the side jet engines.

[0006] The entire flight of the launch vehicle uses two forms of definition for the body coordinate system. A traditional implementation method is to start from the initial moment calculated by the navigation calculation and control system simulation model, and perform independent navigation calculations and calculations of the dynamics and kinematics equations of the simulation model in the two coordinate systems respectively. At the moment of switching the body coordinate system, the numerical values of the entire set of calculation parameters are switched. This method is relatively intuitive to understand, but it has deficiencies. The deficiency is that the synchronous independent calculation of the corresponding parts in the two coordinate systems introduces almost double the amount of calculation, greatly increasing the calculation load of the flight control computer and the simulation computer, and the two calculations need to provide their own calculation initial values, increasing the calculation process and calculation amount of the pre-launch control software and the control system simulation model.

[0007] In view of the above defects or improvement requirements of the prior art, the present invention provides a method for designing the coordinate system conversion and realizing the control simulation during the turning flight process of a launch vehicle. Before the separation of the second-stage body and the last-stage body, the navigation, guidance, and attitude control calculations and the control system simulation calculations are carried out using the second-stage body coordinate system. After the second-stage separation, starting from the moment of switching the body coordinate system, the navigation, guidance, and attitude control calculations and the control system simulation calculations are carried out using the last-stage body coordinate system. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method for coordinate system conversion during the turning process of a launch vehicle and its control simulation application, which can reduce the calculation load of the flight control computer and the simulation computer, and reduce the calculation complexity of the pre-launch control software and the control system simulation model, thereby improving the operation efficiency of the rocket flight control system.

[0009] In the first aspect, the technical solution adopted by the present invention is a method for coordinate system conversion during the turning process of a launch vehicle. The conversion moment from the second-stage body coordinate system to the last-stage body coordinate system during the flight of the body is selected as the moment when the second-stage separation command is issued. Denote the second-stage body coordinate system before the second-stage separation as O C0 X 10 Y 10 Z 10 , and the origin O C0 is the theoretical position of the center of mass of the second-stage body; the last-stage body coordinate system after the second-stage separation is O C X 1 Y 1 Z 1 , and the origin O C is the theoretical position of the center of mass of the last-stage body; the method includes the following steps:

[0010] S1. Before the moment when the second-stage separation command is issued, align the second-stage body coordinate system O C0 X 10 Y 10 Z 10 with the last-stage body coordinate system OC X 1 Y 1 Z 1 Translate it to the position where it coincides with the coordinate origin O. The axis is opposite to the axis direction. The axis is the same as the axis direction. The axis is the opposite of the axis direction; set the vector in the secondary rocket body coordinate system OX 10 Y 10 Z 10 The coordinates are [x 10 y 10 z 10 T , and in the final-stage rocket body coordinate system OX 1 Y 1 Z 1 The coordinates are [x 1 y 1 z 1 T , then the conversion relationship between the two is:

[0011] S2. Use three Euler angles: pitch angle yaw angle ψ 0 and roll angle γ 0 to describe the azimuth and attitude relationship of the secondary rocket body coordinate system OX 10 Y 10 Z 10 relative to the launch inertial coordinate system OXYZ. The launch inertial coordinate system OXYZ rotates successively around the corresponding coordinate axes according to the "321" rotation sequence by ψ 0 、γ 0 to obtain the rocket body coordinate system OX 10 Y 10 Z 10 , then the coordinates [x y x] in the launch inertial coordinate system T and the coordinates [x 10 y 10 z 10 T in the secondary rocket body coordinate system have the following conversion relationship:

[0012] Among them,

[0013]

[0014] , A0 is an orthonormal matrix, satisfying A0 -1 = A0 T ​​​;

[0015] S3. Set the Euler angles ψ 0 , γ 0 The corresponding standard quaternion is Q0 = [q0 0 q0 1 q0 2 q0 3 T . Calculate the transformation matrix A0 from the secondary rocket body coordinate system OX 10 Y 10 Z 10 to the launch inertial coordinate system OXYZ, and the expression is:

[0016]

[0017] S4. At the moment when the secondary separation command is issued, based on the transformation relationship described in step S1 and the transformation matrix A0 described in step S3, obtain the transformation matrix A from the final-stage rocket body coordinate system OX 1 Y 1 Z 1 to the launch inertial coordinate system OXYZ, and the expression is:

[0018]

[0019]

[0020] S5. Denote the azimuth and attitude Euler angles of the final-stage rocket body coordinate system OX 1 Y 1 Z 1 relative to the launch inertial system OXYZ as the pitch angle yaw angle ψ and roll angle γ. Then, use the Euler angles to calculate the transformation matrix A from the final-stage rocket body coordinate system OX 1 Y 1 Z 1 to the launch inertial coordinate system OXYZ, and the expression is:

[0021]

[0022] S6. According to the transformation matrix A obtained in step S4 and the transformation matrix A calculated using the Euler angles in step S5, under the condition of ψ ∈ (-π / 2, π / 2), obtain the expressions for the corresponding Euler angles from the element values of the transformation matrix A:

[0023]

[0024] S7. According to the final-stage rocket body coordinate system OX obtained in step S6 1 Y 1 Z​1 Euler angles of the azimuth and attitude relationship with respect to the launch inertial coordinate system OXYZ ψ and γ, and the corresponding quaternion Q = [q 0 q 1 q 2 q 3 T The expression of is:

[0025]

[0026] The beneficial effects of the present invention are as follows: By adopting the above-mentioned coordinate system conversion design method for the turning process of a launch vehicle, the conversion matrix between the secondary rocket body coordinate system OX 10 Y 10 Z 10 , the final-stage rocket body coordinate system OX 1 Y 1 Z 1 and the launch inertial coordinate system OXYZ, as well as the corresponding Euler angles and quaternions can be obtained simply. This design method can reduce the computational load of the flight control computer and the simulation computer, and reduce the computational complexity of the pre-launch control software and the control system simulation model, thereby improving the operating efficiency of the rocket flight control system.

[0027] In a second aspect, the technical solution adopted by the present invention is a control simulation application for implementing the coordinate system conversion method for the turning process of a launch vehicle. The control simulation application is implemented in the control simulation system for the turning flight process of the rocket body. The control simulation application includes the coordinate system conversion control simulation implementation process for the attitude dynamics and kinematics calculation process and the coordinate system conversion control simulation implementation process for the navigation calculation process. The conversion moment from the secondary rocket body coordinate system to the final-stage rocket body coordinate system during the rocket body flight process is selected as the moment when the secondary separation command is issued. The coordinate system conversion control simulation implementation process for the attitude dynamics and kinematics calculation process is as follows:

[0028] Before the coordinate system conversion moment, in the secondary rocket body coordinate system, the rocket body attitude angular acceleration is calculated from the torque according to the law of conservation of angular momentum, the rocket body attitude angular rate is obtained by integrating the rocket body attitude angular acceleration, and the quaternion and Euler angles are obtained by integrating the rocket body attitude angular rate;

[0029] At the coordinate system conversion moment, according to the conversion relationship described in step S1, the rocket body attitude angular rate in the secondary rocket body coordinate system is converted into the rocket body attitude angular rate in the final-stage rocket body coordinate system, and based on the torque vector and inertia matrix in the final-stage rocket body coordinate system, the ​Integrate with the initial value to obtain the attitude angular velocity of the rocket body in the last-stage rocket body coordinate system; at the coordinate transformation moment, calculate the transformation matrix A from the OX 1 Y 1 Z 1 of the last-stage rocket body coordinate system to the launch inertial coordinate system OXYZ according to the expression of the transformation matrix A in step S4, and then calculate the Euler angles of the OX 1 Y 1 Z 1 of the last-stage rocket body coordinate system relative to the launch inertial coordinate system OXYZ and the corresponding quaternion Q at the coordinate transformation moment according to the Euler angle expression in step S6 and the quaternion expression in step S7; integrate with the Euler angles ψ, γ obtained at the coordinate transformation moment as the initial value to obtain the Euler angles of the last-stage rocket body coordinate system relative to the launch inertial coordinate system in the last-stage flight segment, and integrate with the quaternion Q obtained at the coordinate transformation moment as the initial value to obtain the quaternion of the last-stage rocket body coordinate system relative to the launch inertial coordinate system in the last-stage flight segment; The coordinate transformation control simulation implementation process of the navigation calculation process is as follows:

[0030] Before the coordinate transformation moment, use the apparent velocity increment value and angular increment value in the secondary rocket body coordinate system to calculate the value at the current sampling moment point minus the value at the previous sampling moment point. The apparent velocity increment value and angular increment value are the apparent velocity increment values and angular increment values along the coordinate axes of the rocket body coordinate system in the pitch channel, yaw channel, and roll channel respectively; at each sampling moment point before the coordinate transformation moment, calculate the corresponding quaternion value at the current sampling moment point in the secondary rocket body coordinate system according to the quaternion value at the previous sampling moment point;

[0031] At the coordinate transformation moment, transform the apparent velocity increment value and angular increment value at the previous sampling moment point from the secondary rocket body coordinate system to the last-stage rocket body coordinate system according to the transformation relation in step S1, and directly use the parameter values in the last-stage rocket body coordinate system for the apparent velocity increment value and angular increment value at the current sampling moment point; starting from the next sampling moment point after the coordinate transformation moment, use the apparent velocity increment value and angular increment value in the last-stage rocket body coordinate system to calculate the value at the current sampling moment point minus the value at the previous sampling moment point; at the coordinate transformation moment, according to the expression of the transformation matrix A0 in step S3, use the previous sampling moment point value Q0(z

[0032] ) of the quaternion Q0 value in the secondary rocket body coordinate system to calculate the OX -1 of the secondary rocket body coordinate system 10 Y 10 Z 10The transformation matrix A0 to the launch inertial coordinate system OXYZ, and then calculate the last-stage rocket body coordinate system OX according to the expression of the transformation matrix A in step S4 1 Y 1 Z 1 The transformation matrix A to the launch inertial coordinate system OXYZ, and then calculate the quaternion Q value at the previous sampling time point corresponding to the last-stage rocket body coordinate system according to the Euler angle expression in step S6 and the quaternion expression in step S7, Q(z -1 ), so as to calculate the quaternion Q value at the current sampling time point of the last-stage rocket body coordinate system; starting from the next sampling time point after the coordinate system conversion moment, the quaternion values at each sampling time point are calculated according to the quaternion value at the previous sampling time point in the last-stage rocket body coordinate system.

[0033] The beneficial effects of the present invention are: according to the above control simulation application for implementing the coordinate system conversion design method in the turning process of the launch vehicle, the navigation calculation parameter values such as quaternions and Euler angles at each sampling calculation time point before and after the coordinate system conversion are calculated. Before the separation of the second-stage rocket body and the last-stage rocket body, the second-stage rocket body coordinate system is used for navigation, guidance, and attitude control calculations and control system simulation calculations; after the second-stage separation, starting from the coordinate system switching moment of the rocket body, the last-stage rocket body coordinate system is used for navigation, guidance, and attitude control calculations and control system simulation calculations. Before and after the coordinate system conversion of the rocket body, the algorithm design and software program implementation are completed based on the second-stage rocket body coordinate system and the last-stage rocket body coordinate system respectively, so that the output attitude control engine switch control instruction controls the rocket body attitude to fly stably near the program attitude angle. This control simulation implementation method reduces the computing load of the flight control computer and the simulation computer, and reduces the computational complexity of the pre-launch control software and the control system simulation model, improving the operation efficiency of the rocket flight control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a schematic diagram of the control simulation system for the rocket body turning flight process in the present invention;

[0035] Figure 2 It is a schematic diagram of the second-stage rocket body coordinate system and the last-stage rocket body coordinate system in the present invention;

[0036] Figure 3 It is the attitude angle curve graph of the flight process before and after the coordinate system conversion of the rocket body in the present invention; among them, Figure 3 (a) is the attitude angle curve graph of the flight process before and after the coordinate system conversion of the rocket body, Figure 3 (b) is Figure 3 The partial enlarged view of (a);

[0037] Figure 4 It is the attitude angle deviation curve graph of the flight process before and after the coordinate system conversion of the rocket body in the present invention; among them,Figure 4 (a) is the attitude angle deviation curve graph during the flight process before and after the conversion of the rocket body coordinate system, Figure 4 (b) is Figure 4 a partial enlarged view of (a);

[0038] Figure 5 is the attitude angle rate curve graph during the flight process before and after the conversion of the rocket body coordinate system of the present invention; Figure 5 (a) is the attitude angle rate curve graph during the flight process before and after the conversion of the rocket body coordinate system; Figure 5 (b) is Figure 5 a partial enlarged view of (a). Specific embodiments

[0039] The following further describes the invention with reference to the accompanying drawings and in combination with specific embodiments, so that those skilled in the art can implement it according to the text of the specification. The protection scope of the present invention is not limited to this specific embodiment.

[0040] Those skilled in the art should understand that in the disclosure of the present invention, the orientation or positional relationships indicated by the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting the present invention.

[0041] In addition, the terms "first", "second", "third", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0042] In the description of the embodiments of the present application, it should also be noted that unless otherwise clearly specified and limited, the terms "set", "installed", "connected", "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific situations.

[0043] In a first aspect, the present invention relates to a method for converting the coordinate system during the turning process of a launch vehicle. The conversion moment of the secondary rocket body coordinate system to the final stage rocket body coordinate system during the flight of the rocket body is selected as the moment when the secondary separation command is issued. Denote the secondary rocket body coordinate system before secondary separation as O C0 X 10 Y 10 Z 10 , and the origin O C0is the theoretical position of the centroid of the second-stage rocket body; the coordinate system of the final-stage rocket body after the second-stage separation is O C X 1 Y 1 Z 1 , and the origin O C is the theoretical position of the centroid of the final-stage rocket body; as Figure 2 shown, where the O C0 Z 10 axis and the O C Z 1 axis are determined by the right-hand rule in their respective coordinate systems; the method includes the following steps:

[0044] S1. Before the second-stage separation command is issued, translate the coordinate system O C0 X 10 Y 10 Z 10 of the second-stage rocket body and the coordinate system O C X 1 Y 1 Z 1 of the final-stage rocket body to the position where the coordinate origins coincide, O, the axis is in the opposite direction to the axis, the axis is in the same direction as the axis, the axis is in the opposite direction to the axis; set the vector in the coordinate system OX of the second-stage rocket body 10 Y 10 Z 10 to be [x 10 y 10 z 10 T , and in the coordinate system OX of the final-stage rocket body 1 Y 1 Z 1 to be [x 1 y 1 z 1 T , then the conversion relationship between the two is:

[0045] S2. Use three Euler angles: pitch angle yaw angle ψ 0 and roll angle γ 0 to describe the azimuth and attitude relationship of the coordinate system OX of the second-stage rocket body 10 Y 10 Z 10 relative to the launch inertial coordinate system OXYZ (by translation to make the coordinate origins coincide). The launch inertial coordinate system OXYZ rotates successively around the corresponding coordinate axes in the "321" rotation sequence by ψ​​0 , γ 0 Obtain the body coordinate system OX 10 Y 10 Z 10 , then the coordinates [x y z] in the launch inertial coordinate system T and the coordinates [x 10 y 10 z 10 T in the secondary body coordinate system have the following transformation relationship:

[0046] Among them,

[0047]

[0048] , A0 is an orthonormal matrix, satisfying A0 -1 = A0 T ;

[0049] S3. Let the Euler angles ψ 0 , γ 0 correspond to the standard quaternion Q0 = [q0 0 q0 1 q0 2 q0 3 . T , calculate the transformation matrix A0 from the secondary body coordinate system OX 10 Y 10 Z 10 to the launch inertial coordinate system OXYZ according to the elements of the quaternion Q0, and the expression is:

[0050]

[0051] The advantage of directly using quaternions for calculation compared with Euler angles is that it can avoid trigonometric function calculations and the problem of different definition ranges of each angle under different transformation orders;

[0052] S4. At the moment when the secondary separation command is issued, according to the transformation relationship described in step S1 and the transformation matrix A0 described in step S3, obtain the transformation matrix A from the final-stage body coordinate system OX 1 Y 1 Z 1 to the launch inertial coordinate system OXYZ, and the expression is:

[0053]

[0054] S5. The final-stage body coordinate system OX 1 Y 1 Z 1The Euler angles of the azimuth and attitude relative to the launch inertial coordinate system OXYZ are denoted as the pitch angle the yaw angle ψ and the roll angle γ. Then, the transformation matrix A from the coordinate system OX 1 Y 1 Z 1 of the last-stage rocket body to the launch inertial coordinate system OXYZ is expressed as:

[0055]

[0056] S6. Based on the transformation matrix A obtained in step S4 and the transformation matrix A calculated using Euler angles in step S5, under the condition of ψ ∈ (-π / 2, π / 2), the expressions for the corresponding Euler angles obtained from the element values of the transformation matrix A are:

[0057]

[0058] S7. According to the Euler angles 1 Y 1 Z 1 of the azimuth and attitude relationship between the coordinate system OX of the last-stage rocket body relative to the launch inertial coordinate system OXYZ, ψ and γ, the corresponding quaternion Q = [q 0 q 1 q 2 q 3 T is expressed as:

[0059]

[0060] Based on the above-derived transformation matrix between the secondary rocket body coordinate system OX 10 Y 10 Z 10 and the last-stage rocket body coordinate system OX 1 Y 1 Z 1 and the launch inertial coordinate system OXYZ, as well as the corresponding Euler angle and quaternion calculation methods, the transformation design of the rocket body coordinate system in the navigation, guidance, and attitude control algorithms, and the transformation design of the rocket body coordinate system in the control system simulation model are carried out. Considering that before and after the coordinate system transformation, the Euler angle / quaternion values describing the rocket body attitude need to be synchronously switched, and at the same time, the forces and torques acting on the rocket body in the rocket body coordinate system also need to be synchronously switched. Therefore, the moment of the transformation from the secondary rocket body coordinate system to the last-stage rocket body coordinate system during the rocket body flight is selected as the moment when the secondary separation command is issued. At this moment, it is in the stage where the attitude control engine is stopped. This selection method can synchronize the coordinate system transformation with the switching of the flight control algorithm and the calculation of the simulation model parameter inter-stage switching, providing great convenience for the calculation of the flight control software and the calculation of the simulation model program.​

[0061] In a second aspect, the present invention relates to a control simulation application for implementing a coordinate system conversion method during the turning process of a launch vehicle. The control simulation application is implemented in a control simulation system for the turning flight process of the rocket body. The control simulation application includes a coordinate system conversion control simulation implementation process for the attitude dynamics and kinematics calculation process and a coordinate system conversion control simulation implementation process for the navigation calculation process. In the control system simulation model, the attitude dynamics and kinematics calculation process describes and calculates relevant physical quantities in the rocket body coordinate system and the launch inertial coordinate system. The coordinate system conversion control simulation implementation process for the attitude dynamics and kinematics calculation process is as follows:

[0062] Before the coordinate system conversion moment, in the secondary rocket body coordinate system, the rocket body attitude angular acceleration is calculated from the torque according to the law of conservation of angular momentum. The rocket body attitude angular rate is obtained by integrating the rocket body attitude angular acceleration, and the quaternion and Euler angles are obtained by integrating the rocket body attitude angular rate.

[0063] At the coordinate system conversion moment, the rocket body attitude angular rate in the secondary rocket body coordinate system is converted to the rocket body attitude angular rate in the final stage rocket body coordinate system and based on the torque vector and inertia matrix in the final stage rocket body coordinate system, an integration operation is performed with the value obtained at the coordinate system conversion moment as the initial value to obtain the rocket body attitude angular rate in the final stage rocket body coordinate system; at the coordinate system conversion moment, the transformation matrix A from the final stage rocket body coordinate system OX Y 1 Y 1 Z 1 to the launch inertial coordinate system OXYZ is calculated according to the expression of the transformation matrix A in step S4. Furthermore, according to the Euler angle expression in step S6 and the quaternion expression in step S7, the Euler angles 1 Y 1 Z 1 of the final stage rocket body coordinate system relative to the launch inertial coordinate system OXYZ at the coordinate system conversion moment are calculated, and the Euler angles ψ, γ and the corresponding quaternion Q are calculated. An integration operation is performed with the Euler angles ψ, γ obtained at the coordinate system conversion moment as the initial value to obtain the Euler angles of the final stage rocket body coordinate system relative to the launch inertial coordinate system in the final stage flight segment, and an integration operation is performed with the quaternion Q obtained at the coordinate system conversion moment as the initial value to obtain the quaternion of the final stage rocket body coordinate system relative to the launch inertial coordinate system in the final stage flight segment;

[0064] The coordinate system conversion control simulation implementation process for the navigation calculation process is as follows:

[0065] Before the coordinate system conversion moment, the numerical subtraction of the current sampling moment point from the previous sampling moment point is calculated using the apparent velocity increment value and the angular increment value in the secondary rocket body coordinate system. The apparent velocity increment value and the angular increment value are the apparent velocity increment values and angular increment values along the coordinate axes of the rocket body coordinate system for the pitch channel, yaw channel, and roll channel respectively (a total of six parameter values); at each sampling moment point before the coordinate system conversion moment, the quaternion value of the corresponding current sampling moment point is calculated in the secondary rocket body coordinate system based on the quaternion value of the previous sampling moment point.

[0066] At the coordinate system conversion moment, the apparent velocity increment value and the angular increment value of the previous sampling moment point are converted from the secondary rocket body coordinate system to the final-stage rocket body coordinate system according to the conversion relation formula in step S1, and the apparent velocity increment value and the angular increment value of the current sampling moment point directly use the parameter values in the final-stage rocket body coordinate system; starting from the next sampling moment point after the coordinate system conversion moment, the numerical subtraction of the current sampling moment point from the previous sampling moment point is calculated using the apparent velocity increment value and the angular increment value in the final-stage rocket body coordinate system; at the coordinate system conversion moment, according to the expression of the conversion matrix A0 in step S3, the previous sampling moment point value Q0(z of the quaternion Q0 value in the secondary rocket body coordinate system is used to calculate the conversion matrix A0 from the secondary rocket body coordinate system OX -1 ) to the launch inertial coordinate system OXYZ, and then according to the expression of the conversion matrix A in step S4, the conversion matrix A from the final-stage rocket body coordinate system OX 10 Y 10 Z 10 to the launch inertial coordinate system OXYZ is calculated, and then according to the Euler angle expression in step S6 and the quaternion expression in step S7, the previous sampling moment point value Q(z of the quaternion Q value in the corresponding final-stage rocket body coordinate system is calculated, so as to calculate the quaternion Q value of the current sampling moment point in the final-stage rocket body coordinate system; starting from the next sampling moment point after the coordinate system conversion moment, at each sampling moment point, the quaternion value of the corresponding current sampling moment point is calculated in the final-stage rocket body coordinate system based on the quaternion value of the previous sampling moment point. 1 Y 1 Z 1 to the launch inertial coordinate system OXYZ, and then the previous sampling moment point value Q(z of the quaternion Q value in the corresponding final-stage rocket body coordinate system is calculated according to the Euler angle expression in step S6 and the quaternion expression in step S7, so as to calculate the quaternion Q value of the current sampling moment point in the final-stage rocket body coordinate system; starting from the next sampling moment point after the coordinate system conversion moment, at each sampling moment point, the quaternion value of the corresponding current sampling moment point is calculated in the final-stage rocket body coordinate system based on the quaternion value of the previous sampling moment point. -1 ) to calculate the quaternion Q value of the current sampling moment point in the final-stage rocket body coordinate system; starting from the next sampling moment point after the coordinate system conversion moment, at each sampling moment point, the quaternion value of the corresponding current sampling moment point is calculated in the final-stage rocket body coordinate system based on the quaternion value of the previous sampling moment point.

[0067] According to the above coordinate system conversion calculation method, the numerical values of navigation calculation parameters such as quaternion and Euler angle at each sampling calculation moment point before and after the coordinate system conversion are calculated. Before and after the rocket body coordinate system conversion, the algorithm design and software program implementation are completed based on the secondary rocket body coordinate system and the final-stage rocket body coordinate system respectively, so that the output attitude control engine switch control instruction can control the rocket body attitude to fly stably near the program attitude angle.

[0068] The forces and moments acting on the rocket body during flight are essentially continuously varying physical quantities, which are only related to the numerical values of the current flight state parameters. The moment of coordinate system transformation from the secondary rocket body coordinate system to the upper stage rocket body coordinate system is taken as the moment when the secondary separation command is issued. Therefore, before secondary separation, the force and moment calculation processes in the control system simulation model are established and solved in the secondary rocket body coordinate system. Starting from the coordinate system transformation moment, they are established and solved in the upper stage rocket body coordinate system, and the overall switching of the force and moment calculation model is completed at the coordinate system transformation moment.

[0069] Embodiment 1:

[0070] A certain three-stage configuration launch vehicle adopts an overall inverted structure layout for the upper stage. During the coasting phase of the secondary stage, it adjusts its attitude by 150° in the yaw direction to complete the turning action, and then issues the secondary separation command. After secondary separation, the upper stage rocket body is adjusted to a yaw angle of 0° in the yaw direction, and then the fairing separation command is issued. Then, the upper stage propulsion engine is started for in-orbit flight.

[0071] Introducing the rocket body coordinate system transformation design of the present invention, the moment when the secondary separation command is issued is selected as the coordinate system transformation moment, and it is transformed from the secondary rocket body coordinate system to the upper stage rocket body coordinate system. For each sampling calculation time point of the control system and each simulation calculation time point of the simulation model before the moment when the secondary separation command is issued, the navigation, guidance, and attitude control algorithms are calculated based on the Euler angles / quaternions / transformation matrices representing the azimuth and attitude relationships between the secondary rocket body coordinate system and the launch inertial coordinate system. The numerical value of the previous sampling time point corresponding to the parameter used in the algorithm is used for the parameter sampling calculation before the point value; the integration algorithm used in the simulation model is based on the secondary rocket body coordinate system to set the initial value and then perform continuous integration operations.

[0072] The parameters representing the azimuth and attitude relationships between the secondary rocket body coordinate system and the launch inertial coordinate system are extracted at the moment when the secondary separation command is issued, where the Euler angles are the pitch angle the yaw angle ψ 0 and the roll angle γ 0 , the standard quaternion is Q0 = [q0 0 q0 1 q0 2 q0 3 T , and the transformation matrix from the secondary rocket body coordinate system to the launch inertial coordinate system is A0. Let any vector projected in the launch inertial coordinate system be [x y z] T , and its coordinates in the secondary rocket body coordinate system be [x 10 y 10 z 10 T , then there is:

[0073] ​​

[0074]

[0075] Starting from the moment when the secondary separation command is issued, the conversion is made to the final-stage rocket body coordinate system. Let the Euler angles representing the relationship between the final-stage rocket body coordinate system and the launch inertial coordinate system at this moment be the pitch angle the yaw angle ψ and the roll angle γ, and the standard quaternion is Q = [q 0 q 1 q 2 q 3 T , and the conversion matrix from the final-stage rocket body coordinate system to the launch inertial coordinate system is A. The coordinates in the final-stage rocket body coordinate system are [x 1 y 1 z 1 T , then there are:

[0076]

[0077]

[0078]

[0079]

[0080] ψ = -sin -1 (a 31 ),

[0081] γ = atan2(a 32 , a 33 ),

[0082]

[0083] The following coordinate system conversion designs are carried out in the navigation calculation algorithm:

[0084] When calculating the difference between the current sampling moment value and the previous sampling moment value along the axis directions of the rocket body coordinate system for the pitch, yaw, and roll channels in terms of the apparent velocity increment / angle increment, at the coordinate system conversion moment, the previous value of the apparent velocity increment / angle increment is converted from the secondary rocket body coordinate system to the final-stage rocket body coordinate system, and the current value directly uses the value in the final-stage rocket body coordinate system; at each sampling moment before the coordinate system conversion moment, the apparent velocity increment / angle increment in the secondary rocket body coordinate system is used to calculate the difference between the current value and the previous sampling moment value; starting from the next sampling moment after the coordinate system conversion moment, the apparent velocity increment / angle increment in the final-stage rocket body coordinate system is used to calculate the difference between the current value and the previous sampling moment value;

[0085] ​​When calculating the quaternion based on the angular increment, it is necessary to calculate the quaternion value at the current sampling time point according to the quaternion value at the previous sampling time point. At the coordinate system conversion moment, according to the previous point value Q0(z -1 ) of the quaternion Q0 value in the secondary rocket body coordinate system, calculate the transformation matrix A0 from the secondary rocket body coordinate system to the launch inertial coordinate system, and then calculate the transformation matrix A from the last-stage rocket body coordinate system to the launch inertial coordinate system, and further calculate the previous point value Q(z -1 ) of the quaternion Q value in the last-stage rocket body coordinate system, so as to further calculate the quaternion value at the current sampling time point in the last-stage rocket body coordinate system. At each sampling time point before the coordinate system conversion moment, use the previous point value of the quaternion in the secondary rocket body coordinate system to calculate the corresponding quaternion value at the current sampling time point; at each time point starting from the next sampling time point after the coordinate system conversion moment, use the previous point value of the quaternion in the last-stage rocket body coordinate system to calculate the corresponding quaternion value at the current sampling time point.

[0086] According to the above coordinate system conversion calculation method, the quaternion, Euler angle and other navigation calculation parameter values at each sampling time point before and after the coordinate system conversion are calculated. The guidance system and the attitude control system complete the algorithm design and software program implementation based on the secondary rocket body coordinate system and the last-stage rocket body coordinate system respectively before and after the coordinate system conversion.

[0087] The design and implementation method of the coordinate system conversion corresponding to the attitude dynamics and kinematics calculations in the control system simulation calculation model are as follows:

[0088] When calculating the attitude angle acceleration rate of the rocket body from the torque according to the law of conservation of angular momentum and further calculating the attitude angle rate, an integral operation is used. Before the coordinate system conversion moment, the calculation is carried out in the secondary rocket body coordinate system; at the coordinate system conversion moment, the attitude angle rate of the secondary rocket body coordinate system is converted into the attitude angle rate of the last-stage rocket body coordinate system Starting from the coordinate system conversion moment, based on the torque vector and the inertia matrix in the last-stage rocket body coordinate system, using the coordinate system conversion moment as the initial value for calculation and integral operation, the attitude angle rate of the rocket body in the last-stage rocket body coordinate system is calculated;

[0089] When calculating the quaternion from the attitude angle rate, an integral operation is used. Before the coordinate system conversion moment, the calculation is carried out in the secondary rocket body coordinate system; at the coordinate system conversion moment, according to the standard quaternion Q0 of the secondary rocket body coordinate system relative to the launch inertial coordinate system, gradually calculate the transformation matrix A from the last-stage rocket body coordinate system to the launch inertial coordinate system, and then calculate the azimuth attitude Euler angles ψ, γ and the corresponding quaternion Q of the last-stage rocket body coordinate system relative to the launch inertial coordinate system, and use the quaternion Q value at the coordinate system conversion moment as the initial value for integral operation to calculate the quaternion of the last-stage rocket body coordinate system relative to the launch inertial coordinate system in the last-stage flight segment;

[0090] Integral operation is used when calculating Euler angles based on attitude angular rates. Before the coordinate system conversion moment, calculations are carried out in the secondary rocket body coordinate system; at the coordinate system conversion moment, according to the Euler angles of the secondary rocket body coordinate system relative to the launch inertial coordinate system ψ 0 and γ 0 , the transformation matrix A from the upper stage rocket body coordinate system to the launch inertial coordinate system is gradually calculated, and then the azimuth attitude Euler angles of the upper stage rocket body coordinate system relative to the launch inertial coordinate system are calculated ψ and γ, with the values of ψ and γ at the coordinate system conversion moment as the initial values for integral operation, and the Euler angles of the upper stage rocket body coordinate system relative to the launch inertial coordinate system in the upper stage flight segment are calculated.

[0091] In the control system simulation model, the force and moment calculation module is established and solved in the secondary rocket body coordinate system before the second-stage separation moment, and is established and solved in the upper stage rocket body coordinate system starting from the coordinate system conversion moment, and the overall switching of the force and moment calculation module is completed at the coordinate system conversion moment.

[0092] After completing the coordinate system conversion design of the above navigation, guidance, and attitude control algorithms and the coordinate system conversion control simulation process of the control system simulation model, a full-flight mathematical simulation test is carried out to verify the correctness and rationality of the design and its implementation. Record the pitch angle yaw angle ψ and roll angle γ of the rocket body during the flight process of the secondary gliding segment and the upper stage gliding segment Ⅰ before and after the rocket body coordinate system conversion, as well as the attitude angle deviation Δψ, Δγ and attitude angular rates ω x1 、ω y1 、ω z1 , and the simulation result curves are shown in Figures 3 to 5 . The moment when the rocket body coordinate system is converted, that is, the moment when the second-stage separation command is issued, is 303.12 s, and the control system sampling calculation period is 10 ms.

[0093] It can be seen from the full-flight control system simulation results that at the moment when the second-stage separation command is issued, the rocket body coordinate system is converted from the secondary rocket body coordinate system to the upper stage rocket body coordinate system, and the corresponding physical parameter values and calculation algorithm programs in the navigation, guidance, and attitude control algorithms and the control system simulation model are all synchronously converted.

[0094] The above methods for rocket body coordinate system conversion, navigation, guidance, and attitude control algorithm design, and control simulation implementation in the reverse flight condition of the launch vehicle are also applicable to the theoretical deduction and engineering applications such as the navigation, guidance, and attitude control algorithm design and the implementation of the control system simulation model program in other cases where there are coordinate system conversions for aircraft / launch vehicles.

Claims

1. A coordinate system conversion method for the turning process of a launch vehicle, characterized in that: The conversion moment from the secondary rocket body coordinate system to the final-stage rocket body coordinate system during the flight of the selected rocket body is set as the moment when the secondary separation command is issued. Denote the secondary rocket body coordinate system before secondary separation as , and the origin is the theoretical position of the center of mass of the secondary rocket body; The coordinate system of the last-stage rocket body after secondary separation is , and the origin is the theoretical position of the centroid of the last-stage rocket body; this method includes the following steps: Before the moment when the secondary separation instruction is issued, translate the secondary rocket body coordinate system and the last-stage rocket body coordinate system to the position where their coordinate origins coincide , The direction of the axis is opposite to that of the axis, The direction of the axis is the same as that of the axis, and the direction of the axis is opposite to that of the axis; set the vector The coordinate in the secondary rocket body coordinate system is , and the coordinate in the is , then the conversion relationship between the two is: ; S2. Use three Euler angles: pitch angle , yaw angle and roll angle to describe the azimuth attitude relationship of the secondary rocket body coordinate system relative to the launch inertial coordinate system . The launch inertial coordinate system rotates successively around the corresponding coordinate axes according to the "321" rotation sequence , , to obtain the rocket body coordinate system . Then the conversion relationship between the coordinates in the launch inertial coordinate system and the coordinates in the secondary rocket body coordinate system is: , where , is an unitary orthogonal matrix and satisfies ; S3. Set Euler angles , , The corresponding standard quaternion is . Calculate the transformation matrix from the secondary rocket body coordinate system to the launch inertial coordinate system according to the elements of the quaternion . The expression is as follows: ； S4. At the moment when the secondary separation instruction is issued, according to the conversion relationship described in step S1 and the conversion matrix described in step S3 , the transformation matrix from the last-stage rocket body coordinate system to the launch inertial coordinate system is obtained, and the expression of the transformation matrix is: ; S5. Denote the Euler angles of the azimuth attitude of the last-stage rocket body coordinate system relative to the launch inertial coordinate system as the pitch angle , yaw angle and roll angle . Then, the transformation matrix from the last-stage rocket body coordinate system to the launch inertial coordinate system calculated using the Euler angles is expressed as: ; S6. The transformation matrix obtained according to step S4 and the transformation matrix calculated using Euler angles in step S5 , under the condition of , the expression for the corresponding Euler angles obtained from the element values of the transformation matrix is: ； S7. Euler angles of the azimuth attitude relationship of the final-stage rocket body coordinate system obtained according to step S6 with respect to the launch inertial coordinate system are calculated, and the corresponding quaternion , and is obtained. The expression of the quaternion is as follows: 。 2. A control simulation method for implementing the coordinate system conversion method for the turning process of the launch vehicle described in claim 1, and the control simulation method is implemented in a control simulation system for the turning flight process of the rocket body, characterized in that: The control simulation method includes a coordinate system conversion control simulation implementation process for the attitude dynamics and kinematics calculation process and a coordinate system conversion control simulation implementation process for the navigation calculation process. The coordinate system conversion control simulation implementation process for the attitude dynamics and kinematics calculation process is as follows: Before the coordinate system conversion moment, in the secondary rocket body coordinate system, calculate the rocket body attitude angular acceleration from the torque according to the law of conservation of angular momentum, calculate the rocket body attitude angular rate by integrating according to the rocket body attitude angular acceleration, and calculate the quaternion and Euler angles by integrating according to the rocket body attitude angular rate; At the coordinate system conversion moment, according to the conversion relationship described in step S1, the rocket body attitude angular rate in the secondary rocket body coordinate system is converted into the rocket body attitude angular rate in the final-stage rocket body coordinate system , and based on the moment vector and the inertia matrix in the final-stage rocket body coordinate system, integration operation is performed with the obtained at the coordinate system conversion moment as the initial value to obtain the rocket body attitude angular rate in the final-stage rocket body coordinate system; at the coordinate system conversion moment, according to the expression of the conversion matrix in step S4, the conversion matrix from the final-stage rocket body coordinate system to the launch inertial coordinate system is calculated, and then according to the Euler angle expression described in step S6 and the quaternion expression described in step S7, the Euler angles of the final-stage rocket body coordinate system relative to the launch inertial coordinate system , , and the corresponding quaternions at the coordinate system conversion moment are calculated. Integration operation is performed with the Euler angles , , obtained at the coordinate system conversion moment as the initial value to obtain the Euler angles of the final-stage rocket body coordinate system relative to the launch inertial coordinate system in the final-stage flight segment. Integration operation is performed with the quaternion obtained at the coordinate system conversion moment as the initial value to obtain the quaternion of the final-stage rocket body coordinate system relative to the launch inertial coordinate system in the final-stage flight segment; The coordinate system conversion control simulation implementation process for the navigation calculation process is as follows: Before the coordinate system conversion moment, use the apparent velocity increment value and angular increment value in the secondary rocket body coordinate system to calculate the value at the current sample time point minus the value at the previous sampling time point. The apparent velocity increment value and angular increment value are the apparent velocity increment values and angular increment values along the coordinate axes of the rocket body coordinate system in the pitch channel, yaw channel, and roll channel respectively; at each sampling time point before the coordinate system conversion moment, calculate the corresponding quaternion value at the current sampling time point according to the quaternion value at the previous sampling time point in the secondary rocket body coordinate system; At the coordinate system conversion moment, the apparent velocity increment value and the angular increment value at the previous sampling moment are converted from the secondary rocket body coordinate system to the final stage rocket body coordinate system according to the conversion relation formula in step S1, and the apparent velocity increment value and the angular increment value at the current sampling moment directly use the parameter values in the final stage rocket body coordinate system; starting from the next sampling moment after the coordinate system conversion moment, the apparent velocity increment value and the angular increment value in the final stage rocket body coordinate system are used to calculate the value at the current sampling moment minus the value at the previous sampling moment; at the coordinate system conversion moment, according to the expression of the conversion matrix adopt the quaternion value at the previous sampling moment of the secondary rocket body coordinate system to calculate the conversion matrix from the secondary rocket body coordinate system to the launch inertial coordinate system and then calculate the conversion matrix from the final stage rocket body coordinate system to the launch inertial coordinate system according to the expression of the conversion matrix in step S4, and further calculate the corresponding quaternion value at the previous sampling moment in the final stage rocket body coordinate system according to the Euler angle expression in step S6 and the quaternion expression in step S7, so as to calculate the quaternion value at the current sampling moment in the final stage rocket body coordinate system; starting from the next sampling moment after the coordinate system conversion moment, the quaternion value at each sampling moment in the final stage rocket body coordinate system is calculated according to the quaternion value at the previous sampling moment.

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