Dynamic modeling method applied to variable-speed control moment gyroscope

Abstract

The invention discloses a dynamic modeling method applied to a variable-speed control moment gyroscope, which comprises the following steps of: splitting the variable-speed control moment gyroscope into three components for modeling respectively, and introducing a working mode module to enable each component to correctly output expected moment and angular momentum according to different working modes. By adopting the mode for modeling, a conventional low-speed frame angular velocity control method of the variable-speed control moment gyroscope and a using method of the backup reaction wheel can be combined, so that a satellite in-orbit process has switching of different maneuvering modes, and a new policy and a new modeling method are provided for ground simulation.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite attitude and orbit control simulation, and particularly relates to a dynamic modeling method for a variable-speed control moment gyroscope. Background Art

[0002] With the development of current agile satellites, the control moment gyroscope, as a control mechanism of a spacecraft, is gradually applied to the attitude control of small satellites. The difference from the traditional attitude control mechanism reaction wheel is that due to the gyroscopic torque caused by the rotation of the low-speed frame of the control moment gyroscope being perpendicular to the frame rotation axis, the generated torque directly acts on the satellite body through the low-speed frame bearing, and the torque transmission has nothing to do with the torque actuator of the frame servo system, so a larger control torque output can be obtained. In order to analyze the control effect of the control moment gyroscope on the satellite attitude through ground simulation, it is necessary to establish a dynamic model of the control moment gyroscope. The variable-speed control moment gyroscope includes a variable-speed high-speed rotor and a low-speed frame shaft. Compared with the fixed-speed control moment gyroscope, its high-speed component can be used as a new torque output component through the change of the rotation speed. The variable-speed control moment gyroscope can be used as a backup component of the reaction wheel by the fixed-angle holding command of the low-speed frame shaft and the rotation speed command of the high-speed rotor. Therefore, the dynamic model of the variable-speed control moment gyroscope can be modeled considering both usage modes.

[0003] Patent CN110597062B proposes a method for modeling and compensating control of the time-delay characteristics of a control moment gyroscope, which is applicable to fields such as high-resolution earth observation spacecraft with requirements for agile maneuvering and high-stability control. First, a time-delay characteristic model of the CMG frame angular velocity is established, and the time-delay characteristic parameters of the CMG are identified through tests of different CMG frame angular velocities, improving the tracking characteristics of the CMG frame angular velocity, and thus improving the attitude stability of the spacecraft. However, the modeling method is not applicable to the variable-speed control moment gyroscope. Patent CN118734652A discloses a method for modeling and analyzing the friction dynamics of a control moment gyroscope, belonging to the field of dynamics. A friction dynamics model of the control moment gyroscope is established, and the bearing kinematic model, the mixed lubrication and friction model, and the rotor-bearing and frame-bearing dynamics models are coupled into one model. Through iterative convergence, more accurate tribological and dynamic coupling solutions and analyses of the control moment gyroscope are achieved. It solves the limitations of the current independent modeling of the tribology and dynamics of the control moment gyroscope, and at the same time provides a theoretical basis for revealing the interaction mechanism between them. The friction dynamics model has high prediction accuracy and can provide technical support for the tribological and dynamic optimization design of the control moment gyroscope, as well as the improvement of system performance and control accuracy. However, it does not classify and model the working modes of the control moment gyroscope, and the control moment gyroscope model cannot be used as a backup means for the reaction wheel model. Summary of the Invention

[0004] Aiming at the problems existing in the prior art, the present invention provides a dynamic modeling method for a variable-speed control moment gyroscope, which splits the variable-speed control moment gyroscope into three components for separate modeling, and introduces a working mode module to enable the correct output of the desired torque and angular momentum among the components according to different working modes. By modeling in this way, the conventional control method of the low-speed frame angular velocity of the variable-speed control moment gyroscope and the usage of the backup reaction wheel can be combined, enabling the satellite to switch between different maneuvering modes during on-orbit operation, and providing new guidelines and modeling methods for ground simulation.

[0005] The technical solution of the present invention is as follows: a dynamic modeling method for a variable-speed control moment gyroscope, and the specific steps are as follows:

[0006] Step 1: Divide the variable-speed control moment gyroscope into three parts for separate modeling. The three parts are a high-speed rotor module, a low-speed frame axis angular velocity module, and a low-speed frame axis angle module;

[0007] The high-speed rotor module is for modeling the high-speed component part of the control moment gyroscope. The high-speed component part of the control moment gyroscope includes a variable-speed high-speed rotor with a structure similar to a reaction wheel. The simulation module input ports of the high-speed rotor module are the high-speed rotor speed command SpdCmd port, the current rotor angle Delta port, and the high-speed rotor initial value port; the simulation module output ports of the high-speed rotor module are the torque Trq output port, the high-speed rotor speed Spd output port, and the high-speed component angular momentum h output port; the high-speed rotor module performs speed integration according to the high-speed rotor speed command and the high-speed speed initial value of the simulation module input port of the high-speed rotor module to obtain the speed, torque, and angular momentum of the high-speed rotor, and determines the output directions of the high-speed rotor torque and angular momentum according to the current rotor angle Delta;

[0008] The low-speed frame axis angular velocity module is for modeling the low-speed frame axis part of the control moment gyroscope. The simulation module input ports of the low-speed frame axis angular velocity module are the frame angular velocity command DeltaCmd port, the high-speed rotor speed Spd port, and the frame angle initial value port; the output ports of the low-speed frame axis angular velocity module are the torque Trq output port, the frame angle Delta port, and the frame angular velocity DeltaSpd port;

[0009] The low-speed gimbal axis angle module models the low-speed gimbal axis part of the control moment gyro. Due to the characteristic of the variable rotational speed of the high-speed rotor of the control moment gyro, in certain cases, it can be used as a backup reaction wheel mode to output torque and angular momentum. The input ports of the low-speed gimbal axis angle module are the fixed angle hold command DeltafixCmd port, the fixed angle initial value DeltaInit port, and the high-speed rotor speed port; the output ports of the low-speed gimbal axis angle module are the current gimbal angle Delta port and the torque output Trq port; similar to the high-speed rotor module, the low-speed gimbal angle is integrated through the current fixed angle hold command and the fixed angle initial value to output the current fixed angle, and the angular momentum and torque output by the high-speed rotor are decomposed by trigonometric functions through the fixed angle state to output the decomposed torque;

[0010] Step 2: After modeling the high-speed rotor module, the low-speed gimbal axis angular velocity module, and the low-speed gimbal axis angle module, introduce a working mode input port to link the three modules; the working mode input ports are divided into a rotational speed mode, a fixed angle hold mode, and a lock-up mode;

[0011] The rotational speed mode is a mode of outputting torque by controlling the low-speed gimbal speed, and it is also the main usage method of the control moment gyro; the fixed angle hold mode is a mode of using the control moment gyro as a backup reaction wheel, which is a backup usage method of the control moment gyro; the lock-up mode is the lock-up state of the control moment gyro before the separation of the satellite and the rocket. Due to the severe vibration during the rocket launch process, it is usually necessary to lock the control moment gyro to protect the low-speed gimbal bearing, and this mode is the initial mode of the control moment gyro;

[0012] Use the working mode module to enable the three simulation modules of the built high-speed rotor module, the low-speed gimbal axis angular velocity module, and the low-speed gimbal axis angle module to output data under different working modes, and obtain a single variable rotational speed control moment gyro simulation model.

[0013] Furthermore, in the low-speed gimbal axis angular velocity module, the angular momentum of the control moment gyro group is determined by the gyro group installation matrix and the gimbal angle vector, as shown in the following formula:

[0014]

[0015] where h is the magnitude of the angular momentum of a single gyro, represents the gimbal angle vectors of n gyros, and A and B are the inertia unit vector matrices when the gimbal angle of each gyro is 90° and 0° respectively;

[0016]

[0017] are the sine and cosine diagonal matrices of the gimbal angle:

[0018]

[0019] In the stellar coordinates, the rotational speeds of the gyro frames of the gyro group The resultant gyroscopic torque T generated can be expressed as:

[0020]

[0021] Among them, the matrix C is the torque matrix of the gyro group and can be expressed as:

[0022] .

[0023] The beneficial effects of the present invention are as follows: A dynamic modeling method applied to a variable-speed control moment gyro is provided. The variable-speed control moment gyro is split into three components for modeling respectively, and a working mode module is introduced to correctly output the desired torque and angular momentum according to different working modes among the components. Modeling in this way can combine the conventional control method of the low-speed frame angular velocity of the variable-speed control moment gyro and the usage of the backup reaction wheel, enabling the satellite to switch between different maneuvering modes during on-orbit operation, and providing new guidelines and modeling methods for ground simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is the simulation model of the high-speed component of the control moment gyro;

[0025] Figure 2 is the simulation model of the low-speed frame angular velocity of the control moment gyro;

[0026] Figure 3 is the simulation model of the low-speed frame angle of the control moment gyro;

[0027] Figure 4 is the simulation model of the control moment gyro;

[0028] Figure 5 is the angular velocity curve of the control moment gyro;

[0029] Figure 6 is the angle curve of the control moment gyro. DETAILED DESCRIPTION OF THE INVENTION

[0030] The present invention will be further described below with reference to the accompanying drawings.

[0031] A dynamic modeling method applied to a variable-speed control moment gyro comprises the following specific steps:

[0032] Step 1: Divide the variable-speed control moment gyro into three parts for modeling respectively, as shown in Figure 1 , Figure 2 , Figure 3, the three parts are respectively a high-speed rotor module, a low-speed frame axis angular velocity module, and a low-speed frame axis angle module;

[0033] Step 2: The high-speed rotor module is for modeling the high-speed component part of the control moment gyro. The high-speed component part of the control moment gyro contains a high-speed rotor with variable speed similar to the structure of a reaction wheel. The simulation module input ports of the high-speed rotor module are the high-speed rotor speed command SpdCmd port, the current rotor angle Delta port, and the high-speed rotor initial value port; the simulation module output ports of the high-speed rotor module are the torque Trq output port, the high-speed rotor speed Spd output port, and the high-speed component angular momentum h output port; the high-speed rotor module performs speed integration based on the high-speed rotor speed command and the high-speed speed initial value of the simulation module input port of the high-speed rotor module to obtain the speed, torque, and angular momentum of the high-speed rotor, and determines the output directions of the high-speed rotor torque and angular momentum according to the current rotor angle Delta;

[0034] Step 3: The low-speed frame axis angular velocity module is for modeling the low-speed frame axis part of the control moment gyro. The simulation module input ports of the low-speed frame axis angular velocity module are the frame angular velocity command DeltaCmd port, the high-speed rotor speed Spd port, and the frame angle initial value port; the output ports of the low-speed frame axis angular velocity module are the torque Trq output port, the frame angle Delta port, and the frame angular velocity DeltaSpd port;

[0035] In the low-speed frame axis angular velocity module, the angular momentum of the control moment gyro group is determined by the gyro group installation matrix and the frame angle vector, as shown in the following formula:

[0036]

[0037] where h is the magnitude of the angular momentum of a single gyro, represents the frame angle vectors of n gyros, and A and B are the inertia unit vector matrices when the frame angles of each gyro are 90° and 0° respectively;

[0038]

[0039] is the frame angle sine and cosine diagonal matrix:

[0040]

[0041] In the body coordinate system, the rotational speed of each gyro frame of the gyro group generates a combined gyro torque T that can be expressed as:

[0042]

[0043] Among them, the matrix C is the torque matrix of the gyro group, which can be expressed as:

[0044] .

[0045] Step 4. The low-speed frame shaft angle module is used to model the low-speed frame shaft portion of the control torque gyro. Due to the variable speed characteristic of the high-speed rotor of the control torque gyro, it can be used as a backup reaction wheel mode to output torque and angular momentum in certain cases. The input ports of the low-speed frame shaft angle module are the fixed angle holding instruction DeltafixCmd port, the fixed angle initial value DeltaInit port, and the high-speed rotor speed port; the output ports of the low-speed frame shaft angle module are the current frame angle Delta port and the torque output Trq port; similar to the high-speed rotor module, the low-speed frame angle is integrated through the current fixed angle holding instruction and the fixed angle initial value to calculate the current fixed angle output, and the angular momentum and torque output by the high-speed rotor are decomposed through trigonometric functions of the fixed angle state to output the decomposed torque;

[0046] Step 5: After the high-speed rotor module, the low-speed frame shaft angular velocity module and the low-speed frame shaft angle module are modeled, a working mode input port is introduced to link the three modules; the working mode input port is divided into a speed mode, a fixed angle holding mode and a locking mode;

[0047] The speed mode is a mode for outputting torque by controlling the speed of the low-speed frame, and is also the main use mode of the control moment gyro; the fixed angle holding mode is a mode in which the control moment gyro is used as a backup reaction wheel, and is a backup use method of the control moment gyro; the locking mode is the locking state of the control moment gyro before the separation of the satellite and the rocket. Due to the violent vibration of the rocket during the launch process, the control moment gyro is usually required to be locked to protect the low-speed frame bearing. This mode is the initial mode of the control moment gyro;

[0048] Using the working mode module, the three simulation modules of the high-speed rotor module, the low-speed frame shaft angular velocity module and the low-speed frame shaft angle module are configured to output data in different working modes, and a single variable speed control torque gyro simulation model is obtained, such as Figure 4 shown.

[0049] Step 6: Bring the built variable speed control torque gyro simulation model into the satellite attitude dynamics model for control simulation. Model the two control torque gyros, make the angular velocity reverse rotation offset the one axis torque and then output the one axis torque to achieve the control of single axis torque control. The results are as follows: Figure 5 , 6 shown.

[0050] Modeling in this way can combine the conventional control method of the low-speed gimbal angular velocity of the variable-speed control moment gyro and the usage of the backup reaction wheel, enabling the satellite to switch between different maneuvering modes during on-orbit operation, and providing new guidelines and modeling methods for ground simulation.

[0051] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A dynamic modeling method for a variable speed controlled moment gyroscope, characterized in that: The specific steps are as follows: Step 1, dividing the variable speed control torque gyro into three parts and modeling them respectively, wherein the three parts are a high-speed rotor module, a low-speed frame shaft angular velocity module and a low-speed frame shaft angle module; The high-speed rotor module is a modeling of the high-speed component part of the control torque gyro. The high-speed component part of the control torque gyro includes a variable speed high-speed rotor with a reaction wheel structure. The simulation module input port of the high-speed rotor module is a high-speed rotor speed command SpdCmd port, a current rotor angle Delta port, and a high-speed rotor initial value port; the simulation module output port of the high-speed rotor module is a torque Trq output port, a high-speed rotor speed Spd output port, and a high-speed component angular momentum h output port; the high-speed rotor module performs speed integration according to the high-speed rotor speed command and the high-speed speed initial value of the simulation module input port of the high-speed rotor module to obtain the speed, torque and angular momentum of the high-speed rotor, and determines the output direction of the high-speed rotor torque and angular momentum according to the current rotor angle Delta; The low-speed frame shaft angular velocity module is used to model the low-speed frame shaft part of the control torque gyro. The simulation module input ports of the low-speed frame shaft angular velocity module are the frame angular velocity instruction DeltaCmd port, the high-speed rotor speed Spd port and the frame angle initial value port; the output ports of the low-speed frame shaft angular velocity module are the torque Trq output port, the frame angle Delta port and the frame angular velocity DeltaSpd port; The low-speed frame shaft angle module is used to model the low-speed frame shaft part of the control torque gyro. The input ports of the low-speed frame shaft angle module are the fixed angle holding instruction DeltafixCmd port, the fixed angle initial value DeltaInit port and the high-speed rotor speed port; the output ports of the low-speed frame shaft angle module are the current frame angle Delta port and the torque output Trq port; the low-speed frame angle is integrated through the current fixed angle holding instruction and the fixed angle initial value to calculate the current fixed angle output, and the angular momentum and torque output by the high-speed rotor are decomposed by trigonometric functions through the fixed angle state to output the decomposed torque; Step 2: After the high-speed rotor module, the low-speed frame shaft angular velocity module and the low-speed frame shaft angle module are modeled, a working mode input port is introduced to link the three modules; the working mode input port is divided into a speed mode, a fixed angle holding mode and a locking mode; The speed mode is a mode for outputting torque by controlling the speed of the low-speed frame, and is also the main use mode of the control moment gyro; the fixed angle holding mode is a mode in which the control moment gyro is used as a backup reaction wheel, and is a backup use method of the control moment gyro; the locking mode is the locking state of the control moment gyro before the separation of the satellite and the rocket. Due to the violent vibration of the rocket during the launch process, the control moment gyro is usually required to be locked to protect the low-speed frame bearing. This mode is the initial mode of the control moment gyro; Using the working mode module, the three simulation modules of the high-speed rotor module, the low-speed frame shaft angular velocity module and the low-speed frame shaft angle module are configured to output data in different working modes to obtain a single variable speed control torque gyro simulation model.

2. The method for dynamic modeling of a variable speed controlled moment gyro according to claim 1, characterized in that: In the low-speed frame axis angular velocity module, the angular momentum of the control torque gyro group is determined by the gyro group installation matrix and the frame angle vector, as shown in the following formula: Where h is the angular momentum of a single gyroscope, represents n gyro frame angle vectors, A and B are the inertia unit vector matrices when each gyro frame angle is 90° and 0° respectively; The frame angle sine and cosine diagonal matrix is: In the stellar coordinates, the rotation speed of each gyro frame in the gyro group is The resulting synthetic gyroscopic torque T can be expressed as: Among them, the matrix C is the torque matrix of the gyro group, which can be expressed as: 。

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