Micro-nano satellite multi-constraint fine control method based on actuator dynamics

Abstract

The application provides a micro-nano satellite multi-constraint fine control method based on actuator dynamics, and belongs to the field of spacecraft control, and comprises the following steps: considering the electromechanical characteristics of the reaction wheel, an attitude deep coupling model of the micro-nano satellite containing the dynamic characteristics of the reaction wheel is established; aiming at the wheel shaft friction and back electromotive force interference of the reaction wheel, a double interference observer is designed to accurately estimate the wheel shaft friction and back electromotive force interference; aiming at the physical constraints of the satellite rotation speed and the reaction wheel current, a nonlinear state-dependent barrier function is designed to convert the constraint state into a tracking control variable; a composite controller is constructed by combining the double interference observer and the nonlinear state-dependent barrier function, and the high-precision controller design of the micro-nano satellite is completed. The application can overcome the multi-class physical constraint problem in the control of the micro-nano satellite, compensate the interference of the reaction wheel, and has the characteristics of high reliability and high accuracy.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft control, specifically relating to a multi-constraint fine control method for micro-nano satellites based on actuator dynamics. Background Technology

[0002] Microsatellites and nanosatellites play an irreplaceable role in space maneuvering missions such as target tracking and on-orbit servicing due to their advantages of low cost and high flexibility. However, the increasingly sophisticated space situation has placed urgent demands on the safety and accuracy of microsatellite maneuvers. Unlike large satellites, microsatellites and nanosatellites are more significantly affected by physical constraints and interference during maneuvers, mainly in the following two aspects:

[0003] On the one hand, the rotational speed of microsatellites and nanosatellites is limited by their mechanical structure and must remain within a safe range during maneuvers to prevent excessive speed from causing safety hazards. Similarly, the current state of the reaction wheel, the actuator for attitude maneuvers of microsatellites and nanosatellites, is also subject to safety limitations imposed by the armature circuit to prevent excessive current from causing mechanical damage or other safety issues. Therefore, to ensure the safety of microsatellite and nanosatellite control, it is necessary to strictly limit the rotational speed of the satellite and the amplitude range of the reaction wheel current.

[0004] On the other hand, since the reaction wheel inevitably suffers from device error interference such as axle friction and back EMF, these multi-source interferences are directly coupled to the system input of the microsatellite and change with the control signal, exhibiting extremely strong composite characteristics. Consequently, the composite interferences such as axle friction and back EMF are easily excited and amplified with changes in the system input during the microsatellite control process, seriously affecting the accuracy of the system and reducing the quality of mission execution.

[0005] Under the influence of various physical constraints and complex interferences, the requirement for safety and accuracy in the attitude control system of micro-nano satellites undoubtedly poses a great challenge to the design of the control system. Some existing studies on physical constraints, such as the literature "Spacecraft Attitude Maneuver Backstepping Control under Multiple Constraints" (Wang Shuo, Wang Yipeng, Sun Jingxu, et al. Spacecraft Attitude Maneuver Backstepping Control under Multiple Constraints [J]. Journal of Astronautics, 2023, 44(12): 1925-1933.), introduce a hyperbolic tangent function to design a virtual angular velocity control law to ensure that the angular velocity is always within the limit range for the spacecraft's angular velocity constraint problem; Chinese patent application CN202211034728.7 addresses the spacecraft's angular velocity constraint by using a second-order command filter to saturate the virtual control signal for angular velocity tracking, while simultaneously designing a hierarchical controller to suppress flexural vibration interference. The above studies have mostly focused on the constraints of the spacecraft's operating state and have achieved good results, but they usually ignore the influence of the physical constraints of the reaction wheel and device errors on the micro-nano satellite system.

[0006] Regarding research on satellite anti-interference, the literature "A Class of High-Order All-Drive Anti-Interference Control for Combined Spacecraft Based on Interference Observer" (Cui Kaixin, Duan Guangren. A Class of High-Order All-Drive Anti-Interference Control for Combined Spacecraft Based on Interference Observer [J]. Acta Aeronautica Sinica, 2024, 45(01): 73-85) introduces a generalized discrete-time high-order all-drive backward difference model and estimates and compensates for input interference and external constant interference in the combined spacecraft, designing a high-order all-drive anti-interference control method. Chinese patent application CN202310821459.7 considers satellite actuator error interference, estimates and learns system interference by designing an interference observer and an adaptive law, and finally designs a composite controller to achieve simultaneous suppression and compensation of system interference.

[0007] While existing research has made some progress, it still exhibits a degree of conservatism in terms of the security and anti-interference precision of satellite control systems in the face of various physical constraints and the effects of complex interference. For example, Chinese patent application CN110456812A, although it constructs a coupled model that can improve anti-interference accuracy and achieves high-precision attitude control based on composite terminal sliding mode control, does not consider the hard constraints of actuators or satellite states, resulting in unsatisfactory control performance.

[0008] Therefore, in order to improve the safety and accuracy of the attitude control system of micro-nano satellites, it is necessary to fully explore the influence mechanism and transmission mechanism of reaction wheel error interference on the dynamics of micro-nano satellites, and to refine the processing of composite interference to improve the control accuracy of micro-nano satellites. At the same time, the rotational speed of the satellite and the current of the reaction wheel should be constrained to ensure the safety of micro-nano satellite operation. Summary of the Invention

[0009] To address the challenge of high-precision attitude control for micro / nano satellites under the combined interference of multiple physical constraints related to the satellite's rotational speed and reaction wheel current, as well as errors in the reaction wheel components, and to overcome the shortcomings of existing technologies in terms of operational safety and anti-interference precision, this invention provides a micro / nano satellite multi-constraint fine control method based on actuator dynamics. This method achieves the separation, estimation, and fine compensation of reaction wheel error interference, improving the satellite's ability to resist combined interference. Simultaneously, it constrains the satellite's rotational speed and reaction wheel current state variables, ensuring the safety of micro / nano satellite control.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A method for multi-constraint fine control of micro / nano satellites based on actuator dynamics includes the following steps:

[0012] The first step is to consider the electromechanical characteristics of the reaction wheel, establish a micro-nano satellite attitude deep coupling model that includes the dynamic characteristics of the reaction wheel, and separate the wheel axle friction interference and back EMF interference of the reaction wheel according to the influence topology.

[0013] The second step is to design a dual-interference observer based on the micro-nano satellite attitude deep coupling model established in the first step, and to estimate the wheel and axle friction interference and back EMF interference after separation, respectively.

[0014] The third step is to design a nonlinear state-dependent obstacle function to convert the constraint state into a tracking control variable, taking into account the physical constraints of the star's rotation speed and the reaction wheel current.

[0015] The fourth step involves constructing a composite controller by combining a dual-interference observer with a nonlinear state-dependent barrier function to precisely compensate for wheel-axle friction interference and back EMF interference in the reaction wheel.

[0016] Furthermore, in the first step, when establishing the deep coupling model of micro-nano satellite attitude, the wheel axle friction interference and back EMF interference are separated according to their action nodes on the electromechanical energy transfer path, laying a topological foundation for the subsequent independent estimation by the dual interference observers.

[0017] Furthermore, in the second step, based on the separated action nodes, the estimated values ​​of wheel axle friction interference and back EMF interference are generated in parallel within the same sampling period.

[0018] Furthermore, in the third step, when constructing the nonlinear state-dependent barrier function, the real-time measured values ​​of the celestial rotation speed and the reaction wheel current are used as independent variables, so that the output of the nonlinear state-dependent barrier function is coupled with the desired tracking error, thereby embedding the physical constraints of the celestial rotation speed and the reaction wheel current into the dynamics of the tracking error.

[0019] Furthermore, the nonlinear state-dependent barrier function generates a monotonically increasing gain near the boundary where the output tends to infinity, ensuring that the celestial rotation speed and the reaction wheel current are always within a safe range.

[0020] Furthermore, in the fourth step, the wheel and axle friction estimates and back EMF estimates output by the dual disturbance observers are first mapped to the control torque and control voltage, respectively, and then superimposed with the correction results generated by the nonlinear state-dependent obstacle function to obtain the superimposed result.

[0021] Furthermore, the composite controller directly drives the control voltage based on the superposition result.

[0022] Furthermore, the output of the microsatellite attitude deep coupling model is simultaneously fed into a dual-disturbance observer and a nonlinear state-dependent barrier function.

[0023] Furthermore, the composite controller makes the nonlinear state-dependent barrier function bounded.

[0024] Furthermore, the control voltage drives the reaction wheel to move, thereby adjusting the actual attitude and angular velocity of the micro-nano satellite.

[0025] Beneficial effects:

[0026] This invention achieves high-precision attitude control while ensuring the safety of critical physical constraints of the spacecraft. By introducing a nonlinear state-dependent barrier function, hard constraints such as the celestial body's angular velocity and the reaction wheel armature current are embedded in the composite controller, effectively preventing actuator overcurrent or platform overspeed, and avoiding system instability or hardware damage. Combined with a dual-disturbance observer based on electromechanical energy topology separation, accurate estimation and channel matching compensation of wheel axle friction and back EMF are performed, which not only improves anti-interference capability but also ensures that the stringent resource and safety constraints of microsatellites are strictly met even under strong disturbances. This invention achieves an organic unity of safety, robustness, and control precision, making it more suitable for practical aerospace missions with limited resources and sensitive operational boundaries. Attached Figure Description

[0027] Figure 1 This is a flowchart of a multi-constraint fine control method for micro / nano satellites based on actuator dynamics according to the present invention;

[0028] Figure 2 This is a control block diagram of a micro / nano satellite multi-constraint fine control method based on actuator dynamics according to the present invention;

[0029] Figure 3 This is a schematic diagram illustrating the variation curve of the satellite's three-axis attitude tracking error during the simulation process;

[0030] Figure 4 This is a schematic diagram showing the change curve of the control torque transmitted from the reaction wheel actuator to the satellite through the reaction force during the simulation process;

[0031] Figure 5 This is a schematic diagram of the change curve of the armature current of the reaction wheel during the simulation process;

[0032] Figure 6 This is a schematic diagram showing the change curve of the satellite's angular velocity during the simulation process;

[0033] Figure 7 This is a schematic diagram showing the change curve of satellite angular velocity during simulation using a traditional PI controller under the same system parameters. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0035] like Figure 1 As shown in the figure, a multi-constraint fine control method for micro / nano satellites based on actuator dynamics according to an embodiment of the present invention includes the following steps:

[0036] The first step is to establish a deep coupling model of micro- and nano-satellite attitude that includes the dynamic characteristics of the reaction wheel. This includes: considering the electromechanical characteristics of the reaction wheel, establishing a deep coupling model of micro- and nano-satellite attitude that includes the dynamic characteristics of the reaction wheel, and separating the wheel axle friction interference and back EMF interference in the reaction wheel device according to the influencing topology.

[0037] The second step involves designing a dual-interference observer to estimate the friction and back potential interference of the reaction wheel axle. This includes: based on the micro / nano satellite attitude deep coupling model established in the first step, designing a dual-interference observer to separately measure the friction interference of the separated wheel axle (i.e., the back potential interference). Figure 1 The reaction wheel friction and back EMF interference in the process are estimated.

[0038] The third step is to design nonlinear state-dependent obstacle functions to transform the constraint states into tracking control variables. This includes designing nonlinear state-dependent obstacle functions to transform the constraint states into tracking control variables for the physical constraints of the celestial rotation speed and reaction wheel current.

[0039] The fourth step involves constructing a composite controller for fine compensation of composite disturbances. This includes: combining a dual-disturbance observer with a nonlinear state-dependent barrier function to construct a composite controller that compensates for wheel and axle friction disturbances and back EMF disturbances (both referring to...) in the reaction wheel device. Figure 1 Fine compensation is performed on the composite interference in the data.

[0040] This invention can overcome the constraints of satellite rotation speed and reaction wheel current in the attitude control of micro and nano satellites, and at the same time compensate for the interference of reaction wheel devices, and has the characteristics of high reliability and high accuracy.

[0041] Specifically, the first step includes:

[0042] Step 1.1: The attitude kinematics and dynamics of micro / nano satellites are described as follows:

[0043] ;

[0044] in, Indicates the roll angle of microsatellites and nanosatellites. Pitch angle and yaw angle The attitude angle vector formed by them This is a transpose operation; for The first derivative; Represents the three-axis angular velocity of micro / nano satellites , , The angular velocity vector formed; for The first derivative, express skew-symmetric matrix; Represents the transition matrix The inverse matrix and the transition matrix Rotation in the order of yaw-pitch-roll can be represented as:

[0045] ;

[0046] The orbital angular velocity vector. This represents the orbital angular rate of the microsatellite's orbit. and These are the moments of inertia of the microsatellite and the moments of inertia of the reaction wheel assembly, respectively. This represents the installation matrix of the reaction wheel assembly; The rotational speed vector of the reaction wheel assembly; express The first derivative.

[0047] Step 1.2: In order to effectively separate the compound interference in the reaction wheel, according to Euler's law, we can obtain:

[0048] ;

[0049] in, ,express The left inverse matrix, This is the inverse operation of a matrix; Indicates the electromagnetic torque coefficient; and These are the armature circuit current vector and the friction torque disturbance vector of the reaction wheel assembly, respectively. This refers to the number of reaction wheels. Indicates the first The armature circuit current of each reaction wheel (hereinafter referred to as armature current).

[0050] Step 1.3: To isolate the effect of back EMF interference on armature current, for the bottom armature circuit of the reaction wheel, Kirchhoff's voltage law can be used to obtain:

[0051] ;

[0052] in, The armature circuit voltage vector of the reaction wheel assembly; and These represent the inductance matrix and the resistance matrix, respectively. This is back EMF interference.

[0053] Step 1.4: Combining steps 1.1-1.3, establish the following micro / nano satellite attitude deep coupling model based on reaction wheel dynamics:

[0054] ;

[0055] Among them, unmatched interference Matching interference .

[0056] Specifically, the second step includes:

[0057] For mismatched interference Matching interference The following dual-interference observer is designed to estimate them:

[0058] ;

[0059] in, and These represent the effects of unmatched interference. The estimated value and matching interference The estimated value; and As intermediate variables, in this invention, all parameters are superscripted with "". "Both represent the first derivative of the corresponding variable; and This represents the gain of the dual observers.

[0060] Specifically, the third step includes:

[0061] Considering the rotational speed of micro and nano satellites During maneuvering, it is constrained by the celestial body's mechanical mechanisms, meaning there exists a range of variation that makes... ,in, and These are the lower and upper bounds of the rotational speed of microsatellites and nanosatellites, respectively. It is a sequence of numbers. , , These represent the angular velocities of the satellite rotating around its roll axis, pitch axis, and yaw axis, respectively.

[0062] Similarly, to avoid safety issues such as mechanical damage to the reaction wheel due to excessive current, it is necessary to control the armature current. Limitation, i.e., the existence of a safe operating domain that makes ,in, and These are the maximum permissible lower bound and the maximum permissible upper bound for the change in armature current of the reaction wheel, respectively. This is the index value of the reaction wheel.

[0063] To ensure that the rotational speed of the microsatellite and the current of the reaction wheel are within physical constraints, the following nonlinear state-dependent barrier function is designed to convert the rotational speed and current states into system tracking variables:

[0064] ;

[0065] The nonlinear state-dependent barrier function designed above With nonlinear state-dependent barrier function It can be verified that:

[0066] It is about A monotonically increasing function, and when They approach each other and hour, They tend towards negative infinity and positive infinity respectively, while when When it is bounded, Satisfy constraints ; It is about A monotonically increasing function, and when They approach each other and hour, They tend towards negative infinity and positive infinity respectively, while when When it is bounded, Satisfy constraints Therefore, by designing a controller, and Bounded, thus ensuring and The constraints are met.

[0067] Specifically, the fourth step includes:

[0068] Define the desired attitude of the micro / nano satellite as: Its first derivative is The composite controller is constructed as follows:

[0069] ;

[0070] in, The intermediate matrix represents the armature circuit voltage vector of the reaction wheel assembly. It is a diagonal matrix. Represents a diagonal matrix consisting of diagonal elements; intermediate matrix A diagonal matrix; the middle matrix It is a diagonal matrix; To control the gain; and For intermediate quantities, they are represented as follows: , ;

[0071] in, , It is a nonlinear state-dependent barrier function vector; and The following are the state variables of a first-order low-pass filter: , ;

[0072] in, and The time constant to be designed; and They are and First derivative; intermediate matrix Represented as ; , These are all stabilization functions, specifically represented as follows:

[0073] ;

[0074] ;

[0075] in, , For design parameters; This refers to the tracking error of microsatellites and nanosatellites.

[0076] The method of this invention for attitude control of micro / nano satellites can guarantee the safety domain of the control system and the convergence performance of satellite attitude errors under physical constraints such as satellite rotation speed and reaction wheel current, as well as combined disturbances such as reaction wheel errors. Compared with existing constraint control and anti-interference control technologies, this invention has coordinated optimization performance under multiple physical constraints and combined disturbances, meeting the safety and accuracy requirements of micro / nano satellite attitude control systems.

[0077] like Figure 2As shown, when the actual attitude of a microsatellite deviates from the signal of the mission target and attitude adjustment is required, a dual-interference observer (i.e., ...) is first designed by combining the microsatellite's attitude kinematics and dynamics with the dynamics of the actuator's reaction wheel (including wheel and axle friction). Figure 2 Two interference observers are used to estimate and separate interference in the system online. Simultaneously, a nonlinear state-dependent barrier function is designed to limit the amplitude of angular velocity and current state, addressing the rotational speed constraints of the microsatellite, the current constraints of the actuators, and back EMF interference, ensuring the safe operation of the system. A composite controller is constructed using the dual interference observers and the nonlinear state-dependent function to generate control voltage commands, which drive the reaction wheel of the actuator to adjust the actual attitude and angular velocity of the microsatellite, guiding it towards the mission objective.

[0078] Example:

[0079] To verify the effectiveness of the control system described in this invention, and to further explain the collaborative working mechanism of the proposed deep coupling modeling method, dual disturbance observer, and nonlinear state-dependent obstacle function, a simulation experiment is conducted through a typical attitude maneuvering mission scenario, and key performance indicators are analyzed.

[0080] The initial state of the microsatellite is selected as follows: , The desired tracking signal is The satellite's moment of inertia matrix is ​​set to... The orbital angular velocity is The reaction flywheel actuator consists of... It consists of several flywheels, and its initial state is set to... t represents time, and the flywheel assembly moment of inertia matrix is ​​set to... Its installation matrix is ​​set as follows:

[0081] .

[0082] Electromagnetic torque coefficient set to The inductance coefficient matrix is ​​set as follows: The resistance coefficient matrix is ​​set as follows: .

[0083] Back EMF interference settings are related to flywheel angle and flywheel speed Nonlinear functions: In the formula, the back electromotive force coefficient is set to ,

[0084] It is about The periodic function is set as follows:

[0085] ;

[0086] in, , is the index value of the reaction wheel.

[0087] Friction torque interference (in Nm) is set as follows:

[0088] .

[0089] Constraints on armature current Constraints on satellite angular velocity The design parameters involved in the method are as follows: , , , , , The simulation results are as follows: Figures 3 to 7 As shown.

[0090] Figure 3 The curves showing the variation of satellite three-axis attitude tracking error are displayed. Figure 3 middle, , , These represent roll angle error, pitch angle error, and yaw angle error, respectively. Figure 3 As can be seen, the attitude error gradually converges and enters the steady-state region within approximately 10 seconds. During the steady-state phase from 20 to 40 seconds, the three-axis attitude error remains consistently within a certain range. The result within the range indicates that the designed controller, under the synergistic effect of the dual disturbance observers, can effectively compensate for the complex disturbances in the system and achieve high-precision attitude tracking control.

[0091] Figure 4 The control torque transmitted to the satellite by the reaction wheel actuator through the reaction force during the simulation is given. , , , These represent the control torque components along the roll axis, pitch axis, and yaw axis, respectively. It can be seen that throughout the entire control process, the control torque inputs on the satellite's three principal axes remain constant. Within the specified range, it meets the performance requirements of conventional micro-nano satellite reaction wheel actuators, indicating that the control strategy has good executability under the constraints.

[0092] Figure 5 The armature current variation curve during the simulation is given. Representative applied in the Armature current on each motor ( );from Figure 5 As can be seen, the armature current remains within the preset safe current limits throughout the entire control process. Inside. Figure 6 The curves showing the change in the satellite's angular velocity during the simulation are presented. , , These represent the angular velocities of the satellite rotating around its roll axis, pitch axis, and yaw axis, respectively; from Figure 6 As can be seen, the satellite's angular velocity remained within the preset safe limits throughout the entire control process. Inside. In contrast, Figure 7 The figure shows the satellite angular velocity variation curves during simulation using a traditional PI controller with the same system parameters. The legend is as follows: Figure 6 Consistent with the observations, it is evident that during the rapid dynamic phase from 0 to 5 seconds, the satellite's pitch axis angular velocity exceeded the safety upper limit within a specific timeframe. This demonstrates that the designed controller, under the synergistic effect of a nonlinear state-dependent barrier function, can complete tracking commands while maintaining the armature current and satellite angular velocity state variables within given constraints. Compared to traditional methods, it effectively prevents electrical circuit damage or mechanical structure damage caused by excessive current or excessive rotational speed, ensuring the safety of micro / nano satellite control.

[0093] In summary, this invention is applicable to micro / nano satellites using reaction wheels as attitude adjustment actuators, and is particularly suitable for mission scenarios requiring high control precision and where there are performance constraints between the actuator and the satellite. The results of the embodiments verify the effectiveness of this invention in achieving high-precision attitude control under combined interference conditions, while ensuring the safety of the control process, demonstrating good practicality and engineering application value. Content not described in detail in this specification belongs to the prior art known to those skilled in the art.

Claims

1. A method for multi-constraint fine control of micro / nano satellites based on actuator dynamics, characterized in that, Includes the following steps: The first step is to consider the electromechanical characteristics of the reaction wheel and establish a deep coupling model of micro-nano satellite attitude that includes the dynamic characteristics of the reaction wheel. The wheel axle friction interference and back EMF interference of the reaction wheel are separated according to the influence topology. When establishing the deep coupling model of micro-nano satellite attitude, the wheel axle friction interference and back EMF interference are separated according to their action nodes on the electromechanical energy transfer path, laying the topological foundation for the subsequent independent estimation by the dual interference observers. The second step involves designing a dual-interference observer based on the micro-nano satellite attitude deep coupling model established in the first step, to estimate the separated wheel axle friction interference and back EMF interference respectively; and, based on the separated action nodes, generating the estimated values ​​of wheel axle friction interference and back EMF interference in parallel within the same sampling period. The third step is to design a nonlinear state-dependent obstacle function to convert the constraint state into a tracking control variable, taking into account the physical constraints of the star's rotation speed and the reaction wheel current. When constructing the nonlinear state-dependent barrier function, the real-time measured values ​​of the planetary rotation speed and the reaction wheel current are used as independent variables, so that the output of the nonlinear state-dependent barrier function is coupled with the desired tracking error, thereby embedding the physical constraints of the planetary rotation speed and the reaction wheel current into the dynamics of the tracking error; the nonlinear state-dependent barrier function generates a monotonically increasing gain near the boundary where the output tends to infinity, ensuring that the planetary rotation speed and the reaction wheel current are always within the safe range. The fourth step involves constructing a composite controller by combining a dual-disturbance observer with a nonlinear state-dependent barrier function to perform fine compensation for wheel and axle friction disturbances and back EMF disturbances in the reaction wheel. In the composite controller, the wheel and axle friction estimates and back EMF estimates output by the dual-disturbance observer are first mapped to the control torque and control voltage, respectively, and then superimposed with the correction results generated by the nonlinear state-dependent barrier function to obtain the superimposed result.

2. The method for multi-constraint fine control of micro / nano satellites based on actuator dynamics as described in claim 1, characterized in that, The composite controller directly drives the control voltage based on the superposition result.

3. The method for multi-constraint fine control of micro / nano satellites based on actuator dynamics as described in claim 1, characterized in that, The output of the microsatellite attitude deep coupling model is simultaneously fed into a dual-disturbance observer and a nonlinear state-dependent barrier function.

4. The method for multi-constraint fine control of micro / nano satellites based on actuator dynamics as described in claim 1, characterized in that, The composite controller makes the nonlinear state-dependent barrier function bounded.

5. The method for multi-constraint fine control of micro / nano satellites based on actuator dynamics as described in claim 2, characterized in that, The control voltage drives the reaction wheel to move, thereby adjusting the actual attitude and angular velocity of the microsatellite.

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