Large-scale satellite robust attitude stabilization method for rotation imbalance disturbance

Abstract

The invention belongs to the technical field of satellite attitude control, and relates to a large-scale satellite robust attitude stabilization method for rotation imbalance disturbance, which comprises the following steps: constructing a rotation imbalance and rigid-flexible coupling dynamic model of a large-scale satellite; a sliding mode observer is adopted to estimate periodic and pulsed unbalanced disturbance; a satellite wide-frequency-band attitude is determined through fusion of a magnetofluid angular velocity sensor and a traditional attitude sensor; an integral sliding mode controller is adopted to suppress unbalanced disturbance and realize global attitude stability of the large satellite; according to the method, high-precision estimation of periodic and pulsed unbalanced moments is realized, and the attitude determination capability under a wide frequency band condition is remarkably improved; compared with a traditional method, the precision and stability of attitude control are obviously improved, and the performance is obviously improved.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a robust attitude stabilization method for large satellites subjected to rotational imbalance disturbances. Background Technology

[0002] New-generation large meteorological satellites, serving as crucial platforms for acquiring global meteorological information and Earth's environmental parameters, typically carry high-speed rotating scanning radiometers, large antennas, and attitude control actuators, imposing stringent sub-arcsecond requirements on attitude stability accuracy. During long-term operation, these rotating components generate significant unbalanced disturbances due to manufacturing and assembly errors, uneven mass distribution, and other factors. These disturbances usually manifest as periodic and impulsive torques, which, acting on the satellite platform, cause attitude deviations and excite flexible vibrations through structural coupling, directly affecting payload imaging quality and measurement accuracy. Existing attitude control methods largely rely on classical feedforward compensation strategies, which struggle to maintain the desired attitude stability, easily leading to accumulated pointing errors and degraded data quality. This is particularly pronounced in large-scale satellites with large moments of inertia and complex flexible structures, making the suppression of unbalanced disturbances even more critical. To achieve high-precision attitude control, broadband attitude determination techniques are needed to simultaneously estimate overall attitude motion and high-frequency micro-disturbances. However, existing methods primarily target low-frequency disturbances, failing to cover broadband characteristics and resulting in decreased pointing accuracy. Therefore, there is an urgent need for a robust attitude stabilization method for large meteorological satellites under rotational unbalanced disturbances, which can achieve high-precision attitude determination and high-stability attitude control under complex disturbance conditions, while taking into account the engineering feasibility and long-term on-orbit stability of the controller. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention proposes a robust attitude stabilization method for large satellites to effectively suppress rotational imbalance disturbances and achieve high-precision, high-stability attitude control. The method involves constructing a dynamic model of rotational imbalance and rigid-flexible coupling for a large meteorological satellite; employing a sliding mode observer to accurately estimate multiple types of imbalance disturbances; utilizing magnetohydrodynamic angular velocity sensor fusion to determine the satellite's attitude over a wide frequency band; and employing an integral sliding mode controller to suppress imbalance disturbances and achieve global attitude stabilization of the satellite.

[0004] A robust attitude stabilization method for large satellites against rotational imbalance disturbances includes the following steps: Step 1: Under the condition of unbalanced disturbances of large satellites, establish a rigid-flexible coupled dynamic model of large satellites based on the angular momentum theorem. By decomposing the variables in the rigid-flexible coupled dynamic model: the angular momentum of the rotating load and the moment of inertia of the satellite, and based on the actual working conditions of large satellites, considering the large satellite has multiple rotating loads and environmental disturbances as well as the high-frequency micro-disturbances of the platform, establish the overall dynamic model of large satellite-platform. Step 2: Design a sliding mode observer that can asymptotically converge the torque error to the equilibrium point, and estimate the periodic and impulsive unbalanced disturbance torque; Step 3: Based on the traditional attitude sensor, a magnetohydrodynamic angular velocity sensor is introduced to construct a measurement model covering the high-frequency and low-frequency bands. The high-frequency and low-frequency measurement models are fused by adaptive Kalman filtering to form a fused measurement model for determining the wideband attitude of large satellites. Step 4: Design a sliding mode surface using a sliding mode observer and the large satellite control equations constructed based on the relationship between three-axis attitude angles and angular velocities. Combine this with the overall dynamics model to design an integral sliding mode controller to improve the steady-state performance of the attitude determined by the fusion measurement model.

[0005] Furthermore, the rigid-flexible coupling dynamic model is as follows: ; ; ; In the formula: , These represent the coordinates of the load's center of mass and the system's center of mass in the inertial reference frame, respectively. This indicates the entire satellite relative to the system's center of mass. angular momentum; Indicates the satellite's angular velocity; Indicates the mass of the rotating load; For the system centroid Pointing to the center of mass of the load ; The platform rotation speed; This indicates the rotational load relative to the load's center of mass. angular momentum; Represents the rigid-flexible coupling matrix of the satellite system; For satellite mode vectors; Represents the net external torque acting on the satellite system; skew-symmetric matrix In particular, For the entire satellite relative to the system's center of mass Moment of inertia: ; In the formula: This indicates the satellite platform relative to the platform's center of mass. Moment of inertia; Represents the system's centroid Pointing to the platform's center of gravity ; Indicates the quality of the satellite platform; It is the identity matrix. This is the transpose operator.

[0006] Furthermore, due to the presence of rotational imbalance disturbances, the moment of inertia... and It is variable and is decomposed into two parts: a constant term *con* and a non-constant term. Therefore, the third equation of the rigid-flexible coupling dynamic model is rewritten as: ; , ; In the formula: Represents the bounded unbalanced torque generated by rotating loads: , express .

[0007] Furthermore, the overall dynamic model is as follows:

[0008]

[0009] ; In the formula: subscript Indicates the number of the rotating load. ; Indicates load The constant of inertia; and Acting on the satellite platform and payload respectively Control torque; Indicates load The resulting unbalanced torque scalar; and These are the structural damping matrix and the frequency matrix, respectively. It is the environmental disturbance torque; It is a small torque disturbance term.

[0010] Furthermore, the design process of the sliding mode observer includes the following steps: S51 will decompose the unbalanced moment scalar along each coordinate axis in the large satellite body coordinate system. and its first derivative Defined as: , ; in: and All are constants; Will The estimated value is set as The construction moment estimation error is: ; Given real numbers , , , , For any unbalanced torque scalar The sliding mode observer is designed as follows: ; In the formula: Represents a symbolic function. ; When using a sliding mode observer to estimate unbalanced moments, it is necessary to prove the error in the moment measurement. Regarding the asymptotic convergence of the equilibrium point: torque error The derivative is expressed as: ; Based on Lyapunov stability theory, select appropriate Lyapunov candidate functions. And differentiate it: ; ; By defining the inequality relations Derivation The final form is: ; Therefore, and It holds true if and only if hour, and Therefore, the sliding mode observer can guarantee torque error. It asymptotically converges to the equilibrium point, thereby accurately estimating periodic or impulsive unbalanced torques.

[0011] Furthermore, the construction process of the fusion measurement model includes the following steps: S61 gives the transfer function of a traditional attitude sensor: ; In the formula: Represents a complex variable; and These represent the noise suppression factor and the power amplification factor, respectively. A magnetohydrodynamic (MHD) angular velocity sensor is introduced, which is excited by the angular velocity signal. The conductive fluid in the annular channel cuts the magnetic field, thereby generating a velocity difference and creating a potential difference between the upper and lower electrodes. The transfer function of the MHD angular velocity sensor is expressed as: ; In the formula: Indicates induced electromotive force; Radial magnetic flux density; Indicates the effective width of the current path; is the root mean square value of the sensor substrate radius; is the viscosity coefficient of the magnetohydrodynamic fluid; The height of the current loop; Let Hartmann number be an expression for the number of Hartmann numbers, where: and These are the density and resistivity of the magnetic fluid, respectively. For high-precision angular velocity measurement, the magnetohydrodynamic angular velocity sensor is represented by a fourth-order complex frequency domain model: ; Where: coefficient and All are constants, determined experimentally; Magnetohydrodynamic angular velocity sensors typically perform well in the high-frequency band, i.e., for micro-angular perturbations on platforms, while in the low-frequency band, i.e., for satellite attitude motion, they work in conjunction with gyroscopes and star sensors. To cover the entire measurement bandwidth, a combined measurement model is proposed, which takes the following form: ; Therefore, the fusion measurement model of the magnetohydrodynamic angular velocity sensor and the traditional attitude sensor is expressed as: ; In the formula: Indicates the actual posture; These represent the state variables of the low-frequency and high-frequency sensing systems, respectively. This indicates the corresponding measurement output; and These represent system noise and measurement noise, respectively; other key coefficient matrices can be derived from the transfer functions of traditional attitude sensors and magnetohydrodynamic angular velocity sensors: , , ; , , ; Adaptive Kalman filtering is used to fuse low-frequency and high-frequency measurement systems; The entire state space is represented as: ; , , , , , ; Status Update: ; Measurement Update: ; In the formula: Represents a discrete state transition matrix; and These are the covariance matrices of the sensing system and the measurement noise, respectively. This represents the expected value of the measured noise. Let be the covariance matrix of the state variables; These represent the Kalman coefficients. Given an initial form for these matrices, the process can be iterated over time to ultimately determine the wideband attitude.

[0012] Furthermore, the design process of the integral sliding mode controller includes the following steps: S71. Constructing the control equations for large satellites: First, given The three-axis attitude angles for ZYX rotation include: roll angle. Pitch angle and yaw angle Give With angular velocity The relationship is as follows: , , ; Define new variables and Then the state space representation of the control system is: ; ; In the formula: This represents the control system input, and its expression is a common construction form for double-limit homogeneous systems. and For nonlinear homogeneous terms; parameters , , ; Given ,inequality If it is established, then and satisfy: ; S72. Based on homogeneity theory, prove the stability of the control system: If a vector field is homogeneous in both the 0 limit and the ∞ limit, then it achieves double-limit homogeneity. The vector field of this control system is It can be expressed in bihomogeneous form as: ; ; therefore, and yes An approximate vector field; in order to simultaneously achieve and To ensure homogeneity, the corresponding weight vector is: ; ; According to homogeneity theory, we can take the homogeneity degree respectively. and It can guarantee the vector field Achieving bihomogeneity; to prove the stability of the global system, selecting appropriate Lyapunov candidate functions. And differentiate it: ; ; Therefore, the function Continuously differentiable and radially unbounded; It holds true if and only if hour, Established; Decomposition The only solution is This proves the asymptotic convergence of the state variables; Give the Lyapunov candidate functions and their derivatives for the zero limit and the ∞ limit respectively: ; ; The control system exhibits asymptotic stability at both limits, thus proving the stability of the global system. S73. Design an integral sliding mode controller: By using a sliding mode observer combined with the governing equations in S71, the sliding surface is designed as follows: ; set up That is, when the system state variables reach the sliding surface, we get: , ; Therefore, it can be seen that the system state variables can converge; the attitude error is defined as... , If we treat it as a controlled variable, then the sliding surface can be rewritten as: ; ; By combining the expression for the sliding surface with the overall dynamic model, the integral sliding mode control law is designed as follows: ; In the formula: , , , Control Law Equivalent to the dynamic model ; It includes unbalanced moments, structural vibrations, and environmental disturbances. The sliding mode convergence law is designed as follows: ; To prove that the sliding surface is reachable under this reaching law, a suitable Lyapunov candidate function is selected. And differentiate it: ; ; Among them, inequalities and It holds true if and only if hour, and This means that the system state variables can reach the sliding surface; in summary, the stability and reachability of sliding mode control have been proven.

[0013] The beneficial effects of this invention are: This invention considers practical engineering applications and systematically constructs a dynamic model of the rotational imbalance of a large meteorological satellite. It accurately describes the rotational imbalance characteristics caused by payload assembly errors and uneven mass distribution, providing a solid theoretical foundation for subsequent control law design. A composite robust control strategy integrating imbalance observation, attitude determination, and controller design is proposed, ensuring high-precision estimation of imbalance disturbances and achieving high-precision attitude estimation over a wide frequency range. Simultaneously, it achieves an organic unity between attitude control and robustness enhancement. Based on this, the steady-state accuracy and dynamic response performance of the target satellite's three-axis attitude stability are effectively improved, and the robustness of the control system to imbalance disturbances, parameter perturbations, and external environmental interference is significantly enhanced. Overall, it achieves an imbalance torque estimation accuracy of 99.0% and a wide-band attitude determination accuracy of 6.24 × 10⁻⁶. -7 The accuracy of the deg method is improved to 49.9% compared to traditional methods; the attitude control accuracy and stability are 9.61×10⁻⁶ respectively. -7 deg and 1.16×10 -7 The performance improvements are 17.9% and 20.6% respectively, with deg / s. This invention provides a solution with both theoretical value and engineering application prospects for the long-term stable operation of large meteorological satellites in complex on-orbit environments. Attached Figure Description

[0014] Figure 1 This is a framework diagram of the large satellite attitude stabilization method. Figure 2 This is a diagram showing the relationship between the rigid-flexible coupled dynamic model and the coordinate system; Figure 3 The following are the estimation results of the periodic unbalanced torque: (a) is the estimation result of the periodic unbalanced torque along the X-axis, (b) is the estimation result of the periodic unbalanced torque along the Y-axis, (c) is the estimation result of the periodic unbalanced torque along the Z-axis, and (d) is the average estimation error curve of the three-axis periodic unbalanced torque. Figure 4 The graphs show the estimation effect of the impulsive unbalanced torque; where: (a) is the estimation effect of the impulsive unbalanced torque, and (b) is the estimation error curve of the impulsive unbalanced torque. Figure 5 The attitude determination effect curves are shown below; where: (a) and (c) on the left are attitude determination effect curves using a magnetohydrodynamic angular velocity sensor, (a) is the three-axis attitude determination effect curve, and (c) is the attitude determination error curve; (b) and (d) on the right are attitude determination effect curves without using a magnetohydrodynamic angular velocity sensor. Figure 6The curves show the effect of rotating load control; where: (a) is the curve of angular velocity changing with time on the X-axis, and (b) is the curve of torque control changing with time on the X-axis; Figure 7 The graphs show the satellite attitude control performance. On the left, (a) and (c) show the satellite attitude control performance based on an integral sliding mode controller. (a) shows the roll, pitch, and yaw angles as attitude angles change over time, and (c) shows the angular velocity as an axis on the XYZ axis as an axis of time. On the right, (b) and (d) show the satellite attitude control performance based on a traditional controller. (b) shows the roll, pitch, and yaw angles as attitude angles change over time, and (d) shows the angular velocity as an axis on the XYZ axis as an axis of time. Detailed Implementation

[0015] Example 1, as Figure 1 and Figure 2 As shown, a method for attitude stabilization of large meteorological satellites under rotational imbalance disturbances includes the following steps: Step 1: Under the condition of unbalanced disturbances of large meteorological satellites, establish a rigid-flexible coupled dynamic model of the target satellite based on the angular momentum theorem. By decomposing the angular momentum of the rotating load and the rotational inertia of the satellite, and based on the actual working conditions of large meteorological satellites, considering the large meteorological satellites have multiple rotating loads and environmental disturbances as well as the high-frequency micro-disturbances of the platform, establish an overall dynamic model of the large meteorological satellite-platform. Step 2: Design a sliding mode observer that can asymptotically converge the torque error to the equilibrium point, and estimate the periodic and impulsive unbalanced disturbance torque; Step 3: Based on the traditional attitude sensor, a magnetohydrodynamic angular velocity sensor is introduced to construct a measurement model covering both high and low frequency bands. The high and low frequency band measurement models are then fused using an adaptive Kalman filter to form a fusion measurement model for determining the broadband attitude of large meteorological satellites. Step 4: Based on the sliding mode observer designed in Step 2, and combined with the control equations of the large meteorological satellite constructed through the relationship between the three-axis attitude angle and angular velocity, design the sliding surface. Then, combined with the overall dynamic model established in Step 1, design the integral sliding mode controller to improve the steady-state performance of attitude control.

[0016] In step one, a dynamic model of rotational imbalance and rigid-flexible coupling for a large meteorological satellite is constructed: ; ; ; In the formula: This indicates the entire satellite relative to the system's center of mass. angular momentum; Indicates the satellite's angular velocity; Indicates the mass of the rotating load; For the system centroid Pointing to the center of mass of the load ; The platform rotation speed; This indicates the rotational load relative to the load's center of mass. Moment of inertia; Represents the rigid-flexible coupling matrix of the satellite system; For satellite mode vectors; Represents the net external torque acting on the satellite system; skew-symmetric matrix In particular, For the entire satellite relative to the system's center of mass Moment of inertia:

[0017] In the formula: This indicates the satellite platform relative to the platform's center of mass. Moment of inertia; Represents the system's centroid Pointing to the platform's center of gravity ; Indicates the quality of the satellite platform; It is an identity matrix.

[0018] Due to rotational imbalance disturbance, the moment of inertia and It is variable and is decomposed into two parts: a constant term "con" and a non-constant term "con". Therefore, the third equation of the coupled dynamics model can be further rewritten as:

[0019] In the formula: Represents the bounded unbalanced torque generated by rotating loads: .

[0020] To consider the specific operating conditions of the target satellite, multiple rotating loads, environmental disturbances, and high-frequency micro-disturbances generated by the platform need to be taken into account, resulting in the following overall satellite dynamics model:

[0021]

[0022]

[0023] In the formula: subscript Indicates the number of the rotating load. The term representing the moment of inertia constant of the load p; and These are the control torques acting on the satellite platform and the payload p, respectively. This represents the unbalanced torque generated by the load p; and These are the structural damping matrix and the stiffness matrix, respectively. It is the environmental disturbance torque; It is a small torque disturbance term.

[0024] In step two, a sliding mode observer is used to achieve accurate estimation of various types of unbalanced disturbances. An observer based on error convergence is designed to estimate the unbalanced torque. The unbalanced torque scalar along each rotation axis direction. Defined as:

[0025] in: and All are constants. The estimated value is set as The estimation error is:

[0026] Given real numbers , , , , For any unbalanced torque scalar The sliding mode observer can be designed as follows:

[0027] In the formula: Represents a symbolic function. .

[0028] If the above sliding mode observer is used to estimate the unbalanced torque, the error needs to be proven. Asymptotic convergence at the equilibrium point. The error... The derivative is expressed as:

[0029] Based on Lyapunov stability theory, select appropriate Lyapunov candidate functions. And differentiate it:

[0030]

[0031] Based on the inequality relationships in the above assumptions It can be deduced The final form is:

[0032] Therefore, and It holds true if and only if hour, and Therefore, the sliding mode observer can guarantee the error. It asymptotically converges to the equilibrium point, thereby accurately estimating various forms of unbalanced torque.

[0033] In step three, satellite broadband attitude determination is achieved using magnetohydrodynamic angular velocity sensor fusion. First, the transfer function of a traditional attitude sensor is given:

[0034] In the formula: Represents a complex variable; and These represent the noise suppression factor and the power amplification factor, respectively. A magnetohydrodynamic (MHD) angular velocity sensor is introduced, which is excited by an angular velocity signal. The conductive fluid in the annular channel cuts the magnetic field, thereby generating a velocity difference and creating a potential difference between the upper and lower electrodes. The transfer function of the MHD angular velocity sensor is expressed as:

[0035] In the formula: Indicates induced electromotive force; Radial magnetic flux density; Indicates the effective width of the current path; is the root mean square value of the sensor substrate radius; is the viscosity coefficient of the magnetohydrodynamic fluid; The height of the current loop; Denotes the Hartmann number, where and These represent the density and resistivity of the magnetofluid, respectively.

[0036] For high-precision angular velocity measurement, magnetohydrodynamic angular velocity sensors can be represented by a fourth-order complex frequency domain model:

[0037] Where: coefficient and All of these are constants and can be determined experimentally.

[0038] Magnetohydrodynamic angular velocity sensors typically perform well in the high-frequency range (i.e., platform micro-angular perturbations), while in the low-frequency range (satellite attitude motion), they work in conjunction with gyroscopes and star sensors. To cover the entire measurement bandwidth, a combined measurement method is proposed, which takes the following form:

[0039] Therefore, the fusion measurement model of the magnetohydrodynamic angular velocity sensor and the traditional attitude sensor can be further expressed as:

[0040] In the formula: Indicates the actual posture; These represent the state variables of the low-frequency and high-frequency sensing systems, respectively. This indicates the corresponding measurement output; and These represent system noise and measurement noise, respectively; other key coefficient matrices are as follows: , ,

[0041] , ,

[0042] Furthermore, an adaptive Kalman filter is employed to fuse the low-frequency and high-frequency measurement systems. The entire state space can be represented as:

[0043] , , , , ,

[0044] Status Update:

[0045] Measurement Update:

[0046] In the formula: Represents a discrete state transition matrix; and These are the covariance matrices of the sensing system and the measurement noise, respectively. This represents the mean of the measured noise. Let be the covariance matrix of the state variables; given the initial form of these matrices, iterative processing can be performed over time to ultimately complete the wideband attitude determination.

[0047] In step four, an integral sliding mode controller is used to suppress unbalanced disturbances and achieve global attitude stability of the satellite. The control equations for the target satellite are constructed. First, given... The Euler angles for the three-axis attitude of the ZYX rotation are as follows: roll angle Pitch angle and yaw angle Give With angular velocity The relationship is as follows: , ,

[0048] Furthermore, define new variables. and Then the state space representation of the control system is:

[0049]

[0050] In the formula: This represents the control system input, and its expression is a common construction form for double-limit homogeneous systems. and For nonlinear homogeneous terms; parameters , , .

[0051] Given ,inequality If it is established, then and satisfy:

[0052] Based on homogeneity theory, prove the stability of the above control system. If the vector field is homogeneous in both the 0 limit and the ∞ limit, then it achieves double-limit homogeneity.

[0053] The vector field of this control system is It can be expressed in bihomogeneous form as:

[0054]

[0055] therefore, and yes An approximate vector field. In order to simultaneously achieve... and To ensure homogeneity, the corresponding weight vector is:

[0056]

[0057] According to homogeneity theory, we can take the homogeneity degree respectively. and It can guarantee the vector field Achieving bihomogeneity. To prove the global system stability, suitable Lyapunov candidate functions are selected. And differentiate it:

[0058]

[0059] Therefore, the function Continuously differentiable and radially unbounded; It holds true if and only if hour, Established; Decomposition The only solution is This proves the asymptotic convergence of the state variables.

[0060] Furthermore, the Lyapunov candidate functions and their derivatives for the 0 limit and ∞ limit cases are given respectively:

[0061]

[0062] Clearly, the control system exhibits asymptotic stability at both limits, thus proving the stability of the global system.

[0063] Based on the state-space equations, an integral sliding mode controller is designed as follows to improve the steady-state performance of attitude control:

[0064] set up (That is, the system state variables reach the sliding surface), from which we can obtain: ,

[0065] Therefore, it can be seen that the system state variables can converge. The attitude error is defined as... , If we treat it as a controlled variable, then the sliding surface can be rewritten as:

[0066]

[0067] Combining the above equation with the satellite coupled dynamics model in step one, the integral sliding mode control law can be designed as follows:

[0068] In the formula: , , , Control Law Equivalent to the dynamic model ; It includes unbalanced moments, structural vibrations, and environmental disturbances. The sliding mode reaching law is designed as follows:

[0069] To prove that the sliding surface is reachable under this reaching law, a suitable Lyapunov candidate function is selected. And differentiate it:

[0070]

[0071] Among them, inequalities and It holds true if and only if hour, and This proves that the system state variables can reach the sliding surface. In summary, the stability and reachability of sliding mode control have been proven.

[0072] To demonstrate the effectiveness of the proposed robust attitude control method, numerical simulations are performed using a certain type of large meteorological satellite as an example.

[0073] I. Simulation Basic Settings (I) Simulation Objects and Core Objectives Using a large meteorological satellite of a certain type as the simulation object, this satellite carries multiple rotating payloads (such as scanning radiometers) and experiences periodic and pulsed imbalance disturbances due to manufacturing and assembly errors and uneven mass distribution. It is also affected by environmental disturbance torques and high-frequency micro-disturbances on the platform. The core simulation objective is to verify the effectiveness of the proposed robust attitude stabilization method in terms of imbalance disturbance estimation accuracy, broadband attitude determination accuracy, and attitude control stability. The sampling time is set to 0.1 seconds. .

[0074] (II) Key Simulation Parameters Based on the actual operating conditions and design requirements of the satellite, the core parameters are set as shown in the table below, providing input for dynamic modeling, observer and controller design:

[0075] II. Module-by-Module Simulation Process and Result Verification (a) Simulation of estimating unbalanced disturbances using a sliding mode observer 1. Simulation Logic Based on the overall dynamic model established in step one, the unbalanced torque term generated by the rotating load is extracted and decomposed into scalar forms along the X, Y, and Z axes of the satellite body coordinate system. Using the sliding mode observer designed in step two, the satellite angular velocity and initial observation values ​​are input, and the estimated value of the unbalanced torque is iteratively calculated. This estimated value is then compared with the preset actual unbalanced torque to verify the accuracy of the estimation.

[0076] 2. Estimation of periodic unbalanced torques Simulation settings: The preset X-axis periodic unbalanced torque is 0.1. (0.2 ) The Y-axis value is 0.08. (0.3 ) The Z-axis value is 0.05. (0.15 ) Simulation duration 50 .

[0077] Results analysis: like Figure 3 As shown in Figures (a) and (c), the estimated curves almost completely overlap with the actual curves, indicating that the observer can accurately track the triaxial periodic perturbations. like Figure 3 Figure (d) shows that the average estimation errors for all three axes are less than 1 × 10⁻⁶. -3 It eventually stabilized at 5×10 -4 The following verifies that the observer's estimation accuracy for periodic disturbances is 1.02 × 10⁻⁶, which is consistent with the estimation accuracy for periodic unbalanced torques in Table 2. -3 Consistent.

[0078] 3. Estimation of Impulsive Unbalanced Torque Simulation settings: preset =0.5 At that time, the applied amplitude was 0.6. The impulsive unbalanced torque, simulation duration 2.5 seconds. .

[0079] Results analysis: like Figure 4 As shown in Figure (a), the observer is 0.1 seconds after the pulse occurs. The actual torque amplitude can be tracked within the time frame with no significant delay; like Figure 4As shown in Figure (b), the peak estimation error is less than 0.2. And at 0.3 It converged to 0.05. The following conditions are met for the requirement of rapid estimation of impulsive disturbances and the estimation accuracy of 3.51 × 10⁻⁶ for impulsive unbalanced torques in Table 2. -3 Consistent.

[0080] (II) Simulation of Attitude Determination for Magnetohydrodynamic Sensor Fusion 1. Simulation Logic Two sets of comparative simulations were built: Experimental group: Based on step three, the traditional attitude sensor and the magnetohydrodynamic angular velocity sensor are integrated, and the wide-band attitude is output through adaptive Kalman filtering; Control group: Using only a traditional attitude sensor and the same filtering algorithm to output attitude. Simulation duration: 100 seconds. The error was determined by comparing the two sets of attitudes.

[0081] 2. Results Analysis like Figure 5 As shown in Figure (a), the experimental group exhibited a three-axis attitude angle fluctuation range of less than ±2. And in 50 It then stabilized at ±0.5. Inside; such as Figure 5 As shown in Figure (b), the control group exhibited attitude angle fluctuations ranging from ±5°. The stabilization time has been delayed to 80. ; like Figure 5 As shown in Figure (c), for the experimental group, the peak attitude determination error was less than 0.3. The steady-state error is less than 0.1. ;like Figure 5 As shown in Figure (d), the control group had a peak error of 0.8. Steady-state error 0.4 ; Based on Table 2, the attitude determination accuracy of the experimental group reached 6.24 × 10⁻⁶. -7 The performance was improved by 49.9% compared to the control group, which verifies that the magnetohydrodynamic sensor has the ability to measure high-frequency micro-perturbations and the wide-band advantage of the fusion method.

[0082] (III) Attitude Control Simulation of Integral Sliding Mode Controller 1. Simulation of Rotating Load Control Simulation logic: For a certain rotating load number of the satellite, an integral sliding mode control law is designed according to step four, where: the sliding surface is the load angular velocity error, the unbalanced torque estimated by the sliding mode observer is input, and the load angular velocity is controlled to be stable.

[0083] Results analysis: like Figure 6 As shown in Figure (a), the X-axis load angular velocity starts from the initial 0. Rise to target 10 Overshoot less than 5%, settling time less than 10 seconds. Steady-state fluctuation is less than ±0.2 ; like Figure 6 As shown in Figure (b), the peak control torque is less than 40. And it remains stable at ±5 in steady state. Within the test, there was no significant chattering, verifying the controller's stable control capability for the rotating load and its rotating load stability accuracy of 4.53 × 10⁻⁶ in Table 2. -4 Consistent, with a 12.5% ​​improvement over traditional methods.

[0084] 2. Satellite Global Attitude Control Simulation Simulation logic: Build two sets of comparative simulations: Experimental group: The integral sliding mode controller designed in step four was used to control the satellite's three-axis attitude angles and angular velocities by inputting the fused attitude determination results and the estimated unbalanced torque values. Control group: A traditional PID controller was used, with the same attitude measurement values ​​input. Simulation duration: 100 seconds. The effects of the two control groups were compared.

[0085] Results analysis: Attitude angle control: such as Figure 7 As shown in Figure (a), for the experimental group: the three-axis attitude angles started from the initial (10, -9, 7.5). Converging to ±0.5 Within, the convergence time is less than 30. ;like Figure 7 As shown in Figure (b), the control group had a convergence time greater than 60 seconds. And the steady-state fluctuation reaches ±1 ; Angular velocity control: such as Figure 7 As shown in Figure (c), the experimental group exhibits a triaxial angular velocity steady-state error of less than ±0.1. ;like Figure 7 As shown in Figure (d), the control group exhibited a steady-state error of ±0.3%. ; Based on Table 2, the attitude angle control accuracy of the experimental group was 9.61 × 10⁻⁶. -4 This represents a 17.9% improvement over the control group, with an angular velocity control accuracy of 1.16 × 10⁻⁶. -4 This represents a 20.6% improvement over the control group, validating the integral sliding mode controller's ability to suppress complex disturbances and its global stability.

[0086] III. Simulation Conclusions Through modular simulation and comparative verification, the effectiveness of the proposed robust attitude stabilization method in the scenario of rotational imbalance disturbance of large satellites has been fully demonstrated: Imbalanced disturbance estimation: The sliding mode observer achieves an estimation accuracy of 1.02 × 10⁻⁶ for periodic and impulsive disturbances, respectively. -3 3.51×10 -3 This meets the requirements for disturbance compensation; Wideband attitude determination: After fusing the magnetohydrodynamic sensor with a traditional sensor, the attitude determination accuracy reaches 6.24 × 10⁻⁶. -7 This method improves upon traditional methods by 49.9%, covering measurement needs across both high and low frequency bands. Stable attitude control: The integral sliding mode controller achieved an attitude angle of (9.61 × 10⁻⁶) / 2.5°. -4 ) and angular velocity (1.16×10 -4 The high-precision control of this method has superior robustness and dynamic performance compared to traditional methods, and can meet the on-orbit mission requirements of large meteorological satellites.

[0087] Table 2:

[0088] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A robust attitude stabilization method for large satellites subjected to rotational imbalance disturbances, characterized in that: The steps include the following: Step 1: Under the condition of unbalanced disturbances of large satellites, establish a rigid-flexible coupled dynamic model of large satellites based on the angular momentum theorem. By decomposing the variables in the rigid-flexible coupled dynamic model: the angular momentum of the rotating load and the moment of inertia of the satellite, and based on the actual working conditions of large satellites, considering the large satellite has multiple rotating loads and environmental disturbances as well as the high-frequency micro-disturbances of the platform, establish the overall dynamic model of large satellite-platform. Step 2: Design a sliding mode observer that can asymptotically converge the torque error to the equilibrium point, and estimate the periodic and impulsive unbalanced disturbance torque; Step 3: Based on the traditional attitude sensor, a magnetohydrodynamic angular velocity sensor is introduced to construct a measurement model covering both high and low frequency bands. The measurement models of the high and low frequency bands are then fused using an adaptive Kalman filter to form a fused measurement model for determining the wideband attitude of large satellites. Step 4: Design a sliding mode surface using a sliding mode observer and the large satellite control equations constructed based on the relationship between three-axis attitude angles and angular velocities. Combine this with the overall dynamics model to design an integral sliding mode controller to improve the steady-state performance of the attitude determined by the fusion measurement model.

2. The robust attitude stabilization method for large satellites against rotational imbalance disturbances according to claim 1, characterized in that: The rigid-flexible coupling dynamic model is as follows: ； ； ； In the formula: , These represent the coordinates of the load's center of mass and the system's center of mass in the inertial reference frame, respectively. This indicates the entire satellite relative to the system's center of mass. angular momentum; Indicates the satellite's angular velocity; Indicates the mass of the rotating load; For the system centroid Pointing to the center of mass of the load ; The platform rotation speed; This indicates the rotational load relative to the load's center of mass. angular momentum; This represents the rigid-flexible coupling matrix of the satellite system. For satellite mode vectors; Represents the net external torque acting on the satellite system; skew-symmetric matrix In particular, For the entire satellite relative to the system's center of mass Moment of inertia: ； In the formula: This indicates the satellite platform relative to the platform's center of mass. Moment of inertia; Represents the system's centroid Pointing to the platform's center of gravity ; Indicates the quality of the satellite platform; It is the identity matrix. This is the transpose operator.

3. A robust attitude stabilization method for large satellites against rotational imbalance disturbances according to claim 2, characterized in that: Due to rotational imbalance disturbance, the moment of inertia and It is variable and is decomposed into two parts: a constant term *con* and a non-constant term. Therefore, the third equation of the rigid-flexible coupling dynamic model is rewritten as: ； , ； In the formula: Represents the bounded unbalanced torque generated by rotating loads: A represents .

4. A robust attitude stabilization method for large satellites against rotational imbalance disturbances according to claim 3, characterized in that: The overall dynamic model is as follows: ； ； ； In the formula: subscript Indicates the number of the rotating load. ; Indicates load The constant of inertia; and Acting on the satellite platform and payload respectively Control torque; Indicates load The resulting unbalanced torque scalar; and These are the structural damping matrix and the frequency matrix, respectively. It is an environmental disturbance torque; It is a small torque disturbance term.

5. A robust attitude stabilization method for large satellites against rotational imbalance disturbances according to claim 4, characterized in that: The design process of the sliding mode observer includes the following steps: S51 will decompose the unbalanced moment scalar along each coordinate axis in the large satellite body coordinate system. and its first derivative Defined as: ， ； in: and All are constants; Will The estimated value is set as The construction moment estimation error is: ； Given real numbers , , , , For any unbalanced torque scalar The sliding mode observer is designed as follows: ； In the formula: Represents a symbolic function. ; When using a sliding mode observer to estimate unbalanced moments, it is necessary to prove the error in the moment measurement. Regarding the asymptotic convergence of the equilibrium point: torque error The derivative is expressed as: ； Based on Lyapunov stability theory, select appropriate Lyapunov candidate functions. And differentiate it: ； ； By defining the inequality relations Derivation The final form is: ； Therefore, and It holds true if and only if hour, and Therefore, the sliding mode observer can guarantee torque error. It asymptotically converges to the equilibrium point, thereby accurately estimating periodic or impulsive unbalanced torques.

6. A robust attitude stabilization method for large satellites against rotational imbalance disturbances according to claim 5, characterized in that: The process of constructing the fusion measurement model includes the following steps: S61 gives the transfer function of a traditional attitude sensor: ； In the formula: Represents a complex variable; and These represent the noise suppression factor and the power amplification factor, respectively. A magnetohydrodynamic (MHD) angular velocity sensor is introduced, which is excited by the angular velocity signal. The conductive fluid in the annular channel cuts the magnetic field, thereby generating a velocity difference and creating a potential difference between the upper and lower electrodes. The transfer function of the MHD angular velocity sensor is expressed as: ； In the formula: Indicates induced electromotive force; Radial magnetic flux density; Indicates the effective width of the current path; is the root mean square value of the sensor substrate radius; is the viscosity coefficient of the magnetohydrodynamic fluid; The height of the current loop; Let Hartmann number be an expression for the number of Hartmann numbers, where: and These are the density and resistivity of the magnetic fluid, respectively. For high-precision angular velocity measurement, the magnetohydrodynamic angular velocity sensor is represented by a fourth-order complex frequency domain model: ； Where: coefficient and All are constants, determined experimentally; Magnetohydrodynamic angular velocity sensors typically perform well in the high-frequency band, i.e., for micro-angular perturbations on platforms, while in the low-frequency band, i.e., for satellite attitude motion, they work in conjunction with gyroscopes and star sensors. To cover the entire measurement bandwidth, a combined measurement model is proposed, which takes the following form: ； Therefore, the fusion measurement model of the magnetohydrodynamic angular velocity sensor and the traditional attitude sensor is expressed as: ； In the formula: Indicates the actual posture; These represent the state variables of the low-frequency and high-frequency sensing systems, respectively. This indicates the corresponding measurement output; and These represent system noise and measurement noise, respectively; other key coefficient matrices can be derived from the transfer functions of traditional attitude sensors and magnetohydrodynamic angular velocity sensors: ， ， ； ， ， ； Adaptive Kalman filtering is used to fuse low-frequency and high-frequency measurement systems; The entire state space is represented as: ； ， ， ， ， ， ； Status Update: ； Measurement Update: ； In the formula: Represents a discrete state transition matrix; and These are the covariance matrices of the sensing system and the measurement noise, respectively. This represents the expected value of the measured noise. Let be the covariance matrix of the state variables; These represent the Kalman coefficients. Given an initial form for these matrices, the process can be iterated over time to ultimately determine the wideband attitude.

7. A robust attitude stabilization method for large satellites against rotational imbalance disturbances according to claim 6, characterized in that: The design process of the integral sliding mode controller includes the following steps: S71. Constructing the control equations for large satellites: First, given The three-axis attitude angles for ZYX rotation include: roll angle. Pitch angle and yaw angle Give With angular velocity The relationship is as follows: , , ； Define new variables and Then the state space representation of the control system is: ； ； In the formula: This represents the control system input, and its expression is a common construction form for double-limit homogeneous systems. and For nonlinear homogeneous terms; parameters , , ; Given ,inequality If it is established, then and satisfy: ； S72. Based on homogeneity theory, prove the stability of the control system: If a vector field is homogeneous in both the 0 limit and the ∞ limit, then it achieves double-limit homogeneity. The vector field of this control system is It can be expressed in bihomogeneous form as: ； ； therefore, and yes An approximate vector field; in order to simultaneously achieve and To ensure homogeneity, the corresponding weight vector is: ； ； According to homogeneity theory, we can take the homogeneity degree respectively. and It can guarantee the vector field Achieving bihomogeneity; to prove the stability of the global system, selecting appropriate Lyapunov candidate functions. And differentiate it: ； ； Therefore, the function Continuously differentiable and radially unbounded; It holds true if and only if hour, Established; Decomposition The only solution is This proves the asymptotic convergence of the state variables; Give the Lyapunov candidate functions and their derivatives for the zero limit and the infinity limit respectively: ； ； The control system exhibits asymptotic stability at both limits, thus proving the stability of the global system. S73. Design an integral sliding mode controller: By using a sliding mode observer combined with the governing equations in S71, the sliding surface is designed as follows: ； set up That is, when the system state variables reach the sliding surface, we get: , ； Therefore, it can be seen that the system state variables can converge; the attitude error is defined as... , If we treat it as a controlled variable, then the sliding surface can be rewritten as: ； ； By combining the expression for the sliding surface with the overall dynamic model, the integral sliding mode control law is designed as follows: ； In the formula: , , , Control Law Equivalent to the dynamic model ; It includes unbalanced moments, structural vibrations, and environmental disturbances. The sliding mode convergence law is designed as follows: ； To prove that the sliding surface is reachable under this reaching law, a suitable Lyapunov candidate function is selected. And differentiate it: ； ； Among them, inequalities and It holds true if and only if hour, and This means that the system state variables can reach the sliding surface; in summary, the stability and reachability of sliding mode control have been proven.

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