A micro-nano satellite orbit transfer maneuver phase attitude composite control method

Abstract

This invention discloses a composite attitude control method for the maneuvering phase of a microsatellite. The method includes: constructing a novel composite actuator based on a zero-momentum gear train and a two-dimensional translational mechanism; establishing and optimizing attitude rotational dynamics and slider translational dynamics models considering inertial principal axis offset and additional disturbance torque; designing an exponentially convergent disturbance observer to monitor thrust eccentricity torque in real time; and designing an attitude control loop MPC (Model Predictive Control) controller and a thrust eccentricity torque compensation loop discrete PID (Proportional-Integral-Derivative) controller to form a dual-closed-loop composite attitude control system. This control method can effectively observe slowly time-varying thrust eccentricity torque, and features high control accuracy and no saturation in the momentum gear train, making it suitable for long-term thrust eccentricity disturbances in microsatellite maneuvering missions.

Description

Technical Field

[0001] This invention belongs to the field of satellite design technology, specifically relating to a composite attitude control method for the orbit change maneuvering phase of a micro / nano satellite. Background Technology

[0002] With technological advancements and increasing demands in navigation, weather forecasting, communication, and resource exploration, spacecraft miniaturization has become a development trend. Against the backdrop of rapid advancements in microelectronics and micromechanical technologies, microsatellites and nanosatellites have gradually attracted widespread attention worldwide. Due to their significant advantages such as light weight, small size, low cost, and short development cycle, they have been widely applied in civilian and military fields, including space remote sensing, constellation networking, and on-orbit rendezvous and docking. As the complexity of space missions continues to increase, the demand for the orbit-changing capabilities of microsatellites and nanosatellites is becoming increasingly urgent. However, the thrust eccentricity caused by thruster operation during orbit changes can impose additional disturbance torque on the satellite, severely interfering with its attitude control. Traditional wheel control or magnetic control methods have extremely limited ability to suppress this interference. Furthermore, due to the limited size of microsatellites and nanosatellites, installing nozzles in multiple directions to ensure multi-directional torque output would make the propulsion system extremely complex, severely affecting the overall system reliability, increasing satellite size, and raising its development cost. Therefore, this patent proposes to use mass moment technology to solve the technical difficulty of controlling long-term thrust eccentricity disturbance during orbit change maneuvers of micro-nano satellites with only a single thruster.

[0003] Mass moment technology alters the position of the system's center of mass by moving the position of a movable mass within the system, thereby adjusting the magnitude of external torque and ultimately achieving the desired attitude control. However, mass moment technology still faces several practical engineering challenges. The movement of the mass mass changes the satellite's moment of inertia and generates additional torque disturbances related to its velocity and acceleration, severely interfering with the satellite's attitude control performance. Furthermore, the mass moment actuator introduces additional mass counterweights, reducing the satellite's efficiency-to-cost ratio, which is inconsistent with the miniaturization trend of micro / nano satellites. Summary of the Invention

[0004] The purpose of this invention is to provide a composite attitude control method for the orbit change maneuver of micro- and nano-satellites, in order to solve the problem of long-term thrust eccentricity disturbance control during the orbit change maneuver of micro- and nano-satellites equipped with only a single thruster.

[0005] The objective of this invention can be achieved through the following technical solution: a composite attitude control method for the orbit change maneuvering phase of a micro / nano satellite, comprising the following steps:

[0006] Step 1: Construct a composite actuator based on a zero-momentum gear train and a two-dimensional translational mechanism.

[0007] The composite actuator comprises a zero-momentum gear train and a two-dimensional translational mechanism. The zero-momentum gear train serves as the moving mass of the two-dimensional translational mechanism. The two-dimensional translational mechanism drives the zero-momentum gear train with constant acceleration, avoiding the drawbacks of introducing additional mass in conventional mass-moment mechanisms. This aligns with the lightweight development trend of micro- and nano-satellites, thus addressing the problem of thrust eccentricity torque interfering with attitude control. Thrust eccentricity torque is caused by the thrust vector extension line not passing through the system's center of mass. Therefore, it can be eliminated by adjusting the position of the center of mass or the direction of the thrust vector. Compared to the vector nozzle scheme, adjusting the position of the system's center of mass is simpler and easier to implement on micro- and nano-satellites with limited mass and volume. When the composite actuator translates to other positions, the satellite's center of mass also changes accordingly. By appropriately adjusting the position of the composite actuator, the satellite system's center of mass can be positioned on the extension line of the thrust vector, thereby eliminating the thrust eccentricity torque. This invention still utilizes the zero-momentum gear train to output three-axis torque to meet the requirements of high-precision attitude control.

[0008] The composite actuator uses a zero-momentum gear train as a single slider in a two-dimensional translational mechanism. In a single-slider two-dimensional translational layout, when the extended displacement line of the composite actuator does not pass through the center of mass, it generates a large disturbance torque on the X-axis, causing attitude jitter in the rolling axis direction, which is detrimental to stable attitude control and the normal operation of onboard components. In contrast, the current industry-optimized layout for the mass moment-moving mass block is a double-symmetric layout. In a double-symmetric layout, the additional inertial torque on the X-axis is canceled out by the opposite slider, which is beneficial for attitude control. However, converting to a double-symmetric layout introduces an additional translational control mechanism, increasing unnecessary mass, and structurally, the zero-momentum gear train is difficult to separate into four independent sliders. Therefore, a single-slider two-dimensional translational layout is still used, and a discrete control algorithm is designed to mitigate the slider's movement and minimize the impact of the additional disturbance torque.

[0009] Step 2: The satellite attitude dynamics model and the translational dynamics model of the composite actuator, considering the inertial principal axis offset and the additional disturbance torque, were established and optimized, as follows:

[0010] Based on the generalized angular momentum theorem, the formula for satellite attitude dynamics in an inertial frame is obtained;

[0011] Transforming the attitude dynamics equations in the formula into a form relative to the orbital frame, this invention assumes that the satellite's orbital change is not significant in a short period of time during the modeling process, thus providing an angular acceleration relative to the inertial frame. The attitude dynamics equations for the relative orbital system are obtained;

[0012] Since the composite actuator only performs two-dimensional translation relative to the celestial body, its motion can be described by only two-dimensional translational dynamics. Thus, the expansion of the translational dynamics equation of the composite actuator in this system can be obtained.

[0013] System disturbance torque T d This mainly includes the additional disturbance torque of the composite actuator and the disturbance torque of the space environment. The space disturbance torque is smaller than the additional disturbance torque; therefore, the impact of the additional disturbance torque of the composite actuator on the satellite attitude is the primary consideration. Additional inertial torque M a It is mainly related to the displacement and acceleration of the mass block, with an additional Coriolis torque M. c It is mainly related to the displacement velocity of the mass block, and the additional gyroscopic torque M g It is mainly related to the position of the mass block.

[0014] Commonly used attitude kinematic equations include those based on Euler angles and those based on quaternions. Euler angles involve a lot of trigonometric function operations and are only advantageous at small angles. Quaternions require a magnitude of 1 when describing attitude, which means there is a normalization constraint. This limits their application in certain scenarios. Modified Rodrigues parameters (MRP) can avoid the normalization constraint of quaternions and have better performance. Therefore, modified Rodrigues parameters are used to describe the attitude of satellites.

[0015] Step 3: Based on the motion characteristics of the composite actuator, an exponential convergence disturbance observer was designed to observe the thrust eccentricity torque in real time.

[0016] Analysis of the motion characteristics of the composite actuator by the motion model shows that the disturbances to the satellite system include thrust eccentric torque, slider additional disturbance torque, space environment torque, etc., among which thrust eccentric torque accounts for the majority in terms of magnitude.

[0017] Considering the strong coupling, uncertain model parameters, and unmodeled dynamics in the attitude control of micro / nano satellites with moving parts, a dual-closed-loop attitude stabilization control system based on an exponentially convergent disturbance observer was designed. In the attitude control loop, a zero-momentum wheel system serves as the actuator for three-axis stabilization control of the satellite. The compensation control loop utilizes a mass moment actuator to adjust the satellite system's center of mass position in real time to minimize the thrust eccentricity torque. Simultaneously, an exponentially convergent disturbance observer is designed to estimate the attitude disturbance torque. This serves two purposes: firstly, to avoid constant deviations in the attitude control loop, and secondly, to provide input to the thrust eccentricity torque compensation loop for position control of the composite actuator. It is noted that the composite actuator can also utilize the thrust eccentricity torque to unload the satellite system's angular momentum, thereby addressing the momentum wheel speed saturation problem.

[0018] Step 4: Based on the exponentially convergent disturbance observer, a dual-closed-loop attitude stabilization control system was designed, consisting of an attitude control loop MPC controller and a thrust eccentricity torque compensation loop discrete PID controller.

[0019] To address the nonlinearity and multiple constraints in attitude control of micro and nano satellites, a linear MPC control algorithm is selected to design the attitude law, thereby considering all constraints of the system at the design level.

[0020] The attitude control loop discretizes and linearizes the satellite attitude dynamics model and the translational dynamics model of the composite actuator, and designs a linear MPC controller to obtain the optimal control input for the momentum wheel. The compensation control loop uses the output value of the thrust eccentric torque disturbance observer as the input of the PID controller and the desired slider displacement as the controller output. The two-dimensional translational mechanism drives the zero momentum wheel system to complete the closed-loop control with constant acceleration.

[0021] Compared with the prior art, the significant advantages of this invention are:

[0022] (1) The proposed attitude composite control method has the ability to balance the thrust eccentricity moment and output high-precision attitude control moment, which improves the attitude control accuracy of micro and nano satellites during orbit change maneuvers. The satellite does not need to be equipped with an additional attitude control thruster.

[0023] (2) The proposed composite actuator has the ability to unload the momentum wheel system, and the satellite does not need to install an additional attitude control thruster to unload the momentum wheel, thus saving the consumption of attitude control propellant;

[0024] (3) The proposed thrust eccentricity moment compensation control loop algorithm can balance the center of mass in real time, which greatly reduces the impact of propellant consumption on the performance of the attitude and orbit control system. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the operation of a composite actuator.

[0026] Figure 2 This is a flowchart of the attitude control system process.

[0027] Figure 3 Figure 1 shows the force diagram of the motion of the mass moment slider, where Figure (a) shows the two-dimensional translational layout of a single slider and Figure (b) shows the double symmetric layout.

[0028] Figure 4 These are attitude parameter variation curves, where Figure (a) is the MRP variation curve, Figure (b) is the angular velocity variation curve, and Figure (c) is the momentum wheel speed variation curve of the composite actuator.

[0029] Figure 5 Figure 1 shows the variation curves of thrust eccentricity moment and exponential convergence disturbance observer. Figure 2 shows the variation curves of thrust eccentricity moment and disturbance observer on the Y-axis, and Figure 3 shows the variation curves of thrust eccentricity moment and disturbance observer on the Z-axis. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0031] Combination Figures 1-5 The present invention discloses a composite attitude control method for the orbit change maneuvering phase of a micro / nano satellite, comprising the following steps:

[0032] Step 1: Construct a composite actuator based on a zero-momentum gear train and a two-dimensional translational mechanism.

[0033] Combination Figure 1 The composite actuator includes a zero-momentum wheel system and a two-dimensional translational mechanism. The zero-momentum wheel system is used as the moving mass of the two-dimensional translational mechanism. The two-dimensional translational mechanism drives the zero-momentum wheel system to move with constant acceleration, avoiding the drawback of introducing additional mass in conventional mass moment mechanisms. This is in line with the development direction of lightweighting micro and nano satellites, thus solving the problem of attitude control interference caused by thrust eccentricity torque.

[0034] The thrust eccentricity moment is caused by the thrust vector extension line not passing through the system's center of mass. Therefore, it can be eliminated by adjusting the position of the center of mass or the direction of the thrust vector. Compared to the vector nozzle scheme, adjusting the position of the system's center of mass is simpler and easier to implement on micro- and nano-satellites with limited mass and volume. When the composite actuator translates to other positions, the satellite's center of mass will also change accordingly. By adjusting the position of the composite actuator, the satellite system's center of mass can be positioned on the extension line of the thrust vector, thereby eliminating the thrust eccentricity moment. This invention still utilizes a zero-momentum gear train to output three-axis torque to meet the requirements of high-precision attitude control.

[0035] Combination Figure 3 The composite actuator uses a zero-momentum gear train as a single slider in a two-dimensional translational mechanism. In a single-slider two-dimensional translational layout, when the extended displacement line of the composite actuator does not pass through the center of mass, it generates a large disturbance torque on the X-axis, causing attitude jitter in the rolling axis direction, which is detrimental to stable attitude control and the normal operation of onboard components. In contrast, the current industry-optimized layout for the mass moment-moving mass block is a double-symmetric layout. In a double-symmetric layout, the additional inertial torque on the X-axis is canceled out by the opposite slider, which is beneficial for attitude control. However, converting to a double-symmetric layout introduces an additional translational control mechanism, increasing unnecessary mass, and structurally, the zero-momentum gear train is difficult to separate into four independent sliders. Therefore, a single-slider two-dimensional translational layout is still used, and a discrete control algorithm is designed to mitigate the slider's movement and minimize the impact of the additional disturbance torque.

[0036] Step 2: Establish and optimize the satellite attitude dynamics model and the translational dynamics model of the composite actuator, taking into account the inertial principal axis offset and the additional disturbance torque, as follows:

[0037] According to the generalized angular momentum theorem, the kinematic equations of satellite attitude in the inertial frame are obtained as follows:

[0038]

[0039] In the formula: J S Let J be the moment of inertia of the satellite shell in this system. C Let ω be the moment of inertia of the composite actuator in this system. bi The angular velocity of the satellite relative to its orbital system. Let h be the angular acceleration of the satellite's own system relative to its orbital system. W For the angular momentum of the zero-momentum wheel in the compound actuator, C W J is the installation matrix of the zero-momentum gear train of the composite actuator in this system. W The moment of inertia of the zero-momentum gear train section of the composite actuator. T is the angular acceleration of the zero-momentum gear train section of the composite actuator. d For the system disturbance torque, d s For the system modeling error, T P The thrust eccentricity moment acting on the satellite, T P =(r T -r s )×F t r T For the thrust direction in this system, r s Let F be the radius vector of the satellite's center of mass in this system. t For thruster thrust. U d These are considered as unknown disturbances, including disturbance factors such as thrust disturbance torque and environmental disturbance torque.

[0040] The satellite attitude dynamics equations in the inertial frame are transformed into a form relative to the orbital frame. In the modeling process, this invention assumes that the satellite's orbital changes are not significant over a short period, thus incorporating angular acceleration relative to the inertial frame. The attitude dynamic equations of the relative orbital system are obtained as follows:

[0041]

[0042] In the formula: ω bo This represents the angular velocity of the satellite relative to its orbital system within this system. Let A be the angular acceleration of the satellite relative to its orbital system. bo Let ω be the rotation matrix from the orbital system to the home system. oi Let I be the angular velocity of the orbital frame relative to the inertial frame.W For the satellite's inertial tensor

[0043] Since the composite actuator only undergoes two-dimensional translation relative to the celestial body, its motion can be described using only two-dimensional translational dynamics. The gravitational force G acting on the composite actuator is... W It can be represented as:

[0044] G W =m W G / (m B +m W )

[0045] In the formula: G is the gravitational force acting on the satellite system, m W For the quality of composite actuators, m B Let be the remaining mass of the satellite excluding the composite actuator. Therefore, the force equation for the composite actuator can be derived as follows:

[0046]

[0047] In the formula: F W R represents the resultant force acting on the system during the translation of the composite actuator. s Let r be the radius vector of the satellite's center of mass in the inertial frame. s p is the radius vector of the satellite's center of mass in this system. W For the composite actuator in the inertial frame, the radius vector is the system-wide radius vector. Let the radius vector acceleration of the satellite's center of mass in the inertial frame be denoted as . Let be the radius vector acceleration of the satellite's center of mass in this system. The radius-vector acceleration of the composite actuator in the inertial frame is given by the system itself.

[0048] Therefore, the translational dynamics equation of the composite actuator in this system can be obtained, that is, the translational dynamics model of the composite actuator:

[0049]

[0050] In the formula: F env For space environment forces, r B The location of the satellite's center of mass within this system. Let the velocity of the satellite's center of mass within this system be denoted as . Let r be the position acceleration of the satellite's center of mass within this system. B The change is caused by propellant consumption during the operation of the propulsion system. The radius vector velocity of the composite actuator in its own system within the inertial frame is given. p is the radius-vector acceleration of the composite actuator in its own system within an inertial frame. W ω represents the position of the composite actuator within its own system in the inertial frame. biThe angular velocity of the satellite relative to its orbital system. This is the angular acceleration of the satellite system relative to its orbital system.

[0051] System disturbance torque T d This mainly includes the additional disturbance torque of the composite actuator and the disturbance torque of the space environment. The space disturbance torque is smaller than the additional disturbance torque; therefore, the impact of the additional disturbance torque of the composite actuator on the satellite attitude is the primary consideration. Additional inertial torque M a It is mainly related to the displacement and acceleration of the mass block, with an additional Coriolis torque M. c It is mainly related to the displacement velocity of the mass block, and the additional gyroscopic torque M g It is mainly related to the position of the mass block.

[0052] Commonly used attitude kinematic equations include those based on Euler angles and those based on quaternions. Euler angle equations involve numerous trigonometric function operations and are only advantageous at small angles. Quaternions, when describing attitude, require a magnitude of 1, meaning they impose a normalization constraint, which limits their application in certain scenarios. Modified Rodrigues parameters (MRP) avoid the normalization constraint inherent in quaternions, resulting in superior performance. Therefore, we adopt the modified Rodrigues parameter-based approach to describe satellite attitude. The satellite attitude kinematic equations based on the orbital frame are as follows:

[0053]

[0054] Where: σ bo Here are the corrected Rodrigues parameters for this system relative to the inertial frame. I represents the corrected Rodrigues parameter of this system relative to the inertial frame. 3×3 For the identity matrix, the operator [·] × Represents a skew-symmetric matrix of vectors.

[0055] The error attitude dynamics equations have a simpler expression, making them easier to design attitude tracking control algorithms and significantly simplifying the expression of the control law. The target system is defined as a coordinate system established with the desired satellite attitude as its origin.

[0056] The attitude error dynamics expression, i.e., the satellite attitude dynamics model, can be obtained:

[0057]

[0058] In the formula: ω e Let be the angular velocity of this system relative to the target system. Let A be the angular acceleration of this system relative to the target system. e Let ω be the attitude transformation matrix from the target system to the home system. d U represents the angular velocity of the target system relative to the orbital system within the target frame.d These are considered as unknown disturbances, including disturbance factors such as thrust disturbance torque and environmental disturbance torque.

[0059] Define the target to correct the Rodriguez parameter σ d The target frame represents the attitude relative to the orbital frame, and the error correction Rodrigues parameter σ represents this attitude. e To express the attitude of our system relative to the target system, we can obtain the error attitude kinematic equations as follows:

[0060]

[0061] Analysis of the motion characteristics of the composite actuator using a motion model reveals that the disturbances experienced by the micro-nano satellite system include thrust eccentric torque, slider-induced disturbance torque, and space environment torque, among which thrust eccentric torque accounts for the majority in terms of magnitude.

[0062] Combination Figure 3 The workflow of a micro / nano satellite system is demonstrated. In the attitude control loop, a zero-momentum wheel system acts as the actuator for three-axis stabilization control. The compensation control loop utilizes a mass moment actuator to adjust the satellite system's center of mass position in real time to minimize thrust eccentricity torque. Simultaneously, an exponentially convergent disturbance observer is designed to estimate attitude disturbance torque. This serves two purposes: firstly, to prevent constant deviations in the attitude control loop, and secondly, to provide input to the thrust eccentricity torque compensation loop for position control of the composite actuator. Notably, the composite actuator can also utilize thrust eccentricity torque to unload the satellite system's angular momentum, thereby addressing the momentum wheel speed saturation problem.

[0063] Step 3: Design an exponential convergence disturbance observer based on the motion characteristics of the composite actuator to observe the thrust eccentricity torque in real time.

[0064] Considering the strong coupling of attitude control, uncertain model parameters, and unmodeled dynamic factors in micro / nano satellites with moving parts, an estimated attitude disturbance torque is designed. This torque serves two purposes: firstly, it helps prevent constant deviations in the attitude control loop; secondly, it acts as an input to the thrust eccentricity torque compensation loop to achieve position control of the composite actuator. It is noted that the composite actuator can also utilize the thrust eccentricity torque to unload the satellite system's angular momentum, thereby addressing the momentum wheel speed saturation problem.

[0065] The exponentially convergent disturbance observer is:

[0066]

[0067] Let Z be the observations of the exponentially convergent interference observer, K be the auxiliary parameter, and Z be the converged result. Let ω be the derivative of the convergent result. do Let be the angular velocity of the target system relative to the orbital system. Let be the angular acceleration of the target system relative to the orbital system. Micro-thrusters do not exhibit the rapid combustion and rapid changes in the center of mass characteristic of solid thrusters. Therefore, the thrust variation during operation is not significant. Consequently, the eccentric torque generated by the micro-thruster can be treated as a slow, time-varying disturbance because... It is certain that the observed exponent converges to the disturbance d, and the convergence accuracy depends on the value of parameter K.

[0068] Step 4: Based on the exponentially convergent disturbance observer, design the attitude control loop MPC controller and the thrust eccentricity torque compensation discrete PID controller. The attitude control loop MPC controller and the thrust eccentricity torque compensation discrete PID controller together constitute a dual closed-loop composite attitude control system to achieve high-precision attitude stability control of the satellite during thruster operation.

[0069] The attitude control loop discretizes and linearizes the satellite attitude dynamics model and the translational dynamics model of the composite actuator, and designs a linear MPC controller to obtain the optimal control input for the momentum wheel. The compensation control loop uses the output value of the thrust eccentric torque disturbance observer as the input of the PID controller and the desired slider displacement as the controller output. The two-dimensional translational mechanism drives the zero momentum wheel system to complete the closed-loop control with constant acceleration.

[0070] The attitude control loop uses a zero-momentum wheel system as the actuator to perform three-axis stabilization control of the satellite, while the compensation control loop uses a mass moment actuator to adjust the position of the satellite system's center of mass in real time to minimize the thrust eccentricity torque.

[0071] To address the nonlinearity and multiple constraints in attitude control of micro and nano satellites, a linear MPC control algorithm is selected to design the attitude law, thereby considering all constraints of the system at the design level.

[0072] First, the satellite attitude dynamics model and the translational dynamics model of the composite actuator are discretized. Then, the state prediction time domain is defined as N. p Design an MPC control algorithm. The prediction equation in the prediction layer at time k can be expressed as:

[0073] X k+1|k =Φx k|k +S x,k Δx k|k +S u,k Δu W,k|k +S d,k ΔU k|k

[0074] In the formula:

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] Among them, S u,k Let S be the control matrix sequence at time k. x,k Let S be the state matrix sequence at time k. d,k Let B be the sequence of interference matrices at time k. u,k Let B be the control moment matrix at time k. d,k Let ΔU be the error moment matrix at time k. k|k Let A be the sequence of disturbance torques at time k. k Let A be the state matrix at time k. k+1 To predict the state matrix at time k+1, Let Φ be the state matrix at time k under state i-1 of the counting variables, where i and j are both counting variables, and x is the state matrix at time k. k|k This is the initial state. These are the state parameters at the corresponding time. N represents the magnitude of the change in the control torque of the momentum wheel under the corresponding state. p To control the time domain, X k+1|k This is the state prediction sequence for time k+1 at time k.

[0081] The objective function is set as follows:

[0082]

[0083] In the formula: J is the objective function; on the right side of the equation, the first term represents the weighted sum of errors, the second term represents the weighted sum of inputs, and the third term represents the terminal error; Q, R, and F are the weight matrices for their respective terms; x is the state variable; x(k+i,k) is the predicted state variable at time k to time k+i; u W The control torque for the momentum wheel is Δu. W (k+i|k) represents the change in the predicted momentum wheel control torque at time k with respect to time k+1; Δx k|k Let ΔT be the state input sequence in the time domain predicted at time k in incremental form. k|k Let k be the expected input sequence in the time domain for prediction at time k, expressed in incremental form.

[0084] The finite-time-domain constrained MPC problem at time k can be described as follows:

[0085]

[0086] Where: X, X f Let U represent the set of state constraints in the prediction time domain, and let Δu represent the set of input constraints in the prediction time domain.k u represents the change in the momentum wheel control torque at time k. k+1|k ΔU represents the two-stage change in predicted momentum from time k to time k+1. d (k) represents the increment of the disturbance torque at time k relative to the previous time, and Δx(k+1) represents the state increment at time k+1 relative to time k.

[0087] To solve the objective function, the above problem can be transformed into a QP problem, given the initial state x. k|k Then, the planning algorithm will calculate a set of predicted optimal control inputs. And the predicted optimal state trajectory Then predict the first value Δu of the input. k|k It can be used as the control input for the current cycle.

[0088] Design a position control algorithm for a composite actuator, specifically using a PID control algorithm:

[0089] The thrust eccentricity moment compensation loop exponentially converges to interfere with the observer's observations. As input, its control objective is In this scenario, to avoid excessively high control command frequency causing large disturbance torque on the slider, a discrete control algorithm is required. The control command is directly the desired position, and the motor itself completes closed-loop control with constant acceleration. Furthermore, considering the difficulty in estimating the system's center of mass and thrust vector direction during actual control, and the need to avoid constant deviations in the control results, an incremental discrete PID control algorithm is adopted to control the position of the composite actuator.

[0090] Define the discrete period as t, then the incremental PID control algorithm is designed as follows:

[0091]

[0092] In the formula: the displacement p of the composite actuator in the y and z directions W =[p y ;p z ], All are observations of the observer in the y, z directions at the corresponding time, t p t d t i All of these are parameters to be designed. This represents the displacement of the composite actuator or its position vector within the system.

[0093] The designed attitude control system is applied to the attitude stabilization control of micro-nano satellites during orbit change maneuvers. Numerical simulation verification and analysis are conducted to verify the effectiveness of the scheme and the accuracy of the algorithm.

[0094] The satellite is defined as a 3U CubeSat with its nozzle in the -X direction. The composite actuator is mounted in the YOZ plane of this system, with dimensions of 49*49*22mm, therefore its maximum displacement in the YZ direction is 20mm. The control cycle of the thrust eccentricity moment compensation loop is set to 20s, and the control cycle of the attitude control loop is set to 1s. Other parameters are shown in Table 1 below.

[0095] Table 1 Initial Settings of Simulation Parameters

[0096]

[0097]

[0098] Combination Figure 4 The attitude control loop converged rapidly, stabilizing the attitude after 50 seconds, completing three-axis stable attitude control. The control accuracy after stabilization was better than 1×10⁻⁶. -3 °, attitude stability better than 1×10 -4 ° / s, proving that the dual closed-loop attitude control system designed in this paper can complete high-precision three-axis attitude control during the operation of the thruster, and that the momentum wheel does not remain in a reasonable range during the control process.

[0099] Combination Figure 5 The displacement of the composite actuator successfully compensated for the thrust eccentricity torque of the thruster, and the exponential convergence disturbance observer converged rapidly, completing convergence approximately 15 seconds after the start of observation. No divergence was observed after convergence, and the observation accuracy was better than 1×10⁻⁶. -5 Nm. When the slider movement causes a change in the thrust eccentricity torque, the observer can also track the change well, proving that the control strategy of exponentially convergent disturbance observer plus discrete PID can effectively eliminate thrust eccentricity error.

[0100] The above describes a composite attitude control method for the orbital maneuvering phase of a micro / nano satellite, which can effectively overcome thrust eccentricity torque, achieve high-precision attitude control during thruster operation, and the control system has high stability.

Claims

1. A composite attitude control method for the orbital maneuvering phase of a micro / nano satellite, characterized in that, The steps are as follows: Step 1: Construct a composite actuator based on a zero-momentum gear train and a two-dimensional translational mechanism; The composite actuator uses a zero-momentum gear train as a single slider in a two-dimensional translational mechanism; Step 2: Establish and optimize the satellite attitude dynamics model and the translational dynamics model of the composite actuator, taking into account the inertial principal axis offset and the additional disturbance torque; Step 3: Design an exponential convergence disturbance observer based on the motion characteristics of the composite actuator to observe the thrust eccentricity torque in real time; Step 4: Based on the exponentially convergent disturbance observer, design the attitude control loop MPC controller and the thrust eccentricity torque compensation discrete PID controller. The attitude control loop MPC controller and the thrust eccentricity torque compensation discrete PID controller together constitute a dual closed-loop composite attitude control system to achieve high-precision attitude stability control of the satellite during thruster operation.

2. The attitude composite control method for the orbit change maneuvering phase of a micro / nano satellite according to claim 1, characterized in that, In the second step, a satellite attitude dynamics model considering inertial principal axis offset and additional perturbation torque is established and optimized, as follows: The satellite attitude dynamics model is as follows: In the formula: ω e Let be the angular velocity of this system relative to the target system. Let A be the angular acceleration of this system relative to the target system. e Let ω be the attitude transformation matrix from the target system to the home system. d Let be the angular velocity of the target system relative to the orbital system within the target frame. U represents the angular acceleration of the target system relative to the orbital system within the target system. d These are considered unknown disturbances, including disturbance factors such as thrust disturbance torque and environmental disturbance torque; J S Let J be the moment of inertia of the satellite shell in this system. C Let A be the moment of inertia of the composite actuator in this system. bo Let ω be the rotation matrix from the orbital system to the home system. oi C is the angular velocity of the orbital frame relative to the inertial frame. W J is the installation matrix of the zero-momentum gear train of the composite actuator in this system. W The moment of inertia of the zero-momentum gear train section of the composite actuator. This refers to the angular acceleration of the zero-momentum gear train section of the composite actuator.

3. The attitude composite control method for the orbit change maneuvering phase of a micro / nano satellite according to claim 2, characterized in that, In the second step, the translational dynamics model of the composite actuator is as follows: Translational dynamics model of the composite actuator: In the formula: F W m is the resultant force acting on the system when the composite actuator moves in translation. W For the quality of composite actuators, m B For the remaining mass of the satellite excluding the composite actuator, F env For space environment forces, F t For thruster thrust, r B The location of the satellite's center of mass within this system. Let the velocity of the satellite's center of mass within this system be denoted as . Let the position acceleration of the satellite's center of mass within this system be denoted as . The radius vector velocity of the composite actuator in its own system within the inertial frame is given. p is the radius-vector acceleration of the composite actuator in its own system within an inertial frame. W ω represents the position of the composite actuator within its own system in the inertial frame. bi The angular velocity of the satellite relative to its orbital system. This is the angular acceleration of the satellite system relative to its orbital system.

4. The attitude composite control method for the orbit change maneuvering phase of a micro / nano satellite according to claim 3, characterized in that, In the third step, an exponentially convergent disturbance observer is designed based on the motion characteristics of the composite actuator to observe the thrust eccentricity torque in real time, as follows: The exponentially convergent disturbance observer is: in, Let Z be the observations of the exponentially convergent interference observer, K be the auxiliary parameter, and Z be the converged result. h is the derivative of the convergent result. W J represents the angular momentum of the zero-momentum wheel in the compound actuator. S Let J be the moment of inertia of the satellite shell in this system. C Let ω be the moment of inertia of the composite actuator in this system. do Let be the angular velocity of the target system relative to the orbital system. U is the angular acceleration of the target system relative to the orbital system. d Consider it an unknown interference; Since micro-thrusters do not exhibit the rapid combustion and rapid change of the center of mass seen in solid thrusters, the thrust variation during operation is not significant. Therefore, the eccentric torque generated by the micro-thruster can be treated as a slow, time-varying disturbance. It is certain that the observed exponent converges to the disturbance d, and the convergence accuracy depends on the value of parameter K.

5. The attitude composite control method for the orbit change maneuvering phase of a micro / nano satellite according to claim 4, characterized in that, Step 4: Based on the exponentially convergent disturbance observer, design an attitude control loop MPC controller and a thrust eccentricity torque compensation discrete PID controller. The attitude control loop MPC controller and the thrust eccentricity torque compensation discrete PID controller together constitute a dual closed-loop composite attitude control system to achieve high-precision attitude stability control of the satellite during thruster operation, as detailed below: The attitude control loop discretizes and linearizes the satellite attitude dynamics model and the translational dynamics model of the composite actuator, and designs a linear MPC controller to obtain the optimal control input for the momentum wheel; the compensation control loop uses the output value of the thrust eccentric torque disturbance observer as the input of the PID controller and the desired slider displacement as the controller output. The two-dimensional translational mechanism drives the zero momentum wheel system to complete the closed-loop control with constant acceleration. The attitude control loop uses a zero-momentum wheel system as the actuator to perform three-axis stability control of the satellite, while the compensation control loop uses a mass moment actuator to adjust the position of the satellite system's center of mass in real time to minimize the thrust eccentricity torque. To address the nonlinearity and multiple constraints in attitude control of micro and nano satellites, a linear MPC control algorithm is selected to design the attitude law, thereby considering all constraints of the system at the design level.

6. The attitude composite control method for the orbit change maneuver phase of a micro / nano satellite according to claim 5, characterized in that, In the fourth step, the MPC control algorithm is designed, as follows: First, the satellite attitude dynamics model and the translational dynamics model of the composite actuator are discretized. Then, the state prediction time domain is defined as N. p Design the MPC control algorithm; The prediction equation in the prediction layer at time k is expressed as: X k+1|k =Φx k|k +S x,k Δx k|k +S u,k Δu W,k|k +S d,k ΔU k|k In the formula: Among them, S u,k Let S be the control matrix sequence at time k. x,k Let S be the state matrix sequence at time k. d,k Let B be the sequence of interference matrices at time k. u,k Let B be the control moment matrix at time k. d,k Let ΔU be the error moment matrix at time k. k|k Let A be the sequence of disturbance torques at time k. k Let A be the state matrix at time k. k+1 To predict the state matrix at time k+1, Let Φ be the state matrix at time k under state i-1 of the counting variables, where i and j are both counting variables, and x is the state matrix at time k. k|k This is the initial state. For the state parameters at the corresponding time, Δu W,k|k ,Δu W,k+1|k …Δu W,k+Np|k N represents the magnitude of the change in the control torque of the momentum wheel under the corresponding state. p To control the time domain, X k+1|k The state prediction sequence from time k to time k+1; Δx k|k Let ΔT be the state input sequence in the time domain predicted at time k in incremental form. k|k The expected input sequence in the time domain at time k is represented in incremental form. The objective function is set as follows: In the formula: J is the objective function; on the right side of the equation, the first term represents the weighted sum of errors, the second term represents the weighted sum of inputs, and the third term represents the terminal error; Q, R, and F are the weight matrices for their respective terms; x is the state variable; x(k+i,k) is the predicted state variable at time k to time k+i; u W The control torque for the momentum wheel is Δu. W (k+i|k) represents the change in the predicted momentum wheel control torque at time k to time k+1; The MPC problem with finite-time constraints at time k is described as follows: min J k (x k|k ,D k ) wrtΔu k s.t.u k+1|k ∈U x k+i|k ∈X,i=1,2,…,N p -1 Δx(k+1)=A(x 0,i )Δx(k)+B u (x 0,i )Δu W (k)+B d (x 0,i )ΔU d (k) Where: X, X f Let U represent the set of state constraints in the prediction time domain, and let Δu represent the set of input constraints in the prediction time domain. k u represents the change in the momentum wheel control torque at time k. k+1|k ΔU represents the two-stage change in predicted momentum from time k to time k+1. d (k) represents the increment of the disturbance torque at time k relative to the previous time, and Δx(k+1) represents the state increment at time k+1 relative to time k. To solve the objective function, the above problem is transformed into a QP problem, given the initial state x. k|k Then, the planning algorithm will calculate a set of predicted optimal control inputs. And the predicted optimal state trajectory Then predict the first value Δu of the input. k|k As the control input for the current cycle.

7. The attitude composite control method for the orbit change maneuvering phase of a micro / nano satellite according to claim 6, characterized in that, In the fourth step, the position control algorithm for the composite actuator, namely the PID control algorithm, is designed as follows: The thrust eccentricity moment compensation loop exponentially converges to interfere with the observer's observations. As input, its control objective is An incremental discrete PID control algorithm is used to control the position of the composite actuator; Define the discrete period as t, then the incremental PID control algorithm is designed as follows: In the formula: the displacement p of the composite actuator in the y and z directions W =[p y ;p z ], and All are observations of the observer in the y, z directions at the corresponding time, t p t d t i All of these are parameters to be designed. This represents the displacement of the composite actuator or its position vector within the system.

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