Adaptive robust sliding mode attitude control method for disk satellites

Abstract

An adaptive robust sliding mode attitude control method for a disk satellite belongs to the technical field of disk satellite attitude control. This invention addresses existing sliding mode variable structure control methods for disk satellite attitude control, addressing issues such as the lack of consideration of moment of inertia uncertainty and environmental torque interference, resulting in low control accuracy. The method includes placing mass blocks on the roll and pitch axes; establishing a disk satellite attitude dynamics model and expanding it to obtain disk satellite expansion dynamics equations corresponding to the electric propulsion force eccentric torque and aerodynamic torque; defining an adaptive robust sliding mode function based on the disk satellite's current and desired attitudes; and designing a Lyapunov function based on the adaptive robust sliding mode function. Finally, combining the adaptive robust sliding mode control law to obtain attitude control laws for the roll and pitch axes, calculating the displacements of the mass blocks on the x and y axes of the body coordinate system, and simultaneously combining the adaptive laws for the roll and pitch axes to perform attitude control. This invention is used for attitude control of disk satellites.

Description

Technical Field

[0001] The invention relates to an adaptive robust sliding mode attitude control method for a disk satellite, belonging to the technical field of disk satellite attitude control. Background Art

[0002] A disk satellite is a flat-shaped satellite with low mass, multiple payloads and high-density stacking. Its typical structure is a sandwich plate made of composite materials, such as Figures 1 to 3 As shown. It has a diameter of 1m, a thickness of 2.5cm, and a mass of approximately 2.5kg. The surface area of ​​its single disk is much larger than the total surface area of ​​any traditional cube satellite. There is an equipment compartment in the middle of the satellite, which can be used to install electronic equipment with different functions according to mission requirements. Subsystems such as attitude control, orbit control, and power supply are distributed and installed in the interlayer inside the satellite. Figure 1 and Figure 3 shown.

[0003] The internal components of the disk satellite are mainly divided into the following three parts: measurement components, execution components and central control unit. The measurement components mainly include digital sun sensors, fiber optic gyroscope components, star sensors, magnetometers and GNSS receivers; the execution components mainly include mass torque, magnetic torquer and propulsion system; flywheel, magnetic torquer and central control unit are mainly composed of computers (shared with the integrated electronic system computer). The internal structure of the disk satellite equipped with the mission module is as follows: Figure 4 shown.

[0004] Due to the special geometric shape of disk satellites and the uncertainty of distributed components, it is difficult to install a complete control system for the entire satellite. Therefore, there is currently no attitude control system that is particularly suitable for disk satellites.

[0005] During satellite on-orbit operation, the presence of environmental torques and the uncertainty of the moment of inertia parameters require the designed attitude control law to possess high robustness and parameter adaptability. Sliding mode variable structure control is an effective control method, but traditional sliding mode variable structure control methods require bounds on system uncertainty and lack observational estimation of environmental torques, making them incapable of achieving attitude stability control for disk satellites. Summary of the Invention

[0006] Aiming at the problem that the existing sliding mode variable structure control method for disk satellite attitude control does not consider the uncertainty of moment of inertia and environmental torque interference, and has low control accuracy, the present invention provides an adaptive robust sliding mode attitude control method for disk satellite.

[0007] The present invention provides an adaptive robust sliding mode attitude control method for a disk satellite, comprising:

[0008] Four guide rails are installed in a square shape inside the disk satellite, with a mass block placed on each rail. One pair of rails is parallel to the x-axis of the satellite's coordinate system, and the other pair is parallel to the y-axis of the satellite's coordinate system. The x-axis direction of the satellite's coordinate system is set as the roll axis direction, and the y-axis direction of the satellite's coordinate system is set as the pitch axis direction.

[0009] Establish an attitude dynamics model for the disk satellite, and expand the attitude dynamics model based on the current attitude of the disk satellite to obtain the disk satellite expansion dynamics equation corresponding to the electric propulsion force eccentric torque and aerodynamic torque;

[0010] An adaptive robust sliding mode function is defined based on the current attitude and expected attitude of the disk satellite, and then a Lyapunov function is designed based on the adaptive robust sliding mode function.

[0011] The adaptive robust sliding mode control law of the roll axis is defined according to the disk satellite expansion dynamics equation, and the attitude control law of the roll axis is obtained by combining the Lyapunov function. The displacement of the mass block on the y-axis of the body coordinate system is then calculated using the attitude control law of the roll axis.

[0012] At the same time, the adaptive robust sliding mode control law of the pitch axis is defined according to the disk satellite expansion dynamics equation, and the attitude control law of the pitch axis is obtained by combining the Lyapunov function. The displacement of the mass block on the x-axis of the body coordinate system is then calculated using the attitude control law of the pitch axis.

[0013] In order to make the derivative of the Lyapunov function less than zero, satisfy the sliding mode condition, and make the satellite control system stably move to the sliding mode surface, the adaptive laws of the roll axis and pitch axis are designed;

[0014] Finally, the motion of the mass block is controlled by an actuator based on the displacement of the mass block on the y-axis of the body coordinate system, the displacement of the mass block on the x-axis of the body coordinate system, and the adaptive laws of the roll axis and pitch axis. The two mass blocks on the two guide rails in the same direction synchronously produce the same displacement under the same driving force of the actuator, so that the current attitude of the disk satellite tends to the desired attitude, realizing the three-axis stable attitude control of the disk satellite.

[0015] According to the adaptive robust sliding mode attitude control method of the disk satellite of the present invention, the attitude dynamics model of the disk satellite is:

[0016]

[0017] Where I c ∈R 3×3 is the satellite’s moment of inertia matrix, ω B =[ω x ω y ω z ] Tis the angular velocity of the satellite body coordinate system relative to the inertial coordinate system, ω x 、ω y 、ω z is the angular velocity ω B The x-axis, y-axis, and z-axis components of T t is the eccentric torque of the electric propulsion force, T d is the aerodynamic torque, T h is the environmental interference torque, T m is the disturbance torque generated by the movement of the four mass blocks on the satellite body, M d The time-varying interference torque;

[0018] The time-varying slow disturbance torque M is obtained by using the disturbance observer d Observed values and make compensation.

[0019] According to the adaptive robust sliding mode attitude control method of the disk satellite of the present invention, the disk satellite deployment dynamics equation is:

[0020]

[0021] Where I x , I y , I z is the moment of inertia matrix I c The x-axis, y-axis, and z-axis components of

[0022]

[0023] is the roll angle, θ is the pitch angle, ψ is the yaw angle, ω o is the orbital angular velocity, m x , m y are the masses of the mass blocks moving on the x-axis and y-axis respectively, m is the total mass of the satellite system, F tx 、F ty 、F tz are the x-axis, y-axis and z-axis components of the electric propulsion force in the body coordinate system, l x Characterizes the displacement of the mass block on the x-axis of the body coordinate system, l y Characterizes the displacement of the mass block on the y-axis of the body coordinate system, r x 、r y is the position r of the electric propulsion force action point in the satellite body coordinate system t The x-axis and y-axis components, T mx 、T my 、T mz is the disturbance torque T m In the x-axis, y-axis and z-axis components of the satellite body coordinate system, F px 、F py 、Fpz are the x-axis, y-axis and z-axis components of the aerodynamic force in the satellite body coordinate system,

[0024] Angular velocity ω B for:

[0025]

[0026] According to the adaptive robust sliding mode attitude control method of the disk satellite of the present invention, the adaptive robust sliding mode function s is defined as:

[0027]

[0028] Where s1(t) is the roll angle adaptive robust sliding mode function, s2(t) is the pitch angle adaptive robust sliding mode function, c1 is the roll angle error coefficient, c2 is the pitch angle error coefficient, e1(t) is the roll angle attitude tracking error, e2(t) is the pitch angle tracking error, e2(t) = θ d -θ, is the desired roll angle, θ d is the desired pitch angle;

[0029] The derivative of the adaptive robust sliding mode function is:

[0030]

[0031] According to the adaptive robust sliding mode attitude control method of the disk satellite of the present invention, the Lyapunov function V is defined as:

[0032]

[0033] Will As the moment of inertia matrix I c The estimated value of the moment of inertia matrix I c The error value γ is a constant, γ>0.

[0034] According to the adaptive robust sliding mode attitude control method of the magnetic disk satellite of the present invention, the adaptive robust sliding mode control law u1 of the roll axis is defined as follows:

[0035]

[0036] Expand the Lyapunov function V and substitute the variables in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function V to obtain the Lyapunov function V1 of the roll axis:

[0037]

[0038] γ1 is the γ corresponding to the roll axis, for The x-axis component of For I x The estimated value of

[0039] according to The adaptive robust sliding mode control law u1 of the roll axis is obtained as:

[0040]

[0041] Where k1 is the coefficient of the approach rate of the roll axis, η1 is the switching function coefficient of the roll axis, and sign is the switching function.

[0042] According to the adaptive robust sliding mode attitude control method of the magnetic disk satellite of the present invention, the displacement l of the mass block on the y-axis of the body coordinate system is calculated. y for:

[0043]

[0044] According to the adaptive robust sliding mode attitude control method of the magnetic disk satellite of the present invention, the adaptive robust sliding mode control law u2 of the pitch axis is defined as follows:

[0045]

[0046] Then expand the Lyapunov function V and substitute the variables in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function V to obtain the Lyapunov function V2 of the pitch axis:

[0047]

[0048] γ2 is the γ corresponding to the pitch axis, for The y-axis component of For I y The estimated value of

[0049] according to The adaptive robust sliding mode control law u2 of the pitch axis is obtained as:

[0050]

[0051] Where k2 is the coefficient of the approach rate of the pitch axis, and η2 is the switching function coefficient of the pitch axis.

[0052] According to the adaptive robust sliding mode attitude control method of the magnetic disk satellite of the present invention, the displacement l of the mass block on the x-axis of the body coordinate system is calculated. x for:

[0053]

[0054] According to the adaptive robust sliding mode attitude control method of a magnetic disk satellite of the present invention, the adaptive laws of the roll axis and the pitch axis are defined as:

[0055]

[0056] Beneficial Effects of the Invention: The inventive method, combining electric propulsion technology with mass-torque technology and the geometric configuration of a disk satellite, enables more stable and accurate satellite attitude adjustment and control. The inventive method utilizes thrust eccentric torque as the satellite's active control torque and aerodynamic torque as the satellite's auxiliary control torque to achieve three-axis stable control of the satellite.

[0057] Aiming at the problems of unknown disturbance, nonlinearity, parameter uncertainty and other issues in the disk satellite model, the method of the present invention designs a disturbance observer for estimating the disturbance torque, thereby controlling the torque compensation and realizing high-precision attitude control. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a schematic diagram of the structure of the disk satellite of the present invention with four guide rails and an internal equipment compartment installed;

[0059] Figure 2 yes Figure 1 Side view of

[0060] Figure 3 This is a schematic diagram of the structure of the inner interlayer of the disk satellite of the present invention;

[0061] Figure 4 This is a schematic diagram of the internal structure of the disk satellite equipped with the mission module;

[0062] Figure 5 is a flow chart of the adaptive robust sliding mode attitude control method for a disk satellite according to the present invention;

[0063] Figure 6 It is a schematic diagram of Euler axis / angle attitude description;

[0064] Figure 7 It is the force analysis diagram of the mass-moment system;

[0065] Figure 8 It is a schematic diagram of the source of thrust eccentric torque;

[0066] Figure 9 It is a schematic diagram of the x-axis interference torque;

[0067] Figure 10 It is a schematic diagram of the y-axis interference torque;

[0068] Figure 11 It is a schematic diagram of the z-axis interference torque;

[0069] Figure 12 It is the curve diagram of disk satellite attitude angle change;

[0070] Figure 13 It is a curve diagram of the change of disk satellite attitude angular rate;

[0071] Figure 14 It is the changing curve of adaptive robust sliding mode function;

[0072] Figure 15 It is a flow chart of the disk satellite control system. DETAILED DESCRIPTION

[0073] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0074] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0075] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0076] Specific implementation method 1. Combination Figures 1 to 5 As shown, the present invention provides an adaptive robust sliding mode attitude control method for a disk satellite, comprising:

[0077] Four guide rails are installed in a square shape inside the disk satellite, with a mass block placed on each rail. One pair of rails is parallel to the x-axis of the satellite's coordinate system, and the other pair is parallel to the y-axis of the satellite's coordinate system. The x-axis direction of the satellite's coordinate system is set as the roll axis direction, and the y-axis direction of the satellite's coordinate system is set as the pitch axis direction.

[0078] Establish an attitude dynamics model for the disk satellite, and expand the attitude dynamics model based on the current attitude of the disk satellite to obtain the disk satellite expansion dynamics equation corresponding to the electric propulsion force eccentric torque and aerodynamic torque;

[0079] An adaptive robust sliding mode function is defined based on the current attitude and expected attitude of the disk satellite, and then a Lyapunov function is designed based on the adaptive robust sliding mode function.

[0080] The adaptive robust sliding mode control law of the roll axis is defined according to the disk satellite expansion dynamics equation, and the attitude control law of the roll axis is obtained by combining the Lyapunov function. The displacement of the mass block on the y-axis of the body coordinate system is then calculated using the attitude control law of the roll axis.

[0081] At the same time, the adaptive robust sliding mode control law of the pitch axis is defined according to the disk satellite expansion dynamics equation, and the attitude control law of the pitch axis is obtained by combining the Lyapunov function. The displacement of the mass block on the x-axis of the body coordinate system is then calculated using the attitude control law of the pitch axis.

[0082] In order to make the derivative of the Lyapunov function less than zero, satisfy the sliding mode condition, and make the satellite control system stably move to the sliding mode surface, the adaptive laws of the roll axis and pitch axis are designed;

[0083] Finally, the motion of the mass block is controlled by an actuator based on the displacement of the mass block on the y-axis of the body coordinate system, the displacement of the mass block on the x-axis of the body coordinate system, and the adaptive laws of the roll axis and pitch axis. The two mass blocks on the two guide rails in the same direction synchronously produce the same displacement under the same driving force of the actuator, so that the current attitude of the disk satellite tends to the desired attitude, realizing the three-axis stable attitude control of the disk satellite.

[0084] Given the unique geometry of disk satellites and the limited normal height of the disk surface, a disturbance observer combined with adaptive robust sliding mode control can be used to control the attitude of disk satellites based on mass-torque technology and electric propulsion. This invention utilizes thrust eccentric torque as the satellite's active control torque and aerodynamic torque as the auxiliary control torque to achieve three-axis stabilization of the satellite. By analyzing actuators such as the electric thruster and mass-torque, an accurate satellite attitude dynamics and kinematics model is established. The impact of environmental disturbance torques, the additional disturbance torque generated by mass motion on the satellite body, the uncertainty of the moment of inertia, and the thrust eccentric torque on the attitude control of disk satellites is analyzed. This embodiment utilizes an observer to estimate internal and external disturbances and designs an adaptive robust sliding mode variable structure controller for disturbance feedforward compensation, ultimately achieving stable attitude control of disk satellites.

[0085] Electric propulsion can provide long-term continuous small thrust, and based on the structural characteristics of disk satellites, it can perform low-orbit flight missions in the direction of low resistance; aerodynamic assisted control uses mass moment control technology to generate control torque by configuring active mass blocks and using small displacements of the mass blocks.

[0086] The mass blocks of disk satellites are usually installed in the direction of the main axis of the spacecraft. The configurations of the mass blocks mainly include single slider, double slider and triple slider. The specific number and position of the movable mass blocks are determined by the geometric characteristics of the satellite and the attitude control requirements. In this embodiment, the mass blocks are installed on the roll axis and pitch axis according to the geometric structure and control requirements of the disk satellite. Considering the mechanical interference phenomenon during the movement process and the additional interference torque generated by the movement, in this embodiment, two pairs of guide rails are perpendicular to each other, and a bisymmetrical layout of four mass blocks is adopted. The two symmetrical mass blocks on the two parallel guide rails receive instructions simultaneously. Driven by the same driving force, they move the same displacement inside the satellite, thereby changing the center of mass of the satellite system and achieving attitude adjustment.

[0087] The satellite attitude kinematic model is generally expressed in the form of quaternions. A coordinate system can be rotated around the Euler axis e by the Euler angle Φ to achieve coincidence with any coordinate system. The diagram of quaternion description of attitude is as follows Figure 6 As shown in the figure. a y a z a is the initial inertial coordinate system, x b y b z b is the spacecraft body coordinate system.

[0088] The attitude kinematic equation described by quaternion is:

[0089]

[0090] Where q=[q0 q v ] T is the attitude quaternion, q0 is the quaternion standard, q v is the vector part of the quaternion, q v × Represented by the vector q v The generated antisymmetric matrix, E3, represents the 3×3 identity matrix.

[0091] The attitude error quaternion q of the disk satellite e for:

[0092]

[0093] In the formula is quaternion multiplication; q d The quaternion representing the desired attitude. Since the quaternion itself has constraints, we only need to take q e The vector part of is used as the input parameter of the controller.

[0094] Define common coordinate systems, O I X I Y I ZI is the geocentric equatorial inertial coordinate system, O o X o Y o Z o is the satellite orbit coordinate system, O b x b y b z b is the spacecraft body coordinate system. b is the satellite body mass center, O s is the center of mass of the system. c is the main moment of inertia of the disk satellite system, m o is the mass of the satellite itself, R c is the position vector of the satellite's mass center in the inertial coordinate system, dm is the satellite's micro-element mass, and r represents the position vector of the system's mass center relative to the micro-element of the mass block in the inertial coordinate system. When the mass block moves, the mass block inside the satellite is considered as a point mass, and mass represents the active point mass. The force analysis diagram of the entire disk satellite system is shown in the figure below. Figure 7 shown.

[0095] Furthermore, the attitude dynamics model of the disk satellite is:

[0096]

[0097] Where I c ∈R 3×3 is the satellite’s moment of inertia matrix, ω B =[ω x ω y ω z ] T is the angular velocity of the satellite body coordinate system relative to the inertial coordinate system, ω x 、ω y 、ω z is the angular velocity ω B The x-axis, y-axis, and z-axis components of T t is the eccentric torque of the electric propulsion force, is the aerodynamic torque, T h is the environmental disturbance torque, T m is the disturbance torque generated by the movement of the four mass blocks on the satellite body, M d It is the time-varying interference torque;

[0098] The time-varying slow disturbance torque M is obtained by using the exponential convergence disturbance observer d Observed values and make compensation.

[0099] Throughout the attitude control process, the thrust eccentric torque acts as the active control torque, and the aerodynamic torque acts as the auxiliary control torque, ensuring three-axis stable attitude control of the disk satellite. The following is a detailed analysis of the active control torque and time-varying fast disturbance torque acting on the disk satellite.

[0100] 1) Additional interference torque generated by the motion of the mass block:

[0101] Since the mass block inside the satellite only moves in a straight line along the x-axis and y-axis of the satellite body, during the entire satellite attitude process, the forces acting on the mass block mainly include the internal constraint force of the guide rail and the active driving force provided by the motor. Therefore, only two-dimensional plane motion equations are needed to accurately describe the movement of the mass block inside the satellite.

[0102] According to the Euler equation and the momentum theorem of a mass system, the translational dynamics equation of the moving mass block inside the satellite is established:

[0103]

[0104]

[0105] Where p x , p y A is the coordinate representation of the mass block moving along the x-axis and y-axis in this system; ib F is the coordinate transformation matrix from the satellite system to the inertial system; ax， F ay is the constraint force of the satellite system on the two mass blocks; F cx , F cy is the active control force of the satellite system on the two mass blocks; G is the gravity of the satellite system.

[0106] According to the force of the entire disk satellite system, the force F exerted by the mass block on the satellite body i for:

[0107]

[0108] Where m i is the mass of the mass block, where i is x, y, R is the position vector of the satellite body micro-element mass in the inertial system, represents the position vector of the mass block in this system, and g is the gravitational acceleration.

[0109] The interference torque T generated by the movement of the four mass blocks on the satellite body m for:

[0110]

[0111] 2) Environmental interference torque:

[0112] Since the aerodynamic drag of low-orbit satellites is much greater than other environmental forces, the environmental interference force can be approximately simplified to aerodynamic drag. The entire control system only considers the impact of the aerodynamic torque generated by the variable center of mass on the satellite attitude.

[0113] T d =-r s ×(F g +F s +F m +F d )≈-r s ×F d ,

[0114] Where r s is the change in the center of mass position of the satellite system, It is the representation of the center of mass of the entire satellite system in this system.

[0115] F g is the gravity gradient force, F s is the solar radiation force, F m is the geomagnetic force, F d For gas power.

[0116] The expression of aerodynamic force is:

[0117]

[0118] Where C D is the drag coefficient; ρ is the atmospheric density; V R A is the speed of the atmosphere relative to the aircraft; p is the area of ​​the frontal surface; v is the unit vector in the direction of the incoming flow.

[0119] r s ,F d Substitute into the aerodynamic torque equation:

[0120]

[0121] Where S represents the area of ​​the frontal surface, C bo is the coordinate transformation matrix from the orbital system to the current system; F p is the expression of aerodynamic force in this system:

[0122] F p =C bo F d .

[0123] 3) Thrust eccentric torque:

[0124] Ideally, the thrust of the electric propulsion system is along the x-axis of the satellite system, r tis the position of the thrust application point within the satellite's system, ideally [-0.5, 0, 0] m. When the disk satellite's attitude is controlled to a three-axis stable state, the thrust of the electric thruster ideally passes through the satellite's center of mass, generating no eccentric thrust torque and thus no interference with the satellite's attitude control. If the disk satellite does not reach the ideal attitude, the satellite actively controls the eccentric torque generated by the electric thruster to adjust to the desired attitude.

[0125] In the actual working process of the electric propulsion system, the eccentric thrust moment is caused by the fact that the thrust vector does not pass through the system center of mass of the aircraft. The sources of the eccentric thrust moment are mainly the following six aspects:

[0126] like Figure 8 In the figure, α is the angular deviation between the disk satellite's inertial axis and the geometric longitudinal axis; β is the installation angle deviation of the electric thruster; κ is the angular deviation of the thrust vector relative to the longitudinal axis of the electric thruster; l C is the distance deviation between the disk satellite's center of mass and the satellite's geometric longitudinal axis; l M The distance deviation caused by the misalignment between the longitudinal axis of the electric propulsion system and the geometric longitudinal axis of the satellite; l T It is the distance deviation caused by the misalignment between the thrust vector and the longitudinal axis of the electric propulsion unit.

[0127] F t is the thrust vector of the electric thruster, and its ideal value is [0.02, 0, 0] T N, when the satellite is not adjusted to the desired attitude, the eccentric torque T of the electric thruster t for:

[0128] T t =(r t -r s )×F t =△r×F t .

[0129] Due to the motion of the mass block inside the disk satellite, the center of mass of the satellite system shifts by r s The thrust arm of the electric propulsion system is changed from the original r t becomes Δr, and the expansion formula of the force arm is:

[0130]

[0131] The expansion formula of the resulting thrust eccentric torque is:

[0132]

[0133] 3) Disturbance observer design:

[0134] Because the attitude control system model of a disk satellite is subject to unknown disturbances, nonlinearity, coupling, and parameter uncertainty, an exponential disturbance observer is designed. This observer equates the difference between the actual object and the nominal model caused by external disturbances and model parameter changes to the control input, thereby observing the equivalent disturbance. This observer then introduces equivalent compensation into the control to achieve complete control of the disturbance.

[0135] For the disk satellite model, the main disturbances to be considered are: the additional disturbance torque T generated by the motion of the mass block inside the satellite m and additional moment of inertia Among them I m is the additional moment of inertia, the satellite's environmental disturbance torque T h , the remanent magnetic moment T of the satellite system b and unknown environmental disturbance torque M s etc., the sum of the slow time-varying interference of the satellite system is M d :

[0136]

[0137] Since the fast time-varying disturbance generated by the mass motion has a great influence on the satellite attitude control system, this factor needs to be considered when designing the subsequent attitude control law. Therefore, the disturbance observer only needs to observe and compensate for the slow time-varying disturbance of the satellite system, that is, the disturbance observer only needs to observe and track the slow time-varying disturbance M of the satellite system. d and compensate for the disturbance, thus improving the control system accuracy.

[0138] Through the interference analysis of the satellite body, the complete attitude dynamics equation is obtained:

[0139]

[0140] The disturbance torque observed by the observer is The bandwidth of the disturbance observer is L, which is a positive number. The equation for designing and constructing the disturbance observer is as follows:

[0141]

[0142] Define an auxiliary variable parameter z:

[0143]

[0144] Taking the derivative we get:

[0145]

[0146] So the disturbance observer is designed as:

[0147]

[0148] The disturbance error of the disturbance observer is defined as e, and we have:

[0149]

[0150] The interference error is:

[0151]

[0152] Due to the additional interference torque T m It is related to the position, velocity and acceleration of the mass block and is a fast time-varying interference. This interference torque will cause chattering in the satellite system and requires real-time observation of the change of this torque. Therefore, there is no need for an interference observer to observe and compensate for it. The remaining interference torques are slow time-varying interferences and the change of the interference torque is much slower than the update dynamics of the observer, so it can be assumed that The error equation of the observer is obtained as:

[0153]

[0154] The analytical solution of the observer error is:

[0155] e(t)=e(t0)e -Lt ,

[0156] Where t0 is the initial time.

[0157] Since the value of e(t0) is deterministic, the designed observer can converge exponentially to the satellite system’s slow time-varying interference M d .

[0158] Due to the unknown disturbance, nonlinearity, parameter uncertainty and environmental interference in the disk satellite attitude control system model, the disk satellite attitude control system has non-negligible system interference. Figures 9 to 11 It can be seen that the value of the interference torque is about 10 -7 N·m, indicating that the designed disturbance observer can observe equivalent disturbances and track the disturbance torque. By using the disturbance observer to observe the disturbance torque, equivalent compensation is introduced into the control system, achieving complete control of the disturbance, improving the accuracy of the disk satellite attitude control system, and reducing the uncertainty of the disk satellite model, thereby ensuring the stability and accuracy of the attitude control system simulation model.

[0159] 4) Attitude control law design and stability description:

[0160] Because the mass moves only on guide rails along the x- and y-axes, attitude control for disk satellites requires only designing mass moment control laws for the roll and pitch axes. The thrust eccentric moment serves as the satellite's active control moment, while the aerodynamic moment serves as the satellite's auxiliary control moment. Yaw attitude is controlled by the thrust eccentric moment. The control torque generated by the cross product of center of mass displacement and electric propulsion force actively controls the satellite's attitude, thus achieving three-axis stable control for the entire disk satellite control system.

[0161] Going further, the dynamic equation of disk satellite expansion is:

[0162]

[0163] Where I x , I y , I z is the moment of inertia matrix I c The x-axis, y-axis, and z-axis components of

[0164]

[0165] is the roll angle, θ is the pitch angle, ψ is the yaw angle, ω o is the orbital angular velocity, m x , m y are the masses of the mass blocks moving on the x-axis and y-axis respectively, m is the total mass of the satellite system, F tx 、F ty 、F tz are the x-axis, y-axis and z-axis components of the electric propulsion force in the body coordinate system, l x Characterizes the displacement of the mass block on the x-axis of the body coordinate system, l y Characterizes the displacement of the mass block on the y-axis of the body coordinate system, r x 、r y is the position r of the electric propulsion force action point in the satellite body coordinate system t The x-axis and y-axis components, [r x , r y ,0] T is the installation position of the electric thruster, T mx 、T my 、T mz is the disturbance torque T m In the x-axis, y-axis and z-axis components of the satellite body coordinate system, F px 、F py 、F pz are the x-axis, y-axis and z-axis components of the aerodynamic force in the satellite body coordinate system,

[0166] Angular velocity ω B for:

[0167]

[0168] In this embodiment, the adaptive robust sliding mode function s is defined as:

[0169]

[0170] Where s1(t) is the roll angle adaptive robust sliding mode function, s2(t) is the pitch angle adaptive robust sliding mode function, c1 is the roll angle error coefficient, c2 is the pitch angle error coefficient, c1 and c2 are constants greater than 0;

[0171] e1(t) is the roll angle attitude tracking error, e2(t) is the pitch angle tracking error, e2(t) = θ d -θ, is the desired roll angle, θ d is the desired pitch angle;

[0172] The derivative of the adaptive robust sliding mode function is:

[0173]

[0174] Define the Lyapunov function V as:

[0175]

[0176] Will As the moment of inertia matrix I c The estimated value of the moment of inertia matrix I c The error value γ is a constant, γ>0.

[0177] Define the adaptive robust sliding mode control law u1 of the roll axis:

[0178]

[0179] Expand the Lyapunov function V and substitute the variables in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function V to obtain the Lyapunov function V1 of the roll axis:

[0180]

[0181] γ1 is the γ corresponding to the roll axis, for The x-axis component of For I x The estimated value of

[0182] According to the derivative of the Lyapunov function The adaptive robust sliding mode control law u1 of the roll axis is obtained as:

[0183]

[0184] Where k1 is the coefficient of the approach rate of the roll axis, η1 is the switching function coefficient of the roll axis, and sign is the switching function.

[0185] Calculate the displacement l of the mass block on the y-axis of the body coordinate system y for:

[0186]

[0187] Since the two-stage sliding mode control law includes a switching function and a sliding mode control law, the switching function sign(s) can effectively offset the external disturbance term, so the disturbance term does not need to be considered when designing the sliding mode control law.

[0188] Similarly, define the adaptive robust sliding mode control law u2 of the pitch axis:

[0189]

[0190] Then expand the Lyapunov function V and substitute the variables in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function V to obtain the Lyapunov function V2 of the pitch axis:

[0191]

[0192] γ2 is the γ corresponding to the pitch axis, for The y-axis component of For I y The estimated value of

[0193] According to the Lyapunov function The adaptive robust sliding mode control law u2 of the pitch axis is obtained as:

[0194]

[0195] Where k2 is the coefficient of the approach rate of the pitch axis, and η2 is the switching function coefficient of the pitch axis.

[0196] Calculate the displacement l of the mass block on the x-axis of the body coordinate system x for:

[0197]

[0198] In this embodiment, in order to ensure that the derivative of the Lyapunov function is less than zero and satisfies the sliding mode condition, the sliding mode function of the satellite control system can stably move to the sliding mode surface, the adaptive laws of the roll axis and pitch axis are defined as:

[0199]

[0200] The following proves that the derivative of the Lyapunov function is less than zero, thereby proving that the sliding mode function system of the satellite control system satisfies the sliding mode conditions and converges to the sliding mode region. This only proves that the derivative of the Lyapunov function is less than zero for the roll axis, and the same is true for the pitch axis.

[0201]

[0202]

[0203] According to the LaSalle invariance principle, the above closed-loop system is an asymptotically stable system if and only if s = 0, The above proof shows that the system meets the sliding mode conditions and can converge to the sliding mode region. The disk satellite control system has good stability and accuracy.

[0204] Combine Figure 15 ,A simulation experiment of the disk satellite attitude control system is carried out. ,The relevant parameter settings such as the disk satellite basic ,parameters, initial orbit parameters and simulation parameters are shown in Table 1.

[0205] Table 1 Disk satellite parameters

[0206]

[0207]

[0208] Figure 12 Figure 1 shows the attitude angle curve for a magnetic disk satellite. The roll channel returns to the desired attitude in approximately 300 seconds, the roll channel returns to the desired attitude in approximately 450 seconds, and the yaw angle returns to a stable attitude in approximately 360 seconds. When the satellite system issues a command, the actuator adjusts the attitude, causing the attitude angle to fluctuate and then gradually stabilize. The designed magnetic disk satellite attitude control system ensures timely command response and accurate attitude adjustment.

[0209] Figure 13Figure 1 shows the attitude angular velocity curve for a magnetic disk satellite. The roll channel returns to the desired attitude around 350s, the roll channel returns to the desired attitude around 420s, and the yaw angle returns to a stable attitude around 400s. When the satellite system issues a command, the actuator performs attitude adjustments, causing attitude angle fluctuations with a peak value of and gradually stabilizing. The resulting angular velocity changes range from -0.00014° / s to 0.00014° / s. The designed magnetic disk satellite attitude control system ensures timely command response and accurate attitude adjustments.

[0210] Figure 14 is the sliding mode function curve of the disk satellite, and the value of the sliding mode function is about 10 -4 The sliding mode function of the roll axis approaches zero around 300s, and the sliding mode function of the pitch axis approaches zero around 450s. The sliding mode function eventually approaches zero, indicating that the moving point can approach the sliding mode region.

[0211] The simulation results above show that, throughout the attitude control process, the thrust eccentric torque acts as the active control torque, and the aerodynamic torque acts as the auxiliary control torque, enabling three-axis stable attitude control of the disk satellite. The designed adaptive robust sliding mode control law enables stable and accurate attitude adjustment and control, enabling the satellite to operate stably in the desired attitude.

[0212] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in conjunction with other described embodiments.

Claims

1. An adaptive robust sliding mode attitude control method for a disk satellite, characterized in that include, Four guide rails are installed in a square shape inside the disk satellite, with a mass block placed on each rail. One pair of rails is parallel to the x-axis of the satellite's coordinate system, and the other pair is parallel to the y-axis of the satellite's coordinate system. The x-axis direction of the satellite's coordinate system is set as the roll axis direction, and the y-axis direction of the satellite's coordinate system is set as the pitch axis direction. Establish an attitude dynamics model for the disk satellite, and expand the attitude dynamics model based on the current attitude of the disk satellite to obtain the disk satellite expansion dynamics equation corresponding to the electric propulsion force eccentric torque and aerodynamic torque; An adaptive robust sliding mode function is defined based on the current attitude and expected attitude of the disk satellite, and then a Lyapunov function is designed based on the adaptive robust sliding mode function. The adaptive robust sliding mode control law of the roll axis is defined according to the disk satellite expansion dynamics equation, and the attitude control law of the roll axis is obtained by combining the Lyapunov function. The displacement of the mass block on the y-axis of the body coordinate system is then calculated using the attitude control law of the roll axis. At the same time, the adaptive robust sliding mode control law of the pitch axis is defined according to the disk satellite expansion dynamics equation, and the attitude control law of the pitch axis is obtained by combining the Lyapunov function. The displacement of the mass block on the x-axis of the body coordinate system is then calculated using the attitude control law of the pitch axis. In order to make the derivative of the Lyapunov function less than zero, satisfy the sliding mode condition, and make the satellite control system stably move to the sliding mode surface, the adaptive laws of the roll axis and pitch axis are designed; Finally, the motion of the mass block is controlled by an actuator based on the displacement of the mass block on the y-axis of the body coordinate system, the displacement of the mass block on the x-axis of the body coordinate system, and the adaptive laws of the roll and pitch axes. The two masses on the two guide rails in the same direction produce the same displacement synchronously under the same driving force of the actuator, so that the current attitude of the disk satellite tends to the desired attitude, realizing the three-axis stable attitude control of the disk satellite. The attitude dynamics model of the disk satellite is: Where I c ∈R 3×3 is the satellite’s moment of inertia matrix, ω B =[ω x ω y ω z ] T is the angular velocity of the satellite body coordinate system relative to the inertial coordinate system, ω x 、ω y 、ω z is the angular velocity ω B The x-axis, y-axis, and z-axis components of T t is the eccentric torque of the electric propulsion force, T d is the aerodynamic torque, T h is the environmental disturbance torque, T m is the disturbance torque generated by the movement of the four mass blocks on the satellite body, M d It is the time-varying interference torque; The time-varying slow disturbance torque M is obtained by using the disturbance observer d Observed values and make compensation.

2. The adaptive robust sliding mode attitude control method for a disk satellite according to claim 1, characterized in that: The dynamic equation of disk satellite expansion is: Where I x , I y , I z is the moment of inertia matrix I c The x-axis, y-axis, and z-axis components of is the roll angle, θ is the pitch angle, ψ is the yaw angle, ω o is the orbital angular velocity, m x , m y are the masses of the mass blocks moving on the x-axis and y-axis respectively, m is the total mass of the satellite system, F tx 、F ty 、F tz are the x-axis, y-axis and z-axis components of the electric propulsion force in the body coordinate system, l x Characterizes the displacement of the mass block on the x-axis of the body coordinate system, l y Characterizes the displacement of the mass block on the y-axis of the body coordinate system, r x 、r y is the position r of the electric propulsion force action point in the satellite body coordinate system t The x-axis and y-axis components, T mx 、T my 、T mz is the disturbance torque T m In the x-axis, y-axis and z-axis components of the satellite body coordinate system, F px 、F py 、F pz are the x-axis, y-axis and z-axis components of the aerodynamic force in the satellite body coordinate system, Angular velocity ω B for:

3. The adaptive robust sliding mode attitude control method for a disk satellite according to claim 2, characterized in that: Define the adaptive robust sliding mode function s as: Where s1(t) is the roll angle adaptive robust sliding mode function, s2(t) is the pitch angle adaptive robust sliding mode function, c1 is the roll angle error coefficient, c2 is the pitch angle error coefficient, e1(t) is the roll angle attitude tracking error, e2(t) is the pitch angle tracking error, e2(t) = θ d -θ, is the desired roll angle, θ d is the desired pitch angle; The derivative of the adaptive robust sliding mode function is:

4. The adaptive robust sliding mode attitude control method for a disk satellite according to claim 3, characterized in that: Define the Lyapunov function V as: Will As the moment of inertia matrix I c The estimated value of the moment of inertia matrix I c The error value γ is a constant, γ>

0.

5. The adaptive robust sliding mode attitude control method for a disk satellite according to claim 4, characterized in that: Define the adaptive robust sliding mode control law u1 of the roll axis: Expand the Lyapunov function V and substitute the variables in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function to obtain the Lyapunov function V1 of the roll axis: γ1 is the γ corresponding to the roll axis, for The x-axis component of For I x The estimated value of according to The adaptive robust sliding mode control law u1 of the roll axis is obtained as: Where k1 is the coefficient of the approach rate of the roll axis, η1 is the switching function coefficient of the roll axis, and sign is the switching function.

6. The adaptive robust sliding mode attitude control method for a disk satellite according to claim 5, characterized in that: Calculate the displacement l of the mass block on the y-axis of the body coordinate system y for:

7. The adaptive robust sliding mode attitude control method for a disk satellite according to claim 6, characterized in that: Define the adaptive robust sliding mode control law u2 of the pitch axis: Then expand the Lyapunov function V and substitute the variables in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function V to obtain the Lyapunov function V2 of the pitch axis: γ2 is the γ corresponding to the pitch axis, for The y-axis component of For I y The estimated value of according to The adaptive robust sliding mode control law u2 of the pitch axis is obtained as: Where k2 is the coefficient of the approach rate of the pitch axis, and η2 is the switching function coefficient of the pitch axis.

8. The adaptive robust sliding mode attitude control method for a disk satellite according to claim 7, characterized in that: Calculate the displacement l of the mass block on the x-axis of the body coordinate system x for:

9. The adaptive robust sliding mode attitude control method for a disk satellite according to claim 8, characterized in that: The adaptive laws for the roll and pitch axes are defined as:

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