CN116853527A - Self-adaptive robust sliding mode attitude control method for magnetic disk satellite - Google Patents
Self-adaptive robust sliding mode attitude control method for magnetic disk satellite Download PDFInfo
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Abstract
A self-adaptive robust sliding mode attitude control method for a disk satellite belongs to the technical field of disk satellite attitude control. The invention aims at solving the problems that the existing sliding mode variable structure control method is used for controlling the attitude of a disk satellite, the uncertainty of moment of inertia and the interference of environmental moment are not considered, the control precision is low and the like. Comprises a mass block arranged on a rolling shaft and a pitching shaft; establishing an attitude dynamics model of a disk satellite, and expanding to obtain a disk satellite expansion dynamics equation corresponding to the eccentric moment and aerodynamic moment of electric propulsion; defining a self-adaptive robust sliding mode function based on the current gesture and the expected gesture of the disk satellite, and designing a Lyapunov function based on the self-adaptive robust sliding mode function; and combining the self-adaptive robust sliding mode control law to obtain the attitude control laws of the rolling shaft and the pitching shaft, calculating the displacement of the mass block in the x-axis and the y-axis of the body coordinate system, and simultaneously combining the self-adaptive laws of the rolling shaft and the pitching shaft to perform attitude control. The invention is used for controlling the attitude of the disk satellite.
Description
Technical Field
The invention relates to a self-adaptive robust sliding mode attitude control method of a magnetic disk satellite, and belongs to the technical field of magnetic disk satellite attitude control.
Background
The disk satellite is a flat-shaped configuration, low mass, multi-load carrying and high density stacking capable flat-plate satellite, the typical construction of which is a sandwich plate of composite material, as shown in fig. 1-3. The diameter of the material is 1m, the thickness of the material is 2.5cm, and the mass of the material is about 2.5kg. Its individual disk surface area is much larger than the total surface area of any conventional cube satellite. The equipment cabin is arranged in the middle of the satellite, electronic equipment with different functions can be installed according to task requirements, and the structures of attitude control, orbit control, power supply aliquoting systems and the like which are installed in the interlayer inside the satellite in a distributed mode are shown in fig. 1 and 3.
The internal components of the disk satellite are mainly divided into the following three parts, namely a measuring part, an executing part and a central control unit. The measuring component mainly comprises a digital sun sensor, an optical fiber gyro assembly, a star sensor, a magnetometer, a GNSS receiver and the like; the execution part mainly comprises a mass moment, a magnetic torquer, a propulsion system and the like; the flywheel and magnetic torquer central control unit mainly comprises a computer (shared by the computer and a comprehensive electronic system). The internal structure of the disk satellite on which the task module is mounted is shown in fig. 4.
Because of the uncertainty of the special geometry and distribution components of the magnetic disk satellites, it is difficult to install a complete control system for the whole satellite, and therefore, no attitude control system particularly suitable for the magnetic disk satellites exists at present.
The existence of environmental moment and uncertainty of rotational inertia parameters during the in-orbit operation of satellites require a high robustness and parameter adaptation capability of the designed attitude control law. The sliding mode variable structure control is an effective control method, but the traditional sliding mode variable structure control method needs a boundary value of system uncertainty, and does not observe and estimate environmental moment, so that stable attitude control of a magnetic disk satellite cannot be realized.
Disclosure of Invention
Aiming at the problems that the existing sliding mode variable structure control method is used for controlling the attitude of a disk satellite, rotational inertia uncertainty and environmental torque interference are not considered, and the control precision is low, the invention provides a self-adaptive robust sliding mode attitude control method of the disk satellite.
The invention relates to a self-adaptive robust sliding mode attitude control method of a disk satellite, which comprises the following steps of,
four guide rails are arranged in the magnetic disk satellite in a square outline, and a mass block is arranged on each guide rail; one pair of guide rails is parallel to the x axis of the satellite body coordinate system, and the other pair of guide rails is parallel to the y axis of the satellite body coordinate system; setting the x-axis direction of the satellite body coordinate system as the rolling axis direction and the y-axis direction of the satellite body coordinate system as the pitching axis direction;
establishing a posture dynamics model of the magnetic disk satellite, and expanding the posture dynamics model based on the current posture of the magnetic disk satellite to obtain a magnetic disk satellite expansion dynamics equation corresponding to the eccentric moment and the aerodynamic moment of the electric propulsion;
defining a self-adaptive robust sliding mode function based on the current gesture and the expected gesture of the disk satellite, and designing a Lyapunov function based on the self-adaptive robust sliding mode function;
defining a self-adaptive robust sliding mode control law of a rolling shaft according to a magnetic disk satellite expansion dynamics equation, obtaining a posture control law of the rolling shaft by combining with a Lyapunov function, and calculating the posture control law of the rolling shaft to obtain the displacement of the mass block on the y axis of the body coordinate system;
meanwhile, defining a self-adaptive robust sliding mode control law of a pitching axis according to a magnetic disk satellite unfolding dynamics equation, obtaining a posture control law of the pitching axis by combining with a Lyapunov function, and obtaining displacement of the mass block in an x-axis of a body coordinate system by calculating the posture control law of the pitching axis;
in order to enable the derivative of the Lyapunov function to be smaller than zero, meet the sliding mode condition, enable the satellite control system to stably move to the sliding mode surface, and design the self-adaptive law of a rolling shaft and a pitching shaft;
and finally, controlling the mass block to move through an actuating mechanism according to 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 self-adaptive laws of the rolling shaft and the pitching shaft, wherein the two mass blocks on the two guide rails in the same direction synchronously generate the same displacement under the same driving force of the actuating mechanism, so that the current posture of the magnetic disk satellite tends to the expected posture, and the triaxial stable posture control of the magnetic disk satellite is realized.
According to the self-adaptive robust sliding mode attitude control method of the disk satellite, the attitude dynamics model of the disk satellite is as follows:
in which I c ∈R 3×3 Is the rotational inertia matrix of the satellite, omega B ＝[ω x ω y ω z ] T Is the angular velocity omega of the satellite body coordinate system relative to the inertial coordinate system x 、ω y 、ω z Is the angular velocity omega B X-axis, y-axis and z-axis components of (a); t (T) t For the eccentric moment of electric propulsion, T d Is aerodynamic moment, T h T is the environmental disturbance moment m The disturbing moment generated by the movement of four mass blocks to the satellite body is M d Is a time-varying slow disturbance moment;
observing time-varying interference moment M by adopting interference observer d Is of the observed value of (2)And compensates.
According to the self-adaptive robust sliding mode attitude control method of the disk satellite, the expansion dynamics equation of the disk satellite is as follows:
in which I x ，I y ，I z For moment of inertia matrix I c X-axis, y-axis and z-axis components of (c):
is the roll angle, θ is the pitch angle, ψ is the yaw angle, ω o For track angular velocity, m x ，m y Mass block masses moving on x axis and y axis respectively, m is total mass of satellite system, F tx 、F ty 、F tz For the x-axis, y-axis and z-axis components of the electric propulsion in the body coordinate system, l x Representing the displacement of the mass block on the x-axis of the body coordinate system, l y Representing displacement of mass block on y axis of body coordinate system, r x 、r y For the position r of the electric propulsion action point in the satellite body coordinate system t X-axis and y-axis components of (C), T mx 、T my 、T mz As disturbance moment T m In the x-axis, y-axis and z-axis components of the satellite body coordinate system, F px 、F py 、F pz For the x-axis, y-axis and z-axis components of aerodynamic forces in the satellite body coordinate system,
angular velocity omega B The method comprises the following steps:
according to the self-adaptive robust sliding mode attitude control method of the disk satellite, the self-adaptive robust sliding mode function s is defined as follows:
s in 1 (t) is a roll angle adaptive robust sliding mode function, s 2 (t) is a pitch adaptive robust sliding mode function, c 1 C is the roll angle error coefficient 2 E is the pitch angle error coefficient 1 (t) is the roll angle attitude tracking error,e 2 (t) is pitch attitude tracking error, e 2 (t)＝θ d -θ，/>To expect the roll angle, θ d Is the desired pitch angle;
the derivative of the adaptive robust sliding mode function is:
according to the self-adaptive robust sliding mode attitude control method of the disk satellite, a Lyapunov function V is defined as follows:
will beAs a moment of inertia matrix I c The estimated value of (2) is the moment of inertia matrix I c Error value +.>Gamma is a constant, gamma > 0.
According to the self-adaptive robust sliding mode attitude control method of the disk satellite, the self-adaptive robust sliding mode control law u of the rolling shaft is defined 1 ：
Developing Lyapunov function V, andsubstituting the variable in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function V to obtain the Lyapunov function V of the rolling shaft 1 ：
γ 1 For the gamma of the corresponding roll axis,is->X-axis component of>Is I x Is used for the estimation of the (c),
according toObtaining a self-adaptive robust sliding mode control law u of the rolling shaft 1 The method comprises the following steps:
k in 1 Is the coefficient of approach rate of the rolling shaft, eta 1 Is the switching function coefficient of the rolling shaft, sign is the switching function.
According to the self-adaptive robust sliding mode attitude control method of the disk satellite, the displacement l of the mass block on the y axis of the body coordinate system is calculated y The method comprises the following steps:
according to the self-adaptive robust sliding mode attitude control method of the disk satellite, a self-adaptive robust sliding mode control law u of a pitching axis is defined 2 ：
Expanding the Lyapunov function, substituting the variable in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function to obtain the Lyapunov function of the pitching axis 2 ：
γ 2 For y corresponding to the pitch axis,is->Y-axis component of>Is I y Is used for the estimation of the (c),
according toObtaining a self-adaptive robust sliding mode control law u of a pitching axis 2 The method comprises the following steps:
k in 2 Is the coefficient of approach rate of pitching axis, eta 2 Is the switching function coefficient of the pitch axis.
According to the self-adaptive robust sliding mode attitude control method of the disk satellite, the displacement l of the mass block on the x axis of the body coordinate system is calculated x The method comprises the following steps:
according to the self-adaptive robust sliding mode attitude control method of the disk satellite, the self-adaptive law of the rolling shaft and the pitching shaft is defined as:
the invention has the beneficial effects that: the method combines the electric propulsion technology, the mass moment technology and the geometric configuration of the magnetic disk satellite for design, so that the satellite can realize posture adjustment and posture control more stably and accurately. The method uses the thrust eccentric moment as the active control moment of the satellite and the aerodynamic moment as the auxiliary control moment of the satellite, so as to realize the triaxial stable control of the satellite.
The method designs the disturbance observer aiming at the problems of unknown disturbance, nonlinearity, uncertain parameters and the like of the disk satellite model, and is used for estimating disturbance moment so as to control moment compensation and realize high-precision attitude control.
Drawings
FIG. 1 is a schematic view of the structure of a disk satellite with four guide rails and an internal equipment compartment;
FIG. 2 is a side view of FIG. 1;
FIG. 3 is a schematic illustration of the internal interlayer structure of a disk satellite according to the present invention;
FIG. 4 is a schematic diagram of the internal architecture of a disk satellite with a task module mounted thereon;
FIG. 5 is a flow chart of an adaptive robust sliding mode attitude control method for a disk satellite according to the present invention;
FIG. 6 is a schematic illustration of Euler axis/angular pose descriptions;
FIG. 7 is a diagram of a mass moment system force analysis;
FIG. 8 is a schematic diagram of a thrust eccentric moment source;
FIG. 9 is a schematic diagram of an x-axis disturbance moment;
FIG. 10 is a schematic diagram of y-axis disturbance moment;
FIG. 11 is a schematic illustration of a z-axis disturbance moment;
FIG. 12 is a graph of disk satellite attitude angle change;
FIG. 13 is a graph of disk satellite attitude angular rate change;
FIG. 14 is a graph of adaptive robust sliding mode function variation;
fig. 15 is a flow chart diagram of a disk satellite control system.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
The present invention provides a method for controlling the attitude of a self-adaptive robust sliding mode of a disk satellite, which comprises,
four guide rails are arranged in the magnetic disk satellite in a square outline, and a mass block is arranged on each guide rail; one pair of guide rails is parallel to the x axis of the satellite body coordinate system, and the other pair of guide rails is parallel to the y axis of the satellite body coordinate system; setting the x-axis direction of the satellite body coordinate system as the rolling axis direction and the y-axis direction of the satellite body coordinate system as the pitching axis direction;
establishing a posture dynamics model of the magnetic disk satellite, and expanding the posture dynamics model based on the current posture of the magnetic disk satellite to obtain a magnetic disk satellite expansion dynamics equation corresponding to the eccentric moment and the aerodynamic moment of the electric propulsion;
defining a self-adaptive robust sliding mode function based on the current gesture and the expected gesture of the disk satellite, and designing a Lyapunov function based on the self-adaptive robust sliding mode function;
defining a self-adaptive robust sliding mode control law of a rolling shaft according to a magnetic disk satellite expansion dynamics equation, obtaining a posture control law of the rolling shaft by combining with a Lyapunov function, and calculating the posture control law of the rolling shaft to obtain the displacement of the mass block on the y axis of the body coordinate system;
meanwhile, defining a self-adaptive robust sliding mode control law of a pitching axis according to a magnetic disk satellite unfolding dynamics equation, obtaining a posture control law of the pitching axis by combining with a Lyapunov function, and obtaining displacement of the mass block in an x-axis of a body coordinate system by calculating the posture control law of the pitching axis;
in order to enable the derivative of the Lyapunov function to be smaller than zero, meet the sliding mode condition, enable the satellite control system to stably move to the sliding mode surface, and design the self-adaptive law of a rolling shaft and a pitching shaft;
and finally, controlling the mass block to move through an actuating mechanism according to 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 self-adaptive laws of the rolling shaft and the pitching shaft, wherein the two mass blocks on the two guide rails in the same direction synchronously generate the same displacement under the same driving force of the actuating mechanism, so that the current posture of the magnetic disk satellite tends to the expected posture, and the triaxial stable posture control of the magnetic disk satellite is realized.
Aiming at the characteristic that the magnetic disk satellite has special geometric shape and limited normal height of the disk surface, the magnetic disk satellite attitude control can be carried out by adopting a mode of combining an interference observer and self-adaptive robust sliding mode control based on a mass moment technology and an electric propulsion technology. The invention uses the thrust eccentric moment as the active control moment of the satellite and the aerodynamic moment as the auxiliary control moment of the satellite, thereby realizing the triaxial stable control of the satellite. By analyzing the executing mechanisms such as the electric propeller, the mass moment and the like, an accurate satellite attitude dynamics and kinematics model is established, and the influence of the environment interference moment, the additional interference moment generated by the mass block motion on the satellite body, the uncertainty of the moment of inertia and the thrust eccentric moment on the disk satellite attitude control is analyzed. According to the embodiment, the internal and external interference can be estimated by using the observer, the adaptive robust sliding mode variable structure controller is designed to perform interference feedforward compensation, and finally the stable control of the attitude of the magnetic disk satellite is realized.
The electric propulsion force can provide long-term continuous small thrust, and a low-orbit flight task is executed along a low-resistance direction based on the structural characteristics of a magnetic disk satellite; aerodynamic force assisted control utilizes a mass moment control technique to generate a control moment by configuring a movable mass and utilizing a small displacement of the mass.
The mass blocks of the magnetic disk satellite are usually arranged in the main shaft direction of the aircraft, and the configuration of the mass blocks mainly comprises a single slide block, a double slide block, a three slide block and the like. The specific number and location of the movable masses is determined by the geometric characteristics of the satellites and attitude control requirements. In this embodiment, the mass is mounted on the roll axis and pitch axis according to the geometry and control requirements of the disk satellites. In consideration of the mechanical interference phenomenon in the motion process and the additional interference moment generated by the motion, in the embodiment, two pairs of guide rails are perpendicular to each other, and the double symmetrical layout of four mass blocks is adopted. The two symmetrical mass blocks positioned on the two parallel guide rails simultaneously receive instructions, and move the same displacement in the satellite under the drive of the same driving force, so that the mass center of the satellite system is changed, and the gesture adjustment is realized.
The satellite attitude kinematic model generally adopts a quaternion expression form, and the superposition with any coordinate system can be realized by rotating the Euler angle phi around the Euler axis e by one coordinate system. The quaternion description gesture is schematically shown in fig. 6. X in the figure a y a z a X is the initial inertial coordinate system b y b z b Is a spacecraft body coordinate system.
The gesture kinematics equation described by the quaternion is:
in which q= [ q ] 0 q v ] T Is a gesture quaternion, q 0 Is a quaternion scale part, q v Is a quaternion vector part, q v × Represented by vector q v The resulting antisymmetric matrix, E 3 Representing a 3 x 3 identity matrix.
Attitude error quaternion q of magnetic disk satellite e The method comprises the following steps:
in the middle ofIs quaternion multiplication; q d The quaternion representing the expected gesture only needs to take q because the quaternion is self-contained e Is used as the input parameter of the controller.
Defining a common coordinate system, O I X I Y I Z I Is the equatorial inertial coordinate system of the earth, O o X o Y o Z o Is a satellite orbit coordinate system, O b x b y b z b Is a spacecraft body coordinate system. Wherein O is b Is the mass center of the satellite body, O s Is the system centroid. I c Is the main moment of inertia, m, of a disk satellite system o R is the mass of the satellite body c The method is characterized in that the method is a position vector of a satellite centroid in an inertial coordinate system, dm is the satellite body infinitesimal mass, and r represents the position vector of the system centroid relative to a mass infinitesimal under the inertial system; the mass inside the satellite is considered as a mass when it moves, mass representing an active mass. The force analysis diagram of the whole system of the disk satellite is shown in fig. 7.
Further, the attitude dynamics model of the disk satellite is:
in which I c ∈R 3×3 Is the rotational inertia matrix of the satellite, omega B ＝[ω x ω y ω z ] T Is the angular velocity omega of the satellite body coordinate system relative to the inertial coordinate system x 、ω y 、ω z Is the angular velocity omega B X-axis, y-axis and z-axis components of (a); t (T) t Is an electric propulsion eccentric moment, an aerodynamic moment and T h Is the environmental interferenceMoment, T m The disturbing moment generated by the movement of four mass blocks to the satellite body is M d Is a time-varying slow disturbance moment;
observing by adopting an exponential convergence disturbance observer to obtain time-varying slow disturbance moment M d Is of the observed value of (2)And compensates.
In the whole attitude control process, the thrust eccentric moment is used as an active control moment, the aerodynamic moment is used as an auxiliary control moment, and the triaxial stable attitude control is carried out on the magnetic disk satellite. The active control moment and the time-varying fast disturbance moment which are applied to the magnetic disk satellite are analyzed in detail in the following.
1) Additional disturbance moment generated by mass movement:
because the mass block only moves in the satellite along the x axis and the y axis of the satellite body in a linear direction, the mass block receives forces mainly including internal constraint force of the guide rail and active driving force provided by the motor in the whole satellite attitude process, and therefore the movement of the mass block in the satellite can be accurately described only by a two-dimensional plane movement equation.
According to Euler equation and particle system momentum theorem, establishing a translational dynamics equation of a motion mass block in the satellite:
wherein p is x ，p y Coordinate representation of the mass under the system for x-axis and y-axis motion; a is that ib The coordinate transformation matrix from the satellite body system to the inertial system; f (F) ax， F ay The restraining force of the satellite system on the two mass blocks; f (F) cx ，F cy Active control force of the satellite system on the two mass blocks; g is the gravity of the satellite system.
According to the stress condition of the whole system of the disk satellite, the acting force F of the mass block to the satellite body i The method comprises the following steps:
m is in i The mass is a mass block, wherein i is x, y, R is a position vector of satellite body infinitesimal mass in an inertial system, and g is gravitational acceleration.
Interference moment T generated by movement of four mass blocks on satellite body m The method comprises the following steps:
2) Environmental disturbance moment:
since the low-orbit satellite aerodynamic drag is much greater than other environmental forces, the environmental disturbance forces can be approximately reduced to aerodynamic drag. The whole control system only considers the influence of aerodynamic moment generated by the variable centroid on the satellite attitude.
T d ＝-r s ×(F g +F s +F m +F d )≈-r s ×F d ，
Wherein r is s For a change in the position of the centroid of the satellite system,is an under-the-body representation of the centroid of the entire satellite system.
F g For gravity gradient force, F s For solar radiation force, F m Is geomagnetic force, F d Is aerodynamic.
The aerodynamic force is expressed as:
c in the formula D Is a resistanceA force coefficient; ρ is the atmospheric density; v (V) R Is the velocity of the atmosphere relative to the aircraft; a is that p Is the area of the head-on flow; v is the unit vector in the incoming flow direction.
Will r s ,F d Take into the aerodynamic moment equation:
s represents the area of the head-on flow surface, C bo A coordinate transformation matrix from a track system to a body system; f (F) p The representation of aerodynamic forces under the system:
F p ＝C bo F d 。
3) Thrust eccentric moment:
ideally, the thrust of the electric propeller is along the x-axis direction of the satellite body system, r t For the position of the thrust point of the motive force in the satellite body system, the ideal value is [ -0.5,0]m. When the attitude of the magnetic disk satellite is controlled to be in a triaxial stable state, the thrust of the electric propeller passes through the mass center of the satellite in an ideal state, and the eccentric moment of the thrust cannot be generated, so that the attitude control of the satellite cannot be interfered. When the magnetic disk satellite does not reach the ideal posture, the satellite is actively controlled by the eccentric moment generated by the electric propeller, so that the satellite is adjusted to the required posture.
In the actual working process of the electric propeller, the thrust eccentric moment is caused by that the generated thrust vector does not pass through the system centroid of the aircraft, the sources of the thrust eccentric moment mainly have the following six aspects,
as shown in fig. 8. Alpha in the figure is the angle deviation between the disk satellite inertial main shaft and the geometric longitudinal shaft; beta is the installation angle deviation of the electric propeller; kappa is the angular deviation of the thrust vector relative to the longitudinal axis of the electric propeller; l (L) C The distance deviation between the mass center of the magnetic disk satellite and the geometric longitudinal axis of the satellite is shown; l (L) M The distance deviation caused by the misalignment of the longitudinal axis of the electric propeller and the geometric longitudinal axis of the satellite is avoided; l (L) T Which is the distance deviation caused by the misalignment of the thrust vector and the longitudinal axis of the electric propeller.
F t Is the thrust vector of the electric propeller, and the ideal value is [0.02,0,0 ]] T N, when the satellite is not adjusted to the expected attitude, the eccentric moment T of the electric propeller t The method comprises the following steps:
T t ＝(r t -r s )×F t ＝△r×F t 。
the satellite system centroid shifts by r due to mass movement inside the disk satellite s The force arm of the electric propeller thrust force is changed from the original r t Becomes Deltar, and the expansion of the acting force arm is as follows:
the expansion of the thrust eccentric moment thus produced is:
3) Interference observer design:
because the attitude control system model of the magnetic disk satellite has unknown disturbance, nonlinearity, coupling, parameter uncertainty and other factors, an exponential disturbance observer is designed, and the difference between an actual object and a nominal model caused by external disturbance and model parameter change is equivalent to a control input end, namely equivalent disturbance is observed. And introducing equivalent compensation in the control to realize complete control of interference.
For the disk satellite model, the mainly considered disturbances are: additional disturbance moment T generated by movement of mass inside satellite m And additional moment of inertiaWherein I is m For additional moment of inertia, the satellite's ambient disturbance moment T h Residual moment T of satellite system b And unknown ambient disturbance moment M s The sum of the slow time-varying interference of the satellite system is M d ：
Since the fast time-varying disturbances generated by the mass motion have a great influence on the satellite attitude control system, this factor needs to be taken into account in the subsequent attitude control law design. So the interference observer only needs to observe and compensate the satellite system slow time-varying interference, namely the interference observer only needs to observe and track the satellite system slow time-varying interference M d And compensates for the disturbance, improving control system accuracy.
And obtaining a complete attitude kinetic equation through interference analysis of the satellite body:
the disturbance moment observed by the observer isThe bandwidth of the interference observer is L, which is a positive number; the equations for designing and constructing the disturbance observer are as follows:
defining an auxiliary variable parameter z:
and (3) deriving to obtain:
the disturbance observer is designed to:
defining the interference error of the interference observer as e, and:
the interference error is:
due to additional disturbance moment T m The disturbance moment can bring buffeting phenomenon to the satellite system, and the change condition of the moment needs to be observed in real time, so that an interference observer is not needed to observe and compensate the disturbance moment. The rest disturbance moment belongs to slow time-varying disturbance, the disturbance moment change is far slower than the update dynamic of the observer, so that can be assumedThe error equation for the observer is obtained as:
the error resolution of the observer is:
e(t)＝e(t 0 )e -Lt ，
t is in 0 Is the initial time.
Due to e (t) 0 ) The value of (2) can be determined, and the designed observer can exponentially converge on the slow time-varying interference M of the satellite system d 。
Because the magnetic disk satellite attitude control system model has the problems of unknown disturbance, nonlinearity, parameter uncertainty, environmental interference and the like, the magnetic disk satellite attitude control system has non-negligible system interference. As can be seen from fig. 9 to 11, the disturbance torque has a value of about 10 -7 N.m, description of designThe disturbance observer of (2) can observe equivalent disturbance and track disturbance moment. By means of the observation value of the disturbance observer to the disturbance moment, equivalent compensation is introduced in control, complete control of disturbance is achieved, accuracy of a magnetic disk satellite attitude control system is improved, uncertainty of a magnetic disk satellite model is reduced, and therefore stability and accuracy of an attitude control system simulation model are guaranteed.
4) Posture control law design and stability description:
because the mass block only moves on the guide rails on the x axis and the y axis, the attitude control of the magnetic disk satellite only needs to design the mass moment control law of the rolling axis and the pitching axis, the thrust eccentric moment is the active control moment of the satellite, and the aerodynamic moment is the auxiliary control moment of the satellite, so that the attitude control of the satellite is realized. The gesture of yaw axis is controlled by the eccentric moment of thrust, and the satellite gesture is actively controlled by the control moment generated by mass center displacement and electric propulsion cross multiplication, so that the whole disk satellite control system realizes triaxial stable control.
Still further, the disk satellite expansion dynamics equation is:
in which I x ，I y ，I z For moment of inertia matrix I c X-axis, y-axis and z-axis components of (c):
is the roll angle, θ is the pitch angle, ψ is the yaw angle, ω o For track angular velocity, m x ，m y Mass block masses moving on x axis and y axis respectively, m is total mass of satellite system, F tx 、F ty 、F tz The x-axis, y-axis and z-axis components of the body coordinate system for electric propulsion，l x Representing the displacement of the mass block on the x-axis of the body coordinate system, l y Representing displacement of mass block on y axis of body coordinate system, r x 、r y For the position r of the electric propulsion action point in the satellite body coordinate system t X-axis, y-axis components, [ r ] x ，r y ，0] T For mounting position of electric propulsion, T mx 、T my 、T mz As disturbance moment T m In the x-axis, y-axis and z-axis components of the satellite body coordinate system, F px 、F py 、F pz For the x-axis, y-axis and z-axis components of aerodynamic forces in the satellite body coordinate system,
angular velocity omega B The method comprises the following steps:
in this embodiment, the adaptive robust sliding mode function s is defined as:
s in 1 (t) is a roll angle adaptive robust sliding mode function, s 2 (t) is a pitch adaptive robust sliding mode function, c 1 C is the roll angle error coefficient 2 C is the pitch angle error coefficient 1 、c 2 Is constant, greater than 0;
e 1 (t) is the roll angle attitude tracking error,e 2 (t) is pitch attitude tracking error, e 2 (t)＝θ d -θ，/>To expect the roll angle, θ d Is the desired pitch angle;
the derivative of the adaptive robust sliding mode function is:
defining Lyapunov function V as:
will beAs a moment of inertia matrix I c The estimated value of (2) is the moment of inertia matrix I c Error value +.>Gamma is a constant, gamma > 0.
Adaptive robust sliding mode control law u defining the roll axis 1 ：
Expanding the Lyapunov function, substituting the variable in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function to obtain the Lyapunov function of the rolling shaft 1 ：
γ 1 For the gamma of the corresponding roll axis,is->X-axis component of>Is I x Is used for the estimation of the (c),
derivative according to Lyapunov functionObtaining a self-adaptive robust sliding mode control law u of the rolling shaft 1 The method comprises the following steps:
k in 1 Is the coefficient of approach rate of the rolling shaft, eta 1 Is the switching function coefficient of the rolling shaft, sign is the switching function.
Calculating to obtain the displacement l of the mass block on the y axis of the body coordinate system y The method comprises the following steps:
the two-stage control law of the sliding mode control comprises a switching function and a sliding mode control law. The switching function sign(s) can effectively counteract the external disturbance term, so that the disturbance term does not need to be considered when designing the sliding mode control law.
Similarly, an adaptive robust sliding mode control law u defining the pitch axis 2 ：
Expanding the Lyapunov function, substituting the variable in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function to obtain the Lyapunov function of the pitching axis 2 ：
γ 2 For y corresponding to the pitch axis,is->Y-axis component of>Is I y Is used for the estimation of the (c),
according to Lyapunov functionObtaining a self-adaptive robust sliding mode control law u of a pitching axis 2 The method comprises the following steps:
k in 2 Is the coefficient of approach rate of pitching axis, eta 2 Is the switching function coefficient of the pitch axis.
Calculating to obtain the displacement l of the mass block on the x axis of the body coordinate system x The method comprises the following steps:
in this embodiment, in order to ensure that the derivative of the Lyapunov function is smaller than zero, and the sliding mode condition is satisfied, the sliding mode function of the satellite control system can stably move to the sliding mode surface, and the adaptive law of the rolling axis and the pitching axis is defined as:
the following demonstrates that the derivative of the Lyapunov function is less than zero, thus demonstrating that the sliding mode function system of the satellite control system can meet the sliding mode condition and the system can converge to the sliding mode region. Only the derivative of the Lyapunov function of the roll axis is demonstrated to be less than zero, the same thing as the pitch axis.
According to lasale invariance principle, the above-described closed loop system is a progressive stabilizing system which, if and only if s=0,the above-mentioned demonstration shows that the system meets the slip form condition, can converge to the slip form area, the satellite control system of the magnetic disk has very good stability and accuracy.
In connection with fig. 15, a simulation experiment is performed on a disk satellite attitude control system, and relevant parameter settings such as a disk satellite basic parameter, an orbit initial parameter, a simulation parameter and the like are shown in table 1.
TABLE 1 disk satellite parameters
FIG. 12 is a graph of disk satellite attitude angle change with roll path at about 300s for a desired attitude, at about 450s for a roll path, and at about 360s for a steady attitude. After the satellite system sends out an instruction, the executing mechanism adjusts the gesture, the gesture angle fluctuates and gradually tends to a stable state, and the designed magnetic disk satellite gesture control system can respond to the instruction in time and adjust the gesture accurately.
FIG. 13 is a graph of disk satellite attitude angular velocity change with roll path at about 350s for a desired attitude, at about 420s for a desired attitude, and at about 400s for a steady attitude. After the satellite system sends out an instruction, the executing mechanism adjusts the gesture, the gesture angle fluctuates, and the fluctuation peak value is gradually in a stable state. The angular velocity variation results in a range of-0.00014 DEG/s to 0.00014 DEG/s. The designed magnetic disk satellite attitude control system can respond to timely instructions and accurately adjust the attitude.
FIG. 14 is a graph showing the variation of the sliding mode function of a disk satellite, the sliding mode function having a value of about 10 -4 . The sliding mode function of the roll axis approaches zero at around 300s and the sliding mode function of the pitch axis approaches zero at around 450 s. The sliding mode function can eventually go to zero, indicating that the motion point can approach the sliding mode region.
According to the simulation result, in the whole attitude control process, the thrust eccentric moment is used as an active control moment, the aerodynamic moment is used as an auxiliary control moment, and the triaxial stable attitude control of the magnetic disk satellite can be performed. The designed self-adaptive robust sliding mode control law can stably and accurately carry out attitude adjustment and attitude control, so that the satellite can stably operate in an expected attitude.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (10)
1. A self-adaptive robust sliding mode attitude control method of a disk satellite is characterized by comprising the following steps of,
four guide rails are arranged in the magnetic disk satellite in a square outline, and a mass block is arranged on each guide rail; one pair of guide rails is parallel to the x axis of the satellite body coordinate system, and the other pair of guide rails is parallel to the y axis of the satellite body coordinate system; setting the x-axis direction of the satellite body coordinate system as the rolling axis direction and the y-axis direction of the satellite body coordinate system as the pitching axis direction;
establishing a posture dynamics model of the magnetic disk satellite, and expanding the posture dynamics model based on the current posture of the magnetic disk satellite to obtain a magnetic disk satellite expansion dynamics equation corresponding to the eccentric moment and the aerodynamic moment of the electric propulsion;
defining a self-adaptive robust sliding mode function based on the current gesture and the expected gesture of the disk satellite, and designing a Lyapunov function based on the self-adaptive robust sliding mode function;
defining a self-adaptive robust sliding mode control law of a rolling shaft according to a magnetic disk satellite expansion dynamics equation, obtaining a posture control law of the rolling shaft by combining with a Lyapunov function, and calculating the posture control law of the rolling shaft to obtain the displacement of the mass block on the y axis of the body coordinate system;
meanwhile, defining a self-adaptive robust sliding mode control law of a pitching axis according to a magnetic disk satellite unfolding dynamics equation, obtaining a posture control law of the pitching axis by combining with a Lyapunov function, and obtaining displacement of the mass block in an x-axis of a body coordinate system by calculating the posture control law of the pitching axis;
in order to enable the derivative of the Lyapunov function to be smaller than zero, meet the sliding mode condition, enable the satellite control system to stably move to the sliding mode surface, and design the self-adaptive law of a rolling shaft and a pitching shaft;
and finally, controlling the mass block to move through an actuating mechanism according to 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 self-adaptive laws of the rolling shaft and the pitching shaft, wherein the two mass blocks on the two guide rails in the same direction synchronously generate the same displacement under the same driving force of the actuating mechanism, so that the current posture of the magnetic disk satellite tends to the expected posture, and the triaxial stable posture control of the magnetic disk satellite is realized.
2. The method for adaptively controlling the sliding mode attitude of a disk satellite according to claim 1, wherein,
the attitude dynamics model of the disk satellite is as follows:
in which I c ∈R 3×3 Is the rotational inertia matrix of the satellite, omega B ＝[w x w y w z ] T Is the angular velocity omega of the satellite body coordinate system relative to the inertial coordinate system x 、ω y 、ω z Is the angular velocity omega B X-axis, y-axis and z-axis components of (a); t (T) t For the eccentric moment of electric propulsion, T d Is aerodynamic moment, T h T is the environmental disturbance moment m The disturbing moment generated by the movement of four mass blocks to the satellite body is M d Is a time-varying slow disturbance moment;
observing time-varying interference moment M by adopting interference observer d Is of the observed value of (2)And compensates.
3. The method for adaptively controlling the sliding mode attitude of a disk satellite according to claim 2, wherein,
the disk satellite expansion dynamics equation is:
in which I x ，I y ，I z For moment of inertia matrix I c X-axis, y-axis and z-axis components of (c):
is the roll angle, θ is the pitch angle, ψ is the yaw angle, ω o For track angular velocity, m x ，m y Mass block masses moving on x axis and y axis respectively, m is total mass of satellite system, F tx 、F ty 、F tz For the x-axis, y-axis and z-axis components of the electric propulsion in the body coordinate system, l x Representing the displacement of the mass block on the x-axis of the body coordinate system, l y Representing displacement of mass block on y axis of body coordinate system, r x 、r y For the position r of the electric propulsion action point in the satellite body coordinate system t X-axis and y-axis components of (C), T mx 、T my 、T mz As disturbance moment T m In the x-axis, y-axis and z-axis components of the satellite body coordinate system, F px 、F py 、F pz For the x-axis, y-axis and z-axis components of aerodynamic forces in the satellite body coordinate system,
angular velocity omega B The method comprises the following steps:
4. the method for adaptively controlling the sliding mode attitude of a disk satellite according to claim 3, wherein,
defining an adaptive robust sliding mode function s as:
s in 1 (t) is a roll angle adaptive robust sliding mode function, s 2 (t) is a pitch adaptive robust sliding mode function, c 1 C is the roll angle error coefficient 2 E is the pitch angle error coefficient 1 (t) is the roll angle attitude tracking error,e 2 (t) is pitch attitude tracking error, e 2 (t)＝θ d -θ，/>To expect the roll angle, θ d To expect to diveElevation angle;
the derivative of the adaptive robust sliding mode function is:
5. the method for adaptively controlling the sliding mode attitude of a disk satellite as set forth in claim 4, wherein,
defining Lyapunov function V as:
will beAs a moment of inertia matrix I c The estimated value of (2) is the moment of inertia matrix I c Error value +.>Gamma is a constant, gamma > 0.
6. The method for adaptively controlling the sliding mode attitude of a disk satellite as set forth in claim 5, wherein,
adaptive robust sliding mode control law u defining the roll axis 1 ：
Expanding the Lyapunov function, substituting the variable in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function to obtain the Lyapunov function of the rolling shaft 1 ：
γ 1 For the gamma of the corresponding roll axis,is->X-axis component of>Is I x Is used for the estimation of the (c),
according toObtaining a self-adaptive robust sliding mode control law u of the rolling shaft 1 The method comprises the following steps:
k in 1 Is the coefficient of approach rate of the rolling shaft, eta 1 Is the switching function coefficient of the rolling shaft, sign is the switching function.
7. The method for adaptively controlling the sliding mode attitude of a disk satellite as set forth in claim 6, wherein,
calculating to obtain the displacement l of the mass block on the y axis of the body coordinate system y The method comprises the following steps:
8. the method for adaptively controlling the sliding mode attitude of a disk satellite as set forth in claim 7, wherein,
adaptive robust sliding mode control law u defining pitch axis 2 ：
Expanding the Lyapunov function, substituting the variable in the disk satellite expansion dynamics equation into the expansion of the Lyapunov function to obtain the Lyapunov function of the pitching axis 2 ：
γ 2 For y corresponding to the pitch axis,is->Y-axis component of>Is I y Is used for the estimation of the (c),
according toObtaining a self-adaptive robust sliding mode control law u of a pitching axis 2 The method comprises the following steps:
k in 2 Is the coefficient of approach rate of pitching axis, eta 2 Is the switching function coefficient of the pitch axis.
9. The method for adaptively controlling the sliding mode attitude of a disk satellite according to claim 8, wherein,
calculating to obtain the mass block on the x axis of the body coordinate systemDisplacement l x The method comprises the following steps:
10. the method for adaptively controlling the sliding mode attitude of a disk satellite according to claim 9, wherein,
the roll and pitch axis adaptive laws are defined as:
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