Attitude cooperative control method suitable for ultra-static satellite

Abstract

The invention discloses an attitude cooperative control method suitable for a statically indeterminate satellite, and the method comprises the steps: firstly building a statically indeterminate satellite attitude dynamic model, then carrying out the modeling of disturbance, adding the model into the attitude dynamic model, obtaining an attitude dynamic model containing the disturbance, and then integrating the control characteristics of an ADRC and a PID, thereby achieving the cooperative control of the attitude of the statically indeterminate satellite. And designing a control law switching strategy of the ADRC controller and the PID controller, and finally, based on the control law switching strategy, adopting the ADRC controller and the PID controller to control the disturbed attitude dynamics model. According to the invention, the control output during large-angle deviation can be limited, and the control precision during long-term stability can be guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to an attitude collaborative control method applicable to an ultra-quiet satellite. Background Art

[0002] In recent years, with the rapid development of aerospace technology, space missions such as remote sensing information acquisition and in-orbit non-cooperative target approach have placed higher demands on satellites for functions such as continuous Earth gaze, large-angle side swing, single-line array 3D imaging, and observable swath expansion. These requirements necessitate both ultra-agility and ultra-high precision in satellites, meaning they must possess high attitude maneuverability and maintain ultra-high pointing accuracy during these maneuvers. Therefore, research on ultra-agile satellites capable of achieving both ultra-fast maneuverability and high stability is of great significance. Currently, it is difficult for agile satellites, both domestically and internationally, to achieve both the requirements for rapid maneuverability and the ability to output precise torque at the end of the maneuver to maintain high pointing accuracy.

[0003] Space environmental interference, moment of inertia parameter uncertainty, and actuator torque errors are key factors affecting satellite attitude control accuracy. During large-angle attitude maneuvers, the coupled nature of the control model can severely impact the convergence speed and stability of the control system. Therefore, research in precision attitude control focuses on ensuring that the attitude controller possesses the ability to decouple control and mitigate the effects of interference and model parameter uncertainty.

[0004] The growing demand for long-term on-orbit missions for agile satellites and the increasing complexity of these missions have placed high demands on the attitude control systems of these satellites for both precision and stability. However, this increased flexibility comes with some challenges. First, due to the limited ratings of actuators and sensors, as well as the internal disturbances and parameter uncertainties of gyroscopic coupling, high-speed maneuvers can easily lead to severe saturation. Furthermore, modern satellites often use low-rigidity attachments and carry large antennas or solar cells. When these are subjected to excessive rotational acceleration, they can cause sustained vibrations and even deteriorate attitude stability, reducing the performance of some high-precision payloads and sensors. The aforementioned work focuses solely on stability, ignoring the rapid response to saturation issues. In reality, agile satellites should ensure both stability and rapid response.

[0005] Ultra-quiet satellite platforms are required to have the control capability of high-precision and rapid pointing and tracking targets. However, there is a certain contradiction between the high precision and rapidity of attitude control. Rapid attitude tracking control requires a large control torque to improve maneuverability, but the large torque output often brings a large disturbance torque interference, thus affecting the attitude control accuracy. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to address the defects involved in the background technology and provide an attitude collaborative control method suitable for ultra-quiet satellites, which can not only limit the control output during large angle deviations but also ensure the control accuracy during long-term stability.

[0007] The present invention adopts the following technical solutions to solve the above technical problems:

[0008] A coordinated attitude control method for an ultra-quiet satellite comprises the following steps:

[0009] Step 1) Derived the satellite attitude dynamics equation with the reaction flywheel as the actuator according to the momentum theorem, and established the attitude dynamics model;

[0010] Step 1.1), the total momentum of the spacecraft and the reaction flywheel H = I a ω b +I w ω w =H b +H w , where I w is the moment of inertia of the reaction flywheel relative to its own axis of rotation; I a is the moment of inertia of the spacecraft including the flywheel relative to the origin of the spacecraft coordinate system, i.e., the center of mass of the system; ω b is the angular velocity of the spacecraft body relative to the inertial coordinate system; ω w is the angular velocity of the flywheel relative to the spacecraft body; H b =I a ω b is the angular momentum of the spacecraft; H w =I w ω w is the relative angular momentum generated by the rotation of the flywheel relative to the spacecraft;

[0011] From the moment of momentum theorem we can get: Right now: Where, is the control torque of the motor on the flywheel shaft, T d is the external disturbance torque; H b 、H w derivative with respect to time;

[0012] When the moment of inertia of the spacecraft and the flywheel is a constant, Where, are ω b 、ω w derivative with respect to time;

[0013] In step 1.2), the satellite attitude is expressed in Euler angles to describe the satellite attitude motion. That is, the attitude angular velocity equation expressed in Euler angles is established. According to Euler's "3-2-1" rotation of ψ, θ, and φ, the coordinate transformation matrix from the inertial coordinate system Nxyz to the satellite body coordinate system Bxyz is obtained as follows:

[0014]

[0015] The motion equation of the attitude can be obtained from the Euler angle rotation sequence. The body angular velocity of the spacecraft attitude relative to the inertial coordinate system is expressed in the spacecraft body coordinate system as follows:

[0016]

[0017] The inverse solution of the satellite attitude dynamics equation with the reaction flywheel as the actuator is as follows:

[0018]

[0019] Step 2) Modeling the disturbances and adding them to the attitude dynamics model to obtain an attitude dynamics model that includes disturbances, including external disturbances caused by atmospheric drag, tidal forces, solar radiation pressure, and the following small disturbances: air disturbance force, measurement disturbance force, and electromagnetic disturbance force;

[0020] Step 3), design a PID controller, which is represented by T ctr =K p θ e +K d ω e +K i ∫θ e dt, where T ctr is the controller output, K p , K d , K i are the proportional term coefficient, differential term coefficient, and integral term coefficient of the PID controller respectively; θ e 、ω e They are attitude angle error and body angular velocity error respectively;

[0021] Step 4) Design an active disturbance rejection controller ADRC, wherein the active disturbance rejection controller ADRC includes a tracking differentiator TD, an extended state observer ESO and a state error feedback control law SEF;

[0022] The tracking differentiator TD arranges a suitable transition process for the desired signal and achieves fast tracking by allowing the controlled system to track the transition process. The discrete form of the nonlinear tracking differentiator TD is expressed as:

[0023]

[0024] Where, fh is the characterization parameter of the fastest control comprehensive function; θ d is the desired attitude angle; θ t 、ω t They are the attitude angle signal and the body angular velocity signal after the tracking differentiator transition process respectively; r is the velocity factor parameter, h0 is the filter factor parameter, and h is the integration time step; the fastest control comprehensive function fhan(θ td ,ω t ,r,h) is expressed as:

[0025]

[0026] Where, d, d0, a0, a are all transition state variables of the most rapid control comprehensive function, + td To control the target attitude angle, the sign(·) function is a sign function;

[0027] The extended state observer (ESO) expands the disturbance generated by model uncertainty into the system state and estimates it in real time. The linear extended state observer is expressed as:

[0028]

[0029] Where θ e is the attitude angle error, θ t 、ω t are the attitude angle signal and the body angular velocity signal after the transition process of the tracking differentiator respectively; z1 is the signal observation quantity, z2 is the first-order signal observation quantity, and z3 is the second-order signal observation quantity; β1 is the gain parameter corresponding to the signal state variable of the extended state observer ESO, β2 is the gain parameter corresponding to the first-order signal state variable of the extended state observer ESO, and β3 is the gain parameter corresponding to the second-order state variable of the extended state observer ESO; I a is the moment of inertia of the spacecraft including the flywheel relative to the origin of the spacecraft coordinate system, i.e., the center of mass of the system, T ctr Controller output.

[0030] An error compensation loop is introduced at the controller output, and the total disturbance z3 estimated by the extended state observer ESO is used as the feedforward compensation control quantity. At the same time, a linear error feedback control law is introduced, and the controller output is:

[0031] T ctr =k1·(θ t -θ d )+k2·(ω t -ω d )-I a z3;

[0032] Where, ω dis the desired body angular velocity;

[0033] The state error feedback control law SEF is used to solve the control variable u0 output by the controller in the control system. Its nonlinear error feedback control law is expressed as:

[0034]

[0035] Where x1 is the signal after tracking the differentiator TD transition process, x2 is its differential signal, z1 and z2 are the state observations of x1 and x2 respectively; e1 is the error signal, e2 is the error differential signal; k1 and k2 are the controller parameters of the proportional link and the differential link respectively, fal() is the nonlinear function that determines the control interval, a1 is the nonlinear factor corresponding to the error signal e1, a2 is the nonlinear factor corresponding to the error differential signal e2, and the δ parameter determines the linear interval size of the nonlinear function fal(e,a,δ); the nonlinear function Where a is the exponential parameter variable of the δ parameter, which determines the linear interval size of the nonlinear function fal(e, a, δ);

[0036] Step 5) Integrate the control characteristics of the ADRC controller and the PID controller to design a control law switching strategy for the ADRC controller and the PID controller. Based on the control law switching strategy, the ADRC controller and the PID controller are used to control the disturbed posture dynamics model:

[0037] Step 5.1), determine the attitude angle error θ e Is it less than the preset first threshold θ lim1 , and determine the body angular velocity error ω e Is it less than the preset second threshold ω lim1 ; If θ e >θ lim1 or ω e >ω lim1 , using ADRC controller until θ e ≤θ lim1 And ω e ≤ω lim1 ;

[0038] Step 5.2), determine the attitude angle error θ e Less than the preset third threshold θ lim2 , and determine the body angular velocity error ω e Is it less than the preset fourth threshold ω lim2 ; If θ e >θ lim2 or ω e >ω lim2 , use PID controller with small parameters until θ e≤θ lim2 And ω e ≤ω lim2 ; If θ e ≤θ lim2 And ω e ≤ω lim2 , using PID controller with large parameters for control.

[0039] As a further optimization scheme of the attitude coordinated control method applicable to ultra-quiet satellites of the present invention, the disturbance model of the atmospheric drag in step 2) is: Where, f drag is the atmospheric drag perturbation acceleration, C d is the drag coefficient; ρ represents the atmospheric density at the orbit where the spacecraft is located; A p is the drag area of the spacecraft; v s represents the velocity vector of the spacecraft relative to the atmosphere, v s is its modulus value; m is the mass of the spacecraft.

[0040] As a further optimization scheme of the attitude coordinated control method applicable to ultra-quiet satellites of the present invention, the disturbance model of the solar radiation pressure in step 2) is: Where, f spr is the acceleration of the spacecraft caused by solar radiation pressure, P s is the solar radiation pressure; C s is the light pressure radiation coefficient; A s is the solar radiation area of the spacecraft; m is the mass of the spacecraft; AU is one astronomical unit; r Sun is the position vector of the sun in the Nxyz system, r Sun is its modulus; ν is the Earth's shielding coefficient to the Sun;

[0041] Where a is the apparent radius of the sun; b is the apparent radius of the earth; c is the apparent distance between the two celestial bodies;

[0042] a, b, and c are calculated according to the following formula:

[0043]

[0044] Where r Sun and r Ear are the radii of the sun and the earth respectively; r NB is the position vector of the spacecraft in the Nxyz system, r NB Its modulus value.

[0045] As a further optimization scheme of the attitude cooperative control method applicable to ultra-quiet satellites of the present invention, in step 4), a is set to 1 and δ is set to 0.1. At this time, the nonlinear function fal is converted into a linear function, and the linear error feedback control law is simplified to:

[0046]

[0047] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0048] 1. The collaborative control strategy combines the advantages of ADRC controller and PID controller, effectively reducing the control torque output while achieving ultra-high precision and ultra-fast maneuvering control performance.

[0049] 2. Accurately model the environmental disturbance torque and analyze its impact on the cooperative control system, further verifying the robustness of the cooperative control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is the block diagram of the spacecraft attitude PID control system;

[0051] Figure 2 This is the structural block diagram of the second-order active disturbance rejection controller ADRC control system;

[0052] Figure 3 Coordinated attitude control strategy for ultra-high precision and ultra-fast maneuvers;

[0053] Figure 4 This is the diagram of the change of the resultant torque of the ultra-quiet satellite under disturbance;

[0054] Figure 5 This is the graph of attitude control torque variation of ultra-quiet satellite;

[0055] Figure 6 This is a graph showing the change in attitude angle control error of a super-static satellite. DETAILED DESCRIPTION

[0056] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings:

[0057] The present invention can be implemented in many different forms and should not be considered to be limited to the embodiments described herein. On the contrary, these embodiments are provided to make this disclosure thorough and complete and will fully convey the scope of the invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0058] The present invention discloses a coordinated attitude control method applicable to an ultra-quiet satellite, comprising the following steps:

[0059] Step 1) Based on the moment of momentum theorem, the satellite attitude dynamics equations with the reaction flywheel as the actuator are derived and the attitude dynamics model is established. The total moment of momentum H of the spacecraft and the reaction flywheel is:

[0060] H=I a ω b +I w ω w =H b +H w

[0061] Where, I w is the moment of inertia of the reaction flywheel relative to its own axis of rotation; I a is the moment of inertia of the spacecraft including the flywheel relative to the origin of the spacecraft coordinate system (system center of mass); ω b is the angular velocity of the spacecraft body relative to the inertial coordinate system; ω w is the angular velocity of the flywheel relative to the spacecraft body; H b =I a ω b is the angular momentum of the spacecraft, H w =I w ω w is the relative angular momentum generated by the rotation of the flywheel relative to the spacecraft.

[0062] According to the momentum theorem, we can get:

[0063]

[0064] Right now:

[0065] Where, is the control torque of the motor on the flywheel shaft, T d is the external disturbance torque; H b 、H w The derivative with respect to time.

[0066] When the moment of inertia of the spacecraft and the flywheel is a constant, the above formula can be expressed as:

[0067]

[0068] Where, are ω b 、ω w The derivative with respect to time.

[0069] Using Euler angles to represent satellite attitude and describe satellite attitude motion, we can establish the attitude angular velocity equation expressed in Euler angles. By rotating ψ, θ, and φ according to Euler's "3-2-1", we can obtain the coordinate transformation matrix from the inertial coordinate system Nxyz to the satellite body coordinate system Bxyz:

[0070]

[0071] The motion equation of the attitude can be obtained from the Euler angle rotation sequence. The body angular velocity of the spacecraft attitude relative to the inertial coordinate system can be expressed in the spacecraft body coordinate system as follows:

[0072]

[0073] The inverse solution is:

[0074]

[0075] Step 2) and add it to the attitude dynamics model to obtain an attitude dynamics model including disturbances. The external disturbances in the disturbance modeling are mainly disturbances caused by the space environment such as atmospheric resistance, tidal force, and solar radiation pressure. The frequency of change of the quasi-steady-state acceleration is no more than 0.01 Hz and is related to the orbital period of the spacecraft flying around the earth. The magnitude of the quasi-steady-state acceleration can be estimated based on theory and is generally no more than 10 -6 g0 level. Atmospheric drag is related to factors such as atmospheric density, the speed of the satellite relative to the atmosphere, and the satellite's surface mass ratio. The atmospheric density varies with the orbital altitude and is affected by factors such as solar radiation intensity, geomagnetic activity index, and season. In low-Earth orbit, the microgravity acceleration caused by atmospheric drag is usually around 10 -8 ~10 -7 The g0 magnitude range. Tidal forces are related to factors such as orbital angular velocity, attitude motion, and distance from the center of mass. The microgravity acceleration caused by tidal forces is small in the tangential direction (speed direction) of the orbital plane, but large in the radial and normal directions of the orbital plane, usually not exceeding 10 -7 The solar radiation pressure is caused by the momentum exchange caused by solar photons hitting the surface of the spacecraft. It manifests itself as an inertial directional pressure on Earth-orbiting satellites, causing a perturbation on the orbital eccentricity. The total electromagnetic radiation energy received per unit time from the sun on a unit area perpendicular to the sun's rays at a distance equal to the average distance between the sun and the earth, outside the earth's atmosphere, is 1371W / m 2 The microgravity acceleration caused by solar radiation pressure is generally 10 -9 g0 level.

[0076] The calculation formula of atmospheric drag perturbation acceleration is: Where C d is the resistance coefficient, usually in the range of 1.5≤C d ≤3.0. ρ represents the atmospheric density at the orbit where the spacecraft is located. A p is the drag area of the spacecraft. s represents the velocity vector of the spacecraft relative to the atmosphere, vs is its modulus value. m is the mass of the spacecraft.

[0077] The acceleration of the spacecraft caused by solar radiation pressure is expressed as follows: Where, P s (=4.560×10 -6 N / m 2 ) is the solar radiation pressure. C s A is the light pressure radiation coefficient, usually ranging from 1.2 to 1.9. s is the solar radiation area of the spacecraft. AU(=1.496×10 11 m) is one astronomical unit. Sun is the position vector of the sun in the Nxyz system, r Sun Its modulus. v is the Earth's shielding coefficient from the Sun, which is between [0,1]. v = 0 indicates that the spacecraft is in the umbra; v = 1 indicates that the spacecraft is in the illuminated region; and ν = 0 to 1 indicates that the spacecraft is in the penumbra.

[0078] Where a is the apparent radius of the Sun, b is the apparent radius of the Earth, and c is the apparent distance between the two celestial bodies.

[0079] a, b, and c are calculated according to the following formula:

[0080]

[0081] Where r Sun and r Ear are the radii of the sun and the earth respectively; r NB is the position vector of the spacecraft in the Nxyz system, r NB Its modulus value.

[0082] The calculation formula of atmospheric drag perturbation acceleration shows that the atmospheric drag perturbation acceleration is proportional to the velocity vector v of the spacecraft relative to the atmosphere. s Related. Due to v s It is related to the orbital period of the spacecraft and shows approximately the same periodicity as the orbital period. Therefore, the atmospheric drag perturbation acceleration has the same periodicity as the orbital period of the spacecraft.

[0083] The acceleration formula of solar radiation pressure on spacecraft shows that the acceleration of solar radiation pressure perturbation is related to the position r of the sun in the Nxyz system. s Therefore, for Earth-orbiting satellites, the solar radiation pressure perturbation acceleration has the same periodicity as the Earth's orbital period. In addition, the solar radiation area of a spacecraft changes with the attitude of the Earth-oriented spacecraft, and the solar radiation pressure perturbation acceleration usually also shows a periodicity related to the spacecraft's orbital period.

[0084] In addition, other external disturbances include the following small disturbances: (1) Air disturbance force, which comes from the residual air disturbance inside the satellite, and its size is related to the air density (or pressure) and relative motion speed. (2) Measurement disturbance force, which comes from the disturbance introduced by the measurement process of the measurement sensor, and its size is related to the measurement mechanism. (3) Electromagnetic disturbance force, which comes from the electromagnetic interference of the satellite platform on the one hand and the effect of the earth's magnetic field on the other hand. (4) Other disturbance forces, such as temperature fluctuation disturbance, cosmic rays and high-energy particle impact, etc., are usually small.

[0085] Figure 4 This is a diagram showing the change in the resultant torque of a super-quiet satellite subjected to disturbances.

[0086] Step 3), PID controller design, PID (Proportional Integral and Derivative) control is a classic automatic control algorithm, which consists of three parts: proportional (Proportional, P), integral (Integral, I) and derivative (Derivative, D), such as Figure 1 As shown. The basic principle of PID control is to measure the error between the actual output and the expected output of the system, and then perform proportional, integral and differential operations on the error signal. Finally, the results of these three parts are linearly combined to form the control quantity, thereby adjusting the system to achieve the purpose of eliminating errors and stabilizing the system. The PID controller can be expressed as:

[0087] T ctr =K p θ e +K d ω e +K i ∫θ e dt;

[0088] Where, T ctr is the controller output, K p , K d , K i are the proportional term coefficient, differential term coefficient and integral term coefficient of the PID controller respectively; θ e and ω e are attitude angle error and body angular velocity error respectively.

[0089] Step 4) Active Disturbance Rejection Control (ADRC) is designed. The ADRC consists of a tracking differentiator (TD), an extended state observer (ESO), and a state error feedback control law (SEF). Figure 2 As shown. The tracking differentiator TD arranges a suitable transition process for the desired signal and achieves fast tracking by allowing the controlled system to track the transition process. Due to the existence of the transition process, the error variation trend between the controller input signal and the actual output signal of the system becomes smooth, making it easier to achieve a control effect with small overshoot and fast tracking speed. The discrete form of the nonlinear tracking differentiator TD can be expressed as:

[0090]

[0091] Where fh is the characterization parameter of the fastest control synthesis function, θ d is the desired attitude angle; θ t and ω t They are the attitude angle signal and the body angular velocity signal after the tracking differentiator transition process respectively; r is the velocity factor parameter, h0 is the filter factor parameter, and h is the integration time step; the fastest control comprehensive function fhan(θ td ,ω t ,r,h) is expressed as:

[0092]

[0093] Where d, d0, a0, a are the transition state variables of the fastest control synthesis function, θ td To control the target attitude angle, the sign(·) function is a sign function.

[0094] The extended state observer (ESO) expands the disturbances generated by model uncertainty into system states and estimates them in real time. The disturbances observed by the ESO include not only external disturbances imposed on the hyperquiescent satellite by external factors such as the space environment, but also internal disturbances caused by model uncertainty and system parameter adjustments. The error compensation loop (SEF) compensates for the total disturbance in real time through feedforward, transforming the uncertain system containing unknown disturbances into an "integrator series" control system. This can be expressed using a linear extended state observer as:

[0095]

[0096] Where z1 is the signal observation, z2 is the first-order signal observation, and z3 is the second-order signal observation; β1 is the gain parameter corresponding to the signal state variable of the extended state observer ESO, β2 is the gain parameter corresponding to the first-order signal state variable of the extended state observer ESO, and β3 is the gain parameter corresponding to the second-order state variable of the extended state observer ESO.

[0097] An error compensation loop is introduced at the controller output, and the total disturbance z3 estimated by the extended state observer ESO is used as the feedforward compensation control quantity. At the same time, a linear error feedback control law is introduced, and the controller output is:

[0098] T ctr =k1·(θ t -θ d )+k2·(ω t -ω d )-I a z3

[0099] Where, ω d is the desired body angular velocity.

[0100] In active disturbance rejection control (ADRC), state error signals e1 = x1 - z1 and e2 = x2 - z2 are constructed based on the tracking signal and its derivative signal output by the tracking differentiator TD and the observation signal based on the extended state observer ESO. The state error feedback control law SEF linearly or nonlinearly combines the error signal e1 and the error derivative signal e2 to solve for the control variable u0 output by the controller in the control system. The nonlinear error feedback control law is expressed as:

[0101]

[0102] Where x1 is the signal after tracking the differentiator TD transition process, x2 is its differential signal, z1 and z2 are the state observations of x1 and x2 respectively; e1 is the error signal, e2 is the error differential signal; k1 and k2 are the controller parameters of the proportional link and the differential link respectively, fal() is the nonlinear function that determines the control interval, a1 is the nonlinear factor corresponding to the error signal e1, a2 is the nonlinear factor corresponding to the error differential signal e2, and the δ parameter determines the linear interval size of the nonlinear function fal(e,a,δ); the nonlinear function Where a is the exponential parameter variable of the δ parameter, which determines the linear interval size of the nonlinear function fal(e, a, δ).

[0103] When a is 1 and δ is 0.1, the nonlinear function fal is transformed into a linear function, and the linear error feedback control law is simplified to:

[0104]

[0105] Step 5), based on the design of a collaborative controller of ADRC and PID, the ADRC controller designs a transition process for the desired signal by tracking the differentiator, thereby avoiding a large control output caused by direct error feedback. However, the introduction of the transition process brings a certain deviation to the control accuracy of the attitude angle and the body angular velocity in steady state, which makes it difficult to meet the performance requirements of ultra-quiet satellites for ultra-high precision and ultra-fast maneuvers. The PID controller directly performs feedback control on the error, which will produce a large control output when the initial error is large, which may lead to limited output of the actuator. However, the method of directly performing feedback control on the error in steady state is beneficial to improving the control accuracy of the attitude angle and the body angular velocity. In view of the control requirements of ultra-high precision and ultra-fast maneuvers of ultra-quiet satellites, the present invention integrates the control characteristics of the ADRC controller and the PID controller PID, designs a control law switching strategy for the ADRC controller and the PID controller, and adopts the anti-disturbance controller ADRC and the PID controller based on the control law switching strategy to control the disturbed attitude dynamics model, which can not only limit the control output during large angle deviations but also ensure the control accuracy during long-term stability. Figure 3 As shown, the control strategy is as follows:

[0106] Step 5.1), determine the attitude angle error θ e and the body angular velocity error ω e Are they all less than the preset threshold θ lim1 and ω lim1 If θ e ≤θ lim1 And ω e ≤ω lim1 , then further determine the attitude angle error θ e and the body angular velocity error ω e Are they all less than the preset threshold θ lim2 and ω lim2 ; On the contrary, use ADRC controller until θ e ≤θ lim1 And ω e ≤ω lim1 .

[0107] Step 5.2), determine the attitude angle error θ e and the body angular velocity error ω e Are they all less than the preset threshold θ lim2 and ω lim2 If θ e ≤θ lim2 And ω e ≤ω lim2 , use the PID controller with large parameters to control until the task is completed; otherwise, use the PID controller with small parameters to control until θ e ≤θ lim2 And ω e≤ω lim2 .

[0108] The core idea of the attitude coordinated control strategy for ultra-high precision and ultra-fast maneuvering is to use the attitude angle error θ e and the body angular velocity error ω e Switch controller or switch controller parameters. When the attitude angle error θ e Or the body angular velocity error ω e Greater than the preset threshold θ lim1 and ω lim1 When the attitude angle error θ is θ, the ADRC controller is used to avoid generating large control output by tracking the expected signal during the transition process. e and the body angular velocity error ω e are all less than the preset threshold θ lim1 and ω lim1 , is greater than the preset threshold θ lim2 and ω lim2 When the attitude angle error θ is e and the body angular velocity error ω e are all less than the preset threshold θ lim2 and ω lim2 When the PID controller is used with large parameters, a stronger control output is used to maintain a high-precision control level of the attitude angle and the angular velocity of the body during long-term operation. Figure 5 is the change diagram of attitude control torque of super-quiet satellite, Figure 6 This is a graph showing the change in attitude angle control error of a super-static satellite.

[0109] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as such, will not be interpreted in an idealized or overly formal sense.

[0110] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A coordinated attitude control method for an ultra-quiet satellite, characterized in that: The following steps are involved: Step 1) Derived the satellite attitude dynamics equation with the reaction flywheel as the actuator according to the momentum theorem, and established the attitude dynamics model; Step 1.1), the total momentum of the spacecraft and the reaction flywheel H = I a ω b +I w ω w =H b +H w , where I w is the moment of inertia of the reaction flywheel relative to its own axis of rotation; I a is the moment of inertia of the spacecraft including the flywheel relative to the origin of the spacecraft coordinate system, i.e., the center of mass of the system; ω b is the angular velocity of the spacecraft body relative to the inertial coordinate system; ω w is the angular velocity of the flywheel relative to the spacecraft body; H b =I a ω b is the angular momentum of the spacecraft; H w =I w ω w is the relative angular momentum generated by the rotation of the flywheel relative to the spacecraft; From the moment of momentum theorem we can get: Right now: Where, is the control torque of the motor on the flywheel shaft, T d is the external disturbance torque; H b 、H w derivative with respect to time; When the moment of inertia of the spacecraft and the flywheel is a constant, Where, are ω b 、ω w derivative with respect to time; In step 1.2), the satellite attitude is expressed in Euler angles to describe the satellite attitude motion. That is, the attitude angular velocity equation expressed in Euler angles is established. According to Euler's "3-2-1" rotation of ψ, θ, and φ, the coordinate transformation matrix from the inertial coordinate system Nxyz to the satellite body coordinate system Bxyz is obtained as follows: The motion equation of the attitude can be obtained from the Euler angle rotation sequence. The body angular velocity of the spacecraft attitude relative to the inertial coordinate system is expressed in the spacecraft body coordinate system as follows: The inverse solution of the satellite attitude dynamics equation with the reaction flywheel as the actuator is as follows: Step 2) Modeling the disturbances and adding them to the attitude dynamics model to obtain an attitude dynamics model that includes disturbances, including external disturbances caused by atmospheric drag, tidal forces, solar radiation pressure, and the following small disturbances: air disturbance force, measurement disturbance force, and electromagnetic disturbance force; Step 3), design a PID controller, which is represented by T ctr =K p θ e +K d ω e +K i ∫θ e dt, where T ctr is the controller output, K p , K d , K i are the proportional term coefficient, differential term coefficient, and integral term coefficient of the PID controller respectively; θ e 、ω e They are attitude angle error and body angular velocity error respectively; Step 4) Design an active disturbance rejection controller ADRC, wherein the active disturbance rejection controller ADRC includes a tracking differentiator TD, an extended state observer ESO and a state error feedback control law SEF; The tracking differentiator TD arranges a suitable transition process for the desired signal and achieves fast tracking by allowing the controlled system to track the transition process. The discrete form of the nonlinear tracking differentiator TD is expressed as: Where, fh is the characterization parameter of the fastest control comprehensive function; θ d is the desired attitude angle; θ t 、ω t They are the attitude angle signal and the body angular velocity signal after the tracking differentiator transition process respectively; r is the velocity factor parameter, h0 is the filter factor parameter, and h is the integration time step; the fastest control comprehensive function fhan(θ td ,ω t ,r,h) is expressed as: Where, d, d0, a0, a are all transition state variables of the most rapid control comprehensive function, + td To control the target attitude angle, the sign(·) function is a sign function; The extended state observer (ESO) expands the disturbance generated by model uncertainty into the system state and estimates it in real time. It is expressed as follows using a linear extended state observer: Where θ e is the attitude angle error, θ t 、ω t are the attitude angle signal and the body angular velocity signal after the transition process of the tracking differentiator respectively; z1 is the signal observation quantity, z2 is the first-order signal observation quantity, and z3 is the second-order signal observation quantity; β1 is the gain parameter corresponding to the signal state variable of the extended state observer ESO, β2 is the gain parameter corresponding to the first-order signal state variable of the extended state observer ESO, and β3 is the gain parameter corresponding to the second-order state variable of the extended state observer ESO; I a is the moment of inertia of the spacecraft including the flywheel relative to the origin of the spacecraft coordinate system, i.e., the center of mass of the system, T ctr Controller output. An error compensation loop is introduced at the controller output, and the total disturbance z3 estimated by the extended state observer ESO is used as the feedforward compensation control quantity. At the same time, a linear error feedback control law is introduced, and the controller output is: T ctr =k1·(θ t -θ d )+k2·(ω t -oh d )-I a ·z3; Where, ω d is the desired body angular velocity; The state error feedback control law SEF is used to solve the control variable u0 output by the controller in the control system. Its nonlinear error feedback control law is expressed as: Where x1 is the signal after tracking the differentiator TD transition process, x2 is its differential signal, z1 and z2 are the state observations of x1 and x2 respectively; e1 is the error signal, e2 is the error differential signal; k1 and k2 are the controller parameters of the proportional link and the differential link respectively, fal() is the nonlinear function that determines the control interval, a1 is the nonlinear factor corresponding to the error signal e1, a2 is the nonlinear factor corresponding to the error differential signal e2, and the δ parameter determines the linear interval size of the nonlinear function fal(e,a,δ); the nonlinear function Where a is the exponential parameter variable of the δ parameter, which determines the linear interval size of the nonlinear function fal(e, a, δ); Step 5) Integrate the control characteristics of the ADRC controller and the PID controller to design a control law switching strategy for the ADRC controller and the PID controller. Based on the control law switching strategy, the ADRC controller and the PID controller are used to control the disturbed posture dynamics model: Step 5.1), determine the attitude angle error θ e Is it less than the preset first threshold θ lim1 , and determine the body angular velocity error ω e Is it less than the preset second threshold ω lim1 ; If θ e >θ lim1 or ω e >ω lim1 , using ADRC controller until θ e ≤θ lim1 And ω e ≤ω lim1 ; Step 5.2), determine the attitude angle error θ e Less than the preset third threshold θ lim2 , and determine the body angular velocity error ω e Is it less than the preset fourth threshold ω lim2 ; If θ e >θ lim2 or ω e >ω lim2 , use PID controller with small parameters until θ e ≤θ lim2 And ω e ≤ω lim2 ; If θ e ≤θ lim2 And ω e ≤ω lim2 , using PID controller with large parameters for control.

2. The attitude coordinated control method for an ultra-quiet satellite according to claim 1, wherein: The disturbance model of the atmospheric resistance in step 2) is: Where, f drag is the atmospheric drag perturbation acceleration, C d is the drag coefficient; ρ represents the atmospheric density at the orbit where the spacecraft is located; A p is the drag area of the spacecraft; v s represents the velocity vector of the spacecraft relative to the atmosphere, v s is its modulus value; m is the mass of the spacecraft.

3. The attitude coordinated control method for an ultra-quiet satellite according to claim 2, wherein: The disturbance model of solar radiation pressure in step 2) is: Where, f spr is the acceleration of the spacecraft caused by solar radiation pressure, P s is the solar radiation pressure; C s is the light pressure radiation coefficient; A s is the solar radiation area of the spacecraft; m is the mass of the spacecraft; AU is one astronomical unit; r Sun is the position vector of the sun in the Nxyz system, r Sun is its modulus; v is the shielding coefficient of the earth to the sun; Where a is the apparent radius of the sun; b is the apparent radius of the earth; c is the apparent distance between the two celestial bodies; a, b, and c are calculated according to the following formula: Where r Sun and r Ear are the radii of the sun and the earth respectively; r NB is the position vector of the spacecraft in the Nxyz system, r NB Its modulus value.

4. The attitude coordinated control method for an ultra-quiet satellite according to claim 1, wherein: In step 4), a is set to 1 and δ is set to 0.

1. At this time, the nonlinear function fal is converted into a linear function, and the linear error feedback control law is simplified to:

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