CN109760854B

CN109760854B - Volume-controllable inflatable antenna and unfolding volume control method thereof

Info

Publication number: CN109760854B
Application number: CN201910042936.3A
Authority: CN
Inventors: 向晓霞; 杨峰; 任维佳; 杜志贵
Original assignee: Changsha Tianyi Space Technology Research Institute Co Ltd
Current assignee: Changsha Tianyi Space Technology Research Institute Co Ltd
Priority date: 2019-01-17
Filing date: 2019-01-17
Publication date: 2020-11-27
Anticipated expiration: 2039-01-17
Also published as: CN112357115A; CN109760854A; CN112357122A; CN112357115B; CN112357122B

Abstract

The invention relates to a volume-controllable gas-filled antenna comprising at least a satellite thruster, at least one acquisition module and at least one adjustment module, the first adjustment module being configured to: determining first antenna adjustment control information based on the orbital transfer environment monitoring information; determining a desired projected consumption of the satellite propulsor for performing the particular event; and determining a track-transfer demand mixing proportion coefficient corresponding to the satellite thruster and the inflation antenna respectively and a first control instruction and a second control instruction corresponding to the track-transfer demand mixing proportion coefficient based on the first antenna adjustment control information and the estimated consumption, so that a first adjustment module of the inflation antenna receives the first control instruction in a mode of performing aerodynamic compensation on a second adjustment module of the satellite thruster receiving the second control instruction, and performing at least one adjustment correction based on second aerodynamic information, acquired by a second acquisition module at a second moment, associated with an area related to the ignition track-transfer position to execute at least one related specific event.

Description

Volume-controllable inflatable antenna and unfolding volume control method thereof

Technical Field

The invention relates to the technical field of aerospace, in particular to a volume-controllable inflatable antenna.

Background

The orbit of the low orbit satellite can rapidly reach a predetermined orbit and spread the work due to its low operation height. And the low orbit satellite has a shorter orbit running period, has less time intervals passing through the same point, and is more frequent than the traditional satellite in the aspect of reconnaissance work, so that more information can be obtained. Meanwhile, because the orbit height of the low orbit satellite is lower than that of the traditional satellite, the aerodynamic force of the low orbit satellite is tens of orders of magnitude higher than that of the traditional satellite, the operation of the spacecraft is influenced by the existence of the atmosphere, the spacecraft is decelerated and accelerated under the action of a long time, and accordingly the low orbit satellite needs to be subjected to speed compensation regularly. In addition, the density of the rarefied high-rise atmosphere is greatly changed by the influence of external factors such as solar motion, revolution of the earth, rotation, geomagnetic motion, and the like. Although the aerodynamic forces acting on a satellite are much smaller than the gravitational forces of the earth, the orbit and attitude of the satellite can be greatly affected by the accumulation over time. Therefore, if the conventional satellite orbit control method is adopted, only the jet device is used for eliminating the aerodynamic force as the disturbance force, not only the jet actuator of the satellite is frequently started to correct the satellite orbit deviation, but also a large amount of energy and fuel are consumed in the period. The satellite orbital transfer is one of the most common operations of spacecrafts in space operation, wherein the maneuvering of a low-orbit satellite on an orbital plane in space is a maneuvering process common to space mission maneuvering, but the maneuvering process has high fuel consumption under the influence of atmosphere so as to greatly limit the maneuvering capability of the low-orbit satellite in space, so that the research on the low-orbit orbital plane transfer problem has great significance for the space maneuvering mission of the low-orbit satellite.

However, if a rail maneuver can be performed with deceleration assistance from aerodynamic forces, a significant amount of fuel can be saved compared to conventional pulse maneuvers, and thus, pneumatically assisted rail maneuvers are considered to be a potentially significant rail maneuver strategy. On the one hand, for the problem of transferring the low-rail track surface, considering the low energy of the low-rail track, the track height close to the atmospheric height and other factors, it is difficult to complete the track surface transferring process if only directly assisted by aerodynamic force singly. While on the other hand, while a single direct use of conventional pulse maneuver strategies can increase track energy, large amounts of fuel are consumed for a wide range of low-rail track surface transfer processes. Therefore, the low-orbit plane transfer maneuver based on aerodynamic force assistance and pulse is combined, not only can the ground-orbit plane transfer process be completed, but also the energy consumption of the satellite can be effectively reduced by the aid of aerodynamic force to assist the orbit control, more fuel support is provided for the execution of the follow-up tasks of the spacecraft, the development cost of the satellite is reduced, the economic value is higher, and a new thought and strategy are provided for the future research of low-cost and low-power-consumption satellites.

Furthermore, it is likely that in space flight, the inflation process of large inflatable structures that are not effectively controlled can cause entanglement of the structure and damage other spacecraft hardware. Therefore, it is necessary to deploy the inflatable antenna in a manner that is well controlled in both time and space terms. A deployment control mechanism employs a segmented control valve technique in which a long gas tube is segmented into segments, a pressure regulating valve is installed at the beginning of each segment, and the tubes are sequentially controlled to deploy as inflation gas enters. Another deployment control mechanism is the use of elongated coil springs that are placed within the inflation tube along the inner wall of the tube and the tube deployment is controlled by balancing the inflation pressure and the spring return force. Yet another deployment control mechanism is the use of a long adhesive strip adhered to the outside of the tube and distributed along the length of the tube, which produces a certain resistance when the tube is inflated, thereby allowing deployment to be controlled. Various structures have been disclosed in the prior art, all of which can control the size of the parabolic surface to be unfolded, i.e. the size of the volume to be unfolded, by controlling the inflation process. For example:

chinese patent (publication No. CN201038320) discloses a receiving antenna for use in space, which includes: the main reflecting surface is used for receiving signals, the auxiliary reflecting surface is positioned above the main reflecting surface and used for receiving the signals reflected by the main reflecting surface, and at least three auxiliary reflecting surface positioning cables are used for fixing the auxiliary reflecting surface; the main inflatable arm, the inflatable stabilizing support, the top inflatable ring and the inflatable sub-arm ring which are formed by foldable hoses capable of inflating and deflating in the pipe are inflated and deflated through an air delivery conduit connected with the main inflatable arm.

The receiving antenna that this patent provided receives the thread gluing constraint and can not bounce after curling folding to can break through the constraint of thread gluing gradually when the gas tube inflation, can realize unfolding in order.

Chinese patent (publication number CN103928743B) discloses a loading and unfolding control mechanism for a rib plate type inflatable unfolding parabolic antenna, which belongs to the technical field of rib plate type inflatable unfolding parabolic antennas, and solves the problem that no effective loading mechanism exists and the unfolding process of the rib plate type inflatable unfolding parabolic antenna can not be effectively controlled currently, and the loading mechanism and the unfolding control mechanism are included; the loading mechanism is characterized in that a connecting piece of the loading mechanism is arranged below a fixed disc of the unfolding control mechanism and connected through a bolt, the number of blades of the loading mechanism is the same as that of supporting cross rods and rib plate pressure rods of the unfolding control mechanism, the supporting cross rods are arranged corresponding to blade cracks, and notches are arranged on two sides of each blade.

The unfolding control mechanism provided by the patent can effectively control the unfolding process of the rib plate type inflatable unfolding parabolic antenna, so that the rib plate type inflatable unfolding parabolic antenna can be unfolded according to an ideal unfolding sequence, path and speed.

Therefore, based on the inflatable antenna system with controllable volume, the common antenna rotation driving system provided in the prior art is combined, so that the beam pointing direction of the satellite antenna can be adjusted, for example, a six-degree-of-freedom position and posture adjusting device of a satellite-borne antenna disclosed in the Chinese patent (with the publication number of CN109004361A), the purpose of respectively controlling the unfolding process and the pointing direction adjusting process of the inflatable antenna can be achieved, and meanwhile, due to the adjustability of the antenna, the antenna can be controlled to point back to the ground station again when the satellite orbit is inclined, so that the times of north-south position protection of the satellite can be effectively reduced, the fuel consumption is reduced, and the on-orbit service life of the satellite is prolonged.

In addition to satellite orbital transfer in the space operation of a spacecraft, the same problem exists in satellite orbit maintenance. Communication and marine satellites are typically arranged in a circular orbit, called a geostationary or geostationary orbit, having the same period of rotation as the earth to provide synchronous rotational speed. Ideally, such satellites should be positioned in an orbital plane that coincides with the equatorial plane of the earth, so that the satellite antenna can be pointed at a desired terrestrial location. In general, geostationary satellites are momentum stabilized by rotating around themselves or by providing a momentum wheel that maintains the spin axis perpendicular to the equatorial plane and aligns the earth beam boresight axis perpendicular to the spin axis. In this ideal situation, the earth beam boresight is always directed to the region of the sub-satellite points when the satellite rotates synchronously with the earth. Several factors can cause orbital drift that tilts the satellite orbit relative to the nominal equatorial orbital plane. This track tilt can accumulate over time, producing roll and yaw pointing errors. In particular, the gravitational effects of the sun and moon on the satellites and the variations in the gravitational field of the earth created by the non-spherical shape of the earth cause orbital perturbation effects that tilt the plane of the satellite orbit relative to the ideal equatorial plane. The net effect of these orbital disturbance effects is to cause the satellite orbit to tilt, slowly drifting at a rate of 0.75 ° to 0.95 ° per year.

The spacecraft can follow the motion rule of a Kepler orbit in an ideal perturbation-free environment and stably run on orbit for a long time. However, various orbit perturbation factors, such as earth oblateness perturbation, atmospheric perturbation, sunlight pressure perturbation, sun and moon perturbation, inevitably exist in the real environment, so that the spacecraft deviates from the predetermined orbit, and related tasks, especially precise tasks, are performed on the spacecraft, thereby causing deviation and inconvenience. Therefore, it is a necessary task to conduct orbit keeping control research on long-term on-orbit spacecraft, and the research is also the basis for the spacecraft to perform other tasks. The rail maintaining strategy provided in the prior art has a large-thrust pulse type control scheme, a small-thrust continuous control scheme and the like. In the ideal orbit control process, the position of the spacecraft at the current moment is measured and compared with a nominal orbit to determine the momentum of the orbit parameter, and then the orbit control engine is started to generate pulses to correct the orbit, so that the aim of maintaining the orbit is fulfilled. On the other hand, in a common satellite system, a propeller is generally used to regularly correct the inclination of the orbit by consuming fuel, and then the antenna is pointed away from the earth station to cause pointing mismatch loss, which can seriously affect the communication quality between the satellite and the earth, especially when the satellite antenna beam is narrow. Specifically, this position maintenance effect may require 20% of the initial total weight of the satellite over a 10 year period, with propellant accounting for a major portion, approximately 90% for orbital corrections and the remainder for other in-orbit maneuvers, including pitch error corrections, whereby the operating life of the satellite is limited by the fuel required for spatial position maintenance.

In order to solve the problems of low orbit height, large aerodynamic resistance, fast orbit attenuation and the like of a low-orbit satellite, the generally adopted method is to reduce the windward area of the satellite so as to reduce the aerodynamic resistance. However, the current pneumatic auxiliary orbit transfer technology is to enter and exit the atmosphere at an orbit speed during the orbit transfer, and the adoption of aerodynamic force for maintaining the orbit during the orbit running is a little more demanding.

Chinese patent (publication number CN201511000976.X) discloses a low orbit constellation deployment method based on assistance of Mars atmosphere, relates to a Mars atmosphere and a Mars constellation deployment method under a gravity system thereof, and belongs to the technical field of aerospace. The patent solves for the required velocity pulse applied by the initial orbit into the atmosphere and the velocity pulse applied by the aircraft into the target orbit by optimizing the control rate to meet the aerodynamic requirements. The detector releases the loaded aircraft from a far fire point position and enters the atmosphere by applying the required aircraft to enter the atmospheric velocity pulse from an initial orbit, performs aerodynamic force assisted orbit transfer in the atmosphere by optimizing the given control rate, and positions the aircraft on a target orbit by applying the required velocity pulse applied when the aircraft enters the target orbit, and deploys a plurality of constellation aircrafts on the respective target orbits to realize the deployment of the whole constellation.

Since mars and the earth have the atmosphere, and orbital maneuver by the atmosphere can save a great deal of fuel compared with the traditional Hotman transfer, the method for deploying constellations by the mars atmosphere provided by the patent can effectively save the energy consumption of the deployment process, and can save more fuel for maintaining the subsequent constellations, and is also suitable for the process of orbital transfer by the earth atmosphere. However, since the method provided by the patent only considers the boosting process of the aerodynamic force to reduce the required speed pulses Δ v1 and Δ v2, different atmospheric information is not fully considered and the situation when the aerodynamic force influences the track transfer process as resistance is not given, and the application range is limited.

Chinese patent (publication number CN201610801621.9) discloses a low-orbit orbital plane transfer method based on combination of pulse and pneumatic assistance, relates to a large-range orbital plane transfer method of an earth low-orbit spacecraft, and belongs to the field of aerospace. Firstly, establishing a kinetic equation of the number of tracks and the flight process in the atmosphere; the spacecraft is flexibly transferred to a large elliptical orbit by applying pulses, and off-orbit pulses are applied to a far place to enable the spacecraft to enter the atmosphere; selecting an optimization target as the maximum change amount of the track surface, giving constraints and obtaining the optimal control rate and the terminal state quantity meeting the aerodynamic force requirement to complete the pneumatic auxiliary track surface transfer; the spacecraft flies out of the atmosphere and runs to the height of the target orbit along the transfer orbit, and the orbit determination pulse is applied to enable the spacecraft to enter the target orbit.

Compared with a method for directly applying maneuver, the low-orbit plane transfer method based on the combination of pulse and pneumatic assistance provided by the patent replaces the traditional direct pulse maneuver, the change capability or change amount of the orbit plane is obviously increased under the constraint of total speed pulse, and the orbit plane transfer of the low-orbit spacecraft can be completed with lower fuel consumption. The method for transferring the track has the advantages that quick maneuvering is required from the evaluation condition of the performance index, the time optimization problem of completing the track transfer scheme needs to be considered, but when the track transfer scheme is considered to be completed, only the optimal fuel consumption problem is considered, so that maneuvering strategies from an initial track to a target freezing track are too long in time consumption, and the optimal fuel consumption problem is not considered and the time optimization problem is not considered.

A spacecraft relative orbit transfer trajectory optimization method based on time-fuel optimal control in Chinese patent (with publication number CN104536452B) relates to a spacecraft relative orbit transfer trajectory optimization method. In order to solve the problem that the thrust amplitude is limited in the relative orbit coordinate system of the tracked spacecraft, the existing method only considers time optimization or only considers the problem of fuel consumption. Firstly, establishing a relative orbit motion dynamic model to respectively design active control quantities ux, uy and uz applied along three axes; the relative orbital motion dynamics model is then decoupled into three subsystems: after the three subsystems are decoupled, the total performance index of the tracking spacecraft, considering the transfer time and the fuel consumption, is converted into the single-axis performance index of each axis, and finally the time-fuel optimal control law is obtained to control the tracking spacecraft.

According to the spacecraft relative orbit transfer trajectory optimization method based on the time-fuel optimal control, a time-fuel optimal control law is obtained to control the tracked spacecraft, compared with some schemes only considering time optimal or only considering fuel consumption problems, the spacecraft relative orbit transfer trajectory optimization method based on the time-fuel optimal control considers the transfer time and the fuel consumption problems at the same time, and can find a time-fuel optimal control scheme under the specific gravity by adjusting the specific gravities of the transfer time and the fuel consumption problems. However, in the orbit transfer optimization method provided by the patent, the utilization rate of the aerodynamic force is extremely low only for a single power-assisted mode adopting aerodynamic force assistance, so that the method adopting the time-fuel optimal control law to control the tracking spacecraft still has the problems of low fuel saving degree and long transfer time.

Disclosure of Invention

In view of the deficiencies of the prior art, the present invention provides a volume-controllable inflatable antenna, comprising at least a satellite thruster, at least one acquisition module and at least one adjustment module, wherein the first adjustment module for adjusting the position and the attitude of the inflatable antenna is configured to:

determining at least one ignition track-changing position based on the initial track and the target track acquired by the first acquisition module, generating track-changing environment monitoring information based on first aerodynamic information which is acquired by the second acquisition module at a first moment and is associated with an area related to the ignition track-changing position, and determining first antenna adjustment control information based on the track-changing environment monitoring information;

determining at least one instruction for executing a specific event of interest based on the initial orbit and the target orbit, and upon receiving at least one instruction for executing a specific event of interest, determining a required pre-estimated consumption of the satellite propulsor for executing the specific event;

and determining a track-changing demand mixing proportionality coefficient corresponding to the satellite thruster and the inflation antenna and a first control instruction and a second control instruction corresponding to the track-changing demand mixing proportionality coefficient based on the first antenna adjustment control information and the estimated consumption, so that the first adjustment module of the inflation antenna receives the first control instruction in a mode of performing aerodynamic compensation on a second adjustment module of the satellite thruster receiving the second control instruction, and performs at least one adjustment correction based on second aerodynamic information, acquired by the second acquisition module at a second moment, associated with an area related to the ignition track-changing position to execute at least one related specific event.

According to a preferred embodiment, the first antenna adjustment control information determined by the first adjustment module based on the tracking environment monitoring information at least comprises a first pointing adjustment duration for antenna pointing adjustment and a first spreading adjustment duration for antenna specific surface area adjustment, and a first moving duration is determined based on one of the first pointing adjustment duration and the first spreading adjustment duration which is larger in value, wherein the first adjustment module determines an antenna initial adjustment position corresponding to the first moving duration in combination with the ignition tracking position and the initial track when the first moving duration does not exceed a preset duration threshold, so that a position where the antenna starts to be adjusted and is located on the initial track can be determined based on the antenna initial adjustment position.

According to a preferred embodiment, the first adjustment module is further configured for performing the steps of:

s1: determining at least one preset allocation specific gravity for establishing a dynamic association relationship between the first pointing adjustment duration and the first deployment adjustment duration in response to the first movement duration exceeding the preset duration threshold;

s2: the preset distribution proportion is updated in a mode of gradually reducing the first unfolding adjustment time length and correspondingly gradually increasing the first direction adjustment time length so as to determine a second direction adjustment time length which corresponds to the preset distribution proportion and is used for updating the first direction adjustment time length and a second unfolding adjustment time length which corresponds to the preset distribution proportion and is used for updating the first unfolding adjustment time length;

s3: therefore, the second moving duration for updating the first moving duration is determined based on the larger value of the updated first pointing adjustment duration and the updated first unfolding adjustment duration, and the updated first moving duration is compared with the preset duration threshold again;

s4: and repeating the steps S1 to S3 in sequence until the first moving time length does not exceed the preset time length threshold value, stopping and outputting the first pointing adjustment time length, the first unfolding adjustment time length and the initial antenna adjustment position corresponding to the first moving time length so as to realize an optimized solution between the estimated loss minimization and the maximum track change efficiency.

According to a preferred embodiment, the second adjustment module comprises at least an environmental monitoring unit configured to:

acquiring current aerodynamic force information which is acquired in real time at a first moment when a satellite is located at the initial adjustment position of the satellite, is related to an area related to the initial adjustment position of the satellite and is used for providing a parameter set required by atmosphere prediction, and performing prediction calculation based on a position relation between the area related to the ignition orbital transfer position and the initial adjustment position of the satellite to generate first aerodynamic force information located in the area related to the ignition orbital transfer position;

and acquiring second aerodynamic information which is acquired in real time and is related to the area related to the ignition orbital transfer position and used for adjusting and correcting the ignition orbital transfer position of the satellite at a second moment when the satellite is positioned at the ignition orbital transfer position.

According to a preferred embodiment, the second adjustment module is configured to determine, upon receiving at least one instruction to perform a specific event of interest, a required estimated consumption of the satellite thrusters for performing the specific event, the second adjustment module being configured to:

when the first adjusting module determines at least one ignition track-changing position based on the initial track and the target track acquired by the first acquiring module, a track-changing prediction planning process of successfully transferring the ignition track-changing position from the initial track to the target track from the ignition track-changing position in a mode of neglecting the track-changing environment monitoring information is completed by combining the initial track, the target track and the ignition track-changing position, and the corresponding expected consumption amount required to be consumed for completing the track-changing prediction planning process is generated.

According to a preferred embodiment, the second adjusting module is configured to determine the orbital transfer demand mixing scaling factors corresponding to the satellite thruster and the inflation antenna, respectively, based on the first antenna adjustment control information and the estimated consumption amount, under the condition that the aerodynamic assistance factor of the orbital transfer environment monitoring information is determined at a first time, where:

when the aerodynamic assistance coefficient is smaller than 1, judging that the aerodynamic information influences the execution process of a related specific event in a resistance mode, determining a track change demand mixing proportion coefficient corresponding to the inflation antenna in a mode of reducing the influence of the aerodynamic information to the maximum extent by means of the inflation antenna by the second adjusting module, and then determining a track change demand mixing proportion coefficient corresponding to the satellite thruster in a mode of increasing the estimated consumption to the minimum extent on the basis of the track change demand mixing proportion coefficient corresponding to the inflation antenna;

when the aerodynamic assistance coefficient is larger than 1, the second adjusting module judges that the aerodynamic information influences the execution process of a related specific event in an assistance mode, determines an orbital transfer demand mixing scaling coefficient corresponding to the air-filled antenna in a mode of utilizing the aerodynamic information to the maximum extent by means of the air-filled antenna, and then determines the orbital transfer demand mixing scaling coefficient corresponding to the satellite thruster in a mode of reducing the estimated consumption to the maximum extent on the basis of the orbital transfer demand mixing scaling coefficient corresponding to the air-filled antenna; and the sum of the orbit-transfer requirement mixing proportionality coefficients respectively corresponding to the satellite thruster and the inflatable antenna is equal to 1.

According to a preferred embodiment, the second adjusting module further comprises an adjusting and correcting unit configured to: and acquiring an error correction coefficient of first antenna adjustment control information corresponding to the first aerodynamic information at a second moment according to the deviation between the second aerodynamic information and the first aerodynamic information, performing adjustment correction within a small adjustment range on satellite pointing information corresponding to the second moment and corresponding satellite deployment information respectively based on the error correction coefficient so that the satellite can accurately correspond to the actually measured second aerodynamic information during the execution of the related specific event, and updating the orbital transfer demand mixing proportion coefficient correspondingly based on the corrected first antenna adjustment control information so that the consumption provided by the satellite propeller during the execution of the related specific event can be further accurately controlled.

A method for controlling the deployment volume of an inflatable antenna at least comprises the following steps: determining at least one ignition track transfer position based on the obtained initial track and the target track, generating track transfer environment monitoring information based on first aerodynamic information which is obtained at a first moment and is associated with an area related to the ignition track transfer position, and determining first antenna adjustment control information based on the track transfer environment monitoring information;

and determining the orbital transfer demand mixing proportionality coefficient corresponding to the satellite thruster and the inflation antenna respectively and a first control instruction and a second control instruction corresponding to the orbital transfer demand mixing proportionality coefficient based on the first antenna adjustment control information and the estimated consumption, so that the inflation antenna receives the first control instruction in a mode of performing aerodynamic compensation on the satellite thruster receiving the second control instruction, and performing at least one adjustment correction based on second aerodynamic information acquired at a second moment and associated with the area related to the ignition orbital transfer position to execute at least one related specific event.

According to a preferred embodiment, the deployment volume control method comprises at least the following steps: the first antenna adjustment control information determined based on the orbital transfer environment monitoring information at least comprises a first pointing adjustment duration for antenna pointing adjustment and a first spreading adjustment duration for antenna specific surface area adjustment, and a first moving duration is determined based on one of the first pointing adjustment duration and the first spreading adjustment duration which is larger in value, wherein an antenna initial adjustment position corresponding to the first moving duration is determined by combining the ignition orbital transfer position and the initial track when the first moving duration does not exceed a preset duration threshold, so that the position, where the antenna starts to be adjusted, of the initial track can be determined based on the antenna initial adjustment position.

According to a preferred embodiment, the deployment volume control method further comprises the steps of:

According to a preferred embodiment, the process of adjusting the correction comprises at least the following steps: and acquiring an error correction coefficient of first antenna adjustment control information corresponding to the first aerodynamic information at a second moment according to the deviation between the second aerodynamic information and the first aerodynamic information, performing adjustment correction within a small adjustment range on satellite pointing information corresponding to the second moment and corresponding satellite deployment information respectively based on the error correction coefficient so that the satellite can accurately correspond to the actually measured second aerodynamic information during the execution of the related specific event, and updating the orbital transfer demand mixing proportion coefficient correspondingly based on the corrected first antenna adjustment control information so that the consumption provided by the satellite propeller during the execution of the related specific event can be further accurately controlled.

According to a preferred embodiment, the orbit change demand mixing proportionality coefficient corresponding to each of the satellite thruster and the inflation antenna is determined based on the first antenna adjustment control information and the estimated consumption amount under the condition of aerodynamic assistance coefficient by judging the orbit change environment monitoring information at a first time, wherein:

when the aerodynamic assistance coefficient is smaller than 1, judging that the aerodynamic information influences the execution process of the related specific event in a resistance mode, determining a track-changing demand mixing proportion coefficient corresponding to the inflation antenna in a mode of reducing the influence of the aerodynamic information to the maximum extent by means of the inflation antenna, and then determining a track-changing demand mixing proportion coefficient corresponding to the satellite thruster in a mode of increasing the estimated consumption to the minimum extent on the basis of the track-changing demand mixing proportion coefficient corresponding to the inflation antenna;

when the aerodynamic assistance coefficient is larger than 1, judging that the aerodynamic information influences the execution process of a related specific event in an assistance mode, determining a track change demand mixing proportion coefficient corresponding to the inflation antenna in a mode of utilizing the aerodynamic information to the maximum extent by means of the inflation antenna, and then determining a track change demand mixing proportion coefficient corresponding to the satellite thruster in a mode of reducing the estimated consumption to the maximum extent on the basis of the track change demand mixing proportion coefficient corresponding to the inflation antenna;

and the sum of the orbit-transfer requirement mixing proportion coefficients respectively corresponding to the satellite propeller and the inflatable antenna is equal to 1.

According to a preferred embodiment, the process of determining the estimated consumption required comprises at least the following steps: when the first adjusting module determines at least one ignition track-changing position based on the initial track and the target track acquired by the first acquiring module, a track-changing prediction planning process of successfully transferring the ignition track-changing position from the initial track to the target track from the ignition track-changing position in a mode of neglecting the track-changing environment monitoring information is completed by combining the initial track, the target track and the ignition track-changing position, and the corresponding expected consumption amount required to be consumed for completing the track-changing prediction planning process is generated.

According to a preferred embodiment, the method further comprises the steps of: acquiring current aerodynamic force information which is acquired in real time at a first moment when a satellite is located at the initial adjustment position of the satellite, is related to an area related to the initial adjustment position of the satellite and is used for providing a parameter set required by atmosphere prediction, and performing prediction calculation based on a position relation between the area related to the ignition orbital transfer position and the initial adjustment position of the satellite to generate first aerodynamic force information located in the area related to the ignition orbital transfer position;

The inflatable antenna provided by the invention at least has the following beneficial technical effects:

(1) according to the volume-controllable inflatable antenna provided by the invention, the atmospheric resistance borne by the satellite is effectively utilized by increasing and decreasing the specific surface area, namely the relative volume of the antenna, and meanwhile, the pointing deviation duration and the fuel consumption of the antenna during the orbit transfer are taken into consideration, so that the in-orbit operation life of the satellite is effectively prolonged, the pointing adaptation loss duration caused by the pointing deviation of the antenna is effectively reduced, the real-time performance and the orbit changing precision of the satellite transfer process are improved, and the fuel consumption required by the orbit changing transfer is reduced.

(2) According to the method, the prediction-correction process of the antenna adjustment is completed by setting the relevant aerodynamic force information acquired at different moments, the sectional adjustment can be quickly and approximately adjusted in place to reduce the orbit transfer time, and the uncertainty of the prediction result of the front section is corrected by the adjustment of the subsequent antenna with smaller amplitude, so that the error of the prediction result caused by time fluctuation and space difference can be converged into an allowable error range, the purpose of enabling the satellite orbit transfer process to be more stable is achieved by the sectional adjustment, the defect that the fluctuation and the adjustment error are larger due to one-time adjustment in the prior art is overcome, and the accuracy and the position accuracy of the satellite orbit transfer can be effectively improved.

Drawings

Fig. 1 is a simplified module connection diagram of a preferred embodiment of the gas filled antenna provided by the present invention.

List of reference numerals

1: the first obtaining module 2: the second acquisition module 3: first adjusting module

4: the second adjustment module 201: the environment monitoring unit 202: adjustment correction unit

Detailed Description

The present invention will be described in detail with reference to the accompanying drawings.

As shown in fig. 1, a volume-controllable inflatable antenna comprises at least a satellite thruster, at least one acquisition module, and at least one adjustment module, wherein a first adjustment module for adjusting the position and the attitude of the inflatable antenna is configured to:

According to the volume-controllable inflatable antenna provided by the invention, the atmospheric resistance borne by the satellite is effectively utilized by increasing and decreasing the specific surface area, namely the relative volume of the antenna, and meanwhile, the pointing deviation duration and the fuel consumption of the antenna during the orbit transfer are taken into consideration, so that the in-orbit operation life of the satellite is effectively prolonged, the pointing adaptation loss duration caused by the pointing deviation of the antenna is effectively reduced, the real-time performance and the orbit changing precision of the satellite transfer process are improved, and the fuel consumption required by the orbit changing transfer is reduced. In addition, the preference of real-time performance or fuel consumption can be adjusted for actual conditions, and the orbital transfer demand mixing proportion coefficient is preset, so that the satellite can be rapidly transferred under the action of aerodynamic force or the fuel consumption is minimum according to a given coefficient, and an optimal control strategy capable of meeting the actual engineering demand is obtained.

According to the method, the prediction-correction process of the antenna adjustment is completed by setting the relevant aerodynamic force information acquired at different moments, the sectional adjustment can be quickly and approximately adjusted in place to reduce the orbit transfer time, and the uncertainty of the prediction result is corrected through the smaller fluctuation range of the subsequent antenna, so that the error of the prediction result caused by time fluctuation and space difference can be converged into an allowable error range, the satellite orbit transfer is more stable, the defects of large fluctuation and adjustment error caused by one-time adjustment in the prior art are overcome, and the accuracy and position precision of the satellite orbit transfer can be effectively improved.

Preferably, the first aerodynamic information is estimated according to the current first aerodynamic information at the current position, including the direction and the wind power, but certain errors are certainly caused, so that new first aerodynamic information needs to be acquired and determined again after the ignition track-changing position is reached, and the prediction program is improved according to the first aerodynamic information; the first aerodynamic information generates corresponding new antenna adjustment control information, and the second orbital transfer is carried out based on the new antenna adjustment control information, so that the orbital transfer accuracy is accurate.

Preferably, the satellite propulsion system may be a conventional chemical propulsion system or an electric propulsion system, and thus the ignition orbital transfer position is not limited to the selection of the satellite propulsion system, and the ignition orbital transfer position may be an electric propulsion orbital transfer position. The electric propulsion transfer orbit control method for the geostationary orbit spacecraft, disclosed in the Chinese patent with the publication number of CN201610041639.3, shows that compared with the traditional chemical propulsion system, the electric propulsion system has the advantages of high specific impulse, accurately adjustable thrust, high control precision, greatly reduced propellant requirement for completing the same space mission and the like.

Preferably, the second obtaining module may be an airborne avionics device that performs sensing, measuring, calculating and outputting of atmospheric parameters, and provides real-time aerodynamic information including a real-time atmospheric parameter set required for atmospheric prediction to the second adjusting module. The aerodynamic force information can comprise drag coefficient, lift coefficient, roll moment coefficient and the like. The prior art mainly comprises two types of traditional atmosphere data systems and embedded atmosphere data systems. The traditional atmospheric data system takes an airspeed head extending out of a machine body as a mark, combines other sensors (an attack angle/sideslip angle/total temperature sensor) to realize direct measurement of total pressure, static pressure, an attack angle, a sideslip angle and total temperature, then utilizes an atmospheric data computer to carry out relevant resolving and correction to complete measurement of atmospheric data, has simple measurement principle, earliest development and mature and stable technology, and is widely applied to domestic and foreign military aircraft and civil aircraft. An embedded atmospheric data system is a system that measures the pressure distribution of the aircraft surface by means of an array of pressure sensors embedded at different locations on the aircraft nose (or wing) and obtains atmospheric parameters from the pressure distribution. The technology is provided and developed, and the level of the atmospheric data sensing technology is comprehensively improved. The device not only is convenient for stealth, but also effectively solves the problem of atmospheric data measurement during flight with large attack angle and high Mach number, and greatly improves the application range of the atmospheric data system. Preferably, the instruction for executing the relevant specific event may be an instruction for instructing the satellite to perform orbital transfer or to correct the orbital deviation of the satellite, and includes at least necessary information such as an initial orbit and a target orbit required for orbital transfer.

According to a preferred embodiment, the first antenna adjustment control information determined by the first adjustment module based on the tracking environment monitoring information at least comprises a first pointing adjustment duration for antenna pointing adjustment and a first spreading adjustment duration for antenna specific surface area adjustment, and a first moving duration is determined based on one of the first pointing adjustment duration and the first spreading adjustment duration which is larger in value, wherein the first adjustment module determines an antenna initial adjustment position corresponding to the first moving duration in combination with the ignition tracking position and the initial track when the first moving duration does not exceed a preset duration threshold, so that a position where the antenna starts to be adjusted and is located on the initial track can be determined based on the antenna initial adjustment position. Preferably, the first moving time period is a time period required for the satellite to move from the initial satellite adjusting position to the ignition orbital transfer position along the initial orbit, and the first moving time period can be calculated because parameters such as the initial orbit, the ignition orbital transfer position and the speed of the satellite are known.

Preferably, when the dynamic association relationship is that the distribution weight coefficient corresponding to one of the distribution weight coefficients changes, the distribution weight coefficient corresponding to the other distribution weight coefficient also changes correspondingly, that is, the preset duration threshold value is dynamically changed gradually along with the repeated execution times of the steps, and the change trend can be gradually reduced.

Preferably, the first pointing adjustment duration and the first unfolding adjustment duration are determined based on the first aerodynamic information, wherein the first unfolding adjustment duration does not exceed the adjustment duration for moving the whole antenna from the fully unfolded position to the fully folded position, that is, the antenna can be unfolded to be fully unfolded if the first aerodynamic information is assistance, and can be folded to be fully folded to reduce the resistance area if the first aerodynamic information is resistance, but must be adjusted to the first pointing adjustment duration corresponding to the first aerodynamic information; at least one movement duration may be determined based on a greater one of the first pointing adjustment duration and the first deployment adjustment duration, and the movement duration may be combined with the ignition derailment position to determine an antenna initial adjustment position. The antenna initial adjustment position is the position where the antenna starts to adjust the pointing direction and the spreading area, and it is guaranteed that the antenna is adjusted to the preset pointing direction and the preset spreading area based on the predicted first aerodynamic information when the antenna rotates to the ignition track changing position.

When the moving time length does not exceed the preset threshold time length, namely the moving time length is the preset threshold time length which is separated from the alignment between the antenna and the ground field within an acceptable range in the moving time length, the preset threshold time length can limit the adjustable degree of the antenna through presetting, so that the phenomenon that the antenna rotates and/or is excessively unfolded when aerodynamic force information is utilized/reduced to the maximum degree can be avoided, the time length of misalignment with the ground field is greatly prolonged, and the communication quality between the satellite and the earth is seriously influenced; when the moving time length exceeds the preset threshold value time length, the preset distribution proportion between the first pointing adjustment time length and the first unfolding adjustment time length is controlled, so that the short misalignment time length can be reached under the condition of reaching a better assistance degree until the newly obtained moving time length does not exceed the preset threshold value time length. Or a preference obtained by re-analyzing a large amount of data acquired when the orbit of another satellite is changed, by means of which a preferred preset distribution weight can be directly set.

The travel time period is the greater deployment time period between the steering time period and the deployment time period, since it may not be fully deployed after steering is in place, or the travel time period is the greater steering time period between the steering time period and the deployment time period when the deployment/retraction has been completed and the steering is not completed. If the steering time length is less than the unfolding time length, namely the antenna has already steered to the right position but is not completely unfolded to the right position, the moving time length is the larger unfolding time length between the steering time length and the unfolding time length, and the satellite is separated from aligning with the ground field in the moving time length; if the steering duration is longer than the unfolding duration, that is, the antenna is unfolded in place but is not completely steered in place, at this time, the moving duration is the larger steering duration between the steering duration and the unfolding duration, that is, the larger duration in the two cases is the same. After the satellite completes the orbit transfer task, the antenna needs to be recovered to align to the ground field, so that new steering time and new unfolding time need to be obtained after the antenna state is judged again. The auxiliary combustion thruster can be assisted to conduct rail changing to the maximum extent, fuel consumption is reduced, meanwhile, the time length of misalignment with a ground field is reduced to the maximum extent, rail changing is conducted rapidly, and communication connection between the antenna and the ground field is recovered rapidly.

Preferably, the prediction calculation process may be: the multivariate information database based on other satellites is established by information interaction with a plurality of other satellites, the multivariate information database at least comprises corresponding relations between the current aerodynamic information and the first aerodynamic information of other satellites under different position relations, the correspondence may include a one-to-one correspondence between actual data or a coefficient proportional relationship or a trend of change with a time period from the first time to the second time that provides a prediction of aerodynamic information, so that the current satellite can quickly obtain the predicted first aerodynamic information through the known position relation and the current aerodynamic information only through an information matching mode, the stratospheric atmosphere based on high-altitude flight mainly moves horizontally, the airflow is relatively stable and the predictability is high, the large amount of actual data support thereby reduces aerodynamic prediction computation processes and enables rapid and reliable acquisition of predictive information. Preferably, the predictive computation process may also be a meteorological model formulated according to a differential equation describing atmospheric behavior in a certain time domain and space domain characterized by given initial and boundary conditions, respectively, as provided in chinese patent publication No. CN 105874479A. Preferably, the positional relationship between the area involved in the ignition derailment position and the initial satellite adjustment position may be a relative displacement value between two points along the initial orbit. However, due to the existence of temporal fluctuation and spatial difference, a certain error exists between the prediction result and the actual temporal actual position, and the error can be converged into an allowable error range through a subsequent further correction process.

when the first adjusting module determines at least one ignition track-changing position based on the initial track and the target track acquired by the first acquiring module, a track-changing prediction planning process of successfully transferring the ignition track-changing position from the initial track to the target track from the ignition track-changing position in a mode of neglecting the track-changing environment monitoring information is completed by combining the initial track, the target track and the ignition track-changing position, and the corresponding expected consumption amount required to be consumed for completing the track-changing prediction planning process is generated. Preferably, the orbital transfer prediction planning process is to acquire the speeds of the satellites on the initial orbit and the target orbit on the premise of the initial orbit and the target orbit and the ignition orbital transfer point, and predict and calculate the predicted consumption of the satellite thruster required for completing the specific event on the basis of the condition that the influence of the orbital transfer environment monitoring information, namely aerodynamic force, on the satellite transfer orbit is not considered.

According to a preferred embodiment, the second adjusting module is configured to determine the orbital transfer demand mixing scaling factors corresponding to the satellite thruster and the inflation antenna, respectively, based on the first antenna adjustment control information and the estimated consumption amount under the condition that the aerodynamic assistance factor of the orbital transfer environment monitoring information is determined at the first time. Preferably, in the method, the device and the storage medium for forecasting the middle-term orbit of the low-orbit spacecraft disclosed in, for example, chinese patent publication No. CN108820260A, the perturbation of the atmospheric resistance, which is the most important perturbation force influencing factor in the orbit determination and orbit forecasting models, is decomposed, and specific methods for respectively determining the atmospheric density parameter, the spacecraft equivalent windward area parameter and the atmospheric resistance coefficient are provided. Or a measuring method for determining the pneumatic parameters in the aircraft starting parameter measuring method disclosed in the Chinese patent with the publication number of CN 107588921A. In addition, for example, chinese patent publication No. CN102809377B discloses an aircraft inertia/pneumatic model combined navigation method, in which an inertial navigation system is assisted by navigation parameters calculated by a pneumatic model, and the resultant force and moment applied to an aircraft can be obtained by solving known pneumatic parameters, profile parameters, control quantities, and motion parameter information of the aircraft according to a kinetic equation of the aircraft and the pneumatic parameters of the aircraft provided by the inertial navigation system. Similarly, by combining the determined expansion degree and relative pointing direction of the inflatable antenna with known parameters of the satellite, a parameter set required by atmosphere prediction, which is composed of an atmospheric density parameter, a spacecraft equivalent frontal area parameter, an atmospheric resistance coefficient and the like, can be determined, and then a resultant external force and moment applied to the satellite by aerodynamic force information can be obtained by solving a kinetic equation and/or an aerodynamic equation, so that the atmospheric influence is quantized.

When the aerodynamic assistance coefficient is smaller than 1, the second adjusting module determines that the aerodynamic information influences the execution process of the related specific event in a resistance mode, determines the orbital transfer demand mixing scaling coefficient corresponding to the inflation antenna in a mode of reducing the influence of the aerodynamic information to the maximum extent by means of the inflation antenna, and then determines the orbital transfer demand mixing scaling coefficient corresponding to the satellite thruster in a mode of increasing the estimated consumption to the minimum extent on the basis of the orbital transfer demand mixing scaling coefficient corresponding to the inflation antenna.

The aerodynamic auxiliary coefficient can be an included angle which is based on the aerodynamic vector in the first aerodynamic information and the flying direction vector when the ignition is switched to the orbit and has a variation range of 0-180 degrees, and the ratio of a fixed angle to the included angle is the aerodynamic auxiliary coefficient. Preferably, the orbital transfer environment monitoring information which can be judged according to the collected first aerodynamic force information at the first moment includes the aerodynamic force auxiliary coefficient.

One of the fixed angles may be any value between 0 ° and 90 °, for example, 35 °, 45 ° or 90 °, the fixed angle is determined according to whether the current aerodynamic vector can be increased or decreased by rotating the antenna to point and/or adjusting the antenna to unfold, for example, when the included angle is 180 °, that is, when the aerodynamic force affects the satellite orbit change in the form of resistance, and it is determined that the aerodynamic force assist coefficient is smaller than 1, at this time, the turning and unfolding degree of the pneumatic antenna can be determined in a manner of maximally decreasing the influence of the aerodynamic force information, for example, the pneumatic antenna can be completely folded or rotated to the reverse side of the windward side, and the windage coefficient can be decreased by decreasing the windage area. Thereby enabling determination of first antenna adjustment control information based on the tracking environment monitoring information.

After the first antenna adjustment control information is determined, the atmospheric influence can be quantified, and therefore the resultant force and moment exerted by the aerodynamic force information on the satellite can be obtained. And generating the corresponding estimated consumption required for completing the orbital transfer estimation planning process and the corresponding estimated resultant external force and the estimated torque applied to the satellite based on the orbital transfer estimation planning process. The value obtained by dividing the total external force or moment exerted by the aerodynamic force information on the satellite by the total external force or moment exerted by the aerodynamic force information on the satellite and the sum of the expected total external force or expected moment exerted by the satellite propeller on the satellite is the orbital transfer demand mixing scaling factor corresponding to the inflation antenna, and then the sum of the orbital transfer demand mixing scaling factors respectively corresponding to the satellite propeller and the inflation antenna is equal to 1, so that the orbital transfer demand mixing scaling factor corresponding to the satellite propeller determined in a manner of reducing the estimated consumption to the maximum extent on the basis of the determination of the orbital transfer demand mixing scaling factor corresponding to the inflation antenna is obtained.

It should be noted that the above-mentioned embodiments are exemplary, and that those skilled in the art, having benefit of the present disclosure, may devise various arrangements that are within the scope of the present disclosure and that fall within the scope of the invention. It should be understood by those skilled in the art that the present specification and figures are illustrative only and are not limiting upon the claims. The scope of the invention is defined by the claims and their equivalents.

Claims

1. A volumetrically controllable inflatable antenna comprising at least a satellite thruster, at least two acquisition modules, and at least two adjustment modules, wherein a first adjustment module for adjusting the position and attitude of the inflatable antenna is configured to:

determining a first control instruction and a second control instruction corresponding to the orbital transfer demand mixing proportionality coefficient respectively corresponding to the satellite thruster and the inflation antenna and a corresponding first control instruction and a second control instruction based on the first antenna adjustment control information and the estimated consumption, so that the first adjustment module of the inflation antenna receives the first control instruction in a mode of performing aerodynamic compensation on a second adjustment module of the satellite thruster receiving the second control instruction, and performs at least one adjustment correction based on second aerodynamic information, acquired by the second acquisition module at a second moment, associated with an area related to the ignition orbital transfer position to execute at least one related specific event;

the first antenna adjustment control information determined by the first adjustment module based on the tracking environment monitoring information at least includes a first pointing adjustment duration for antenna pointing adjustment and a first spreading adjustment duration for antenna specific surface area adjustment, and determines a first movement duration based on one of the first pointing adjustment duration and the first spreading adjustment duration, which is larger in value, wherein,

the first adjusting module is used for determining an antenna initial adjusting position corresponding to the first moving duration by combining the ignition track-changing position and the initial track when the first moving duration does not exceed a preset duration threshold, so that the position, where the antenna starts to be adjusted, of the initial track can be determined based on the antenna initial adjusting position;

the first adjustment module is further configured to perform the steps of:

s4: and repeating the steps S1-S3 in sequence until the first moving time length does not exceed the preset time length threshold value, stopping and outputting the first pointing adjustment time length, the first unfolding adjustment time length and the antenna initial adjustment position corresponding to the first moving time length so as to realize an optimized solution between the estimated consumption minimization and the maximum orbital transfer efficiency.

2. The gas filled antenna of claim 1, wherein the second adjustment module comprises at least an environmental monitoring unit configured to:

3. The gas filled antenna of claim 2, wherein the second adjustment module is configured to determine a projected consumption required by the satellite propulsor to perform a particular event of interest upon receiving at least one instruction to perform the particular event, the second adjustment module configured to:

when the first adjusting module determines at least one ignition track-changing position based on the initial track and the target track acquired by the first acquiring module, the track-changing prediction planning process of successfully transferring the ignition track-changing position from the initial track to the target track from the ignition track-changing position in a mode of neglecting the track-changing environment monitoring information is completed by combining the initial track, the target track and the ignition track-changing position, and the corresponding prediction consumption consumed for completing the track-changing prediction planning process is generated.

4. The inflation antenna of claim 3, wherein the second adjustment module is configured to determine the orbital transfer demand mixing scaling factor for the satellite thruster and the inflation antenna based on the first antenna adjustment control information and the estimated consumption amount under the condition of determining the aerodynamic assistance factor of the orbital transfer environment monitoring information at a first time, wherein:

when the aerodynamic assistance coefficient is larger than 1, the second adjusting module judges that the aerodynamic information influences the execution process of a related specific event in an assistance mode, determines an orbital transfer demand mixing scaling coefficient corresponding to the air-filled antenna in a mode of utilizing the aerodynamic information to the maximum extent by means of the air-filled antenna, and then determines the orbital transfer demand mixing scaling coefficient corresponding to the satellite thruster in a mode of reducing the estimated consumption to the maximum extent on the basis of the orbital transfer demand mixing scaling coefficient corresponding to the air-filled antenna;

5. The gas filled antenna of claim 4, wherein the second adjustment module further comprises an adjustment modification unit configured to:

and acquiring an error correction coefficient of first antenna adjustment control information corresponding to the first aerodynamic information at a second moment according to the deviation between the second aerodynamic information and the first aerodynamic information, performing adjustment correction within a small adjustment range on satellite pointing information corresponding to the second moment and corresponding satellite deployment information respectively based on the error correction coefficient so that the satellite can accurately correspond to the actually measured second aerodynamic information during the execution of the related specific event, and updating the orbital transfer demand mixing proportion coefficient correspondingly based on the corrected first antenna adjustment control information so that the consumption provided by the satellite propeller during the execution of the related specific event can be further accurately controlled.

6. A method for controlling the deployment volume of an inflatable antenna, comprising at least the steps of:

determining at least one ignition track transfer position based on the obtained initial track and the target track, generating track transfer environment monitoring information based on first aerodynamic information which is obtained at a first moment and is associated with an area related to the ignition track transfer position, and determining first antenna adjustment control information based on the track transfer environment monitoring information;

determining a first control instruction and a second control instruction corresponding to the orbital transfer demand mixing proportionality coefficient respectively corresponding to the satellite thruster and the inflation antenna based on the first antenna adjustment control information and the estimated consumption, so that the inflation antenna receives the first control instruction in a manner of performing aerodynamic compensation on the satellite thruster receiving the second control instruction, and performing at least one adjustment correction based on second aerodynamic information acquired at a second moment and associated with an area related to the ignition orbital transfer position to execute at least one related specific event;

the deployment volume control method comprises at least the following steps:

the first antenna adjustment control information determined based on the tracking environment monitoring information includes at least a first pointing adjustment duration for antenna pointing adjustment and a first deployment adjustment duration for antenna specific surface area adjustment, and the first movement duration is determined based on one of the first pointing adjustment duration and the first deployment adjustment duration, which is larger in value, wherein,

determining an initial antenna adjustment position corresponding to the first movement duration in combination with the ignition track-changing position and the initial track in response to the first movement duration not exceeding a preset duration threshold, so that a position where the antenna starts to be adjusted and is located on the initial track can be determined based on the initial antenna adjustment position;

the deployment volume control method further comprises the steps of: