阅读说明：本技术 一种基于气动力辅助的超低轨卫星轨道控制方法 (Ultra-low orbit satellite orbit control method based on aerodynamic force assistance ) 是由 王悦 张靖奕 于 2021-08-26 设计创作，主要内容包括：本发明公开一种基于气动力辅助的超低轨卫星轨道控制方法：S1：根据已知卫星瞬时轨道要素,卫星平均轨道要素；S2：根据卫星平均轨道要素与目标平均轨道要素差距以及误差容限大小,确定卫星所处控制状态；S3：根据卫星所处控制状态及第一控制方法确定所需气动力方向,确定气动舵偏转方向；S4：将卫星全部受力代入摄动方程,得到新的瞬时轨道要素；S5：利用新的瞬时轨道要素计算空间误差,判断空间误差径向分量是否大于给定最大值；若是,返回S2,重复S2～S5；若否,步骤S3中第一控制方法替换为第二控制方法,返回S2,重复S2～S5。本发明可保证超低轨卫星完成对地观测的主要任务,可利用超低地球轨道处的独特大气环境。(The invention discloses an ultra-low orbit satellite orbit control method based on aerodynamic force assistance, which comprises the following steps: s1: averaging the orbit elements of the satellite according to the known instantaneous orbit elements of the satellite; s2: determining the control state of the satellite according to the difference between the average orbit element of the satellite and the target average orbit element and the error tolerance; s3: determining the required aerodynamic direction according to the control state of the satellite and the first control method, and determining the deflection direction of the aerodynamic rudder; s4: substituting all stresses of the satellite into a perturbation equation to obtain a new instantaneous orbit element; s5: calculating a space error by using the new instantaneous orbit element, and judging whether the radial component of the space error is greater than a given maximum value or not; if yes, returning to S2, and repeating S2-S5; if not, the first control method is replaced with the second control method in step S3, the process returns to S2, and S2 to S5 are repeated. The invention can ensure that the ultra-low orbit satellite completes the main task of earth observation and can utilize the unique atmospheric environment at the ultra-low earth orbit.)

1. An ultra-low orbit satellite orbit control method based on aerodynamic assistance is characterized in that: the method comprises the following steps:

s1: according to the known instantaneous orbit elements of the satellite, the average orbit elements of the satellite at the moment are obtained by using a flat-heel estimation algorithm;

s2: determining the control state of the satellite according to the difference between the satellite average orbit element and the target average orbit element and the size of the error tolerance;

s3: determining a required aerodynamic direction according to the control state of the satellite and a first control method, so as to determine the deflection direction of the aerodynamic rudder;

s4: substituting all stresses of the satellite into a perturbation equation to carry out integration to obtain a new instantaneous orbit element;

s5: calculating a spatial error by using the new instantaneous orbit element, and judging whether a radial component of the spatial error is greater than a given maximum value; if yes, returning to the step S2, and repeatedly executing the step S2 to the step S5; if not, the first control method in step S3 is replaced with the second control method, the process returns to step S2, and steps S2 to S5 are repeated.

2. The ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 1, wherein: the specific process of step S2 is as follows:

wherein the average semi-major axis a of the satellite_mAverage semi-major axis of interest a_m0Error margin Δ a; if the initial time a_m≤a_m0Then the semi-major axis needs to be controlled to be increased until a_m＞a_m0+ Δ a; if the initial time a_m＞a_m0Then the semi-major axis needs to be controlled to decrease until a_m＜a_m0- Δ a; when a thereafter_m＜a_m0Δ a then controls the semi-major axis to increase until a_m＞a_m0+ Δ a; when a is_m＞a_m0+ Δ a controls the semi-major axis to decrease until a_m＜a_m0- Δ a, cycled; where Δ a is a positive number representing the magnitude of the semi-major axis error tolerance;

wherein the average orbital element x of the satellite_mTarget mean orbit element x_m0Error margin Δ x; if x_m-x_m0If the | is less than or equal to the Δ x, the satellite is in the error tolerance range and does not need to be controlled; if x_m-x_m0If delta x is greater than the threshold, the satellite exceeds the upper limit of the error tolerance and needs to be controlled to reduce; if x_m-x_m0- Δ x, the satellite exceeds the lower margin of error tolerance and needs to be controlled for increase; wherein the average orbital element x of the satellite_mIncluding satellite mean orbital inclination i_mMean satellite riseCrossing point right ascension omega_mMean eccentricity of the satellite e_xmAnd e_ym(ii) a Target average orbital element x_m0Including a target average orbital inclination i_m0Target mean intersection right ascension omega_m0Target average eccentricity e_xm0And e_ym0(ii) a The error margin Δ x is a positive number representing the magnitude of the error margin.

3. The ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 1, wherein: the first control method described in step S3 is to control the semimajor axis of the satellite using thrust and control the orbital inclination, right ascension and eccentricity of the satellite using aerodynamic force.

4. The ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 3, characterized in that: the control method of the satellite orbit inclination angle and the ascent intersection right ascension specifically comprises the following steps:

considering the position of the satellite in orbit, i.e. the latitude argument u, the control is divided into the following 9 cases:

case (1): when the satellite orbit inclination angle exceeds the upper limit of the error tolerance and the satellite ascension point exceeds the upper limit of the error tolerance, applying negative control when the satellite latitude argument is in a first quadrant and applying positive control when the satellite latitude argument is in a third quadrant;

case (2): when the satellite orbit inclination angle exceeds the upper limit of the error tolerance and the ascension point of the satellite is within the range of the error tolerance, applying negative control when the latitude argument of the satellite is in a first quadrant and a fourth quadrant, and applying positive control when the latitude argument of the satellite is in a second quadrant and a third quadrant;

case (3): when the satellite orbit inclination angle exceeds the upper limit of the error tolerance and the satellite ascension point exceeds the lower limit of the error tolerance, applying negative control when the satellite latitude argument is in a fourth quadrant and applying positive control when the satellite latitude argument is in a second quadrant;

case (4): when the satellite orbit inclination angle is in the error tolerance range and the satellite ascension point exceeds the upper limit of the error tolerance, applying negative control when the satellite latitude argument is in a first quadrant and a second quadrant, and applying positive control when the satellite latitude argument is in a third quadrant and a fourth quadrant;

case (5): when the satellite orbit inclination angle is within the error tolerance range and the satellite ascent point ascent is within the error tolerance range, no control is required to be applied;

case (6): when the satellite orbit inclination angle is in the error tolerance range and the satellite ascension point exceeds the lower limit of the error tolerance, applying negative control when the satellite latitude argument is in a third quadrant and a fourth quadrant, and applying positive control when the satellite latitude argument is in a first quadrant and a second quadrant;

case (7): when the satellite orbit inclination angle exceeds the lower limit of the error tolerance and the ascension of the satellite intersection point exceeds the upper limit of the error tolerance, applying negative control when the latitude argument of the satellite is in the second quadrant and applying positive control when the latitude argument of the satellite is in the fourth quadrant;

case (8): when the satellite orbit inclination angle exceeds the lower limit of the error tolerance and the ascension point of the satellite is within the range of the error tolerance, applying negative control when the latitude argument of the satellite is in the second quadrant and the third quadrant, and applying positive control when the latitude argument of the satellite is in the first quadrant and the fourth quadrant;

case (9): when the inclination angle of the satellite orbit exceeds the lower limit of the error tolerance and the ascension of the satellite intersection point exceeds the lower limit of the error tolerance, negative control is applied when the amplitude angle of the satellite latitude is in the third quadrant, and positive control is applied when the amplitude angle of the satellite latitude is in the first quadrant.

5. The ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 3, characterized in that: the control method of the satellite eccentricity ratio specifically comprises the following steps:

radial force F_rThe method is mainly used for controlling the orbit inclination angle and the ascent crossing right ascension of the satellite, and considering the position of the satellite on the orbit, namely the latitude argument u, the control is divided into the following 9 conditions:

case (1): when the eccentricity x-direction component of the satellite exceeds the lower limit of the error tolerance and the y-direction component exceeds the lower limit of the error tolerance, applying negative control when the latitude argument of the satellite is in a fourth quadrant and applying positive control when the latitude argument of the satellite is in a second quadrant;

case (2): when the eccentricity x-direction component of the satellite exceeds the lower limit of the error tolerance and the y-direction component of the satellite is in the range of the error tolerance, negative control is applied when the latitude argument of the satellite is in a third quadrant and a fourth quadrant, and positive control is applied when the latitude argument of the satellite is in a first quadrant and a second quadrant;

case (3): when the eccentricity x-direction component of the satellite exceeds the lower limit of the error tolerance and the y-direction component exceeds the upper limit of the error tolerance, applying negative control when the latitude argument of the satellite is in the third quadrant and applying positive control when the latitude argument of the satellite is in the first quadrant;

case (4): when the eccentricity x-direction component of the satellite is in the error tolerance range and the y-direction component exceeds the lower limit of the error tolerance, negative control is applied when the latitude argument of the satellite is in a first quadrant and a fourth quadrant, and positive control is applied when the latitude argument of the satellite is in a second quadrant and a third quadrant;

case (5): when the eccentricity x-direction component of the satellite is within the error tolerance range and the y-direction component of the satellite is within the error tolerance range, no control is required to be applied;

case (6): when the eccentricity x-direction component of the satellite is in the error tolerance range and the y-direction component exceeds the upper error tolerance limit, negative control is applied when the latitude argument of the satellite is in the second quadrant and the third quadrant, and positive control is applied when the latitude argument of the satellite is in the first quadrant and the fourth quadrant;

case (7): when the eccentricity x-direction component of the satellite exceeds the upper limit of the error tolerance and the y-direction component exceeds the lower limit of the error tolerance, applying negative control when the latitude argument of the satellite is in the first quadrant and applying positive control when the latitude argument of the satellite is in the third quadrant;

case (8): when the x-direction component of the satellite eccentricity exceeds the upper limit of the error tolerance and the y-direction component is in the range of the error tolerance, negative control is applied when the latitude argument of the satellite is in a first quadrant and a second quadrant, and positive control is applied when the latitude argument of the satellite is in a third quadrant and a fourth quadrant;

case (9): when the eccentricity x-direction component of the satellite exceeds the lower error tolerance limit and the y-direction component exceeds the upper error tolerance limit, negative control is applied when the latitude argument of the satellite is in the second quadrant, and positive control is applied when the latitude argument of the satellite is in the fourth quadrant.

6. The ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 3, characterized in that: the control method of the satellite semi-major axis specifically comprises the following steps:

thrust F in tracking direction_uThe device is mainly used for controlling the semi-major axis of the satellite; because the difference between other orbit elements and the target orbit can affect the deflection condition of the control plane, so as to affect the resistance received by the satellite, when the semimajor axis is smaller than or larger than the target semimajor axis, 81 conditions are respectively controlled; thrust F according to the direction of the applied track_uThe 81 cases are integrated into the following 16 cases:

case (1): the inclination angle of the satellite orbit and the ascension of the ascending intersection simultaneously exceed the upper limit or the lower limit of the error tolerance, and the x-direction component and the y-direction component of the satellite eccentricity simultaneously exceed the upper limit or the lower limit of the error tolerance; if the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (2): the satellite orbit inclination angle and the ascension crossing point simultaneously exceed the upper limit or the lower limit of an error tolerance, and one of the x-direction component and the y-direction component of the satellite eccentricity is within the error tolerance range; if the semi-major axis of the satellite needs to be controlled to be increased, applying a thrust which is greater than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying a thrust which is greater than or equal to the sum of the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (3): the satellite orbit inclination angle and the ascension of the ascending intersection simultaneously exceed the upper limit or the lower limit of an error tolerance, one of the x-direction component and the y-direction component of the satellite eccentricity exceeds the upper limit of the error tolerance, and the other exceeds the lower limit of the error tolerance; if the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (4): the satellite orbit inclination angle and the ascension point of the ascending intersection simultaneously exceed the upper limit or the lower limit of an error tolerance, and the x-direction component and the y-direction component of the satellite eccentricity are in the error tolerance range; if the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in a first quadrant and a third quadrant, and applying thrust which is greater than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in a second quadrant and a fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (5): one of the satellite orbit inclination angle and the ascension of the ascending intersection point is within the error tolerance range, and the x-direction component and the y-direction component of the satellite eccentricity simultaneously exceed the upper limit or the lower limit of the error tolerance; if the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in a first quadrant and a third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in a second quadrant and a fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (6): one of the satellite orbit inclination angle and the rising point right ascension is within an error tolerance range, and one of the x-direction component and the y-direction component of the satellite eccentricity is within the error tolerance range; if the semi-long axis of the satellite needs to be controlled to be increased, applying a thrust which is greater than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body; if the semi-long axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body;

case (7): one of the satellite orbit inclination angle and the ascension of the ascending intersection point is within the error tolerance range, one of the x-direction component and the y-direction component of the satellite eccentricity exceeds the upper limit of the error tolerance, and the other exceeds the lower limit of the error tolerance; if the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (8): one of the satellite orbit inclination angle and the rising point right ascension is within an error tolerance range, and the x-direction component and the y-direction component of the satellite eccentricity are within the error tolerance range; if the semi-long axis of the satellite needs to be controlled to be increased, thrust which is larger than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body is applied; if the semi-long axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body;

case (9): the inclination angle of the satellite orbit and the ascension angle of the ascending intersection exceed an upper limit and another lower limit of the error tolerance, and the x-direction component and the y-direction component of the satellite eccentricity exceed the upper limit or the lower limit of the error tolerance simultaneously; if the semi-major axis of the satellite needs to be controlled to be increased, thrust which is greater than or equal to the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the first quadrant and the third quadrant, and thrust which is greater than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (10): the inclination angle of the satellite orbit and the ascension angle of the ascending intersection are beyond the upper limit of the error tolerance, and the other one of the upper limit and the lower limit of the error tolerance and the x-direction component and the y-direction component of the satellite eccentricity is within the error tolerance range; if the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (11): the inclination angle of the satellite orbit and the ascension angle of the ascending intersection exceed an upper limit and another lower limit of an error tolerance, and the eccentricity of the satellite exceeds an upper limit and another lower limit of the error tolerance respectively; if the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (12): the inclination angle of the satellite orbit and the ascension angle of the ascending intersection are beyond the upper limit of the error tolerance, and the eccentricity x-direction component and the eccentricity y-direction component of the satellite are within the error tolerance range; if the semi-major axis of the satellite needs to be controlled to be increased, thrust which is greater than or equal to the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the first quadrant and the third quadrant, and thrust which is greater than or equal to the sum of the resistance generated by deflection of the vertical rudder and the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust which is less than or equal to the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the first quadrant and the third quadrant, and thrust which is less than or equal to the sum of the resistance generated by deflection of the vertical rudder and the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (13): the inclination angle of the satellite orbit and the ascension of the ascending intersection point are both within the error tolerance range, and the x-direction component and the y-direction component of the satellite eccentricity simultaneously exceed the upper limit or the lower limit of the error tolerance; if the semi-major axis of the satellite needs to be controlled to be increased, thrust which is greater than or equal to the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the first quadrant and the third quadrant, and thrust which is greater than or equal to the sum of the resistance generated by deflection of the horizontal rudder, radial force and the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust which is less than or equal to the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the first quadrant and the third quadrant, and thrust which is less than or equal to the sum of the resistance generated by deflection of the horizontal rudder and the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (14): the satellite orbit inclination angle and the ascension point right ascension are both within the error tolerance range, and one of the x-direction component and the y-direction component of the satellite eccentricity is within the error tolerance range; if the semi-major axis of the satellite needs to be controlled to be increased, applying a thrust which is more than or equal to the sum of the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body;

case (15): the inclination angle of the satellite orbit and the ascension of the ascending intersection point are both in the error tolerance range, one of the x-direction component and the y-direction component of the satellite eccentricity exceeds the upper limit of the error tolerance, and the other exceeds the lower limit of the error tolerance; if the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in a first quadrant and a third quadrant, and applying thrust which is greater than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in a second quadrant and a fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant;

case (16): the inclination angle of the satellite orbit and the ascension point right ascension are both in the error tolerance range, and the x-direction component and the y-direction component of the satellite eccentricity are both in the error tolerance range; if the semi-major axis of the satellite needs to be controlled to be increased, thrust which is more than or equal to the atmospheric resistance of the satellite body is applied; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust less than or equal to the atmospheric resistance of the satellite body.

7. The ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 1, wherein: the step S4 specifically includes: the perturbation equation in step S3 is integrated to obtain the instantaneous orbit element at the next time, taking into account the influence of the earth' S aspheric gravity, the sun-moon gravity, the sunlight pressure, the atmospheric resistance, and the aerodynamic force generated by the pneumatic rudder.

8. The ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 1, wherein: the step S5 specifically includes:

to accurately describe the deviation of the actual position of the satellite from the nominal orbital position at any latitude, a space error variable E ═ E (E) is defined_N,E_R)^TRepresenting the vector difference between the nominal track and the intersection of the actual track with the reference plane, E_NNormal component of spatial error, E_RIs the radial component of the spatial error;

let the difference between the actual track element and the nominal track element be (delta a, delta i, delta omega, delta e)_x、δe_y) Then, the normal and radial errors of the pipeline radius are respectively:

wherein the lower corner m represents the orbit element of the nominal orbit, n is the orbit angular velocity of the nominal orbit, ω_eThe rotational angular velocity of the earth;

if E is_RGreater than a given maximum value E_RmaxThe control method in step S3 is changed to the second control method.

9. An ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 8, wherein: the second control method is to control the semimajor axis and eccentricity of the satellite by thrust and control the orbital inclination angle and the right ascension of the satellite by pneumatic power.

10. An ultra-low orbit satellite orbit control method based on aerodynamic assistance as claimed in claim 9, wherein: the second control method comprises the following specific processes;

obtaining flat roots a and e by using flat root estimation method_x、e_yIn contrast to the target average orbit element, considering the position of the satellite on the orbit, i.e. latitude argument u, when the semi-major axis is smaller or larger than the target semi-major axis, there are 9 cases of control respectively:

case (1): the eccentricity x-direction component of the satellite exceeds the lower limit of the error tolerance, and the y-direction component of the satellite exceeds the lower limit of the error tolerance; if the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in the first quadrant; if the semi-long axis of the satellite needs to be controlled to be reduced, thrust smaller than total resistance is applied when the latitude argument of the satellite is in the first quadrant;

case (2): the eccentricity x-direction component of the satellite exceeds the lower limit of the error tolerance, and the y-direction component of the satellite is in the range of the error tolerance; if the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a first quadrant and a fourth quadrant; if the semi-long axis of the satellite needs to be controlled to be reduced, thrust smaller than total resistance is applied when the latitude argument of the satellite is in the first quadrant and the fourth quadrant;

case (3): the eccentricity x-direction component of the satellite exceeds the lower limit of the error tolerance, and the y-direction component of the satellite exceeds the upper limit of the error tolerance; if the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a fourth quadrant; if the semi-long axis of the satellite needs to be controlled to be reduced, thrust smaller than total resistance is applied when the latitude argument of the satellite is in a fourth quadrant;

case (4): the eccentricity x-direction component of the satellite is within the error tolerance range, and the y-direction component exceeds the lower limit of the error tolerance; if the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a first quadrant and a second quadrant; if the semi-long axis of the satellite needs to be controlled to be reduced, thrust smaller than total resistance is applied when the latitude argument of the satellite is in a first quadrant and a second quadrant;

case (5): the eccentricity x-direction component of the satellite is within the error tolerance range, and the y-direction component of the satellite is within the error tolerance range; at the moment, no matter how the semi-major axis of the satellite needs to be controlled to change, thrust equal to total resistance is applied;

case (6): the eccentricity x-direction component of the satellite is within the error tolerance range, and the y-direction component exceeds the upper limit of the error tolerance; if the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a third quadrant and a fourth quadrant; if the semi-long axis of the satellite needs to be controlled to be reduced, thrust smaller than total resistance is applied when the latitude argument of the satellite is in a third quadrant and a fourth quadrant;

case (7): the eccentricity x-direction component of the satellite exceeds the upper limit of the error tolerance, and the y-direction component of the satellite exceeds the lower limit of the error tolerance; if the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a second quadrant; if the semi-long axis of the satellite needs to be controlled to be reduced, thrust smaller than total resistance is applied when the latitude argument of the satellite is in a second quadrant;

case (8): the eccentricity x-direction component of the satellite exceeds the upper limit of the error tolerance, and the y-direction component of the satellite is in the range of the error tolerance; if the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a second quadrant and a third quadrant; if the semi-long axis of the satellite needs to be controlled to be reduced, thrust smaller than total resistance is applied when the latitude argument of the satellite is in the second quadrant and the third quadrant;

case (9): the eccentricity x-direction component of the satellite exceeds the upper limit of the error tolerance, and the y-direction component of the satellite exceeds the upper limit of the error tolerance; if the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a third quadrant; if the semi-long axis of the satellite needs to be controlled to be reduced, thrust smaller than total resistance is applied when the latitude argument of the satellite is in the third quadrant;

during a period of time not mentioned in the above 9 cases, a thrust equal to the total resistance is applied.

Technical Field

The invention relates to the technical field of spacecraft orbit dynamics, in particular to an ultra-low orbit satellite orbit control method based on aerodynamic force assistance.

Background

The ultra-low earth orbit is an earth orbit with the average orbit height lower than 450km, the ultra-low orbit satellite is a satellite working on the ultra-low orbit, the orbit height is between a dense atmosphere and a traditional near-earth orbit, a blank interval from the ground to the outer space is made up, and the ultra-low earth orbit can execute some special tasks and has unique advantages. Compared with the traditional low earth orbit satellite, the ultra-low orbit satellite has the advantages of lower orbit height, higher atmospheric density and larger influence caused by aerodynamic force. One of the primary uses of ultra-low orbit satellites is in earth observation, during which it is often desirable for the attitude of the satellite to remain stable to earth. Therefore, how to make reasonable use of aerodynamic force, while assisting the track control, to reduce the adverse effect on the task requires more intensive research.

At present, the autonomous orbit control methods applied to ultra-low orbit satellites and low orbit satellites mainly have two categories, one is to convert an autonomous control problem into a formation flight problem, one of the satellites is virtual and only operates under the action of gravity, and an optimization method is utilized to obtain a control method with minimum thrust or minimum cost; the other type utilizes the non-resistance flight technology, accurately measures the atmospheric resistance through a satellite-borne instrument, and applies control force to compensate the atmospheric resistance so as to maintain the track. However, the methods all consider the pneumatic force as a resistance force, apply a control force for compensation or offset, and ignore the potential application of the pneumatic force as a track control force.

Disclosure of Invention

In view of the above, the invention provides an ultra-low orbit satellite orbit control method based on aerodynamic assistance, which is used for realizing a control strategy for maintaining an ultra-low orbit satellite orbit on the premise that a satellite attitude keeps three axes stable to the ground, and ensuring that the deviation between the actual position of the satellite and the nominal orbit position at any latitude is within a given range.

The invention provides an ultra-low orbit satellite orbit control method based on aerodynamic force assistance, which comprises the following steps:

s1: according to the known instantaneous orbit elements of the satellite, the average orbit elements of the satellite at the moment are obtained by using a flat-heel estimation algorithm;

s2: determining the control state of the satellite according to the difference between the satellite average orbit element and the target average orbit element and the size of the error tolerance;

s3: determining a required aerodynamic direction according to the control state of the satellite and a first control method, so as to determine the deflection direction of the aerodynamic rudder;

s4: substituting all stresses of the satellite into a perturbation equation to carry out integration to obtain a new instantaneous orbit element;

s5: calculating a spatial error by using the new instantaneous orbit element, and judging whether a radial component of the spatial error is greater than a given maximum value; if yes, returning to the step S2, and repeatedly executing the step S2 to the step S5; if not, the first control method in step S3 is replaced with the second control method, the process returns to step S2, and steps S2 to S5 are repeated.

In a possible implementation manner, in the above ultra-low orbit satellite orbit control method based on aerodynamic assistance provided by the present invention, in step S1, an average orbit element of the satellite at that time is obtained by using a flat-heel estimation algorithm according to known instantaneous orbit elements of the satellite, which specifically includes:

and filtering short period terms of the track elements by using a flat heel estimation algorithm to obtain average track elements.

In a possible implementation manner, in the above ultra-low-orbit satellite orbit control method based on aerodynamic assistance provided by the present invention, step S2 determines the control state of the satellite according to the difference between the average orbit element of the satellite and the target average orbit element and the magnitude of the error tolerance, specifically including:

mean semi-major axis a of satellite_mAverage semi-major axis of interest a_m0Error margin Δ a. If the initial time a_m≤a_m0Then the semi-major axis needs to be controlled to be increased until a_m＞a_m0+ Δ a; if the initial time a_m＞a_m0Then the semi-major axis needs to be controlled to decrease until a_m＜a_m0- Δ a. When a thereafter_m＜a_m0Δ a then controls the semi-major axis to increase until a_m＞a_m0+ Δ a; when a is_m＞a_m0+ Δ a controls the semi-major axis to decrease until a_m＜a_m0Δ a, so cycle. Where Δ a is a positive number representing the magnitude of the semi-major axis error tolerance.

Mean orbital element x of satellite_mTarget mean orbit element x_m0Error margin Δ x. If x_m-x_m0If the | is less than or equal to the Δ x, the satellite is in the error tolerance range and does not need to be controlled; if x_m-x_m0If delta x is greater than the threshold, the satellite exceeds the upper limit of the error tolerance and needs to be controlled to reduce; if x_m-x_m0< - Δ x, the satellite exceeds the lower error tolerance limit and needs to be controlled for its increase. Wherein the average orbital element x of the satellite_mIncluding satellite mean orbital inclination i_mMean satellite elevation cross point right ascension omega_mMean eccentricity of the satellite e_xmAnd e_ym(ii) a Target average orbital element x_m0Including a target average orbital inclination i_m0Target mean intersection right ascension omega_m0Target average eccentricity e_xm0And e_ym0(ii) a The error margin Δ x is a positive number representing the magnitude of the error margin.

In a possible implementation manner, in the above ultra-low-orbit satellite orbit control method based on aerodynamic assistance provided by the present invention, step S3, determining a required aerodynamic direction according to the control state of the satellite and the first control method, so as to determine a deflection direction of the aerodynamic rudder, specifically includes:

the first control method is to control the semi-major axis of the satellite by thrust and control the orbital inclination angle, the ascension and eccentricity of the satellite by aerodynamic force, and the specific control method is as follows:

in the geocentric inertial coordinate system, the orbit element variation considering the perturbation acceleration is as follows:

s301. control method of inclination angle and rising intersection right ascension of satellite orbit

According to the first two terms of the perturbation equation, the orbit inclination angle and the rising intersection right ascension only have the normal acceleration f_hRelated, so the normal force F_hThe method is mainly used for controlling the orbital inclination angle and the rising point right ascension of the satellite. Considering the position of the satellite in orbit, i.e. the latitude argument u, the control is divided into the following 9 cases:

case (1): when the inclination angle of the satellite orbit exceeds the upper limit of the error tolerance and the ascension of the satellite intersection point exceeds the upper limit of the error tolerance, negative control is applied when the amplitude angle of the satellite latitude is in the first quadrant, and positive control is applied when the amplitude angle of the satellite latitude is in the third quadrant.

Case (2): when the satellite orbit inclination angle exceeds the upper limit of the error tolerance and the satellite ascension point is within the range of the error tolerance, negative control is applied when the latitude argument of the satellite is in the first quadrant and the fourth quadrant, and positive control is applied when the latitude argument of the satellite is in the second quadrant and the third quadrant.

Case (3): when the inclination angle of the satellite orbit exceeds the upper limit of the error tolerance and the ascension of the satellite intersection point exceeds the lower limit of the error tolerance, negative control is applied when the latitude argument of the satellite is in the fourth quadrant, and positive control is applied when the latitude argument of the satellite is in the second quadrant.

Case (4): when the inclination angle of the satellite orbit is in the error tolerance range and the ascension of the satellite intersection point exceeds the upper limit of the error tolerance, negative control is applied when the latitude argument of the satellite is in the first quadrant and the second quadrant, and positive control is applied when the latitude argument of the satellite is in the third quadrant and the fourth quadrant.

Case (5): when the satellite orbit inclination angle is within the error tolerance range and the satellite ascent point ascent is within the error tolerance range, no control needs to be applied.

Case (6): when the inclination angle of the satellite orbit is in the error tolerance range and the ascension of the satellite intersection point exceeds the lower limit of the error tolerance, negative control is applied when the latitude argument of the satellite is in the third quadrant and the fourth quadrant, and positive control is applied when the latitude argument of the satellite is in the first quadrant and the second quadrant.

Case (7): when the inclination angle of the satellite orbit exceeds the lower limit of the error tolerance and the ascension of the satellite intersection point exceeds the upper limit of the error tolerance, negative control is applied when the latitude argument of the satellite is in the second quadrant, and positive control is applied when the latitude argument of the satellite is in the fourth quadrant.

Case (8): when the satellite orbit inclination angle exceeds the lower limit of the error tolerance and the ascension point of the satellite is within the range of the error tolerance, negative control is applied when the latitude argument of the satellite is in the second quadrant and the third quadrant, and positive control is applied when the latitude argument of the satellite is in the first quadrant and the fourth quadrant.

Case (9): when the inclination angle of the satellite orbit exceeds the lower limit of the error tolerance and the ascension of the satellite intersection point exceeds the lower limit of the error tolerance, negative control is applied when the amplitude angle of the satellite latitude is in the third quadrant, and positive control is applied when the amplitude angle of the satellite latitude is in the first quadrant.

S302, control method of satellite eccentricity

Radial force F_rThe method is mainly used for controlling the orbit inclination angle and the ascent crossing right ascension of the satellite, and considering the position of the satellite on the orbit, namely the latitude argument u, the control is divided into the following 9 conditions:

case (1): when the eccentricity x-direction component of the satellite exceeds the lower limit of the error tolerance and the y-direction component exceeds the lower limit of the error tolerance, negative control is applied when the latitude argument of the satellite is in a fourth quadrant, and positive control is applied when the latitude argument of the satellite is in a second quadrant.

Case (2): when the x-direction component of the satellite eccentricity exceeds the lower error tolerance limit and the y-direction component is within the error tolerance range, negative control is applied when the latitude argument of the satellite is in the third quadrant and the fourth quadrant, and positive control is applied when the latitude argument of the satellite is in the first quadrant and the second quadrant.

Case (3): when the eccentricity x-direction component of the satellite exceeds the lower error tolerance limit and the y-direction component exceeds the upper error tolerance limit, negative control is applied when the latitude argument of the satellite is in the third quadrant, and positive control is applied when the latitude argument of the satellite is in the first quadrant.

Case (4): when the x-direction component of the satellite eccentricity is within the error tolerance range and the y-direction component exceeds the lower limit of the error tolerance, negative control is applied when the latitude amplitude of the satellite is in the first quadrant and the fourth quadrant, and positive control is applied when the latitude amplitude of the satellite is in the second quadrant and the third quadrant.

Case (5): when the satellite eccentricity x-direction component is within the error tolerance range and the y-direction component is within the error tolerance range, no control needs to be applied.

Case (6): when the x-direction component of the satellite eccentricity is within the error tolerance range and the y-direction component exceeds the upper error tolerance limit, negative control is applied when the latitude argument of the satellite is in the second quadrant and the third quadrant, and positive control is applied when the latitude argument of the satellite is in the first quadrant and the fourth quadrant.

Case (7): when the eccentricity x-direction component of the satellite exceeds the upper error tolerance limit and the y-direction component exceeds the lower error tolerance limit, negative control is applied when the latitude argument of the satellite is in the first quadrant, and positive control is applied when the latitude argument of the satellite is in the third quadrant.

Case (8): when the x-direction component of the satellite eccentricity exceeds the upper error tolerance limit and the y-direction component is within the error tolerance range, negative control is applied when the latitude argument of the satellite is in the first quadrant and the second quadrant, and positive control is applied when the latitude argument of the satellite is in the third quadrant and the fourth quadrant.

Case (9): when the eccentricity x-direction component of the satellite exceeds the lower error tolerance limit and the y-direction component exceeds the upper error tolerance limit, negative control is applied when the latitude argument of the satellite is in the second quadrant, and positive control is applied when the latitude argument of the satellite is in the fourth quadrant.

S303. control method of satellite semimajor axis

Thrust F in tracking direction_uMainly used for controlling the semi-major axis of the satellite. The deviation condition of the control surface can be influenced due to the difference between other track elements and the target track, thereby influencing the deviation condition of the control surfaceThe satellite is subjected to a certain amount of resistance, so that when the semi-major axis is smaller or larger than the target semi-major axis, there are 81 cases of control, respectively. Thrust F according to the direction of the applied track_uThe 81 cases are integrated into the following 16 cases:

case (1): the satellite orbit inclination angle and the ascent crossing right angle simultaneously exceed the upper limit or the lower limit of the error tolerance, and the x-direction component and the y-direction component of the satellite eccentricity simultaneously exceed the upper limit or the lower limit of the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (2): the satellite orbit inclination angle and the ascent crossing right angle simultaneously exceed the upper limit or the lower limit of the error tolerance, and one of the x-direction component and the y-direction component of the satellite eccentricity is within the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, applying a thrust which is greater than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying a thrust which is greater than or equal to the sum of the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (3): the satellite orbit inclination angle and the ascension of the ascending point exceed the upper limit or the lower limit of the error tolerance at the same time, and the eccentricity x-direction component and the eccentricity y-direction component of the satellite exceed the upper limit of the error tolerance and exceed the lower limit of the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (4): the satellite orbit inclination angle and the ascent crossing right ascension simultaneously exceed the upper limit or the lower limit of the error tolerance, and the x-direction component and the y-direction component of the satellite eccentricity are within the error tolerance range. If the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in a first quadrant and a third quadrant, and applying thrust which is greater than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in a second quadrant and a fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (5): one of the satellite orbit inclination angle and the rising point right ascension is within the error tolerance range, and the x-direction component and the y-direction component of the satellite eccentricity simultaneously exceed the upper limit or the lower limit of the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in a first quadrant and a third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in a second quadrant and a fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (6): one of the satellite orbit inclination angle and the ascension point of the elevation point is within a tolerance range of error, and one of the x-direction component and the y-direction component of the satellite eccentricity is within a tolerance range of error. If the semi-long axis of the satellite needs to be controlled to be increased, applying a thrust which is greater than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body.

Case (7): one of the satellite orbit inclination angle and the rising point right ascension is within the error tolerance range, and the eccentricity of the satellite is within the range of the upper limit and the lower limit of the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (8): one of the satellite orbit inclination angle and the rising point right ascension is within an error tolerance range, and the x-direction component and the y-direction component of the satellite eccentricity are within the error tolerance range. If the semi-long axis of the satellite needs to be controlled to be increased, thrust which is larger than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body is applied; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder and the atmospheric resistance of the satellite body.

Case (9): the inclination angle and the elevation crossing point of the satellite orbit exceed an upper limit and another lower limit of the error tolerance, and the x-direction component and the y-direction component of the eccentricity of the satellite simultaneously exceed the upper limit or the lower limit of the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, thrust which is greater than or equal to the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the first quadrant and the third quadrant, and thrust which is greater than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (10): the inclination angle of the satellite orbit and the ascension angle of the ascending cross point exceed an upper limit of an error tolerance and exceed a lower limit of the error tolerance, and one of the x-direction component and the y-direction component of the satellite eccentricity is within the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder, resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder, the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (11): the inclination angle and the elevation crossing point of the satellite orbit exceed an upper limit and a lower limit of an error tolerance respectively, and the eccentricity x-direction component and the eccentricity y-direction component exceed an upper limit and a lower limit of an error tolerance respectively. If the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is greater than or equal to the sum of resistance generated by deflection of the vertical rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (12): the inclination angle of the satellite orbit and the ascension angle of the ascending intersection are within the range of the error tolerance, one exceeds the upper limit of the error tolerance, and the other exceeds the lower limit of the error tolerance, and the x-direction component and the y-direction component of the satellite eccentricity are within the range of the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, thrust which is greater than or equal to the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the first quadrant and the third quadrant, and thrust which is greater than or equal to the sum of the resistance generated by deflection of the vertical rudder and the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the vertical rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (13): the satellite orbit inclination angle and the ascension of the ascending point are both within the error tolerance range, and the x-direction component and the y-direction component of the satellite eccentricity simultaneously exceed the upper limit or the lower limit of the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, thrust which is greater than or equal to the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the first quadrant and the third quadrant, and thrust which is greater than or equal to the sum of the resistance generated by deflection of the horizontal rudder, radial force and the atmospheric resistance of the satellite body is applied when the latitude argument of the satellite is in the second quadrant and the fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the sum of the resistance generated by deflection of the horizontal rudder and the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (14): the satellite orbit inclination angle and the rising point right ascension are both within a tolerance range of error, and one of the x-direction component and the y-direction component of the satellite eccentricity is within the tolerance range of error. If the semi-major axis of the satellite needs to be controlled to be increased, applying a thrust which is more than or equal to the sum of the resistance generated by the deflection of the horizontal rudder, the radial force and the atmospheric resistance of the satellite body; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of the resistance generated by the deflection of the horizontal rudder and the atmospheric resistance of the satellite body.

Case (15): the satellite orbit inclination angle and the ascension of the ascending intersection point are both within the error tolerance range, and the eccentricity x-direction component and the eccentricity y-direction component of the satellite exceed the upper limit of the error tolerance and exceed the lower limit of the error tolerance. If the semi-major axis of the satellite needs to be controlled to be increased, applying thrust which is greater than or equal to the sum of resistance generated by deflection of the horizontal rudder, radial force and atmospheric resistance of the satellite body when the latitude argument of the satellite is in a first quadrant and a third quadrant, and applying thrust which is greater than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in a second quadrant and a fourth quadrant; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust which is less than or equal to the sum of resistance generated by deflection of the horizontal rudder and atmospheric resistance of the satellite body when the latitude argument of the satellite is in the first quadrant and the third quadrant, and applying thrust which is less than or equal to the atmospheric resistance of the satellite body when the latitude argument of the satellite is in the second quadrant and the fourth quadrant.

Case (16): the satellite orbit inclination angle and the rising point right ascension are both within the error tolerance range, and the x-direction component and the y-direction component of the satellite eccentricity are both within the error tolerance range. If the semi-major axis of the satellite needs to be controlled to be increased, thrust which is more than or equal to the atmospheric resistance of the satellite body is applied; and if the semi-major axis of the satellite needs to be controlled to be reduced, applying thrust less than or equal to the atmospheric resistance of the satellite body.

The above provides a range of thrust selections, within which thrust values may be varied from the satellite orbit element to the target orbit element. Therefore, the thrust with different magnitude can be selected according to the change situation of the satellite orbit element, and one constant thrust which can satisfy all the situations can also be selected.

In a possible implementation manner, in the above ultra-low orbit satellite orbit control method based on aerodynamic assistance provided by the present invention, step S4, the method includes substituting all stresses of the satellite into a perturbation equation to perform integration, so as to obtain a new instantaneous orbit element, and specifically includes: the perturbation equation in step S3 is integrated to obtain the instantaneous orbit element at the next time, taking into account the influence of the earth' S aspheric gravity, the sun-moon gravity, the sunlight pressure, the atmospheric resistance, and the aerodynamic force generated by the pneumatic rudder.

In a possible implementation manner, in the aerodynamic assistance-based ultra-low orbit satellite orbit control method provided by the invention, step S5 is to calculate a spatial error by using the instantaneous orbit element, and determine whether a radial component of the spatial error is greater than a given maximum value; if yes, returning to the step S2, and repeatedly executing the step S2 to the step S5; if not, replacing the first control method in the step S3 with the second control method, returning to the step S2, and repeatedly executing the steps S2 to S5, which specifically includes:

to accurately describe the deviation of the actual position of the satellite from the nominal orbital position at any latitude, a space error variable E ═ E (E) is defined_N,E_R)^TRepresenting the vector difference between the nominal track and the intersection of the actual track with the reference plane (the plane consisting of the radial and normal directions in the track coordinate system), E_NNormal component of spatial error, E_RIs the radial component of the spatial error.

Let the difference between the actual track element and the nominal track element be (delta a, delta i, delta omega, delta e)_x、δe_y) Then, the normal and radial errors of the pipeline radius are respectively:

wherein the lower corner m represents the orbit element of the nominal orbit, n is the orbit angular velocity of the nominal orbit, ω_eIs the rotational angular velocity of the earth.

If E is_RGreater than a given maximum value E_RmaxThe control method in step S3 is changed to the second control method. The second control method is to control the semimajor axis and eccentricity of the satellite simultaneously by thrust and control the orbital inclination angle and the right ascension of the satellite by pneumatic power, and the specific control method is as follows.

Obtaining flat roots a and e by using flat root estimation method_x、e_yIn contrast to the target average orbit element, considering the position of the satellite on the orbit, i.e. latitude argument u, when the semi-major axis is smaller or larger than the target semi-major axis, there are 9 cases of control respectively:

case (1): the eccentricity of the satellite exceeds the lower error tolerance limit in the x-direction component and exceeds the lower error tolerance limit in the y-direction component. If the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in the first quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust smaller than the total resistance is applied when the latitude argument of the satellite is in the first quadrant.

Case (2): the eccentricity x-direction component of the satellite exceeds the lower limit of the error tolerance, and the y-direction component of the satellite is within the range of the error tolerance. If the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a first quadrant and a fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust smaller than the total resistance is applied when the latitude argument of the satellite is in the first quadrant and the fourth quadrant.

Case (3): the eccentricity of the satellite exceeds the lower error tolerance limit in the x-direction component and exceeds the upper error tolerance limit in the y-direction component. If the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust less than the total resistance is applied when the latitude argument of the satellite is in the fourth quadrant.

Case (4): the eccentricity of the satellite is within the error tolerance range in the x-direction component, and the error tolerance lower limit is exceeded in the y-direction component. If the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a first quadrant and a second quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust smaller than the total resistance is applied when the latitude argument of the satellite is in the first quadrant and the second quadrant.

Case (5): the eccentricity of the satellite is within the tolerance of the error in the x-direction component and within the tolerance of the error in the y-direction component. At this time, a thrust equal to the total resistance is applied regardless of the variation of the semi-major axis of the satellite that needs to be controlled.

Case (6): the eccentricity of the satellite is within the error tolerance range in the x-direction component, and the error tolerance upper limit is exceeded in the y-direction component. If the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a third quadrant and a fourth quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust smaller than the total resistance is applied when the latitude argument of the satellite is in the third quadrant and the fourth quadrant.

Case (7): the eccentricity of the satellite exceeds the upper error tolerance limit in the x-direction component and exceeds the lower error tolerance limit in the y-direction component. If the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a second quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust smaller than the total resistance is applied when the latitude argument of the satellite is in the second quadrant.

Case (8): the eccentricity x-direction component of the satellite exceeds the upper limit of the error tolerance, and the y-direction component of the satellite is within the range of the error tolerance. If the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a second quadrant and a third quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust smaller than the total resistance is applied when the latitude argument of the satellite is in the second quadrant and the third quadrant.

Case (9): the eccentricity of the satellite exceeds the upper limit of the error tolerance in the x-direction component and exceeds the upper limit of the error tolerance in the y-direction component. If the semi-long axis of the satellite needs to be controlled to be increased, thrust larger than total resistance is applied when the latitude argument of the satellite is in a third quadrant; if the semi-major axis of the satellite needs to be controlled to be reduced, thrust smaller than the total resistance is applied when the latitude argument of the satellite is in the third quadrant.

During a period of time not mentioned in the above 9 cases, a thrust equal to the total resistance is applied.

According to the ultralow-orbit satellite orbit control method based on aerodynamic force assistance, orbit control is carried out by aerodynamic force assistance, two control methods are provided for different orbit conditions, and the deviation distance between the actual position of a satellite and the nominal orbit position at any latitude can be controlled within a given range on the premise that the satellite attitude keeps three axes stable to the ground. The algorithm can ensure that the ultra-low earth orbit satellite completes the main task of earth observation, can effectively utilize the unique atmospheric environment at the ultra-low earth orbit, fully exerts the pneumatic force effect, and has good popularization prospect in the aspect of guaranteeing the long service life of the ultra-low earth orbit satellite in the aspect of in-orbit operation.

Drawings

FIG. 1 is a schematic flow chart of an ultra-low orbit satellite orbit control method based on aerodynamic assistance according to the invention;

FIGS. 2 a-f are schematic diagrams illustrating orbital element changes of an ultra-low orbit satellite with a small orbital inclination;

FIGS. 3 a-f are variation diagrams of orbit elements of an ultra-low orbit satellite with a large orbit inclination angle;

FIG. 4 is a diagram of spatial error variation of an ultra-low orbit satellite with a large orbital inclination;

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only illustrative and are not intended to limit the present invention.

The invention provides an ultra-low orbit satellite orbit control method based on aerodynamic force assistance, which comprises the following steps:

s1: according to the known instantaneous orbit elements of the satellite, the average orbit elements of the satellite at the moment are obtained by using a flat-heel estimation algorithm;

s2: determining the control state of the satellite according to the difference between the satellite average orbit element and the target average orbit element and the size of the error tolerance;

s3: determining a required aerodynamic direction according to the control state of the satellite and a first control method, so as to determine the deflection direction of the aerodynamic rudder;

s4: substituting all stresses of the satellite into a perturbation equation to carry out integration to obtain a new instantaneous orbit element;

s5: calculating a spatial error by using the new instantaneous orbit element, and judging whether a radial component of the spatial error is greater than a given maximum value; if yes, returning to the step S2, and repeatedly executing the step S2 to the step S5; if not, the first control method in step S3 is replaced with the second control method, the process returns to step S2, and steps S2 to S5 are repeated.

The invention provides an ultra-low orbit satellite orbit control method based on aerodynamic force assistance, the supported equipment comprises a GPS receiver, a thruster, an aerodynamic rudder and an on-board computer, and the target is an ultra-low orbit satellite. The method comprises the steps of determining instantaneous orbit elements of a satellite through a GPS receiver, calculating average orbit elements by using a flat-heel estimation algorithm, solving the direction of pneumatic force required by control by using the aerodynamic force assistance-based ultra-low orbit satellite orbit control method, and controlling the change of the satellite to target orbit elements, thereby realizing a control strategy for maintaining the ultra-low orbit satellite orbit.

The following describes in detail a specific implementation of the above-mentioned ultra-low orbit satellite orbit control method based on aerodynamic assistance according to a specific embodiment and with reference to fig. 1.

Example 1:

in the first step, according to the known instantaneous orbit elements of the satellite, the average orbit element of the satellite at the moment is obtained by using a flat-tracking estimation method.

Since the average track element is often used for track control, the short-period term of the track element needs to be filtered out by using a flat-tracking estimation method to obtain the average track element.

And secondly, determining the control state of the satellite according to the difference between the average orbit element of the satellite and the target average orbit element and the size of the error tolerance.

Mean semi-major axis a of satellite_mAverage semi-major axis of interest a_m0Error margin Δ a. If the initial time a_m≤a_m0Then the semi-major axis needs to be controlled to be increased until a_m＞a_m0+ Δ a; if the initial time a_m＞a_m0Then the semi-major axis needs to be controlled to decrease until a_m＜a_m0- Δ a. When a thereafter_m＜a_m0Δ a then controls the semi-major axis to increase until a_m＞a_m0+ Δ a; when a is_m＞a_m0+ Δ a controls the semi-major axis to decrease until a_m＜a_m0Δ a, so cycle. Where Δ a is a positive number representing the magnitude of the semi-major axis error tolerance. Mean orbital element x of satellite_mTarget mean orbit element x_m0Error margin Δ x. If x_m-x_m0If the | is less than or equal to the Δ x, the satellite is in the error tolerance range and does not need to be controlled; if x_m-x_m0If delta x is greater than the threshold, the satellite exceeds the upper limit of the error tolerance and needs to be controlled to reduce; if x_m-x_m0< - Δ x, the satellite exceeds the lower error tolerance limit and needs to be controlled for its increase.

Wherein the average orbital element x of the satellite_mIncluding satellite mean orbital inclination i_mMean satellite elevation cross point right ascension omega_mMean eccentricity of the satellite e_xmAnd e_ym(ii) a Target average orbital element x_m0Including a target average orbital inclination i_m0Target mean intersection right ascension omega_m0Eyes and eyesStandard mean eccentricity e_xm0And e_ym0(ii) a The error margin Δ x is a positive number representing the magnitude of the error margin.

And thirdly, determining the required aerodynamic direction according to the control state of the satellite and the first control method, thereby determining the deflection direction of the aerodynamic rudder.

In a first control method, the control of the track elements i, Ω is as follows:

TABLE 1

Wherein, F_hdThe magnitude of the normal force generated by the control surface is N; f_hThe unit is N, positive represents that positive control force is needed, namely the pneumatic rudder needs to be positively deflected, and negative represents that negative control force is needed, namely the pneumatic rudder needs to be reversely deflected.

For track element e_x、e_yThe control of (2) is as follows:

TABLE 2

The control of track element a is as follows in table 3:

TABLE 3

TABLE 4

Wherein, F_uThrust in the direction of the track, F_uhResistance to vertical rudder deflection, F_urThe resistance generated by the deflection of the horizontal rudder and the d are the atmospheric resistance of the body, and the unit is N.

TABLE 3

Provided is a range of thrust selections, within which thrust values can be varied from the track element to the target track element. Therefore, the thrust with different magnitude can be selected according to the change condition of the track element, and a larger constant thrust which can satisfy all conditions can be selected.

And fourthly, substituting all stresses of the satellite into a perturbation equation to carry out integration to obtain a new instantaneous orbit element.

In the geocentric inertial coordinate system, the orbit element variation considering the perturbation acceleration is as follows:

the influence of the non-spherical gravity of the earth, the sun-moon gravity, the sunlight pressure, the atmospheric resistance and the aerodynamic force generated by the pneumatic rudder is considered, and the perturbation equation above is integrated to obtain the instantaneous orbit element at the next moment.

Fifthly, calculating a space error by using the new instantaneous orbit element, and judging whether the radial component of the space error is greater than a given maximum value or not; if yes, returning to the second step, and repeatedly executing the second step to the fifth step; and if not, replacing the first control method in the third step with the second control method, returning to the second step, and repeatedly executing the second step to the fifth step.

To accurately describe the deviation of the actual position of the satellite from the nominal orbital position at any latitude, a space error variable E ═ E (E) is defined_N,E_R)^TRepresenting the vector difference between the nominal track and the intersection of the actual track with the reference plane (the plane consisting of the radial and normal directions in the track coordinate system), E_NNormal component of spatial error, E_RIs the radial component of the spatial error.

Let the difference between the actual track element and the nominal track element be (delta a, delta i, delta omega, delta e)_x、δe_y) Then, the normal and radial errors of the spatial error are respectively:

wherein the lower corner m represents the orbit element of the nominal orbit, n is the orbit angular velocity of the nominal orbit, ω_eIs the rotational angular velocity of the earth.

If E is_RGreater than a given maximum value E_RmaxThe control method in step S3 is changed to the second control method. The second control method is to control the semimajor axis and the eccentricity simultaneously by using thrust and control the track inclination angle and the ascent intersection right ascension by using aerodynamic force, and the specific control method is as follows.

Obtaining flat roots a and e by using flat root estimation method_x、e_yTaking into account the position of the satellite in the orbit, i.e. the latitude, in contrast to the target mean orbit elementThe amplitude u is controlled in 9 cases when the semimajor axis is smaller or larger than the target semimajor axis.

The semi-major axis is smaller than the target semi-major axis, and the following table 5 is controlled:

TABLE 5

The semi-major axis is larger than the target semi-major axis, and the following table 6 is controlled:

TABLE 6

Wherein x is more than or equal to 0 and is the difference between thrust and resistance, and the unit is N, and can be adjusted according to the actual situation; f_zThe total resistance is N; let F be in the time not covered in the table_u＝F_z。

The invention provides the ultra-low orbit satellite orbit control method based on aerodynamic force assistance, which uses different control methods according to different control targets (target orbit and error tolerance): for the control condition that the target orbit inclination angle is small or the error tolerance is large, a first control method can be used, and aerodynamic force generated by the pneumatic rudder is fully utilized to assist the orbit control; for control situations where the target orbit trajectory inclination is large or the error margin is small, a second control method may be used to reduce the effect of the rudder and thereby better control the orbit. And finally, the target of ensuring the deviation between the actual position of the satellite and the nominal orbit position in a given range at any latitude is realized through different control methods.

The performance of the above-mentioned ultra-low orbit satellite orbit control method based on aerodynamic assistance provided in embodiment 1 of the present invention is explained in two aspects below.

(1) The accuracy of the first control method in the ultra-low orbit satellite orbit control method based on aerodynamic assistance provided in embodiment 1 of the present invention is analyzed by solving the orbit element change of the ultra-low orbit satellite with a small orbit inclination within five days.

When the perturbation equation is used for calculation, the non-spherical gravity of the earth is kept to the fourth order, and the sunlight pressure selects a spherical model and cylindrical earth shadow modularity. For near-circular orbits and near-equators, suitable orbital elements are a, i_x、i_y、e_x、e_yAnd u, the initial values of the track elements, the target track elements and the error margins are shown in table 7.

TABLE 7

Fig. 2 a-f are orbital element variation graphs, in which the solid line represents the average number of actual orbits of the satellite, the dotted line represents the average number of target orbits, and the double-dashed line represents the upper and lower limits of the error tolerance. As can be seen from fig. 2 a-f, each track element can be maintained within a margin of error. After the control of the target track element is entered, as can be seen from fig. 2a, the variation range of the semi-major axis is 6577.886366807677-6578.388251446397km, and the variation range is 0.50188463871 km; as can be seen from FIG. 2b, the track inclination angle x varies from-0.003099101996106 to 0.002957863384509 degrees with a variation range of 0.006056965380615 degrees; as can be seen from FIG. 2c, the track inclination angle y varies from-0.003274206189226 to 0.002974751403617 degrees with a variation of 0.006248957592843 degrees; as can be seen from FIG. 2d, the variation range of the eccentricity x is-1.859108482484272 × 10^-4-1.314080001365552×10^-4The variation amplitude is 3.173188483849824 multiplied by 10^-4(ii) a As can be seen from FIG. 2e, the variation range of the eccentricity y is-1.770974058195304 × 10^-4-2.111765372029691×10^-4The variation amplitude is 3.882739430224995 multiplied by 10^-4。

(2) The accuracy of the second control method in the ultra-low orbit satellite orbit control method based on aerodynamic assistance provided in embodiment 1 of the present invention is analyzed by solving the orbit elements and spatial error variations of the ultra-low orbit satellite with a large orbit inclination within five days.

When the perturbation equation is used for calculation, the non-spherical gravity of the earth is kept to the fourth order, and the sunlight pressure selects a spherical model and cylindrical earth shadow modularity. For near-circular orbits, suitable orbital elements are a, Ω, i, e_x、e_yAnd u, the initial values of the track elements, the target track elements and the error margins are shown in Table 8. Wherein E is_RmaxFor a given maximum value of the radial component of the spatial error (2000m), R_EThe radius of the earth.

TABLE 8

In order to accurately calculate the accuracy of the second control method, the control is always performed using the second control method in embodiment 1. FIGS. 3 a-f are graphs showing the variation of the track elements, and various line types are shown in the same meaning as FIG. 2. Fig. 4 is a graph of spatial error variation, where the solid line is the magnitude of the total spatial error, the double-dashed line is the magnitude of the normal component of the spatial error, and the dashed line is the magnitude of the radial component of the spatial error.

As can be seen from fig. 3 a-f, other track elements than track pitch angle can be maintained within the error tolerance. As can be seen from FIG. 3a, the variation range of the semi-major axis is 6574.527461608649-6575.682500004711km, and the variation range is 1.155038396062082 km; with reference to fig. 3c, the maximum deviation of the right ascension at the intersection point is calculated to be 0.003569510497853 °; as can be seen from FIG. 3d, the variation range of the eccentricity x is-2.408082013267672 × 10^-4-2.259284306066677×10^-4The variation amplitude is 4.667366319334349 multiplied by 10^-4(ii) a As can be seen from FIG. 3e, the variation range of the eccentricity y is-2.468402868525201 × 10^-4-5.577782614885356×10^-5The variation amplitude is 3.0261811300137366 multiplied by 10^-4. Because the track inclination angle is controlled by using the aerodynamic force which is continuous tiny force, when the track inclination angle exceeds the error tolerance range, a certain time is neededTo be controlled back within error tolerance, as calculated in conjunction with fig. 3b, when the rate of change of track inclination is about 5.0465747961511 x 10^-4Degree/day.

As can be seen from fig. 4, the spatial error radial component maximum value is 1933.557452839258m, which is smaller than the given spatial error radial component maximum value (2000 m). The normal component of the spatial error is small, and the maximum value of the total spatial error is 1937.651433869488m, so that the aim of ensuring the deviation of the actual position of the satellite and the nominal orbit position in a given range at any latitude is fulfilled.

According to the ultralow-orbit satellite orbit control method based on aerodynamic force assistance, orbit control is carried out by aerodynamic force assistance, two control methods are provided for different orbit conditions, and the deviation distance between the actual position of a satellite and the nominal orbit position at any latitude can be controlled within a given range on the premise that the satellite attitude keeps three axes stable to the ground. The algorithm can ensure that the ultra-low earth orbit satellite completes the main task of earth observation, can effectively utilize the unique atmospheric environment at the ultra-low earth orbit, fully exerts the pneumatic force effect, and has good popularization prospect in the aspect of guaranteeing the long service life of the ultra-low earth orbit satellite in the aspect of in-orbit operation.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.