Numerical iterative evaluation method for in-plane small control quantity based on orbit phase evolution

Abstract

The application discloses an in-plane small control quantity numerical iteration evaluation method based on orbit phase evolution, and through satellite pre-control and post-control orbit roots and high-precision orbit dynamics model, the time integral effect of in-plane small control quantity is utilized, the phase difference of post-control satellite orbit is taken as a control effect evaluation criterion, and in view of the limited calculation precision of an analytic model, numerical iteration is adopted in calibration, so that the effectiveness of the calibration method is ensured. The application can improve the control effect evaluation precision of a spacecraft when performing in-plane adjustment of a small control quantity orbit, thereby improving the orbit control precision of the satellite, effectively saving the fuel consumption of the satellite, and the method has high reliability, strong operability, and is easy to popularize and use, and has certain economic benefits for on-orbit operation of the spacecraft and important guiding significance for mission implementation.

Description

Technical Field

[0001] This invention belongs to the technical field of spacecraft measurement and control methods, specifically relating to a numerical iterative evaluation method for in-plane small control quantities based on orbital phase evolution. Background Technology

[0002] On-orbit calibration of the orbit control thrust coefficient involves comprehensively calibrating various errors that primarily affect orbit control performance, such as thruster thrust error and satellite attitude error, based on the deviation between the measured orbital elements and the target orbital elements. Generally, due to the influence of on-orbit operating conditions and the environment, the thrust magnitude of the orbit control thruster exhibits a certain deviation, and this deviation is often the main factor affecting orbit control performance. Therefore, it is necessary to calibrate the thrust coefficient after each orbit control operation so that the calibrated coefficient can be used in subsequent orbit control operations, thereby improving orbit control accuracy.

[0003] With the continuous development of aerospace technology, advanced propulsion technologies such as electric propulsion, laser propulsion, and ion propulsion have emerged, characterized by high specific impulse and high efficiency. These technologies allow satellites to eliminate the complex and heavy propulsion-related equipment found in chemical propulsion systems, enabling them to carry less fuel and thus more payload. Consequently, they have gained widespread popularity in engineering applications in recent years. However, the thrust of these types of thrusters is typically in the range of tens to hundreds of millinewtons, significantly lower than that of traditional chemical thrusters. This results in a smaller orbital control quantity generated within the same timeframe. Furthermore, limitations in orbital accuracy mean that traditional methods of calibrating small control quantities using the average control quantity from orbital elements or velocity increments lead to low accuracy in control performance evaluation and make it difficult to precisely calibrate thruster performance. When a satellite performs in-plane orbital adjustments with small control quantities, the time integral effect can indirectly reflect the control effect. Therefore, orbital phase evolution can be used to indirectly evaluate the control effect under small in-plane control quantities, improving the evaluation accuracy during in-plane orbital adjustments through the time integral effect. Summary of the Invention

[0004] The purpose of this invention is to provide a numerical iterative evaluation method for in-plane small control quantities based on orbital phase evolution, which can improve the accuracy of control effect evaluation when spacecraft make in-plane adjustments to orbits with small control quantities.

[0005] The technical solution adopted in this invention is: a numerical iterative evaluation method for in-plane small control quantities based on orbital phase evolution. It utilizes the time integral effect of in-plane small control quantities by using the orbital elements before and after satellite control and a high-precision orbital dynamics model, and takes the phase difference of the satellite orbit after control as the evaluation criterion for control effect. Numerical iteration is used in calibration to ensure the effectiveness of the calibration method.

[0006] The invention is further characterized by:

[0007] The numerical iterative evaluation method for in-plane small control quantities based on orbital phase evolution specifically includes: determining the satellite orbit at the current moment and the pre-control satellite orbit at the intermediate control moment; setting initial values ​​for iterative calibration; calculating the temporary orbit latitude argument and the post-control orbit latitude argument; calculating the phase evolution quantity; calculating the control velocity increment correction quantity based on the orbital phase evolution quantity; calculating the actual control velocity increment; calculating the satellite position and velocity vector at the intermediate control moment; calculating the satellite position and velocity vector at the temporary orbit; calculating the satellite temporary orbit elements; calculating the temporary orbit elements based on a high-precision dynamic model; calculating the temporary orbit latitude argument; calculating the phase difference between the temporary orbit and the post-control satellite orbit; determining whether the phase difference meets the accuracy requirements; and calibrating the thruster coefficients.

[0008] The numerical iterative evaluation method for in-plane small control variables based on orbital phase evolution specifically includes the following steps:

[0009] Step 1: Determine the current T e Satellite orbital parameters at any given time, including the semi-major axis a of the satellite orbit. e eccentricity e e Inclination angle i e Right ascension of ascending node Ω e Argument of perigee ω e Angle M near the point e Determine the control intermediate time T s The pre-control satellite orbital parameters, including the semi-major axis a of the satellite orbit. s eccentricity e s Inclination angle i s Right ascension of ascending node Ω s Argument of perigee ω s Angle M near the point s ;

[0010] Step 2: Set initial values ​​for iterative calibration, including the time T of the temporary track. m =T s semi-major axis a m =a s eccentricity e m =e s Inclination angle i m =i s Right ascension of ascending node Ω m =Ω s Argument of perigee ω m =ω s Angle M near the point m =M s The actual controlled speed increment Δv = 0;

[0011] Step 3: Calculate the temporary orbital latitude argument u mAnd control orbital latitude angle u e ;

[0012]

[0013] Where arctan2(*,*) is the arctangent calculation function, E m It is the temporary orbital approach angle, E e It is the angle of approach to the control track;

[0014] Step 4: Calculate the phase evolution Δu;

[0015] Δu=u e -u m

[0016] Step 5: Calculate the control velocity increment correction δv based on the orbital phase evolution Δu;

[0017]

[0018] Among them, f m It is a true anterior angle, calculated by the following formula:

[0019]

[0020] Step 6: Calculate the actual control speed increment Δv;

[0021] Δv=Δv+δv

[0022] Step 7: Calculate the satellite position vector in the control intermediate time in the J2000.0 coordinate system. and velocity vector

[0023]

[0024] Among them, F1(T s ,a s ,e s i s ,Ω s ,ω s M s (Based on satellite orbital time T) s , semi-major axis a s eccentricity e s Inclination angle i s Right ascension of ascending node Ω s Argument of perigee ω s Angle of Approach M in Peace s Calculate satellite position vector and velocity vector The function;

[0025] Step 8: Calculate the temporary orbital satellite position vector in the J2000.0 coordinate system. and velocity vector

[0026]

[0027]

[0028] Here, |*| is the modulus calculation for the vector;

[0029] Step 9: Based on the time T of the satellite's temporary orbit. m ,Location speed Update the calculation of the semi-major axis a of the satellite's temporary orbital elements. m eccentricity e m Inclination angle i m Right ascension of ascending node Ω m Argument of perigee ω m Angle M near the point m ;

[0030]

[0031] in, It is based on the satellite orbital time T m ,Location speed A function for calculating satellite orbital elements;

[0032] Step 10: Extrapolate the temporary orbital elements based on the high-precision dynamic model and calculate T. e Temporary orbital elements at any given time, including parameters such as the semi-major axis a of the satellite orbit. me eccentricity e me Inclination angle i me Right ascension of ascending node Ω me Argument of perigee ω me Angle M near the point me ;

[0033] [T e ,a me ,e me i me ,Ω me ,ω me M me ] = F3(T m ,a m ,e m i m ,Ω m ,ω m M m )

[0034] Among them, F3(T m ,a m ,e m i m ,Ω m ,ω m M m ) is a function that extrapolates satellite orbital elements based on a high-precision dynamic model;

[0035] Step 11, Calculate T e Temporary orbital latitude angle u me ;

[0036]

[0037] Among them, E me It is a temporary track deflection angle;

[0038] Step 12: Calculate the phase difference δu between the temporary orbit and the post-controlled satellite orbit;

[0039] δu=|u me -u e |

[0040] Step 13: Determine whether the phase difference δu meets the accuracy requirements. If it does, i.e., δu < δ, where δ is the threshold for iterative calculation, proceed to step 14; otherwise, go to step 3.

[0041] Step 14: Calibrate the thrust coefficient;

[0042]

[0043] Where, Δv s It is the theoretical velocity increment, k s It is the thrust coefficient, Δv s and k s Obtained from the track change control parameters.

[0044] In step 3, the temporary track deviation angle E m And the approach angle E of the track after control e From the equation Obtained through iterative calculation.

[0045] In step 11, the temporary track deviation angle E me From equation E me =M me +e me sinE me Obtained through iterative calculation.

[0046] The beneficial effects of this invention are as follows: The numerical iterative evaluation method for in-plane small control quantities based on orbital phase evolution utilizes the pre- and post-control orbital elements and a high-precision orbital dynamics model. It leverages the time integral effect of the in-plane small control quantities and uses the phase difference of the post-control satellite orbit as the control effect evaluation criterion. Considering the limited computational accuracy of the analytical model, numerical iteration is employed during calibration to ensure the effectiveness of the calibration method. This invention can improve the accuracy of control effect evaluation when spacecraft perform in-plane adjustments to orbits with small control quantities, thereby improving the orbital control accuracy of satellites, effectively saving satellite fuel consumption. Furthermore, the method is highly reliable, easy to operate, and readily applicable, offering certain economic benefits for spacecraft on-orbit operation and providing important guidance for mission implementation. Attached Figure Description

[0047] Figure 1 This is a flowchart illustrating the numerical iterative evaluation method for in-plane small control variables based on orbital phase evolution according to the present invention. Detailed Implementation

[0048] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0049] This invention provides a numerical iterative evaluation method for in-plane small control variables based on orbital phase evolution. The spacecraft used is a near-Earth satellite with an electric propulsion system and a thrust of 40 millinewtons. It performs semi-major axis control within the orbital plane, with a control variable of 5 meters. Figure 1 As shown, the specific steps are as follows:

[0050] (1) Determine the current T e The satellite orbit at any given time, including parameters such as the semi-major axis a of the satellite orbit. e eccentricity e e Inclination angle i e Right ascension of ascending node Ω e Argument of perigee ω e Angle M near the point e Determine the control intermediate time T s The pre-control satellite orbit, parameters including the semi-major axis a of the satellite orbit. s eccentricity e s Inclination angle i s Right ascension of ascending node Ω s Argument of perigee ω s Angle M near the point s .

[0051] (2) Set initial values ​​for iterative calibration, including the time T of the temporary track. m =T s semi-major axis a m =a s eccentricity e m =es Inclination angle i m =i s Right ascension of ascending node Ω m =Ω s Argument of perigee ω m =ω s Angle M near the point m =M s The actual controlled speed increment Δv = 0.

[0052] (3) Calculate the temporary orbital latitude argument u m And control orbital latitude angle u e ;

[0053]

[0054] Where arctan2(*,*) is the arctangent calculation function, and the temporary orbital approach angle E m And the approach angle E of the track after control e From the equation Obtained through iterative calculation.

[0055] (4) Calculate the phase evolution Δu.

[0056] Δu=u e -u m

[0057] (5) Calculate the control speed increment correction δv based on the orbital phase evolution.

[0058]

[0059] Among them, f m It is a true anterior angle, calculated by the following formula:

[0060]

[0061] (6) Calculate the actual control speed increment Δv.

[0062] Δv=Δv+δv

[0063] (7) Calculate the position vector of the satellite in the control intermediate time in the J2000.0 coordinate system. and velocity vector

[0064]

[0065] Among them, F1(T s ,a s ,e s i s ,Ω s ,ω sM s (Based on satellite orbital time T) s , semi-major axis a s eccentricity e s Inclination angle i s Right ascension of ascending node Ω s Argument of perigee ω s Angle of Approach M in Peace s Calculate satellite position vector and velocity vector The function.

[0066] (8) Calculate the temporary orbital satellite position vector in the J2000.0 coordinate system. and velocity vector

[0067]

[0068]

[0069] Here, |*| is the modulus calculation for a vector.

[0070] (9) Based on the time T of the satellite's temporary orbit m ,Location speed Update the calculation of the semi-major axis a of the satellite's temporary orbital elements. m eccentricity e m Inclination angle i m Right ascension of ascending node Ω m Argument of perigee ω m Angle M near the point m ;

[0071]

[0072] in, It is based on the satellite orbital time T m ,Location speed A function for calculating the orbital elements of a satellite.

[0073] (10) Extrapolate the temporary orbital elements based on the high-precision dynamic model and calculate T. e Temporary orbital elements at any given time, including parameters such as the semi-major axis a of the satellite orbit. me eccentricity e me Inclination angle i me Right ascension of ascending node Ω me Argument of perigee ω me Angle M near the point me ;

[0074] [T e ,ame ,e me i me ,Ω me ,ω me M me ] = F3(T m ,a m ,e m i m ,Ω m ,ω m M m )

[0075] Among them, F3(T m ,a m ,e m i m ,Ω m ,ω m M m ) is a function that extrapolates satellite orbital elements based on a high-precision dynamic model.

[0076] (11) Calculate T e Temporary orbital latitude angle u me ;

[0077]

[0078] Among them, the temporary orbital near-point angle E me From equation E me =M me +e me sinE me Obtained through iterative calculation.

[0079] (12) Calculate the phase difference δu between the temporary orbit and the controlled satellite orbit.

[0080]

[0081] (13) Determine whether the phase difference δu meets the accuracy requirements. If it does, i.e., δu < δ, where δ is the threshold for iterative calculation, which can be manually selected as needed, then proceed to step 14; otherwise, proceed to step 3.

[0082] (14) Calibrate the thruster coefficient;

[0083]

[0084] Where, Δv s It is the theoretical velocity increment, k s This is the thrust coefficient used in this control, Δv s and k s Obtained from the track change control parameters.

Claims

1. A numerical iterative evaluation method for in-plane small control variables based on orbital phase evolution, characterized in that, By using pre- and post-control orbital elements and a high-precision orbital dynamics model, and leveraging the time integral effect of small in-plane control variables, the phase difference of the post-control satellite orbit is used as the control effect evaluation criterion. Numerical iteration is employed during calibration to ensure the effectiveness of the calibration method. Specifically, the method includes the following steps: Step 1: Determine the current situation Satellite orbital parameters at any given time, including the semi-major axis of the satellite orbit. eccentricity ,inclination Right ascension of ascending node perigee argument , near point angle Determine the control intermediate time. The pre-control satellite orbital parameters, including the semi-major axis of the satellite orbit. eccentricity ,inclination Right ascension of ascending node perigee argument , near point angle ; Step 2: Set initial values ​​for iterative calibration, including the time for the temporary track. semi-major shaft eccentricity ,inclination Right ascension of ascending node perigee argument , near point angle Actual control speed increment ; Step 3: Calculate the temporary orbital latitude argument. And control orbital latitude angle ; in, It is the arctangent calculation function. It is a temporary track deflection angle. It is the angle of approach to the control track; Step 4: Calculate the phase evolution. ; Step 5: Based on orbital phase evolution Calculate the control speed increment correction amount ; in, f m It is a true anterior angle, calculated by the following formula: Step 6: Calculate the actual control speed increment ; Step 7: Calculate the satellite position vector in the control intermediate time in the J2000.0 coordinate system. and velocity vector ; in, To be based on satellite orbit time semi-major shaft eccentricity ,inclination Right ascension of ascending node Perigeal argument Peace Angle Calculate satellite position vector and velocity vector The function; Step 8: Calculate the temporary orbital satellite position vector in the J2000.0 coordinate system. and velocity vector ; in, It is a modulo calculation of a vector; Step 9: Based on the time of the satellite's temporary orbit ,Location ,speed Update the calculation of the semi-major axis of the satellite's temporary orbital elements. eccentricity ,inclination Right ascension of ascending node perigee argument , near point angle ; in, It is based on satellite orbit time ,Location ,speed A function for calculating satellite orbital elements; Step 10: Extrapolate the temporary orbital elements based on the high-precision dynamic model and calculate... Temporary orbital elements at any given time, including parameters such as the semi-major axis of the satellite orbit. eccentricity ,inclination Right ascension of ascending node perigee argument , near point angle ; in, It is a function that extrapolates satellite orbital elements based on a high-precision dynamic model; Step 11, Calculation Temporary orbital latitude angle ; in, It is a temporary track deflection angle; Step 12: Calculate the phase difference between the temporary orbit and the post-control satellite orbit. ; Step 13: Determine the phase difference Does it meet the accuracy requirements? If it does, then... ,in If the threshold is calculated iteratively, proceed to step 14; otherwise, go to step 3. Step 14: Calibrate the thrust coefficient; in, It is the theoretical speed increment. It is the thrust coefficient. and Obtained from the track change control parameters.

2. The numerical iterative evaluation method for in-plane small control variables based on orbital phase evolution as described in claim 1, characterized in that, In step 3, the temporary track deflection angle and control of the orbital approach angle From the equation Obtained through iterative calculation.

3. The numerical iterative evaluation method for in-plane small control variables based on orbital phase evolution as described in claim 1, characterized in that, In step 11, the temporary track deflection angle From the equation Obtained through iterative calculation.

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