Optimization Method for Successive Orbit Transfer Strategies of Geostationary Satellites with Chemical Propulsion and Electric Propulsion

Abstract

The present invention discloses an optimization method for the sequential orbit transfer strategy of a geostationary satellite using chemical propulsion and electric propulsion. First, the initial in-orbit state information of the satellite is collected. Secondly, the velocity increments in the chemical propulsion and electric propulsion stages are estimated using the optimal two-impulse transfer, a four-impulse orbit transfer model for rendezvousing with a virtual target star is established, and an intelligent optimization algorithm is used to solve for the optimal intermediate orbit. Finally, taking the satellite's initial in-orbit as the starting orbit and the optimal intermediate orbit as the terminal orbit, the orbit transfer strategy in the chemical propulsion stage is solved; taking the optimal intermediate orbit as the starting orbit and the GEO orbit that the satellite is to reach as the terminal orbit, the orbit transfer strategy in the electric propulsion stage is solved. The method disclosed by the present invention realizes the overall optimization of the sequential orbit transfer using chemical propulsion and electric propulsion by estimating the energy consumption in the electric propulsion stage using the optimal two-impulse transfer, and has the advantages of excellent calculation results and fast calculation speed.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace navigation, and specifically relates to an optimization method for the successive orbit transfer strategy of chemical propulsion and electric propulsion of geostationary satellites. Background Art

[0002] Because the electric propulsion technology can provide a specific impulse far greater than that of chemical propulsion, thus saving the fuel consumption of satellite orbit control, it is more and more widely equipped on new geostationary satellites. In order to balance the orbit transfer time efficiency and the energy consumption of position keeping, some geostationary satellites are equipped with both a chemical propulsion system and an electric propulsion system at the same time. The chemical propulsion system is used for orbit transfer from GTO to GEO, and the electric propulsion system is used for position keeping control on the GEO orbit. However, when a launch vehicle fails and the satellite's injection orbit deviates from the predetermined orbit, and the satellite cannot enter the GEO orbit only relying on the chemical propulsion system, all the fuel of the chemical propulsion can be used to send the satellite into an intermediate orbit first, and then the electric propulsion is used to transfer the satellite from this intermediate orbit to the GEO orbit. This two-stage successive ignition mode of chemical propulsion and electric propulsion poses great difficulties for the optimization of the orbit transfer strategy: in order to save the fuel consumption and transfer time of the electric propulsion stage, it is necessary to optimize the intermediate orbit of the two orbit transfer stages, and while fully utilizing the orbit transfer ability of chemical propulsion, provide an initial state closest to the target GEO orbit for the electric propulsion stage. However, due to the significant differences between the optimization models of chemical propulsion orbit transfer strategy and electric propulsion orbit transfer strategy, it is difficult to conduct overall optimization to obtain the optimal intermediate orbit. Summary of the Invention

[0003] The present invention provides an optimization method for the successive orbit transfer strategy of chemical propulsion and electric propulsion of geostationary satellites, which is used to solve the problem that it is difficult to conduct overall optimization of the two-stage successive orbit transfer strategy of chemical propulsion and electric propulsion in the prior art.

[0004] The technical solution adopted by the present invention is that the optimization method for the successive orbit transfer strategy of chemical propulsion and electric propulsion of geostationary satellites is specifically implemented according to the following steps:

[0005] Step 1, collect the initial state information of the satellite injection.

[0006] Step 2, in both the chemical propulsion orbit transfer stage and the electric propulsion orbit transfer stage, use the optimal two-impulse transfer velocity increment as the estimate of the required velocity increment for each stage. Assume a virtual target star, whose orbital semi-major axis, eccentricity and inclination are the same as those of the GEO orbit that the satellite is to reach, and its right ascension of the ascending node, argument of perigee and mean anomaly are freely selected as design variables. Establish a four-impulse orbit transfer optimization model for the satellite to rendezvous with the virtual target star, and use an intelligent optimization algorithm to solve for the two-stage intermediate orbit that minimizes the estimated value of the required velocity increment in the electric propulsion stage.

[0007] Step 3: Taking the satellite's in-orbit injection orbit as the starting orbit and the intermediate orbit obtained in Step 2 as the terminal orbit, solve the optimal chemical propulsion orbit transfer strategy; taking the intermediate orbit obtained in Step 2 as the starting orbit and the GEO orbit that the satellite needs to reach as the terminal orbit, solve the optimal electric propulsion orbit transfer strategy.

[0008] The features of the present invention also lie in:

[0009] Among them, the initial state information of the satellite's in-orbit injection collected in Step 1 includes: the initial moment, and the position vector and velocity vector of the satellite in the geocentric J2000 inertial system at this moment;

[0010] Among them, the specific content of establishing the four-impulse orbit transfer optimization model for the satellite to rendezvous with the virtual target star in Step 2 is as follows:

[0011] The design variables of the four-impulse orbit transfer optimization model for the satellite to rendezvous with the virtual target star are shown in Equation (1):

[0012] X = [t1, Δv1, ψ1, θ1, t2, Δv2, ψ2, θ2, t3, t4, Ω f , ω f , M f (1)

[0013] In the formula, t1, t2, t3, t4 are the moments of the four orbit transfers, Δv1 and Δv2 are the magnitudes of the velocity increments of the first and second orbit transfers respectively, ψ1, θ1, ψ2, θ2 are the yaw angles and pitch angles of the velocity increment directions of the first and second orbit transfers in the orbital system respectively, Ω f , ω f , M f are the right ascension of the ascending node, argument of perigee and mean anomaly of the virtual target star respectively. The optimization objective is shown in Equation (2), and the constraints are shown in Equations (3)(4)(5)(6):

[0014]

[0015] s.t. t i > t i-1 , i = 1,..., 4 (3)

[0016] |r + (t4) - r f (t4)| = 0 (4)

[0017] |v + (t4) - v f (t4)| = 0 (5)

[0018] Δv1 + Δv2 = Δv chemical (6)

[0019] Wherein, Δv3 and Δv4 are respectively the velocity increments of the third and fourth orbit maneuvers. is the size of the semi-major axis of the orbit after the second orbit maneuver, and a s is the nominal semi-major axis size of the GEO orbit, w is the semi-major axis weight, and r + (t4) and v + (t4) are the satellite position vector and velocity vector after the fourth orbit maneuver, and r f (t4) and v f (t4) are the position vector and velocity vector of the virtual target star at the fourth orbit maneuver moment, and Δv chemical is the total velocity increment that the chemical propulsion system fuel can provide.

[0020] Among them, in the model calculation process of step 2, the two-body model is adopted for the orbit extrapolation in the non-powered section.

[0021] The calculation methods of the position and velocity after the first and second orbit maneuvers are as shown in the formula:

[0022]

[0023] In the formula, and are respectively the satellite position vector and velocity vector before the maneuver, and are respectively the satellite position vector and velocity vector after the maneuver, and M is the coordinate transformation matrix from the orbital system to the inertial system.

[0024] The position and velocity before the third orbit maneuver are determined by the first two orbit maneuvers. The position and velocity after the fourth orbit maneuver are the same as those of the virtual target star at the t4 moment, thus forming a Lambert problem, and there is an analytical method to solve it.

[0025] Among them, in step 2, the differential evolution algorithm is adopted to solve the optimization model in step 2, and a set of design variables X * is obtained to minimize the index in formula (2). Using this set of design variables and combining with formula (7), the optimal intermediate orbit in the chemical propulsion and electric propulsion stages can be obtained.

[0026] The beneficial effects of the present invention are:

[0027] The method for optimizing the sequential orbit maneuver strategy of a geostationary satellite's chemical propulsion and electric propulsion of the present invention is applicable to the overall optimization and solution of the optimal intermediate orbit during the sequential orbit maneuvers of a geostationary satellite's chemical propulsion and electric propulsion. In both the chemical propulsion orbit maneuver stage and the electric propulsion orbit maneuver stage of this method, the optimal two-pulse transfer is adopted as the estimation of the required velocity increment in each stage, which solves the problem that the accurate optimization models of chemical propulsion and electric propulsion are significantly different and the two-stage orbit maneuvers cannot be optimized uniformly. Compared with the existing calculation methods, it has the following advantages:

[0028] (1) By adopting the optimal two - pulse transfer optimization to replace the complex electric propulsion transfer optimization, the present invention can optimize the orbit transfer in the chemical propulsion stage as a whole, obtaining an optimal intermediate orbit in an overall sense. Compared with the method of solving and calculating by stages, it can save more electric propulsion fuel and orbit transfer time.

[0029] (2) By using fewer pulses as the estimation of the velocity increment for two - stage orbit transfer, the present invention has a fast calculation speed and meets the requirements of rapid planning and calculation. Description of the Drawings

[0030] Figure 1 It is a flowchart of the optimization method for the chemical propulsion and electric propulsion successive orbit transfer strategy of the geostationary satellite of the present invention. Detailed Embodiment

[0031] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0032] The optimization method for the chemical propulsion and electric propulsion successive orbit transfer strategy of the geostationary satellite of the present invention, as Figure 1 shown, the specific calculation process includes the following steps:

[0033] Step 1: Collect the initial state information of the satellite's orbit entry, including: the initial time, and the position vector and velocity vector of the satellite in the geocentric J2000 inertial system at this time.

[0034] Step 2: In both the chemical propulsion orbit transfer stage and the electric propulsion orbit transfer stage, adopt the optimal two - pulse transfer velocity increment as the estimation of the required velocity increment for each stage. Suppose a virtual target star, whose orbital semi - major axis, eccentricity, and inclination are the same as those of the GEO orbit that the satellite is to reach, and its right ascension of the ascending node, argument of perigee, and mean anomaly are freely selected. Establish a four - pulse orbit transfer optimization model for the rendezvous of the satellite and the virtual target star, and use an intelligent optimization algorithm to solve for the two - stage intermediate orbit that minimizes the estimated value of the required velocity increment in the electric propulsion stage.

[0035] The design variables of the four - pulse orbit transfer optimization model for the rendezvous of the satellite and the virtual target star are shown in Equation (1):

[0036] X = [t1, Δv1, ψ1, θ1, t2, Δv2, ψ2, θ2, t3, t4, Ω f , ω f , M f (1)

[0037] In the formula, t1, t2, t3, t4 are the times of the 4 orbit transfers, Δv1, Δv2 are the magnitudes of the velocity increments of the first and second orbit transfers respectively, ψ1, θ1, ψ2, θ2 are the yaw angles and pitch angles of the velocity increment directions of the first and second orbit transfers in the orbital system, Ω f , ω f,M f They are the right ascension of the ascending node, argument of perigee, and mean anomaly of the virtual target star. The optimization objective is shown in Equation (2), and the constraints are shown in Equations (3), (4), (5), and (6):

[0038]

[0039] s.t.t i >t i-1 ,i = 1,...,4 (3)

[0040] |r + (t4)-r f (t4)| = 0 (4)

[0041] |v + (t4)-v f (t4)| = 0 (5)

[0042] Δv1 + Δv2 = Δv chemical (6)

[0043] In the formula, Δv3 and Δv4 are the velocity increments of the third and fourth orbit maneuvers respectively, is the size of the semi-major axis of the orbit after the second orbit maneuver, a s is the nominal semi-major axis size of the GEO orbit, w is the semi-major axis weight, r + (t4) and v + (t4) are the satellite position vector and velocity vector after the fourth orbit maneuver, r f (t4) and v f (t4) are the position vector and velocity vector of the virtual target star at the fourth orbit maneuver moment, Δv chemical is the total velocity increment that the chemical propulsion system fuel can provide;

[0044] During the calculation process of the above model, the two-body model is used for the orbit extrapolation in the coasting phase;

[0045] The calculation methods of the position and velocity after the first and second orbit maneuvers are as shown in the formula:

[0046]

[0047] In the formula, and are the satellite position vector and velocity vector before the maneuver respectively, and are the satellite position vector and velocity vector after the maneuver respectively, and M is the coordinate transformation matrix from the orbital system to the inertial system;

[0048] The position and velocity before the third orbit transfer are determined by the previous two orbit transfers. The position and velocity after the fourth orbit transfer are the same as those of the virtual target satellite at time t4, thus forming a Lambert problem, for which there is an analytical method to solve.

[0049] Preferably, the differential evolution algorithm is used to solve the optimization model in step 2 to obtain a set of design variables X that minimize the index in equation (2). * , and using this set of design variables in combination with equation (7), the optimal intermediate orbits for the chemical propulsion and electric propulsion phases can be obtained. The differential evolution algorithm has been described in many public literatures.

[0050] Step 3: Taking the satellite's injection orbit as the initial orbit and the intermediate orbit obtained in step 2 as the terminal orbit, solve the optimal chemical propulsion orbit transfer strategy; taking the intermediate orbit obtained in step 2 as the initial orbit and the GEO orbit that the satellite needs to reach as the terminal orbit, solve the optimal electric propulsion orbit transfer strategy.

[0051] The methods for calculating the optimal orbit transfer strategy for pure chemical propulsion and pure electric propulsion have been described in many public literatures.

Claims

1. Optimization method for the successive orbit transfer strategy of a geostationary satellite using chemical propulsion and electric propulsion, characterized in that, The implementation is specifically carried out in the following steps: Step 1: Collect the initial state information of the satellite's orbit injection; Step 2: In both the chemical propulsion orbit transfer stage and the electric propulsion orbit transfer stage, the optimal two-impulse transfer velocity increment is used as the estimation of the required velocity increment for each stage. Assume a virtual target star with the same semi-major axis, eccentricity, and inclination as the GEO orbit that the satellite is to reach. Its right ascension of the ascending node, argument of perigee, and mean anomaly are freely selected as design variables. Establish a four-impulse orbit transfer optimization model for the satellite to rendezvous with the virtual target star, and use an intelligent optimization algorithm to solve for the two-stage intermediate orbit that minimizes the estimated value of the required velocity increment in the electric propulsion stage. The specific content of establishing the four-impulse orbit transfer optimization model for the satellite to rendezvous with the virtual target star is as follows: The design variables of the four-impulse orbit transfer optimization model for the satellite to rendezvous with the virtual target star are shown in Equation (1): （1） In the formula, is the time of the fourth orbit transfer, are the magnitudes of the velocity increments of the first and second orbit transfers respectively, are the yaw angle and pitch angle of the velocity increment directions of the first and second orbit transfers in the orbital system respectively, are the right ascension of the ascending node, argument of perigee and mean anomaly of the virtual target star. The optimization objective is shown in Equation (2), and the constraints are shown in Equations (3), (4), (5) and (6): （2） （3） （4） （5） （6） Wherein, are the velocity increments of the third and fourth orbit transfers respectively, is the size of the semi-major axis of the orbit after the second orbit transfer, is the nominal semi-major axis size of the GEO orbit, is the semi-major axis weight, and are the position vector and velocity vector of the satellite after the fourth orbit transfer, and are the position vector and velocity vector of the virtual target star at the moment of the fourth orbit transfer, is the total velocity increment that the fuel of the chemical propulsion system can provide; Step 3: Using the satellite's orbit injection orbit as the starting orbit and the intermediate orbit obtained in Step 2 as the terminal orbit, solve for the optimal chemical propulsion orbit transfer strategy; using the intermediate orbit obtained in Step 2 as the starting orbit and the GEO orbit that the satellite is to reach as the terminal orbit, solve for the optimal electric propulsion orbit transfer strategy.

2. The method for optimizing the successive orbit transfer strategy of geostationary satellite chemical propulsion and electric propulsion according to claim 1, characterized in that, The initial state information of the satellite's orbit injection collected in Step 1 includes: the initial time, and the position vector and velocity vector of the satellite in the geocentric J2000 inertial system at this time.

3. The method for optimizing the geostationary satellite chemical propulsion and electric propulsion sequential orbit transfer strategy according to claim 1, wherein In the model calculation process of Step 2, the two-body model is used for the orbit extrapolation in the coasting phase; The calculation methods for the position and velocity after the first and second orbit transfers are shown in the formula: （7） In the formula, and are respectively the satellite position vector and velocity vector before maneuver, and are respectively the satellite position vector and velocity vector after maneuver, is the coordinate transformation matrix from the orbital system to the inertial system; The position and velocity before the third orbit transfer are determined by the previous two orbit transfers. The position and velocity after the fourth orbit transfer are the same as those of the virtual target satellite at moment, thus forming a Lambert problem, and there is an analytical method to solve it.

4. The method for optimizing the successive orbit transfer strategy of geostationary satellite chemical propulsion and electric propulsion according to claim 1, wherein In step 2, the differential evolution algorithm is used to solve the optimization model in step 2 to obtain a set of design variables that minimize the index in Equation (2). Using this set of design variables and combining with Equation (7), the optimal intermediate orbit in the chemical propulsion and electric propulsion stages can be obtained.

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