Dynamic modeling and simulation of deploying process for space solar power satellite receiver

To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array （SPS-ALPHA） solar receiver, the symplectic Runge-Kutta method is used to simulate the simplified model with the consideration of the Rayleigh damping effect. The system containing the Rayleigh damping can be separated and transformed into the equivalent nondamping system formally to insure the application condition of the symplectic Runge-Kutta method. First, the Lagrange equation with the Rayleigh damping governing the motion of the system is derived via the variational principle. Then, with some reasonable assumptions on the relations among the damping, mass, and stiffness matrices, the Rayleigh damping system is equivalently converted into the nondamping system formally, so that the symplectic Runge-Kutta method can be used to simulate the deploying process for the solar receiver. Finally, some numerical results of the symplectic Runge-Kutta method for the dynamic properties of the solar receiver are reported. The numerical results show that the proposed simplified model is valid for the deploying process for the SPS-ALPHA solar receiver, and the symplectic Runge-Kutta method can preserve the displacement constraints of the system well with excellent long-time numerical stability.

Distributed vibration control of a large solar power satellite

To deal with the vibration problem of the solar power satellite(SPS),the distributed vibration control approach is investigated in this paper.Taking the Multi-Rotary joints SPS as the research objective,the control unit(CU)and the location relationship matrix are rstly de ned for distributed controller design according to the con guration of SPS.The dynamic model of each CU is therefore established based on the nite element method.The dynamic model of the whole SPS structure is then developed using the CU models,and is updated along with on-orbit assembly.The distributed cooperative controller,using proportional and di erential feedback and the interaction feedback among adjacent CUs,is proposed to suppress vibration.The close-loop distributed cooperative control system is then achieved by integrating all distributed controllers,and the asymptotic stability is proofed by the Lyapunov's stability theorem.To verify the feasibility of the proposed control system,three numerical cases are nally presented.The results demonstrate that the distributed cooperative controllers can e ectively suppress vibration during on-orbit assembly and operation after assembly,and the closed-loop system has good fault tolerance.

Estimation of BDS pseudorange biases with high temporal resolution:feasibility,affecting factors,and necessity

A common practice adopted for the pseudorange bias estimation and calibration assumes that Global Navigation Satellite System satellite-dependent pseudorange biases vary gently over time.Whereupon satellite pseudorange biases are routinely estimated and provided as the products with low temporal resolution,e.g.,hourly or daily,by the agencies.The story sounds unquestionably perfect under the acquainted assumption.To validate the inadequacy of the above hypothesis we herein present an approach to the estimate the BeiDou Navigation Satellite System(BDS)pseudorange biases with high temporal resolution.Its feasibility,affecting factors,and necessity are discussed.Concretely,the Geometry-Free function models are first constructed to retrieve the linear combination of the pseudorange biases;then the pseudorange Observable-specific Signal Bias(OSB)values with respect to baseline frequencies(e.g.,BDS C2I/C6I)are estimated along with the ionosphere modeling;subsequently,all multi-frequency pseudorange OSBs are determined by using the ionospheric information with constraint conditions;finally,the possible Differential Code Bias sets are attainable with the estimated pseudorange OSBs.Using the observation data of four months when the estimated BDS pseudorange biases are stable,their reliability is demonstrated with the stability at the level of sub-nanosecond and the BeiDou-3 Navigation Satellite System(BDS-3)values more stable than that of BeiDou-2 Navigation Satellite System(BDS-2).The comparison between the estimated pseudorange biases and the Chinese Academy of Sciences products reveals that the accuracy of the estimated pseudorange biases is 0.2–0.4 ns.Moreover,the large magnitude of the short-term pseudorange bias variation in the tens of nanoseconds for the BDS-2 and BDS-3 are found in years 2021 and 2022,which are affected by two types of the satellite flex power for the BDS-2 and BDS-3,respectively.We stress that it’s necessary to estimate the BDS pseudorange biases with high temporal resolution in the case of the satellite flex power and the products currently provided by the agencies cannot reflect the true quantity under the circumstance.