Application of the Nonlinear Tschauner-Hempel Equations to Satellite Relative Position Estimation and Control

Vepa, Ranjan

doi:10.1017/s0373463317000364

Cited by 6 publications

(2 citation statements)

References 18 publications

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“…The concept of MPC is explained by Rawlings (2000). The methodology considered is based on the implementation due to Vepa (2018), but altered to suit the current application. To illustrate the process of synthesis of a linear control law at each time step, a typical discrete time system is defined as,…”

Section: Control Law Synthesis: Nonlinear Model Predictive Controlmentioning

confidence: 99%

Active blade pitch control and stabilization of a wind turbine driven PMSG for power output regulation

2022

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A common strategy in controlling a permanent magnet synchronous generator (PMSG) driven by a wind turbine is the maximization of output power of the wind turbine itself. A control strategy must be adopted, is to deliver a desired reduced amount of power whenever it is required. In order to realize the direct control of wind turbine output power across a wide range of wind speeds, a linearized parameter varying dynamic model of the nonlinear wind turbine system including wind disturbances is developed and used in this paper. The stability of the wind turbine system is analyzed and a blade pitch controller is designed, based on the linearized, parameter-varying, model-predictive control and is validated. Thus, the wind turbine is regulated in a way that the generator delivers the demanded power output to the load. Moreover, the blade pitch control system also performs the key function of augmenting the stability of the wind turbine, for the right choice of the gains.

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Section: Control Law Synthesis: Nonlinear Model Predictive Controlmentioning

confidence: 99%

Active blade pitch control and stabilization of a wind turbine driven PMSG for power output regulation

2022

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“…Until recently, space missions have predominantly taken place in Low Earth Orbit (LEO) or Geostationary Orbit (GEO) [1]. Relative equations of motion like the Hill-Clohessy-Wiltshire (HCW) [2] and those of Tschauner-Hempel [3] have been tested and validated over the years for proximity operations in circular and elliptical orbits around Earth. These equations are only valid for a two-body system where the spacecraft is influenced by one planet's gravity alone.…”

Section: Introductionmentioning

confidence: 99%

Rendezvous and Proximity Operations in Cislunar Space Using Linearized Dynamics for Estimation

Zuehlke,

Tiwari,

Jebari

et al. 2023

Aerospace

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As interest in Moon exploration grows, and efforts to establish an orbiting outpost intensify, accurate modeling of spacecraft dynamics in cislunar space is becoming increasingly important. Contrary to satellites in Low Earth Orbit (LEO), where it takes around 5 ms to communicate back and forth with a ground station, it can take up to 2.4 s to communicate with satellites near the Moon. This delay in communication can make the difference between a successful docking and a catastrophic collision for a remotely controlled satellite. Moreover, due to the unstable nature of trajectories in cislunar space, it is necessary to design spacecraft that can autonomously make frequent maneuvers to stay on track with a reference orbit. The communication delay and unstable trajectories are exactly why autonomous navigation is critical for proximity operations and rendezvous and docking missions in cislunar space. Because spacecraft computational hardware is limited, reducing the computational complexity of navigational algorithms is both desirable and often necessary. By the introduction of a linear system approach to the deputy spacecraft motion, this research avoids the computational burden of integrating the deputy relative equations of motion. In this research, the relative CR3BP equations of motion are derived and linearized using a matrix exponential approximation. This research continues the development of the matrix exponential linearized relative circular restricted three-body problem (CR3BP) equations by applying the dynamics model to estimation and control applications. A simulation is performed to compare state estimation results obtained from using the linearized equations of motion utilizing a Kalman filter and for state estimation utilizing an unscented Kalman filter with the full nonlinear equations of motion. The linearized exponential model is shown to be sufficient for state estimation in the presence of noisy measurements for an example scenario. Additionally, a linear quadratic regulator (LQR) controller was added to optimally control a deputy spacecraft to rendezvous with a chief spacecraft in cislunar space. The contribution of this work is twofold: to provide a proof of concept that the matrix exponential solution for the linearized relative CR3BP equations can be used as the dynamics model for state estimation, as well as to simulate an optimal rendezvous maneuver in the presence of measurement noise.

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Invariant relative orbits for spacecraft formation flying in high-order gravitational field

He²,

et al. 2021

Acta Astronautica

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Application of the Nonlinear Tschauner-Hempel Equations to Satellite Relative Position Estimation and Control

Cited by 6 publications

References 18 publications

Active blade pitch control and stabilization of a wind turbine driven PMSG for power output regulation

Active blade pitch control and stabilization of a wind turbine driven PMSG for power output regulation

Rendezvous and Proximity Operations in Cislunar Space Using Linearized Dynamics for Estimation

Invariant relative orbits for spacecraft formation flying in high-order gravitational field

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