Optimal Continuous/Impulsive Control for Lorentz-Augmented Spacecraft Formations

Sobiesiak, Ludwik A.; Damaren, Christopher J.

doi:10.2514/1.g000334

Cited by 24 publications

(26 citation statements)

References 18 publications

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“…The time interval over which the Gramian is calculated is the synodic period of the spacecraft with respect to the geomagnetic field, i.e., the time it takes for the spacecraft to reach the same point in the Earth's magnetic field. As has been previously noted [9,13], this is the natural period of the magnetic field variations seen by the spacecraft. Figure 2 illustrates the dominant components of ν 0 , namely ν 0 a and ν 0 i .…”

Section: Controllability Of the Lorentz-augmented Systemmentioning

confidence: 68%

“…From previous work [13], it is known that the system described by Eq. (14) is not fully controllable.…”

Section: Controllability Of the Lorentz-augmented Systemmentioning

confidence: 99%

“…Previous work [12,13] on the subject of formation keeping using the Lorentz force has focused on supplementing Lorentz-force actuation with thruster actuation in order to achieve controllability of the system. Using impulsive thruster actuation [13] was shown to be particularly effective in maintaining the desired formation while also minimizing the required amount of the thruster control effort.…”

Section: Formation Controlmentioning

confidence: 99%

“…Using impulsive thruster actuation [13] was shown to be particularly effective in maintaining the desired formation while also minimizing the required amount of the thruster control effort.…”

Section: Formation Controlmentioning

confidence: 99%

“…The effects of the Lorentz force on the classical orbital elements have been fully described in [10] and also partially described and used in [11] to establish new J 2invariant and ground-track-repeating orbits. Mean differential element formation control has been explored previously in [12,13], where it was identified that relative spacecraft dynamics are not completely controllable using solely the Lorentz force; optimal strategies combining the Lorentz force with either continuous or impulsive thruster actuation were proposed to fully control the relative dynamics.…”

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confidence: 99%

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Controllability of Lorentz-Augmented Spacecraft Formations

Sobiesiak

Damaren

2015

Journal of Guidance, Control, and Dynamics

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Nomenclature a = semimajor axis, m b = magnetic field vector, T e = eccentricity f = true anomaly, rad h = specific angular momentum magnitude, m 2 ∕s i = inclination, rad J n = nth zonal harmonic coefficient M = mean anomaly, rad m = mass, kg m = magnetic dipole vector, A · m 2 n = mean motion, rad∕s p = semilatus rectum, m q = electrical charge, C q 1 = e cos ω q 2 = e sin ω r = orbit radius magnitude, m r = position vector, m v = velocity vector, m∕s W = controllability Gramian z = orbital element vector ΔV = Delta-v magnitude, m∕s δt = Dirac Delta function θ = true latitude, rad λ = mean latitude, rad μ = gravitational parameter, m 3 ∕s 2 ν = Gramian eigenvector Φ = state transition matrix Ω = right ascension of ascending node, rad ω = angular velocity vector, rad∕s ω = argument of periapsis, rad Subscripts c = chief d = deputy L = Lorentz force-related r = reference quantity = Earth-related quantity Superscript · = mean element quantity

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Section: Controllability Of the Lorentz-augmented Systemmentioning

confidence: 68%

“…From previous work [13], it is known that the system described by Eq. (14) is not fully controllable.…”

Section: Controllability Of the Lorentz-augmented Systemmentioning

confidence: 99%

Section: Formation Controlmentioning

confidence: 99%

Section: Formation Controlmentioning

confidence: 99%

mentioning

confidence: 99%

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Controllability of Lorentz-Augmented Spacecraft Formations

Sobiesiak

Damaren

2015

Journal of Guidance, Control, and Dynamics

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Passivity‐based control design frameworks for hybrid nonlinear time‐varying dynamical systems

Sharifi

Damaren

2023

Intl J Robust & Nonlinear

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This article proposes two novel passivity‐based control design frameworks for hybrid nonlinear dynamical systems involving an interacting mixture of continuous‐time and discrete‐time dynamics whose dynamical properties evolve periodically over time. By deriving the Kalman–Yakubovich–Popov (KYP) conditions characterizing dissipativeness for hybrid nonlinear time‐dependent dynamical systems, a hybrid computational algorithm, which alternates between continuous‐time and discrete‐time subsystems at an appropriate sequence of time instants, is then proposed to solve the resultant equations in an interacting manner. Two passivity‐based control schemes are then developed by utilizing the foregoing KYP conditions in tandem with the passivity theorem. The overall framework consists mainly of three steps. The hybrid output dynamics of the plant are first determined judiciously to satisfy the passivity specifications. A hybrid nonlinear controller is then designed to meet the input strict passivity requirements. The stability of the closed‐loop system is finally established by interconnecting the plant and the controller through negative feedback. Practical considerations for appropriately implementing the derived hybrid algorithms are then discussed in detail. The efficacy of the proposed control schemes is ultimately assessed via a multi‐dimensional system with a hybrid source of actuation.

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