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EnglishThe authors tackle time synchronisation of two (possibly non-identical) second-order dynamical systems whose state space possess the structure of a Lie group. Synchronisation is treated as a non-linear control problem on Lie groups. They present a control theory inspired by the proportional–integral–derivative (PID) regulation principle. The resulting L-PID control scheme is applied to sync the rotational component of motions in physical systems. A model-dependent version of the L-PID, equipped with a dynamics-cancelling component, is theoretically proven to converge to zero control error by a Lyapunov stability analysis. Furthermore, they present Lie-group-tailored numerical techniques to implement the devised PID regulation theory and test such numerical schemes on two dynamical systems, namely, a gyrostat satellite and a quadrotor drone. As a further extension, they present an empirical translational synchronisation algorithm for two drones based on a pair of concurring L-PID and projected-PID controllers.
| Titolo: | Extension of a PID control theory to Lie groups applied to synchronising satellites and drones | |
| Autori: | MENOTTA, CLAUDIO [Software] | |
| Data di pubblicazione: | 2020 | |
| Rivista: | ||
| Abstract: | The authors tackle time synchronisation of two (possibly non-identical) second-order dynamical systems whose state space possess the structure of a Lie group. Synchronisation is treated as a non-linear control problem on Lie groups. They present a control theory inspired by the proportional–integral–derivative (PID) regulation principle. The resulting L-PID control scheme is applied to sync the rotational component of motions in physical systems. A model-dependent version of the L-PID, equipped with a dynamics-cancelling component, is theoretically proven to converge to zero control error by a Lyapunov stability analysis. Furthermore, they present Lie-group-tailored numerical techniques to implement the devised PID regulation theory and test such numerical schemes on two dynamical systems, namely, a gyrostat satellite and a quadrotor drone. As a further extension, they present an empirical translational synchronisation algorithm for two drones based on a pair of concurring L-PID and projected-PID controllers. | |
| Handle: | http://hdl.handle.net/11566/286583 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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