Extension of a PID control theory to Lie groups applied to synchronising satellites and drones. Issue 17 (8th October 2020)

• Record Type: Journal Article
• Authors: Fiori, Simone; Cervigni, Italo; Ippoliti, Mattia; Menotta, Claudio
• Is Part Of: IET control theory & applications. Volume 14:Issue 17(2020)
• Page Start: 2628
• Page End: 2642
• Publication Date: 2020-10-08
• Subjects: control system synthesis -- stability -- adaptive control -- Lyapunov methods -- nonlinear control systems -- synchronisation -- Lie groups -- three‐term control; PID control theory -- projected‐PID controllers -- empirical translational synchronisation algorithm -- test such numerical schemes -- Lie‐group‐tailored numerical techniques -- zero control error -- dynamics‐cancelling component -- physical systems -- resulting L‐PID control scheme -- proportional–integral–derivative regulation principle -- nonlinear control problem -- second‐order dynamical systems -- time synchronisation -- drones -- synchronising satellites -- Lie group; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2020.0226
• Languages: English
• ISSNs: 1751-8644

Abstract

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.