For a PID-controlled motion system under Coulomb friction described by a differential inclusion, we present a hybrid model comprising logical states indicating whether the closed loop is in stick or in slip, thereby resembling a hybrid automaton. A key step for this description is the addition of a timer exploiting a peculiar semiglobal dwell time of the original dynamics, which then removes defective and unwanted nonconverging Zeno solutions from the hybrid model. Through it, we then revisit an existing proof of global asymptotic stability, which is significantly simplified by way of a smooth weak Lyapunov function. The relevance of the proposed hybrid representation is also illustrated on a novel control strategy resetting the PID integrator and hinging upon the proposed hybrid model.

Hybrid model formulation and stability analysis of a PID-controlled motion system with Coulomb friction / Bisoffi, A.; Beerens, R.; Zaccarian, L.; Heemels, W. P. M. H.; Nijmeijer, H.; van de Wouw, N.. - 52:16(2019), pp. 84-89. (Intervento presentato al convegno 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 tenutosi a Vienna, Austria nel 4-6 September, 2019) [10.1016/j.ifacol.2019.11.760].

Hybrid model formulation and stability analysis of a PID-controlled motion system with Coulomb friction

Zaccarian L.;
2019-01-01

Abstract

For a PID-controlled motion system under Coulomb friction described by a differential inclusion, we present a hybrid model comprising logical states indicating whether the closed loop is in stick or in slip, thereby resembling a hybrid automaton. A key step for this description is the addition of a timer exploiting a peculiar semiglobal dwell time of the original dynamics, which then removes defective and unwanted nonconverging Zeno solutions from the hybrid model. Through it, we then revisit an existing proof of global asymptotic stability, which is significantly simplified by way of a smooth weak Lyapunov function. The relevance of the proposed hybrid representation is also illustrated on a novel control strategy resetting the PID integrator and hinging upon the proposed hybrid model.
2019
IFAC-PapersOnLine
RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS
Elsevier B.V.
Bisoffi, A.; Beerens, R.; Zaccarian, L.; Heemels, W. P. M. H.; Nijmeijer, H.; van de Wouw, N.
Hybrid model formulation and stability analysis of a PID-controlled motion system with Coulomb friction / Bisoffi, A.; Beerens, R.; Zaccarian, L.; Heemels, W. P. M. H.; Nijmeijer, H.; van de Wouw, N.. - 52:16(2019), pp. 84-89. (Intervento presentato al convegno 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 tenutosi a Vienna, Austria nel 4-6 September, 2019) [10.1016/j.ifacol.2019.11.760].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/259083
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