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

A. Bisoffi, R. Beerens, L. Zaccarian, W.P.M.H. Heemels, H. Nijmeijer, N. van de Wouw

Research output: Contribution to journalConference articleAcademicpeer-review

2 Citations (Scopus)
43 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)84-89
Number of pages6
Issue number16
Publication statusPublished - Sep 2019
Event11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 - Vienna, Austria
Duration: 4 Sep 20196 Sep 2019

Bibliographical note

Part of special issue:
11th IFAC Symposium on Nonlinear Control Systems NOLCOS 2019: Vienna, Austria, 4–6 September 2019


  • hybrid systems
  • nonlinear systems
  • Coulomb friction
  • Lyapunov methods
  • global asymptotic stability
  • PID control


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