We consider the feedback interconnection of a strictly proper single input single output plant with a play (equivalently backlash) operator. Under the standard assumption that the linear feedback is exponentially stable we characterize the set of equilibria of the arising nonlinear closed-loop system and show that it is a bounded set containing the origin. Then we provide necessary and sufficient conditions for global exponential stability of this set, that correspond to exponential stability of the open-loop dynamics. We prove our main result by proposing a novel model for the play operator, corresponding to a constrained differential inclusion. With this representation, we also show that the nonlinear closed loop under consideration can be projected to a subspace where it evolves like a switching linear system. We illustrate our results by some numerical simulations illustrating a few possible scenarios.

Necessary and sufficient stability conditions for equilibria of linear SISO feedbacks with a play operator / Cocetti, Matteo; Zaccarian, Luca; Bagagiolo, Fabio; Bertolazzi, Enrico. - ELETTRONICO. - 49:18(2016), pp. 211-216. [10.1016/j.ifacol.2016.10.165]

Necessary and sufficient stability conditions for equilibria of linear SISO feedbacks with a play operator

Cocetti, Matteo;Zaccarian, Luca;Bagagiolo, Fabio;Bertolazzi, Enrico
2016

Abstract

We consider the feedback interconnection of a strictly proper single input single output plant with a play (equivalently backlash) operator. Under the standard assumption that the linear feedback is exponentially stable we characterize the set of equilibria of the arising nonlinear closed-loop system and show that it is a bounded set containing the origin. Then we provide necessary and sufficient conditions for global exponential stability of this set, that correspond to exponential stability of the open-loop dynamics. We prove our main result by proposing a novel model for the play operator, corresponding to a constrained differential inclusion. With this representation, we also show that the nonlinear closed loop under consideration can be projected to a subspace where it evolves like a switching linear system. We illustrate our results by some numerical simulations illustrating a few possible scenarios.
Kidlington
Elsevier
Necessary and sufficient stability conditions for equilibria of linear SISO feedbacks with a play operator / Cocetti, Matteo; Zaccarian, Luca; Bagagiolo, Fabio; Bertolazzi, Enrico. - ELETTRONICO. - 49:18(2016), pp. 211-216. [10.1016/j.ifacol.2016.10.165]
Cocetti, Matteo; Zaccarian, Luca; Bagagiolo, Fabio; Bertolazzi, Enrico
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/180452
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