We consider set-point regulation and L2 robust stability properties of a class of reset control systems consisting of a minimum-phase relative degree-one linear SISO plant controlled by a novel first-order reset element (FORE). These results rely on necessary and sufficient conditions for exponential and L2 finite gain stability of a class of planar reset systems consisting of a scalar linear plant controlled by the novel FORE. We show that the L2 gain of the planar reset system decreases to zero as the pole and/or the gain of the FORE are increased to infinity. A number of stability results, including Lyapunov conditions for Lp and exponential stability, for a larger class of reset and hybrid systems are presented and used to prove our main results.
Stability and performance of SISO control systems with First Order Reset Elements
Zaccarian, Luca
2011-01-01
Abstract
We consider set-point regulation and L2 robust stability properties of a class of reset control systems consisting of a minimum-phase relative degree-one linear SISO plant controlled by a novel first-order reset element (FORE). These results rely on necessary and sufficient conditions for exponential and L2 finite gain stability of a class of planar reset systems consisting of a scalar linear plant controlled by the novel FORE. We show that the L2 gain of the planar reset system decreases to zero as the pole and/or the gain of the FORE are increased to infinity. A number of stability results, including Lyapunov conditions for Lp and exponential stability, for a larger class of reset and hybrid systems are presented and used to prove our main results.File | Dimensione | Formato | |
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