Reset Control Systems with Reset Band: Well-posedness and Limit Cycles Analysis

Reset controllers provide a simple way to improve performance when controlling strongly traded-off plants. A reset controller operates most of the time as a linear system, but when some condition holds, it performs a zero resetting action on its state. Recently, some generalizations have been proposed: anticipation of the condition with the so-called reset band, relaxation of the action applying partial reset, etc. There is a lack of analysis tools for reset systems with reset band. In this paper we address the problem of existence, detection and stability of limit cycles by means of Poincare maps. The results give also information on pathologies such as Zenoness. The presented approach is complementary to describing function analysis, in order to reveal the ability of reset controllers for overcoming fundamental limitations in the frequency domain.