Band-Passing Nonlinearity in Reset Elements

Abstract

This article addresses nonlinearity in reset elements and its effects. Reset elements are known for having less phase lag based on describing function (DF) analysis compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This article investigates the steady-state higher-order harmonics for reset elements with one resetting state and proposes an architecture and a method of design that allows for band-passing the nonlinearity and its effects, namely, higher-order harmonics and phase advantage. The nonlinearity of reset elements is not entirely useful for all frequencies, for example, they are useful for reducing phase lag at crossover frequency regions; however, higher-order harmonics can compromise tracking and disturbance rejection performance at lower frequencies. Using the proposed “phase shaping” method, one can selectively suppress the nonlinearity of a single-state reset element in a desired range of frequencies and allow the nonlinearity to provide its phase benefit in a different desired range of frequencies. This can be especially useful for the reset elements in the framework of the “constant in gain, lead in phase” (CgLp) filter, which is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation—the waterbed effect.