  This paper addresses nonlinearity in reset elements and their effects. Reset
elements are known for having less phase lag compared to their linear
counterparts; however, they are nonlinear elements and produce higher-order
harmonics. This paper investigates the higher-order harmonics for reset
elements with one resetting state and proposes an architecture and a method of
design which 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, e.g., they are useful for reducing
phase lag at cross-over frequency region; however, higher-order harmonics can
compromise tracking and disturbance rejection performance at lower frequencies.
Using proposed "phase shaping" method, one can selectively suppress
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 "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.
