  This paper presents the tuning of a reset-based element called "Constant in
gain and Lead in phase" (CgLp) in order to achieve desired precision
performance in tracking and steady state. CgLp has been recently introduced to
overcome the inherent linear control limitation - the waterbed effect. The
analysis of reset controllers including ones based on CgLp is mainly carried
out in the frequency domain using describing function with the assumption that
the relatively large magnitude of the first harmonic provides a good
approximation. While this is true for several cases, the existence of
higher-order harmonics in the output of these elements complicates their
analysis and tuning in the control design process for high precision motion
applications, where they cannot be neglected. While some numerical
observation-based approaches have been considered in literature for the tuning
of CgLp elements, a systematic approach based on the analysis of higher-order
harmonics is found to be lacking. This paper analyzes the CgLp behaviour from
the perspective of first as well as higher-order harmonics and presents simple
relations between the tuning parameters and the gain-phase behaviour of all the
harmonics, which can be used for better tuning of these elements. The presented
relations are used for tuning a controller for a high-precision positioning
stage and results used for validation.
