  This work presents a novel 'Constant in gain Lead in phase' (CgLp) element
using nonlinear reset technique. PID is the industrial workhorse even to this
day in high-tech precision positioning applications. However, Bode's gain phase
relationship and waterbed effect fundamentally limit performance of PID and
other linear controllers. This paper presents CgLp as a controlled nonlinear
element which can be introduced within the framework of PID allowing for wide
applicability and overcoming linear control limitations. Design of CgLp with
generalized first order reset element (GFORE) and generalized second order
reset element (GSORE) (introduced in this work) is presented using describing
function analysis. A more detailed analysis of reset elements in frequency
domain compared to existing literature is first carried out for this purpose.
Finally, CgLp is integrated with PID and tested on one of the DOFs of a planar
precision positioning stage. Performance improvement is shown in terms of
tracking, steady-state precision and bandwidth.
