Tuning of 'Constant in Gain Lead in Phase (CgLp)' Reset Controller using Higher-orDer Sinusoidal Input Describing Function (HOSIDF)

Due to development of technology, linear controllers cannot satisfy requirements of high-tech industry. One solution is using nonlinear controllers such as reset elements to overcome this big barrier. In literature, the Constant in gain Lead in phase (CgLp) compensator is a novel reset element developed to overcome the inherent linear controller limitations. However, a tuning guideline for these controllers has not been proposed so far. In this paper, a recently developed method named higher-order sinusoidal input describing function (HOSIDF), which gives deeper insight into the frequency behaviour of non-linear controllers compared to sinusoidal input describing function (DF), is used to obtain a straight-forward tuning method for CgLp compensators. In this respect, comparative analyses on tracking performance of these compensators are carried out. Based on these analyses, tuning guidelines for CgLp compensators are developed and validated on a high-tech precision positioning stage. The results show the effectiveness of the developed tuning method.