This paper 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 and generalized second-order reset element (introduced in this paper) 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.@en

This paper presents a novel nonlinear (reset) disturbance observer for dynamic compensation of bounded nonlinearities like hysteresis in piezoelectric actuators. Proposed Resetting Disturbance Observer (RDOB) utilizes a novel Constant-gain Lead-phase (CgLp) element based on the concept of reset control. The fundamental limitations of linear DOB which results in contradictory requirements and in a dependent design between DOB and feedback controller are analysed. Two different configurations of RDOB which attempt to alleviate these problems from different perspectives are presented and an example plant is used to highlight the improvement. Stability criteria are presented for both configurations. Performance improvement seen with both RDOB configurations compared to linear DOB is also verified on a practical piezoelectric setup for hysteresis compensation and results analysed.@en