'Constant in gain lead in phase' element-application in precision motion control

Niranjan Saikumar, Rahul Kumar Sinha, Hassan Hossein Nia Kani*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

23 Citations (Scopus)
119 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1176-1185
JournalIEEE/ASME Transactions on Mechatronics
Issue number3
Publication statusPublished - 2019

Bibliographical note

Accepted Author Manuscript


  • mechatronics
  • Motion control
  • nonlinear control
  • precision control
  • reset control


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