Design of the footprints of uncertainty for a class of typical interval type-2 fuzzy PI and PD controllers

Haibo Zhou; Chaolong Zhang; Shuaixia Tan; Yu Dai; Ji'an Duan

doi:10.1016/j.isatra.2020.08.009

Design of the footprints of uncertainty for a class of typical interval type-2 fuzzy PI and PD controllers

ISA Trans. 2021 Feb:108:1-9. doi: 10.1016/j.isatra.2020.08.009. Epub 2020 Aug 14.

Authors

Haibo Zhou¹, Chaolong Zhang², Shuaixia Tan³, Yu Dai⁴, Ji'an Duan⁵

Affiliations

¹ College of Mechanical and Electrical Engineering, Central South University, Changsha, Hunan 410083, China; State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, Hunan 410083, China. Electronic address: zhouhaibo@csu.edu.cn.
² College of Mechanical and Electrical Engineering, Central South University, Changsha, Hunan 410083, China; State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, Hunan 410083, China. Electronic address: clzhang@csu.edu.cn.
³ Zhuzhou Times New Material Technology CO., LTD, Zhuzhou, Hunan 412007, China. Electronic address: tanshx@csrzic.com.
⁴ College of Mechanical and Electrical Engineering, Central South University, Changsha, Hunan 410083, China; State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, Hunan 410083, China. Electronic address: daiyu_6@aliyun.com.
⁵ College of Mechanical and Electrical Engineering, Central South University, Changsha, Hunan 410083, China; State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, Hunan 410083, China. Electronic address: duanjian@csu.edu.cn.

PMID: 32838970
DOI: 10.1016/j.isatra.2020.08.009

Abstract

The Footprint of Uncertainty (FOU) for an Interval type-2 (IT2) input fuzzy set is a key parameter of IT2 fuzzy PI and PD (FPI and FPD) controllers because it provides additional options to handle uncertainties. Because the effects of FOUs on IT2 FPI and FPD controller are still unclear, it is necessary to provide a guideline for designing the FOUs. In this study, from the input-output relationship of IT2 FPI and FPD controllers using typical and popular configuration, the variation trend of variable gains, in relation to the increase of FOUs, was analyzed. It is mathematically proven that variable gains of typical controllers decrease or not increase as the FOUs increase. These theoretical results can be extended to provide a guideline for designing FOUs of typical IT2 FPI and FPD controllers. Real-time response of linear voice coil motor is used to show the effectiveness of our results.

Keywords: Footprint of uncertainty; IT2 fuzzy control; Proportional–differential (PD) control; Proportional–integral (PI) control.