Polynomial-based Stability Analysis of Modified IMC-PID Controller for Piezoelectric Actuator System in Time Delay Environment

Abstract

Piezoelectric actuators are widely used in several industrial applications requiring precision positioning. However, the positioning accuracy of this nonlinear actuator is severely limited by physical phenomenon such as hysteresis, uncertainties. Accordingly, to improve the performance of piezo micro–nano positioning system, appropriate control laws are designed to linearize the hysteresis through closed-loop approaches. A modified internal model controller (MIMC) is useful with regard to efficient computational hardware resource utilization when compared with the conventional approach provided the resulting controller is stable. This paper focuses on one such widely used and computationally inexpensive control framework in the form of PID-based MIMC to mitigate hysteretic nonlinearity in piezoelectric actuators with the aim to investigate the time delay uncertainty handling range of the controller. The system stability pertaining to time delay has been analyzed numerically and the maximum delay that the system can withstand without losing its stability, i.e. the delay margin has been determined using polynomial-based approach. It has been found that upon increasing the delay beyond a specific critical value, the controller performance is limited and the system turns unstable. Simulations carried out in time delay environment validate the theoretically achieved results.

KEYWORDS:

• Hysteresis and controller
• Piezo actuator
• Stability
• Time delay

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the funding received from Indo French Center for the Promotion of Advanced Research (IFCPAR/CEFIPRA) for carrying out the project work.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Indo-French Centre for the Promotion of Advanced Research: [Grant Number GAP210312].

Notes on contributors

Sandip Jana

Sandip Jana Sandip Jana received his BTech degree in electrical engineering from Maulana Abul Kalam Azad University of Technology, West Bengal, India in 2015 and the MTech degree in power electronics and machine drives from National Institute of Technology, Durgapur, India in 2017. He visited as a research fellow Group of Electrical Engineering, CNRS-Centrale Supelec, UPSud et UPMC, Paris during January-February 2020 and engaged as a junior research fellow of a Indo French project (IFCPAR/CEFIPRA). Currently, he is working as a CSIR-senior research fellow at CSIR-CMERI and PhD research scholar at AcSIR, India. His current research interests include power electronics converters, application of power electronics converters in renewable energy systems, piezo electric actuator system, inchworm motor control and is an author of about 10 papers published in international publications. Email: [email protected]

Saikat Kumar Shome

Saikat Kumar Shome is working as a senior scientist in CSIR CMERI Durgapur, a national R&D institute under Ministry of Science and Technology, Govt of India for about last 10 years. He has done his BTech in computer science and engineering followed by MTech in mechatronics and PhD in engineering from AcSIR. He was selected amongst 10 students nationwide to persue masters as a scientist trainee from CSIR as a PGRPE scholar with a consistent academic record having secured above 90% marks in Class X, XII, BTech, MTech and PhD. He is also associated with Academy of Scientific and Innovative Research (AcSIR), as an asst professor. His research areas include IoT, cyber physical system, machine learning, embedded systems, WSN, etc. He has been involved in several national and international research projects as PI (Indo French, Indo UK) and Co-PI with about 35 international publications. Shome is the recipient of ITS fellowship from Govt of India, SERB, INSA and has guided several students of BTech, MTech and Integrated Dual Degree of AcSIR and IIEST, Shibpur and received several awards including Best Paper at IEEE Industrial Electronics Society (IEEE IECON), Vienna, Austria.

Arpita Mukherjee

Arpita Mukherjee is working in the area of electrical control in CSIR CMERI, Durgapur as a senior scientist. Her areas of interest include statistical signal processing, nonlinear control, electrical motors, etc. and she has published about 20 papers in reputed journals and conferences. Email: [email protected]