Variable Fractional Order (VFO) PID Control for Precision Positioning

A Frequency Domain Approach

Master thesis (2019)

Authors

N.N. Nagda Mechanical Engineering

Contributors

J.W. van Wingerden Team Jan-Willem van Wingerden - Mechanical, Maritime and Materials Engineering (graduation committee member)
G. Giordano Team Tamas Keviczky - Mechanical, Maritime and Materials Engineering (mentor)
S. Hassan HosseinNia Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering (mentor)
N. Saikumar Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering (mentor)
Faculty
Mechanical Engineering, Mechanical Engineering
Copyright: © 2019 Neel Nagda
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Published Date

26-08-2019

Language

English

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Faculty

Mechanical Engineering

Abstract

Stringent control demands from the high-tech mechatronics industry have warranted the need to explore potentially advantageous non-linear controllers. Variable Fractional Order (VFO) calculus provides one such avenue to build non-linear PID-like controllers. VFO calculus is the generalization of integer order differentiation and integration, where, in addition to the possibility of orders being real or even complex, the orders can vary as a function of a variable like time, temperature, etc. However, in this nascent field of VFO control, the focus has mainly been on controller tuning by time domain optimization of the performance for certain specific trajectories or cost functions. On the other hand, Frequency domain tools allow for analysis and tuning of controllers for performance over a wide range of exogenous inputs. For smooth adoption into industry, it is important to develop a frequency domain framework for working with VFO control. Describing function (DF) analysis is a method to obtain an approximate Frequency Response Function (FRF)-like function for non-linear systems. In this thesis, DF analysis is used for developing VFO PID controllers in the frequency domain from an industry compatibility point of view and the closed loop performance of these controllers in controlling a precision positioning stage is examined.