Modeling and Control of Robotic Manipulators: A Fractional Calculus Point of View

This paper deals with the fractional-order modeling, stability analysis and control of robotic manipulators, namely a single flexible link robotic manipulator (SFLRM) and 2DOF Serial Flexible Joint Robotic Manipulator (2DSFJ). The control law is derived using Pole Placement (PP) method. This paper uses Mittag–Leffler function for the analysis of SFLRM in the time domain. The stability analysis of the fractional model is carried in a transformed Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega }$$\end{document}-Domain, and from the analysis, it is observed that the response of the fractional model of SFLRM robotic manipulator is stable. The main motive behind this analysis is to understand the fractional behavior of robotic manipulators, and it is well known from literature that most of the real-world systems have their own fractional behavior. Furthermore, a real-time SFLRM and 2DSFJ setups are considered to validate the results obtained and it is found that the control law suggested by PP method improves the settling time of the robotic manipulators.