On selection of improved fractional model and control of different systems with experimental validation

Abstract

A major challenge in fractional order calculus applied to control systems is the selection of fractional values to satisfy the required set of dynamical characteristics pertaining to controllers or model. The research work of this paper is divided into three levels. The first level is centered around deriving an accurate fractional model corresponding to real systems using a novel algorithm. The second level is to select a dynamical system model from literature whose fractional model is already in existence and then apply the proposed algorithm to derive an accurate fractional model for improved system performance. The third level comprises of experimental validation of the proposed study. Two robotic manipulators are considered: serial flexible link robotic manipulator, and serial flexible joint robotic manipulator, both with two degrees of freedom. Their fractional equivalent model is derived using the proposed algorithm, and then a controller is designed for three different scenarios i.e fractional model and integer Controller, integer model and fractional controller, fractional model and fractional controller. The simulated results are compared with the experimentally examined results and it is found that the proposed fractional model of these robotic manipulators are highly accurate and more reliable. The examined results show significantly improved performance using the fractional controller and fractional model and this shows the strong evidence of reliability of the fractional model in control system design.