Fractional-Order $\hbox{PI}^{\lambda}\hbox{D}^{\mu}$ and Active Disturbance Rejection Control of Nonlinear Two-Mass Drive System

Abstract

This study presents the application of a fractional-order PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</sup> and an active disturbance rejection (ADR) controller to a nonlinear two-mass system. A complete state-space mathematical model for a nonlinear two-mass system is first developed. Then, a fractional-order PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</sup> controller and an ADR controller are both designed to regulate the speed of the system. Design procedures for both controllers are given in detail. Finally, corresponding results are compared. The extended state observer in the ADR controller is tested for torsional torque and the load machine speed with open-loop and closed-loop control structures. Performance analysis for both of the proposed controllers is confirmed by experimental results. Obtained results are also compared with the results given in the literature for the same system.