Geometrical design of fractional PD ^μ controllers for linear time-invariant fractional-order systems with time delay

This article presents a simple procedure that allows a practical design of fractional –PD ^μ controllers for single-input single-output linear time-invariant fractional-order systems subject to a constant time delay. The methodology is based on a geometric approach, which provides practical guidelines to design stabilizing and non-fragile PD ^μ controllers. The simplicity of the proposed approach is illustrated by considering several numerical examples encountered in the control literature. Moreover, with the aim of showing the performance of the PD ^μ over a classical PD controller, both controllers were implemented at the end of the article in an experimental test-bench consisting a teleoperated robotic system.