Fractional-order PID Plus Derivative Controllers for Speed Control of Serving Robot

PID controllers have long been the cornerstone of industrial automation and robotics due to their simplicity and effectiveness. However, the primary challenge in using PID control for the speed of serving robots is its inefficiency in dynamic environments. Therefore, this paper proposes an extended version of PID in both traditional and fractional forms, augmented with higher-order derivative terms, for enhanced speed control. The extended controllers will be incorporating second and third derivative actions (PIDD<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>, PIDD<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>D<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>) and their fractional counterparts $\left({P{I^\lambda }{D^\mu },P{I^\lambda }{D^\mu }{D^{{\mu _2}}},P{I^\lambda }{D^\mu }{D^{{\mu _2}}}{D^{{\mu _3}}}}\right)$,. The proposed controllers are designed for a one-wheel serving robot using a simplified transfer function model. The performance analysis under fixed and variable set-points, as well as disturbance rejection, demonstrates that the $P{I^\lambda }{D^\mu }{D^{{\mu _2}}}{D^{{\mu _3}}}$ controller achieves the best time-domain metrics, including minimal rise time (0.1225 s), reduced overshoot (20.8%), and improved stability. Results confirm that integrating fractional orders with higher-order derivatives significantly enhances control robustness and responsiveness compared to traditional PID designs.