“…The fractional DD-PID is compared with the standard DD-PID in a scenario, where the position reference is a sinus of amplitude equal to 1 rad and frequency of 1 Hz, and a varying load τ l is applied to the flexible link (a sinusoidal of 1 Nm and 15Hz, see Villagra and Balaguer (2011) for more details) Figure 4 shows the response of the closed loop system to the sinusoidal excitation with 4 different configurations: the best PID, the best DD-PID (n = 1), the best fractional DD-PID and the best configuration (K P , K I , K D , α) for two controllers with fixed fractional derivative order (n = 0.7 and n = 1.2). Note that the optimal configuration in each case is obtained by minimizing the Integral Absolute Error (IAE) via a sequential combination of two nonlinear optimizers: Sequential Quadratic Programming and Nelder Mead.…”