From PID to PIDD2α: Performance improvement with a fractional double derivative action

This paper analyzes the performance achievable by means of PIDD${}^{2\alpha }$ controllers, that is, PID controllers with an additional fractional double derivative action. In particular, the performance obtained with an optimized tuning of the parameters is compared with those of standard PID controllers, of fractional-order PID (FOPID) controllers and of Proportional–Integral–Double-Derivative (PIDD or PIDD${}^2$) controllers. In all the cases the parameters are determined by minimizing the integrated absolute error either in the set-point or load disturbance step response, with a constraint on the maximum sensitivity. A wide set of benchmark processes (both self and non self-regulating) are considered so that general conclusions about the impact that these controllers can have in the process industry can be drawn.