Improvement of the Control System Performance based on Fractional-Order PID Controllers and Models with Robustness Considerations

In this paper we assess the performance improvement achievable by using one degree-of-freedom fractional-order proportional-integral-derivative controllers (FOPI/FOPID) instead of their integer-order counterparts (PI/PID). To this end, we take into account a single-pole fractional-order model, which has the advantage of representing a wide variety of process dynamics, ranging from over-damped (first-order models) to under-damped behaviors, depending on the fractional order α. In the proposed analysis we consider a combined performance index which deals with the trade-off between servo and regulatory control modes. Moreover, the performance of the closed-loop system is optimized subject to a robustness constraint, expressed as a target maximum sensitivity of either 1.4 or 2.0. The obtained performance assessment results are shown for different values of the fractional order α of the model and for different normalized dead times, thus quantitatively evaluating the benefits achievable with fractional controllers on a wide variety of process dynamics