Explicit model-based real PID tuning for efficient load disturbance rejection

In the process control, many PID loops are primarily devoted to rejecting load disturbances, and some of them are crucial for the quality of the overall plant operation. In such a scenario, automatic tuning is highly desired. However, load disturbance rejection calls for strong feedback up to quite high frequencies with respect to the dominant plant dynamics, on which most tuning rules are centered. As such it is difficult for a rule to yield good and, above all, uniform results in the face of all the various process structures it can be confronted with. In this paper, we propose an explicit model-based PID tuning rule specifically targeted at the problem just evidenced. The rule minimizes the magnitude of the nominal disturbance-to-output frequency response, at the same time preventing that magnitude to exhibit a peak or a plateau around its maximum. This characteristic, together with tuning the PID derivative filter, leads to sharp disturbance rejection without incurring in an excessive control sensitivity to high-frequency measurement noise and mitigates the problems caused by heterogeneous process dynamics. The proposed approach is assessed by comparing the rule with selected counterparts, on a literature benchmark with different process structures. A laboratory experiment is finally presented to show that our rule can withstand real-world operating conditions.