A previous paper addressed the "PI + p" controller (a PI augmented with an additional, stable pole) and demonstrated its advantages over standard PIs, particularly if tuned with a combined model-relay-based method along the "contextual" approach proposed in another recent work. This manuscript extends the scenario to the PID + p structure, with obvious meaning, and applies the contextual approach to its autotuning. Benchmark tests and a quite realistic simulation example support the proposal. (C) 2012 Elsevier Ltd. All rights reserved.