The Ziegler-Nichols process dynamics characterization is based on the estimation of the ultimate gain k(u) and ultimate frequency omega(u). The angle phi of the tangent to the Nyquist curve at the frequency omega(u) is introduced, as an additional parameter in the frequency domain. The essential dynamic characteristics of the process can be captured by using the tangent rule, proposed here as an extension of the Ziegler-Nichols approach. The validity of the tangent rule is confirmed by using the PID controller optimization on a test batch consisting of stable, integrating and unstable processes, including dead-time. Parameters k(u), omega(u) and phi can be determined from the sustained oscillations. using the phase-locked loop identifier module. (C) 2009 Elsevier Ltd. All rights reserved.