Root locus analysis of Dahlin controller

The root locus has been studied in detail in case the closed loop time constant of the Dahlin controller is varying. Based on the analysis and obtained properties of the root locus, the following factor can be qualitatively explained that if the closed loop time constant is decreased, the robustness becomes worse. Also if there is a plant-model mismatch, the smaller closed loop time constant results in ringing. The position of the ringing pole located on the negative real axis can be estimated too. One of the ways for eliminating ringing in Dahlin control system is to increase the closed loop time constant.