This paper describes tuning PID controllers for a plant approximated by a first-order lag plus deadtime system using optimization. Graphs by which the optimal PID parameters can be obtained are presented as functions of a normalized deadtime and a perturbation of plant characteristics caused by changes in dynamics. To evaluate the control performance, the disturbance suppression and the reference tracking properties are presented compared to those by the partial model matching method designed for the same plant. It is found that the effectiveness of the proposed tuning method is shown by simulations.