This paper considers a design method for PID controllers to achieve the robustness to the uncertainty
of the time delay for the first-order plus time delay system (FOPTD). Initially, the stabilizing regions
of the PID controller gains are determined by a graphical stability method. Then, we specify two
simultaneous design specifications: gain margin and phase crossover frequency. These specifications
give a set of stabilizing PID controllers. To get a unique PID controller, we introduce an additional
constraint which is finding the smallest absolute value of the slope of the open-loop system
magnitude at the specified phase crossover frequency. The obtained PID controller is located in the
stability region, and also robust to system time delay variation due to the proposed constraint.