This paper proposes a frequency transfer function synthesis of a later compensated PID controller for an approximated low order model. The proposed method identifies the parameter vector of PID controller from a linear system that is formed by rearranging a loop frequency transfer function synthesis including the filter compensated PID controller obtained from the given frequency response bounds. And an example for the turbine speed control system of Chungju hydropower plant is given to illustrate the feasibilities of suggested schemes.