IntroductionThe proportional–integral–derivative controller is widely usedin chemical process due to its simple structure. A recent surveyshows that the ratio of applications of PID control, conven-tional advanced control, and model predictive control is about100:10:1 (Shamsuzzoha, 2013). Conventional PID control coulddisplay a good effect in invariant time linear systems with-out time delays. However, time delay is common in most ofthe chemical process due to recycle loops and transportationdelays. It is difficult for traditional PID controller to guaranteethe stability of time delay processes. Furthermore, it’s moredifficult to design the PID controller for a process with timedelay, which is open-loop unstable. Because of this, the tuningof PID controller is needed. But it is difficult to tune PID param-eters properly in industrial processes.It is an important research issue that to design a simple PIDcontroller for process engineers. The direct synthesis method(Chen and Seborg, 2002; Lee et al., 1998) and the IMC-PID∗