Study on the relationships between two typical modeling methods in process control

There are two typical modeling methods for PID design and tuning in process control: step response method and self-oscillation method. The former usually results in a first-order plus dead-time model and the later gives ultimate gain and ultimate frequency of controlled plant. Usually the two modeling methods are considered different. The aim of this paper is to bridge the gap between them. In this paper, some internal relationships between the two modeling methods are studied. Analytical mapping expressions between them are derived with time domain and frequency domain analysis method, respectively. This implies that PID design and tuning techniques need not be limited to either step response method or the self-oscillation method only. Thus, the designer can have more choices for PID controller design and tuning.