Shape factor for the relay feedback autotuning

ABSTRACT Relay in the feedback loop produces a stable oscillation whose cyclic steady state response contains process information of ultimate gain and ultimate period. By measuring these process data and Ziegler-Nichols type tuning rules, PID controllers can be designed. Due to its simplicity and performances, this earlier relay feedback method becomes one of the standard methods for autotuning of PID controllers. Later the first-order plus time delay (FOPTD) models are used for the relay feedback method with additional process data such as the process steady-state gain, improving autotuning performances. Like other FOPTD model-based methods, this FOPTD model-based relay feedback method is very popular in the field. However, for some high-order processes, the FOPTD model-based method shows oscillatory closed-loop responses that are not acceptable. For such processes, the critically damped second-order plus time delay (C2PTD) identifiable with the same three process information of steady state gain, ultimate gain and ultimate period can be used. Unfortunately, the C2PTD model-based relay feedback method cannot cover the whole range of processes. One solution is the selective use of FOPTD and C2PTD models. For this purpose of selection, a shape factor that uses the process measurement of average residence time is proposed here. GRAPHICAL ABSTRACT