Process frequency response estimation from relay feedback

In this paper, a method for process frequency response identification is proposed, which can identify multiple points on process frequency response from a single relay feedback test. The process input and output transients resulting from a relay feedback cannot be directly converted to the frequency domain to obtain a process frequency response using FFT. A decay exponential is then proposed to modify the process input and output, so that the process frequency response can be identified with the help of FFT. Real-time testing of the method on various processes gives quite accurate process frequency responses, especially in the frequency range [0,ω(c)], which is important for control design and process modelling. The method inherits and extends the advantages of the original relay auto-tuning technique. It can be easily applied to PID auto-tuning and to transfer function modelling.