A technique for frequency response identification from relay feedback

In this paper, a new method for process frequency response identification is proposed, which can identify multiple points on a process frequency response from a single relay feedback test. The process output and input responses to the test are decomposed into the transient parts and the stationary cycle parts. These parts are then transformed to their frequency responses using the DFT and digital integration, respectively, to obtain the process frequency response. Real-time tests of the method on various processes give quite accurate process frequency responses, especially in the important frequency range from zero to the critical frequency. The testing conditions for our identification are the same as those for the step testing. The multiple points on process frequency response identified are very useful for process modeling and controller tuning. A real-time PID controller auto-tuning experiment which employs the proposed identification method is presented to demonstrate the applicability of our method.