Parameter estimation from relay autotuning with asymmetric limit cycle data

Obtaining the parameters for PID controllers based on limit cycle informati on for the process in a relay controlled feedback loop has become an accept ed practical procedure. Often the only information used is the frequency an d amplitude of the limit cycle, which then using the describing function an alysis provides estimates for the ultimate gain and frequency of the proces s. Alternatively, limit cycle measurements may be used to estimate the para meters of an assumed transfer function, usually again using describing func tion analysis. Both these methods can work well but may lead to problems in cases where the describing function analysis is inaccurate. In this paper. it is shown how the parameters of first and second order plant transfer fu nctions. stable or unstable, with time delay can be found exactly, assuming no measurement errors, from measurements of the parameters of a single asy mmetrical limit cycle in a relay controlled feedback loop. Examples are giv en to compare the approach with results using the describing function metho d and also to show how good controller design based on a first or second or der time delay model can be achieved for plants of higher order. (C) 2001 E lsevier Science Ltd. All rights reserved.