The paper introduces the A-locus method which is an exact method for limit cycle investigation in relay controlled loops for parameter estimation for stable FOPDT and SOPDT transfer functions. The method has also been extended to unstable FOPDT and SOPDT transfer functions since it is possible to have unstable plant models for some chemical processes. The method gives two advantages. First, the steady-state gain can be calculated from the relay feedback test. Secondly, all parameters of a SOPDT transfer function can be obtained, using only one relay test. The obtained parameters are exact if there are no measurement errors or disturbances.