Obtaining the parameters for PID controllers based on limit cycle information from the process in a relay controlled feedback loop has become an accepted practical procedure. If the form of the plant transfer function is known, exact expressions for the limit cycle frequency and amplitude can be derived in terms of the plant parameters, so that their measurements, assumed error free, can be used to calculate the parameter values. In the literature to date the solutions have only been considered for odd symmetrical limit cycles which will not be the situation when constant disturbances exist. Use of these expressions will lead to errors when the limit cycle is not odd symmetrical. This paper reports on exact parameter estimation for stable and unstable FOPDT or SOPDT plant transfer functions from relay autotuning under static load disturbances where the limit cycles are asymmetrical.