Obtaining the parameters for PID controllers based on limit cycle information for 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 so that their measurements, assumed error free, can be used to calculate the true parameter value. In the literature, parameter estimation for an assumed form of the plant transfer function has generally been considered for disturbance free cases, except a recently published work of the author. In this paper additional simulation results are reported on exact parameter estimation from relay autotuning under static load disturbances.