Exact Parameter Estimation using Relay Feedback Control

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 been considered for stable or unstable first order plus dead time (FOPDT) or second order plus dead time (SOPDT) plant transfer functions. The SOPDT process may also have a stable or an unstable zero. This paper reports on exact parameter estimation for the SOPDT plant transfer function with a zero, stable or unstable, by a single relay feedback test.