Shape factor of relay response curves and its use in autotuning

Identification of process parameters using single relay feedback test is mostly used in practice. Limit cycle data along with shape factor of the response curves are important to identify the correct model structure and corresponding model parameters. Time domain analytical expressions are helpful in deriving conditions to estimate process parameters accurately. Second order plus dead time (SOPDT) processes are utilized to represent all different shapes with minimal number of model parameters. Provided with analytical expressions for relay feedback responses, identification algorithms are formulated and three different model structures are categorized. The autotuning procedure consists of the following steps. First, a relay feedback test is conducted and relay response is recorded for analysis. If the response is not symmetric we do a biased relay test to restore the symmetry, otherwise, we proceed for system identification. After finding out model structures and parameters suitable tuning rules are suggested for different ranges of dead time to time constant ratio (D/τ) and damping coefficient (ξ) values. Closed-loop performances of the identified systems with and without measurement noise are found to be satisfactory.