Identification of transfer function models from the relay feedback test

A MIMO process is considered to be composed of several single-input-multi-output (SIMO) processes. In this article, a method for identifying such SIMO process is devised. To identify each SIMO process, a single run of relay feedback experiment on a particular input is required. For each of such experiments, models of FOPDT (First-Order-Plus-Dead-Time) or of SOPDT (Second-Order-Plus-Dead-Time) are identified. Estimation of the parameters is carried out one-by-one and does not involve least square minimization. Direct application of these SIMO identification to MIMO processes is thus illustrated. The accuracy of each estimated gain can be controlled within one single run of experiment. A sufficient condition for the experiments to ensure robustness of the resulting model is presented. Thus, this proposed method can be applied to some MIMO processes even they are ill-conditioned.