Frequency-domain closed-loop identification of multivariable systems for feedback control

A frequency-domain identification method for multivariable systems is presented. The method emphasizes accurate identification of the process's gain directionality that is shown to be important for feedback control. The method requires closed-loop testing in addition to conventional open-loop testing, and combines open-loop and closed-loop data such that the derived model matches both the system's frequency-response matrix and its inverse accurately. The method is used to identify a model for a nonideal high-purity distillation column and is shown to capture the gain directionality of the process more accurately than the conventional method.