Experiments to obtain input/output data for system identification of some systems can be conducted only with the controllers in action. Estimating an open-loop system model using closed-loop data offers many difficulties, particularly when noise is present in the measurements. In this paper, a new indirect non-linear system identification technique using a non-linear auto regressive moving average with exogenous input (NARMAX) structure and employing input/output data obtained from closed-loop experiments is described for the first time. Furthermore, a new method to estimate the linear multivariable open-loop transfer function from closed-loop data using an algebraic equation set is presented. The effectiveness of the proposed linear and non-linear identification approaches is illustrated by simulation studies on a non-linear physical system.
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