System identification using the feedback loop

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Identification of systems operating in closed loop has long been of prime interest in industrial applications. The fundamental problem with closed-loop data is the correlation between the unmeasurable noise and the input. This is the reason why several methods that work in open loop fail when applied to closed-loop data. The prediction error based approaches to the closed-loop system are divided to direct method and indirect method. Both of direct and indirect methods are known to be applied to the closed-loop data without critical modification. But the direct method induces the bias error in the experimental frequency response function and this bias error may deteriorates the parameter estimation performance