Three stage procedure for closed loop identification

Identification in closed loop is demanded for open loop unstable plants and may give in general more suitable models for control design [Sch92]. To obtain a parametric model description the closed loop data is used by a standard open loop estimation algorithm. This may lead to a mismatch because the noise acting at the output corrupts the plant input too. A reconstruction of the noise free plant input was proposed by [VSdB95], Our proposed algorithm uses an additional step to reconstruct an undisturbed plant output. In a first step a transfer function estimation (alpha-sensitivity) is used to construct the noise free plant input by help of the reference sequence. In a second step an additional transfer function (gamma-sensitivity) is estimated to reconstruct the noise free plant output. A third step uses standard open loop techniques to estimates the model parameters. It is shown by an elaborate simulation example that this procedure provides more accurate results.