A novel two-stage identification of unstable systems

Identification of Linearized Models and Robust Control of Physical Systems

“…Then, in the second stage, lowerorder models are derived from the estimated high-order model using a frequency-weighted estimation scheme. To handle the model order selection, and the identification of the plant, especially an unstable one, approaches proposed in and (Shahab and Doraiswami, 2009) are employed respectively.…”

“…However, the derivation of the plant transfer function from the closedloop transfer function may itself be prone to errors due to inaccuracies in the model of the subsystem connected in cascade with the plant. The two-stage approach, itself a form of an indirect method, is based on first identifying the sensitivity and the complementary sensitivity functions using a subspace Multi-Input, Multi-Output (MIMO) identification scheme (Shahab & Doraiswami, 2009). In the second stage, the plant transfer function is obtained from the estimates of the plant input and output generated by the first stage.…”

“…Crucial issues in the identification of physical systems include the unknown order of the model, the partially or totally unknown statistics of the noise and disturbances affecting data, and the fact that the plant is operating in a closed-loop configuration. To tackle these issues, a number of schemes designed to (a) attenuate the effect of unknown noise and disturbances (Doraiswami, 2005), (b) reliably select the model order of the identified system and (c) identify a plant operating in a closed-loop (Shahab and Doraiswami, 2009) have been developed and are presented here for completeness. The model uncertainty associated with the identified model is itself modeled as additive perturbations in both the plant numerator and the denominator polynomials so as to develop robust controllers using the mixed-sensitivity H ∞ controller design procedure (Kwakernaak, 1993).…”