Automatic Determining of a Modulating Function

This article shows how modulating functions can be generated automatically and used to identify selected parameters of commensurable fractional systems. Existing methods use universal modulating functions. These have to be adjusted to each single problem. The proposed method uses a model based auxiliary system which is derived from the actual system, but has a fixed structure. The problem of applying a suitable modulating function is transformed into a control problem. Taking an additional precondition into account, each parameter can be separately identified. A study of the practical applicability and a numerical example complete the article.