### Novel Tuning Expressions for Fractional Order ([PD]^beta and [PI]^alpha) Controllers Using a Generalized Plant Structure

#### Abstract

The available tuning expressions in the literature for three-parameter-fractional-controllers such as [PD]^beta and [PI]^alpha are specific to the given class of plant transfer function. If one intends to design such controllers for a new plant, then the tuning expressions meeting required specifications need to be derived accordingly. This is a tedious and work intensive process. To overcome such difficulty, this paper presents novel tuning expressions of [PD]^beta and [PI]^alpha controllers which are readily usable for any class of integer or fractional order LTI plant. Such unification is accomplished by defining a generalized plant structure. The usefulness of these expressions is demonstrated by considering several integer and fractional order plant examples. The results confirm correctness of proposed framework.

#### Keywords

fractional order controller; generalized plant structure; [PD]^beta; [PI]^alpha; Oustaloup approximation