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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.