On Complement And Adjunct As Experiential Elements In The Cardiff Grammar

Fawcett (2010: 115n):

5. In contrast, the concepts of 'Complement' and "Adjunct' — but not 'Predicator' — have a central role in the Cardiff Grammar. Here, a Complement is an 'experiential' element of the clause that is 'predicted' by the Process (i.e., a Participant Role), while an Adjunct is one that is not (i.e., a Circumstantial Role) — or an element expressing a different type of meaning. 

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To be clear, the notion of 'Complement' and 'Adjunct' as experiential meanings is inconsistent with the notion of experiential meaning, since neither is a construal of experience as meaning.  Halliday & Matthiessen (1999: 511):

Ideationally, the grammar is a theory of human experience; it is our interpretation of all that goes on around us, and also inside ourselves. There are two parts to this: one the representation of the processes themselves, which we refer to as the "experiential"; the other the representation of the relations between one process and another, and it is this that we refer to as the "logical". The two together constitute the "ideational" metafunction, whereby language construes our experiential world.

Moreover, as such, neither is structurally related to a Process. Halliday & Matthiessen (2014: 451):

A multivariate structure is a configuration of different functional relationships … . Note that, although it is the functions that are labelled, the structure actually consists of the relationships among them.