This paper presents work towards a formal framework to support model-based integrated design and optimization of mechatronic products for early-phase conceptual design. This paper describes an integrated design framework through the introduction of its software implementation and a specific use case. The contribution is to introduce mathematical formalism to define the concepts, semantics, computation rules and system architectures of the formal framework. The advantage of the formal definitions is to clearly expose functionality and the limitations of the design framework and facilitate the software implementation. The modelling capability of the framework is enhanced to include non-linear mechatronic components, such as a two degrees-of-freedom arm. Further, an optimal proportional-integral-derivative control component is added to the software library supporting the framework.