Relationship between coupling and the controllability Grammian in co-design problems

Optimization of smart products requires optimizing the design of both the artifact and its controller. The existence of coupling between these problems currently cannot be established until they are solved. If coupling is expected to be present, then the problem is often solved as a simultaneous optimization. In this paper, it is shown that in several classical control problem formulations the presence of coupling can be established a priori by evaluating derivatives of the controllability Grammian. The concepts developed are demonstrated on a simple positioning gantry example.