Positivity embedding for noncolocated and nonsquare flexible structures

Positivity based control design for flexible structures provides closed-loop stability regardless of parametric variations and unmodeled dynamics. The usual requirement of square plants with rate sensors colocated with actuators for positive realness severely limits the achievable performance. In this paper, we show that these limitations can be eliminated by embedding the plant dynamically and invoking the positivity theorem. Significant performance improvement in the closed-loop system can be gained without sacrificing the unconditional robustness guaranteed by positivity. Furthermore, the problem of preserving positive realness under plant perturbation is also addressed and is shown to be equivalent to a stability robustness problem. An example using the Draper tetrahedral truss structure is used to demonstrate the effectiveness of dynamic embeddings.