Positivity embedding for noncolocated and nonsquare flexible systems

摘要

Positivity based control design for flexible structures provides closed-loop stability regardless of parameter variations and unmodeled dynamics. The present framework requires the plant to be square and the actuators colocated with rate sensors. These constraints severely limit achievable performance in control systems using the positivity approach. In this paper, a dynamic embedding is derived to render a nonsquare plant with noncolocated actuators and sensors positive real. The dynamic embedding is parametrized for general flexible structures. A numerical algorithm is developed to compute the embedding parameters. The Draper tetrahedral truss structure is used to demonstrate the design of dynamic embeddings. Relaxing the colocation constraint in a positivity based design significantly improves the closed-loop performance.