Optimal strictly positive real approximations for stable transfer functions

In this paper, we consider the problem of finding the optimal strictly positive real (SPR) approximation to a given stable transfer function. The transfer function is further assumed to be strictly proper and the SPR approximation is constrained to have the same pole structure. The optimization is carried out using the (weighted) H₂ -norm and the problem is reduced to a strictly convex quadratic programming problem with linear inequality constraints. At the heart of the method is a parameterization for all SPR compensators which possess a given denominator polynomial. Motivation for the problem stems from the robust stability provided by SPR compensation for passive plants such as flexible structures with colocated sensing and actuation. A numerical example is provided as well as the experimental implementation of an optimal approximation to the control of a single flexible link manipulator