Abstract: An important technique in design of controllers for fluid flow is that of compensator design. The use of compensators allows for measurement of the state at a small number of places in the fluid and estimation of the state based on those measurements. However, questions arise regarding what states to measure, what locations to place sensors and how to design low order (practical controllers). One approach to low order compensator design has been discussed in [J.A. Burns and B.B. King, "A Reduced Basis Approach to the Design of Low Order Feedback Controllers for Nonlinear Continuous Systems", Journal of Vibration and Control, 4(1998), pp. 297-323] and uses the spatial characteristic of feedback gains to design reduced order controllers. That work relies on approximating the gains for the infinite dimensional system by a small number of low order polynomials (constants or linear elements). As we show through numerical examples for the simply supported Euler Bernoulli beam, the spatial structure of the approximating feedback gains can depend on the inner product chosen for the Hilbert space. The reason for this is that the inner product shapes the Galerkin approximations and projections. Recently it was shown that stability behavior for approximations could be improved by using an inner product different than the standard energy inner product. In this paper we explore the effects of inner product choice on the structure of approximate feedback functional gains.