In this paper we consider the p)roblem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems. We concentrate on a system wi)hl unbounded input and output operators governed by Burgers' equation. We use a linearized model to compute loworder-finite-dimensional control laws by minimizing certain energy functionals. We then apply these laws to the nonlinear model. Standard approaches to this p)roblem employ model/controller redurtion techniques in conjunction with LQG theory. The approach used here is based on the finite-dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.