In this paper, the authors discuss a reduced basis approach to the development of low-order nonlinear feedback controllers for hybrid distributed parameter systems. This approach involves the use of distributed parameter control theory to design "optimal" infinite dimensional feedback control laws and approximation theory to design and compute low-order finite dimensional compensators. The resulting finite dimensional controller combines a nonlinear observer with a linear feedback law to produce a practical design. The authors concentrate on a weakly nonlinear distributed parameter system to illustrate the ideas.