A backstepping controller for a nonlinear partial differential equation model of compression system instabilities

We prove the existence and uniqueness of solutions in Sobolev spaces for the Moore-Greitzer nonlinear partial differential equation model for compression system instabilities with mild conditions on the shape of the compressor characteristic and on the throttle control. To achieve this, the model is reformulated as an evolution equation on a Banach space. Using this new representation, we design a backstepping control of the model. Global stabilization of any axisymmetric equilibrium to the right of the peak of the compressor characteristic is achieved. We also study finite dimensional Galerkin projections of the partial differential equation. We show that truncated control laws stabilize truncated models.