Pulse detonation engine is a kind of new engine for spacecraft, it is difficult to control for there is no moving parts in engine combustion chamber and detonation speed is very fast. The engine model was given based on thermodynamics equations in the paper. A multi-rate digital controller for a pulse detonation engine based on the engine model was also given. The simulation results show that the control method is effective. The detonation engine model provides a basis for developing and validating controllers capable of controlling the engine.