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ABSTRACT. This paper is a report of work in progress, part of the Caltech MURI Program: Novel Energetic Materials to Stabilize Rocket Motors. The primary technical objective of the MURI Program is to understand the connections between propellant composition and chemistry, and the dynamical behavior observed in solid propellant rocket motors. Here we are concerned with the theoretical framework in which chamber dynamics are investigated; and certain aspects of combustion dynamics represented by the response function which is ultimately the macroscopic realization of the propellant chemistry and combustion. Some results are given to illustrate possible influences of the frequency spectrum of the response function on linear and nonlinear motions in a solid rocket. A simple model is described which is extended eventually to provide a way to model phenomenologically some of the observed characteristics of the combustion dynamics of a burning solid propellant.

Active control of longitudinal pressure oscillations in a combustion chamber is studied theoretically by means of a low order model obtained by systematic reduction from a complete representation. The formulation is based on the derivation of a generalized wave equation that accommodates the effects of mean flow, combustion, noise and control action. By using spatial averaging, the equations describing the dynamics of the chamber are reduced to a set of coupled ordinary differential equations, representing the motions of a system of coupled oscillators. The form of the resulting equations is particularly convenient for model reduction and for introducing feedback control terms, while retaining all physical processes.The oscillator equations are then rewritten in state-space form. Simulations are carried out to investigate in a unified fashion various aspects of the problem. These include the influences of noise, parameter uncertainties, unmodeled modes and a single timedelay.A criterion is derived that guarantees stability of the controlled closed-loop system in the presence of those quantities. The particular controller used here is based on a standard LQR design, but any design technique can be used as long as the stability criterion is fulfilled.