The trick in any kind of feedback circuit such as this, is to prevent positive feedback and instability (the classic public address system squeal). The feedback phase will vary with frequency depending upon the size of the chamber, thus compensation could be rather complex. You would probably need to plot the gain and phase of the microphone output to speaker input versus frequency to determine the characteristics required of the compensation network to provide a stable feedback loop.
But as Mike asked, where are you getting harmonics? They are likely just from simple speaker distortion. Are you trying to generate high levels of sound?