Robert L. Clark
Dept. of Mech. Eng. and Mater. Sci., Duke Univ., Durham, NC 27708-0300
An alternative method of implementing adaptive feedforward control is presented in this work based upon independent modal space control of reverberant systems. Multivariable control theory is used to derive the optimal feedforward compensators, and when the error sensors are constructed in modal coordinates, the optimal compensators reduce to a single coefficient filter per control channel (assuming the reference signal is available). If the control inputs are also implemented in modal coordinates, then the control system is termed noninteracting since each mode is orthogonal to the other. Adaptive feedforward modal space control is ideal for implementation of time-averaged gradient descent algorithms such as Newton's method since the optimal filter coefficient is obtained from a single iteration of the algorithm, and is insensitive to changes in the resonant characteristics of the reverberant system. Formulating the control system in modal coordinates also clearly illustrates the effects of causality and nonminimum phase characteristics on the ultimate performance of any adaptive control system, whether it is implemented in physical coordinates or modal coordinates.