### ASA 127th Meeting M.I.T. 1994 June 6-10

## 5aNS11. Adaptive feedforward modal space control.

**Robert L. Clark
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*Dept. of Mech. Eng. and Mater. Sci., Duke Univ., Durham, NC 27708-0300
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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.