### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 3pEA8. The use of neural networks for optimum actuator grouping in time
domain active control applications.

**G. Clark Smith
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Chris R. Fuller
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*Vib. and Acoust. Labs., Dept. of Mech. Eng., Virginia Polytechnic Inst.
and State Univ., Blacksburg, VA 24061-0238
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**Richard J. Silcox
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*NASA Langley Res. Ctr., Hampton, VA 23665-0001
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Previous work has demonstrated the benefit of grouping actuators to
decrease the number of degrees of freedom in an active control system. In this
work, a time-domain cost function was developed for on-line actuator grouping
and active structural acoustic control (ASAC) of a simply-supported beam
excited with a broadband disturbance. Actuators are considered grouped when
their compensators are equal. Therefore, the cost function presented here
incorporates a mean-square error term related to the structure-borne noise and
an additional nonquadratic term which penalizes the controller for differences
between respective compensator coefficients. The backpropagation neural network
algorithm provides the proper procedure to determine the minimum of this cost
function. The main disadvantage of using such a stochastic gradient technique
while searching the prescribed control surface is converging to local minima. A
resolution to this problem is discussed which incorporates using a variety of
initialization conditions. Two scenarios are considered here: grouping
actuators based upon weights determined by converging the filtered-x LMS
algorithm and simultaneously grouping and controlling with the compensator
weights started at zero. Computer simulations demonstrate the ability of this
new form of the cost function to simultaneously group actuators and control the
structure-borne noise with either initial conditions.