Title page for ETD etd-23198-182545

Type of Document Master's Thesis
Author Smith, G. Clark II
Author's Email Address gcs@duke.edu
URN etd-23198-182545
Title Optimum Actuator Grouping in Feedforward Active Control Applications
Degree Master of Science
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Fuller, Christopher R. Committee Chair
Burdisso, Ricardo A. Committee Member
Silcox, Richard J. Committee Member
  • Active Structural Acoustic Control
  • Actuator Grouping
  • Neural Networks
Date of Defense 1994-10-06
Availability unrestricted
Previous work has demonstrated the benefit of grouping

actuators to increase the controllability of an active

control system, without increasing the number of control

channels. By driving two or more secondary sources with

the same control input, one is also able to reduce the

hardware cost and complexity. In this work, a time domain

cost function is developed for on-line actuator grouping

and active structural acoustic control (ASAC) of a

simply-supported beam excited with a broadband disturbance.

Three PZT actuators are mounted on the beam structure to

control the wavenumber components corresponding to five

radiation angles. The propagation angles are selected to

represent the total radiated sound power. The point force

disturbance is bandlimited random noise which encompasses

the first three modes of beam vibration. Actuators are

considered grouped when their compensators are equal.

Therefore, the cost function presented here incorporates

an additional non-quadratic term which penalizes the

controller for differences between the feedforward

compensator coefficients. The backpropagation neural

network algorithm provides the proper procedure to

determine the minimum of this cost function.

The main disadvantage of using a stochastic gradient

technique, while searching the prescribed control surface,

is convergence to local minima. In this thesis, a

resolution to this problem is suggested which incorporates

using a variety of initial conditions. Two initialization

conditions are considered: grouping actuators based upon

weights determined by converging the filtered-x LMS

algorithm and simultaneously grouping and controlling with

the compensator weights initialized to small arbitrary

numbers. Test cases of heavy and light grouping parameters

were evaluated from both initial conditions. The computer

simulations demonstrate the ability of this new form of the

cost function to group actuators and control the error

response with either initial condition. The heavy grouping

cases achieved the same one channel control system from

both initial conditions. The performance of the one channel

solution was 1.5 dB lower than the performance of the

ungrouped filtered-x LMS solution. The ability to select

the different levels of grouping was demonstrated when

the algorithm was initialized with the filtered-x LMS

weights and run with light grouping parameters. For this

case, the on-line algorithm grouped two actuators, but

allowed the third actuator to exist independently. The

performance of the two channel control system was only

0.6 dB less than the performance of the filtered-x LMS

solution. In all grouping cases investigated, the

convergence times of the grouping algorithm were within

the same order as for the filtered-x LMS algorithm.

The effect of uncorrelated error sensor noise on the

actuator groupings is also briefly discussed.

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