Optimum Actuator Grouping in Feedforward Active Control Applications
Smith, G. Clark II
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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.
- Masters Theses