Active control of noise and vibration has been previously demonstrated in finite and infinite systems undergoing single and multiple-frequency excitations. Control of broadband noise and vibration has also been reported, but it tends to be limited to infinite and semi-infinite systems. Here, four new adaptive feedforward control algorithms were developed for attenuating the response generated by finite structural systems. The algorithms are based on the filtered-X Least Mean Square (LMS) adaptive algorithm. A system identification of the plant control loop is required to implement this algorithm. An autoregressive moving-average (ARMA) model was used for the system identification since it provides the most computationally-efficient means of representing the frequency response function (FRF) of a lightly-damped structure. In the first control system, an adaptive finite impulse response (FIR) or nonrecursive filter was used as the compensator. A second control approach was realized by employing a recursive compensator. These two algorithms were modified using an equation error minimization technique to form two additional control systems, which eliminate certain stability requirements of the ARMA system identification. Each algorithm was simulated and then demonstrated experimentally.

Lastly, an analysis of control system causality was developed to determine the importance of this topic with regard to controlling finite structural systems. An exemplary parametric study of one of the four control systems presented, will demonstrate the analytical tool by examining the effects of system damping, compensator order, and a time delay in the control path, which is responsible for acausal control solutions. It was determined that control is always achievable, despite a delay in the control path, and also that control system performance can be improved by increasing the order of the control compensator. Both of these results were verified experimentally.