Feedforward control of acausal systems under broadband deterministic forcing

Abstract

We present some discrete-time perspectives on the active vibration control of a simple acausal system subjected to deterministic but broadband excitation. Here, exact vibration cancellation is not possible with bounded control forces. However, on penalizing high control forces using a weighting factor, we obtain a one parameter family of finite-time optimal feedforward (FTOF) controllers that substantially reduce vibration levels through bounded control forces. These controllers require knowledge of the future of the forcing, and are thus acausal. However, only a finite amount of the future needs to be known for practical purposes. These future values are predicted using a neural network. The FTOF controllers perform better than a direct application of the standard LMS algorithm. An LMS algorithm which uses several future values of the forcing performs better still. Some recommendations are made for practical applications