Causality analysis of feedforward-controlled systems with broadband inputs

In recent years adaptive feedforward control algorithms have been successfully implemented to attenuate the response of systems under persistent disturbances such as single and multiple tones as well as random inputs. System causality is not an issue when the excitation is sinusoidal because of its deterministic nature. However, causality is a very important factor in broadband control. Though significant deterioration in the performance of noncausal control systems have been reported in the literature, analytical tools are virtually nonexistent to predict the behavior of broadband controllers. The main objective of this research is to develop an approach to investigate system causality. A formulation is presented to address the effectiveness of a control configuration as a function of the filter size, delay time, and dynamic properties of the structure. The technique is illustrated in a simple numerical example and the results are also corroborated experimentally.