Limitations of FxLMS in Feedforward Active Vibration Control of a Nonlinear Two-Degree-of-Freedom System

Active control systems are often used to surmount the challenges associated with passive noise and vibration control measures to control low frequency disturbances, since they achieve control without the application of large or heavy control treatments. Historically, linear active control strategies have been used in feedforward control systems to drive the control source to minimise the signal measured at the error sensor. Amongst the various control algorithms available, the Filtered-reference Least Mean Squares (FxLMS) algorithm has become extremely popular in the last few decades due to its relatively good performance and high level of robustness, as well as simplicity in both design and application. However, when the system under control contains nonlinearities, either in the primary or secondary paths, the performance of the FxLMS algorithm can degrade dramatically. This paper explores the performance limitations of the FxLMS algorithm when applied to the control of a two degree of freedom mass-spring-damper system with linear and cubic nonlinear stiffness terms. The aim of this study is to improve understanding of and inspire better design of nonlinear control systems. The statistical uncertainty present in the linear plant model and control filter is discussed, as well as the effect of this on control performance and control effort. The effect of nonlinearity on the maximum convergence parameter of the algorithm is also discussed.