Tsai M., Huang C., Yeh C.

In this paper, a hybrid control architecture is proposed which integrates FX-LMS (Filtered-x Least Mean Square) adaptive feedforward control with FSCF-LQG (Frequency Shaping Cost Functionals Linear Quadratic Gaussian) feedback control into one design. The focus of this paper is to investigate the interaction of the FX-LMS and FSCF algorithms. Since one of the major disadvantages of the adaptive feedforward controllers is its poor transient response due to their long learning process. The shortcoming can be effectively corrected with the proposed hybrid control. The transient and steady state response are greatly improved by using the integrated control design. To analyze the hybrid control algorithm, theoretical analysis is developed. The optimal convergence coefficient for the adaptive feedforward control is discussed. It is found that the FSCF-LQG controller with the FX-LMS algorithm should be designed simultaneously to achieve better performance. Based on the derivation, the parameters of the FSCF-LQG controller with the FX-LMS algorithm are optimally tuned to achieve better transient response and convergence performance as compared to applying the FX-LMS alone. Furthermore, the effects of the phase errors of the estimated secondary plant for narrowband disturbance rejection are investigated. Finally, the hybrid control is applied to an active-passive isolation system. Root locus technique is applied to provide more physical interpretation of the proposed algorithm. Analytical results demonstrate that the proposed method can achieve better transient and steady state responses as compared to single feedforward or feedback design.