Non-minimum Phase Secondary Path Research Articles

Hybrid vibration absorber with detached design for global vibration control

A new hybrid vibration absorber, with detached passive and active parts, is designed, analyzed and tested. This is an alternative approach in case the traditional bundled hybrid vibration absorber with collocated active and passive control elements cannot be applied. In fixed-free structures like buildings and towers, a passive dynamic vibration absorber is very popular for vibration control at or near the free ends. Active control may be introduced to improve performance, but space or weight may be limited in some applications. It may not be practical to attach an actuator near the passive part. The new approach provides more flexibility to retrofit a passive dynamic vibration absorber into a high performance hybrid vibration absorber by installing the actuator at a more suitable location than collocated with the passive part. The proposed hybrid vibration absorber is based on the pole-placement control strategy. Its controller is able to deal with a possible nonminimum-phase secondary path caused by noncollocated actuator sensors. This feature does not exist in a bundled hybrid vibration absorber with collocated actuator sensors. The performance of the new hybrid vibration absorber is analyzed in this study. Experimental and simulation results are used to verify the theoretical results and demonstrate the excellent performance of the new hybrid vibration absorber for vibration control at multiple points. A bundled hybrid vibration absorber with collocated passive and active elements is compared with the proposed hybrid vibration absorber with detached control elements, using experimental and simulation results. It was found that the vibration attenuation performance of the proposed hybrid vibration absorber can be better than the traditional bundled hybrid vibration absorber. The optimal actuator location, which is not necessarily the coupling point of the passive resonator, can be selected numerically by a proposed procedure. One could miss a better solution for vibration control if he/she only uses the bundled hybrid vibration absorber without considering the detached hybrid vibration absorber as a possible alternative.

An optimal repetitive control algorithm for periodic impulsive noise attenuation in a non-minimum phase ANC system

In this paper, active control of periodic impulsive noise based on an optimal repetitive control (RC) algorithm is studied. The characteristic equation of the closed-loop active noise control (ANC) system based on the RC algorithm is first obtained, and then the stability condition of the ANC system is derived. According to the stability condition, a novel optimal RC algorithm is developed for an ANC system with a non-minimum phase secondary path. Computer simulations have been carried out to suggest that the proposed algorithm is effective for attenuating periodic impulsive noise, and then the proposed algorithm has been implemented in a digital signal processor (DSP)-based experimental ANC system. Experimental results show that the proposed scheme has good performance for canceling periodic impulsive noise in a non-minimum phase ANC system.

Active control of repetitive impulsive noise in a non-minimum phase system using an optimal iterative learning control algorithm

In this paper, active control of repetitive impulsive noise is studied. An optimal iterative learning control (ILC) algorithm is developed for an active noise control (ANC) system with a non-minimum phase secondary path. A non-causal transversal finite impulse response (FIR) filter is used as the ILC learning filter, and the impulse response coefficients of the FIR filter are designed according to the asymptotically stable and monotonically convergent criterion in time domain. Computer simulations have been carried out to suggest that the proposed algorithm is effective for attenuating repetitive impulsive noise, and then the proposed algorithm has been implemented in an experimental ANC system. Experimental results show that the proposed scheme has good performance for repetitive impulsive noise attenuation in a non-minimum phase ANC system.

Active Transient Vibration Control Using a Novel Repetitive Algorithm

In this paper, active control of periodic transient vibration based on repetitive control (RC) algorithm is studied. According to the stability condition of an active vibration control (AVC) system, a novel non-causal stable inversion approach combined with an optimal criterion is used to design the RC controller for an AVC system with a non-minimum phase secondary path. Computer simulations have been carried out to validate the effectiveness of the proposed algorithm. The plant model used in the computer simulations is obtained from a practical AVC system in our laboratory. Simulation results show that the proposed scheme can significantly reduce periodic transient vibration and the convergence rate is acceptable for a non-minimum phase plant.

Application of Simultaneous Equations Method to ANC System with Non-minimum Phase Secondary Path

In this paper, we propose a method capable of shortening the distance from a noise detection microphone to a loudspeaker in active noise control system with non-minimum phase secondary path. The distance can be basically shortened by forming the noise control filter, which produces the secondary noise provided by the loudspeaker, with the cascade connection of a non-recursive filter and a recursive filter. The output of the recursive filter, however, diverges even when the secondary path includes only a minimum phase component. In this paper, we prevent the divergence by utilizing MINT (multi-input/output inverse theorem) method increasing the number of secondary paths than that of primary paths. MINT method, however, requires a large scale inverse matrix operation, which increases the processing cost. We hence propose a method reducing the processing cost. Actually, MINT method has only to be applied to the non-minimum phase components of the secondary paths. We hence extract the non-minimum phase components and then apply MINT method only to those. The order of the inverse matrix thereby decreases and the processing cost can be reduced. We finally show a simulation result demonstrating that the proposed method successfully works.