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A stability analysis of cluster active control system of sinusoidal sound in free space

Generally, the implementation of fully coupled multichannel active noise control system which has advantages in improving noise reduction and extending quiet zone requires considerable processing power. A practical method to decrease processing power is to decentralize the control; that is, implement many single input, single output independent controllers operating simultaneously instead of a large multiple input, multiple output system. However, the drawback of decentralized control is the risk of global instability. A new method was proposed for constructing an active noise control system to balance the complexity in multichannel systems and instability in the decentralized system. The proposed method consists of several independent multichannel sub-systems called cluster active control system, which is a modified version of the decentralized system and can improve stability at a reasonable computational cost. The purpose of this paper is to derive conditions under which globally stable control system behavior can be obtained in the case of cluster control for a sinusoidal disturbance. Hence, theoretical analysis and simulations are carried out to achieve the main objective which is to give practical conditions derived from the zero-pole map of the control system. These conditions only take into account the geometrical arrangement of the secondary sources and error sensors.