中文摘要：

与集中式有源控制系统相比，集群式系统具有实现成本低、扩展灵活的优点，因此其降噪性能的影响因素研究对工程应用有指导意义。首先对集群式系统进行建模，并用最小二乘法求解出最优次级源强度；然后推导得出集群式系统与集中式系统等效的充分条件；最后，分析了不满足等效条件时，自由空间中控制单元划分和布局方式对降噪性能的影响。结果表明，集群式系统与集中式系统等效的充分条件是：系统误差传感器数小于或等于次级源数，并且控制单元声阻抗矩阵与系统声阻抗矩阵都满秩。在不满足上述条件时，只要满足以下2个条件，集群式系统的性能损失很小：a）各控制单元内误差传感器数要不都大于等于次级源数，要不都小于等于次级源数；b）各控制单元子阻抗矩阵满秩。

英文摘要：

Comparing with the centralized active noise control system, a cluster system has the advantages of low implementation costs and flexible extensions, hence it is helpful to examine the influence factors of noise reduction performance of the cluster active system for engineering applications. Firstly, a theoretical model is established and the optimal strengths of secondary sources are obtained using the least square method. Then sufficient conditions related to equivalent performances of the cluster and centralized system are derived. Finally, the influence of unit partition and layout on noise reduction is analyzed when the equivalent condition cannot meet in a free space. The resuits demonstrate that when the number of the error sensors are less than or equal to that of secondary sources, and the acoustic impedance matrices of the control units and the system are both full rank, the cluster system is equiva- lent to the centralized system. When the equivalent condition isn＇t met, the performance of the cluster system de- grades small if for each unit both of the following conditions are satisfied ： a） the number of the error sensors should be greater than or equal to, or all smaller than or equal to the number of the secondary sources ; h） the sub-imped- ance matrices should be full rank.