Optimization of control source configuration in active control systems using gram-schmidt orthogonalization

In active control systems, the configuration of the control sources greatly affects the performance. In this paper, a method for optimizing the number and location of control sources is proposed. As a criterion for the optimization, the linear independence of the transfer impedance vector is employed. A physical interpretation of the linear independence of the transfer impedance vector is the independent contribution of each control source that is not substitutable by the other sources. In the optimization process, control sources are determined one by one using Gram-Schmidt orthogonalization so that the corresponding transfer impedance vectors are the most linearly independent. The results of the simulation show the optimized configuration to have small control error. Moreover, for the optimized configuration, the transfer impedance matrix exhibits a small condition number, which results in robustness of the system in the face of changes in the environment.