Subspace identification for commensurate fractional order systems using instrumental variables

This paper focuses on the identification of commensurate fractional order systems in time domain. A novel identification method is proposed to determine the coefficient matrixes and fractional differential order. The proposed method is based on principle component analysis (PCA) in subspace family, which has been successfully applied in identifying traditional integer order systems. Utilizing the cost function, the problem of estimating the fractional differential order is transformed into parameter optimization process. An instrumental variable (IV) is used to eliminate the bias of identification results. Numerical simulation validates the proposed method.