Effectivity of Using Model Reference Adaptive System in the Field of Complex Numbers for Parameter Identification

Abstract

The model reference adaptive system (MRAS) is generally described in the field of real numbers. Therefore, the MRAS cannot be directly applicable to the system described by complex numbers such as three-phase ac motors.
In order to apply the MRAS to the discrete-time linear time-invariant system whose coefficients and variables are complex numbers, the authors expand the theory of the MRAS into the field of complex numbers. The hyperstability theory in the field of complex numbers is used to give the asymptotic stability of the suggested algorithm.
The effectiveness of the suggested algorithm is proved by simulation results for the parameter identification. The results show that the convergence time of the parameters using the proposed method can be reduced to one tenth compared with that using the MRAS in the field of real numbers.