Conditions for Parameter Convergence of Model Reference Adaptive Control System using Power Spectrum Analysis

파워 스펙트럼 해석을 이용한 기준 모델 적응제어 시스템의 파라미터 수렴조건

Using Power Spectrum Analysis, conditions of parameter convergence for a Model Reference Adaptive Control (MRAC) system are described. The general Persistent Excitation (PE) condition given in time domain can be transformed to the positiveness of auto-correlation matrix which is represented in frequency domain by the spectra of reference input signal. For an MRAC system designed with relative degree one, the existence and the uniqueness of parameter nominal values due to the variation of input spectra can be analyzed by the PE condition in frequency domain. If the input signal has 2n spectra or more, it can be shown that the nominal values exist independent of adaptive gain, input amplitudes, and magnitudes or numbers of their spectra.