Robust design of model reference adaptive control based on cost function on frequency domain

Recently it has been pointed out that, in the presence of unmodeled high frequency dynamics, the model reference adaptive control system (MRACS) frequently tends to become unstable. In this paper, two new schemes are introduced to recover the strictly positive realness (SPR) of the error system violated by the unmodeled dynamics and attain stable robust adaptive control laws. First, it is clarified that, by using the uncertainty crossover frequency ωu specified a prior from the unmodeled dynamics, a frequency domain approach for designing a frequency selective filter is presented to keep the SPR condition even in more than ωu. Secondly, by introducing an error feedback controller, we can further give much robustness of the SPR condition and improve the adaptive performance for modeling errors and disturbances without violating the model-matching condition. Numerical simulation results of the adaptive control of a dc motor having the two-inertia resonant system are given to examine the effectiveness of the proposed method.