Fast adaptation model reference adaptive control

Abstract

Since adaptive controller does not rely fully on dynamic system models, therefore, there exist a necessity of fast adaptation to achieve improved tracking performance using high adaptive gain. However, attaining fast adaptation using high adaptive gain is a serious limitation of adaptive controllers which may raise certain serious issues. First, it causes large frequency excursions and bursting in the control signal. Second, the differential equation of adaptive law becomes stiff and causes numerical instability. Third, it makes the adaptive system less robust towards uncertainties and unmodelled dynamics. To address these issues of fast adaptation, a new adaptive law based on non-quadratic Lyapunov function is proposed in this paper. A modified form of the proposed adaptive law is also suggested for performance improvement. Through simulation studies, it has been demonstrated that for high adaptive gain, differential equation of the proposed adaptive law does not become stiff. Computational time and number of iterations required to solve the differential equation reducedto a great extent. The control signal is also in the low-frequency range. The Effectiveness of the proposed controller is demonstrated using simulations of a numerical example.