Replacement of Lyapunov's direct method in Model Reference Adaptive Control with Robust Fixed Point Transformations

Abstract

The “Model Reference Adaptive Control (MRAC)” is a popular and efficient controller that normally is designed by the use of Lyapunov's 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> (“direct”) method guaranteeing global asymptotic stability. However, the use of Lyapunov function can entail a relatively complicated tuning that may have disadvantages whenever very fast applications are needed. In this paper an alternative background, the application of “Robust Fixed Point Transformations (RFPT)” working with local basin of attraction of convergence is recommended to simplify this task. As a potential application example the adaptive control of an “Electrostatic Micro-actuator (EμA)” is considered that contains considerable non-linearities. The conclusions of the paper are substantiated by simulation results.