Comparative analysis of a traditional and a novel approach to Model Reference Adaptive Control

In this paper the operation of a recently introduced novel version of the popular “Model Reference Adaptive Controller (MRAC)” is compared with that of a simple version of its possible traditional implementations. The “traditional implementations” normally use Lyapunov's 2nd (“direct”) method for adaptive tuning of the controllers' parameters. This method yields global asymptotic stability but its application technically is difficult. In the current control papers pages are occupied with sophisticated estimations to guarantee the non-positive time-derivative of the Lyapunov function. The here proposed novel approach avoids the use of any Lyapunov function, it works with simple iterations that yield Cauchy sequences that converge to the solution of the control problem. Its advantages are its simplicity and precision, its weak side is the local basin of attraction of the convergence applied. However, simulations testify that for practical applications satisfactory “width” can be obtained for the region of convergence. In this paper a 3 Degree Of Freedom (DOF) paradigm, the cart+beam+hamper system is used in numerical simulations to demonstrate the advantages of the novel approach in comparison with a traditional MRAC controller. It is worth noting that the novel method can be completed with additional tuning for guaranteeing its convergence.