A direct model reference adaptive control for SISO linear time invariant systems with Super-Twisting-like terms

Recently, the authors have proposed [2] a new Direct MRAC (Model Reference Adaptive Control) for SISO, relative degree 1, LTI systems, which has finite-time tracking and parameter convergence. These properties are obtained by adding some strong, i.e. non locally Lipschitz or discontinuous, nonlinearities to the controller and parameter estimation algorithm of the classical MRAC. The Reference Model (RM) in [2] has been restricted to a SPR transfer function with no zeroes. The objective of this paper is to show that the same algorithm used in [2] is valid for any RM, having an SPR transfer function with relative degree one. However, the zero dynamics of the RM precludes the finite time convergence, but the proposed algorithm still converges faster than the classical one. A Lyapunov-based approach is used to prove these properties. Some simulations illustrate how the proposed algorithm provides the MRAC with a much better convergence than the classical algorithm, even in the presence of noise, for RMs with zero dynamics.