A two rule based fuzzy controller applied to the regulation problem of a class of euler-lagrange systems

In this paper we deal with the regulation problem of a class of two degrees of freedom plants described by the Euler-Lagrange equations (E-L systems) [10] using the basic version of the proportional derivative two rule-based fuzzy controller (PD 2RFC)[5] with no assumptions on the parameter r. We use the Lyapunov approach based on the PD 2RFC local property of being a bound sector function with respect to the auxiliary variable σ := k₁e_c + k₂e_c in order to derive the conditions under which the closed loop system attains the asymptotic stability in a broad but finite region where the boundedness condition holds. We illustrate our approach via some simulation results obtained with the rotational/translational proof mass actuator(RTAC) non linear benchmark[11].