Novel approach in the adaptive control of systems having strongly nonlinear coupling between their unmodeled internal degrees of freedom

The application of a novel branch of computational cybernetics is extended to the adaptive control of very inaccurately and partly modeled electromechanical systems also having unmodeled non-linear dynamic coupling with their environment. The method uses "uniform structures" for modeling, and "uniform procedures" for "repetitive" or cumulative learning like in the case of the "traditional" soft computing approaches. But it considerably reduces the number of free parameters tuning with simple, lucid, and explicit algebraic operations of limited number of steps. It is demonstrated via simulation that the control can operate even if strongly nonlinear terms (Coulomb friction and sticking combined with the elastic and viscous terms of the unmodeled external interaction in the Stribeck model), and elastically deformable joints are present. As a paradigm a mechanically 3 DOF SCARA arm actuated by voltage-controlled DC motors is considered. The system has 9 degrees of freedom (6 mechanical and 3 electrical). For the controller only three mechanical degrees can efficiently compensate the effect of the unmodeled degrees of freedom, the external interaction, and the inaccuracy of the modeled part of the robot.