Simple practical methodology of designing novel MRAC controllers for nonlinear plants

Besides realization of precise trajectory tracking a Model Reference Adaptive Controller (MRAC) has also provide the “external controller” with an illusion that instead of the actual system under control it deals with a “reference system” of quite different dynamic properties. The traditional MRAC approaches normally apply either analytical or universal approxi-mators based models and Lyapunov´s 2nd method that can guarantee global (sometimes asymptotic) stability but leaves the question of kinematic and dynamic limitations open. Such details can be clarified by ample numerical computations used either for satisfying the conditions of stability itself or for optimizing the free parameters of the controllers by some Genetic Algorithm or other evolutionary methods. A recently introduced novel family of MRAC controllers the design of which drops Lyapunov´s technique and directly concentrates on the kinematic and dynamic details is based on Robust Fixed Point Transformation (RFPT). It has only three adaptive parameters that can easily be set via only a few simulations. In this paper this simple and practical methodology is exemplified in the design of a new MRAC control for a strongly coupled two mass points - two nonlinear springs system in fully actuated and un-deractuated versions, too.