On the Nonlinear Fuzzy Regulation for under-actuated systems

In this paper, the Takagi-Sugeno (TS) fuzzy modelling and the nonlinear regulation theory are combined in order to construct a controller capable of taking the output of the fuzzy plant to the reference signal generated by an external system. The fuzzy modelling allows the controller to be designed by means of numerical techniques while the resulting stability region is larger than those obtained when simple linear controllers are used to stabilize nonlinear systems. On the other hand, it is well-known that a fuzzy regulator constructed from linear controllers does not solve the regulation problem in general. Therefore, a fully nonlinear regulator is considered in this work. The results are applied on the pendubot, which is an under-actuated electromechanical system with very complex nonlinear dynamics.