Heuristic to tune the compensation gain of modeling uncertainties through the robust multi inversion

In this paper, it is studied a proposal of control signal compensation of nonlinear systems under feedback linearization. An important problem in this context appears when the nonlinear system has differences (or uncertainties) with respect to the nonlinear nominal model used to design the feedback linearization control law. In this case, the practical system in closed-loop can become even unstable. However, a solution proposed in the literature to compensate these differences does not have indications of how to get the gain of the compensation loop. The main contributions of this paper consist in a proposal to determine such a gain and in the investigation of the application of this new control topology in a nonlinear model of a omnidirectional robot. This study of case illustrates that our proposal allows determining compensation gain that leads the the closed-loop system to a better performance.