ABSTRACT
Aside from serving to illustrate procedures for synthesizing a fuzzy controller, several reasons arise for considering the use of a nonlinear control scheme for the pendulum system. Because all linear controllers are designed based on a linearized model of the system, they are inherently valid only for a region about a specific point (in this case, the vertical, θ1 = 0 position). For this reason, such linear controllers tend to be very sensitive to parametric variations, uncertainties, and disturbances. This is indeed the case for the experimental system under study; when an extra weight or sloshing liquid (using a water-tight bottle) is attached at the endpoint of the pendulum, the performance of all linear controllers degrades considerably, often resulting in unstable behavior. Thus, to enhance the performance of the balancing control, one naturally turns to some nonlinear control scheme that is expected to exhibit improved performance in the presence of disturbances and uncertainties in modeling. Two such nonlinear controllers will be investigated here: in the next section, a direct fuzzy controller is constructed and later an adaptive version of this same controller is discussed.
