A case study of one-to-two mapping fuzzy PD controllers on inverted pendulum

In this work, fuzzy PD controllers with a one-to-two mapping inference structure are investigated. Unlike the conventional fuzzy PID controllers, which apply the two-to-one mapping strategy, the present controllers are supposed to keep the most preferred features with the conventional PID controllers, such as the individual control action calculation, reasoning inference without an input coupling effect, and independently nonlinear gain tuning. An inverted pendulum is given as a case study for examining this type of controllers. Simulation results demonstrate that the present controllers produce the best control performance in comparison with the two-to-one and one-to-one fuzzy PD controllers. The reason, we observed, is that one-to-many fuzzy controllers have the best flexibility of forming control forces with a high degree of nonlinearity to drive the process than the other two types of controllers.