Variable Universe Adaptive Fuzzy Control on the Triple Inverted Pendulum and Choosing Contraction-Expansion Factor

In order to solve the slightly complicated structure and the big calculation of integral variable universe adaptive fuzzy controller, as well as the difficulty to choose the contraction-expansion factor, a weighted sum-type variable universe adaptive fuzzy controller is designed. At the same time the general method on how to choose contraction-expansion factor is given. First, based on weighted sum principle, a weighted sum-type variable universe adaptive fuzzy controller is designed, and then two-type contraction-expansion factors are discussed. Second, according to the different kinds of contraction-expansion factors which have been discussed above, two weighted sum-type variable universe adaptive controllers are designed on the triple inverted pendulum. Finally, the simulation results, which are derived from the triple inverted pendulum under the control of the two controllers respectively, are compared. The simulation results not only illustrate the effectiveness of the weighted sum-type variable universe adaptive fuzzy controller for dealing with nonlinear systems, but also manifest the general method on how to choose contraction-expansion factor is very reasonable.