Modeling of an inverted pendulum based on fuzzy clustering techniques

The inverted pendulum is a highly nonlinear and open loop unstable system. To develop an accurate model of the inverted pendulum, different linear and nonlinear methods of identification will be used. However one of the problems encountered during modeling is the collection of experimental data from the inverted pendulum system. Since the output data from the unstable system does not show enough information or dynamics of the system. This can be overcome by designing a feedback controller, which stabilize the system before identification can takes place. Recently Takagi–Sugeno (T–S) fuzzy modeling based on clustering techniques have shown great progress in identification of nonlinear systems. Hence in this paper, Takagi–Sugeno (T–S) model is proposed for an inverted pendulum based on fuzzy c-means, Gustafson–Kessel (G–K) and Gath–Geva clustering techniques. Simulation results show that Gustafson–Kessel (G–K) clustering technique produces satisfactory performance.

► In this paper, Design and implementation of fuzzy model based on fuzzy c-means, G-K and G-G algorithms for the inverted pendulum are discussed.
► Different cluster validation methods are discussed and presented to choose optimum number of cluster.
► Effectiveness of G-K algorithm is verified through simulation studies.
► G-K algorithm can be applied to decompose any nonlinear system into local linear models and can be used to design model based controller.