Multi-strategy fuzzy controller based on polar coordinates

This work presents a multi-strategy fuzzy controller (MSFC) based on the Takagi–Sugeno (T–S) model, where the membership functions are based on polar coordinates. Adopting a polar coordinate system helps to reduce the number of rules significantly, especially when fuzzy variables exhibit extreme values. This approach also allows more rules to be assigned in certain directions (angles) than others, while the radius represents the distance to the reference. The MSFC uses three strategies: constant input (CI), where a predefined gain is set in the exterior rules; standard discrete state–space model linear–quadratic regulator (LQR), in the intermediate rules; and an incremental state–space model LQR (INC-LQR) in the central rule. A technique employing fuzzy fusion is suggested to facilitate smooth transitions among the various methods. The results show that the proposed MSFC in polar coordinates has a faster transient response and zero steady-state error compared to other fuzzy controllers, and it requires fewer rules compared to an MSFC based on Cartesian coordinates.