Patched‐Fuzzy State Feedback Controller for Inverted Pendulum on a Cart Based on <scp>PWA</scp> ‐Fuzzy Model

ABSTRACT Inverted pendulum is an example of a classical problem in control theory that has been widely used for investigating control algorithms like state feedback, artificial neural networks, fuzzy control, and robust control. The piecewise Affine‐fuzzy (PWA‐Fuzzy) approximation of an inverted pendulum on a cart has been investigated in previous literature. The main drawbacks of PWA approximation, i.e., discontinuity in control signal and chattering between different regions, are addressed by the PWA‐Fuzzy model. In this paper, with the aim of stabilizing the system in the open‐loop unstable equilibrium point, a patched‐fuzzy state feedback (PFSF) controller is designed as an improved form of the conventional state feedback controller for the PWA‐Fuzzy model of an inverted pendulum on a cart. Because of the intention to implement the mentioned controller for a real plant, the identification of PWA‐Fuzzy model parameters by the linear least squares method based on the numerical method is presented. Furthermore, the implementation of the mentioned controller using two different techniques, including analog and digital circuits, is presented. Finally, in order to evaluate the proposed method, the simulation and experimental results are compared.