On balancing a cart-pole system using T–S fuzzy model

This paper presents two easily implementable control schemes for balancing a cart-pole system using intelligent control tools. The proposed schemes use the Takagi–Sugeno (T–S) fuzzy model of a nonlinear system. The concept of network inversion is used to design the controller for such a system. In one of the control schemes, the control input, necessary to achieve a desired output, is computed directly through iterative inversion of the fuzzy model. In the other scheme, a parallel distributed compensator form is chosen for the controller and the parameters or the feedback gains of the controller are updated through network inversion. The updating laws are derived using both continuous and discrete time Lyapunov approaches. The inversion based parameter update avoids the need of any sufficient condition or prerequisite constraint as in existing T–S fuzzy model based control designs like LMI techniques and robust control techniques. The proposed controllers have been implemented on the cart pole system both in simulation and real time. A comparative performance analysis for different control algorithms is presented. The performance of the proposed controller is compared with the well established LQR control in real time. The proposed control algorithms work for a wide range of operating regions compared to LQR and are more robust in the sense that they can tolerate an output disturbance of higher magnitude.