T–S fuzzy model with nonlinear consequence and PDC controller for a class of nonlinear control systems

In this paper a new Takagi–Sugeno (T–S) fuzzy model with nonlinear consequence (TSFMNC) is presented which can approximate a class of smooth nonlinear systems, nonlinear dynamical systems and nonlinear control systems. It is also proved that Takagi–Sugeno fuzzy controller with nonlinear consequence (TSFCNC) can be used to approximate a class of nonlinear state-feedback controllers using the so-called parallel distributed compensation (PDC) method. The inverted pendulum problem has been simulated with TSFCNC and compared with Takagi–Sugeno fuzzy controller with linear consequence (TSFCLC) and the results show that TSFCNC performs better than TSFCLC. A real-life example of dynamic positioning of ship is simulated and the results also show that TSFCNC performs better than TSFCLC.