Robust adaptive fuzzy controller applied to double inverted pendulum

The main objective of the present work is to stabilize and maintain the angular position of Double Inverted Pendulum (DIP) system at desired position in presence of disturbances and noise. The system is highly coupled, nonlinear, complex and unstable, thereby making it difficult to control. Genetic algorithm tuned Fuzzy Controller (GFC) and adaptive Neuro-Fuzzy Controller (NFC) is proposed for the purpose, wherein the fuzzy parameters are optimized by genetic algorithm and artificial neural network respectively. The adaptive neuro-fuzzy control technique enjoys powerful learning capability of neural network, whereas genetic algorithm discovers the optimum solutions for the problem. Also a suitable function is proposed for modifying training data set of neuro-fuzzy inference system that leads to Modified Neuro-Fuzzy Controller (MNFC). Linear Quadratic Regulator (LQR) and Fuzzy Logic Controllers (FLC) are also designed for comparative analysis. Intensive simulation studies are carried out to critically examine the performance of designed controllers on the basis of Integral Absolute Error (IAE), settling time, overshoot and steady state error for set-point tracking, disturbance rejection, noise suppression and simultaneous noise & disturbance rejection. The rigorous comparative analysis shows that MNFC exhibits fast and robust control of DIP system in comparison to designed controllers for all cases.