Design of the LQR controller and observer with fuzzy logic GA and GA-PSO algorithm for triple an inverted pendulum and cart system

In this paper, designing of the LQR controller and observer with intelligent tools for the triple inverted pendulum is investigated. Intelligent tools are considered as GA and GA-PSO optimization algorithms and fuzzy logic to qualify achieving LQR gains. The pendulum is swung up from the vertical position to the unstable position. The rules for the controlled swing up are heuristically achieved such that each swing results are controlled. The inverted pendulum and cart system are modeled and constructed their equation based on energy method. Also, the performances of the proposed fuzzy logic controller, GA and GA-PSO tuning LQR gains are investigated and compared. Simulation results show that the fuzzy Logic Controllers are far more superior in terms of overshoot, settling time and response to parameter changes.