A Study of Optimal Control for Under-Actuated Parallel Type—Triple Furuta Pendulum

Stabilization control of parallel type—triple Furuta pendulum (PTFP) or rotary triple parallel inverted pendulum (RTPIP), which belongs to the under-actuated class and development version of rotary inverted pendulum (RIP), is a challenging research topic for researchers in dynamics control field with very few studies being published. This is partly due to the nonlinear, high DOF and unstable characteristics of the system. This paper is to serve as an attempt to develop optimal controller to balance the rotary triple parallel inverted pendulum system. Besides, article presents optimal tuning of linear quadratic regulator (LQR) controller of Genetic Algorithm (GA) for this model. The GA optimizes the weighting matrices of LQR controller so that it can move the base link to a desired position in the minimum change in angle of pendulum from vertically upright position in balancing motions. The entire system has been modeled and tested by MATLAB/SIMULINK toolbox, and performance evaluation were discussed and compared. Simulation results show that the GA-LQR method is more stable than LQR approach in comparison for high-order single input multiple output (SIMO) system.