Synchronization control of parallel dual inverted pendulums

A partially linearized model for the underactuated Euler-Lagrangian system composed of two single linear inverted pendulums is obtained based on the feedback linearization method. Then, the small deviation linearization technique is applied to the partially linearized model to obtain the linear model. For the linear model which is completely controllable, we propose a method to construct a synchronization error signal between the two inverted pendulum systems to guarantee that an augmented system, which contains the original state variables of the two subsystems and the synchronization error, is still completely controllable. For the augmented system an optimal synchronization controller is designed. Experimental results show that the optimal synchronization control system has realized a stable balance of the two inverted pendulums and a precise location of the two cars while they move synchronously. The effect of the optimal synchronization control scheme is better than the usual master-slave synchronization scheme.