Synchronization of Parallel Dual Inverted Pendulums using Optimal Control Theory

Abstract

The inverted pendulum which is used as a benchmark for implementing the control methods, is a highly nonlinear unstable system. In this paper the modeling and control design of nonlinear inverted pendulum-cart dynamic system is presented. A partially linearized model for the under actuated 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 been successful in commanding the pendulums to move in synchronized fashion.