Quasi-optimization of certain parameters for parallel inverted pendulum systems via integrated design of structure/controller

An integrated design of structure/controller for parallel inverted pendulum systems is presented. In practical parallel inverted pendulum systems, existence of a realizable stabilizing controller is inevitably determined depending on the position of center of gravity of two pendulums. In this paper these parameters are set as structural parameters in structural systems and a descriptor form representation is used to express the dynamics of parallel inverted pendulum systems. A state feedback gain and structural parameters are determined based on a design of linear quadratic regulator (LQR), in which a generalized Ricatti equation in LQR problem for the descriptor form representation is reduced to LMI conditions. Main contribution of this paper is to give a method to determine the position of center of gravity of two pendulums for parallel inverted pendulum systems in a sense of suitable for control. Based on the obtained structural parameters, some experimental works are executed. Experimental results show the effectiveness of the proposed design method.